modelling, integration and optimisation for recirculating

Modelling Integration and Optimisation for

Recirculating Cooling Water System Operation

A thesis submitted to The University of Manchester for the degree of

Doctor of Philosophy

In the Faculty of Science and Engineering

2016

Fei Song

School of Chemical Engineering and Analytical Science

2

Table of Contents

List of Figures 3

Abstracthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip4

Declaration 5

Copyright Statement 6

Acknowledgement 7

Chapter 1 Introduction 8

11 Background 8

111 Recirculating cooling water systems 8

112 Operation of recirculating cooling water systems 12

113 Interactions between cooling water systems and processes 13

114 Operation management of cooling water systems 14

12 Motivation 14

13 Aims and objectives 15

14 Thesis outline 16

Chapter 2 17

Publication 1 Operational Optimisation of Mechanical Draft Wet Cooling Towers 17

Chapter 3 18

Publication 2 Operational Optimisation of Recirculating Cooling Water Systems 18

Chapter 4 19

Publication 3 Operational Optimisation of Recirculating Cooling Water Systems for

Improving the Performance of Condensing Turbines 19

Chapter 5 Conclusions and Future Work 20

51 Conclusions 20

52 Future work 21

References 23

Word Count 33521

3

List of Figures

Figure 11 A recirculating cooling water systemhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip8

4

Abstract

The University of Manchester

Fei Song

PhD Chemical Engineering and Analytical Sciences

Modelling Integration and Optimisation for Recirculating Cooling Water System

Operation

2016

Recirculating cooling water systems are extensively used for heat removal from

processes in the process industry Two aspects are focused on to improve the economic

performance of cooling water systems and processes with cooling demand the

integration of key components in cooling water systems including cooling towers

cooler networks and piping networks and the integration of cooling water systems and

processes with cooling demand

For the internal integration of cooling water systems integration models were

established for the operation of cooling water systems in the literature [1] [2] [3]

There are some limitations in the literature they were limited to one cooling tower and

cooler networks in parallel configurations detailed heat transfer in coolers is not

considered in the literature [1] the pressure drop in coolers is ignored in the literature [2]

and [3] To overcome those limitations in the literature in this thesis a nonlinear

integration model of cooling water systems is developed for multiple cooling towers

and cooler networks in both parallel and complex configuration The model includes

cooling tower modelling cooler network modelling and hydraulic modelling In cooling

tower modelling correlation expressions of tower characteristics air inlet conditions

and water inlet conditions are developed to predict temperature of water leaving towers

and humidity of air leaving towers respectively In cooler network modelling detailed

heat transfer in individual coolers is considered In hydraulic modelling pressure drop

in both coolers and pipes are taken into account The nonlinear model is solved by the

solver CONOPT in GAMS to determine the optimal water distribution and air flowrate

For the integration of cooling water systems and processes with cooling demand a new

equation-based simultaneous optimisation method is proposed in which an integration

model of cooling water systems and processes is developed Condensing turbines are

taken as an example to illustrate the method

Case studies prove that the models are effective to solve the problems The standalone

optimisation of cooling water systems reduces the operating cost by 56 compared

with the base case The simultaneous optimisation increases the total profit by 337 kpoundyr

compared with focusing only on maximising the power generation of condensing

turbines

5

Declaration

No portion of the work referred to in this thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institution of learning

Fei Song

6

Copyright Statement

The author of this thesis (including any appendices andor schedules to this thesis) owns

certain copyright of related rights in it (the ldquoCopyrightrdquo) and she has given The

University of Manchester certain rights to use such Copyright including for

administrative purposes

Copies of this thesis either in full or in extracts and whether in hard or electronic copy

may be made only in accordance with the Copyright Designs and Patents Act 1988 (as

amended) and regulation issued under it or when appropriate in accordance with

licensing agreements which the University has from time to time This page much form

part of any such copies made

The ownership of certain Copyright patents designs trademarks and other intellectual

property (the ldquoIntellectual Propertyrdquo) and any reproductions of copyright works in the

thesis for example graphs and tables (ldquoReproductionsrdquo) which may be described in this

thesis may not be owned by the author and may be owned by third parties Such

Intellectual Property and Reproductions cannot and must not be made available for use

without the prior written permission of the owner (s) of the relevant Intellectual

Property andor Reproductions

Further information on the conditions under which disclosure publication and

commercialisation of this thesis the Copyright and any Intellectual Property University

IP Policy (see httpdocumentsmanchesteracukDocuInfoaspxDocID=487) in any

relevant Thesis restriction declarations deposited in the University Library the

University Libraryrsquos regulations (see

httpwwwlibrarymanchesteracukaboutusregulations) and in the Universityrsquos policy

on Presentation of Theses

7

Acknowledgement

I would like to express my gratitude to all those who helped supported and guided me

during my study and the writing of this thesis

I would like to express my sincere gratitude to my supervisor Dr Nan Zhang for his

great patience and constant guidance throughout this process His rigorous attitude

toward research and life has a significant impact on me Special thanks to Prof Robin

Smith and Dr Megan Jobson who give me valuable advice on my writing

I also owe thanks to my dear friends and my colleagues in the CPI who give me support

and help all through these years Special thanks to Yuhang Lou whose rigorous attitude

to her job inspired me Special thanks to my friends and colleagues Chengjun Qian

Luyi Liu Kunpeng Guo and Xiao Yang who provided me advice and helps on my

research and gave me encouragement In addition my special thanks would go to my

best friend Niantai Li

Last but not least I owe my thanks to my beloved parents who gave me both spiritual

and financial support for my study Without them I will not be who I am today Thanks

for their understanding and the wonderful life they provided to me

Chapter 1 Introduction

8


11 Background

111 Recirculating cooling water systems

Recirculating cooling water systems are widely used to reject process heat to keep

processes running efficiently and safely in chemical petrochemical and petroleum

processes refrigeration and air conditioning plants and power stations etc Cooling

water systems consume a large amount of water and power According to the data

collected from some refineries a recirculating cooling water system with 20000 th of

circulating water consumes about 260 th of make-up water and about 4000 kW of

electricity The make-up water consumption and power consumption of the cooling

water system are about half of the total water consumption and about 30 [4] of the

total power consumption of the refinery respectively

Figure 11 A recirculating cooling water system

The basic features of recirculating cooling water systems are shown in Figure 11 There

are three major components in a recirculating cooling water system namely wet cooling

towers cooler networks and piping networks Cooling water used as the cooling


9

medium is pumped and distributed by a piping network to individual coolers that form a

cooler network Cooling water removes the heat from processes and thereby gets a

temperature rise Then hot cooling water from the cooler network is sent to the wet

cooling towers to reject the heat obtained from processes The cold cooling water from

the cooling towers mixed with makeup water is pumped into individual coolers to cool

down processes again

Wet cooling towers are facilities where cold cooling water is produced Hot cooling

water is sent to the top of towers and air is blown to towers from the bottom The

downwards flowing water directly contacts the upwards flowing air As the moisture

content of the saturated air at the water temperature is greater than that of the air a

small portion of cooling water evaporates The latent heat needed by evaporation is

supplied by the remaining water which results in the reduction of water temperature

Besides heat convection occurs due to the temperature difference between water and air

The combination of water evaporation and heat convection is responsible for the final

decrease of water temperature About 80 of the total heat rejected by cooling water is

caused by evaporation [5] Because of the water evaporation contaminants in the

remaining water are concentrated In order to prevent cooling towers coolers and pipes

from fouling corrosion and biological growth some water known as blowdown is

removed to take away some impurities Besides some water known as drift is entrained

by the air Those water losses caused by evaporation blowdown and drift are

compensated by make-up water to keep the flowrate of circulating cooling water

constant Sometimes in order to reduce the heat load of cooling towers some hot

cooling water is discharged as hot blowdown which is shown in Figure 11 In this case

make-up water compensates for the water loss caused by not only evaporation

blowdown and drift but also hot blowdown


10

Wet cooling towers are categorised as natural draft wet cooling towers and mechanical

draft wet cooling towers according to the ways of drawing air through the towers In

natural draft wet cooling towers the buoyancy of the air rising in a tall chimney

provides the driving force for air flowing through towers which results in the large

sizes of towers while fans are used to blow air through the mechanical draft wet cooling

towers As generally used for water flowrate of 45000 th [6] and above natural draft

wet cooling towers are usually used in power stations Natural draft cooling towers

cannot optionally change air flowrate into cooling towers without the help of fans The

advantage of natural draft wet cooling towers is that no power is consumed to blow air

Mechanical draft wet cooling towers are categorised as forced draft wet cooling towers

and induced draft cooling towers by the location of fans Fans are located at the bottom

of forced draft wet cooling towers while they are located at the top of induced draft wet

cooling towers Air flowrate into mechanical draft cooling towers can be adjusted by the

control of fan speed on-off fans operation and use of automatically adjustable pitch

fans [1] which provides a degree of freedom for the operation of cooling water systems

The range and the approach are two important factors that affect cooling tower

performance Range is defined as the difference between the temperature of water

entering and leaving cooling towers Approach is the difference between the

temperature of water leaving cooling towers and ambient wet-bulb temperature that is

an indicator of how much moisture is in the air [1]

Cooler networks used in plants are either in a parallel arrangement or a series and

parallel arrangement Coolers or condensers where cooling water removes heat from

processes are usually shell and tube heat exchangers When cooling water used in

individual coolers is from cooling towers the cooler network is in a parallel

arrangement When cooling water used in coolers is not only that from cooling towers

but also the reuse water from coolers the cooling network is in a series and parallel


11

arrangement Cooler networks in a parallel arrangement are easier to control and

manage than those in a series and parallel arrangement However some cooling water

can be reused in cooler networks in a series and parallel arrangement which reduces the

usage of circulating water and increases the cooling water inlet temperature to cooling

towers

Piping networks distribute cooling water to individual coolers A piping network

consists of pipes pumps valves and pipe fittings When water flows in pipes valves

pipe fittings and coolers friction loss occurs in the cooling water Pumps provide the

energy for the cooling water to overcome the friction and keep the cooling water

circulating in cooling water systems Valves can be adjusted to change the cooling water

flowrate which provides another degree of freedom for the operation of cooling water

systems

The thermal or hydraulic behaviour of individual components is complex In cooling

towers both mass transfer and heat transfer are involved which makes it complicated to

simulate the thermal behaviour of cooling towers In cooler networks except for the

thermal behaviour of individual coolers there are thermal interactions between coolers

for cooler networks in a series and parallel arrangement The hydraulic behaviour of the

network includes pressure drop in both pipes piping fitting valves and coolers In

addition to the complexity of individual components there are strong interactions

between the components of cooling water systems The performance of cooling towers

and piping networks influences the performance of cooler networks The performance

of cooler networks and piping networks has an impact on the performance of cooling

towers The performance of cooling towers and cooler networks provides a requirement

for water distribution determined by piping networks Therefore when the operation of

cooling water systems is determined for a specified process cooling demand cooling

towers cooler networks and piping networks should be considered simultaneously


12

Besides ambient air conditions also have an impact on the thermal performance of

cooling towers The temperature of water leaving cooling towers varies with the

inevitable oscillations of ambient air conditions The ambient air conditions include dry-

bulb temperature wet-bulb temperature and humidity Dry-bulb temperature is ambient

temperature Wet-bulb temperature is an indicator of the moisture content in air The

humidity of air can be calculated with dry-bulb temperature wet-bulb temperature and

pressure

112 Operation of recirculating cooling water systems

The investigation of the operation of cooling water systems in this project includes

cooling water flowrate in individual towers and coolers air flowrate in individual

cooling towers and the resulting make-up water and power consumption Water flowrate

can be adjusted by valves and pumps and air flowrate can be adjusted by fans In a

given cooling tower the ratio of water inlet mass flowrate and air inlet mass flowrate

has an influence on the water outlet temperature Therefore the temperature of water

leaving towers can be altered by changing cooling water flowrate or air flowrate The

adjustable cooling water flowrate and temperature result in that various operations of a

cooling water system achieve the same process cooling demand Different operations

consume the different quantity of make-up water and power The total operating cost

incurred by make-up water and power consumption varies with the change of water

inlet flowrate and air inlet flowrate Therefore the economic performance of a given

cooling water system for a given process cooling load can be improved by changing

water inlet flowrate and air inlet flowrate As the change of power consumption caused

by the change of cooling water flowrate is opposite to the change in power consumption

caused by the change of air flowrate the most economic operation is determined by the

trade-off between cooling water flowrate and air flowrate


13

A study reveals that the energy consumption by a cooling water system can be saved by

about 11 through optimising cooling water flowrate air flowrate and water

distribution in cooling water systems in a petrochemical plant [7] According to the

study [7] for a cooling water system with 20000 th of circulating water in a refinery

the power consumption can be reduced by about 3200 MWh per year and the resulting

economic saving can be as much as 320 kpoundyr

113 Interactions between cooling water systems and processes

Water flowrate in individual coolers and water temperature produced by cooling towers

have a significant influence on the performance of some processes with cooling demand

such as condensing turbines compressor inter-cooling condensation of light

components for distillation pre-cooling for refrigeration compression and so on For

example the decrease in water temperature increases the power generation of

condensing turbines and reduces pressure in distillation columns power consumption

by compressors and refrigerator consumption However the decrease in water

temperature increases the operating cost of cooling water systems Consequently the

improvement in the performance of those processes increases the operating cost of

cooling water systems If the operation of cooling water systems is determined by

minimising the operating cost of cooling water systems only it may have a negative

impact on the performance of processes On the other hand if the operation of cooling

water systems is determined by optimising the performance of processes only the

operating cost of cooling water systems is likely to increase Therefore there is a trade-

off between the economic performance of cooling water systems and that of processes

with cooling demand to improve the overall economic performance

Condensing turbines with surface condensers using cooling water are typical users of

cooling water systems The power generation rate of condensing turbines is impacted by

cooling water flowrate and temperature In this work they are taken as an example of


14

processes with cooling demand to develop a systematic approach to determine the

optimal operation of cooling water systems for the improvement of overall economic

performance of cooling water systems and processes

114 Operation management of cooling water systems

In practice utility sectors manage the operation of cooling towers to achieve the desired

cooling water outlet temperature and process sectors manage the operation of cooler

networks based on the process cooling demand The two sectors do not exchange

detailed information about the behaviour of the overall systems They do not take the

interactions within cooling water systems and the interactions between cooling water

systems and processes into consideration when they manage their operation The

resulting operation of cooling water systems is not always the most cost effective

12 Motivation

The economic performance of cooling water systems can be improved by operational

optimisation of cooling water systems Due to strong interactions between cooling

towers cooler networks and piping networks the operational optimisation of cooling

water systems should be determined by the integration of cooling towers cooler

networks and piping networks Some studies [1] [2] [3] [8] [9] [10] [11] focused on

the design and operation of cooling water systems with the consideration of the

interactions between cooling towers and cooler networks Most of them were carried out

for design optimisation and only a few were performed for operational optimisation of

cooling water systems Some studies [8] and [12] employed the cooling tower models

that are differential equations based on the mass and heat transfer mechanism Although

they provide the accurate prediction the differential equations are difficult to handle in

an optimisation program Some studies [9] and [11] employed simple cooling tower

models that provide less accurate predictions than rigorous models Besides there is no


15

model developed for cooling water systems in those studies that considers all the factors

including detailed heat transfer in coolers pressure drop in coolers and pipes multiple

cooling towers and cooler networks in a complex arrangement

As mentioned above there are interactions between cooling water systems and

processes The focus of economic performance of cooling water systems only is very

likely to miss the opportunity of improving the performance of those processes

Therefore when the optimal operation of cooling water systems is determined the

performance of those processes should be considered with cooling water systems

simultaneously

13 Aims and objectives

The aims of this work include

To determine the optimal operation of cooling water systems for minimising the

operating cost of cooling water systems without affecting process performance

To determine the optimal operation of cooling water systems for improving the

overall performance of cooling water systems and condensing turbines

The steps to achieve the first aim include

Data analysis for the operation of cooling water systems

Model development of mechanical draft wet cooling towers with accurate

prediction for water evaporation rate and cooling water outlet temperature

To develop a cooler network model that considers detailed heat transfer in

coolers and interactions between coolers and cooling towers in which multiple

cooling towers and cooler networks in a series and parallel arrangement are

included

To develop a piping network model including pressure drop in coolers pipes


16

pipe fittings and valves

To develop a model of cooling water systems by integration of cooling towers

cooler networks and piping networks

To solve the problem with the objective of minimising the operating cost of

cooling water systems

The steps to achieve the second aim include

To integrate the models of cooling water systems and processes (eg condensing

turbines)

To optimise cooling water systems and condensing turbines simultaneously for

maximising the total profit

14 Thesis outline

The thesis consists of three papers to cover three main research areas for cooling water

systems In the first paper a regression model of mechanical draft wet cooling towers is

proposed and validated which is then subject to optimisation to minimise the operating

cost of cooling towers for fixed process cooling demand In the second paper a model

of cooling water systems with the integration of cooling towers cooler networks and

piping networks is developed and the operation of cooling water systems is optimised

for minimising the operating cost of cooling water systems again under fixed process

cooling demand In the third paper a model of cooling water systems and condensing

turbines is developed for the operational optimisation of cooling water systems to

maximise the total net profit of cooling water systems and condensing turbines Finally

conclusions and future work are presented

Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers

17

Chapter 2

Publication 1 Operational Optimisation of Mechanical

Draft Wet Cooling Towers

(Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical

Draft Wet Cooling Towers)


1

Operational Optimisation of Mechanical Draft Wet

Cooling Towers

Fei Song Nan Zhang Robin Smith

Centre of Process Integration the University of Manchester Manchester M13 9PL UK

Abstract

Mechanical draft wet cooling towers are widely used in process industries to reject

process heat into the atmosphere Varying operations of cooling towers can achieve the

same process cooling demand with different total operating cost Therefore water and

air mass flowrate entering cooling towers are optimised to improve the economic

performance of cooling towers A nonlinear model of cooling towers is developed for

the operational optimisation In the model correlation expressions of tower

characteristics ambient air conditions air flowrate and inlet water conditions are

proposed to predict air outlet humidity and cooling water outlet temperature The

correlation equation to predict air outlet humidity refers to a correlation proposed by

Qureshi et al [1] The correlation equation to calculate water outlet temperature is

proposed through analysing the effect of key factors on the temperature The correlation

equations are validated with the measured data presented in Simpson and Sherwood [2]

To optimise the operating variables of towers the model is solved by the solver

CONOPT in GAMS The model is proven to be effective to improve the economic

performance of cooling towers by a case study In the case study through optimisation

the operating cost of the cooling tower is reduced by about 69 compared with the

base case

Key words mechanical draft wet cooling towers correlation operational optimisation

Corresponding author Tel +44 1613064384 Fax+44 1612367439

Email nanzhangmanchesteracuk


2

Highlights

A regression model of cooling towers is developed and validated

The regression model is effective to reduce the operating cost of cooling towers

The effect of ambient air conditions on the performance of cooling towers is

investigated

1 Introduction

Recirculating cooling water systems are widely used to reject process heat to the

atmosphere through cooling water in chemical petrochemical and petroleum processes

and power stations etc The basic features of recirculating cooling water systems are

presented in Figure 1 Wet cooling towers are one of the key components in

recirculating cooling water systems as they play a major role in the recycling of cooling

water in recirculating cooling water systems In a recirculating cooling water system

cooling water removes heat from processes resulting in a rise in cooling water

temperature The hot cooling water is sent to wet cooling towers after heat exchange

with processes In wet cooling towers cooling water is cooled down by direct contact

with air After that cold cooling water from wet cooling towers is pumped to remove

heat from processes again As a result cooling water consumption is reduced to about 5

that of a once-through system [3] In addition cooling water can be cooled to below

ambient temperature by the employment of wet cooling towers Compared with the

cooling water temperature created by dry cooling towers the cooling water temperature

produced by wet cooling towers can achieve cooling requirement of most industrial

processes Mechanical draft wet cooling towers are the most common especially in the

petrochemical chemical and petroleum industries and refrigeration and air conditioning

plants The fundamentals of wet cooling towers can be referred to references [4] [5]


3

Figure 1 Recirculating cooling water systems

Inlet air flowrate and inlet cooling water flowrate are two adjustable elements in the

operation of mechanical draft wet cooling towers The inlet air flowrate is adjusted by

fans in mechanical draft wet cooling towers The inlet cooling water flowrate is the

same as the cooling water flowrate that is needed by process heat removal when all the

cooling water used to remove heat from processes enters cooling towers to be cooled

down The cooling water flowrate used to remove process heat can be adjusted by

valves and pumps Therefore the inlet cooling water flowrate of cooling towers is

adjustable According to the fact that the cooling water temperature produced by

cooling towers is affected by the ratio of air mass flowrate and cooling water mass

flowrate into cooling towers recorded in the literature [6] [7] [8] the cooling water

temperature produced by cooling towers is variable when inlet air flowrate or inlet

cooling water flowrate changes Since they are variables cooling water flowrate and

cooling water temperature can be adjusted to satisfy the cooling requirement of

processes in many ways such as a relatively low cooling water flowrate coupled with a

relatively large range or a relatively high cooling water flowrate coupled with a

relatively small range


4

Even though different operations of cooling towers can achieve the same cooling

requirement of processes different operations consume the different quantity of power

and make-up water resulting in the different operating cost that consists of power cost

and make-up water cost Therefore the economic performance of cooling towers can be

improved by optimising inlet cooling water mass flowrate and inlet air mass flowrate

For a given mechanical draft wet cooling tower with a given cooling requirement of

processes when the inlet cooling water mass flowrate is increased the cooling water

temperature difference caused by heat exchange with processes will decrease

accordingly The decrease in the cooling water temperature difference reduces the

demand for air in cooling towers The increase of cooling water flowrate increases

power consumption of water pumps while the decrease of inlet air mass flowrate

reduces power consumption of fans Due to the opposite effect of the change of cooling

water flowrate and air flowrate on power consumption there is a trade-off between inlet

cooling water mass flowrate and inlet air mass flowrate to improve the economic

performance of cooling towers Questions are what the most cost effective operation is

and how it is obtained for an existing cooling tower with specified process cooling

demand Those questions can be solved systematically by the operational optimisation

subject to the model of cooling towers

It is not straightforward to obtain the optimal operation for cooling towers to fulfil the

cooling duty imposed by processes because of the complex thermal behaviour of

cooling towers The operation of cooling towers is not only affected by the tower

characteristics but also the process cooling requirement For one thing the cooling

water outlet temperature of cooling towers is influenced by the air inlet mass flowrate

the cooling water inlet mass flowrate the cooling water inlet temperature and the

characteristic of cooling towers For the other the cooling water inlet flowrate and the

cooling water inlet temperature are adjusted to remove the specified heat from processes

according to cooling water outlet temperature from cooling towers Therefore the


5

interacted air inlet flowrate cooling water inlet flowrate cooling water inlet

temperature and outlet temperature are constrained by both the cooling load of

processes and the thermal behaviour of cooling towers Besides the ambient air

conditions that include dry-bulb temperature wet-bulb temperature and humidity have

an influence on water temperature produced by cooling towers As a result the heat

rejected by processes will vary in accordance with the oscillations of ambient air

conditions when a fixed operation of cooling towers is implemented

Many thermal models were developed for cooling towers in the literature Differential

equations were used to describe heat and mass transfer in cooling towers for design

rating and analytical purposes in the literature [3] [9] [10] [11] [12] [13] [14]

Cooling tower models were based on the film theory in [3] [9] and [11] Merkel [9] was

the first to develop a model for cooling towers with differential equations In this model

water evaporation was neglected to simplify the model and the outlet air was assumed

to be saturated to determine the characteristic of cooling towers Due to the assumptions

water evaporation rate cannot be predicted accurately Kloppers et al [10] provided the

detailed governing equations for mechanical draft counter flow wet cooling towers

based on the Poppe method [11] In this method three governing differential equations

were developed to predict the humidity and enthalpy of outlet air and the transfer

characteristics of towers Without assumptions as made by Merkel the Poppe method

[11] estimates water evaporation rate outlet temperature of cooling water and

characteristics of cooling towers more accurately than the Merkel method [9] The

Poppe method did not consider the heat resistance in the water film while Khan et al [3]

considered the heat resistance in the water film in their model Fisenko et al [12] and

Qureshi et al [13] described evaporative cooling of both water film and water droplets

Qureshi et al [13] employed the model for evaporative cooling of water droplets

developed by Fisenko et al [12] However the model for the water film in the literature

[12] was developed to predict film temperature and thickness averaged temperature of


6

the moist air and density of the water vapour in the air while that in Qureshi et al [13]

was to predict the enthalpy and the humidity of the air In addition Qureshi et al [13]

considered the effect of fouling on the thermal performance of cooling towers in their

model Jaber and Webb [14] extended the effectiveness-NTU method to cooling towers

As it makes the same assumptions as those in the Merkel method [9] the effectiveness-

NTU method provides the estimation close to that of the Merkel method In the

literature optimisation of cooling towers in terms of operation and design was carried

out with different cooling tower models The Merkel method was transformed into an

algebraic equation using the four-point Chebyshev integration technique and applied in

an optimisation program for cooling tower design [15] Rubio-Castro et al [16] applied

the Poppe method to the same optimisation program as that in [15] by using the fourth-

order Runge-Kutta algorithm The application of the Poppe method makes it more

difficult to solve the optimisation problem than that of the Merkel method But the

prediction by the Poppe method is more practical that by the Merkel method as the

assumptions that simplify the Merkel method are not made in the Poppe method Castro

et al [17] employed a correlation model of cooling towers for operational optimisation

of cooling water systems In this model the inlet air flowrate is determined based on the

assumption that the outlet air from cooling towers is saturated and water evaporation

rate was related to the cooling duty of cooling towers only regardless of the effect of

ambient air conditions on water evaporation In addition there were some correlations

established for the transfer characteristics in the literature [18] [19] [20] [21] [22]

[23] [24] for the range of cooling towers in the literature [25] and for the evaporation

ratio in the literature [1]

In summary a detailed phenomenological model of a cooling tower is expressed as

differential equations which cannot be directly used in an optimisation program When

it is applied in an optimisation program with the help of the Runge-Kutta algorithm the

number of variables and equations in the problem will be increased The Merkel method


7

is widely used in optimisation programs because of the simplicity However some

assumptions made in the Merkel method reduce the accuracy of predictions So do the

other models that make the same assumptions as in the Merkel method To overcome

those limitations a regression model of cooling towers will be developed for the

optimisation for cooling tower operation

In this paper the operational optimisation of cooling towers is carried out to determine

the optimal cooling water inlet mass flowrate and air inlet mass flowrate for a given

cooling tower with specified process cooling demand A nonlinear model is developed

for the operational optimisation The model includes mass and energy balance for

cooling towers correlation equations characteristics of fans and pumps and an equation

for the cooling demand In order to make the optimisation program less difficult to solve

correlation functions are developed to estimate the cooling water outlet temperature the

water evaporation and the number of transfer units of mechanical draft wet cooling

towers Power consumption by fans and pumps is determined by the characteristics of

fans and pumps The hydraulic characteristics of cooling towers and piping networks

are not considered here Then the model is applied to optimise cooling water mass

flowrate and air mass flowrate for a given cooling tower subject to the variation of

ambient air conditions in case studies

2 Mechanical Draft Wet Cooling Tower Modelling

Mathematical models are developed for optimising the operation of a given cooling

tower with given cooling requirement of processes The specified cooling requirement

of processes is the target of the operation of cooling towers The operation consists of

cooling water inlet mass flowrate and air inlet mass flowrate Cooling water inlet

temperature cooling water outlet temperature make-up water consumption power

consumption and the resulting operating cost will be changed with the variation of


8

operations Ambient air conditions have an influence on the thermal performance of

cooling towers

As the cooling requirement of processes is satisfied by the operation and the thermal

performance of cooling towers caused by the operation a thermal model of cooling

towers and cooling requirement of processes are used as constraints for the prediction of

the cooling water inlet mass flowrate and the air inlet flowrate Then an objective

function is employed to select the optimum operation among the feasible solutions

In this section a thermal model of cooling towers is established as constraints in the

optimisation model Number of transfer units (NTU) as the transfer characteristic of

cooling towers is one of the main factors that influence the thermal performance of

cooling towers The cooling water outlet temperature of cooling towers indicating the

thermal performance of cooling towers plays a vital role in heat removal from processes

The air outlet humidity is important to predict water evaporation rate and air outlet

conditions Therefore three correlation functions are established to relate the three

variables to other variables and parameters individually An energy balance between

process streams and cooling water is used to make sure the process cooling demand is

satisfied Last but not least the objective function is established to determine the

optimal operation of a given cooling tower which is to minimise the total operating cost

In order to estimate the total operating cost power consumption and make-up water

consumption are calculated

There are some assumptions for the model of cooling towers developed in this paper

The system is at steady state

Negligible heat through the tower walls to the environment

Negligible heat transfer from the tower fans to air or water streams

Constant specific heat capacity of water water vapour and dry air throughout the


9

tower

Uniform cross-sectional area of the tower

No supersaturated air from cooling towers

21 Thermal model of cooling towers

211 Mass and energy balance

In a wet cooling tower water loss in the water stream caused by evaporation is

equivalent to the increase of moisture content in the air which is expressed in equation

(1)

( ) (1)

where and are cooling water inlet and outlet mass flowrate respectively

is dry air mass flowrate and and are air inlet and outlet humidity ratio based on

dry air mass flowrate respectively

The energy balance in towers is carried out by equation (2)

( ) (2)

where is the specific heat capacity of cooling water and are cooling water

inlet and outlet temperature respectively and and are specific enthalpy of air

entering and leaving cooling towers based on the dry air mass flowrate respectively

Water evaporation is considered in both mass balance and energy balance


10

212 Correlation expressions for cooling towers

(1) Characteristics of cooling towers

The Merkel number and the number of transfer units (NTU) are two representations of

transfer characteristics of cooling towers The relationship between NTU and the

Merkel number is shown in equation (A6) in the Appendix The Merkel number can be

calculated by the correlation equation proposed by Johnson [23] which is presented as

equation (A7) in the Appendix Therefore the correlation expression of NTU can be

presented as equation (A8) according to the correlation equation of the Merkel number

With the assumption that the cross section covered by air and water is constant a

correlation equation of the NTU is simplified as

(3)

where is cooling water inlet mass flowrate is dry air mass flowrate is

cooling water inlet temperature and are coefficients

(2) Cooling water outlet temperature

The outlet water temperature of cooling towers needs to be predicted as the outlet water

temperature have an impact on heat removal from processes It is indicated in the

literature [3] that the outlet water temperature is influenced by inlet water temperature

inlet water mass flowrate dry air mass flowrate and inlet wet-bulb temperature The

effect of those factors on the range that is the difference between water inlet temperature

and water outlet temperature is analysed and the results are displayed in Figure 2 All

the calculation for the analysis is implemented by the Poppe method [10] Figure 2 (a) is

a plot between the range and NTU for different value of the mass flowrate ratio

( frasl ) The follow set of input data is used to draw the plot

In Figure 2 (b) a plot between

the range and inlet mass flowrate of cooling water for different value of water inlet


11

temperature is shown The following set of input data is used to draw the plot

In Figure 2 (c) a plot between the range and dry air mass flowrate for different value of

water inlet temperature is generated with the input data

Figure 2 (d) is a

plot between the range and the difference between water inlet temperature and ambient

wet-bulb temperature for different value of the mass flowrate ratio ( frasl ) The plot

is generated with the input data

(a)The range versus NTU

(b)The range versus inlet mass flowrate of cooling water


12

(c)The range versus mass flowrate of dry air

(d)The range versus difference between water inlet temperature and ambient wet-bulb

temperature

Figure 2 Variation of the range versus NTU (a) water inlet mass flowrate (b) dry air mass

flowrate (c) and difference between water inlet temperature and ambient wet-bulb

temperature (d)


13

According to the plots in Figure 2 equation (4) is proposed to predict the outlet

temperature of cooling water from an existing cooling tower

( ) (4)


cooling water inlet temperature is ambient wet-bulb temperature NTU is the

number of transfer units and are coefficients

(3) Air outlet humidity

The air outlet humidity is important for the estimation of water evaporation and air

outlet conditions Therefore the correlation model is developed for the air outlet

humidity A correlation equation for water evaporation percentage was proposed and

validated by Qureshi et al [1] which is presented as equation (A17) in the Appendix

The water evaporation ratio (ER) can be expressed as equation (5)

( )

w (5)

where is cooling water inlet mass flowrate is dry air mass flowrate and and

are air inlet and outlet humidity ratio based on dry air mass flowrate respectively

Combining equations (5) and (A17) equation (6) is obtained

( )

w ( ) ( ) ( ) (6)


14

where and are cooling water inlet and outlet temperature respectively and

and are ambient dry-bulb temperature and ambient wet-bulb temperature

respectively

Equation (6) is rearranged to be equation (7)

( ( ) ( ) ( )) (7)

According to equation (7) equation (8) is proposed to predict air outlet humidity

( ( ) ( ) ( ))

(8)

where γ -γ are coefficients

213 Cooling requirement of processes

The cooling water from a cooling tower mixed with make-up water is distributed into

individual coolers to remove heat from processes The cooling water temperature into

coolers can be determined by equation (9)

( ) (9)

where is the specific heat capacity of cooling water is cooling water inlet

mass flowrate is cooling water outlet temperature is the mass flowrate of the

make-up water is the temperature of the make-up water and is the temperature of

the water stream after make-up

The process cooling demand achieved by cooling water can be presented as equation

(10)


15

( ) (10)


mass flowrate is cooling water inlet temperature and is the temperature of the

water stream after make-up

The equations for thermal properties of cooling water and air are presented in Appendix

Those thermal properties of cooling water and air related to temperature are calculated

at the mean temperature of water entering and leaving towers

22 Economic performance of cooling towers

221 Make-up water consumption

When there is no hot blowdown removed the make-up water is consumed to

compensate for the water losses mainly caused by water evaporation Water evaporation

rate is calculated by the humidity difference between inlet air and outlet air as

represented by equation (11) The humidity of air leaving a tower is predicted by

equation (8)

( ) (11)

where is water evaporation rate is dry air mass flowrate and and are air

inlet and outlet humidity ratio based on dry air mass flowrate respectively

The consumption of make-up water is expressed as equation (12)

(12)


16

where is the cycles of concentration defined as the ratio between the concentration

of dissolved solids in the circulating water and in makeup water [26] The cycles of

concentration are taken as parameters

222 Power consumption

Power consumption of mechanical draft wet cooling towers consists of power

consumption of fans and pumps The power needed by fans is related to the air mass

flowrate and characteristics of fans In general form the power needed by a given fan

can be written as equation (13)

( ) (13)

where is power consumption of fans and is dry air mass flowrate

Power consumed by pumps to compensate for the friction loss of cooling water is

determined by cooling water volumetric flowrate and characteristics of the pumps

Equations (14) - (16) are used to calculate power consumption by pumps [27]

(14)

( ) (15)

w

(16)

where is the volumetric flowrate of water flowing through the pump is the

mass flowrate of water flowing through the pump is the pressure head provided by

the pump is the pump efficiency and is the power consumed by the pump


17

Note that it is assumed that the pressure head provided by fans and pumps satisfies the

head requirement within the limitation boundary of cooling water flowrate and dry air

flowrate

23 Practical constraints

The practical constraints include the limitation boundary of cooling water inlet mass

flowrate air inlet mass flowrate the ratio of cooling water inlet mass flowrate and air

inlet mass flowrate the cooling water inlet temperature and the cooling water outlet

temperature

(17)

(18)

w

w

w

(19)

(20)

(21)


cooling water inlet temperature and is cooling water outlet temperature

24 Objective function

In this problem the objective function is to minimise the operating cost expressed as

equation (22) The operating cost (TOC) includes make-up water cost and power cost


18

( ) (22)

where is mass flowrate of make-up water is power consumption of fans is

power consumption of pumps and C1 and C2 are unit cost of make-up water and power

respectively

3 Model validation

A cooling tower presented in Simpson and Sherwood [2] is used to illustrate the

accuracy of those correlation equations The coefficients in the correlations are

regressed for the cooling tower with the least square method

Measured data for cooling water inlet mass flowrate dry air mass flowrate and cooling

water inlet temperature and the corresponding calculated value of NTU are required to

determine the coefficients (α1-α4) in the correlation for NTU The value of NTU cannot

be measured directly but it can be predicted by the phenomenological models of

cooling towers In this paper the Poppe method presented in [10] is used to calculate

the value of NTU When the Poppe method is applied to calculate the value of NTU the

interface temperature is assumed to be 05 K less than water temperature in cooling

towers [28]

The coefficients (β -β ) in equations (4) are regressed by the least square method with

the measured data of cooling water inlet and outlet temperature cooling water inlet

mass flowrate dry air mass flowrate and air inlet wet-bulb temperature as well as the

calculated value of NTU

The coefficients (γ -γ ) in equations (8) are regressed by the least square method with



19

mass flowrate dry air mass flowrate and air inlet dry-bulb temperature wet-bulb

temperature and humidity

The measured data used to predict the coefficients in equations (3) (4) and (8) is

presented in Table A1 in the Appendix The coefficients in the regression model of the

cooling tower are presented in Table 1

Table 1 Coefficients for the cooling tower in Simpson and Sherwood [2]

(a) Coefficients in equation (3)

α1 α2 α3 α4

95846 06568 -12569 -04216

(b) Coefficients in equation (4)

β1 β2 β3 β4 β5

40099 -17177 08672 -21377 08165

(c) Coefficients in equation (8)

γ1 γ2 γ3 γ4 γ5 γ6 γ7

-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00


20

(a) Predicted outlet water temperature versus measured outlet water temperature

(b) Predicted outlet air humidity versus measured outlet air humidity

Figure 3 Measured versus predicted values

A good agreement between predicted values by regression models and the measured

data is reached which is shown in Figure 3 With the regressed coefficients the cooling

water outlet temperature and the air outlet humidity can be calculated for any operating

y=x

y=x

R2=0992

R2=0996


21

conditions within the range of measurement The accuracy of these regressed equations

is validated with other measured data for the cooling tower that is not used for the

coefficient regression The comparison results are listed in Table 2

Table 2 Comparison of wo and two between the regressed model and the measured data

provided by Simpson and Sherwood [2]

No 1 2 3 4 5 6

Measured

data

(degC) 2933 3667 4100 3889 4033 3572

(degC) 2966 3192 3550 3111 3361 3311

(degC) 2111 2111 2388 2388 2667 2944

(kgs) 1186 1178 1157 1174 1157 1156

(kgs) 1132 1132 0881 1132 1008 1258

Calculated

data

(degC)

Measured 2433 2633 2800 2844 3044 3122

Correlation 2415 2642 2818 2851 3016 3106

Relative

difference () 073 -036 -065 -024 092 051

(10-2

kgkg

dry air)

Measured 2192 2835 3108 3223 3454 3301

Correlation 2168 2878 3119 3229 3419 3305

Relative

difference

()

111 -151 -037 -017 103 -011

The relative differences between the correlations and the measured data in terms of the

cooling water outlet temperature and the air outlet humidity are no more than 10 and

20 respectively Therefore the correlation equations predict the cooling water outlet

temperature and the air outlet humidity accurately

4 Solution Method

Before the model is applied the coefficients in equations (3) (4) and (8) are regressed

for the given cooling tower by the least square method with measured data or operation


22

data After that the objective function is minimised with the input data of the given

process cooling demand unit cost of make-up water and power the cycles of

concentration and the ambient air conditions (dry-bulb temperature wet-bulb

temperature and humidity) subject to the constraints composed of equations (1) - (4)

and (8) - (16) and the practical constraints including equations (17) - (21) As the model

includes nonlinear equations the optimisation problem is a nonlinear problem

Therefore the problem is solved by the solver CONOPT in software GAMS as

CONOPT is well suited for models with nonlinear constraints Before solving the

problem the initial values are assigned to the variables After optimisation the optimal

cooling water inlet mass flowrate and dry air mass flowrate into the cooling tower are

determined for the specified cooling load and the consequent cooling water outlet

temperature of the cooling tower power consumption make-up water consumption and

operating cost are obtained

5 Case Studies

Two case studies are presented to illustrate the application of the model developed

above to determine the optimal operation of a cooling tower in various ambient air

conditions In Case 1 the base case is optimised for a given cooling tower with

specified process cooling demand The variation of ambient air conditions causes the

change of the thermal performance of cooling towers The variation of the thermal and

economic performance of the cooling tower with the change of ambient air conditions is

examined in Case 2 Then operating variables of the cooling tower are optimised

corresponding to individual ambient air conditions In Case 2 it is investigated whether

it is worthwhile to optimise the operating variables when the ambient air conditions

change


23

51 Base case

A cooling tower with a fan and a pump is employed to complete the specified cooling

requirement of processes The specified process cooling demand is 9928 MW The

ambient air conditions are listed in Table 3 which include dry-bulb temperature wet-

bulb temperature humidity and enthalpy 7920 th cooling water and 7200 th dry air

are used to cool down the processes The make-up water temperature is assumed to be

the same as the ambient temperature The unit cost of make-up water is 03 poundt and the

unit cost of electricity is 01 poundkWh 4 cycles of concentration are used There are some

practical constraints listed in Table 4 such as the upper bound of cooling water inlet

and outlet temperature and limitation boundary of cooling water and dry air mass

flowrate The thermal and economic performance of the cooling tower is presented in

Table 6

Table 3 Ambient air conditions and process cooling demand

Cases Base case Case 1 Case2

Condition 1 Condition 2 Condition 3

Ambient air

conditions

tdbi (degC) 3028 3028 3533 2950 2600

twbi (degC) 2565 2565 2944 2500 2250

wi (10

-2kgkg dry air)

190 190 239 183 158

ii (kJkg) 7913 7913 9688 7636 6645

Process cooling demand (MW) 9928

Table 4 Practical constraints

Cooling water inlet temperature (degC) Upper bound 4800

Cooling water outlet temperature (degC) Upper bound 3500

Cooling water mass flowrate (th) Upper bound 8640

Lower bound 4320

Dry air mass flowrate (th) Upper bound 9720

Lower bound 3600

Upper bound 17

Lower bound 07

Approach (degC) Lower bound 33


24

52 Case study 1

The mass flowrate of cooling water and dry air entering the tower is optimised with the

model developed and the proposed solution method in last section The objective is to

minimise the operating cost of the tower Before optimisation the coefficients in the

regression models of the cooling tower the fan and the pump are regressed The

regression models are provided in Table 5 There are 20 equations and 22 variables in

this optimisation problem

Table 5 Models of the cooling tower the pump and the fan

Unit Models

Cooling tower

( times times ( ) times

( ) times ( ))

7

7

( )

Pump

( )

Fan [17]

( )

The optimisation results are presented in Table 6 Through optimisation the cooling

requirement of processes is satisfied and the total operating cost is reduced by 175 poundh

(approximately equivalent to 140 kpoundyr) when the cooling water inlet flowrate reduces

from 7920 th to 5760 th and the dry air flowrate increases from 7200 th to around

9187 th As the water mass flowrate is decreased the range that is the temperature

difference between the inlet water and the outlet water is supposed to increase to


25

achieve the cooling requirement The range is increased from 108 degC to 149 degC by the

increase of the air mass flowrate Therefore the cooling requirement of processes is

achieved by the decrease of inlet cooling water flowrate and the increase of the air mass

flowrate Although the cooling requirement of processes is fixed the cooling duty of the

cooling tower is slightly increased as the change of the operating variables results in a

slight increase of evaporation rate The increase of the evaporation rate leads to 47 th

more make-up water consumption than that in the base case In respect of power

consumption the decrease of water flowrate results in the decrease of power

consumption of the pump by around 290 kW while the increase of the air flowrate

increases the power consumption of the fan by about 100 kW As a result the overall

power consumption reduces by about 190 kW through optimisation As the increase in

the cost of make-up water is less than the decrease in the cost of power the total

operating cost decreases

Table 6 Optimisation results

Cases Base

case

Case

1

Case 2

Before optimisation After optimisation

Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Operating

conditions

Inlet water

flowrate (th) 7920 5760 5760 6280 5641 7137

Inlet dry air

flowrate (th) 7200 9187 9187 7533 9441 4996

Cooling

water

Inlet

temperature

(degC)

4100 4385 4385 4644 4351 4062

Outlet

temperature

(degC)

3020 2895 3166 2849 2676 3274 2830 2869

Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193

Cooling duty of cooling

towers (MW) 1039 1041 858 1071 1188 1052 1039 1029

Heat rejected by processes

(MW) 9928 8079 10240 11442 9928

Evaporation rate (th) 1304 1339 1181 1368 1466 1404 1331 1226


26

Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Make-up water

consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635

Power

consumption

(kW)

Fan 353 450 450 450 450 377 462 240

Pump 1631 1344 1344 1344 1344 1396 1333 1503

Total 1984 1794 1794 1794 1794 1773 1795 1743

Cost (poundh)

Make-up

water 522 536 473 547 587 561 532 490

Power 1983 1794 1794 1794 1794 1773 1795 1743

Total 2505 2330 2267 2341 2381 2334 2327 2233

53 Case study 2

In this case three different ambient air conditions are used to investigate the effect of

the ambient air conditions on the thermal and economic performance of the cooling

tower The ambient air conditions are listed in Table 3 The optimal value of operating

variables of the cooling tower obtained in Case 1 is implemented under individual air

conditions The resulting thermal and economic performance of the cooling tower is

presented in Table 6

It is noticed that the process cooling demand cannot be satisfied by the fixed operation

when the ambient air becomes hot and humidity while excessive heat is removed by the

fixed operation when the ambient air becomes cold and dry In the condition 1 the heat

rejected by processes is around 81 MW which is about 18 MW less than the cooling

requirement In conditions 2 and 3 the heat rejected by processes is around 104 MW

and 114 MW respectively which are about 5 and 15 MW more than the cooling

requirement That is because the cooling water outlet temperature is increased with the

increase of inlet dry-bulb temperature wet-bulb temperature and humidity when the

cooling water inlet flowrate the dry air flowrate and the cooling water inlet temperature

are fixed as shown in Table 6


27

A fixed operation of cooling towers under different ambient air conditions results in that

either the cooling demand is not satisfied or the excessive heat is removed from

processes Therefore the operating variables of towers are supposed to be adjusted for

individual ambient air conditions to complete the cooling demand and to reduce the

operating cost at the same time Operational optimisation of the tower is performed

under individual ambient air conditions The optimisation results are listed in Table 6

Through optimisation the specified cooling demand is satisfied no matter what the

ambient air conditions are and the operating cost is minimised In the condition 1

through optimisation the cooling water inlet mass flowrate is increased by about 520 th

while the dry air mass flowrate is decreased by around 1654 th compared with the

operation obtained in Case 1 As the cooling load is increased from about 81 MW to

around 99 MW the cooling water flowrate is increased to complete the cooling demand

The large decrease of air flowrate is caused by the reduction of the range of cooling

water and the increase of cooling water inlet temperature which results in the reduction

of the total power consumption The optimal operation of the cooling tower leads to the

increase of evaporation rate and thereby the make-up water consumption is increased

As a result the overall operating cost is higher than that in Case 1 The dry-bulb

temperature the wet-bulb temperature and the humidity in conditions 2 and 3 are lower

than those in case 1 Through optimisation the cooling water inlet mass flowrate is

decreased by approximate 120 th while the air mass flowrate is increased by about 250

th in condition 2 The increase of the air mass flowrate is mainly caused by the increase

of the range The increase of power consumed by the fan is more than the decrease of

power consumed by the pump and thereby the total power consumption is increased

Due to the reduced water evaporation rate the make-up water consumption is decreased

As a result the total operating cost is reduced by 03 poundh The operating cost in

condition 2 is quite close to that in case 1 as the ambient air conditions are almost the

same In condition 3 the cooling water inlet mass flowrate is increased which results in

the decrease of the range The dry air mass flowrate is largely reduced which is caused


28

by the large reduce of the range and the favourable ambient air conditions The overall

power consumption is reduced by about 50 kW As the water evaporation rate decreases

the make-up water consumption is reduced by 32 th Therefore the total operating cost

is decreased by nearly 10 poundh In summary the operational optimisation of a cooling

tower carried out for each air condition allows the cooling demand to be completed with

the minimum total operating cost no matter how the ambient air conditions change The

benefit from the optimisation is obvious when ambient air conditions change a lot

while the benefit from the optimisation is little when ambient air conditions change

slightly

6 Conclusions

Various operating conditions of a given cooling tower can achieve the cooling

requirement of processes resulting in different total operating cost Therefore the

operational optimisation of cooling towers is necessary to improve the economic

performance A model of mechanical draft wet cooling towers is developed for an

operational optimisation program to optimise water inlet flowrate and air inlet flowrate

of cooling towers to improve the economic performance of cooling towers In this

model correlation functions are established to predict water outlet temperature air

outlet humidity and number of transfer units The regression functions correlate tower

characteristics air conditions and water conditions to predict water outlet temperature

and water evaporation rate The model considers more factors that influence water

outlet temperature and water evaporation rate than the regression model developed in

Castro et al [17] The correlation expressions are verified with the literature data [2]

The solver CONOPT is proposed to solve the NLP problem in GAMS The model is

proven to be effective to determine the optimal operating conditions and to improve the

economic performance of cooling towers by a case study In the case study the total

operating cost is improved by 69 through optimisation compared with that in the

base case


29

In addition the effect of the ambient air conditions on the operation and the resulting

thermal and economic performance of the cooling tower are investigated The results

reveal that a fixed operation of the cooling tower cannot satisfy the cooling requirement

of processes when the ambient air becomes hot and humidity while it removes

excessive heat when the ambient air becomes cold and dry The optimisation of the

cooling tower under different ambient air conditions not only completes the specified

cooling demand but also reduces the operating cost

The model of cooling towers is based on mechanical draft wet cooling towers

Therefore the application of the model is appropriate to mechanical draft wet cooling

towers The model of nature draft wet cooling towers is not developed here but can refer

to the model proposed in this paper The operation of cooling towers is determined with

the consideration of the transfer characteristic of cooling towers and the process cooling

demand regardless of the effect of cooler networks and piping networks on the

operation In fact the cooling water inlet temperature is determined by the structure of

individual coolers and the arrangement of cooler networks besides the factors

considered in this paper In future work therefore the detailed cooler network will be

taken into account when the operation of cooling towers is optimised


30

Nomenclature

Parameters

A cross sectional area of fill in a cooling tower (m2)

C1 unit cost of makeup water (poundt)

C2 unit cost of power (poundkWh)

cc cycles of concentration

ifgwo latent heat of water evaluated at 27315K (Jkg)

ii enthalpy of inlet air-water vapour mixture per unit mass of dry air (Jkg

dry air)

Lfi the height of fill in a cooling tower (m)

Q the cooling load of processes (W)

tm temperature of makeup water (degC)

tdbi air inlet dry-bulb temperature of a cooling tower (degC)

twbi air inlet wet-bulb temperature of a cooling tower (degC)

wi humidity ratio of inlet air into cooling towers (kgkg dry air)

Variables

Cpa the specific heat of dry air (JkgdegC)

Cpv specific heat of saturated water vapor (JkgdegC)

Cpw the specific heat of cooling water (JkgdegC)

ER evaporation ratio

Hp pressure head provided by pumps (m)

ifgw latent heat of water (Jkg)

ima enthalpy of the airndashwater vapour mixture per unit mass of dry air (Jkg dry

air)

imasw enthalpy of saturated air evaluated at the local bulk water temperature (Jkg

dry air)

io enthalpy of outlet air-water vapour mixture per unit mass of dry air (Jkg

dry air)

iv enthalpy of the water vapour at the bulk water temperature (Jkg)

Lef the Lewis factor

ma mass flowrate of dry air in a cooling tower (kgs)


31

Mep Merkel number

me evaporation rate (kgs)

mm mass flowrate of makeup water (kgs)

mw mass flowrate of cooling water in a cooling tower (kgs)

mwi mass flowrate of inlet cooling water into a cooling tower (kgs)

mwo mass flowrate of outlet cooling water from a cooling tower (kgs)

NTU number of transfer units

p pressure (Pa)

ps vapour pressure of saturated water vapour (Pa)

pswb vapour pressure of saturated water vapour evaluated at the wet-bulb

temperature (Pa)

Pf power consumed by fans (kW)

Pp power consumed by pumps (kW)

Qw volumetric flowrate of cooling water (m3s)

T temperature K

tdb dry-bulb temperature (degC)

tc inlet temperature of cooling water into coolers (degC)

TOC total operating cost (poundh)

tw cooling water temperature in a cooling tower (degC)

twb wet-bulb temperature (degC)

twi inlet temperature of cooling water into cooling towers (degC)

two outlet temperature of cooling water from cooling towers (degC)

w humidity ratio (kgkg dry air)

wo humidity ratio of outlet air from a cooling tower (kgkg dry air)

wsw humidity ratio of saturated air at water temperature (kgkg dry air)

ηp pump efficiency

Subscripts

a air

db dry-bulb

e evaporation

f fans

i inlet


32

m make-up water

o outlet

p pumps

P Poppe method

s saturation

v vapor

w cooling water

wb wet-bulb

References

[1] Qureshi BA and Zubair SM 2006 Prediction of Evaporation Losses in Wet Cooling

Towers Heat Transfer Eng 27(9) pp 86-92

[2] Simpson WM and Sherwood TW 1946 Performance of Small Mechanical Draft Cooling

Towers Refrigerating Engineering 52 (6) pp 525-543 and 574-576

[3] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter Flow

Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778

[4] Singham JR 1983 Heat Exchanger Design Handbook Hemisphere Publishing Corporation

New York USA

[5] Mills AE 1999 Basic Heat and Mass Transfer Prentice Hall Upper Saddle River USA

[6] Lemouari M Boumaza M and Mujtaba IM 2007 Thermal Performances Investigation of

a Wet Cooling Tower Applied Thermal Engineering 27 pp 902ndash909

[7] Lemouari M and Boumaza M 2010 Experimental Investigation of the Performance

Characteristics of a Counter Flow Wet Cooling Tower International Journal of Thermal

Sciences 49 pp2049-2056

[8] Alwan DAlDH Maid IW and Soheel AH 2013 Numerical and Experimental Study of

Counter Flow Cooling Tower Performance with Difference Packs Porosity and Configuration

Al-Rafidain Engineering 21 (6) pp 101-115

[9] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash128

[10] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass

Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and

Mass Transfer 48 pp 765ndash777

[11] Poppe M and Rogener H 1991 Berechnung von Ruckkuhlwerken VDI-Warmeatlas Mi 1ndash

Mi 15

[12] Fisenko SP Petruchik AI and Solodukhin AD 2002 Evaporative Cooling of Water In a

Natural Draft Cooling Tower Int J Heat Mass Transfer 45 pp 4683ndash4694


33

[13] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with

Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989

[14] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU Method

ASME J Heat Transfer 111(4) pp 837ndash843

[15] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP

Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical Engineering

Research and Design 88 (5-6) pp 614-625

[16] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A 2011

Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a Rigorous

Model Applied Thermal Engineering 31 pp 3615-3628

[17] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in Cooling

Water Systems Trans IChemE 78 (part A) pp 192-201

[18] Baker DR and Shryock HA 1961 A Comprehensive Approach to the Analysis of Cooling

Tower Performance Journal of Heat Transfer pp 339ndash350

[19] Kroumlger DG 2004 Air-Cooled Heat Exchangers and Cooling Towers PennWell Corp Tulsa

Oklahoma

[20] Milosavljevic N and Heikkilauml P 2001 A Comprehensive Approach to Cooling Tower

Design Applied Thermal Engineering 21 pp 899ndash915

[21] Goshayshi HR and Missenden JF 2000 The Investigation of Cooling Tower Packing in

Various Arrangements Applied Thermal Engineering 20 pp 69ndash80

[22] Kloppers JC and Kroumlger DG 2005 Refinement of the Transfer Characteristic Correlation

of Wet-Cooling Tower Fills Heat Transfer Engineering 26(4) pp 35-41

[23] Johnson BM 1989 Cooling Tower Performance Prediction and Improvement Volume 1

Applications Guide EPRI Report GS-6370 Volume 2 Knowledge Base EPRI Report GS-

6370 EPRI Palo Alto

[24] Singla RK Singh K and Das R 2016 Tower Characteristics Correlation and Parameter

Retrieval in Wet Cooling Tower with Expanded Wire Mesh Packing Applied Thermal

Engineering 96 pp 240ndash249

[25] Shahali P Rahmati M Alavi SR and Sedaghat A 2016 Experimental Study on

Improving Operating Conditions of Wet Cooling Towers Using Various Rib Numbers of

Packing International Journal of Refrigeration 65 pp 80ndash91

[26] Mc Kelvey KK and Brooke M 1959 The Industrial Cooling Tower Elsevier Publishing

Amsterdam

[27] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power

Characteristics of Pump of a Pump Group Journal of Water Resources Planning and

Management 134 pp88-93

[28] Webb R L 1984 A Unified Theoretical Treatment for Thermal Analysis of Cooling Towers

Evaporative Condensers and Fluid Coolers ASHRAE Trans 90(2) pp 398ndash415


34

Appendix

1) Data information

The data used to validate the correlations of cooling towers are presented in Table A1

Table A1 Measured data for the regression of coefficients in equations (3) (4) and (8) for a

cooling tower in Simpson and Sherwood [2]

No twi

(degC)

two

(degC)

tdbi

(degC)

twbi

(degC)

wi

(kgkg dry air)

ma

(kgs)

mwi

(kgs)

wo

(kgkg dry air)

1 4144 2600 3411 2111 00104 1158 0754 00284

2 2872 2422 2900 2111 00125 1186 1259 00215

3 3450 2622 3050 2111 00119 1186 1259 00271

4 3878 2933 3500 2667 00188 1264 1008 00323

5 3878 2933 3500 2667 00188 1250 1008 00323

6 3967 2622 3400 2111 00105 1174 0881 00284

7 3500 2867 3461 2667 00190 1156 0881 00285

8 4361 2789 3500 2388 00141 1158 0754 00316

9 4306 2972 3572 2667 00185 1155 0754 00337

10 3806 3089 3594 2944 00236 1142 0754 00321

11 4778 3217 3617 2944 00235 1142 0754 00400

12 3378 2472 3250 2111 00110 1179 0881 00238

13 4144 3000 3617 2667 00183 1156 0881 00340

14 4061 3172 3417 2944 00244 1147 0881 00359

15 4350 3217 3533 2944 00239 1147 0881 00383

16 3672 3139 3272 2944 00250 1155 1008 00329

17 3322 2550 2883 2111 00126 1186 1008 00244

18 3844 2678 2950 2111 00123 1186 1008 00290

19 3661 2944 3250 2667 00199 1161 1132 00314

20 4100 3050 3294 2667 00197 1161 1132 00364

21 3611 2972 3111 2667 00204 1166 1258 00314

22 4022 3078 3133 2667 00203 1166 1258 00364

23 3956 3011 3206 2667 00200 1008 1008 00349

24 3950 3006 3106 2667 00205 1051 1008 00344

25 3944 3000 3333 2667 00195 1108 1008 00341

26 3978 2967 3167 2667 00202 0947 1008 00357

2) The Poppe method [10]

There are some basic assumptions in the Poppe method listed as follows

bull The system is at steady state


35

bull Heat and mass transfer in a direction normal to the flows only

bull Negligible heat and mass transfer through the tower walls to the environment

bull Negligible heat transfer from the tower fans to air or water streams

bull Constant water water vapour and dry air specific heats throughout the tower

bull Constant heat and mass transfer coefficients throughout the tower

bull Water lost by drift is negligible

bull Uniform temperature throughout the water stream at any cross section

bull Uniform cross-sectional area of the tower

bull No resistance to heat flow in the interface

The governing equations of the Poppe method are expressed as equations (A1) ndash (A3)

w

( w ) w

w ( ) w ( w ) v- ( w ) w (A1)

w

w

( w ) w

w ( ) w ( w ) v- ( w ) w

(A2)

w

( w ) ( w ) ( ) v ( w ) w (A3)

where is enthalpy of the airndashwater vapour mixture per unit mass of dry air is

enthalpy of saturated air evaluated at the local bulk water temperature is humidity

of saturated air at water temperature is the Lewis factor is enthalpy of the water

vapour at the bulk water temperature is humidity of cooling water is temperature

of cooling water is the Merkel number calculated by the Poppe method is

mass flowrate of cooling water and is mass flowrate of dry air

w

w

(

w ( )) (A4)


36

The Lewis factor is expressed as equation (A5)

w w

w

0 w w

w 1

(A5)

The relationship of NTU and the Merkel number is expressed by equation (A6)

w

(A6)

The correlation expression for the prediction of the Merkel number is expressed by

equation (A7) according to Johnson [23]

w

( ) (A7)

The correlation expression for the prediction of NTU is expressed by equation (A8)

combining equations (A6) with (A7)

w

(A8)

where is the height of fill is the cross sectional area of fill and c1- c4 are

coefficients

The equations for properties of water and air

The enthalpy of the air-water vapor mixture per unit mass of dry air is

( ) [ ( )] (A9)


37

The specific heat of dry air at constant pressure is

times times times times 7 (A10)

The water vapor pressure is

(A11)

7

7

times [ ( 7 frasl ) +]

times [ 7 ( 7 frasl ) ] (A12)

The specific heat of saturated water vapour is

times times times (A13)

The specific heat of water is

times times times times (A14)

The latent heat of water is


is obtained from above equation where T=27315K

The humidity ratio of air is

( w )

w w

( w )

77 w (A16)


38

The correlation equation of evaporation ratio of cooling towers proposed by Qureshi et

al [1] is presented as equation (A17)

( ) ( ) ( ) (A17)

where ER is evaporation ratio and are cooling water inlet and outlet

temperature respectively and and are ambient dry-bulb temperature and wet-

bulb temperature respectively

Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems

18

Chapter 3

Publication 2 Operational Optimisation of

Recirculating Cooling Water Systems

(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating

Cooling Water Systems)


1

Operational Optimisation of Recirculating Cooling

Water Systems



Abstract

Recirculating cooling water systems are extensively used for heat removal in the

process industry The economic performance can be improved by integration of key

components in cooling water systems The integration of cooling water systems was

carried out for the cooling water system operation in the literature [1] [2] [3] Models

were developed for cooling water systems in [1] [2] [3] which is limited to one

cooling tower and cooler networks with a parallel configuration In addition the model

in the literature [1] did not consider the detail heat transfer in coolers and the model in

the literature [2] and [3] did not include the pressure drop in coolers To overcome those

limitations in this paper an NLP model is developed for operational optimisation of

cooling water systems The model takes multiple cooling towers and cooler networks in

both parallel and complex configurations into account The model developed by Song et

al [4] is employed for cooling tower modelling The detailed heat transfer in coolers is

expressed The hydraulic model takes pressure drop in coolers pipes and pipe fittings

into consideration The NLP model is solved by the solver CONOPT in GAMS for

minimising the total operating cost A case study proves that the model is effective to

improve the economic performance by integration of cooling water systems In the case

study through optimisation the operating cost is reduced by about 6 compared with

the base case

Key words recirculating cooling water systems integration model operational

optimisation




2

Highlights

An integration model of recirculating cooling water systems is developed

Multiple cooling towers and cooler networks in parallel and series configurations

are considered

Detailed heat transfer in coolers and pressure drop in coolers and pipes are taken

into account

The model is effective to improve the economic performance

The effect of ambient air conditions on the performance of cooling water systems is

investigated

1 Introduction

The recirculating cooling water systems are commonly used to reject process heat to the

atmosphere in order to keep processes running efficiently and safely in chemical

petrochemical and petroleum processes power stations etc A typical recirculating

cooling water system consists of three key components that are mechanical draft wet

cooling towers cooler networks and piping networks as shown in Figure 1 Cooling

water is pumped and distributed by piping networks to individual coolers for process

heat removal After heat exchange in coolers cooling water is heated while processes

are cooled Hot cooling water from cooler networks formed by coolers is sent to wet

cooling towers In wet cooling towers when the cooling water directly contacts air

blown by fans water evaporation and heat convection occur resulting in the

temperature reduction of cooling water Due to water evaporation some cooling water

is lost which is replenished by make-up water The cold cooling water from cooling

towers mixed with the make-up water is pumped to individual coolers again In this way

cooling water recirculates in cooling water systems


3


The operation of cooling water systems includes circulating water flowrate in cooling

water systems cooling water flowrate through individual coolers and air flowrate into

cooling towers Circulating water flowrate in cooling water systems and cooling water

flowrate into individual coolers can be adjusted by valves and pumps Air flowrate into

cooling towers can be adjusted by fans Cooling water outlet temperature of cooling

towers which determines the cooling water inlet temperature of individual coolers can

be changed by the adjustment of circulating water flowrate and air flowrate into cooling

towers The same cooling requirement of processes can be satisfied by various

operations of cooling water systems as cooling water flowrate and temperature into

individual coolers are alterable The same cooling requirement can be achieved by

either a relatively low flowrate of circulating water in cooling water systems

accompanied by a large temperature increase of cooling water after heat removal or a

relatively high flowrate of circulating water in cooling water systems accompanied by a

small temperature increase of cooling water after heat removal When cooling water

temperature change after heat removal is small the cooling water temperature recovery

in cooling towers is achieved by low air flowrate When cooling water temperature


4

change is large the cooling water temperature recovery in cooling towers is attained by

high air flowrate Therefore the specified cooling requirement can be achieved by

increasing circulating water flowrate with decreasing air flowrate into cooling towers or

by decreasing circulating water flowrate with increasing air flowrate into cooling towers

Although various operations can achieve the same cooling requirement the resulting

make-up water consumption and power consumption are probably different Because

the change of circulating water flowrate is contrary to the change of air flowrate the

change of power consumption by pumps is contrary to the change of power

consumption by fans When the decrease in power consumption cannot offset the

increase in power consumption the total power consumption will change with

operations of cooling water systems In addition make-up water consumption depends

on the operation as well as water evaporation depends on the operation of cooling water

systems Therefore the total operating cost caused by power and make-up water

consumption varies with the change of operations The economic performance of

cooling water systems can be improved by a trade-off between circulating water

flowrate and air flowrate

In the operation of cooling water systems circulating water flowrate and cooling water

into individual coolers are determined by the characteristics of piping networks and

pumps Any change of cooling water flowrate in one of the coolers influences not only

the cooling water outlet temperature from the cooler but also the cooling water flowrate

through other coolers and their cooling water outlet temperature

The thermal interaction between cooling towers and cooler networks is complex Cold

cooling water from cooling towers mixed with make-up water is distributed to

individual coolers Therefore the cooling water outlet temperature of cooling towers

determines the cooling water inlet temperature of coolers For given coolers the cooling


5

water inlet temperature and flowrate determine the process outlet temperature and the

cooling water outlet temperature from coolers when the flowrate and the inlet properties

of processes are constant For the given cooling requirement the cooling water flowrate

and temperature into individual coolers must allow processes to achieve their specified

temperature After heat exchange the hot cooling water from cooler networks is sent to

cooling towers Therefore the cooling water into cooling towers is the same as the

cooling water out of cooler networks in terms of flowrate and temperature In given

cooling towers cooling water outlet temperature of cooling towers depends on cooling

water inlet temperature cooling water inlet flowrate and air inlet flowrate The cooling

water outlet temperature of cooling towers must achieve the requirement for cooling

water inlet temperature of coolers which affects the air flowrate into cooling towers in

turn

In addition ambient air conditions including dry-bulb temperature wet-bulb

temperature and humidity have an impact on the thermal performance of cooling towers

The variation of ambient air conditions changes the performance of cooling towers and

thereby that of the overall cooling water system

In practice the operation of cooling towers and the operation of cooler networks are

usually carried out by two separate sectors Utility sectors in charge of cooling towers

adjust the air flowrate to cool down the cooling water to the desired temperature that

usually relies on the design data Process sectors operating cooler networks changes the

cooling water flowrate into coolers until the temperature of processes reaches their

requirement Both sectors do not concern about the effect of their operations on the

other components of cooling water systems The operation of cooling water systems is

hardly the most economical without considering the interactions between different

sectors


6

Many studies on cooling towers and cooler networks were carried out separately in

previous studies Some models of cooling towers were proposed in [4] [5] [6] [7] [8]

[9] [10] [11] The optimisation of cooling towers based on different models was

studied in [12] [13] [14] [15] Besides the previous studies on cooling towers some

studies on cooler network design modelling and optimisation were investigated in [16]

[17] [18] [19] [20] [21] The stage-wise superstructure was developed for cooler

networks by Ponce-Ortega et al [16] which allowed bypass and splitting of cooling

water The number of processes determined the number of stages in order to include

arrangements completely in series Mass balance and energy balance are carried out for

cooler networks Film heat transfer coefficients of processes and cooling water were

treated as parameters The pressure drop and cooler configuration were not considered

The stage-wise superstructure of cooler networks developed in [16] was applied by

Ponce-Ortega et al [17] The detailed cooler design and pressure drop in coolers were

included in the model Two-step sequential approach was proposed for the optimisation

of cooling water systems by Sun et al [18] The first step is to determine the optimal

cooler network with a superstructure of a cooler network For the purpose of simplicity

and operability there is a limit to the serial number of coolers in each parallel branch

pipe Mass balance and energy balance were performed for cooler networks The second

step is to determine the optimal pump network for the optimal cooler network with the

method developed by Sun et al [19] An analytical methodology was developed to

target and design cooler networks by Shenoy et al [20] Firstly the Unified Targeting

Algorithm was applied to decide the target of the minimum cooling water flowrate

Then the Nearest-Neighbors Algorithm was used to design the cooler network with the

maximum cooling water reuse This method did not consider energy consumption

Picoacuten-Nuacutentildeez et al [21] developed a thermal-hydraulic model of cooling networks for

flexible design and operation of cooling networks


7

Due to strong interactions between the components in cooling water systems there has

been a growing interest in the integration of cooling water systems for analysis and

optimisation of cooling water systems In 2000 Castro et al [1] established an

optimisation model for a cooling water system to determine the optimum operating

conditions of cooling water systems The model was developed for a cooling water

system with one cooling tower and a cooler network in a parallel configuration

including a regressed model of cooling towers an energy balance of coolers and a

hydraulic model of piping networks The detailed heat transfer in heat exchangers was

not expressed Cortinovis et al [2] developed a mathematical model for the systematic

performance analysis of cooling water systems with a cooling tower and a cooler

network in a parallel arrangement The model included a phenomenological model of

cooling towers with an empirical model of mass transfer coefficient a detailed heat

transfer model of individual coolers and a hydraulic model of piping networks The

pressure drop in heat exchangers was not considered in the hydraulic model Later on

Cortinovis et al [3] extended the model developed in [2] to optimise the operation of

cooling water systems Picoacuten-Nuacutentildeez et al [22] introduced a simplified model to

investigate the steady state response of cooling networks to temperature disturbances

The model was established on the basis of cooling tower thermal effectiveness and

cooler network thermal effectiveness The hydraulic performance of the network was

not considered Kim and Smith [23] developed a methodology to design the cooling

water network and a methodology to debottleneck cooling water systems with the

consideration of the interaction of cooler networks and cooling towers In their work

pinch analysis was applied to determine the target of cooling water flowrate in cooling

water network Pinch analysis is a graphical method that is unable to take pressure drop

in piping networks cost and forbidden connections into account Therefore the method

developed by Kim and Smith [23] can be used to design a cooling water system with the

minimum cold utility usage rather than a cooling water system with the minimum total

cost Afterwards Kim and Smith [24] developed a mathematical model for the retrofit


8

design of cooling water systems In their work the pressure drop in both heat

exchangers and pipes was considered Ponce-Ortega et al [25] developed an MINLP

model for the optimisation of cooling water system design The model included detailed

design model of cooling towers a stage-wise superstructure of cooler networks detailed

design model of coolers and pressure drop calculation in coolers It should be noted that

the models mentioned above were developed for cooling water systems with a single

cooling tower However cooling water systems in most large-scale industries contain

multiple cooling towers Some studies on the design of the cooling water system with

multiple cooling towers were made in the literature [26] [27] [28] In the literature [26]

[27] a superstructure of cooler networks was developed which included all the possible

connections between cooling towers and coolers and all the possibilities of cooling

water reuse between coolers Mass balance and energy balance of cooler network were

implemented Multiple cooling towers were represented by their inlet temperature

outlet temperature and maximum capacity rather than the model of cooling towers in

the literature [26] while a phenomenological model of cooling towers developed by

Kroumlger et al [29] was employed to predict the performance of cooling towers in

Literature [27] Rubio-Castro [28] developed an MINLP model for optimisation of

cooling water system design The model included a model for sizing the cooling towers

based on the Merkel method [5] in which pressure drop characteristics of the types of

packing were considered and a stage-wise superstructure for cooler network design was

employed However the pressure drop in piping networks was not considered

Although so many studies have been made on either individual components of cooling

water systems or the integration of cooling water systems for analysis and optimisation

of cooling water systems most studies solved the design problems of cooling water

systems and few studies worked on the operational optimisation of existing cooling

water systems In the few articles [1] [2] [3] on the investigation of cooling water

system operation models developed are limited to single cooling towers and cooler


9

networks in parallel configurations The model in the literature [1] overlooked the

detailed heat transfer in coolers and the model in the literature [2] [3] did not consider

the pressure drop in coolers when the hydraulic modelling was carried out

In this work therefore an NLP model is developed with the integration of cooling

towers cooler networks and piping networks for the operational optimisation of cooling

water systems to improve the economic performance of cooling water systems The

operation of cooling water systems includes the flowrate of water into individual

coolers and cooling towers and the flowrate of air into individual cooling towers Cooler

networks both in a parallel arrangement and in a complex arrangement are considered in

the model Multiple cooling towers are included in the model as well The model

developed by Song et al [4] is employed for cooling tower modelling The prediction of

water evaporation takes the ambient air conditions into consideration A detailed heat

transfer model is used for cooler modelling with the consideration of the effect of

cooling water flowrate on the overall heat transfer coefficients of individual coolers

The pressure drop of cooling water side in coolers and the pressure drop in pipes piping

fittings and valves are included in the hydraulic model of piping networks The effect of

cooling water flowrate on the pressure drop is taken into account The cooling

requirement of processes is represented by the outlet temperature of processes from

coolers The process outlet temperature is required to be either fixed or flexible in a

range which is decided by the process requirement When the process outlet

temperature can be flexible in a range the cooling requirement is satisfied as long as the

target temperature of processes after heat rejection is in the specified range The effect

of process outlet temperature from coolers on the performance of processes is not

considered


10

2 Recirculating Cooling Water System Modelling

As the three major components in cooling water systems have strong interactions the

model of cooling water systems consists of models of cooling towers cooler networks

and piping networks The detailed models are presented below

21 Cooling tower modelling

The model of cooling towers developed by Song et al [4] is employed which is

presented as equations (A1) - (A8) in Appendix A (A) The model includes regression

models of number of transfer units air outlet humidity and cooling water outlet

temperature mass and heat balance of cooling towers and a regression model of

characteristics of fans The cooling water outlet temperature is an important element for

heat transfer in coolers The air outlet humidity can be used to predict water evaporation

The fan characteristic model is used to calculate power consumption by fans

22 Cooler network modelling

The cooler network model consists of models of coolers interactions between coolers

and interactions between cooling towers and coolers The model of coolers includes

energy balance and heat transfer equations Both the parallel arrangement and the series

and parallel arrangement of cooler networks are taken into account in the cooler

network model as they are commonly used in plants

221 Cooler modelling

1) The model of coolers

There are some assumptions made in cooler modelling

bull The properties of cooling water related to temperature are calculated at the

mean temperature of inlet and outlet of individual coolers


11

bull Heat transfer coefficient of processes is constant

bull The properties of processes are constant

bull Heat losses to the environment are negligible

bull Cooling water is set to flow in the tube side and hot streams are set to flow in

the shell side

bull The fouling resistant of cooling water and processes are constant

Heat balance and heat transfer equations are used to simulate individual coolers which

is referenced as equations (B1) - (B9) in Appendix A (B) They are used to estimate the

cooling water outlet temperature and process outlet temperature of individual coolers

and at the same time to make sure the cooling requirement of processes is satisfied in

given coolers The process heat capacity flowrate and inlet temperature of coolers are

taken as parameters as they cannot be changed by cooling water systems When the

process outlet temperature is flexible in a specified range the process outlet temperature

is variable

The effect of cooling water flowrate on the heat transfer coefficient and the pressure

drop of cooling water is considered Heat transfer coefficient and pressure drop of the

tube side are calculated by the equation developed by Wang et al [30] which are

presented as equations (B9) and (B10) respectively in Appendix A (B) In calculation of

the overall heat transfer coefficient the fouling resistance of both processes and cooling

water is considered with a fixed value The validation of heat transfer coefficient and

pressure drop developed by Wang et al [30] is presented in Appendix A (B)

222 Network modelling

The network model reflects both interactions between cooling towers and cooler

networks and interactions between coolers The network model is developed for cooler


12

networks in parallel arrangements shown in Figure 2 and those in series and parallel

arrangements shown in Figure 3

Figure 2 A cooling water system with a cooler network in a parallel arrangement

Figure 3 A cooling water system with a cooler network in a series and parallel

arrangement


13

1) Cooler networks in parallel arrangements

In parallel arrangements cooling water from cooling towers is the source of cooling

water into coolers and cooling towers are the sinks of cooling water from coolers In the

modelling j is the set of cooling towers and q is the set of coolers

(1) Mass balance

The water from cooling tower j mixed with make-up water is distributed to cooler q

Therefore the mass flowrate of water flowing through point a in Figure 2 is the sum of

water from cooling tower j to cooler q which is represented by equation (1)

( ) sum ( ) (1)

where ( ) is mass flowrate of water entering cooling tower j and ( ) is mass

flowrate of water from cooling tower j to cooler q

The mass flowrate of water entering cooling tower j is the sum of water from cooler q to

cooling tower j which is represented by equation (2)

( ) sum ( ) (2)

where ( ) is mass flowrate of water from cooler q to cooling tower j

The mass balance of inlet and outlet of coolers is expressed as equations (3) - (4)

( ) sum ( ) (3)

( ) sum ( ) (4)


14

where m (q) is mass flowrate of water flowing through cooler q

(2) Energy balance

The temperature of cooling water provided by cooling tower j is calculated by equation

(5) as the cooling water provided by cooling tower j is the mixture of cooling water

from cooling tower j and its corresponding make-up water

( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

(5)

where ( ) is mass flowrate of make-up water for cooling tower j ( ) is the

specific heat capacity of circulating water in tower j ( ) is the specific heat

capacity of make-up water for tower j ( ) is temperature of water leaving tower j

( ) is temperature of make-up water for tower j and ( ) is water temperature at point

a in Figure 2

The cooling water inlet temperature of cooling tower j is predicted by equation (6)

( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)

where ( ) is the specific heat capacity of water going through cooler q ( ) is

temperature of water entering cooling tower j and ( ) is temperature of water

leaving cooler q

If the cooling tower j provides cooling water for the cooler q then the inlet temperature

of cooling water into the cooler q is calculated by the following equation

( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)


15

where ( ) is mass flowrate of water flowing through cooler q ( ) is the

specific heat capacity of water going through cooler q ( ) is temperature of water

entering cooler q ( ) is mass flowrate of water from cooling tower j to cooler q

( ) is the specific heat capacity of circulating water in tower j and ( ) is water

temperature at point a in Figure 2

2) Cooler networks in series and parallel arrangements

In series and parallel arrangements there are two kinds of sources for cooling water into

coolers which are cooling water from cooling towers and that from coolers (reuse

cooling water) and two kinds of sinks for cooling water from coolers which are cooling

towers and coolers The equations describing the mass and energy balance for point a

and b in Figure 2 are used to present the mass and energy balance for point arsquo and brsquo in

Figure 3 respectively The difference between the series and parallel arrangements and

the parallel arrangements is coolers that use cooling water from other coolers and that

provide cooling water to other coolers Mass balance and energy balance for those

coolers are presented as follows

(1) Mass balance

In the case of using reuse cooling water as the only source cooling water into a cooler q

is the mixture of cooling water from other cooler k which is expressed by equation (8)

( ) sum ( ) ( ) (8)

where m (q) is mass flowrate of water flowing through cooler q and ( ) is mass

flowrate of water from cooler k to cooler q


16

In the case that a cooler q uses both cooling water from cooling tower j and cooling

water from cooler k the flowrate of cooling water into the cooler q is expressed by

equation (9)

( ) sum ( ) sum ( ) ( ) (9)

where m (q) is mass flowrate of water flowing through cooler q ( ) is mass

flowrate of water from cooler k to cooler q and ( ) is mass flowrate of water from

cooling tower j to cooler q

Equations (10) and (11) are used to carry out the mass balance for the outlet of cooler q

discharging water to another cooler k only and both other cooler k and cooling tower j

respectively

( ) sum ( ) ( ) (10)

( ) sum ( ) sum ( ) ( ) (11)


flowrate of water from cooler q to cooler k and ( ) is mass flowrate of water from

cooler q to cooling tower j

(2) Energy balance

For a cooler q receiving cooling water from other cooler k the energy balance for the

inlet of these coolers is developed as equation (12)

( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)


17

where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )

are the specific heat capacity of water going through cooler k and cooler q respectively

( ) is temperature of water entering cooler q and ( ) is temperature of water

leaving cooler k

For a cooler q using cooling water from both cooling tower j and other cooler k the

energy balance for the inlet of these coolers is developed as equation (13)

( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )

(13)



( ) temperature of water entering cooler q ( ) is temperature of water leaving

cooler k ( ) is mass flowrate of water from cooling tower j to cooler q ( ) is

the specific heat capacity of circulating water in tower j and ( ) is water temperature at

point a in Figure 2

23 Piping network modelling

The model of piping networks includes mechanical energy balance and the

characteristics of pumps With this model water distribution in individual coolers is

determined and power consumption by pumps is predicted

231 Water distribution

There are some assumptions made in piping network modelling

bull There is no heat loss from pipes pipe fittings and valves to the environment

bull There is one splitter corresponding to each cooling tower which provides


18

cooling water to coolers and one mixer corresponding to each cooling tower that

mixes hot water from coolers

In the piping network modelling inlet (S1) and outlet (S2) of individual coolers inlet

(S5) and outlet (S6) of individual cooling towers individual splitters (S3) and individual

mixers (S4) are taken as nodes respectively as shown in Figure 4 Mechanical energy

balance between the nodes is carried out by employing the Bernoulli equation

Figure 4 A piping network

Mechanical energy balance is conducted between the outlet (S6) of cooling tower j and

its corresponding splitter (S3) which is expressed as equation (14)

( ) ( )

( )

w( ) ( ) ( )

( )

( )

w( ) ( ) (14)

where ( ) and ( ) are elevation of the outlet of cooling tower j (at node S6) and

splitter j (at node S3) respectively ( ) and ( ) are velocity of water leaving

cooling tower j and that of water going through splitter j respectively ( ) and ( )

are pressure of water at the outlet of cooling tower j and that of water at splitter j

respectively ( ) is density of water ( ) is the friction loss between node s6 of


19

cooling tower j and splitter j ( ) is energy provided by pump j and g is gravitational

constant

Mechanical energy balance between splitter j and the inlet (S1) of the cooler q which

uses cooling water from splitter j is presented as equation (15)

( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (15)

where ( ) is elevation of the inlet of cooler q ( ) is velocity of water going

through cooler q ( ) is pressure of water at the inlet of cooler q ( ) is density of

water and ( ) is the friction loss between splitter j and inlet of cooler q

For cooler q using cooling water from other cooler k mechanical energy balance

between outlet (S2) of cooler k and inlet (S1) of cooler q is presented as equation (16)

( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (k q) (16)

where ( ) is elevation of the outlet of cooler k ( ) is velocity of water going

through cooler k ( ) is pressure of water at the inlet of cooler q ( ) is density of


Mechanical energy balance between outlet (S2) of cooler q and the mixer j (S4) which

is receiving cooling water from cooler q is expressed as equation (17)

( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (17)


20

where ( ) is elevation of mixer j ( ) is velocity of water going through mixer j

( ) is pressure of water at mixer j ( ) is density of water at the mixer j and

( ) is the friction loss between outlet of cooler q and mixer j

Mechanical energy balance between the inlet (S5) of cooling tower j and the

corresponding mixer (S4) is expressed as equation (18)

( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (18)

where ( ) is elevation of the inlet of cooling tower j ( ) is velocity of water

entering cooling tower j ( ) is pressure of water at the inlet of cooling tower j ( )

is density of water at the inlet of cooling tower j and ( ) is the friction loss

between the mixer j and the inlet of cooling tower j

Pressure drop in cooler q is calculated to express the relationship between the pressure

of inlet (S1) of cooler q and that of outlet (S2) of cooler q

( ) ( ) ( ) (19)

where ( ) is pressure of water at the inlet of cooler q ( ) is pressure of water at

the outlet of cooler q and ( ) is pressure drop in cooler q

The calculation of pressure drop in cooling water side of coolers applies the equation

developed by Wang et al [30] which is presented as equation (B10)

The Darcy-Weisbach equation is used to estimate friction loss in pipes pipe fittings and

valves Equivalent length is used to calculate friction loss in pipe fittings and valves

The Colebrook-White equation [31] is applied for friction factor calculation


21

232 Pump modelling

The characteristics of pumps and the characteristics of piping networks are combined to

determine water distribution in individual coolers and the power consumed by pumping

cooling water

A model developed by Ulanicki et al [32] is used to represent the characteristics of

pumps which is shown in Appendix A (C) The coefficients (a1-a3 and b1-b3) in the

model are needed to be corrected for a given pump


Besides models mentioned above some practical constraints are presented as equations

(20) - (28)

The temperature difference between process streams and cooling water is no less than

the minimum temperature approach

( ) ( ) (20)

( ) ( ) (21)

where ( ) and ( ) are temperature of process stream entering cooler q and

leaving cooler q respectively ( ) and ( ) are temperature of water entering cooler

q and leaving cooler q respectively and is the minimum temperature difference

There is an upper bound for the temperature of cooling water entering cooling towers to

avoid fouling scaling and corrosion


22

( ) ( ) (22)

In practice the approach which is the difference between the temperature of cooling

water leaving cooling towers and the wet-bulb temperature of inlet air should be no less

than 28 degC [33]

( ) (23)

The cooling water in individual coolers is in the turbulent region

( ) (24)

where ( ) is the Reynolds number of cooling water in cooler q

For a given cooling tower there are limits for cooling water flowrate and air flowrate to

keep cooling tower working properly

( ) ( ) ( )

(25)

( ) ( ) ( )

(26)

The pressure drop in individual coolers is no greater than the maximum allowance

( ) ( ) (27)

The assumption that outlet air of cooling tower j is not supersaturated is satisfied by

equation (28)

( ) ( ) (28)


23

where ( ) and ( ) are dry-bulb temperature and wet-bulb temperature of air

leaving cooling tower j respectively


The objective of operational optimisation is to minimise the operating cost The

operating cost (TOC) includes cost of makeup water and cost of power needed by fans

and pumps which is expressed as

Min sum ( ) sum ( ( ) ( )) (29)

where C1 and C2 are unit cost of make-up water and electricity respectively ( ) is

make-up water for cooling tower j ( ) is power consumption of pump j and ( ) is

power consumption of fan j

3 Solution Method

Before the model is applied to optimise the operation of cooling water systems model

correction for cooling towers pumps and fans is carried out with the measured data or

the operating data of the given equipment The coefficients in the model can be

achieved by the regression of coefficients in the models with the least square method

After that the objective function is minimised subject to the model constraints and the

practical constraints If the cooler network is in a parallel configuration equations (8) -

(13) and (16) are excluded If the cooler network is in a series and parallel configuration

all the equations mentioned above are included As there are nonlinear equations in the

model the NLP problem is formed The solver CONOPT is employed to solve the

problem in software GAMS as the solver CONOPT is well suited for models with very

nonlinear constraints Before optimisation initial values are assigned to the variables


24

such as mass flowrate of cooling water entering individual coolers and towers air

flowrate entering individual towers and so on

4 Case Studies

Two case studies are used to illustrate the application of the proposed model The

operational optimisation is carried out for a simplified subset of a refinery cooling water

system to cool down nine processes in which there are two forced draft wet cooling

towers two pumps and nine coolers The specifications of the cooling water system are

illustrated below in detail

The specifications of process streams are presented in Table 1 which include the

temperature of process streams entering and leaving coolers (represented as inlet

temperature and outlet temperature respectively) the heat capacity flowrate and heat

transfer coefficient as well as fouling resistance

Table 1 Specifications of processes

Process

streams

Inlet temp

degC

Outlet temp

degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance

msup2degCW

C1 60 Upper 450

1704 987 000018 Lower 420

C2 120 Upper 795

482 286 000018 Lower 750

C3 95 500 586 732 000018

C4 100 Upper 595

707 448 000035 Lower 550

C5 105 Upper 545

447 748 000053 Lower 500

C6 90 Upper 595

1004 488 000018 Lower 550

C7 75 Upper 445

602 913 000018 Lower 400

C8 150 Upper 1000

394 180 000018 Lower 950

C9 125 Upper 645

513 346 000053 Lower 600


25

The specifications of coolers are presented in Table 2 in terms of area number of tubes

tube passes tube diameter and length of tube

Table 2 Cooler specifications

Coolers Area

(m^2)

Number

of tubes

Tube

passes

Tube inside

diameter

(mm)

Tube outside

diameter

(mm)

Length of

tube

(m)

Thermal

conductivity of tube

wall (wmdegC)

C1 3506 1006 2 15 19 60 50

C2 1589 610 2 15 19 45 50

C3 2135 610 2 15 19 60 50

C4 2539 980 4 15 19 45 50

C5 1685 366 2 20 25 60 50

C6 2606 1006 2 15 19 45 50

C7 2004 588 4 20 25 45 50

C8 1641 468 2 15 19 60 50

C9 2539 980 4 15 19 45 50

The pipe specifications in terms of equivalent length of pipes and pipe fittings diameter

and roughness are given in Table 3

Table 3 Pipe specifications

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002

S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002

S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002

S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002

S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002

S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002

S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002


26

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002

S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002

S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002

S2(C1)

-S1(C2) 1200 023 00002

S2(C6)

-S1(C8) 1300 023 00002

The cycles of concentration are set to be 4 for blowdown discharge The fouling

resistance of cooling water is assumed to be 528e-4 msup2degCW The unit cost of make-up

water and the unit cost of electricity are 03 poundt and 01 poundkWh respectively

41 Base case

The cooling water system is operated in the ambient air conditions listed in Table 4 The

operating conditions in the base case are provided in Figure 5 which include the

cooling water inlet flowrate of individual cooling towers the temperature of cooling

water entering individual towers the temperature of cooling water leaving individual

cooling towers dry air flowrate in individual cooling towers and cooling water

distribution in individual coolers The data at the top in Figure 5 is the operating

conditions in the base case The thermal and economic performance of the cooling water

system determined by the operation is shown in Table 6 and the outlet temperature of

individual processes from coolers is listed in Table 7

Table 4 Ambient air conditions

Ambient air conditions

Make-up water

temperature (degC) Dry-bulb temperature

(degC)

Wet-bulb

temperature (degC)

Humidity (kgkg

dry air)

Enthalpy

(kJkg)

318 271 205 855 318


27

Figure 5 Comparison of optimal operation and operation in base case

42 Case study 1

Before optimisation the coefficients in the regression models of cooling towers pumps

and fans are regressed and presented in Table 5

Table 5 Models of cooling towers pumps and fans

Units Models

Cooling

towers 1

( ) ( ) ( )

( )

( ) times times ( ( ) ( )) times

( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )


28

Units Models

2

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )

Pumps

1

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

2

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

Fans

1 ( ) ( ) ( )

( )

2 ( ) ( ) ( )

( )

In this case the operating cost of the cooling water system is to be minimised with the

same process cooling requirement satisfied by adjusting cooling water distribution in

individual coolers and dry air flowrate into individual coolers The model of cooling

water systems developed for cooler networks in a series and parallel arrangement is

applied and solved by CONOPT in GAMS with the objective of the operating cost

minimisation There are 438 variables and 412 equations in this optimisation problem

The optimal operating conditions are presented in Figure 5 which are the data at the

bottom The resulting thermal and economic performance of the cooling water system is

listed in Table 6 and the outlet temperature of individual processes from coolers is

shown in Table 7


29

Through optimisation the operating cost of the cooling water system is decreased by 28

kpoundyr which is shown in Table 6 and the temperature of process streams leaving coolers

satisfies the requirement which is shown in Table 7 The cooling water flowrate in the

tower 1 is decreased by 107 th which results in a decrease of the range of the tower 1

The temperature of water entering the tower 1 is increased by 08 ordmC which results in a

decrease of air flowrate The decrease of both water flowrate and air flowrate reduces

the power consumption by about 25 kW compared with the base case The cooling

water flowrate of the tower 2 is reduced by around 100 th which leads to the increase

of the range of the tower 2 The increased range of the tower 2 requires a larger air

flowrate of the tower 2 The resulting dry air flowrate is increased by around 130 th

The decrease of power consumption caused by the decrease of cooling water flowrate of

the cooling tower 2 is 9 kW more than the increase of power consumption by the

increase of air flowrate of the tower 2 Therefore the total power consumption of the

cooling tower 2 is saved by 9 kW The total power consumption of the cooling water

system is reduced by about 34 kW The total make-up water consumption in the cooling

water system after optimisation is almost the same as before optimisation Consequently

the total operating cost of the cooling water system is reduced mainly because of the

reduction of power consumption in this case

The cooling water flowrate entering the coolers that use water from cooling towers only

is reduced to enhance the temperature of water leaving coolers and thereby the

temperature of water entering towers The coolers that reuse cooling water from other

coolers take full advantage of the cooling water that can be reused Therefore the

overall cooling water flowrate is reduced


30

Table 6 Comparison of the optimal operating conditions and the operating conditions in

the base case

Base case Case 1 Difference

Cooling

towers

The range (degC) Cooling tower 1 110 118 -08

Cooling tower 2 109 124 15

The approach

(degC)


Cooling tower 2 41 34 -07

Make-up water flowrate (th)



Total 409 403 -06

Power

consumption

(kW)

Pumps



Total 4184 3829 -355

Fans



Total 865 882 17

Total 5049 4711 -338

Cost

Water(poundh) 1227 1209 -018

Electricity(poundh) 5049 4711 -338

Total operating cost (poundh) 6276 5920 -356

Total operating cost (poundyr) 502k 474k 28k

Table 7 Comparison of outlet temperature of process fluid from individual coolers

Hot streams

Outlet temperature of process fluids from individual coolers

(degC)

Base case Optimisation

C1 450 450

C2 795 795

C3 500 500

C4 595 595


31

Hot streams


(degC)


C5 545 545

C6 595 595

C7 445 445

C8 1000 1000

C9 645 645

43 Case study 2

The thermal performance of cooling towers is affected by ambient air conditions In this

case the thermal performance of cooling water systems under different ambient air

conditions with the same operation of cooling water systems is studied After that the

operating variables of cooling water systems are optimised for each ambient air

condition with the aim of minimising the operating cost Three different ambient air

conditions listed in Table 8 are used to investigate the effect of air conditions on the

performance of cooling water systems The cooling requirement is kept the same as

stated in Table 1



Ambient air

conditions

Dry-bulb temperature (degC) 355 275 325

Wet-bulb temperature (degC) 290 242 280

Humidity (kgkg dry air) 229 178 223

Enthalpy (kJkg) 946 731 898

Make-up water temperature (degC) 355 275 325

The optimal operation of the cooling water system obtained in Case 1 is implemented in

individual air conditions The thermal performance of the operation under the three

ambient air conditions is listed in Table 9 In the conditions 1 and 3 the process streams

cannot be cooled down to the upper bound of the temperature requirement which means


32

that the operation cannot achieve the specified cooling requirement of processes The

ambient air conditions in the conditions 1 and 3 are less favourable to mass and heat

transfer in cooling towers than the air conditions in Case 1 as they have higher dry-bulb

temperature wet-bulb temperature and humidity than the air conditions in Case 1

Therefore the operation of the cooling water system obtained for certain ambient air

conditions probably may not achieve the cooling requirement of processes when

ambient air conditions become disadvantageous to water evaporation and heat

convection in cooling towers In the condition 2 the temperature of the process streams

leaving coolers are below the upper bound of the temperature when the optimal

operation of the cooling water system obtained in Case 1 is carried out As the ambient

air conditions in the condition 2 have lower dry-bulb temperature wet-bulb temperature

and humidity than the ambient air conditions used in Case 1 the ambient air conditions

in the condition 2 is more favourable to water evaporation and heat convection in the

cooling towers than the ambient air conditions in Case 1 Therefore the operation of the

cooling water system obtained in Case 1 reduces the process temperature to the value

below the upper bound of the requirement when the ambient air conditions become

more favourable to water evaporation and heat convection than the ambient air

conditions used to determine the operation Comparing the process outlet temperature in

the three conditions listed in Table 9 it is shown that the cooling duty of cooling water

systems increases with the decrease of dry-bulb temperature wet-bulb temperature and

humidity when the operation of cooling water systems did not change with the variation

of ambient air conditions

Table 9 Comparison of outlet temperature of processes from individual coolers between

before and after optimization for individual conditions

Outlet temperature of processes (

degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

1

Case 1 458 800 510 604 555 603 455 1006 654

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -08 -05 -10 -09 -10 -08 -10 -06 -09


33


degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

2

Case 1 439 787 485 582 530 584 430 991 631

Optimisation 450 766 500 595 545 592 441 982 644

Difference 10 -23 14 12 14 07 10 05 -01

Condition

3

Case 1 454 798 505 599 550 599 450 1003 650

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -04 -03 -05 -04 -05 -04 -05 -03 -05

As shown above a fixed operation of cooling water systems under different ambient air

conditions results in that either the cooling demand is not satisfied or the excessive heat

is removed from processes Therefore the operating variables of cooling water systems

are supposed to be adjusted for individual ambient air conditions to complete the

cooling demand and to reduce the operating cost at the same time With the model

developed in this work the operation of the cooling water system is optimised for

individual conditions with the objective of minimising the operating cost The optimal

operations of the cooling water system for individual conditions are displayed in Figure

6 The resulting power consumption make-up water consumption and operating cost are

listed in Table 10 The outlet temperature of processes from coolers is presented in

Table 9

Through optimisation the process streams are cooled to the specified temperature in the

three conditions In the conditions 1 and 3 both the cooling water flowrate and dry air

flowrate into individual cooling towers are increased to reduce the process outlet

temperature of coolers to the upper bound of the temperature requirement In the

condition 2 the cooling water flowrate in individual cooling towers is increased while

the air flowrate in individual cooling towers is decreased The process outlet

temperature of most coolers is increased which reduces the cooling duty of the cooling

water system From the economic perspective the total operating cost of the cooling

water system in the conditions 1 and 3 is increased after optimisation That is mainly


34

because the cooling duty of the cooling water system is increased after optimisation

which results in the increase of cooling water flowrate and air flowrate in individual

cooling towers The total operating cost of the cooling water caused by the optimal

operation in the condition 2 is about 2 less than that caused by the operation obtained

in Case 1 as the cooling duty of the cooling water system decreases

From the comparison of the optimisation results of the three conditions it is noted that

both the optimal power consumption and make-up water consumption reduce with the

decrease of dry-bulb temperature wet-bulb temperature and humidity As a result the

optimal operating cost of the cooling water system reduces with the decrease of dry-

bulb temperature wet-bulb temperature and humidity As the dry-bulb temperature

wet-bulb temperature and humidity in the condition 1 are higher than those in the

condition 3 the driving force for water evaporation and heat convection in the condition

1 is smaller than that in the condition 3 Therefore the cooling water flowrate and the

air flowrate into cooling towers in the condition 1 are larger than those in the condition

3 to achieve the same cooling requirement Therefore the power consumption by

pumping cooling water and blowing air in the condition 1 is more than that in the

condition 3 In the time condition 2 the driving force for water evaporation and heat

convection is larger than that in the condition 3 However the optimal cooling water

flowrate of the cooling water system in the condition 2 is slightly higher than that in the

condition 3 which results in that the optimal air flowrate of individual cooling towers in

the condition 2 is reduced to almost half of that in the condition 3 Although the cooling

duty of individual cooling towers in the three conditions is no big difference after

optimisation water evaporation reduces with the decrease of dry-bulb temperature That

is because heat convection rate increases with the decrease of dry-bulb temperature and

as a result the cooling duty of water evaporation reduces Therefore water evaporation

reduces with the decrease of dry-bulb temperature which results in the reduction of

make-up water consumption with the decrease of dry-bulb temperature


35

In summary a fixed operation of cooling water systems either fails to complete the

cooling requirement of processes or fulfils the cooling requirement with the processes

excessively cooled when the ambient air conditions change Operational optimisation

for individual air conditions allows the cooling requirement of all the processes to be

satisfied and improves the economic performance of cooling water systems under the

ambient air conditions that are more favourable to water evaporation and heat

convection

Figure 6 Optimal operation of the cooling water system under different ambient air

conditions


36

Table 10 Comparison of results between before and after optimization for individual condtions


Case 1 Optimisation Difference Case 1 Optimisation Difference Case 1 Optimisation Difference

Cooling

towers

Make-up water

flowrate (th)

1 231 241 10 217 207 -10 220 226 06

2 189 195 06 176 168 -08 180 183 03

Total 420 436 16 393 375 -18 400 409 09 Cooling duty (MW) 2302 2363 061 2395 2337 -058 2313 2342 029

Convective heat transfer

(MW) 097 071 -026 352 385 033 217 201 -016

Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045

Pumps Power

consumption (kW)

1 2173 2469 296 2173 2307 134 2173 2197 24

2 1657 1951 294 1657 1769 112 1657 1723 66

Total 3830 4420 590 3830 4076 246 3830 3920 90

Fans Power

consumption (kW)

1 460 639 179 444 305 -139 452 597 145

2 419 538 119 405 239 -166 412 496 84

Total 879 1177 298 849 544 -305 864 1093 229

Total power consumption (kW) 4709 5597 888 4679 4620 -59 4694 5013 319

Cost (poundh)

Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027

Power 4709 5597 888 4679 4620 -059 4694 5013 319

Total 5969 6905 936 5858 5745 -113 5894 6240 346


37

5 Conclusions

The economic performance of cooling water systems can be improved by the

integration of key components in cooling water systems Although some integration

models were developed for the cooling water system operation in the literature [1] [2]

[3] there are some limitations in those models only one cooling tower and cooler

networks in a parallel configuration are considered either detailed heat transfer or

pressure drop in coolers is ignored To overcome those limitations a nonlinear model

is developed for the operational optimisation of cooling water systems with the

integration of cooling towers cooler networks and piping networks In cooling tower

modelling the regression model of mechanical draft wet cooling towers developed by

Song et al [4] is employed to predict the thermal performance of cooling towers The

cooler network model includes detailed heat transfer equations for coolers and the

mass and energy balance for the interactions between coolers and cooling towers The

model takes multiple cooling towers and cooler networks in a series and parallel

arrangement into consideration The mechanical energy balance is carried out for

piping networks to distribute cooling water in individual coolers and to predict the

power consumption by pumps The pressure drop in both pipes pipe fittings valves

and cooling water side of coolers are considered For the optimisation the model is

solved by the solver CONOPT in GAMS With the model of cooling water systems

and the solution method the optimal cooling water mass flowrate entering individual

towers and coolers and air mass flowrate entering individual coolers are determined to

satisfy the process cooling demand with the minimum operating cost of cooling water

systems The model is proven to be effective to improve the economic performance

by integration of cooling water systems by a case study In the case study through

optimisation the operating cost of the cooling water system is about 6 less than that

in the base case

Due to the effect of ambient air conditions on the thermal performance of cooling

towers a fixed operation of cooling water systems may cause problems that the

specified process cooling demand cannot be achieved when ambient air become hot

and wet or that the cooling of processes is excessive which results in the unnecessary

operating cost when ambient air become cold and dry The optimisation of cooling

water systems under different ambient air conditions not only allows the process


38

cooling demand to be completed but also minimises the operating cost of cooling

water systems under different ambient air conditions With the increase of ambient

dry-bulb temperature wet-bulb temperature and humidity the optimal power

consumption and make-up water consumption increase and the resulting operating

cost increases

The operational optimisation of cooling water systems is implemented to minimise

the operating cost of cooling water systems for a specified process cooling demand

The specification for the process outlet temperature from coolers is considered in this

paper In fact the outlet temperature has an effect on the performance of some

processes such as condensing turbines pre-cooling of compression refrigeration

inter-cooling of compressors condensation of light components for distillation and so

on However the effect of the outlet temperature on the performance of processes is

not considered in this work and thereby it should be considered in future work

Nomenclature

Sets

j set of cooling towers

k set of coolers

q set of coolers

Parameters

Ao(q) area of cooler q (m2)




CPh(q) heat capacity flowrate of process q (WdegC)

Cpwm specific heat of makeup water (JkgdegC)

di(q) tube inside diameters of cooler q (m)

din(q) pipe diameter connected with cooler q inlet (m)

do(q) tube outside diameters of cooler q (m)

dout(q) pipe diameter connected with cooler q outlet (m)

g gravitational constant 981m2s

ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg

C)


39

ii enthalpy of inlet air into cooling towers (Jkg dry air)

k(q) thermal conductivity of tube wall of cooler q (WmdegC)

Lt(q) tube length of cooler q (m)

np(q) number of passes of cooler q

nt(q) number of tubes of cooler q

Ri(q) fouling factor of tube side in cooler q (m2 deg

C W)

Ro(q) fouling factor of shell side in cooler q (m2 deg

C W)

tdbi dry-bulb temperature (degC)


twbi wet-bulb temperature (degC)

thi(q) inlet temperature of process fluids into cooler q (degC)

wi humidity of the air into cooling towers (kgkg dry air)

zs1(q) elevation at node s1 of cooler q (m)

zs2(k) elevation at node s2 of cooler k (m)


zs3(j) elevation of splitter j (m)

zs4(j) elevation of mixer j (m)

zs5(j) elevation at node s5 of cooling tower j (m)


a1-a3 coefficients

b1-b3 coefficients

Variables

Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)

Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)

f(q) correction factor of cooler q

hfs2s1(kq) friction loss between node s2 of cooler k and node s1 of cooler q (m3s)

hfs2s4(qj) friction loss between node s2 of cooler q and mixer j (m3s)

hfs3s1(jq) friction loss between splitter j and s3 of cooler q (m3s)

hfs4s5(j) friction loss between mixer j and node s5 of cooling tower j (m3s)

hfs6s3(j) friction loss between node s6 of cooling tower j and splitter j (m3s)

hi(q) heat transfer coefficient in tube side of cooler q (Wm-2

degC

-1)

Hp(j) pressure head provided by pump j (m)

io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)

kw(q) thermal conductivity of cooling water in cooler q (WmdegC)


40

m(jq) mass flowrate from cooling tower j to cooler q (kgs)

m(qj) mass flowrate from cooler q to cooling tower j (kgs)

m(kq) mass flowrate from cooler k to cooler q (kgs)

m(qk) mass flowrate from cooler q to cooler k (kgs)

ma(j) mass flowrate of dry air (kgs)

mc(q) mass flowrate of cooling water in cooler q (kgs)

me(j) evaporation rate of cooling tower j (kgs)

mm(j) mass flowrate of makeup water of cooling tower j (kgs)

mwi(j) mass flowrate of cooling water into cooling tower j (kgs)

mwo(j) mass flowrate of cooling water from cooling tower j (kgs)

NTU(j) the number of transfer units of cooling tower j

ps1(q) pressure at node s1 of cooler q (Pa)

ps2(k) pressure at node s2 of cooler k (Pa)


ps3(j) pressure at splitter j (Pa)

ps4(j) pressure at mixer j (Pa)

ps5(j) pressure at node s5 of cooling tower j (Pa)


Pf(j) power consumption by fan j (kW)

Pp(j) power consumed by pump j (kW)

Qw(j) volumetric flowrate of cooling water through pump j (m3s)

Re(q) Reynolds number of tube side in cooler q

t(j) temperature of mixture of cooling water from cooling tower j and make-up water

(degC)

tci(q) inlet temperature of cooling water into cooler q (degC)

tco(q) outlet temperature of cooling water from cooler q (degC)

tho(q) outlet temperature of process fluids from cooler q (degC)

tdbo(j) air outlet dry-bulb temperature of cooling tower j (degC)

twi(j) inlet temperature of cooling water into cooling tower j (degC)

twbo(j) air outlet wet-bulb temperature of cooling tower j (degC)

two(j) outlet temperature of cooling water from cooling tower j (degC)


us1(q) cooling water velocity at node s1 of cooler q (ms)

us2(k) cooling water velocity at node s2 of cooler k (ms)



41

us3(j) cooling water velocity at splitter j (ms)

us4(j) cooling water velocity at mixer j (ms)

us5(j) cooling water velocity at node s5 of cooling tower j (ms)


uw(q) velocity of cooling water in tubes of cooler q (ms)

uin(q) velocity of cooling water into cooler q (ms)

uout(q) velocity of cooling water out of cooler q (ms)

Uo(q) overall heat transfer coefficient of cooler q (Wm2deg

C)

W(j) energy provided by pump j (m3s)

wo(j) humidity of the air from cooling towers (kgkg dry air)

Greek Symbols

α coefficients

β coefficients

γ coefficients

(q) viscosity of cooling water in cooler q (kgm-1

s-1

)

( ) efficiency of pump j

density of air (kgm3)

(j) density of cooling water in cooling tower j (kgm3)

(k) density of cooling water in cooler k (kgm3)

(q) density of cooling water in cooler q (kgm3)

( ) pressure drop of tube side in cooler q (Pa)

( ) logarithmic mean temperature of cooler q (degC)

minimum temperature difference (degC)

Subscripts

a air

db dry bulb

f fans

i insideinlet

o outsideoutlet

p pumps

s1-s6 nodes

w cooling water

wb wet bulb


42

References

[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in

Cooling Water Systems Trans IChemE 78 (part A) pp 192-201

[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 Integrated Analysis of

Cooling Water Systems Modeling and Experimental Validation Applied Thermal

Engineering 29 pp 3124-3131

[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for

Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-

2209

[4] Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical Draft Wet

Cooling Towers

[5] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash

128

[6] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU

Method ASME J Heat Transfer 111(4) pp 837ndash843




[8] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter

Flow Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778



[10] Khan JR Qureshi BA and Zubair SM 2004 A Comprehensive Design and

Performance Evaluation Study of Counter Flow Wet Cooling Towers Int J Refrig 27 pp

914-923

[11] Kloppers JC and Krӧger DG 2005 Cooling Tower Performance Evaluation Merkel

Poppe and e-NTU Methods Analysis Trans ASME J Engrg GasTurbines and Power 127

pp 1-7

[12] Soumlylemez MS 2001 On the Optimum Sizing of Cooling Towers Energy Conversion and

Management 42(7) pp 783-789

[13] Soumlylemez MS 2004 On the Optimum Performance of Forced Draft Counter Flow

Cooling Towers Energy Conversion and Management 45 pp 2335-2341


Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical

Engineering Research and Design 88 (5-6) pp 614-625

[15] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A

2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a


43

Rigorous Model Applied Thermal Engineering 31 pp 3615-3628

[16] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2007 MINLP

Synthesis of Optimal Cooling Networks Chemical Engineering Science 62 pp 5728-5735

[17] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2009 A Disjunctive

Programming Model for Simultaneous Synthesis and Detailed Design of Cooling Networks

Ind Eng Chem Res 48 2991ndash3003

[18] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems Considering

Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39 pp 49-54

[19] Sun J Feng X Wang YF Deng C and Chu KH 2014 Pump Network Optimization

for A Cooling Water System Energy 1-7

[20] Shenoy AU and Shenoy UV 2013 Targeting and Design of CWNs Energy 55 pp

1033-1043

[21] Picon-Nunez M Canizalez-Daacutevalos L and Polley GT 2011 Modelling the Thermo-

Hydraulic Performance of Cooling Networks and Its Implications on Design Operation and

Retrofit Chapter 9 Evaporation Condensation and Heat transfer Dr Amimul Ahsan (Ed)

InTech

[22] Picon-Nunez M Nila-Gasca C and Morales-Fuentes A 2007 Simplified Model for the

Determination of the Steady State Response of Cooling Systems Applied Thermal

Engineering 27 pp1173ndash1181

[23] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering

Science 56(12) pp 3641-3658

[24] Kim JK and Smith R 2003 Automated Retrofit Design of Cooling-Water Systems

Process Systems Engineering 49(7) pp 1712-1730

[25] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization

Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34

pp 117ndash195

[26] Majozi T and Moodley A 2008 Simultaneous Targeting and Design for Cooling Water

Systems with Multiple Cooling Water Supplies Computers and Chemical Engineering 32

pp 540ndash551

[27] Gololo KV and Majozi T 2011 On Synthesis and Optimization of Cooling Water

Systems with Multiple Cooling Towers Ind Eng Chem Res 50 3775ndash3787

[28] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013

Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal


[29] Kroumlger D G 2004 Air-Cooled Heat Exchangers and Cooling Towers Mass Transfer and

Evaporative Cooling PennWell Corporation Oklahoma USA


44

[30] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified

Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59

[31] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened

Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381


Characteristics of a Pump Group Journal of Water Resources Planning and Management

134 pp 88-93

[33] Li KW and Priddy AP 1985 Power Plant System Design John Wiley amp Sons New

York USA

[34] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and

Chemical Plants Gulf Publishing Houston vol 2

Appendix

Appendix A Models

(A) Cooling tower modelling

A correlation of the NTU of cooling tower j is represented as

( ) ( ) ( )

( ) (A1)

where NTU is the number of transfer units of tower j ( ) is cooling water inlet

mass flowrate of tower j ( ) is dry air mass flowrate and ( ) is cooling water

inlet temperature of tower j

A correlation of air outlet humidity is expressed as

( ) ( ( ) ( )) ( ) ( ( ) ) ( )

( ) (A2)

where ( ) is cooling water inlet mass flowrate of tower j ( ) is dry air mass

flowrate is ambient air humidity ratio based on dry air mass flowrate ( ) is air

outlet humidity ratio based on dry air mass flowrate of tower j respectively ( ) and

( ) are cooling water inlet and outlet temperature of tower j respectively and


45

and are ambient dry-bulb temperature and ambient wet bulb temperature

respectively

A correlation of cooling water outlet temperature is expressed as

( ) ( ) ( ) ( ) ( )

( ( ) ) (A3)


mass flowrate of tower j ( ) is dry air mass flowrate ( ) and ( ) are cooling

water inlet and outlet temperature of tower j respectively and is ambient wet

bulb temperature

The coefficients ( - and - ) in equations (2) and (3) are determined by

the characteristics of cooling towers which can be regressed by the least square

method

Mass balance of cooling tower j

( ) ( ) ( ) ( ( ) ) (A4)

Energy balance of cooling tower j

( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)

where ( ) and ( ) are cooling water inlet and outlet mass flowrate of tower j

respectively is dry air mass flowrate ( ) is the specific heat capacity of

cooling water in tower j ( ) and ( ) are cooling water inlet and outlet

temperature of tower j respectively is specific enthalpy of ambient air and ( ) is

specific enthalpy of air leaving cooling tower j based on the dry air mass flowrate

respectively


46

Water evaporation rate in a cooling tower j is expressed as equation (A6)

( ) ( ) ( ( ) ) (A6)

The flowrate of make-up water is calculated by equation (A7)

( ) ( )

(A7)

where ( ) is make-up water flowrate of tower j ( ) is evaporation rate of tower

j and cc is the cycles of concentration defined as the ratio between the concentration

of dissolved solids in the circulating water and in makeup water

Characteristic of fans j is represented as [34]

( ) 0 ( ) ( )

1 (A8)

where ( ) is power consumption of fan j ( ) is dry air mass flowerate of tower j

is density of ambient air and is air inlet humidity ratio based on dry air mass

flowrate

(B) Heat exchanger modelling

Energy balance of cooler q is expressed as equation (B1)

( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)

where ( ) is heat capacity flowrate of process q ( ) and ( ) are

temperature of process fluids entering and leaving cooler q respectively ( ) is

mass flowrate of cooling water in cooler q ( ) is specific heat of cooling water

of cooler q and ( ) and ( ) are temperature of cooling water entering and

leaving cooler q respectively


47

Heat transfer in cooler q is expressed as equation (B2)

( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)



overall heat transfer coefficients in cooler q ( ) is area of cooler q Δ ( ) is

logarithmic mean temperature of cooler q and ( ) is correction factor of cooler q

The overall heat transfer coefficient based on the outside area is written as

( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (B3)

where ( ) is overall heat transfer coefficient of cooler q ( )and ( ) are heat

transfer coefficient in tube side and shell side of cooler q respectively ( ) and

( ) are tube inside and outside diameters of cooler q respectively ( ) and ( )

are fouling factor of tube side and shell side in cooler q respectively and ( ) is

thermal conductivity of tube wall of cooler q

The correction factor is expressed as

( ) ( ) ( )

h ( ) ( ) (B4)

S( ) h ( ) h ( )

( ) ( ) (B5)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )

( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (B6)

For S( )

( ) radic (q)

(q)

( ) ( radic ) ( ) ( radic )frasl (B7)


48

The logarithmic mean temperature difference is written as equation (B8)

Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(B8)

where Δ ( ) is logarithmic mean temperature difference in cooler q ( ) and

( ) are temperature of process fluids entering and leaving cooler q respectively

and ( ) and ( ) are temperature of cooling water entering and leaving cooler q

respectively

The heat transfer coefficient of the stream in the tube side is written as

( ) w( )

( ) ( )

w ( ) μw( )

w( )

(B9)

where ( ) is heat transfer coefficient in tube side of cooler q ( ) is tube inside

diameters of cooler q ( ) is thermal conductivity of cooling water in cooler q

( ) is specific heat of cooling water of cooler q ( ) is Reynolds number of

tube side in cooler q and ( ) is viscosity of cooling water in cooler q

The pressure drop of the tube side is written as

( ) 7 ( ) R ( ) 8 ( ) w( ) w( )

( ) ( ( ) ) ( ) ( )

( ) ( ( ) ( )

) (B10)

where ( ) is pressure drop in tube side of cooler q ( ) is number of tube passes

in cooler q ( ) is Reynolds number of tube side in cooler q ( ) is tube length of

cooler q ( ) is density of cooling water in cooler q ( ) is velocity of cooling

water in cooler q and ( ) and ( ) are velocity of cooling water entering and



49

The fluid velocity in the tube side is written as

( ) ( ) ( )

w( ) ( ) ( ) (B11)

where ( ) is velocity of cooling water in cooler q ( ) is mass flowrate of

cooling water in cooler q ( ) is number of tube pass in cooler q ( ) is density

of cooling water in cooler q ( ) is number of tubes in cooler q and ( ) is tube

inside diameter in cooler q

The inlet fluid velocity of cooler q is written as

( ) ( )

w( ) n( ) (B12)

where ( ) is velocity of cooling water entering cooler q ( ) is mass flowrate of

cooling water in cooler q ( ) is density of cooling water in cooler q and ( ) is

pipe diameter connected with cooler q inlet

The outlet fluid velocity of cooler q is written as

( ) ( )

w( ) ut( ) (B13)

where ( ) is velocity of cooling water leaving cooler q ( ) is mass flowrate

of cooling water in cooler q ( ) is density of cooling water in cooler q and

( ) is pipe diameter connected with cooler q outlet

The models of heat transfer coefficient and pressure drop in tube side developed by

Wang et al [30] are validated by some heat exchangers provided in [30] The Stream

data and geometry of heat exchangers are presented in Appendix B The results of

heat transfer coefficients and pressure drop for those heat exchangers are listed in

Table A1 The results obtained by equations proposed by Wang et al [30] are

compared with the results calculated by the software HTRI From Table A1 it is seen


50

that heat transfer coefficients and pressure drops calculated from the model proposed

by Wang et al [30] are similar to the values obtained by HTRI

Table A1 Modelling results

No 1 2 3 4 5

ht

(W(m2 K))

Wang 12072 57689 14026 15846 75662

HTRI 12993 56440 14700 16169 73632

Relative error () -709 221 -459 -200 276

∆Pt

(kPa)

Wang 688 287 886 693 261

HTRI 712 297 868 735 268

Relative error () -337 -337 207 -571 -261

(C) Characteristics of pumps [32]

The efficiency of pump j is expressed as equation (C1)

( ) ( ) ( ) ( ) (C1)

where ( ) is efficiency of pump j and ( ) is volumetric flowrate of cooling water

going through pump j

The pressure head of pump j is written as equation (C2)

( ) ( ( ) ) (C2)

where ( ) is pressure head of pump j

The power consumed by pump j is calculated by the following equation

( ) ( ) w ( )

( ) (C3)


51

where ( ) is power consumption by pump j and ( ) is mass flowrate of cooling

water going through pump j

Appendix B Data information

The stream data and heat exchanger geometry used to validate the equations of heat

transfer coefficient and pressure drop in tube side provided by Wang et al [30] are

presented in Table A2 and Table A3 respectively

Table A2 Stream data [30]

No 1 2 3 4 5

Streams Tube Shell Tube Shell Tube Shell Tube Shell Tube Shell

Specific heat

(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223

Thermal

conductivity

(WmK)

0137 0133 0633 0623 0123 0106 0089 0091 0087 0675

Viscosity

(mPa s) 040 360 062 071 289 120 033 110 180 030

Density

(kgm3) 785 850 991 994 820 790 702 801 786 957

Flow rate

(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390

Inlet

temperature

(degC)

2000 380 480 330 517 2100 2270 1120 1700 770

Fouling

resistance (10-4

m2KW)

35 53 70 40 35 35 53 53 88 53


52

Table A3 Heat exchanger geometry [30]

No 1 2 3 4 5

Tube pitch (m) 003175 002500 002540 003125 002500

Number of tubes 124 3983 528 1532 582

Number of tube passes 4 2 6 2 4

Tube length L (m) 4270 9000 5422 9000 7100

Tube effective length (m) 4170 8821 5219 8850 7062

Tube conductivity (WmK) 5191 5191 5191 5191 5191

Tube pattern

(tube layout angle) 90deg 90deg 90deg 90deg 90deg

Tube inner diameter (m) 00212 00150 00148 00200 00150

Tube outer diameter (m) 00254 00190 00191 00250 00190

Inner diameter of tube-side inlet

nozzle (m) 01023 04380 01280 03370 01540

Inner diameter of tube-side outlet

nozzle (m) 01023 04380 01280 03370 01540

Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines

19

Chapter 4


Recirculating Cooling Water Systems for Improving

the Performance of Condensing Turbines


Cooling Water Systems for Improving the Performance of Condensing Turbines)


1


Water Systems for Improving the Performance of

Condensing Turbines



Abstract

The overall economic performance of cooling water systems and processes with

cooling demand can be improved by the integration of cooling water systems and

processes Condensing turbines with surface condensers using cooling water are

typical users of cooling water systems Therefore condensing turbines are taken as

examples of processes with cooling demand to illustrate the requirement of the

integration The increase of power generation in condensing turbines is at the cost of

the increase of operating cost of cooling water systems Therefore there is a trade-off

between power generation in condensing turbines and the operating cost of cooling

water systems to improve the overall economic performance of cooling water systems

and condensing turbines To solve this problem an equation-based integration model

of condensing turbines and cooling water systems is developed It includes

recirculating cooling water system modelling developed by Song et al [1] turbine

modelling based on mass and energy balance and condenser modelling Both

superheated steam and saturated steam leaving condensing turbines are considered

Detailed heat transfer in condensers is expressed for both the cooling of superheated

steam and that of saturated steam The model is optimised by the solver CONOPT in

GAMS A case study proves that the model is effective to improve the economic

performance In the case study the simultaneous optimisation increases the total

profit by 337 kpoundyr compared with focusing only on maximising the power

generation of condensing turbines

Key words recirculating cooling water systems condensing turbines integration

model operational optimisation




2

Highlights

bull An equation-based integration model of cooling water systems and condensing

turbines is established

bull In condenser modeling the cooling of superheated steam and saturated steam is

considered

bull The integration model is proven to be effective to improve the economic

performance

1 Introduction


environment in the process industry in order to keep processes working efficiently or

safely The operation of cooling water systems determines the outlet temperature of

processes from coolers The operating variables of cooling water systems include

cooling water flowrate entering individual cooling towers and coolers and air inlet

flowrate entering individual coolers For some processes their performance is

sensitive to the temperature obtained by cooling Condensing turbines with surface

condensers using cooling water are examples of those processes Condensing turbines

are devices that generate power by expanding steam to vacuum pressure The vacuum

pressure is created by condensing the steam out of turbines by cooling water in

condensers The power generation rate is influenced by the vacuum pressure that is

determined by the outlet temperature of condensate from condensers

It is noted that power generation rate by turbines is promoted by the increase of

vacuum in corresponding condensers when the other operating conditions of the

condensing turbine is fixed The increase of the vacuum in the condenser requires

lower cooling water temperature andor higher cooling water flowrate provided by

cooling water systems However the higher cooling water flowrate and the lower

cooling water temperature increase the operating cost of cooling water systems as the

higher cooling water flowrate increases the power consumption by pumps and a lower

cooling water temperature increases air flowrate and thereby increases the power

consumption by fans Although the operating cost of cooling water systems is

increased the profit of condensing turbines is also increased If the operation of

cooling water systems is determined by minimising the operating cost of cooling


3

water systems there will be an economic loss from condensing turbines If the

operation of cooling water systems is determined by maximising the profit of

condensing turbines there will be an increase in the operating cost of cooling water

systems Therefore both the economic performance of cooling water systems and that

of condensing turbines should be considered simultaneously to determine the optimal

operation of cooling water systems The optimal operation of cooling water systems is

determined by the trade-off between the revenue of power generation and the

operating cost of cooling water systems to maximise the total profit of cooling water

systems and condensing turbines In addition there is a trade-off between cooling

water flowrate and air flowrate to determine the optimal operation of cooling water

systems A cooling requirement of processes can be achieved by either increase of

cooling water flowrate with decrease of air flowrate or decrease of cooling water

flowrate with increase of air flowrate No matter how the operation is altered the

effect of the variation of cooling water flowrate is contrary to that of air flowrate on

power consumption Therefore there is a trade-off between cooling water flowrate

and air flowrate to determine the cost-effective operation of cooling water systems

Cooling water systems consist of three major components which are wet cooling

towers piping networks and cooler networks Wet cooling towers are used to produce

cold cooling water for process heat removal Mechanical draft wet cooling towers are

very common in recirculating cooling water systems as they can produce cooling

water with different temperature by adjusting air flowrate into cooling towers Piping

networks distribute cooling water to individual coolers Cooler networks are where

processes reject heat to cooling water Condensers are part of cooler networks The

cooling water flowrate into condensers is determined by the characteristics of pumps

and piping networks The cooling water inlet temperature of condensers is determined

by the cooling water outlet temperature of cooling towers The cooling water outlet

temperature of cooling towers is affected by the cooling water inlet temperature of

cooling towers However the cooling water inlet temperature of cooling towers is

determined by the cooling water outlet temperature of both condensers and coolers

The cooling water outlet temperature of condensers and coolers is dependent on the

cooling load of processes Cooling water inlet flowrate and inlet temperature of

condensers have an influence on the vacuum created in condensers The vacuum

pressure of condensers determines the steam outlet state from condensing turbines and


4

thereby determines the power generation of condensing turbines In reverse the steam

outlet state from condensing turbines has an influence on the cooling duty of

condensers and thereby the cooling duty of cooling water systems Therefore there is

a complex thermal behaviour of cooling water systems and condensing turbines

In previous studies Castro et al [2] Cortinovis et al [3] Song et al [1] separately

implemented operational optimisation of cooling water systems with the integration of

the major components of cooling water systems Models of cooling water systems

were developed in their works including models of cooling towers cooler networks

and piping networks Castro et al [2] did not consider heat transfer model of coolers

Cortinovis et al [3] did not consider the pressure drop in coolers in the hydraulic

model Both Castro et al [2] and Cortinovis et al [3] developed a model for cooling

water systems with single cooling tower and cooler networks in a parallel

arrangement In the model developed by Song et al [1] water evaporation was related

to cooling water mass flowrate and dry air mass flowrate into cooling towers and

ambient air conditions while in [2] and [3] the effect of air flowrate and ambient air

conditions on water evaporation is not considered Both a heat transfer model and

pressure drop in coolers and pipes were included in the model by Song et al [1] In

addition cooler networks in series and parallel configurations as well as multiple

cooling towers were taken into consideration

Laskowski et al [4] analysed the effect of cooling water flowrate and temperature on

the performance of condensing turbines based on data from simulators and the actual

measurement Laković et al [5] investigated the effect of cooling water temperature

and flowrate on the performance of condensers and condensing turbines with a

thermodynamic model of condensers and turbines In the literature [6] [7] the

cooling water inlet flowrate and temperature into condensers were optimised to

maximise the power output by the trade-off between power generation of condensing

turbines and power consumption by pumping water in which correlation models of

condensers steam turbines and pumps were included In the literature [8] [9] the

effect of air flowrate into cooling towers and ambient air conditions on the energy

efficiency of power plants was analysed with the consideration of the performance of

cooling towers and condensing turbines The Merkel method [10] was applied to

estimate the cooling water outlet temperature of cooling towers in [8] [9]


5

Condensers were simulated by heat transfer equations with the assumption that steam

into condenser was at the saturated state and the power generation was calculated by

mass and energy balance

Even though cooling water systems and condensing turbines were paid attention to

separately in the past few years there was few literature focusing on operational

optimisation of cooling water systems with the integration of cooling water systems

and condensing turbines In the literature [11] a modular-based optimisation method

was proposed for a waste-and-energy cogeneration plant to maximise the net power

output In the method an optimisation code compiled in Matlab interacted with a

commercial design and simulation software Thermoflex to determine the optimal

performance of the plant In this model power generation and power consumption

were considered while water consumption was ignored As the modular-based

optimisation has less advantage than the equation-based optimisation approach in

terms of robustness speed and power an equation-based optimisation method is

proposed to integrate cooling water systems and processes with cooling demand in

this paper In this method an integration model of cooling water systems and

condensing turbines will be developed to determine the optimal cooling water

flowrate entering individual towers coolers and condensers and air flowrate entering

individual towers The performance of the other processes is not considered in the

model but the cooling requirement of these processes is taken into account Except

cooling water temperature and cooling water flowrate the other elements that affect

the performance of condensing turbines are not considered in this paper

In the following sections a model for the operational optimisation of cooling water

systems is developed The model includes models of cooling water systems power

generation of condensing turbines and heat transfer of condensers The model of

cooling water systems developed by Song et al [1] is applied Then a case study is

used to illustrate the application of the model In the case study the optimal

operations of cooling water systems with different objectives are compared The

objectives include minimising the operating cost of cooling water systems

maximising the profit of power generation by condensing turbines and maximising

the total profit of cooling water systems and condensing turbines Conclusions and

future work are made in the last section


6

2 Model Development

In order to determine the operation of cooling water systems to improve the overall

economic performance of cooling water systems and condensing turbines models

power generation of condensing turbines and heat transfer rate of condensers are

included besides the model of cooling water systems

21 Recirculating cooling water system modelling

An optimisation model of recirculating cooling water systems developed by Song et al

[1] is applied in this paper The model includes models of cooling towers cooler

networks piping networks The cooling requirement of processes is taken into

account The detailed model is presented in Appendix A)

22 Turbine modelling

221 Steam outlet properties

Power generation of condensing turbines is dependent on the state of inlet steam and

outlet steam steam flowrate and turbine efficiency The state of inlet steam and the

flowrate of inlet steam are parameters As it changes with load the isentropic

efficiency is assumed to be constant when the load is constant

Isentropic efficiency of condensing turbine i is defined as equation (1)

( ) n( ) ut( )

n( ) ( ) (1)

where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i

and that of steam leaving condensing turbine i respectively and ( ) is specific

enthalpy of steam at the outlet pressure having the same entropy as the inlet steam in

condensing turbine i

The enthalpy of the outlet steam is calculated by equation (2) rearranged from

equation (1)


7

( ) ( ) ( ( ) ( )) ( ) (2)

The enthalpy of steam at the outlet pressure having the same entropy as the inlet

steam is determined by the outlet pressure which is unknown when the inlet state

of steam is given

(1) Superheated steam

When the entropy of the inlet steam is greater than the entropy of the saturated steam

at the outlet pressure the temperature of the steam leaving turbine i that has the same

entropy as the inlet steam can be calculated by IAPWS-IF 97 [12] for the calculation

of entropy for superheated steam which is expressed as equation (B1) in Appendix B)

( ) is calculated by IAPWS-IF 97 [12] for the calculation of enthalpy for

superheated steam which is expressed as equation (B2) in Appendix B)

The steam outlet temperature of turbines is needed for the calculation of heat transfer

in condensers The steam outlet temperature of turbine i is determined by the

calculation of enthalpy for superheated steam presented in the IAPWS-IF 97 [12]

which is expressed as equation (B3) in Appendix B)

(2) Saturated steam

When the entropy of the inlet steam is less than the entropy of the saturated steam at

the outlet pressure the steam at the outlet pressure having the same entropy as the

inlet steam is saturated The dryness of the steam at the outlet pressure having the

same entropy as the inlet steam in condensing turbine i is calculated by equation (3)

S ( ) ( ) S ( ) ( ( )) S ( ) (3)

where S ( ) is the entropy of the saturated steam at the exhaust pressure of turbine i

S ( ) is the entropy of the saturated liquid and ( ) is dryness of steam at the outlet

pressure having the same entropy as the inlet steam in condensing turbine i S ( ) and

S ( ) are represented by equations (B4)and (B5) in Appendix B)


8

When the steam at the outlet pressure having the same entropy as the inlet steam is

saturated the enthalpy is calculated by equation (4)

( ) ( ) ( ) ( ( )) ( ) (4)

where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i

and ( ) is the enthalpy of the saturated liquid They are represented by equations (B

6) and (B7) in Appendix B)

The dryness of the steam leaving turbines is needed for the calculation of mass

flowrate of steam that is condensed in condensers The dryness of the steam is

calculated by equation (5)

( ) ut( ) ( )

( ) ( ) (5)


( ) is the enthalpy of the saturated and ( ) is specific enthalpy of steam leaving


The saturated temperature of the steam leaving turbine i is calculated by equation (B8)

in Appendix B) The equation represents the relationship between temperature and

pressure of saturated steam in the IAPWS-IF 97 [12]

222 Power generation

Power generation of condensing turbine i is calculated by equation (6)

( ) ( ) ( ) ( ( ) ( )) (6)


and that of steam leaving condensing turbine i respectively ( ) is the mass flowrate

of steam entering turbine i and ( ) is mechanical efficiency of condensing turbine i


9

23 Condenser modelling

1) Superheated inlet steam of condensers

Cooling water systems and condensing turbines are connected by condensers The

cooling water flowrate in cooling water systems is distributed to condensers to

condense the steam from condensing turbines The cooling water flowrate and cooling

water temperature into condensers determine the temperature of condensate The

temperature of the condensate determines the pressure of steam out of condensing

turbines Therefore the condensate temperature is needed to be predicted to determine

the outlet pressure of steam from condensing turbines and the outlet temperature of

cooling water from condensers is needed for the determination of the operation of


If the steam into the condenser i is superheated the mass flowrate of the steam to be

condensed in the condenser i is the same as the flowrate of the steam going through

turbine i which is expressed as equation (7)

( ) ( ) (7)

where ( ) is the mass flowrate of steam entering turbine i and ( ) is the mass

flowrate of steam entering condenser i

It is assumed that there are no heat and pressure loss in the pipes connecting

condensing turbines and condensers Therefore the properties of steam leaving

turbines are the same as those of steam entering condensers The properties of steam

and water in different conditions are calculated by IAPWS-IF 97 [12]

The condensate from condenser i is assumed to be saturated Therefore the condenser

i is divided into two zones which are desuperheating zone and condensing zone The

heat transfer equations for condensers presented in Smith [13] are employed which

are presented in Appendix C) The heat transfer in the desuperheating zone is

expressed by equations (C2) and (C4) The inlet steam temperature of the

desuperheating zone in condenser i is the same as the outlet steam temperature of


10

condensing turbine i which is ( ) calculated by equation (B3) The outlet steam

temperature of the desuperheating zone in condenser i is the saturated temperature of

the steam at the vacuum pressure which is ( ) calculated by equation (B8) The

inlet and outlet cooling water temperature of the desuperheating zone in condenser i is

represented by ( ) and ( ) The heat transfer in the condensing zone is

expressed by equations (C3) and (C5) In the condensing zone of condenser i the

temperature of the steam side is kept at ( ) The inlet and outlet cooling water

temperature of the condensing zone in condenser i is represented by ( ) and ( )

The logarithmic mean temperature of the desuperheating zone and the condensing

zone in condenser i is calculated by equations (8) and (9) respectively

( ) ( ut( ) ( )) ( ( ) ( ))

ut( ) t ( )

( ) t ( )

(8)

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(9)

2) Saturated inlet steam of condensers

If the outlet steam from the turbine i is saturated the mass flowrate of the steam to be

condensed in the condenser i is calculated by equation (10)

( ) ( ) ( ) (10)

where ( ) is the mass flowrate of steam entering turbine i ( ) is the mass

flowrate of steam entering condenser i and ( ) is dryness of the steam leaving

turbine i

There is only the condensing zone in condenser i The heat transfer in the condensing

zone is expressed by equations (C3) and (C5) The temperature of the steam side is

kept at ( ) The inlet and outlet cooling water temperature of condenser i is

represented by ( ) and ( ) The logarithmic mean temperature of the condensing

zone in condenser i is calculated by equations (11)


11

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(11)

Because condensers are part of cooler networks in cooling water systems the

interactions between condensers coolers and cooling towers are represented by the

model of cooler networks

24 Objective functions

The objective function is to maximise the total profit of cooling water systems and

condensing turbines which is represented by equation (12)

Max (12)

The total profit (TNP) of cooling water systems and condensing turbines includes the

revenue of power generation (PR) by condensing turbines and the operating cost of

cooling water systems (TOC)

The revenue of condensing turbines is expressed as equation (13)

sum ( ) (13)

where ( ) is power generated by turbine i is unit cost of power

The operating cost of cooling water systems consists of the cost of make-up water and

the cost of power consumed by pump j and fan j which is presented as equation (14)

sum ( ) sum ( ( ) ( )) (14)

where ( ) is make-up water consumption of tower j ( ) is power consumption

by pump j and ( ) is power consumption by fan j


12

3 Solution Method

The regression of coefficients in the models for cooling towers pumps and fans is

implemented according to the measured data or the operating data of individual

equipment before models of cooling towers pumps and fans are used to determine

the operation of cooling water systems The regression of coefficients is realised by

the least square method

With the input data consisting of ambient air conditions process specifications steam

inlet conditions of condensing turbines cooler configurations condenser

configurations and pipe specifications the objective function is maximised subject to

the constraints composed of models of cooling water systems condensers and

condensing turbines as well as the practical constraints to determine the optimal

operating conditions of cooling water systems and the resulting economic

performance of cooling water systems and condensing turbines When the cooler

network is in a parallel configuration equations (A29) - (A34) are excluded When

the outlet steam of condensing turbines is superheated equations (3) - (5) (10) (11)

(B4) and (B5) are excluded When the outlet steam of condensing turbines is saturated

equations (7) - (9) (B1) - (B3) (C1) (C2) and (C4) are excluded As the model

contains nonlinear equations the solver CONOPT is selected to solve the model in the

software GAMS CONOPT is appropriate to solve highly nonlinear problems

4 Case Studies

A simplified subset of a cooling water system in a refinery is employed in the case

study which consists of a forced draft wet cooling tower 12 coolers and a condenser

in a series and parallel arrangement a pump a fan 12 process streams and a

condensing turbine Some processes can reuse the cooling water from the condenser

while the other processes and the steam condensation in the condenser use the cooling

water from the cooling tower as the only source The flowrate of cooling water into

individual coolers and the condenser can be changed by the adjustment of valves

The specifications of processes are listed in Table 1 including heat capacity flowrate

temperature specifications heat transfer coefficient and fouling resistance


13

Table 1 Process specifications

Processes Temperature

entering coolers

degC

Temperature leaving

coolers degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance

msup2degC W Upper Lower

C1 998 650 600 735 1864 000035

C2 847 600 550 1167 2375 000035

C3 781 650 600 4367 3625 000035

C4 787 600 550 3356 4747 000035

C5 951 600 550 669 2106 000035

C6 952 600 550 2159 4747 000035

C7 637 450 400 2492 7036 000018

C8 676 450 400 1612 7347 000018

C9 642 500 450 3050 4686 000018

C10 742 500 450 2198 3903 000018

C11 635 450 400 2955 8277 000018

C12 696 500 450 2201 4820 000018

The geometry of coolers is presented in Table 2

Table 2 Geometry of coolers

Coolers Number of

tubes

Tube

passes

Tube

diameter

(mm)

Tube

length

(m)

Cross sectional

area (m2)

Heat transfer

area (m2)

C1 1234 2 19times2 6 01090 4346

C2 742 2 25times2 9 01285 5184

C3 1452 2 19times2 9 01290 7642

C4 1452 2 19times2 9 01290 7642

C5 588 2 25times2 9 01018 4108

C6 1452 2 19times2 9 01290 7642

C7 1424 4 19times2 9 00745 7495

C8 988 2 19times2 9 00873 5249

C9 1234 2 19times2 9 01090 6556

C10 1452 2 19times2 9 01290 7642

C11 1452 2 19times2 9 01290 7642

C12 860 4 25times2 9 00745 5956


14

The specifications for the condensing turbine and the condenser are listed in Table 3

The inlet steam conditions the turbine efficiency and the condenser configuration are

provided

Table 3 Specifications of the condensing turbine and the condenser

Inlet steam

Mass flowrate (th) 666

Pressure (bara) 40

Temperature (degC) 360

Turbine

Isentropic efficiency 075

Mechanical efficiency 096

Minimum power generation

requirement (kW) 13190

Condenser

Area (m2) 1984

Number of tubes 3023

Tube passes 1

Tube diameter (mm) 25times25

Tube length (m) 836

Tube pitch (m) 0032

Shell diameter (m) 149

The ambient air conditions unit cost of make-up water and power and the other

information are shown in Table 4

Table 4 Other information for optimisation

Ambient air

conditions

Dry-bulb temperature (degC) 350

Wet-bulb temperature (degC) 285

Humidity (kgkg dry air) 00222

Cooling towers Cycles of concentration 4

Make-up water temperature (degC) 350

Unit cost Water(poundt) 03

Power(poundkWh) 01

Working hours (hyr) 8000


15

Some practical constraints are listed in Table 5


Cooling towers

Water mass flowrate

(th)

Upper bound 9000

Lower bound 5000

Air mass flowrate

(th)

Upper bound 12600

Lower bound 5000

Ratio of water mass flowrate

and air mass flowrate

Upper bound 15

Lower bound 07

Inlet water temperature(degC) Upper bound 480

Approach temperature(degC) Lower bound 28

Coolers

Minimum temperature difference(degC) 100

Water velocity (ms) Upper bound 20

Lower bound 05

Condensers Vapor fraction of outlet steam Lower bound 088

With the information provided above the system is optimised with the aim of

minimising the operating cost of the cooling water system maximising the power

generation of the condensing turbine and maximising of the overall profit of the

cooling water system and the condensing turbine in Case 1 Case 2 and Case 3

respectively

41 Base case

The operation of the cooling water system is presented in Figure 2 The thermal and

economic performance of the cooling water system and the condensing turbine caused

by the operation are recorded in Table 6 and Table 7 which include make-up water

and power consumption of the cooling water system the power generation of the

condensing turbine the operating cost of the cooling water system the total profit of

the cooling water system and the condensing turbine and the outlet temperature of

individual processes from coolers


16

Figure 2 Operation in base case

Table 6 Comparison of results

Units Results Base case Case

1

Case

2

Case

3

Cooling

water system

Operation

Circulating water

flowrate (th) 7560 6047 9000 6414

Air flowrate (th) 8237 7267 12053 7258

Inlet temperature of

cooling water into

the cooling tower

(degC)

430 456 405 449

Outlet temperature

of cooling water

from the cooling

tower (degC)

320 319 313 321

Water

consumption

Make-up water

(th) 183 181 187 181

Power

consumption

Fans (kW) 398 351 582 350

Pumps (kW) 1568 1372 1877 1411

Total (kW) 1966 1723 2459 1762

Operating cost (poundyr) 2012k 1813k 2416k 1844k

Condensing

turbine

Inlet cooling water mass flowrate (th) 5287 3908 6796 4246

Power generation (kW) 13360 13190 13528 13234

Profit from power generation (poundyr) 10688k 10552k 10822k 10587k

Total profit (poundyr) 8676k 8739k 8406k 8743k


17

Table 7 Outlet temperature of processes from coolers or condensers

Base

case

Case

1

Case

2

Case

3

C1 640 650 648 650

C2 592 600 600 600

C3 643 650 650 650

C4 592 600 600 600

C5 590 600 600 600

C6 592 600 600 600

C7 450 450 450 450

C8 440 450 450 450

C9 500 500 500 500

C10 500 500 500 500

C11 445 450 450 450

C12 500 500 500 500

Condensate from the condenser 488 509 467 504

42 Case study 1

Before optimisation the coefficients in the models of the cooling tower the pump and

the fan are regressed and presented in Table 8

Table 8 Models of the cooling tower pump and fan

Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan

( )

Processes

Outlet temperature (⁰C)

Cases


18

In Case 1 the system that includes the cooling water system and the condensing

turbine is optimised for minimising the operating cost of the cooling water system

with the method proposed in the previous section The optimal operating conditions

are described in Figure 3 and the consequent operating cost power generation total

profit of the overall system and the outlet temperature of processes from coolers or the

condenser are listed in Table 6 and Table 7

Figure 3 Optimal operation for minimising the operating cost

Through operational optimisation the operating cost of the cooling water system is

minimised by reducing cooling water flowrate and air flowrate Due to the reduction

of cooling water flowrate and air flowrate the consequent power consumption is

reduced by 243 kW The cooling water into the condenser is reduced to reduce the

overall cooling water flowrate in the cooling water system As a result of the decrease

of cooling water flowrate the temperature of the condensate from the condenser is

increased by about 2 degC and the corresponding power generation rate of the

condensing turbine is decreased by 170 kW to the minimum requirement As the

decrease of power consumption is greater than the decrease of power generation the

total profit of the cooling water systems and the condensing turbine increases by 63


19

kpoundyr For the other processes their outlet temperature from coolers satisfies the

cooling requirement

43 Case study 2

In Case 2 the operational optimisation of the cooling water system is performed for

maximising the power generation of the condensing turbine with the proposed method

The optimal operation is presented in Figure 4 and the corresponding thermal and

economic performance of the overall system is presented in Table 6 and Table 7

Figure 4 Optimal operation for maximising power generation

The power generation of the condensing turbine is increased by 168 kW through

optimisation In order to maximise the power generation by the condensing turbine

the cooling water used by the condenser is increased as much as possible to reduce the

temperature of the condensate from the condenser Air flowrate is increased as well to

reduce the outlet temperature of cooling water from the cooling tower in order to

reduce the temperature of the condensate However the increase of cooling water and

air flowrate increase power consumption of the cooling water system by 493 kW

Although the power generation of the condensing turbine is increased the total profit

of the cooling water system and the condensing turbine is decreased by 270 kpoundyr


20

That is because the increase of the operating cost of the cooling water system is

greater than the increase of the profit from the power generation of the condensing

turbine The outlet temperature of all the processes from coolers is within the required

temperature range The operation of cooling water systems for the maximum power

generation of condensing turbines reduces the outlet temperature of process 1 by

02 degC

44 Case study 3

In Case 3 the optimal operating conditions of the cooling water system are

determined for maximising the total profit of the cooling water system and the

condensing turbine by the method proposed in the previous section The optimal

operating conditions are shown in Figure 5 The resulting thermal and economic

performance of the cooling water system and the condensing turbine is recorded in

Table 6 and Table 7

Figure 5 Optimal operation for maximising the total profit


21

Through operational optimisation for maximisation of the total profit of the cooling

water system and the condensing turbine the total profit is 67 kpoundyr more than that in

base case by decreasing cooling water and air flowrate Cooling water flowrate into

the condenser is decreased resulting in the decrease of power consumption by the

pump Cooling water temperature into the condensers is increased which leads to a

drop of air flowrate The decrease of air flowrate reduces the power consumption of

the fan The power consumption in the cooling water system is reduced by about 200

kW The reduction of power consumption lowers the operating cost of cooling water

systems However due to the reduction of the cooling water flowrate and the increase

of the cooling water temperature into condensers the power generation of the

condensing turbine is reduced by around 100 kW As the saving of power

consumption in the cooling water system is more than the power generation reduction

of the condensing turbine the total profit of the condensing turbine and the cooling

water system is increased The outlet temperature of processes from coolers presented

in Table 7 illustrates that the cooling requirement of processes is fulfilled by the

operation determined in Case 3

45 Discussion

Both the operating cost of the cooling water system and the power generation of the

condensing turbine obtained by minimising the operating cost of cooling water

systems are the least in the three cases Both the operating cost of the cooling water

system and the power generation of the condensing turbine obtained by maximising

the power generation of the condensing turbine are the most in the three cases

However none of those two cases obtains the optimal total profit of the cooling water

system and the condensing turbine In the case of minimising the operating cost of

cooling water systems the operating cost is reduced but opportunities to improve the

power generation of the condensing turbine are lost In the case of maximising the

power generation of the condensing turbine the power generation of the condensing

turbine is improved but the increase of the resulting power consumption is greater

than the increase of the power generation which decreases the total profit When the

performance of the cooling water system and the performance of the condensing

turbine are considered simultaneously as in Case 3 the profit from the power

generation of the condensing turbine and the operating cost of the cooling water


22

system are traded off to improve the total profit of the cooling water system and the

condensing turbine The total profit obtained by optimising the overall economic

performance of the cooling water system and the condensing turbine is improved by

337 kpoundyr compared with that obtained by maximising the power output of the

condensing turbine The circulating water flowrate determined by optimising the

overall economic performance of the cooling water system and the condensing turbine

is increased by about 370 th compared with that determined by minimising the

operating cost of the cooling water system

5 Conclusions

The integration of cooling water systems and processes with cooling demand provides

opportunities to improve the overall economic performance In the literature [11] a

modular-based optimisation method was developed for a waste-to-energy

cogeneration plant to maximise the net power output In this paper an equation-based

optimisation method is proposed for the integration of cooling water systems and

processes with cooling demand Condensing turbines are taken as examples of

processes An equation-based model is developed for the integration of cooling water

systems and condensing turbines In the proposed model the detailed model of

cooling water systems developed by Song et al [1] is employed a turbine model

based on the mass and energy balance is established to calculate the power generation

of turbines and the state of the exhaust steam from turbines and a detailed heat

transfer equation for condensers is used to calculate the pressure of exhaust steam

leaving turbines and the cooling water temperature leaving condensers The model

can be used for cooler networks in either parallel arrangements or series and parallel

arrangements and for either the cooling of superheated steam or the cooling of

saturated steam in condensers The model is optimised by the solver CONOPT in

GAMS to determine the optimal cooling water flowrate entering individual towers

coolers and condensers and air flowrate entering individual towers A case study

proves that the proposed method is effective to improve the economic performance by

the integration of cooling water systems and processes In the case study the

simultaneous optimisation increases the total profit by 337 kpoundyr compared with

focusing only on maximising the power generation of condensing turbines


23

In this work the cooling requirement of the other processes except condensing

turbines is considered instead of the performance of processes If the operation of

cooling water systems has an influence on the economic performance of processes

the performance of the processes is preferred to be taken into account with the

performance of cooling water systems The method developed in this work can be

extended to cooling water systems with other processes such as compressor inter-

cooling condensation of light components for distillation pre-cooling for

compression refrigeration and so on In future work therefore the integration of

cooling water systems with processes whose performance is affected by the operation

of cooling water systems is performed to determine the optimal operation of cooling

water systems and the outlet temperature of processes from coolers

Nomenclature

Sets

i set of condensing turbines

j set of cooling towers pumps fans

k q set of coolers

Parameters

Ac(i) area of condenser i (m2)







di(q) inside tube diameters of cooler q (m)


do(q) outside tube diameters of cooler q (m)


Ds(i) shell diameter of condenser i (m)

g gravitational constant (981m2s)


C)

Hin(i) specific enthalpy of steam into condensing turbine i (kJkg)



24


Lt(i) tube length of condensing turbine i (m)


ms(i) mass flowrate of steam into condensing turbine i (kgs)

np(i) tube pass of condenser i

np(q) tube pass of cooler q

nt(i) number of tubes of condenser i


NR(i) number of tubes in a vertical row of condenser i

pt(i) vertical tube pitch in condenser i (m)


C W)


C W)

Sin(i) entropy of inlet steam of condensing turbine i (kJdegC)

tdbi inlet air dry-bulb temperature (degC)


twbi inlet air wet-bulb temperature (degC)



z(m) elevation of node m (m)

z(n) elevation of node n (m)

a1-a3 coefficients

b1-b3 coefficients

Variables

Acn(i) area of the condensation zone in condenser i (m2)

Ads(i) area of the desuperheating zone in condenser i (m2)




hc(i) heat transfer coefficient of condensation in condenser i (Wm2deg

C)

hf (mn) friction loss between node m and node n (m3s)

hi(q) heat transfer coefficient in tube side of cooler q (Wm2deg

C)

Hf(i) specific enthalpy of saturated liquid in condenser i (kJkg)

Hg(i) specific enthalpy of saturated vapor in condenser i (kJkg)

His(i) specific enthalpy of steam at the outlet pressure having the same entropy as the inlet

steam in condensing turbine i (kJkg)

Hout(i) specific enthalpy of steam out of condensing turbine i (kJkg)

Hp(j) head pressure provided by pump j (m)


25



kl(i) thermal conductivity of condensate in condenser i (WmdegC)

L(i) tube length in condensing zone in condenser i (m)





ma(j) mass flowrate of dry air through cooling tower j (kgs)


mcs(i) mass flowrate of steam condensed in condenser i (kgs)






p(m) pressure at node m (Pa)

p(n) pressure at node n (Pa)


Pout(i) pressure of steam out of turbine i (MPa)


PR profit of power generation (poundyr)

Qcn(i) heat transfer duty for the condensing zone in condenser i (kW)

Qds(i) heat transfer duty for the desuperheating zone in condenser i (kW)



Sg(i) entropy of saturated steam at outlet pressure of condensing turbine i (kJdegC)

Sf(i) entropy of saturated liquid at outlet pressure of condensing turbine i (kJdegC)


(oC)






Tcc(i) saturated steam temperature of condenser i (degC)

Trsquocc(i) saturated steam temperature of condenser i (K)

Tis(i) temperature of steam at the outlet pressure having the same entropy as the inlet


26

steam of condensing turbine i (K)

Tout(i) temperature of steam from turbine i (degC)

Trsquoout(i) temperature of steam from turbine i (K)

TNP total net profit (poundyr)

TOC total operating cost (poundyr)

u(m) cooling water velocity at node m (ms)

u(n) cooling water velocity at node n (ms)




Ucn(i) overall heat transfer coefficient of the condensing zone in condenser i (Wm2deg

C)

Uds(i) overall heat transfer coefficient of the desuperheating zone in condenser i (Wm2deg

C)


C)

vf(i) dryness of outlet steam from condensing turbine i

vfis(i) dryness of steam at the outlet pressure having the same entropy as the inlet steam in


wo(j) humidity of the air from cooling tower j (kgkg dry air)


Wt(i) power generation by condensing turbine i (kW)

Greek Symbols

α β γ coefficients

(i) viscosity of the condensate in condenser i (kgm-1

s-1

)


s-1

)

ηis(i) isentropic efficiency of condensing turbine i

ηm(i) mechanical efficiency of condensing turbine i




(m) density of cooling water at node m (kgm3)

(n) density of cooling water at node n (kgm3)



Δtcnm(i) logarithmic mean temperature for the condensing zone in condenser i (degC)

Δtdsm(i) logarithmic mean temperature for the desuperheating zone in condenser i (degC)

Subscripts

a air


27

db dry bulb

f fans

i insideinlet

m n nodes

o outsideoutlet

p pumps

w cooling water

wb wet bulb

m mean value

cn condensing zone

ds Desuperheating zone

References

[1] Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating Cooling

Water Systems





2209

[4] Laskowski R Smyk A Lewandowski J and Rusowicz A 2015 Cooperation of A

Steam Condenser with A Low-Pressure Part of a Steam Turbine in Off-Design Conditions

American Journal of Energy Research 3 (1) pp 13-18

[5] Laković MS Stojiljković MM Laković SV Stefanović VP and Mitrović DD

2010 Impact of the Cold End Operating Conditions on Energy Efficiency of The Steam

Power Plantsrdquo Thermal Science 14 pp S53-S66

[6] Wang YM and Zhang LZ 2011 Optimal Operation of Cold End System for Steam

Turbine in Coal-Fired Power Plant 2011 International Conference on Materials for

Renewable Energy amp Environment pp 1645-1649

[7] Zheng L Chen C Xie D and Zhang H 2013 Optimisation of the Cold-End System of

the 1000 MW Ultra-Supercritical Units by VB Trans Tech Publications 694-697 pp 778-

781

[8] Laković MS Laković SV and BANJAC MJ 2012 Analysis of the Evaporative Towers

Cooling System of a Coal-Fired Power Plant Thermal Science 16 pp S375-S385

[9] Laković M Banjac M and Jovic M 2015 Improving the Energy Efficiency of the Coal

Fired Power Plant by Adjusting the Hydraulic Load of the Cooling Tower System Sci-Afric

J Sci Issues Res Essays 3(12) pp 873-880


28


128

[11] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and

Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry

Cooling System Applied Energy 115 pp 65ndash74

[12] IAPWS 2007 Revised Release on the IAPWS Industrial Formulation 1997 for the

Thermodynamic Properties of Water and Steam Available from httpwwwiapwsorg

[13] Smith R 2005 Chemical Process Design and Integration John Wiley amp Sons Ltd







[17] Ulanicki B Kahler J and Coulbeck B 2008 Modeling the Efficiency and Power


134 pp 88-93

[18] Mueller AC in Hewitt GF 1992 Handbook of Heat Exchanger Design Begell House Inc

Appendix

A) Recirculating cooling water system modelling

The model of cooling water systems developed by Song et al [1] includes models of

wet cooling towers cooler networks and piping networks which are presented as

follows

A1) Mechanical draft wet cooling tower modelling

There are some basic assumptions listed as follows








29

Mass and energy balance of cooling tower j are represented as equation (A1) - (A2)

( ) ( ) ( ) ( ( ) ) (A1)

( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)

The regression model of wet cooling tower j includes equation (A3) - (A5)

( ) ( ) ( )

( ) (A3)

( ) ( ( ) ( )) ( ) ( ( ) )

( ) ( )

(A4)

( ) ( ) ( ) ( ) ( )

( ( ) ) (A5)

Water evaporation rate in a cooling tower j is calculated by equation (A6)

( ) ( ) ( ( ) ) (A6)

The flowrate of make-up water for cooling tower j is calculated by equation (A7)

( ) ( )

(A7)

where cc is the cycle of concentration defined as the ratio between the concentration


The characteristic of fans j is represented by equation (A8) [14]

( ) 0 ( ) ( )

1 (A8)


30

A2) Cooler network modelling

A21 Cooler modeling

The model of cooler networks includes models of coolers and cooler networks The

cooler model is given as equations (A9) - (A21)


bull The properties of streams are constant

bull Heat transfer coefficient of hot streams is assumed to be constant

bull The properties of streams which are related to temperature are calculated at

the average of inlet and outlet temperature in individual coolers


bull Streams in both tube and shell are in turbulent flow

bull Cooling water is set to flow in the tube and hot streams are set to flow in the

shell

Energy balance of cooler q is expressed as equation (A9)

( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)

Heat transfer in cooler q is expressed as equation (A10)

( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)

The overall heat transfer coefficient of cooler q based on the outside area is written as

( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (A11)

The correction factor of cooler q is written as equations (A12) - (A15)

( ) ( ) ( )

h ( ) ( ) (A12)


31

S( ) h ( ) h ( )

( ) ( ) (A13)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )

( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (A14)

For S( )

( ) radic (q)

(q)

( ) ( radic ) ( ) ( radic )frasl (A15)

The logarithmic mean temperature difference

Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(A16)

The heat transfer coefficient of the stream q in the tube side is written as equation

(A17) [15]

( ) w( )

( ) ( )

w( ) μw( )

w( )

(A17)

The pressure drop of the tube side is calculated by equation (A18) [15]

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ( ) ) ( )

( ) ( ) ( ( ) ( )

)

(A18)

The fluid velocity is written as

( ) ( ) ( )

w( ) ( ) ( ) (A19)


32

( ) ( )

w( ) n( ) (A20)

( ) ( )

w( ) ut( ) (A21)

A22 Network modelling

In cooler network modelling mass balance and energy balance are carried out for

cooler networks in parallel arrangements and in series and parallel arrangements

(1) Mass and energy balance of cooler networks in parallel arrangements are

expressed as equations (A22) ndash (A27)

( ) sum ( ) (A22)

( ) sum ( ) (A23)

( ) sum ( ) (A24)

( ) sum ( ) (A25)

( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) (A26)

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)

If the jth cooling tower provides cooling water for the qth coolers then the inlet

temperature of cooling water into the qth cooler is calculated by the following

equation

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)


33

(2) Mass and energy balance of cooler networks in series and parallel arrangements

( ) sum ( ) ( ) (A29)

( ) sum ( ) sum ( ) ( ) (A30)

( ) sum ( ) ( ) (A31)

( ) sum ( ) sum ( ) ( ) (A32)

( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)

( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )

( )) ( ) (A34)

A3) Piping network modelling


bull There is no heat loss from the piping

bull There are one splitter corresponding to each cooling tower which provides

cooling water to individual coolers and one mixer corresponding to each

cooling tower that collect hot water from individual coolers

bull Equivalent length is used in friction loss calculation

1) Mechanical energy balance between two connected nodes m and n is performed

by the Bernoulli Equation as equation (A35)

( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (A35)

The Darcy-Weisbash equation is used for friction loss prediction The Colebrook-

White equation is used for friction factor calculation [16]

2) Pump modelling [17]


34

( ) ( ) ( ) ( ) (A36)

( ) ( ( ) ) (A37)

( ) ( ) w ( )

( ) (A38)

B) Thermal properties of steam and water

The temperature of the steam leaving turbine i that has the same entropy as the inlet

steam is calculated equation (B1)

S ( ) (

( ) ((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B1)

Where ( ) is temperature of steam at the outlet pressure having the same entropy as

the inlet steam of turbine i and ( ) is pressure of steam leaving turbine i

( ) is calculated by equation (B2)

( ) ((sum

( )

) (sum ( ( ))

( )

)) (B2)

The steam outlet temperature of turbine i is determined by equation (B3)


35

( ) ((sum

ut ( )

) (sum ( ( ))

ut ( )

)) (B3)

where ( ) is temperature of steam leaving turbine i

The entropy of the saturated steam at the exhaust pressure of turbine i and the entropy

of the saturated liquid are represented by equations (B4) and (B5) respectively

S ( ) (

( )

((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B4)

where ( ) is saturated temperature of steam at the outlet pressure from turbine i

S ( ) (

( )

(sum ut( )

( )

)

sum ut( )

( )

) (B5)

The enthalpy of the saturated steam at the exhaust pressure of turbine i and that of the

saturated liquid are represented by equations (B6) and (B7)

( ) ((sum

( )

) (sum ( ( ))

( )

)) (B6)


36

( ) (sum ut( )

( )

) (B7)


in Appendix B)

( ) ( ( )

( ) ( ( ) ( ) ( )) )

(B8)

( ) ( )

( )

( )

( )

(B9)

( ) ( )

( )

( )

( )

(B10)

( ) ( )

( )

7 ( )

( )

(B11)

Where

are coefficients whose value is presented in [12]

C) Condenser modelling

Assumptions

bull Steam is condensed in the shell side of condensers and cooling water is in the

tube side of condensers

bull No pressure drop is in the shell side of condensers

bull Condensate is at the saturated state

When heat exchange involves desuperheating and condensation condensers can be

divided into two zones When desuperheating and condensation is on the shell side of

a horizontal condenser the model of condensers can be expressed by the following

equations [13]

The total heat transfer area of condenser i is the sum of the area for each zone

( ) ( ) ( ) (C1)


37

The area of each zone can be calculated by equations (C2) and (C3) respectively

( ) ( )

( ) ( ) (C2)

( ) n( )

( ) n ( ) (C3)

( ) ( ) ( ) ( ) (C4)

( ) ( ) ( ) ( ) (C5)

Uds and Ucn are calculated by equation (A11)

The condensing film coefficient for condensation in shell side of condenser i is

expressed as equation (C6) [18]

( ) ( ) ( )

( ) ( )

μ ( ) ( )

( )

(C6)

( ) ( )

( ) (C7)

( ) n( )

( ) ( ) (C8)

The heat transfer coefficient of cooling water is calculated by equation (A17) The

heat transfer coefficient of superheated steam can be calculated by heat transfer

coefficient equation for shell side developed by Wang et al [15]

Chapter 5 Conclusions and Future Work

20


51 Conclusions

For the operational optimisation of industrial cooling water systems there are two

main areas of investigation in this project

bull Standalone optimisation of overall cooling water systems including

mechanical wet cooling towers cooler networks and piping networks

bull Simultaneous optimisation of cooling water systems and processes with

cooling requirement

To address the first area some literature [1] [2] [3] proposed models of cooling

water systems that integrate cooling towers cooler networks and piping networks

However they have some limitations all of them are limited to one cooling tower and


considered in the literature [1] the pressure drop in coolers is ignored for the

hydraulic modelling in the literature [2] and [3] To overcome those limitations

therefore a nonlinear model of recirculating cooling water systems is developed for

operational optimisation of cooling water systems in this work In this model

mechanical draft wet cooling tower modelling cooler network modelling and piping

network modelling are all included Multiple cooling towers and cooler networks in

both a parallel configuration and a series and parallel configuration are taken into

consideration In cooling tower modelling a regression model of mechanical draft wet

cooling towers is developed to predict the water evaporation rate and the cooling

water outlet temperature The regression model is validated by some published data

In cooler network modelling detailed heat transfer equations for individual coolers

are included to predict the thermal performance of coolers and mass and energy

balance are carried out to represent the interactions between cooling towers and

coolers Hydraulic calculation of networks takes pressure drop in pipes pipe fittings

and coolers into account The model is optimised by the solver CONOPT in GAMS to

determine the optimal cooling water flowrate entering individual coolers and towers

and air flowrate entering individual towers In a case study through optimisation the

total operating cost of a cooling water system with specified process cooling demand

is reduced by about 6 compared with that in the base case


21

To exploit the interactions between processes and cooling water systems in the second

area condensing turbines are taken as examples of cooling water using processes

whose performance is affected by the conditions of cooling water In the literature

[13] a modular-based optimisation method was proposed to integrate condensing

turbines with cooling towers for maximising the net power output In this thesis an

equation-based model is developed to combine cooling water systems and condensing

turbines The model is optimised by the solver CONOPT in the software GAMS to

determine the optimal cooling water flowrate entering individual coolers condensers

and towers and air flowrate entering individual towers In a case study it is shown

that the simultaneous optimisation of a cooling water system and a condensing turbine

increases the profit by 337 kpoundyr compared with focusing only on maximising the

power generation of condensing turbines

In summary it is shown from this research that there is a clear need to optimise the

operation of industrial cooling water systems both on a standalone basis and on a

combined basis with processes in cooling demands The developed methodologies

have been validated and proven to be effective in dealing with the two challenges as

shown in corresponding case studies

52 Future work

As shown in the literature the research on operational management of overall cooling

water systems has been very limited Even though some progress has been made in

this project there is still much room of improvement to be made including a few

areas listed below

Model improvement of cooling water systems in the current method the

operating cost does not include cost of chemicals used to treat cooling water

and cost of blowdown treatment The cooling water treatment and blowdown

treatment could be incorporated in the model

Improvement of the solution algorithms as the model is nonconvex the

obtained optimisation results are possibly global optimum which could be

investigated in the future


22

Extended integration between cooling water systems and processes with

cooling demands in this research only condensing turbines are integrated

with cooling water systems However there are many processes that require

cooling water such as compressor inter-cooling condensation of light

components for distillation and pre-cooling for compression refrigeration The

improvement of the performance of those processes increases the operating

cost of cooling water systems Therefore the method proposed to improve the

overall performance of cooling water systems and condensing turbines can be

extended to the other processes

Online optimisation as the thermal performance of cooling water system

changes frequently with the continuous change of ambient air conditions the

online optimisation combined with control systems allows the operation to be

adjusted with the variation of ambient air conditions to reduce the operating

cost

Cooling water system design and retrofit various options could be available to

improve the configuration of cooling water systems such as adding a

connection between coolers to allow cooling water to be reused if possible

and better load distribution of cooling water pumping systems etc Such

options typically require systematic consideration at the design and retrofit

stage the methodology of which could be developed in the future

23

References





2209

[3] Cortinovis GF Ribeiro MT Paiva JL Song TW and Pinto JM 2009 Integrated

Analysis of Cooling Water Systems Modelling and Experimental Validation Applied

Thermal Engineering 29 pp 3124-3131

[4] httpjnyuhanggovcnnewsshowaspxartid=704ampclassid=5

[Accessed at 20 Dec 2016]

[5] Kelly NW and Swenson LK 1956 Comparative Performance of Cooling Tower

Packing Arrangements Chem Eng Prog 52(7) pp 263-268

[6] Cooling Tower chapter 7 Bureau of Energy Efficiency pp 135-151

[7] Improving the Energy Efficiency of Cooling Systems

httpwwwdhigroupcomuploadpublicationsscribd195443742-Improving-

the-energy-eff-iciency-of-cooling-systems-DHI-Solutionpdf



Science 56(12) pp 3641-3658



pp 117ndash195




[11] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems

Considering Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39

pp 49-54







2

Table of Contents

List of Figures 3

Abstracthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip4

Declaration 5

Copyright Statement 6

Acknowledgement 7

Chapter 1 Introduction 8

11 Background 8

111 Recirculating cooling water systems 8

112 Operation of recirculating cooling water systems 12

113 Interactions between cooling water systems and processes 13

114 Operation management of cooling water systems 14

12 Motivation 14

13 Aims and objectives 15

14 Thesis outline 16

Chapter 2 17

Publication 1 Operational Optimisation of Mechanical Draft Wet Cooling Towers 17

Chapter 3 18

Publication 2 Operational Optimisation of Recirculating Cooling Water Systems 18

Chapter 4 19

Publication 3 Operational Optimisation of Recirculating Cooling Water Systems for

Improving the Performance of Condensing Turbines 19

Chapter 5 Conclusions and Future Work 20

51 Conclusions 20

52 Future work 21

References 23

Word Count 33521

3

List of Figures


4

Abstract


Fei Song



Operation

2016






























turbines

5

Declaration




Fei Song

6

Copyright Statement
























7

Acknowledgement

















8


11 Background
















9



























10




























11





towers







systems
















12







pressure




















13




























14












12 Motivation















15









simultaneously














included



16








turbines)



14 Thesis outline













17

Chapter 2






1


Cooling Towers



Abstract

















base case





2

Highlights




investigated

1 Introduction




















3



















4





























5





























6





























7



























8


cooling towers

























9

tower







(1)

( ) (1)





( ) (2)






10











(3)
















11




Figure 2 (d) is a







12



temperature



temperature (d)


13



( ) (4)










( )

w (5)




( )

w ( ) ( ) ( ) (6)


14



respectively


( ( ) ( ) ( )) (7)


( ( ) ( ) ( ))

(8)






( ) (9)






(10)


15

( ) (10)













equation (8)

( ) (11)




(12)


16









( ) (13)





(14)

( ) (15)

w

(16)





17



flowrate





temperature

(17)

(18)

w

w

w

(19)

(20)

(21)







18

( ) (22)



respectively

3 Model validation











towers [28]








19








α1 α2 α3 α4

95846 06568 -12569 -04216


β1 β2 β3 β4 β5

40099 -17177 08672 -21377 08165


γ1 γ2 γ3 γ4 γ5 γ6 γ7

-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00


20







y=x

y=x

R2=0992

R2=0996


21






No 1 2 3 4 5 6

Measured

data

(degC) 2933 3667 4100 3889 4033 3572

(degC) 2966 3192 3550 3111 3361 3311

(degC) 2111 2111 2388 2388 2667 2944

(kgs) 1186 1178 1157 1174 1157 1156

(kgs) 1132 1132 0881 1132 1008 1258

Calculated

data

(degC)

Measured 2433 2633 2800 2844 3044 3122

Correlation 2415 2642 2818 2851 3016 3106

Relative

difference () 073 -036 -065 -024 092 051

(10-2

kgkg

dry air)

Measured 2192 2835 3108 3223 3454 3301

Correlation 2168 2878 3119 3229 3419 3305

Relative

difference

()

111 -151 -037 -017 103 -011





4 Solution Method




22














5 Case Studies










change


23

51 Base case











Table 6




Ambient air

conditions

tdbi (degC) 3028 3028 3533 2950 2600

twbi (degC) 2565 2565 2944 2500 2250

wi (10

-2kgkg dry air)

190 190 239 183 158

ii (kJkg) 7913 7913 9688 7636 6645






Lower bound 4320


Lower bound 3600

Upper bound 17

Lower bound 07



24

52 Case study 1








Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan [17]

( )








25















Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Operating

conditions

Inlet water

flowrate (th) 7920 5760 5760 6280 5641 7137

Inlet dry air

flowrate (th) 7200 9187 9187 7533 9441 4996

Cooling

water

Inlet

temperature

(degC)

4100 4385 4385 4644 4351 4062

Outlet

temperature

(degC)

3020 2895 3166 2849 2676 3274 2830 2869

Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193


towers (MW) 1039 1041 858 1071 1188 1052 1039 1029


(MW) 9928 8079 10240 11442 9928



26

Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Make-up water

consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635

Power

consumption

(kW)

Fan 353 450 450 450 450 377 462 240

Pump 1631 1344 1344 1344 1344 1396 1333 1503

Total 1984 1794 1794 1794 1794 1773 1795 1743

Cost (poundh)

Make-up

water 522 536 473 547 587 561 532 490

Power 1983 1794 1794 1794 1794 1773 1795 1743

Total 2505 2330 2267 2341 2381 2334 2327 2233

53 Case study 2


















27






























28









slightly

6 Conclusions

















base case


29



















30

Nomenclature

Parameters







dry air)







Variables








air)


dry air)


dry air)





31

Mep Merkel number







p pressure (Pa)



temperature (Pa)




T temperature K











ηp pump efficiency

Subscripts

a air

db dry-bulb

e evaporation

f fans

i inlet


32

m make-up water

o outlet

p pumps

P Poppe method

s saturation

v vapor

w cooling water

wb wet-bulb

References








New York USA















Mi 15




33
















Oklahoma









6370 EPRI Palo Alto








Amsterdam







34

Appendix

1) Data information




No twi

(degC)

two

(degC)

tdbi

(degC)

twbi

(degC)

wi

(kgkg dry air)

ma

(kgs)

mwi

(kgs)

wo

(kgkg dry air)

1 4144 2600 3411 2111 00104 1158 0754 00284

2 2872 2422 2900 2111 00125 1186 1259 00215

3 3450 2622 3050 2111 00119 1186 1259 00271

4 3878 2933 3500 2667 00188 1264 1008 00323

5 3878 2933 3500 2667 00188 1250 1008 00323

6 3967 2622 3400 2111 00105 1174 0881 00284

7 3500 2867 3461 2667 00190 1156 0881 00285

8 4361 2789 3500 2388 00141 1158 0754 00316

9 4306 2972 3572 2667 00185 1155 0754 00337

10 3806 3089 3594 2944 00236 1142 0754 00321

11 4778 3217 3617 2944 00235 1142 0754 00400

12 3378 2472 3250 2111 00110 1179 0881 00238

13 4144 3000 3617 2667 00183 1156 0881 00340

14 4061 3172 3417 2944 00244 1147 0881 00359

15 4350 3217 3533 2944 00239 1147 0881 00383

16 3672 3139 3272 2944 00250 1155 1008 00329

17 3322 2550 2883 2111 00126 1186 1008 00244

18 3844 2678 2950 2111 00123 1186 1008 00290

19 3661 2944 3250 2667 00199 1161 1132 00314

20 4100 3050 3294 2667 00197 1161 1132 00364

21 3611 2972 3111 2667 00204 1166 1258 00314

22 4022 3078 3133 2667 00203 1166 1258 00364

23 3956 3011 3206 2667 00200 1008 1008 00349

24 3950 3006 3106 2667 00205 1051 1008 00344

25 3944 3000 3333 2667 00195 1108 1008 00341

26 3978 2967 3167 2667 00202 0947 1008 00357





35











w

( w ) w

w ( ) w ( w ) v- ( w ) w (A1)

w

w

( w ) w

w ( ) w ( w ) v- ( w ) w

(A2)

w

( w ) ( w ) ( ) v ( w ) w (A3)







w

w

(

w ( )) (A4)


36


w w

w

0 w w

w 1

(A5)


w

(A6)



w

( ) (A7)



w

(A8)


coefficients



( ) [ ( )] (A9)


37




(A11)

7

7


times [ 7 ( 7 frasl ) ] (A12)









( w )

w w

( w )

77 w (A16)


38



( ) ( ) ( ) (A17)





18

Chapter 3






1


Water Systems



Abstract


















the base case


optimisation




2

Highlights



are considered


into account



investigated

1 Introduction
















3



















4



























5












turn













sectors


6




























7






























8





























9
























considered


10

























11





the shell side









is variable












12





arrangement


13





(1) Mass balance




( ) sum ( ) (1)





( ) sum ( ) (2)



( ) sum ( ) (3)

( ) sum ( ) (4)


14


(2) Energy balance




( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

(5)





a in Figure 2


( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)



leaving cooler q



( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)


15
















(1) Mass balance



( ) sum ( ) ( ) (8)




16



equation (9)

( ) sum ( ) sum ( ) ( ) (9)






respectively

( ) sum ( ) ( ) (10)

( ) sum ( ) sum ( ) ( ) (11)




(2) Energy balance



( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)


17




leaving cooler k



( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )

(13)






point a in Figure 2










18










( ) ( )

( )

w( ) ( ) ( )

( )

( )

w( ) ( ) (14)







19


constant



( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (15)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (k q) (16)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (17)


20






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (18)







( ) ( ) ( ) (19)









21

232 Pump modelling



cooling water






(20) - (28)



( ) ( ) (20)

( ) ( ) (21)







22

( ) ( ) (22)



than 28 degC [33]

( ) (23)


( ) (24)




( ) ( ) ( )

(25)

( ) ( ) ( )

(26)


( ) ( ) (27)


equation (28)

( ) ( ) (28)


23







Min sum ( ) sum ( ( ) ( )) (29)




3 Solution Method













24



4 Case Studies











Process

streams

Inlet temp

degC

Outlet temp

degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance

msup2degCW

C1 60 Upper 450

1704 987 000018 Lower 420

C2 120 Upper 795

482 286 000018 Lower 750

C3 95 500 586 732 000018

C4 100 Upper 595

707 448 000035 Lower 550

C5 105 Upper 545

447 748 000053 Lower 500

C6 90 Upper 595

1004 488 000018 Lower 550

C7 75 Upper 445

602 913 000018 Lower 400

C8 150 Upper 1000

394 180 000018 Lower 950

C9 125 Upper 645

513 346 000053 Lower 600


25




Coolers Area

(m^2)

Number

of tubes

Tube

passes

Tube inside

diameter

(mm)

Tube outside

diameter

(mm)

Length of

tube

(m)

Thermal


wall (wmdegC)

C1 3506 1006 2 15 19 60 50

C2 1589 610 2 15 19 45 50

C3 2135 610 2 15 19 60 50

C4 2539 980 4 15 19 45 50

C5 1685 366 2 20 25 60 50

C6 2606 1006 2 15 19 45 50

C7 2004 588 4 20 25 45 50

C8 1641 468 2 15 19 60 50

C9 2539 980 4 15 19 45 50




Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002

S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002

S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002

S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002

S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002

S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002

S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002


26

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002

S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002

S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002

S2(C1)

-S1(C2) 1200 023 00002

S2(C6)

-S1(C8) 1300 023 00002




41 Base case












Make-up water


(degC)

Wet-bulb

temperature (degC)

Humidity (kgkg

dry air)

Enthalpy

(kJkg)

318 271 205 855 318


27


42 Case study 1




Units Models

Cooling

towers 1

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )


28

Units Models

2

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )

Pumps

1

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

2

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

Fans

1 ( ) ( ) ( )

( )

2 ( ) ( ) ( )

( )










shown in Table 7


29

























30


the base case


Cooling

towers



The approach

(degC)






Total 409 403 -06

Power

consumption

(kW)

Pumps



Total 4184 3829 -355

Fans



Total 865 882 17

Total 5049 4711 -338

Cost

Water(poundh) 1227 1209 -018





Hot streams


(degC)


C1 450 450

C2 795 795

C3 500 500

C4 595 595


31

Hot streams


(degC)


C5 545 545

C6 595 595

C7 445 445

C8 1000 1000

C9 645 645

43 Case study 2








stated in Table 1



Ambient air

conditions











32


























degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

1

Case 1 458 800 510 604 555 603 455 1006 654

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -08 -05 -10 -09 -10 -08 -10 -06 -09


33


degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

2

Case 1 439 787 485 582 530 584 430 991 631

Optimisation 450 766 500 595 545 592 441 982 644

Difference 10 -23 14 12 14 07 10 05 -01

Condition

3

Case 1 454 798 505 599 550 599 450 1003 650

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -04 -03 -05 -04 -05 -04 -05 -03 -05











Table 9











34





























35







convection


conditions


36




Cooling

towers

Make-up water

flowrate (th)

1 231 241 10 217 207 -10 220 226 06

2 189 195 06 176 168 -08 180 183 03



(MW) 097 071 -026 352 385 033 217 201 -016

Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045

Pumps Power

consumption (kW)

1 2173 2469 296 2173 2307 134 2173 2197 24

2 1657 1951 294 1657 1769 112 1657 1723 66

Total 3830 4420 590 3830 4076 246 3830 3920 90

Fans Power

consumption (kW)

1 460 639 179 444 305 -139 452 597 145

2 419 538 119 405 239 -166 412 496 84

Total 879 1177 298 849 544 -305 864 1093 229


Cost (poundh)

Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027

Power 4709 5597 888 4679 4620 -059 4694 5013 319

Total 5969 6905 936 5858 5745 -113 5894 6240 346


37

5 Conclusions

























in the base case








38





cost increases









Nomenclature

Sets


k set of coolers

q set of coolers

Parameters













C)


39







C W)


C W)













a1-a3 coefficients

b1-b3 coefficients

Variables










degC

-1)





40
























(degC)













41









C)



Greek Symbols

α coefficients

β coefficients

γ coefficients


s-1

)









Subscripts

a air

db dry bulb

f fans

i insideinlet

o outsideoutlet

p pumps

s1-s6 nodes

w cooling water

wb wet bulb


42

References








2209


Cooling Towers


128












914-923



pp 1-7











43












1033-1043




InTech





Science 56(12) pp 3641-3658





pp 117ndash195



pp 540ndash551









44







134 pp 88-93


York USA



Appendix

Appendix A Models



( ) ( ) ( )

( ) (A1)





( ) ( ( ) ( )) ( ) ( ( ) ) ( )

( ) (A2)






45


respectively


( ) ( ) ( ) ( ) ( )

( ( ) ) (A3)




bulb temperature



method


( ) ( ) ( ) ( ( ) ) (A4)


( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)






respectively


46


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)





( ) 0 ( ) ( )

1 (A8)



flowrate



( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)







47


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)






( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (B3)







( ) ( ) ( )

h ( ) ( ) (B4)

S( ) h ( ) h ( )

( ) ( ) (B5)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



48


Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(B8)




respectively


( ) w( )

( ) ( )

w ( ) μw( )

w( )

(B9)






( ) 7 ( ) R ( ) 8 ( ) w( ) w( )

( ) ( ( ) ) ( ) ( )

( ) ( ( ) ( )

) (B10)







49


( ) ( ) ( )

w( ) ( ) ( ) (B11)






( ) ( )

w( ) n( ) (B12)





( ) ( )

w( ) ut( ) (B13)











50




No 1 2 3 4 5

ht

(W(m2 K))

Wang 12072 57689 14026 15846 75662

HTRI 12993 56440 14700 16169 73632

Relative error () -709 221 -459 -200 276

∆Pt

(kPa)

Wang 688 287 886 693 261

HTRI 712 297 868 735 268

Relative error () -337 -337 207 -571 -261



( ) ( ) ( ) ( ) (C1)




( ) ( ( ) ) (C2)



( ) ( ) w ( )

( ) (C3)


51








No 1 2 3 4 5


Specific heat

(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223

Thermal

conductivity

(WmK)

0137 0133 0633 0623 0123 0106 0089 0091 0087 0675

Viscosity

(mPa s) 040 360 062 071 289 120 033 110 180 030

Density

(kgm3) 785 850 991 994 820 790 702 801 786 957

Flow rate

(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390

Inlet

temperature

(degC)

2000 380 480 330 517 2100 2270 1120 1700 770

Fouling

resistance (10-4

m2KW)

35 53 70 40 35 35 53 53 88 53


52


No 1 2 3 4 5

Tube pitch (m) 003175 002500 002540 003125 002500

Number of tubes 124 3983 528 1532 582


Tube length L (m) 4270 9000 5422 9000 7100



Tube pattern





nozzle (m) 01023 04380 01280 03370 01540


nozzle (m) 01023 04380 01280 03370 01540


19

Chapter 4







1



Condensing Turbines



Abstract


























2

Highlights




considered


performance

1 Introduction

























3



































4


































5


































6

2 Model Development

















( ) n( ) ut( )

n( ) ( ) (1)






equation (1)


7

( ) ( ) ( ( ) ( )) ( ) (2)



of steam is given












(2) Saturated steam





S ( ) ( ) S ( ) ( ( )) S ( ) (3)






8



( ) ( ) ( ) ( ( )) ( ) (4)







( ) ut( ) ( )

( ) ( ) (5)









( ) ( ) ( ) ( ( ) ( )) (6)





9















( ) ( ) (7)














10











( ) ( ut( ) ( )) ( ( ) ( ))

ut( ) t ( )

( ) t ( )

(8)

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(9)




( ) ( ) ( ) (10)



turbine i







11

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(11)







Max (12)





sum ( ) (13)




sum ( ) sum ( ( ) ( )) (14)




12

3 Solution Method



















4 Case Studies











13



entering coolers

degC

Temperature leaving

coolers degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance


C1 998 650 600 735 1864 000035

C2 847 600 550 1167 2375 000035

C3 781 650 600 4367 3625 000035

C4 787 600 550 3356 4747 000035

C5 951 600 550 669 2106 000035

C6 952 600 550 2159 4747 000035

C7 637 450 400 2492 7036 000018

C8 676 450 400 1612 7347 000018

C9 642 500 450 3050 4686 000018

C10 742 500 450 2198 3903 000018

C11 635 450 400 2955 8277 000018

C12 696 500 450 2201 4820 000018



Coolers Number of

tubes

Tube

passes

Tube

diameter

(mm)

Tube

length

(m)

Cross sectional

area (m2)

Heat transfer

area (m2)

C1 1234 2 19times2 6 01090 4346

C2 742 2 25times2 9 01285 5184

C3 1452 2 19times2 9 01290 7642

C4 1452 2 19times2 9 01290 7642

C5 588 2 25times2 9 01018 4108

C6 1452 2 19times2 9 01290 7642

C7 1424 4 19times2 9 00745 7495

C8 988 2 19times2 9 00873 5249

C9 1234 2 19times2 9 01090 6556

C10 1452 2 19times2 9 01290 7642

C11 1452 2 19times2 9 01290 7642

C12 860 4 25times2 9 00745 5956


14



provided


Inlet steam


Pressure (bara) 40


Turbine





Condenser

Area (m2) 1984


Tube passes 1


Tube length (m) 836

Tube pitch (m) 0032





Ambient air

conditions







Power(poundkWh) 01



15



Cooling towers

Water mass flowrate

(th)

Upper bound 9000

Lower bound 5000

Air mass flowrate

(th)

Upper bound 12600

Lower bound 5000



Upper bound 15

Lower bound 07



Coolers



Lower bound 05






respectively

41 Base case









16




1

Case

2

Case

3

Cooling

water system

Operation

Circulating water

flowrate (th) 7560 6047 9000 6414

Air flowrate (th) 8237 7267 12053 7258


cooling water into

the cooling tower

(degC)

430 456 405 449

Outlet temperature

of cooling water

from the cooling

tower (degC)

320 319 313 321

Water

consumption

Make-up water

(th) 183 181 187 181

Power

consumption

Fans (kW) 398 351 582 350

Pumps (kW) 1568 1372 1877 1411

Total (kW) 1966 1723 2459 1762


Condensing

turbine






17


Base

case

Case

1

Case

2

Case

3

C1 640 650 648 650

C2 592 600 600 600

C3 643 650 650 650

C4 592 600 600 600

C5 590 600 600 600

C6 592 600 600 600

C7 450 450 450 450

C8 440 450 450 450

C9 500 500 500 500

C10 500 500 500 500

C11 445 450 450 450

C12 500 500 500 500


42 Case study 1




Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan

( )

Processes


Cases


18



















19


cooling requirement

43 Case study 2
















20






02 degC

44 Case study 3






Table 6 and Table 7



21

















45 Discussion

















22









5 Conclusions
























23












Nomenclature

Sets



k q set of coolers

Parameters















C)




24












C W)


C W)









a1-a3 coefficients

b1-b3 coefficients

Variables







C)



C)








25






























(oC)










26












C)


C)


C)







Greek Symbols



s-1

)


s-1

)












Subscripts

a air


27

db dry bulb

f fans

i insideinlet

m n nodes

o outsideoutlet

p pumps

w cooling water

wb wet bulb

m mean value

cn condensing zone


References


Water Systems





2209












781







28


128















134 pp 88-93


Appendix




follows










29


( ) ( ) ( ) ( ( ) ) (A1)

( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)


( ) ( ) ( )

( ) (A3)

( ) ( ( ) ( )) ( ) ( ( ) )

( ) ( )

(A4)

( ) ( ) ( ) ( ) ( )

( ( ) ) (A5)


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)




( ) 0 ( ) ( )

1 (A8)


30


A21 Cooler modeling











shell


( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)


( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (A11)


( ) ( ) ( )

h ( ) ( ) (A12)


31

S( ) h ( ) h ( )

( ) ( ) (A13)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(A16)


(A17) [15]

( ) w( )

( ) ( )

w( ) μw( )

w( )

(A17)


( ) ( ) ( ) ( ) ( ) ( )

( ) ( ( ) ) ( )

( ) ( ) ( ( ) ( )

)

(A18)


( ) ( ) ( )

w( ) ( ) ( ) (A19)


32

( ) ( )

w( ) n( ) (A20)

( ) ( )

w( ) ut( ) (A21)






( ) sum ( ) (A22)

( ) sum ( ) (A23)

( ) sum ( ) (A24)

( ) sum ( ) (A25)

( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) (A26)

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)



equation

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)


33


( ) sum ( ) ( ) (A29)

( ) sum ( ) sum ( ) ( ) (A30)

( ) sum ( ) ( ) (A31)

( ) sum ( ) sum ( ) ( ) (A32)

( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)

( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )

( )) ( ) (A34)










( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (A35)





34

( ) ( ) ( ) ( ) (A36)

( ) ( ( ) ) (A37)

( ) ( ) w ( )

( ) (A38)




S ( ) (

( ) ((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B1)




( ) ((sum

( )

) (sum ( ( ))

( )

)) (B2)



35

( ) ((sum

ut ( )

) (sum ( ( ))

ut ( )

)) (B3)




S ( ) (

( )

((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B4)


S ( ) (

( )

(sum ut( )

( )

)

sum ut( )

( )

) (B5)



( ) ((sum

( )

) (sum ( ( ))

( )

)) (B6)


36

( ) (sum ut( )

( )

) (B7)


in Appendix B)

( ) ( ( )

( ) ( ( ) ( ) ( )) )

(B8)

( ) ( )

( )

( )

( )

(B9)

( ) ( )

( )

( )

( )

(B10)

( ) ( )

( )

7 ( )

( )

(B11)

Where



Assumptions








equations [13]


( ) ( ) ( ) (C1)


37


( ) ( )

( ) ( ) (C2)

( ) n( )

( ) n ( ) (C3)

( ) ( ) ( ) ( ) (C4)

( ) ( ) ( ) ( ) (C5)




( ) ( ) ( )

( ) ( )

μ ( ) ( )

( )

(C6)

( ) ( )

( ) (C7)

( ) n( )

( ) ( ) (C8)





20


51 Conclusions






cooling requirement

























21


















52 Future work




areas listed below









22














cost







23

References





2209














Science 56(12) pp 3641-3658



pp 117ndash195






pp 49-54







3

List of Figures


4

Abstract


Fei Song



Operation

2016






























turbines

5

Declaration




Fei Song

6

Copyright Statement
























7

Acknowledgement

















8


11 Background
















9



























10




























11





towers







systems
















12







pressure




















13




























14












12 Motivation















15









simultaneously














included



16








turbines)



14 Thesis outline













17

Chapter 2






1


Cooling Towers



Abstract

















base case





2

Highlights




investigated

1 Introduction




















3



















4





























5





























6





























7



























8


cooling towers

























9

tower







(1)

( ) (1)





( ) (2)






10











(3)
















11




Figure 2 (d) is a







12



temperature



temperature (d)


13



( ) (4)










( )

w (5)




( )

w ( ) ( ) ( ) (6)


14



respectively


( ( ) ( ) ( )) (7)


( ( ) ( ) ( ))

(8)






( ) (9)






(10)


15

( ) (10)













equation (8)

( ) (11)




(12)


16









( ) (13)





(14)

( ) (15)

w

(16)





17



flowrate





temperature

(17)

(18)

w

w

w

(19)

(20)

(21)







18

( ) (22)



respectively

3 Model validation











towers [28]








19








α1 α2 α3 α4

95846 06568 -12569 -04216


β1 β2 β3 β4 β5

40099 -17177 08672 -21377 08165


γ1 γ2 γ3 γ4 γ5 γ6 γ7

-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00


20







y=x

y=x

R2=0992

R2=0996


21






No 1 2 3 4 5 6

Measured

data

(degC) 2933 3667 4100 3889 4033 3572

(degC) 2966 3192 3550 3111 3361 3311

(degC) 2111 2111 2388 2388 2667 2944

(kgs) 1186 1178 1157 1174 1157 1156

(kgs) 1132 1132 0881 1132 1008 1258

Calculated

data

(degC)

Measured 2433 2633 2800 2844 3044 3122

Correlation 2415 2642 2818 2851 3016 3106

Relative

difference () 073 -036 -065 -024 092 051

(10-2

kgkg

dry air)

Measured 2192 2835 3108 3223 3454 3301

Correlation 2168 2878 3119 3229 3419 3305

Relative

difference

()

111 -151 -037 -017 103 -011





4 Solution Method




22














5 Case Studies










change


23

51 Base case











Table 6




Ambient air

conditions

tdbi (degC) 3028 3028 3533 2950 2600

twbi (degC) 2565 2565 2944 2500 2250

wi (10

-2kgkg dry air)

190 190 239 183 158

ii (kJkg) 7913 7913 9688 7636 6645






Lower bound 4320


Lower bound 3600

Upper bound 17

Lower bound 07



24

52 Case study 1








Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan [17]

( )








25















Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Operating

conditions

Inlet water

flowrate (th) 7920 5760 5760 6280 5641 7137

Inlet dry air

flowrate (th) 7200 9187 9187 7533 9441 4996

Cooling

water

Inlet

temperature

(degC)

4100 4385 4385 4644 4351 4062

Outlet

temperature

(degC)

3020 2895 3166 2849 2676 3274 2830 2869

Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193


towers (MW) 1039 1041 858 1071 1188 1052 1039 1029


(MW) 9928 8079 10240 11442 9928



26

Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Make-up water

consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635

Power

consumption

(kW)

Fan 353 450 450 450 450 377 462 240

Pump 1631 1344 1344 1344 1344 1396 1333 1503

Total 1984 1794 1794 1794 1794 1773 1795 1743

Cost (poundh)

Make-up

water 522 536 473 547 587 561 532 490

Power 1983 1794 1794 1794 1794 1773 1795 1743

Total 2505 2330 2267 2341 2381 2334 2327 2233

53 Case study 2


















27






























28









slightly

6 Conclusions

















base case


29



















30

Nomenclature

Parameters







dry air)







Variables








air)


dry air)


dry air)





31

Mep Merkel number







p pressure (Pa)



temperature (Pa)




T temperature K











ηp pump efficiency

Subscripts

a air

db dry-bulb

e evaporation

f fans

i inlet


32

m make-up water

o outlet

p pumps

P Poppe method

s saturation

v vapor

w cooling water

wb wet-bulb

References








New York USA















Mi 15




33
















Oklahoma









6370 EPRI Palo Alto








Amsterdam







34

Appendix

1) Data information




No twi

(degC)

two

(degC)

tdbi

(degC)

twbi

(degC)

wi

(kgkg dry air)

ma

(kgs)

mwi

(kgs)

wo

(kgkg dry air)

1 4144 2600 3411 2111 00104 1158 0754 00284

2 2872 2422 2900 2111 00125 1186 1259 00215

3 3450 2622 3050 2111 00119 1186 1259 00271

4 3878 2933 3500 2667 00188 1264 1008 00323

5 3878 2933 3500 2667 00188 1250 1008 00323

6 3967 2622 3400 2111 00105 1174 0881 00284

7 3500 2867 3461 2667 00190 1156 0881 00285

8 4361 2789 3500 2388 00141 1158 0754 00316

9 4306 2972 3572 2667 00185 1155 0754 00337

10 3806 3089 3594 2944 00236 1142 0754 00321

11 4778 3217 3617 2944 00235 1142 0754 00400

12 3378 2472 3250 2111 00110 1179 0881 00238

13 4144 3000 3617 2667 00183 1156 0881 00340

14 4061 3172 3417 2944 00244 1147 0881 00359

15 4350 3217 3533 2944 00239 1147 0881 00383

16 3672 3139 3272 2944 00250 1155 1008 00329

17 3322 2550 2883 2111 00126 1186 1008 00244

18 3844 2678 2950 2111 00123 1186 1008 00290

19 3661 2944 3250 2667 00199 1161 1132 00314

20 4100 3050 3294 2667 00197 1161 1132 00364

21 3611 2972 3111 2667 00204 1166 1258 00314

22 4022 3078 3133 2667 00203 1166 1258 00364

23 3956 3011 3206 2667 00200 1008 1008 00349

24 3950 3006 3106 2667 00205 1051 1008 00344

25 3944 3000 3333 2667 00195 1108 1008 00341

26 3978 2967 3167 2667 00202 0947 1008 00357





35











w

( w ) w

w ( ) w ( w ) v- ( w ) w (A1)

w

w

( w ) w

w ( ) w ( w ) v- ( w ) w

(A2)

w

( w ) ( w ) ( ) v ( w ) w (A3)







w

w

(

w ( )) (A4)


36


w w

w

0 w w

w 1

(A5)


w

(A6)



w

( ) (A7)



w

(A8)


coefficients



( ) [ ( )] (A9)


37




(A11)

7

7


times [ 7 ( 7 frasl ) ] (A12)









( w )

w w

( w )

77 w (A16)


38



( ) ( ) ( ) (A17)





18

Chapter 3






1


Water Systems



Abstract


















the base case


optimisation




2

Highlights



are considered


into account



investigated

1 Introduction
















3



















4



























5












turn













sectors


6




























7






























8





























9
























considered


10

























11





the shell side









is variable












12





arrangement


13





(1) Mass balance




( ) sum ( ) (1)





( ) sum ( ) (2)



( ) sum ( ) (3)

( ) sum ( ) (4)


14


(2) Energy balance




( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

(5)





a in Figure 2


( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)



leaving cooler q



( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)


15
















(1) Mass balance



( ) sum ( ) ( ) (8)




16



equation (9)

( ) sum ( ) sum ( ) ( ) (9)






respectively

( ) sum ( ) ( ) (10)

( ) sum ( ) sum ( ) ( ) (11)




(2) Energy balance



( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)


17




leaving cooler k



( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )

(13)






point a in Figure 2










18










( ) ( )

( )

w( ) ( ) ( )

( )

( )

w( ) ( ) (14)







19


constant



( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (15)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (k q) (16)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (17)


20






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (18)







( ) ( ) ( ) (19)









21

232 Pump modelling



cooling water






(20) - (28)



( ) ( ) (20)

( ) ( ) (21)







22

( ) ( ) (22)



than 28 degC [33]

( ) (23)


( ) (24)




( ) ( ) ( )

(25)

( ) ( ) ( )

(26)


( ) ( ) (27)


equation (28)

( ) ( ) (28)


23







Min sum ( ) sum ( ( ) ( )) (29)




3 Solution Method













24



4 Case Studies











Process

streams

Inlet temp

degC

Outlet temp

degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance

msup2degCW

C1 60 Upper 450

1704 987 000018 Lower 420

C2 120 Upper 795

482 286 000018 Lower 750

C3 95 500 586 732 000018

C4 100 Upper 595

707 448 000035 Lower 550

C5 105 Upper 545

447 748 000053 Lower 500

C6 90 Upper 595

1004 488 000018 Lower 550

C7 75 Upper 445

602 913 000018 Lower 400

C8 150 Upper 1000

394 180 000018 Lower 950

C9 125 Upper 645

513 346 000053 Lower 600


25




Coolers Area

(m^2)

Number

of tubes

Tube

passes

Tube inside

diameter

(mm)

Tube outside

diameter

(mm)

Length of

tube

(m)

Thermal


wall (wmdegC)

C1 3506 1006 2 15 19 60 50

C2 1589 610 2 15 19 45 50

C3 2135 610 2 15 19 60 50

C4 2539 980 4 15 19 45 50

C5 1685 366 2 20 25 60 50

C6 2606 1006 2 15 19 45 50

C7 2004 588 4 20 25 45 50

C8 1641 468 2 15 19 60 50

C9 2539 980 4 15 19 45 50




Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002

S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002

S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002

S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002

S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002

S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002

S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002


26

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002

S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002

S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002

S2(C1)

-S1(C2) 1200 023 00002

S2(C6)

-S1(C8) 1300 023 00002




41 Base case












Make-up water


(degC)

Wet-bulb

temperature (degC)

Humidity (kgkg

dry air)

Enthalpy

(kJkg)

318 271 205 855 318


27


42 Case study 1




Units Models

Cooling

towers 1

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )


28

Units Models

2

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )

Pumps

1

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

2

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

Fans

1 ( ) ( ) ( )

( )

2 ( ) ( ) ( )

( )










shown in Table 7


29

























30


the base case


Cooling

towers



The approach

(degC)






Total 409 403 -06

Power

consumption

(kW)

Pumps



Total 4184 3829 -355

Fans



Total 865 882 17

Total 5049 4711 -338

Cost

Water(poundh) 1227 1209 -018





Hot streams


(degC)


C1 450 450

C2 795 795

C3 500 500

C4 595 595


31

Hot streams


(degC)


C5 545 545

C6 595 595

C7 445 445

C8 1000 1000

C9 645 645

43 Case study 2








stated in Table 1



Ambient air

conditions











32


























degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

1

Case 1 458 800 510 604 555 603 455 1006 654

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -08 -05 -10 -09 -10 -08 -10 -06 -09


33


degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

2

Case 1 439 787 485 582 530 584 430 991 631

Optimisation 450 766 500 595 545 592 441 982 644

Difference 10 -23 14 12 14 07 10 05 -01

Condition

3

Case 1 454 798 505 599 550 599 450 1003 650

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -04 -03 -05 -04 -05 -04 -05 -03 -05











Table 9











34





























35







convection


conditions


36




Cooling

towers

Make-up water

flowrate (th)

1 231 241 10 217 207 -10 220 226 06

2 189 195 06 176 168 -08 180 183 03



(MW) 097 071 -026 352 385 033 217 201 -016

Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045

Pumps Power

consumption (kW)

1 2173 2469 296 2173 2307 134 2173 2197 24

2 1657 1951 294 1657 1769 112 1657 1723 66

Total 3830 4420 590 3830 4076 246 3830 3920 90

Fans Power

consumption (kW)

1 460 639 179 444 305 -139 452 597 145

2 419 538 119 405 239 -166 412 496 84

Total 879 1177 298 849 544 -305 864 1093 229


Cost (poundh)

Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027

Power 4709 5597 888 4679 4620 -059 4694 5013 319

Total 5969 6905 936 5858 5745 -113 5894 6240 346


37

5 Conclusions

























in the base case








38





cost increases









Nomenclature

Sets


k set of coolers

q set of coolers

Parameters













C)


39







C W)


C W)













a1-a3 coefficients

b1-b3 coefficients

Variables










degC

-1)





40
























(degC)













41









C)



Greek Symbols

α coefficients

β coefficients

γ coefficients


s-1

)









Subscripts

a air

db dry bulb

f fans

i insideinlet

o outsideoutlet

p pumps

s1-s6 nodes

w cooling water

wb wet bulb


42

References








2209


Cooling Towers


128












914-923



pp 1-7











43












1033-1043




InTech





Science 56(12) pp 3641-3658





pp 117ndash195



pp 540ndash551









44







134 pp 88-93


York USA



Appendix

Appendix A Models



( ) ( ) ( )

( ) (A1)





( ) ( ( ) ( )) ( ) ( ( ) ) ( )

( ) (A2)






45


respectively


( ) ( ) ( ) ( ) ( )

( ( ) ) (A3)




bulb temperature



method


( ) ( ) ( ) ( ( ) ) (A4)


( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)






respectively


46


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)





( ) 0 ( ) ( )

1 (A8)



flowrate



( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)







47


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)






( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (B3)







( ) ( ) ( )

h ( ) ( ) (B4)

S( ) h ( ) h ( )

( ) ( ) (B5)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



48


Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(B8)




respectively


( ) w( )

( ) ( )

w ( ) μw( )

w( )

(B9)






( ) 7 ( ) R ( ) 8 ( ) w( ) w( )

( ) ( ( ) ) ( ) ( )

( ) ( ( ) ( )

) (B10)







49


( ) ( ) ( )

w( ) ( ) ( ) (B11)






( ) ( )

w( ) n( ) (B12)





( ) ( )

w( ) ut( ) (B13)











50




No 1 2 3 4 5

ht

(W(m2 K))

Wang 12072 57689 14026 15846 75662

HTRI 12993 56440 14700 16169 73632

Relative error () -709 221 -459 -200 276

∆Pt

(kPa)

Wang 688 287 886 693 261

HTRI 712 297 868 735 268

Relative error () -337 -337 207 -571 -261



( ) ( ) ( ) ( ) (C1)




( ) ( ( ) ) (C2)



( ) ( ) w ( )

( ) (C3)


51








No 1 2 3 4 5


Specific heat

(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223

Thermal

conductivity

(WmK)

0137 0133 0633 0623 0123 0106 0089 0091 0087 0675

Viscosity

(mPa s) 040 360 062 071 289 120 033 110 180 030

Density

(kgm3) 785 850 991 994 820 790 702 801 786 957

Flow rate

(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390

Inlet

temperature

(degC)

2000 380 480 330 517 2100 2270 1120 1700 770

Fouling

resistance (10-4

m2KW)

35 53 70 40 35 35 53 53 88 53


52


No 1 2 3 4 5

Tube pitch (m) 003175 002500 002540 003125 002500

Number of tubes 124 3983 528 1532 582


Tube length L (m) 4270 9000 5422 9000 7100



Tube pattern





nozzle (m) 01023 04380 01280 03370 01540


nozzle (m) 01023 04380 01280 03370 01540


19

Chapter 4







1



Condensing Turbines



Abstract


























2

Highlights




considered


performance

1 Introduction

























3



































4


































5


































6

2 Model Development

















( ) n( ) ut( )

n( ) ( ) (1)






equation (1)


7

( ) ( ) ( ( ) ( )) ( ) (2)



of steam is given












(2) Saturated steam





S ( ) ( ) S ( ) ( ( )) S ( ) (3)






8



( ) ( ) ( ) ( ( )) ( ) (4)







( ) ut( ) ( )

( ) ( ) (5)









( ) ( ) ( ) ( ( ) ( )) (6)





9















( ) ( ) (7)














10











( ) ( ut( ) ( )) ( ( ) ( ))

ut( ) t ( )

( ) t ( )

(8)

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(9)




( ) ( ) ( ) (10)



turbine i







11

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(11)







Max (12)





sum ( ) (13)




sum ( ) sum ( ( ) ( )) (14)




12

3 Solution Method



















4 Case Studies











13



entering coolers

degC

Temperature leaving

coolers degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance


C1 998 650 600 735 1864 000035

C2 847 600 550 1167 2375 000035

C3 781 650 600 4367 3625 000035

C4 787 600 550 3356 4747 000035

C5 951 600 550 669 2106 000035

C6 952 600 550 2159 4747 000035

C7 637 450 400 2492 7036 000018

C8 676 450 400 1612 7347 000018

C9 642 500 450 3050 4686 000018

C10 742 500 450 2198 3903 000018

C11 635 450 400 2955 8277 000018

C12 696 500 450 2201 4820 000018



Coolers Number of

tubes

Tube

passes

Tube

diameter

(mm)

Tube

length

(m)

Cross sectional

area (m2)

Heat transfer

area (m2)

C1 1234 2 19times2 6 01090 4346

C2 742 2 25times2 9 01285 5184

C3 1452 2 19times2 9 01290 7642

C4 1452 2 19times2 9 01290 7642

C5 588 2 25times2 9 01018 4108

C6 1452 2 19times2 9 01290 7642

C7 1424 4 19times2 9 00745 7495

C8 988 2 19times2 9 00873 5249

C9 1234 2 19times2 9 01090 6556

C10 1452 2 19times2 9 01290 7642

C11 1452 2 19times2 9 01290 7642

C12 860 4 25times2 9 00745 5956


14



provided


Inlet steam


Pressure (bara) 40


Turbine





Condenser

Area (m2) 1984


Tube passes 1


Tube length (m) 836

Tube pitch (m) 0032





Ambient air

conditions







Power(poundkWh) 01



15



Cooling towers

Water mass flowrate

(th)

Upper bound 9000

Lower bound 5000

Air mass flowrate

(th)

Upper bound 12600

Lower bound 5000



Upper bound 15

Lower bound 07



Coolers



Lower bound 05






respectively

41 Base case









16




1

Case

2

Case

3

Cooling

water system

Operation

Circulating water

flowrate (th) 7560 6047 9000 6414

Air flowrate (th) 8237 7267 12053 7258


cooling water into

the cooling tower

(degC)

430 456 405 449

Outlet temperature

of cooling water

from the cooling

tower (degC)

320 319 313 321

Water

consumption

Make-up water

(th) 183 181 187 181

Power

consumption

Fans (kW) 398 351 582 350

Pumps (kW) 1568 1372 1877 1411

Total (kW) 1966 1723 2459 1762


Condensing

turbine






17


Base

case

Case

1

Case

2

Case

3

C1 640 650 648 650

C2 592 600 600 600

C3 643 650 650 650

C4 592 600 600 600

C5 590 600 600 600

C6 592 600 600 600

C7 450 450 450 450

C8 440 450 450 450

C9 500 500 500 500

C10 500 500 500 500

C11 445 450 450 450

C12 500 500 500 500


42 Case study 1




Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan

( )

Processes


Cases


18



















19


cooling requirement

43 Case study 2
















20






02 degC

44 Case study 3






Table 6 and Table 7



21

















45 Discussion

















22









5 Conclusions
























23












Nomenclature

Sets



k q set of coolers

Parameters















C)




24












C W)


C W)









a1-a3 coefficients

b1-b3 coefficients

Variables







C)



C)








25






























(oC)










26












C)


C)


C)







Greek Symbols



s-1

)


s-1

)












Subscripts

a air


27

db dry bulb

f fans

i insideinlet

m n nodes

o outsideoutlet

p pumps

w cooling water

wb wet bulb

m mean value

cn condensing zone


References


Water Systems





2209












781







28


128















134 pp 88-93


Appendix




follows










29


( ) ( ) ( ) ( ( ) ) (A1)

( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)


( ) ( ) ( )

( ) (A3)

( ) ( ( ) ( )) ( ) ( ( ) )

( ) ( )

(A4)

( ) ( ) ( ) ( ) ( )

( ( ) ) (A5)


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)




( ) 0 ( ) ( )

1 (A8)


30


A21 Cooler modeling











shell


( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)


( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (A11)


( ) ( ) ( )

h ( ) ( ) (A12)


31

S( ) h ( ) h ( )

( ) ( ) (A13)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(A16)


(A17) [15]

( ) w( )

( ) ( )

w( ) μw( )

w( )

(A17)


( ) ( ) ( ) ( ) ( ) ( )

( ) ( ( ) ) ( )

( ) ( ) ( ( ) ( )

)

(A18)


( ) ( ) ( )

w( ) ( ) ( ) (A19)


32

( ) ( )

w( ) n( ) (A20)

( ) ( )

w( ) ut( ) (A21)






( ) sum ( ) (A22)

( ) sum ( ) (A23)

( ) sum ( ) (A24)

( ) sum ( ) (A25)

( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) (A26)

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)



equation

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)


33


( ) sum ( ) ( ) (A29)

( ) sum ( ) sum ( ) ( ) (A30)

( ) sum ( ) ( ) (A31)

( ) sum ( ) sum ( ) ( ) (A32)

( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)

( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )

( )) ( ) (A34)










( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (A35)





34

( ) ( ) ( ) ( ) (A36)

( ) ( ( ) ) (A37)

( ) ( ) w ( )

( ) (A38)




S ( ) (

( ) ((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B1)




( ) ((sum

( )

) (sum ( ( ))

( )

)) (B2)



35

( ) ((sum

ut ( )

) (sum ( ( ))

ut ( )

)) (B3)




S ( ) (

( )

((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B4)


S ( ) (

( )

(sum ut( )

( )

)

sum ut( )

( )

) (B5)



( ) ((sum

( )

) (sum ( ( ))

( )

)) (B6)


36

( ) (sum ut( )

( )

) (B7)


in Appendix B)

( ) ( ( )

( ) ( ( ) ( ) ( )) )

(B8)

( ) ( )

( )

( )

( )

(B9)

( ) ( )

( )

( )

( )

(B10)

( ) ( )

( )

7 ( )

( )

(B11)

Where



Assumptions








equations [13]


( ) ( ) ( ) (C1)


37


( ) ( )

( ) ( ) (C2)

( ) n( )

( ) n ( ) (C3)

( ) ( ) ( ) ( ) (C4)

( ) ( ) ( ) ( ) (C5)




( ) ( ) ( )

( ) ( )

μ ( ) ( )

( )

(C6)

( ) ( )

( ) (C7)

( ) n( )

( ) ( ) (C8)





20


51 Conclusions






cooling requirement

























21


















52 Future work




areas listed below









22














cost







23

References





2209














Science 56(12) pp 3641-3658



pp 117ndash195






pp 49-54







4

Abstract


Fei Song



Operation

2016






























turbines

5

Declaration




Fei Song

6

Copyright Statement
























7

Acknowledgement

















8


11 Background
















9



























10




























11





towers







systems
















12







pressure




















13




























14












12 Motivation















15









simultaneously














included



16








turbines)



14 Thesis outline













17

Chapter 2






1


Cooling Towers



Abstract

















base case





2

Highlights




investigated

1 Introduction




















3



















4





























5





























6





























7



























8


cooling towers

























9

tower







(1)

( ) (1)





( ) (2)






10











(3)
















11




Figure 2 (d) is a







12



temperature



temperature (d)


13



( ) (4)










( )

w (5)




( )

w ( ) ( ) ( ) (6)


14



respectively


( ( ) ( ) ( )) (7)


( ( ) ( ) ( ))

(8)






( ) (9)






(10)


15

( ) (10)













equation (8)

( ) (11)




(12)


16









( ) (13)





(14)

( ) (15)

w

(16)





17



flowrate





temperature

(17)

(18)

w

w

w

(19)

(20)

(21)







18

( ) (22)



respectively

3 Model validation











towers [28]








19








α1 α2 α3 α4

95846 06568 -12569 -04216


β1 β2 β3 β4 β5

40099 -17177 08672 -21377 08165


γ1 γ2 γ3 γ4 γ5 γ6 γ7

-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00


20







y=x

y=x

R2=0992

R2=0996


21






No 1 2 3 4 5 6

Measured

data

(degC) 2933 3667 4100 3889 4033 3572

(degC) 2966 3192 3550 3111 3361 3311

(degC) 2111 2111 2388 2388 2667 2944

(kgs) 1186 1178 1157 1174 1157 1156

(kgs) 1132 1132 0881 1132 1008 1258

Calculated

data

(degC)

Measured 2433 2633 2800 2844 3044 3122

Correlation 2415 2642 2818 2851 3016 3106

Relative

difference () 073 -036 -065 -024 092 051

(10-2

kgkg

dry air)

Measured 2192 2835 3108 3223 3454 3301

Correlation 2168 2878 3119 3229 3419 3305

Relative

difference

()

111 -151 -037 -017 103 -011





4 Solution Method




22














5 Case Studies










change


23

51 Base case











Table 6




Ambient air

conditions

tdbi (degC) 3028 3028 3533 2950 2600

twbi (degC) 2565 2565 2944 2500 2250

wi (10

-2kgkg dry air)

190 190 239 183 158

ii (kJkg) 7913 7913 9688 7636 6645






Lower bound 4320


Lower bound 3600

Upper bound 17

Lower bound 07



24

52 Case study 1








Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan [17]

( )








25















Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Operating

conditions

Inlet water

flowrate (th) 7920 5760 5760 6280 5641 7137

Inlet dry air

flowrate (th) 7200 9187 9187 7533 9441 4996

Cooling

water

Inlet

temperature

(degC)

4100 4385 4385 4644 4351 4062

Outlet

temperature

(degC)

3020 2895 3166 2849 2676 3274 2830 2869

Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193


towers (MW) 1039 1041 858 1071 1188 1052 1039 1029


(MW) 9928 8079 10240 11442 9928



26

Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Make-up water

consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635

Power

consumption

(kW)

Fan 353 450 450 450 450 377 462 240

Pump 1631 1344 1344 1344 1344 1396 1333 1503

Total 1984 1794 1794 1794 1794 1773 1795 1743

Cost (poundh)

Make-up

water 522 536 473 547 587 561 532 490

Power 1983 1794 1794 1794 1794 1773 1795 1743

Total 2505 2330 2267 2341 2381 2334 2327 2233

53 Case study 2


















27






























28









slightly

6 Conclusions

















base case


29



















30

Nomenclature

Parameters







dry air)







Variables








air)


dry air)


dry air)





31

Mep Merkel number







p pressure (Pa)



temperature (Pa)




T temperature K











ηp pump efficiency

Subscripts

a air

db dry-bulb

e evaporation

f fans

i inlet


32

m make-up water

o outlet

p pumps

P Poppe method

s saturation

v vapor

w cooling water

wb wet-bulb

References








New York USA















Mi 15




33
















Oklahoma









6370 EPRI Palo Alto








Amsterdam







34

Appendix

1) Data information




No twi

(degC)

two

(degC)

tdbi

(degC)

twbi

(degC)

wi

(kgkg dry air)

ma

(kgs)

mwi

(kgs)

wo

(kgkg dry air)

1 4144 2600 3411 2111 00104 1158 0754 00284

2 2872 2422 2900 2111 00125 1186 1259 00215

3 3450 2622 3050 2111 00119 1186 1259 00271

4 3878 2933 3500 2667 00188 1264 1008 00323

5 3878 2933 3500 2667 00188 1250 1008 00323

6 3967 2622 3400 2111 00105 1174 0881 00284

7 3500 2867 3461 2667 00190 1156 0881 00285

8 4361 2789 3500 2388 00141 1158 0754 00316

9 4306 2972 3572 2667 00185 1155 0754 00337

10 3806 3089 3594 2944 00236 1142 0754 00321

11 4778 3217 3617 2944 00235 1142 0754 00400

12 3378 2472 3250 2111 00110 1179 0881 00238

13 4144 3000 3617 2667 00183 1156 0881 00340

14 4061 3172 3417 2944 00244 1147 0881 00359

15 4350 3217 3533 2944 00239 1147 0881 00383

16 3672 3139 3272 2944 00250 1155 1008 00329

17 3322 2550 2883 2111 00126 1186 1008 00244

18 3844 2678 2950 2111 00123 1186 1008 00290

19 3661 2944 3250 2667 00199 1161 1132 00314

20 4100 3050 3294 2667 00197 1161 1132 00364

21 3611 2972 3111 2667 00204 1166 1258 00314

22 4022 3078 3133 2667 00203 1166 1258 00364

23 3956 3011 3206 2667 00200 1008 1008 00349

24 3950 3006 3106 2667 00205 1051 1008 00344

25 3944 3000 3333 2667 00195 1108 1008 00341

26 3978 2967 3167 2667 00202 0947 1008 00357





35











w

( w ) w

w ( ) w ( w ) v- ( w ) w (A1)

w

w

( w ) w

w ( ) w ( w ) v- ( w ) w

(A2)

w

( w ) ( w ) ( ) v ( w ) w (A3)







w

w

(

w ( )) (A4)


36


w w

w

0 w w

w 1

(A5)


w

(A6)



w

( ) (A7)



w

(A8)


coefficients



( ) [ ( )] (A9)


37




(A11)

7

7


times [ 7 ( 7 frasl ) ] (A12)









( w )

w w

( w )

77 w (A16)


38



( ) ( ) ( ) (A17)





18

Chapter 3






1


Water Systems



Abstract


















the base case


optimisation




2

Highlights



are considered


into account



investigated

1 Introduction
















3



















4



























5












turn













sectors


6




























7






























8





























9
























considered


10

























11





the shell side









is variable












12





arrangement


13





(1) Mass balance




( ) sum ( ) (1)





( ) sum ( ) (2)



( ) sum ( ) (3)

( ) sum ( ) (4)


14


(2) Energy balance




( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

(5)





a in Figure 2


( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)



leaving cooler q



( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)


15
















(1) Mass balance



( ) sum ( ) ( ) (8)




16



equation (9)

( ) sum ( ) sum ( ) ( ) (9)






respectively

( ) sum ( ) ( ) (10)

( ) sum ( ) sum ( ) ( ) (11)




(2) Energy balance



( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)


17




leaving cooler k



( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )

(13)






point a in Figure 2










18










( ) ( )

( )

w( ) ( ) ( )

( )

( )

w( ) ( ) (14)







19


constant



( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (15)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (k q) (16)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (17)


20






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (18)







( ) ( ) ( ) (19)









21

232 Pump modelling



cooling water






(20) - (28)



( ) ( ) (20)

( ) ( ) (21)







22

( ) ( ) (22)



than 28 degC [33]

( ) (23)


( ) (24)




( ) ( ) ( )

(25)

( ) ( ) ( )

(26)


( ) ( ) (27)


equation (28)

( ) ( ) (28)


23







Min sum ( ) sum ( ( ) ( )) (29)




3 Solution Method













24



4 Case Studies











Process

streams

Inlet temp

degC

Outlet temp

degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance

msup2degCW

C1 60 Upper 450

1704 987 000018 Lower 420

C2 120 Upper 795

482 286 000018 Lower 750

C3 95 500 586 732 000018

C4 100 Upper 595

707 448 000035 Lower 550

C5 105 Upper 545

447 748 000053 Lower 500

C6 90 Upper 595

1004 488 000018 Lower 550

C7 75 Upper 445

602 913 000018 Lower 400

C8 150 Upper 1000

394 180 000018 Lower 950

C9 125 Upper 645

513 346 000053 Lower 600


25




Coolers Area

(m^2)

Number

of tubes

Tube

passes

Tube inside

diameter

(mm)

Tube outside

diameter

(mm)

Length of

tube

(m)

Thermal


wall (wmdegC)

C1 3506 1006 2 15 19 60 50

C2 1589 610 2 15 19 45 50

C3 2135 610 2 15 19 60 50

C4 2539 980 4 15 19 45 50

C5 1685 366 2 20 25 60 50

C6 2606 1006 2 15 19 45 50

C7 2004 588 4 20 25 45 50

C8 1641 468 2 15 19 60 50

C9 2539 980 4 15 19 45 50




Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002

S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002

S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002

S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002

S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002

S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002

S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002


26

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002

S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002

S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002

S2(C1)

-S1(C2) 1200 023 00002

S2(C6)

-S1(C8) 1300 023 00002




41 Base case












Make-up water


(degC)

Wet-bulb

temperature (degC)

Humidity (kgkg

dry air)

Enthalpy

(kJkg)

318 271 205 855 318


27


42 Case study 1




Units Models

Cooling

towers 1

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )


28

Units Models

2

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )

Pumps

1

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

2

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

Fans

1 ( ) ( ) ( )

( )

2 ( ) ( ) ( )

( )










shown in Table 7


29

























30


the base case


Cooling

towers



The approach

(degC)






Total 409 403 -06

Power

consumption

(kW)

Pumps



Total 4184 3829 -355

Fans



Total 865 882 17

Total 5049 4711 -338

Cost

Water(poundh) 1227 1209 -018





Hot streams


(degC)


C1 450 450

C2 795 795

C3 500 500

C4 595 595


31

Hot streams


(degC)


C5 545 545

C6 595 595

C7 445 445

C8 1000 1000

C9 645 645

43 Case study 2








stated in Table 1



Ambient air

conditions











32


























degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

1

Case 1 458 800 510 604 555 603 455 1006 654

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -08 -05 -10 -09 -10 -08 -10 -06 -09


33


degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

2

Case 1 439 787 485 582 530 584 430 991 631

Optimisation 450 766 500 595 545 592 441 982 644

Difference 10 -23 14 12 14 07 10 05 -01

Condition

3

Case 1 454 798 505 599 550 599 450 1003 650

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -04 -03 -05 -04 -05 -04 -05 -03 -05











Table 9











34





























35







convection


conditions


36




Cooling

towers

Make-up water

flowrate (th)

1 231 241 10 217 207 -10 220 226 06

2 189 195 06 176 168 -08 180 183 03



(MW) 097 071 -026 352 385 033 217 201 -016

Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045

Pumps Power

consumption (kW)

1 2173 2469 296 2173 2307 134 2173 2197 24

2 1657 1951 294 1657 1769 112 1657 1723 66

Total 3830 4420 590 3830 4076 246 3830 3920 90

Fans Power

consumption (kW)

1 460 639 179 444 305 -139 452 597 145

2 419 538 119 405 239 -166 412 496 84

Total 879 1177 298 849 544 -305 864 1093 229


Cost (poundh)

Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027

Power 4709 5597 888 4679 4620 -059 4694 5013 319

Total 5969 6905 936 5858 5745 -113 5894 6240 346


37

5 Conclusions

























in the base case








38





cost increases









Nomenclature

Sets


k set of coolers

q set of coolers

Parameters













C)


39







C W)


C W)













a1-a3 coefficients

b1-b3 coefficients

Variables










degC

-1)





40
























(degC)













41









C)



Greek Symbols

α coefficients

β coefficients

γ coefficients


s-1

)









Subscripts

a air

db dry bulb

f fans

i insideinlet

o outsideoutlet

p pumps

s1-s6 nodes

w cooling water

wb wet bulb


42

References








2209


Cooling Towers


128












914-923



pp 1-7











43












1033-1043




InTech





Science 56(12) pp 3641-3658





pp 117ndash195



pp 540ndash551









44







134 pp 88-93


York USA



Appendix

Appendix A Models



( ) ( ) ( )

( ) (A1)





( ) ( ( ) ( )) ( ) ( ( ) ) ( )

( ) (A2)






45


respectively


( ) ( ) ( ) ( ) ( )

( ( ) ) (A3)




bulb temperature



method


( ) ( ) ( ) ( ( ) ) (A4)


( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)






respectively


46


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)





( ) 0 ( ) ( )

1 (A8)



flowrate



( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)







47


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)






( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (B3)







( ) ( ) ( )

h ( ) ( ) (B4)

S( ) h ( ) h ( )

( ) ( ) (B5)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



48


Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(B8)




respectively


( ) w( )

( ) ( )

w ( ) μw( )

w( )

(B9)






( ) 7 ( ) R ( ) 8 ( ) w( ) w( )

( ) ( ( ) ) ( ) ( )

( ) ( ( ) ( )

) (B10)







49


( ) ( ) ( )

w( ) ( ) ( ) (B11)






( ) ( )

w( ) n( ) (B12)





( ) ( )

w( ) ut( ) (B13)











50




No 1 2 3 4 5

ht

(W(m2 K))

Wang 12072 57689 14026 15846 75662

HTRI 12993 56440 14700 16169 73632

Relative error () -709 221 -459 -200 276

∆Pt

(kPa)

Wang 688 287 886 693 261

HTRI 712 297 868 735 268

Relative error () -337 -337 207 -571 -261



( ) ( ) ( ) ( ) (C1)




( ) ( ( ) ) (C2)



( ) ( ) w ( )

( ) (C3)


51








No 1 2 3 4 5


Specific heat

(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223

Thermal

conductivity

(WmK)

0137 0133 0633 0623 0123 0106 0089 0091 0087 0675

Viscosity

(mPa s) 040 360 062 071 289 120 033 110 180 030

Density

(kgm3) 785 850 991 994 820 790 702 801 786 957

Flow rate

(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390

Inlet

temperature

(degC)

2000 380 480 330 517 2100 2270 1120 1700 770

Fouling

resistance (10-4

m2KW)

35 53 70 40 35 35 53 53 88 53


52


No 1 2 3 4 5

Tube pitch (m) 003175 002500 002540 003125 002500

Number of tubes 124 3983 528 1532 582


Tube length L (m) 4270 9000 5422 9000 7100



Tube pattern





nozzle (m) 01023 04380 01280 03370 01540


nozzle (m) 01023 04380 01280 03370 01540


19

Chapter 4







1



Condensing Turbines



Abstract


























2

Highlights




considered


performance

1 Introduction

























3



































4


































5


































6

2 Model Development

















( ) n( ) ut( )

n( ) ( ) (1)






equation (1)


7

( ) ( ) ( ( ) ( )) ( ) (2)



of steam is given












(2) Saturated steam





S ( ) ( ) S ( ) ( ( )) S ( ) (3)






8



( ) ( ) ( ) ( ( )) ( ) (4)







( ) ut( ) ( )

( ) ( ) (5)









( ) ( ) ( ) ( ( ) ( )) (6)





9















( ) ( ) (7)














10











( ) ( ut( ) ( )) ( ( ) ( ))

ut( ) t ( )

( ) t ( )

(8)

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(9)




( ) ( ) ( ) (10)



turbine i







11

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(11)







Max (12)





sum ( ) (13)




sum ( ) sum ( ( ) ( )) (14)




12

3 Solution Method



















4 Case Studies











13



entering coolers

degC

Temperature leaving

coolers degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance


C1 998 650 600 735 1864 000035

C2 847 600 550 1167 2375 000035

C3 781 650 600 4367 3625 000035

C4 787 600 550 3356 4747 000035

C5 951 600 550 669 2106 000035

C6 952 600 550 2159 4747 000035

C7 637 450 400 2492 7036 000018

C8 676 450 400 1612 7347 000018

C9 642 500 450 3050 4686 000018

C10 742 500 450 2198 3903 000018

C11 635 450 400 2955 8277 000018

C12 696 500 450 2201 4820 000018



Coolers Number of

tubes

Tube

passes

Tube

diameter

(mm)

Tube

length

(m)

Cross sectional

area (m2)

Heat transfer

area (m2)

C1 1234 2 19times2 6 01090 4346

C2 742 2 25times2 9 01285 5184

C3 1452 2 19times2 9 01290 7642

C4 1452 2 19times2 9 01290 7642

C5 588 2 25times2 9 01018 4108

C6 1452 2 19times2 9 01290 7642

C7 1424 4 19times2 9 00745 7495

C8 988 2 19times2 9 00873 5249

C9 1234 2 19times2 9 01090 6556

C10 1452 2 19times2 9 01290 7642

C11 1452 2 19times2 9 01290 7642

C12 860 4 25times2 9 00745 5956


14



provided


Inlet steam


Pressure (bara) 40


Turbine





Condenser

Area (m2) 1984


Tube passes 1


Tube length (m) 836

Tube pitch (m) 0032





Ambient air

conditions







Power(poundkWh) 01



15



Cooling towers

Water mass flowrate

(th)

Upper bound 9000

Lower bound 5000

Air mass flowrate

(th)

Upper bound 12600

Lower bound 5000



Upper bound 15

Lower bound 07



Coolers



Lower bound 05






respectively

41 Base case









16




1

Case

2

Case

3

Cooling

water system

Operation

Circulating water

flowrate (th) 7560 6047 9000 6414

Air flowrate (th) 8237 7267 12053 7258


cooling water into

the cooling tower

(degC)

430 456 405 449

Outlet temperature

of cooling water

from the cooling

tower (degC)

320 319 313 321

Water

consumption

Make-up water

(th) 183 181 187 181

Power

consumption

Fans (kW) 398 351 582 350

Pumps (kW) 1568 1372 1877 1411

Total (kW) 1966 1723 2459 1762


Condensing

turbine






17


Base

case

Case

1

Case

2

Case

3

C1 640 650 648 650

C2 592 600 600 600

C3 643 650 650 650

C4 592 600 600 600

C5 590 600 600 600

C6 592 600 600 600

C7 450 450 450 450

C8 440 450 450 450

C9 500 500 500 500

C10 500 500 500 500

C11 445 450 450 450

C12 500 500 500 500


42 Case study 1




Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan

( )

Processes


Cases


18



















19


cooling requirement

43 Case study 2
















20






02 degC

44 Case study 3






Table 6 and Table 7



21

















45 Discussion

















22









5 Conclusions
























23












Nomenclature

Sets



k q set of coolers

Parameters















C)




24












C W)


C W)









a1-a3 coefficients

b1-b3 coefficients

Variables







C)



C)








25






























(oC)










26












C)


C)


C)







Greek Symbols



s-1

)


s-1

)












Subscripts

a air


27

db dry bulb

f fans

i insideinlet

m n nodes

o outsideoutlet

p pumps

w cooling water

wb wet bulb

m mean value

cn condensing zone


References


Water Systems





2209












781







28


128















134 pp 88-93


Appendix




follows










29


( ) ( ) ( ) ( ( ) ) (A1)

( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)


( ) ( ) ( )

( ) (A3)

( ) ( ( ) ( )) ( ) ( ( ) )

( ) ( )

(A4)

( ) ( ) ( ) ( ) ( )

( ( ) ) (A5)


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)




( ) 0 ( ) ( )

1 (A8)


30


A21 Cooler modeling











shell


( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)


( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (A11)


( ) ( ) ( )

h ( ) ( ) (A12)


31

S( ) h ( ) h ( )

( ) ( ) (A13)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(A16)


(A17) [15]

( ) w( )

( ) ( )

w( ) μw( )

w( )

(A17)


( ) ( ) ( ) ( ) ( ) ( )

( ) ( ( ) ) ( )

( ) ( ) ( ( ) ( )

)

(A18)


( ) ( ) ( )

w( ) ( ) ( ) (A19)


32

( ) ( )

w( ) n( ) (A20)

( ) ( )

w( ) ut( ) (A21)






( ) sum ( ) (A22)

( ) sum ( ) (A23)

( ) sum ( ) (A24)

( ) sum ( ) (A25)

( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) (A26)

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)



equation

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)


33


( ) sum ( ) ( ) (A29)

( ) sum ( ) sum ( ) ( ) (A30)

( ) sum ( ) ( ) (A31)

( ) sum ( ) sum ( ) ( ) (A32)

( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)

( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )

( )) ( ) (A34)










( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (A35)





34

( ) ( ) ( ) ( ) (A36)

( ) ( ( ) ) (A37)

( ) ( ) w ( )

( ) (A38)




S ( ) (

( ) ((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B1)




( ) ((sum

( )

) (sum ( ( ))

( )

)) (B2)



35

( ) ((sum

ut ( )

) (sum ( ( ))

ut ( )

)) (B3)




S ( ) (

( )

((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B4)


S ( ) (

( )

(sum ut( )

( )

)

sum ut( )

( )

) (B5)



( ) ((sum

( )

) (sum ( ( ))

( )

)) (B6)


36

( ) (sum ut( )

( )

) (B7)


in Appendix B)

( ) ( ( )

( ) ( ( ) ( ) ( )) )

(B8)

( ) ( )

( )

( )

( )

(B9)

( ) ( )

( )

( )

( )

(B10)

( ) ( )

( )

7 ( )

( )

(B11)

Where



Assumptions








equations [13]


( ) ( ) ( ) (C1)


37


( ) ( )

( ) ( ) (C2)

( ) n( )

( ) n ( ) (C3)

( ) ( ) ( ) ( ) (C4)

( ) ( ) ( ) ( ) (C5)




( ) ( ) ( )

( ) ( )

μ ( ) ( )

( )

(C6)

( ) ( )

( ) (C7)

( ) n( )

( ) ( ) (C8)





20


51 Conclusions






cooling requirement

























21


















52 Future work




areas listed below









22














cost







23

References





2209














Science 56(12) pp 3641-3658



pp 117ndash195






pp 49-54







5

Declaration




Fei Song

6

Copyright Statement
























7

Acknowledgement

















8


11 Background
















9



























10




























11





towers







systems
















12







pressure




















13




























14












12 Motivation















15









simultaneously














included



16








turbines)



14 Thesis outline













17

Chapter 2






1


Cooling Towers



Abstract

















base case





2

Highlights




investigated

1 Introduction




















3



















4





























5





























6





























7



























8


cooling towers

























9

tower







(1)

( ) (1)





( ) (2)






10











(3)
















11




Figure 2 (d) is a







12



temperature



temperature (d)


13



( ) (4)










( )

w (5)




( )

w ( ) ( ) ( ) (6)


14



respectively


( ( ) ( ) ( )) (7)


( ( ) ( ) ( ))

(8)






( ) (9)






(10)


15

( ) (10)













equation (8)

( ) (11)




(12)


16









( ) (13)





(14)

( ) (15)

w

(16)





17



flowrate





temperature

(17)

(18)

w

w

w

(19)

(20)

(21)







18

( ) (22)



respectively

3 Model validation











towers [28]








19








α1 α2 α3 α4

95846 06568 -12569 -04216


β1 β2 β3 β4 β5

40099 -17177 08672 -21377 08165


γ1 γ2 γ3 γ4 γ5 γ6 γ7

-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00


20







y=x

y=x

R2=0992

R2=0996


21






No 1 2 3 4 5 6

Measured

data

(degC) 2933 3667 4100 3889 4033 3572

(degC) 2966 3192 3550 3111 3361 3311

(degC) 2111 2111 2388 2388 2667 2944

(kgs) 1186 1178 1157 1174 1157 1156

(kgs) 1132 1132 0881 1132 1008 1258

Calculated

data

(degC)

Measured 2433 2633 2800 2844 3044 3122

Correlation 2415 2642 2818 2851 3016 3106

Relative

difference () 073 -036 -065 -024 092 051

(10-2

kgkg

dry air)

Measured 2192 2835 3108 3223 3454 3301

Correlation 2168 2878 3119 3229 3419 3305

Relative

difference

()

111 -151 -037 -017 103 -011





4 Solution Method




22














5 Case Studies










change


23

51 Base case











Table 6




Ambient air

conditions

tdbi (degC) 3028 3028 3533 2950 2600

twbi (degC) 2565 2565 2944 2500 2250

wi (10

-2kgkg dry air)

190 190 239 183 158

ii (kJkg) 7913 7913 9688 7636 6645






Lower bound 4320


Lower bound 3600

Upper bound 17

Lower bound 07



24

52 Case study 1








Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan [17]

( )








25















Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Operating

conditions

Inlet water

flowrate (th) 7920 5760 5760 6280 5641 7137

Inlet dry air

flowrate (th) 7200 9187 9187 7533 9441 4996

Cooling

water

Inlet

temperature

(degC)

4100 4385 4385 4644 4351 4062

Outlet

temperature

(degC)

3020 2895 3166 2849 2676 3274 2830 2869

Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193


towers (MW) 1039 1041 858 1071 1188 1052 1039 1029


(MW) 9928 8079 10240 11442 9928



26

Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Make-up water

consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635

Power

consumption

(kW)

Fan 353 450 450 450 450 377 462 240

Pump 1631 1344 1344 1344 1344 1396 1333 1503

Total 1984 1794 1794 1794 1794 1773 1795 1743

Cost (poundh)

Make-up

water 522 536 473 547 587 561 532 490

Power 1983 1794 1794 1794 1794 1773 1795 1743

Total 2505 2330 2267 2341 2381 2334 2327 2233

53 Case study 2


















27






























28









slightly

6 Conclusions

















base case


29



















30

Nomenclature

Parameters







dry air)







Variables








air)


dry air)


dry air)





31

Mep Merkel number







p pressure (Pa)



temperature (Pa)




T temperature K











ηp pump efficiency

Subscripts

a air

db dry-bulb

e evaporation

f fans

i inlet


32

m make-up water

o outlet

p pumps

P Poppe method

s saturation

v vapor

w cooling water

wb wet-bulb

References








New York USA















Mi 15




33
















Oklahoma









6370 EPRI Palo Alto








Amsterdam







34

Appendix

1) Data information




No twi

(degC)

two

(degC)

tdbi

(degC)

twbi

(degC)

wi

(kgkg dry air)

ma

(kgs)

mwi

(kgs)

wo

(kgkg dry air)

1 4144 2600 3411 2111 00104 1158 0754 00284

2 2872 2422 2900 2111 00125 1186 1259 00215

3 3450 2622 3050 2111 00119 1186 1259 00271

4 3878 2933 3500 2667 00188 1264 1008 00323

5 3878 2933 3500 2667 00188 1250 1008 00323

6 3967 2622 3400 2111 00105 1174 0881 00284

7 3500 2867 3461 2667 00190 1156 0881 00285

8 4361 2789 3500 2388 00141 1158 0754 00316

9 4306 2972 3572 2667 00185 1155 0754 00337

10 3806 3089 3594 2944 00236 1142 0754 00321

11 4778 3217 3617 2944 00235 1142 0754 00400

12 3378 2472 3250 2111 00110 1179 0881 00238

13 4144 3000 3617 2667 00183 1156 0881 00340

14 4061 3172 3417 2944 00244 1147 0881 00359

15 4350 3217 3533 2944 00239 1147 0881 00383

16 3672 3139 3272 2944 00250 1155 1008 00329

17 3322 2550 2883 2111 00126 1186 1008 00244

18 3844 2678 2950 2111 00123 1186 1008 00290

19 3661 2944 3250 2667 00199 1161 1132 00314

20 4100 3050 3294 2667 00197 1161 1132 00364

21 3611 2972 3111 2667 00204 1166 1258 00314

22 4022 3078 3133 2667 00203 1166 1258 00364

23 3956 3011 3206 2667 00200 1008 1008 00349

24 3950 3006 3106 2667 00205 1051 1008 00344

25 3944 3000 3333 2667 00195 1108 1008 00341

26 3978 2967 3167 2667 00202 0947 1008 00357





35











w

( w ) w

w ( ) w ( w ) v- ( w ) w (A1)

w

w

( w ) w

w ( ) w ( w ) v- ( w ) w

(A2)

w

( w ) ( w ) ( ) v ( w ) w (A3)







w

w

(

w ( )) (A4)


36


w w

w

0 w w

w 1

(A5)


w

(A6)



w

( ) (A7)



w

(A8)


coefficients



( ) [ ( )] (A9)


37




(A11)

7

7


times [ 7 ( 7 frasl ) ] (A12)









( w )

w w

( w )

77 w (A16)


38



( ) ( ) ( ) (A17)





18

Chapter 3






1


Water Systems



Abstract


















the base case


optimisation




2

Highlights



are considered


into account



investigated

1 Introduction
















3



















4



























5












turn













sectors


6




























7






























8





























9
























considered


10

























11





the shell side









is variable












12





arrangement


13





(1) Mass balance




( ) sum ( ) (1)





( ) sum ( ) (2)



( ) sum ( ) (3)

( ) sum ( ) (4)


14


(2) Energy balance




( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

(5)





a in Figure 2


( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)



leaving cooler q



( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)


15
















(1) Mass balance



( ) sum ( ) ( ) (8)




16



equation (9)

( ) sum ( ) sum ( ) ( ) (9)






respectively

( ) sum ( ) ( ) (10)

( ) sum ( ) sum ( ) ( ) (11)




(2) Energy balance



( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)


17




leaving cooler k



( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )

(13)






point a in Figure 2










18










( ) ( )

( )

w( ) ( ) ( )

( )

( )

w( ) ( ) (14)







19


constant



( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (15)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (k q) (16)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (17)


20






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (18)







( ) ( ) ( ) (19)









21

232 Pump modelling



cooling water






(20) - (28)



( ) ( ) (20)

( ) ( ) (21)







22

( ) ( ) (22)



than 28 degC [33]

( ) (23)


( ) (24)




( ) ( ) ( )

(25)

( ) ( ) ( )

(26)


( ) ( ) (27)


equation (28)

( ) ( ) (28)


23







Min sum ( ) sum ( ( ) ( )) (29)




3 Solution Method













24



4 Case Studies











Process

streams

Inlet temp

degC

Outlet temp

degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance

msup2degCW

C1 60 Upper 450

1704 987 000018 Lower 420

C2 120 Upper 795

482 286 000018 Lower 750

C3 95 500 586 732 000018

C4 100 Upper 595

707 448 000035 Lower 550

C5 105 Upper 545

447 748 000053 Lower 500

C6 90 Upper 595

1004 488 000018 Lower 550

C7 75 Upper 445

602 913 000018 Lower 400

C8 150 Upper 1000

394 180 000018 Lower 950

C9 125 Upper 645

513 346 000053 Lower 600


25




Coolers Area

(m^2)

Number

of tubes

Tube

passes

Tube inside

diameter

(mm)

Tube outside

diameter

(mm)

Length of

tube

(m)

Thermal


wall (wmdegC)

C1 3506 1006 2 15 19 60 50

C2 1589 610 2 15 19 45 50

C3 2135 610 2 15 19 60 50

C4 2539 980 4 15 19 45 50

C5 1685 366 2 20 25 60 50

C6 2606 1006 2 15 19 45 50

C7 2004 588 4 20 25 45 50

C8 1641 468 2 15 19 60 50

C9 2539 980 4 15 19 45 50




Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002

S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002

S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002

S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002

S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002

S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002

S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002


26

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002

S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002

S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002

S2(C1)

-S1(C2) 1200 023 00002

S2(C6)

-S1(C8) 1300 023 00002




41 Base case












Make-up water


(degC)

Wet-bulb

temperature (degC)

Humidity (kgkg

dry air)

Enthalpy

(kJkg)

318 271 205 855 318


27


42 Case study 1




Units Models

Cooling

towers 1

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )


28

Units Models

2

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )

Pumps

1

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

2

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

Fans

1 ( ) ( ) ( )

( )

2 ( ) ( ) ( )

( )










shown in Table 7


29

























30


the base case


Cooling

towers



The approach

(degC)






Total 409 403 -06

Power

consumption

(kW)

Pumps



Total 4184 3829 -355

Fans



Total 865 882 17

Total 5049 4711 -338

Cost

Water(poundh) 1227 1209 -018





Hot streams


(degC)


C1 450 450

C2 795 795

C3 500 500

C4 595 595


31

Hot streams


(degC)


C5 545 545

C6 595 595

C7 445 445

C8 1000 1000

C9 645 645

43 Case study 2








stated in Table 1



Ambient air

conditions











32


























degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

1

Case 1 458 800 510 604 555 603 455 1006 654

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -08 -05 -10 -09 -10 -08 -10 -06 -09


33


degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

2

Case 1 439 787 485 582 530 584 430 991 631

Optimisation 450 766 500 595 545 592 441 982 644

Difference 10 -23 14 12 14 07 10 05 -01

Condition

3

Case 1 454 798 505 599 550 599 450 1003 650

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -04 -03 -05 -04 -05 -04 -05 -03 -05











Table 9











34





























35







convection


conditions


36




Cooling

towers

Make-up water

flowrate (th)

1 231 241 10 217 207 -10 220 226 06

2 189 195 06 176 168 -08 180 183 03



(MW) 097 071 -026 352 385 033 217 201 -016

Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045

Pumps Power

consumption (kW)

1 2173 2469 296 2173 2307 134 2173 2197 24

2 1657 1951 294 1657 1769 112 1657 1723 66

Total 3830 4420 590 3830 4076 246 3830 3920 90

Fans Power

consumption (kW)

1 460 639 179 444 305 -139 452 597 145

2 419 538 119 405 239 -166 412 496 84

Total 879 1177 298 849 544 -305 864 1093 229


Cost (poundh)

Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027

Power 4709 5597 888 4679 4620 -059 4694 5013 319

Total 5969 6905 936 5858 5745 -113 5894 6240 346


37

5 Conclusions

























in the base case








38





cost increases









Nomenclature

Sets


k set of coolers

q set of coolers

Parameters













C)


39







C W)


C W)













a1-a3 coefficients

b1-b3 coefficients

Variables










degC

-1)





40
























(degC)













41









C)



Greek Symbols

α coefficients

β coefficients

γ coefficients


s-1

)









Subscripts

a air

db dry bulb

f fans

i insideinlet

o outsideoutlet

p pumps

s1-s6 nodes

w cooling water

wb wet bulb


42

References








2209


Cooling Towers


128












914-923



pp 1-7











43












1033-1043




InTech





Science 56(12) pp 3641-3658





pp 117ndash195



pp 540ndash551









44







134 pp 88-93


York USA



Appendix

Appendix A Models



( ) ( ) ( )

( ) (A1)





( ) ( ( ) ( )) ( ) ( ( ) ) ( )

( ) (A2)






45


respectively


( ) ( ) ( ) ( ) ( )

( ( ) ) (A3)




bulb temperature



method


( ) ( ) ( ) ( ( ) ) (A4)


( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)






respectively


46


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)





( ) 0 ( ) ( )

1 (A8)



flowrate



( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)







47


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)






( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (B3)







( ) ( ) ( )

h ( ) ( ) (B4)

S( ) h ( ) h ( )

( ) ( ) (B5)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



48


Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(B8)




respectively


( ) w( )

( ) ( )

w ( ) μw( )

w( )

(B9)






( ) 7 ( ) R ( ) 8 ( ) w( ) w( )

( ) ( ( ) ) ( ) ( )

( ) ( ( ) ( )

) (B10)







49


( ) ( ) ( )

w( ) ( ) ( ) (B11)






( ) ( )

w( ) n( ) (B12)





( ) ( )

w( ) ut( ) (B13)











50




No 1 2 3 4 5

ht

(W(m2 K))

Wang 12072 57689 14026 15846 75662

HTRI 12993 56440 14700 16169 73632

Relative error () -709 221 -459 -200 276

∆Pt

(kPa)

Wang 688 287 886 693 261

HTRI 712 297 868 735 268

Relative error () -337 -337 207 -571 -261



( ) ( ) ( ) ( ) (C1)




( ) ( ( ) ) (C2)



( ) ( ) w ( )

( ) (C3)


51








No 1 2 3 4 5


Specific heat

(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223

Thermal

conductivity

(WmK)

0137 0133 0633 0623 0123 0106 0089 0091 0087 0675

Viscosity

(mPa s) 040 360 062 071 289 120 033 110 180 030

Density

(kgm3) 785 850 991 994 820 790 702 801 786 957

Flow rate

(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390

Inlet

temperature

(degC)

2000 380 480 330 517 2100 2270 1120 1700 770

Fouling

resistance (10-4

m2KW)

35 53 70 40 35 35 53 53 88 53


52


No 1 2 3 4 5

Tube pitch (m) 003175 002500 002540 003125 002500

Number of tubes 124 3983 528 1532 582


Tube length L (m) 4270 9000 5422 9000 7100



Tube pattern





nozzle (m) 01023 04380 01280 03370 01540


nozzle (m) 01023 04380 01280 03370 01540


19

Chapter 4







1



Condensing Turbines



Abstract


























2

Highlights




considered


performance

1 Introduction

























3



































4


































5


































6

2 Model Development

















( ) n( ) ut( )

n( ) ( ) (1)






equation (1)


7

( ) ( ) ( ( ) ( )) ( ) (2)



of steam is given












(2) Saturated steam





S ( ) ( ) S ( ) ( ( )) S ( ) (3)






8



( ) ( ) ( ) ( ( )) ( ) (4)







( ) ut( ) ( )

( ) ( ) (5)









( ) ( ) ( ) ( ( ) ( )) (6)





9















( ) ( ) (7)














10











( ) ( ut( ) ( )) ( ( ) ( ))

ut( ) t ( )

( ) t ( )

(8)

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(9)




( ) ( ) ( ) (10)



turbine i







11

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(11)







Max (12)





sum ( ) (13)




sum ( ) sum ( ( ) ( )) (14)




12

3 Solution Method



















4 Case Studies











13



entering coolers

degC

Temperature leaving

coolers degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance


C1 998 650 600 735 1864 000035

C2 847 600 550 1167 2375 000035

C3 781 650 600 4367 3625 000035

C4 787 600 550 3356 4747 000035

C5 951 600 550 669 2106 000035

C6 952 600 550 2159 4747 000035

C7 637 450 400 2492 7036 000018

C8 676 450 400 1612 7347 000018

C9 642 500 450 3050 4686 000018

C10 742 500 450 2198 3903 000018

C11 635 450 400 2955 8277 000018

C12 696 500 450 2201 4820 000018



Coolers Number of

tubes

Tube

passes

Tube

diameter

(mm)

Tube

length

(m)

Cross sectional

area (m2)

Heat transfer

area (m2)

C1 1234 2 19times2 6 01090 4346

C2 742 2 25times2 9 01285 5184

C3 1452 2 19times2 9 01290 7642

C4 1452 2 19times2 9 01290 7642

C5 588 2 25times2 9 01018 4108

C6 1452 2 19times2 9 01290 7642

C7 1424 4 19times2 9 00745 7495

C8 988 2 19times2 9 00873 5249

C9 1234 2 19times2 9 01090 6556

C10 1452 2 19times2 9 01290 7642

C11 1452 2 19times2 9 01290 7642

C12 860 4 25times2 9 00745 5956


14



provided


Inlet steam


Pressure (bara) 40


Turbine





Condenser

Area (m2) 1984


Tube passes 1


Tube length (m) 836

Tube pitch (m) 0032





Ambient air

conditions







Power(poundkWh) 01



15



Cooling towers

Water mass flowrate

(th)

Upper bound 9000

Lower bound 5000

Air mass flowrate

(th)

Upper bound 12600

Lower bound 5000



Upper bound 15

Lower bound 07



Coolers



Lower bound 05






respectively

41 Base case









16




1

Case

2

Case

3

Cooling

water system

Operation

Circulating water

flowrate (th) 7560 6047 9000 6414

Air flowrate (th) 8237 7267 12053 7258


cooling water into

the cooling tower

(degC)

430 456 405 449

Outlet temperature

of cooling water

from the cooling

tower (degC)

320 319 313 321

Water

consumption

Make-up water

(th) 183 181 187 181

Power

consumption

Fans (kW) 398 351 582 350

Pumps (kW) 1568 1372 1877 1411

Total (kW) 1966 1723 2459 1762


Condensing

turbine






17


Base

case

Case

1

Case

2

Case

3

C1 640 650 648 650

C2 592 600 600 600

C3 643 650 650 650

C4 592 600 600 600

C5 590 600 600 600

C6 592 600 600 600

C7 450 450 450 450

C8 440 450 450 450

C9 500 500 500 500

C10 500 500 500 500

C11 445 450 450 450

C12 500 500 500 500


42 Case study 1




Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan

( )

Processes


Cases


18



















19


cooling requirement

43 Case study 2
















20






02 degC

44 Case study 3






Table 6 and Table 7



21

















45 Discussion

















22









5 Conclusions
























23












Nomenclature

Sets



k q set of coolers

Parameters















C)




24












C W)


C W)









a1-a3 coefficients

b1-b3 coefficients

Variables







C)



C)








25






























(oC)










26












C)


C)


C)







Greek Symbols



s-1

)


s-1

)












Subscripts

a air


27

db dry bulb

f fans

i insideinlet

m n nodes

o outsideoutlet

p pumps

w cooling water

wb wet bulb

m mean value

cn condensing zone


References


Water Systems





2209












781







28


128















134 pp 88-93


Appendix




follows










29


( ) ( ) ( ) ( ( ) ) (A1)

( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)


( ) ( ) ( )

( ) (A3)

( ) ( ( ) ( )) ( ) ( ( ) )

( ) ( )

(A4)

( ) ( ) ( ) ( ) ( )

( ( ) ) (A5)


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)




( ) 0 ( ) ( )

1 (A8)


30


A21 Cooler modeling











shell


( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)


( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (A11)


( ) ( ) ( )

h ( ) ( ) (A12)


31

S( ) h ( ) h ( )

( ) ( ) (A13)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(A16)


(A17) [15]

( ) w( )

( ) ( )

w( ) μw( )

w( )

(A17)


( ) ( ) ( ) ( ) ( ) ( )

( ) ( ( ) ) ( )

( ) ( ) ( ( ) ( )

)

(A18)


( ) ( ) ( )

w( ) ( ) ( ) (A19)


32

( ) ( )

w( ) n( ) (A20)

( ) ( )

w( ) ut( ) (A21)






( ) sum ( ) (A22)

( ) sum ( ) (A23)

( ) sum ( ) (A24)

( ) sum ( ) (A25)

( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) (A26)

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)



equation

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)


33


( ) sum ( ) ( ) (A29)

( ) sum ( ) sum ( ) ( ) (A30)

( ) sum ( ) ( ) (A31)

( ) sum ( ) sum ( ) ( ) (A32)

( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)

( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )

( )) ( ) (A34)










( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (A35)





34

( ) ( ) ( ) ( ) (A36)

( ) ( ( ) ) (A37)

( ) ( ) w ( )

( ) (A38)




S ( ) (

( ) ((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B1)




( ) ((sum

( )

) (sum ( ( ))

( )

)) (B2)



35

( ) ((sum

ut ( )

) (sum ( ( ))

ut ( )

)) (B3)




S ( ) (

( )

((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B4)


S ( ) (

( )

(sum ut( )

( )

)

sum ut( )

( )

) (B5)



( ) ((sum

( )

) (sum ( ( ))

( )

)) (B6)


36

( ) (sum ut( )

( )

) (B7)


in Appendix B)

( ) ( ( )

( ) ( ( ) ( ) ( )) )

(B8)

( ) ( )

( )

( )

( )

(B9)

( ) ( )

( )

( )

( )

(B10)

( ) ( )

( )

7 ( )

( )

(B11)

Where



Assumptions








equations [13]


( ) ( ) ( ) (C1)


37


( ) ( )

( ) ( ) (C2)

( ) n( )

( ) n ( ) (C3)

( ) ( ) ( ) ( ) (C4)

( ) ( ) ( ) ( ) (C5)




( ) ( ) ( )

( ) ( )

μ ( ) ( )

( )

(C6)

( ) ( )

( ) (C7)

( ) n( )

( ) ( ) (C8)





20


51 Conclusions






cooling requirement

























21


















52 Future work




areas listed below









22














cost







23

References





2209














Science 56(12) pp 3641-3658



pp 117ndash195






pp 49-54







6

Copyright Statement
























7

Acknowledgement

















8


11 Background
















9



























10




























11





towers







systems
















12







pressure




















13




























14












12 Motivation















15









simultaneously














included



16








turbines)



14 Thesis outline













17

Chapter 2






1


Cooling Towers



Abstract

















base case





2

Highlights




investigated

1 Introduction




















3



















4





























5





























6





























7



























8


cooling towers

























9

tower







(1)

( ) (1)





( ) (2)






10











(3)
















11




Figure 2 (d) is a







12



temperature



temperature (d)


13



( ) (4)










( )

w (5)




( )

w ( ) ( ) ( ) (6)


14



respectively


( ( ) ( ) ( )) (7)


( ( ) ( ) ( ))

(8)






( ) (9)






(10)


15

( ) (10)













equation (8)

( ) (11)




(12)


16









( ) (13)





(14)

( ) (15)

w

(16)





17



flowrate





temperature

(17)

(18)

w

w

w

(19)

(20)

(21)







18

( ) (22)



respectively

3 Model validation











towers [28]








19








α1 α2 α3 α4

95846 06568 -12569 -04216


β1 β2 β3 β4 β5

40099 -17177 08672 -21377 08165


γ1 γ2 γ3 γ4 γ5 γ6 γ7

-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00


20







y=x

y=x

R2=0992

R2=0996


21






No 1 2 3 4 5 6

Measured

data

(degC) 2933 3667 4100 3889 4033 3572

(degC) 2966 3192 3550 3111 3361 3311

(degC) 2111 2111 2388 2388 2667 2944

(kgs) 1186 1178 1157 1174 1157 1156

(kgs) 1132 1132 0881 1132 1008 1258

Calculated

data

(degC)

Measured 2433 2633 2800 2844 3044 3122

Correlation 2415 2642 2818 2851 3016 3106

Relative

difference () 073 -036 -065 -024 092 051

(10-2

kgkg

dry air)

Measured 2192 2835 3108 3223 3454 3301

Correlation 2168 2878 3119 3229 3419 3305

Relative

difference

()

111 -151 -037 -017 103 -011





4 Solution Method




22














5 Case Studies










change


23

51 Base case











Table 6




Ambient air

conditions

tdbi (degC) 3028 3028 3533 2950 2600

twbi (degC) 2565 2565 2944 2500 2250

wi (10

-2kgkg dry air)

190 190 239 183 158

ii (kJkg) 7913 7913 9688 7636 6645






Lower bound 4320


Lower bound 3600

Upper bound 17

Lower bound 07



24

52 Case study 1








Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan [17]

( )








25















Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Operating

conditions

Inlet water

flowrate (th) 7920 5760 5760 6280 5641 7137

Inlet dry air

flowrate (th) 7200 9187 9187 7533 9441 4996

Cooling

water

Inlet

temperature

(degC)

4100 4385 4385 4644 4351 4062

Outlet

temperature

(degC)

3020 2895 3166 2849 2676 3274 2830 2869

Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193


towers (MW) 1039 1041 858 1071 1188 1052 1039 1029


(MW) 9928 8079 10240 11442 9928



26

Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Make-up water

consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635

Power

consumption

(kW)

Fan 353 450 450 450 450 377 462 240

Pump 1631 1344 1344 1344 1344 1396 1333 1503

Total 1984 1794 1794 1794 1794 1773 1795 1743

Cost (poundh)

Make-up

water 522 536 473 547 587 561 532 490

Power 1983 1794 1794 1794 1794 1773 1795 1743

Total 2505 2330 2267 2341 2381 2334 2327 2233

53 Case study 2


















27






























28









slightly

6 Conclusions

















base case


29



















30

Nomenclature

Parameters







dry air)







Variables








air)


dry air)


dry air)





31

Mep Merkel number







p pressure (Pa)



temperature (Pa)




T temperature K











ηp pump efficiency

Subscripts

a air

db dry-bulb

e evaporation

f fans

i inlet


32

m make-up water

o outlet

p pumps

P Poppe method

s saturation

v vapor

w cooling water

wb wet-bulb

References








New York USA















Mi 15




33
















Oklahoma









6370 EPRI Palo Alto








Amsterdam







34

Appendix

1) Data information




No twi

(degC)

two

(degC)

tdbi

(degC)

twbi

(degC)

wi

(kgkg dry air)

ma

(kgs)

mwi

(kgs)

wo

(kgkg dry air)

1 4144 2600 3411 2111 00104 1158 0754 00284

2 2872 2422 2900 2111 00125 1186 1259 00215

3 3450 2622 3050 2111 00119 1186 1259 00271

4 3878 2933 3500 2667 00188 1264 1008 00323

5 3878 2933 3500 2667 00188 1250 1008 00323

6 3967 2622 3400 2111 00105 1174 0881 00284

7 3500 2867 3461 2667 00190 1156 0881 00285

8 4361 2789 3500 2388 00141 1158 0754 00316

9 4306 2972 3572 2667 00185 1155 0754 00337

10 3806 3089 3594 2944 00236 1142 0754 00321

11 4778 3217 3617 2944 00235 1142 0754 00400

12 3378 2472 3250 2111 00110 1179 0881 00238

13 4144 3000 3617 2667 00183 1156 0881 00340

14 4061 3172 3417 2944 00244 1147 0881 00359

15 4350 3217 3533 2944 00239 1147 0881 00383

16 3672 3139 3272 2944 00250 1155 1008 00329

17 3322 2550 2883 2111 00126 1186 1008 00244

18 3844 2678 2950 2111 00123 1186 1008 00290

19 3661 2944 3250 2667 00199 1161 1132 00314

20 4100 3050 3294 2667 00197 1161 1132 00364

21 3611 2972 3111 2667 00204 1166 1258 00314

22 4022 3078 3133 2667 00203 1166 1258 00364

23 3956 3011 3206 2667 00200 1008 1008 00349

24 3950 3006 3106 2667 00205 1051 1008 00344

25 3944 3000 3333 2667 00195 1108 1008 00341

26 3978 2967 3167 2667 00202 0947 1008 00357





35











w

( w ) w

w ( ) w ( w ) v- ( w ) w (A1)

w

w

( w ) w

w ( ) w ( w ) v- ( w ) w

(A2)

w

( w ) ( w ) ( ) v ( w ) w (A3)







w

w

(

w ( )) (A4)


36


w w

w

0 w w

w 1

(A5)


w

(A6)



w

( ) (A7)



w

(A8)


coefficients



( ) [ ( )] (A9)


37




(A11)

7

7


times [ 7 ( 7 frasl ) ] (A12)









( w )

w w

( w )

77 w (A16)


38



( ) ( ) ( ) (A17)





18

Chapter 3






1


Water Systems



Abstract


















the base case


optimisation




2

Highlights



are considered


into account



investigated

1 Introduction
















3



















4



























5












turn













sectors


6




























7






























8





























9
























considered


10

























11





the shell side









is variable












12





arrangement


13





(1) Mass balance




( ) sum ( ) (1)





( ) sum ( ) (2)



( ) sum ( ) (3)

( ) sum ( ) (4)


14


(2) Energy balance




( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

(5)





a in Figure 2


( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)



leaving cooler q



( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)


15
















(1) Mass balance



( ) sum ( ) ( ) (8)




16



equation (9)

( ) sum ( ) sum ( ) ( ) (9)






respectively

( ) sum ( ) ( ) (10)

( ) sum ( ) sum ( ) ( ) (11)




(2) Energy balance



( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)


17




leaving cooler k



( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )

(13)






point a in Figure 2










18










( ) ( )

( )

w( ) ( ) ( )

( )

( )

w( ) ( ) (14)







19


constant



( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (15)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (k q) (16)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (17)


20






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (18)







( ) ( ) ( ) (19)









21

232 Pump modelling



cooling water






(20) - (28)



( ) ( ) (20)

( ) ( ) (21)







22

( ) ( ) (22)



than 28 degC [33]

( ) (23)


( ) (24)




( ) ( ) ( )

(25)

( ) ( ) ( )

(26)


( ) ( ) (27)


equation (28)

( ) ( ) (28)


23







Min sum ( ) sum ( ( ) ( )) (29)




3 Solution Method













24



4 Case Studies











Process

streams

Inlet temp

degC

Outlet temp

degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance

msup2degCW

C1 60 Upper 450

1704 987 000018 Lower 420

C2 120 Upper 795

482 286 000018 Lower 750

C3 95 500 586 732 000018

C4 100 Upper 595

707 448 000035 Lower 550

C5 105 Upper 545

447 748 000053 Lower 500

C6 90 Upper 595

1004 488 000018 Lower 550

C7 75 Upper 445

602 913 000018 Lower 400

C8 150 Upper 1000

394 180 000018 Lower 950

C9 125 Upper 645

513 346 000053 Lower 600


25




Coolers Area

(m^2)

Number

of tubes

Tube

passes

Tube inside

diameter

(mm)

Tube outside

diameter

(mm)

Length of

tube

(m)

Thermal


wall (wmdegC)

C1 3506 1006 2 15 19 60 50

C2 1589 610 2 15 19 45 50

C3 2135 610 2 15 19 60 50

C4 2539 980 4 15 19 45 50

C5 1685 366 2 20 25 60 50

C6 2606 1006 2 15 19 45 50

C7 2004 588 4 20 25 45 50

C8 1641 468 2 15 19 60 50

C9 2539 980 4 15 19 45 50




Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002

S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002

S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002

S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002

S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002

S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002

S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002


26

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002

S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002

S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002

S2(C1)

-S1(C2) 1200 023 00002

S2(C6)

-S1(C8) 1300 023 00002




41 Base case












Make-up water


(degC)

Wet-bulb

temperature (degC)

Humidity (kgkg

dry air)

Enthalpy

(kJkg)

318 271 205 855 318


27


42 Case study 1




Units Models

Cooling

towers 1

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )


28

Units Models

2

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )

Pumps

1

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

2

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

Fans

1 ( ) ( ) ( )

( )

2 ( ) ( ) ( )

( )










shown in Table 7


29

























30


the base case


Cooling

towers



The approach

(degC)






Total 409 403 -06

Power

consumption

(kW)

Pumps



Total 4184 3829 -355

Fans



Total 865 882 17

Total 5049 4711 -338

Cost

Water(poundh) 1227 1209 -018





Hot streams


(degC)


C1 450 450

C2 795 795

C3 500 500

C4 595 595


31

Hot streams


(degC)


C5 545 545

C6 595 595

C7 445 445

C8 1000 1000

C9 645 645

43 Case study 2








stated in Table 1



Ambient air

conditions











32


























degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

1

Case 1 458 800 510 604 555 603 455 1006 654

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -08 -05 -10 -09 -10 -08 -10 -06 -09


33


degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

2

Case 1 439 787 485 582 530 584 430 991 631

Optimisation 450 766 500 595 545 592 441 982 644

Difference 10 -23 14 12 14 07 10 05 -01

Condition

3

Case 1 454 798 505 599 550 599 450 1003 650

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -04 -03 -05 -04 -05 -04 -05 -03 -05











Table 9











34





























35







convection


conditions


36




Cooling

towers

Make-up water

flowrate (th)

1 231 241 10 217 207 -10 220 226 06

2 189 195 06 176 168 -08 180 183 03



(MW) 097 071 -026 352 385 033 217 201 -016

Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045

Pumps Power

consumption (kW)

1 2173 2469 296 2173 2307 134 2173 2197 24

2 1657 1951 294 1657 1769 112 1657 1723 66

Total 3830 4420 590 3830 4076 246 3830 3920 90

Fans Power

consumption (kW)

1 460 639 179 444 305 -139 452 597 145

2 419 538 119 405 239 -166 412 496 84

Total 879 1177 298 849 544 -305 864 1093 229


Cost (poundh)

Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027

Power 4709 5597 888 4679 4620 -059 4694 5013 319

Total 5969 6905 936 5858 5745 -113 5894 6240 346


37

5 Conclusions

























in the base case








38





cost increases









Nomenclature

Sets


k set of coolers

q set of coolers

Parameters













C)


39







C W)


C W)













a1-a3 coefficients

b1-b3 coefficients

Variables










degC

-1)





40
























(degC)













41









C)



Greek Symbols

α coefficients

β coefficients

γ coefficients


s-1

)









Subscripts

a air

db dry bulb

f fans

i insideinlet

o outsideoutlet

p pumps

s1-s6 nodes

w cooling water

wb wet bulb


42

References








2209


Cooling Towers


128












914-923



pp 1-7











43












1033-1043




InTech





Science 56(12) pp 3641-3658





pp 117ndash195



pp 540ndash551









44







134 pp 88-93


York USA



Appendix

Appendix A Models



( ) ( ) ( )

( ) (A1)





( ) ( ( ) ( )) ( ) ( ( ) ) ( )

( ) (A2)






45


respectively


( ) ( ) ( ) ( ) ( )

( ( ) ) (A3)




bulb temperature



method


( ) ( ) ( ) ( ( ) ) (A4)


( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)






respectively


46


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)





( ) 0 ( ) ( )

1 (A8)



flowrate



( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)







47


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)






( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (B3)







( ) ( ) ( )

h ( ) ( ) (B4)

S( ) h ( ) h ( )

( ) ( ) (B5)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



48


Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(B8)




respectively


( ) w( )

( ) ( )

w ( ) μw( )

w( )

(B9)






( ) 7 ( ) R ( ) 8 ( ) w( ) w( )

( ) ( ( ) ) ( ) ( )

( ) ( ( ) ( )

) (B10)







49


( ) ( ) ( )

w( ) ( ) ( ) (B11)






( ) ( )

w( ) n( ) (B12)





( ) ( )

w( ) ut( ) (B13)











50




No 1 2 3 4 5

ht

(W(m2 K))

Wang 12072 57689 14026 15846 75662

HTRI 12993 56440 14700 16169 73632

Relative error () -709 221 -459 -200 276

∆Pt

(kPa)

Wang 688 287 886 693 261

HTRI 712 297 868 735 268

Relative error () -337 -337 207 -571 -261



( ) ( ) ( ) ( ) (C1)




( ) ( ( ) ) (C2)



( ) ( ) w ( )

( ) (C3)


51








No 1 2 3 4 5


Specific heat

(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223

Thermal

conductivity

(WmK)

0137 0133 0633 0623 0123 0106 0089 0091 0087 0675

Viscosity

(mPa s) 040 360 062 071 289 120 033 110 180 030

Density

(kgm3) 785 850 991 994 820 790 702 801 786 957

Flow rate

(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390

Inlet

temperature

(degC)

2000 380 480 330 517 2100 2270 1120 1700 770

Fouling

resistance (10-4

m2KW)

35 53 70 40 35 35 53 53 88 53


52


No 1 2 3 4 5

Tube pitch (m) 003175 002500 002540 003125 002500

Number of tubes 124 3983 528 1532 582


Tube length L (m) 4270 9000 5422 9000 7100



Tube pattern





nozzle (m) 01023 04380 01280 03370 01540


nozzle (m) 01023 04380 01280 03370 01540


19

Chapter 4







1



Condensing Turbines



Abstract


























2

Highlights




considered


performance

1 Introduction

























3



































4


































5


































6

2 Model Development

















( ) n( ) ut( )

n( ) ( ) (1)






equation (1)


7

( ) ( ) ( ( ) ( )) ( ) (2)



of steam is given












(2) Saturated steam





S ( ) ( ) S ( ) ( ( )) S ( ) (3)






8



( ) ( ) ( ) ( ( )) ( ) (4)







( ) ut( ) ( )

( ) ( ) (5)









( ) ( ) ( ) ( ( ) ( )) (6)





9















( ) ( ) (7)














10











( ) ( ut( ) ( )) ( ( ) ( ))

ut( ) t ( )

( ) t ( )

(8)

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(9)




( ) ( ) ( ) (10)



turbine i







11

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(11)







Max (12)





sum ( ) (13)




sum ( ) sum ( ( ) ( )) (14)




12

3 Solution Method



















4 Case Studies











13



entering coolers

degC

Temperature leaving

coolers degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance


C1 998 650 600 735 1864 000035

C2 847 600 550 1167 2375 000035

C3 781 650 600 4367 3625 000035

C4 787 600 550 3356 4747 000035

C5 951 600 550 669 2106 000035

C6 952 600 550 2159 4747 000035

C7 637 450 400 2492 7036 000018

C8 676 450 400 1612 7347 000018

C9 642 500 450 3050 4686 000018

C10 742 500 450 2198 3903 000018

C11 635 450 400 2955 8277 000018

C12 696 500 450 2201 4820 000018



Coolers Number of

tubes

Tube

passes

Tube

diameter

(mm)

Tube

length

(m)

Cross sectional

area (m2)

Heat transfer

area (m2)

C1 1234 2 19times2 6 01090 4346

C2 742 2 25times2 9 01285 5184

C3 1452 2 19times2 9 01290 7642

C4 1452 2 19times2 9 01290 7642

C5 588 2 25times2 9 01018 4108

C6 1452 2 19times2 9 01290 7642

C7 1424 4 19times2 9 00745 7495

C8 988 2 19times2 9 00873 5249

C9 1234 2 19times2 9 01090 6556

C10 1452 2 19times2 9 01290 7642

C11 1452 2 19times2 9 01290 7642

C12 860 4 25times2 9 00745 5956


14



provided


Inlet steam


Pressure (bara) 40


Turbine





Condenser

Area (m2) 1984


Tube passes 1


Tube length (m) 836

Tube pitch (m) 0032





Ambient air

conditions







Power(poundkWh) 01



15



Cooling towers

Water mass flowrate

(th)

Upper bound 9000

Lower bound 5000

Air mass flowrate

(th)

Upper bound 12600

Lower bound 5000



Upper bound 15

Lower bound 07



Coolers



Lower bound 05






respectively

41 Base case









16




1

Case

2

Case

3

Cooling

water system

Operation

Circulating water

flowrate (th) 7560 6047 9000 6414

Air flowrate (th) 8237 7267 12053 7258


cooling water into

the cooling tower

(degC)

430 456 405 449

Outlet temperature

of cooling water

from the cooling

tower (degC)

320 319 313 321

Water

consumption

Make-up water

(th) 183 181 187 181

Power

consumption

Fans (kW) 398 351 582 350

Pumps (kW) 1568 1372 1877 1411

Total (kW) 1966 1723 2459 1762


Condensing

turbine






17


Base

case

Case

1

Case

2

Case

3

C1 640 650 648 650

C2 592 600 600 600

C3 643 650 650 650

C4 592 600 600 600

C5 590 600 600 600

C6 592 600 600 600

C7 450 450 450 450

C8 440 450 450 450

C9 500 500 500 500

C10 500 500 500 500

C11 445 450 450 450

C12 500 500 500 500


42 Case study 1




Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan

( )

Processes


Cases


18



















19


cooling requirement

43 Case study 2
















20






02 degC

44 Case study 3






Table 6 and Table 7



21

















45 Discussion

















22









5 Conclusions
























23












Nomenclature

Sets



k q set of coolers

Parameters















C)




24












C W)


C W)









a1-a3 coefficients

b1-b3 coefficients

Variables







C)



C)








25






























(oC)










26












C)


C)


C)







Greek Symbols



s-1

)


s-1

)












Subscripts

a air


27

db dry bulb

f fans

i insideinlet

m n nodes

o outsideoutlet

p pumps

w cooling water

wb wet bulb

m mean value

cn condensing zone


References


Water Systems





2209












781







28


128















134 pp 88-93


Appendix




follows










29


( ) ( ) ( ) ( ( ) ) (A1)

( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)


( ) ( ) ( )

( ) (A3)

( ) ( ( ) ( )) ( ) ( ( ) )

( ) ( )

(A4)

( ) ( ) ( ) ( ) ( )

( ( ) ) (A5)


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)




( ) 0 ( ) ( )

1 (A8)


30


A21 Cooler modeling











shell


( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)


( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (A11)


( ) ( ) ( )

h ( ) ( ) (A12)


31

S( ) h ( ) h ( )

( ) ( ) (A13)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(A16)


(A17) [15]

( ) w( )

( ) ( )

w( ) μw( )

w( )

(A17)


( ) ( ) ( ) ( ) ( ) ( )

( ) ( ( ) ) ( )

( ) ( ) ( ( ) ( )

)

(A18)


( ) ( ) ( )

w( ) ( ) ( ) (A19)


32

( ) ( )

w( ) n( ) (A20)

( ) ( )

w( ) ut( ) (A21)






( ) sum ( ) (A22)

( ) sum ( ) (A23)

( ) sum ( ) (A24)

( ) sum ( ) (A25)

( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) (A26)

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)



equation

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)


33


( ) sum ( ) ( ) (A29)

( ) sum ( ) sum ( ) ( ) (A30)

( ) sum ( ) ( ) (A31)

( ) sum ( ) sum ( ) ( ) (A32)

( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)

( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )

( )) ( ) (A34)










( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (A35)





34

( ) ( ) ( ) ( ) (A36)

( ) ( ( ) ) (A37)

( ) ( ) w ( )

( ) (A38)




S ( ) (

( ) ((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B1)




( ) ((sum

( )

) (sum ( ( ))

( )

)) (B2)



35

( ) ((sum

ut ( )

) (sum ( ( ))

ut ( )

)) (B3)




S ( ) (

( )

((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B4)


S ( ) (

( )

(sum ut( )

( )

)

sum ut( )

( )

) (B5)



( ) ((sum

( )

) (sum ( ( ))

( )

)) (B6)


36

( ) (sum ut( )

( )

) (B7)


in Appendix B)

( ) ( ( )

( ) ( ( ) ( ) ( )) )

(B8)

( ) ( )

( )

( )

( )

(B9)

( ) ( )

( )

( )

( )

(B10)

( ) ( )

( )

7 ( )

( )

(B11)

Where



Assumptions








equations [13]


( ) ( ) ( ) (C1)


37


( ) ( )

( ) ( ) (C2)

( ) n( )

( ) n ( ) (C3)

( ) ( ) ( ) ( ) (C4)

( ) ( ) ( ) ( ) (C5)




( ) ( ) ( )

( ) ( )

μ ( ) ( )

( )

(C6)

( ) ( )

( ) (C7)

( ) n( )

( ) ( ) (C8)





20


51 Conclusions






cooling requirement

























21


















52 Future work




areas listed below









22














cost







23

References





2209














Science 56(12) pp 3641-3658



pp 117ndash195






pp 49-54







7

Acknowledgement

















8


11 Background
















9



























10




























11





towers







systems
















12







pressure




















13




























14












12 Motivation















15









simultaneously














included



16








turbines)



14 Thesis outline













17

Chapter 2






1


Cooling Towers



Abstract

















base case





2

Highlights




investigated

1 Introduction




















3



















4





























5





























6





























7



























8


cooling towers

























9

tower







(1)

( ) (1)





( ) (2)






10











(3)
















11




Figure 2 (d) is a







12



temperature



temperature (d)


13



( ) (4)










( )

w (5)




( )

w ( ) ( ) ( ) (6)


14



respectively


( ( ) ( ) ( )) (7)


( ( ) ( ) ( ))

(8)






( ) (9)






(10)


15

( ) (10)













equation (8)

( ) (11)




(12)


16









( ) (13)





(14)

( ) (15)

w

(16)





17



flowrate





temperature

(17)

(18)

w

w

w

(19)

(20)

(21)







18

( ) (22)



respectively

3 Model validation











towers [28]








19








α1 α2 α3 α4

95846 06568 -12569 -04216


β1 β2 β3 β4 β5

40099 -17177 08672 -21377 08165


γ1 γ2 γ3 γ4 γ5 γ6 γ7

-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00


20







y=x

y=x

R2=0992

R2=0996


21






No 1 2 3 4 5 6

Measured

data

(degC) 2933 3667 4100 3889 4033 3572

(degC) 2966 3192 3550 3111 3361 3311

(degC) 2111 2111 2388 2388 2667 2944

(kgs) 1186 1178 1157 1174 1157 1156

(kgs) 1132 1132 0881 1132 1008 1258

Calculated

data

(degC)

Measured 2433 2633 2800 2844 3044 3122

Correlation 2415 2642 2818 2851 3016 3106

Relative

difference () 073 -036 -065 -024 092 051

(10-2

kgkg

dry air)

Measured 2192 2835 3108 3223 3454 3301

Correlation 2168 2878 3119 3229 3419 3305

Relative

difference

()

111 -151 -037 -017 103 -011





4 Solution Method




22














5 Case Studies










change


23

51 Base case











Table 6




Ambient air

conditions

tdbi (degC) 3028 3028 3533 2950 2600

twbi (degC) 2565 2565 2944 2500 2250

wi (10

-2kgkg dry air)

190 190 239 183 158

ii (kJkg) 7913 7913 9688 7636 6645






Lower bound 4320


Lower bound 3600

Upper bound 17

Lower bound 07



24

52 Case study 1








Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan [17]

( )








25















Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Operating

conditions

Inlet water

flowrate (th) 7920 5760 5760 6280 5641 7137

Inlet dry air

flowrate (th) 7200 9187 9187 7533 9441 4996

Cooling

water

Inlet

temperature

(degC)

4100 4385 4385 4644 4351 4062

Outlet

temperature

(degC)

3020 2895 3166 2849 2676 3274 2830 2869

Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193


towers (MW) 1039 1041 858 1071 1188 1052 1039 1029


(MW) 9928 8079 10240 11442 9928



26

Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Make-up water

consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635

Power

consumption

(kW)

Fan 353 450 450 450 450 377 462 240

Pump 1631 1344 1344 1344 1344 1396 1333 1503

Total 1984 1794 1794 1794 1794 1773 1795 1743

Cost (poundh)

Make-up

water 522 536 473 547 587 561 532 490

Power 1983 1794 1794 1794 1794 1773 1795 1743

Total 2505 2330 2267 2341 2381 2334 2327 2233

53 Case study 2


















27






























28









slightly

6 Conclusions

















base case


29



















30

Nomenclature

Parameters







dry air)







Variables








air)


dry air)


dry air)





31

Mep Merkel number







p pressure (Pa)



temperature (Pa)




T temperature K











ηp pump efficiency

Subscripts

a air

db dry-bulb

e evaporation

f fans

i inlet


32

m make-up water

o outlet

p pumps

P Poppe method

s saturation

v vapor

w cooling water

wb wet-bulb

References








New York USA















Mi 15




33
















Oklahoma









6370 EPRI Palo Alto








Amsterdam







34

Appendix

1) Data information




No twi

(degC)

two

(degC)

tdbi

(degC)

twbi

(degC)

wi

(kgkg dry air)

ma

(kgs)

mwi

(kgs)

wo

(kgkg dry air)

1 4144 2600 3411 2111 00104 1158 0754 00284

2 2872 2422 2900 2111 00125 1186 1259 00215

3 3450 2622 3050 2111 00119 1186 1259 00271

4 3878 2933 3500 2667 00188 1264 1008 00323

5 3878 2933 3500 2667 00188 1250 1008 00323

6 3967 2622 3400 2111 00105 1174 0881 00284

7 3500 2867 3461 2667 00190 1156 0881 00285

8 4361 2789 3500 2388 00141 1158 0754 00316

9 4306 2972 3572 2667 00185 1155 0754 00337

10 3806 3089 3594 2944 00236 1142 0754 00321

11 4778 3217 3617 2944 00235 1142 0754 00400

12 3378 2472 3250 2111 00110 1179 0881 00238

13 4144 3000 3617 2667 00183 1156 0881 00340

14 4061 3172 3417 2944 00244 1147 0881 00359

15 4350 3217 3533 2944 00239 1147 0881 00383

16 3672 3139 3272 2944 00250 1155 1008 00329

17 3322 2550 2883 2111 00126 1186 1008 00244

18 3844 2678 2950 2111 00123 1186 1008 00290

19 3661 2944 3250 2667 00199 1161 1132 00314

20 4100 3050 3294 2667 00197 1161 1132 00364

21 3611 2972 3111 2667 00204 1166 1258 00314

22 4022 3078 3133 2667 00203 1166 1258 00364

23 3956 3011 3206 2667 00200 1008 1008 00349

24 3950 3006 3106 2667 00205 1051 1008 00344

25 3944 3000 3333 2667 00195 1108 1008 00341

26 3978 2967 3167 2667 00202 0947 1008 00357





35











w

( w ) w

w ( ) w ( w ) v- ( w ) w (A1)

w

w

( w ) w

w ( ) w ( w ) v- ( w ) w

(A2)

w

( w ) ( w ) ( ) v ( w ) w (A3)







w

w

(

w ( )) (A4)


36


w w

w

0 w w

w 1

(A5)


w

(A6)



w

( ) (A7)



w

(A8)


coefficients



( ) [ ( )] (A9)


37




(A11)

7

7


times [ 7 ( 7 frasl ) ] (A12)









( w )

w w

( w )

77 w (A16)


38



( ) ( ) ( ) (A17)





18

Chapter 3






1


Water Systems



Abstract


















the base case


optimisation




2

Highlights



are considered


into account



investigated

1 Introduction
















3



















4



























5












turn













sectors


6




























7






























8





























9
























considered


10

























11





the shell side









is variable












12





arrangement


13





(1) Mass balance




( ) sum ( ) (1)





( ) sum ( ) (2)



( ) sum ( ) (3)

( ) sum ( ) (4)


14


(2) Energy balance




( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

(5)





a in Figure 2


( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)



leaving cooler q



( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)


15
















(1) Mass balance



( ) sum ( ) ( ) (8)




16



equation (9)

( ) sum ( ) sum ( ) ( ) (9)






respectively

( ) sum ( ) ( ) (10)

( ) sum ( ) sum ( ) ( ) (11)




(2) Energy balance



( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)


17




leaving cooler k



( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )

(13)






point a in Figure 2










18










( ) ( )

( )

w( ) ( ) ( )

( )

( )

w( ) ( ) (14)







19


constant



( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (15)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (k q) (16)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (17)


20






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (18)







( ) ( ) ( ) (19)









21

232 Pump modelling



cooling water






(20) - (28)



( ) ( ) (20)

( ) ( ) (21)







22

( ) ( ) (22)



than 28 degC [33]

( ) (23)


( ) (24)




( ) ( ) ( )

(25)

( ) ( ) ( )

(26)


( ) ( ) (27)


equation (28)

( ) ( ) (28)


23







Min sum ( ) sum ( ( ) ( )) (29)




3 Solution Method













24



4 Case Studies











Process

streams

Inlet temp

degC

Outlet temp

degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance

msup2degCW

C1 60 Upper 450

1704 987 000018 Lower 420

C2 120 Upper 795

482 286 000018 Lower 750

C3 95 500 586 732 000018

C4 100 Upper 595

707 448 000035 Lower 550

C5 105 Upper 545

447 748 000053 Lower 500

C6 90 Upper 595

1004 488 000018 Lower 550

C7 75 Upper 445

602 913 000018 Lower 400

C8 150 Upper 1000

394 180 000018 Lower 950

C9 125 Upper 645

513 346 000053 Lower 600


25




Coolers Area

(m^2)

Number

of tubes

Tube

passes

Tube inside

diameter

(mm)

Tube outside

diameter

(mm)

Length of

tube

(m)

Thermal


wall (wmdegC)

C1 3506 1006 2 15 19 60 50

C2 1589 610 2 15 19 45 50

C3 2135 610 2 15 19 60 50

C4 2539 980 4 15 19 45 50

C5 1685 366 2 20 25 60 50

C6 2606 1006 2 15 19 45 50

C7 2004 588 4 20 25 45 50

C8 1641 468 2 15 19 60 50

C9 2539 980 4 15 19 45 50




Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002

S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002

S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002

S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002

S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002

S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002

S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002


26

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002

S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002

S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002

S2(C1)

-S1(C2) 1200 023 00002

S2(C6)

-S1(C8) 1300 023 00002




41 Base case












Make-up water


(degC)

Wet-bulb

temperature (degC)

Humidity (kgkg

dry air)

Enthalpy

(kJkg)

318 271 205 855 318


27


42 Case study 1




Units Models

Cooling

towers 1

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )


28

Units Models

2

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )

Pumps

1

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

2

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

Fans

1 ( ) ( ) ( )

( )

2 ( ) ( ) ( )

( )










shown in Table 7


29

























30


the base case


Cooling

towers



The approach

(degC)






Total 409 403 -06

Power

consumption

(kW)

Pumps



Total 4184 3829 -355

Fans



Total 865 882 17

Total 5049 4711 -338

Cost

Water(poundh) 1227 1209 -018





Hot streams


(degC)


C1 450 450

C2 795 795

C3 500 500

C4 595 595


31

Hot streams


(degC)


C5 545 545

C6 595 595

C7 445 445

C8 1000 1000

C9 645 645

43 Case study 2








stated in Table 1



Ambient air

conditions











32


























degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

1

Case 1 458 800 510 604 555 603 455 1006 654

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -08 -05 -10 -09 -10 -08 -10 -06 -09


33


degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

2

Case 1 439 787 485 582 530 584 430 991 631

Optimisation 450 766 500 595 545 592 441 982 644

Difference 10 -23 14 12 14 07 10 05 -01

Condition

3

Case 1 454 798 505 599 550 599 450 1003 650

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -04 -03 -05 -04 -05 -04 -05 -03 -05











Table 9











34





























35







convection


conditions


36




Cooling

towers

Make-up water

flowrate (th)

1 231 241 10 217 207 -10 220 226 06

2 189 195 06 176 168 -08 180 183 03



(MW) 097 071 -026 352 385 033 217 201 -016

Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045

Pumps Power

consumption (kW)

1 2173 2469 296 2173 2307 134 2173 2197 24

2 1657 1951 294 1657 1769 112 1657 1723 66

Total 3830 4420 590 3830 4076 246 3830 3920 90

Fans Power

consumption (kW)

1 460 639 179 444 305 -139 452 597 145

2 419 538 119 405 239 -166 412 496 84

Total 879 1177 298 849 544 -305 864 1093 229


Cost (poundh)

Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027

Power 4709 5597 888 4679 4620 -059 4694 5013 319

Total 5969 6905 936 5858 5745 -113 5894 6240 346


37

5 Conclusions

























in the base case








38





cost increases









Nomenclature

Sets


k set of coolers

q set of coolers

Parameters













C)


39







C W)


C W)













a1-a3 coefficients

b1-b3 coefficients

Variables










degC

-1)





40
























(degC)













41









C)



Greek Symbols

α coefficients

β coefficients

γ coefficients


s-1

)









Subscripts

a air

db dry bulb

f fans

i insideinlet

o outsideoutlet

p pumps

s1-s6 nodes

w cooling water

wb wet bulb


42

References








2209


Cooling Towers


128












914-923



pp 1-7











43












1033-1043




InTech





Science 56(12) pp 3641-3658





pp 117ndash195



pp 540ndash551









44







134 pp 88-93


York USA



Appendix

Appendix A Models



( ) ( ) ( )

( ) (A1)





( ) ( ( ) ( )) ( ) ( ( ) ) ( )

( ) (A2)






45


respectively


( ) ( ) ( ) ( ) ( )

( ( ) ) (A3)




bulb temperature



method


( ) ( ) ( ) ( ( ) ) (A4)


( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)






respectively


46


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)





( ) 0 ( ) ( )

1 (A8)



flowrate



( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)







47


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)






( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (B3)







( ) ( ) ( )

h ( ) ( ) (B4)

S( ) h ( ) h ( )

( ) ( ) (B5)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



48


Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(B8)




respectively


( ) w( )

( ) ( )

w ( ) μw( )

w( )

(B9)






( ) 7 ( ) R ( ) 8 ( ) w( ) w( )

( ) ( ( ) ) ( ) ( )

( ) ( ( ) ( )

) (B10)







49


( ) ( ) ( )

w( ) ( ) ( ) (B11)






( ) ( )

w( ) n( ) (B12)





( ) ( )

w( ) ut( ) (B13)











50




No 1 2 3 4 5

ht

(W(m2 K))

Wang 12072 57689 14026 15846 75662

HTRI 12993 56440 14700 16169 73632

Relative error () -709 221 -459 -200 276

∆Pt

(kPa)

Wang 688 287 886 693 261

HTRI 712 297 868 735 268

Relative error () -337 -337 207 -571 -261



( ) ( ) ( ) ( ) (C1)




( ) ( ( ) ) (C2)



( ) ( ) w ( )

( ) (C3)


51








No 1 2 3 4 5


Specific heat

(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223

Thermal

conductivity

(WmK)

0137 0133 0633 0623 0123 0106 0089 0091 0087 0675

Viscosity

(mPa s) 040 360 062 071 289 120 033 110 180 030

Density

(kgm3) 785 850 991 994 820 790 702 801 786 957

Flow rate

(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390

Inlet

temperature

(degC)

2000 380 480 330 517 2100 2270 1120 1700 770

Fouling

resistance (10-4

m2KW)

35 53 70 40 35 35 53 53 88 53


52


No 1 2 3 4 5

Tube pitch (m) 003175 002500 002540 003125 002500

Number of tubes 124 3983 528 1532 582


Tube length L (m) 4270 9000 5422 9000 7100



Tube pattern





nozzle (m) 01023 04380 01280 03370 01540


nozzle (m) 01023 04380 01280 03370 01540


19

Chapter 4







1



Condensing Turbines



Abstract


























2

Highlights




considered


performance

1 Introduction

























3



































4


































5


































6

2 Model Development

















( ) n( ) ut( )

n( ) ( ) (1)






equation (1)


7

( ) ( ) ( ( ) ( )) ( ) (2)



of steam is given












(2) Saturated steam





S ( ) ( ) S ( ) ( ( )) S ( ) (3)






8



( ) ( ) ( ) ( ( )) ( ) (4)







( ) ut( ) ( )

( ) ( ) (5)









( ) ( ) ( ) ( ( ) ( )) (6)





9















( ) ( ) (7)














10











( ) ( ut( ) ( )) ( ( ) ( ))

ut( ) t ( )

( ) t ( )

(8)

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(9)




( ) ( ) ( ) (10)



turbine i







11

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(11)







Max (12)





sum ( ) (13)




sum ( ) sum ( ( ) ( )) (14)




12

3 Solution Method



















4 Case Studies











13



entering coolers

degC

Temperature leaving

coolers degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance


C1 998 650 600 735 1864 000035

C2 847 600 550 1167 2375 000035

C3 781 650 600 4367 3625 000035

C4 787 600 550 3356 4747 000035

C5 951 600 550 669 2106 000035

C6 952 600 550 2159 4747 000035

C7 637 450 400 2492 7036 000018

C8 676 450 400 1612 7347 000018

C9 642 500 450 3050 4686 000018

C10 742 500 450 2198 3903 000018

C11 635 450 400 2955 8277 000018

C12 696 500 450 2201 4820 000018



Coolers Number of

tubes

Tube

passes

Tube

diameter

(mm)

Tube

length

(m)

Cross sectional

area (m2)

Heat transfer

area (m2)

C1 1234 2 19times2 6 01090 4346

C2 742 2 25times2 9 01285 5184

C3 1452 2 19times2 9 01290 7642

C4 1452 2 19times2 9 01290 7642

C5 588 2 25times2 9 01018 4108

C6 1452 2 19times2 9 01290 7642

C7 1424 4 19times2 9 00745 7495

C8 988 2 19times2 9 00873 5249

C9 1234 2 19times2 9 01090 6556

C10 1452 2 19times2 9 01290 7642

C11 1452 2 19times2 9 01290 7642

C12 860 4 25times2 9 00745 5956


14



provided


Inlet steam


Pressure (bara) 40


Turbine





Condenser

Area (m2) 1984


Tube passes 1


Tube length (m) 836

Tube pitch (m) 0032





Ambient air

conditions







Power(poundkWh) 01



15



Cooling towers

Water mass flowrate

(th)

Upper bound 9000

Lower bound 5000

Air mass flowrate

(th)

Upper bound 12600

Lower bound 5000



Upper bound 15

Lower bound 07



Coolers



Lower bound 05






respectively

41 Base case









16




1

Case

2

Case

3

Cooling

water system

Operation

Circulating water

flowrate (th) 7560 6047 9000 6414

Air flowrate (th) 8237 7267 12053 7258


cooling water into

the cooling tower

(degC)

430 456 405 449

Outlet temperature

of cooling water

from the cooling

tower (degC)

320 319 313 321

Water

consumption

Make-up water

(th) 183 181 187 181

Power

consumption

Fans (kW) 398 351 582 350

Pumps (kW) 1568 1372 1877 1411

Total (kW) 1966 1723 2459 1762


Condensing

turbine






17


Base

case

Case

1

Case

2

Case

3

C1 640 650 648 650

C2 592 600 600 600

C3 643 650 650 650

C4 592 600 600 600

C5 590 600 600 600

C6 592 600 600 600

C7 450 450 450 450

C8 440 450 450 450

C9 500 500 500 500

C10 500 500 500 500

C11 445 450 450 450

C12 500 500 500 500


42 Case study 1




Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan

( )

Processes


Cases


18



















19


cooling requirement

43 Case study 2
















20






02 degC

44 Case study 3






Table 6 and Table 7



21

















45 Discussion

















22









5 Conclusions
























23












Nomenclature

Sets



k q set of coolers

Parameters















C)




24












C W)


C W)









a1-a3 coefficients

b1-b3 coefficients

Variables







C)



C)








25






























(oC)










26












C)


C)


C)







Greek Symbols



s-1

)


s-1

)












Subscripts

a air


27

db dry bulb

f fans

i insideinlet

m n nodes

o outsideoutlet

p pumps

w cooling water

wb wet bulb

m mean value

cn condensing zone


References


Water Systems





2209












781







28


128















134 pp 88-93


Appendix




follows










29


( ) ( ) ( ) ( ( ) ) (A1)

( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)


( ) ( ) ( )

( ) (A3)

( ) ( ( ) ( )) ( ) ( ( ) )

( ) ( )

(A4)

( ) ( ) ( ) ( ) ( )

( ( ) ) (A5)


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)




( ) 0 ( ) ( )

1 (A8)


30


A21 Cooler modeling











shell


( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)


( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (A11)


( ) ( ) ( )

h ( ) ( ) (A12)


31

S( ) h ( ) h ( )

( ) ( ) (A13)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(A16)


(A17) [15]

( ) w( )

( ) ( )

w( ) μw( )

w( )

(A17)


( ) ( ) ( ) ( ) ( ) ( )

( ) ( ( ) ) ( )

( ) ( ) ( ( ) ( )

)

(A18)


( ) ( ) ( )

w( ) ( ) ( ) (A19)


32

( ) ( )

w( ) n( ) (A20)

( ) ( )

w( ) ut( ) (A21)






( ) sum ( ) (A22)

( ) sum ( ) (A23)

( ) sum ( ) (A24)

( ) sum ( ) (A25)

( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) (A26)

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)



equation

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)


33


( ) sum ( ) ( ) (A29)

( ) sum ( ) sum ( ) ( ) (A30)

( ) sum ( ) ( ) (A31)

( ) sum ( ) sum ( ) ( ) (A32)

( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)

( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )

( )) ( ) (A34)










( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (A35)





34

( ) ( ) ( ) ( ) (A36)

( ) ( ( ) ) (A37)

( ) ( ) w ( )

( ) (A38)




S ( ) (

( ) ((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B1)




( ) ((sum

( )

) (sum ( ( ))

( )

)) (B2)



35

( ) ((sum

ut ( )

) (sum ( ( ))

ut ( )

)) (B3)




S ( ) (

( )

((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B4)


S ( ) (

( )

(sum ut( )

( )

)

sum ut( )

( )

) (B5)



( ) ((sum

( )

) (sum ( ( ))

( )

)) (B6)


36

( ) (sum ut( )

( )

) (B7)


in Appendix B)

( ) ( ( )

( ) ( ( ) ( ) ( )) )

(B8)

( ) ( )

( )

( )

( )

(B9)

( ) ( )

( )

( )

( )

(B10)

( ) ( )

( )

7 ( )

( )

(B11)

Where



Assumptions








equations [13]


( ) ( ) ( ) (C1)


37


( ) ( )

( ) ( ) (C2)

( ) n( )

( ) n ( ) (C3)

( ) ( ) ( ) ( ) (C4)

( ) ( ) ( ) ( ) (C5)




( ) ( ) ( )

( ) ( )

μ ( ) ( )

( )

(C6)

( ) ( )

( ) (C7)

( ) n( )

( ) ( ) (C8)





20


51 Conclusions






cooling requirement

























21


















52 Future work




areas listed below









22














cost







23

References





2209














Science 56(12) pp 3641-3658



pp 117ndash195






pp 49-54








8


11 Background
















9



























10




























11





towers







systems
















12







pressure




















13




























14












12 Motivation















15









simultaneously














included



16








turbines)



14 Thesis outline













17

Chapter 2






1


Cooling Towers



Abstract

















base case





2

Highlights




investigated

1 Introduction




















3



















4





























5





























6





























7



























8


cooling towers

























9

tower







(1)

( ) (1)





( ) (2)






10











(3)
















11




Figure 2 (d) is a







12



temperature



temperature (d)


13



( ) (4)










( )

w (5)




( )

w ( ) ( ) ( ) (6)


14



respectively


( ( ) ( ) ( )) (7)


( ( ) ( ) ( ))

(8)






( ) (9)






(10)


15

( ) (10)













equation (8)

( ) (11)




(12)


16









( ) (13)





(14)

( ) (15)

w

(16)





17



flowrate





temperature

(17)

(18)

w

w

w

(19)

(20)

(21)







18

( ) (22)



respectively

3 Model validation











towers [28]








19








α1 α2 α3 α4

95846 06568 -12569 -04216


β1 β2 β3 β4 β5

40099 -17177 08672 -21377 08165


γ1 γ2 γ3 γ4 γ5 γ6 γ7

-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00


20







y=x

y=x

R2=0992

R2=0996


21






No 1 2 3 4 5 6

Measured

data

(degC) 2933 3667 4100 3889 4033 3572

(degC) 2966 3192 3550 3111 3361 3311

(degC) 2111 2111 2388 2388 2667 2944

(kgs) 1186 1178 1157 1174 1157 1156

(kgs) 1132 1132 0881 1132 1008 1258

Calculated

data

(degC)

Measured 2433 2633 2800 2844 3044 3122

Correlation 2415 2642 2818 2851 3016 3106

Relative

difference () 073 -036 -065 -024 092 051

(10-2

kgkg

dry air)

Measured 2192 2835 3108 3223 3454 3301

Correlation 2168 2878 3119 3229 3419 3305

Relative

difference

()

111 -151 -037 -017 103 -011





4 Solution Method




22














5 Case Studies










change


23

51 Base case











Table 6




Ambient air

conditions

tdbi (degC) 3028 3028 3533 2950 2600

twbi (degC) 2565 2565 2944 2500 2250

wi (10

-2kgkg dry air)

190 190 239 183 158

ii (kJkg) 7913 7913 9688 7636 6645






Lower bound 4320


Lower bound 3600

Upper bound 17

Lower bound 07



24

52 Case study 1








Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan [17]

( )








25















Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Operating

conditions

Inlet water

flowrate (th) 7920 5760 5760 6280 5641 7137

Inlet dry air

flowrate (th) 7200 9187 9187 7533 9441 4996

Cooling

water

Inlet

temperature

(degC)

4100 4385 4385 4644 4351 4062

Outlet

temperature

(degC)

3020 2895 3166 2849 2676 3274 2830 2869

Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193


towers (MW) 1039 1041 858 1071 1188 1052 1039 1029


(MW) 9928 8079 10240 11442 9928



26

Cases Base

case

Case

1

Case 2


Condition

1

Condition

2

Condition

3

Cond

1

Cond

2

Cond

3

Make-up water

consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635

Power

consumption

(kW)

Fan 353 450 450 450 450 377 462 240

Pump 1631 1344 1344 1344 1344 1396 1333 1503

Total 1984 1794 1794 1794 1794 1773 1795 1743

Cost (poundh)

Make-up

water 522 536 473 547 587 561 532 490

Power 1983 1794 1794 1794 1794 1773 1795 1743

Total 2505 2330 2267 2341 2381 2334 2327 2233

53 Case study 2


















27






























28









slightly

6 Conclusions

















base case


29



















30

Nomenclature

Parameters







dry air)







Variables








air)


dry air)


dry air)





31

Mep Merkel number







p pressure (Pa)



temperature (Pa)




T temperature K











ηp pump efficiency

Subscripts

a air

db dry-bulb

e evaporation

f fans

i inlet


32

m make-up water

o outlet

p pumps

P Poppe method

s saturation

v vapor

w cooling water

wb wet-bulb

References








New York USA















Mi 15




33
















Oklahoma









6370 EPRI Palo Alto








Amsterdam







34

Appendix

1) Data information




No twi

(degC)

two

(degC)

tdbi

(degC)

twbi

(degC)

wi

(kgkg dry air)

ma

(kgs)

mwi

(kgs)

wo

(kgkg dry air)

1 4144 2600 3411 2111 00104 1158 0754 00284

2 2872 2422 2900 2111 00125 1186 1259 00215

3 3450 2622 3050 2111 00119 1186 1259 00271

4 3878 2933 3500 2667 00188 1264 1008 00323

5 3878 2933 3500 2667 00188 1250 1008 00323

6 3967 2622 3400 2111 00105 1174 0881 00284

7 3500 2867 3461 2667 00190 1156 0881 00285

8 4361 2789 3500 2388 00141 1158 0754 00316

9 4306 2972 3572 2667 00185 1155 0754 00337

10 3806 3089 3594 2944 00236 1142 0754 00321

11 4778 3217 3617 2944 00235 1142 0754 00400

12 3378 2472 3250 2111 00110 1179 0881 00238

13 4144 3000 3617 2667 00183 1156 0881 00340

14 4061 3172 3417 2944 00244 1147 0881 00359

15 4350 3217 3533 2944 00239 1147 0881 00383

16 3672 3139 3272 2944 00250 1155 1008 00329

17 3322 2550 2883 2111 00126 1186 1008 00244

18 3844 2678 2950 2111 00123 1186 1008 00290

19 3661 2944 3250 2667 00199 1161 1132 00314

20 4100 3050 3294 2667 00197 1161 1132 00364

21 3611 2972 3111 2667 00204 1166 1258 00314

22 4022 3078 3133 2667 00203 1166 1258 00364

23 3956 3011 3206 2667 00200 1008 1008 00349

24 3950 3006 3106 2667 00205 1051 1008 00344

25 3944 3000 3333 2667 00195 1108 1008 00341

26 3978 2967 3167 2667 00202 0947 1008 00357





35











w

( w ) w

w ( ) w ( w ) v- ( w ) w (A1)

w

w

( w ) w

w ( ) w ( w ) v- ( w ) w

(A2)

w

( w ) ( w ) ( ) v ( w ) w (A3)







w

w

(

w ( )) (A4)


36


w w

w

0 w w

w 1

(A5)


w

(A6)



w

( ) (A7)



w

(A8)


coefficients



( ) [ ( )] (A9)


37




(A11)

7

7


times [ 7 ( 7 frasl ) ] (A12)









( w )

w w

( w )

77 w (A16)


38



( ) ( ) ( ) (A17)





18

Chapter 3






1


Water Systems



Abstract


















the base case


optimisation




2

Highlights



are considered


into account



investigated

1 Introduction
















3



















4



























5












turn













sectors


6




























7






























8





























9
























considered


10

























11





the shell side









is variable












12





arrangement


13





(1) Mass balance




( ) sum ( ) (1)





( ) sum ( ) (2)



( ) sum ( ) (3)

( ) sum ( ) (4)


14


(2) Energy balance




( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

(5)





a in Figure 2


( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)



leaving cooler q



( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)


15
















(1) Mass balance



( ) sum ( ) ( ) (8)




16



equation (9)

( ) sum ( ) sum ( ) ( ) (9)






respectively

( ) sum ( ) ( ) (10)

( ) sum ( ) sum ( ) ( ) (11)




(2) Energy balance



( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)


17




leaving cooler k



( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )

(13)






point a in Figure 2










18










( ) ( )

( )

w( ) ( ) ( )

( )

( )

w( ) ( ) (14)







19


constant



( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (15)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (k q) (16)






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (17)


20






( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (18)







( ) ( ) ( ) (19)









21

232 Pump modelling



cooling water






(20) - (28)



( ) ( ) (20)

( ) ( ) (21)







22

( ) ( ) (22)



than 28 degC [33]

( ) (23)


( ) (24)




( ) ( ) ( )

(25)

( ) ( ) ( )

(26)


( ) ( ) (27)


equation (28)

( ) ( ) (28)


23







Min sum ( ) sum ( ( ) ( )) (29)




3 Solution Method













24



4 Case Studies











Process

streams

Inlet temp

degC

Outlet temp

degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance

msup2degCW

C1 60 Upper 450

1704 987 000018 Lower 420

C2 120 Upper 795

482 286 000018 Lower 750

C3 95 500 586 732 000018

C4 100 Upper 595

707 448 000035 Lower 550

C5 105 Upper 545

447 748 000053 Lower 500

C6 90 Upper 595

1004 488 000018 Lower 550

C7 75 Upper 445

602 913 000018 Lower 400

C8 150 Upper 1000

394 180 000018 Lower 950

C9 125 Upper 645

513 346 000053 Lower 600


25




Coolers Area

(m^2)

Number

of tubes

Tube

passes

Tube inside

diameter

(mm)

Tube outside

diameter

(mm)

Length of

tube

(m)

Thermal


wall (wmdegC)

C1 3506 1006 2 15 19 60 50

C2 1589 610 2 15 19 45 50

C3 2135 610 2 15 19 60 50

C4 2539 980 4 15 19 45 50

C5 1685 366 2 20 25 60 50

C6 2606 1006 2 15 19 45 50

C7 2004 588 4 20 25 45 50

C8 1641 468 2 15 19 60 50

C9 2539 980 4 15 19 45 50




Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002

S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002

S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002

S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002

S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002

S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002

S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002


26

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

Pipe Equivalent

Length

(m)

Diameter

(m)

Roughness

(m)

S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002

S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002

S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002

S2(C1)

-S1(C2) 1200 023 00002

S2(C6)

-S1(C8) 1300 023 00002




41 Base case












Make-up water


(degC)

Wet-bulb

temperature (degC)

Humidity (kgkg

dry air)

Enthalpy

(kJkg)

318 271 205 855 318


27


42 Case study 1




Units Models

Cooling

towers 1

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )


28

Units Models

2

( ) ( ) ( )

( )


( ) times ( ( ) ) ( ) 7

( )

( ) ( ) ( ) ( ) ( )

7

( ( ) )

Pumps

1

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

2

( ) ( ) ( ) ( )

( ) ( ( ) )

( ) ( ) ( )

( )

Fans

1 ( ) ( ) ( )

( )

2 ( ) ( ) ( )

( )










shown in Table 7


29

























30


the base case


Cooling

towers



The approach

(degC)






Total 409 403 -06

Power

consumption

(kW)

Pumps



Total 4184 3829 -355

Fans



Total 865 882 17

Total 5049 4711 -338

Cost

Water(poundh) 1227 1209 -018





Hot streams


(degC)


C1 450 450

C2 795 795

C3 500 500

C4 595 595


31

Hot streams


(degC)


C5 545 545

C6 595 595

C7 445 445

C8 1000 1000

C9 645 645

43 Case study 2








stated in Table 1



Ambient air

conditions











32


























degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

1

Case 1 458 800 510 604 555 603 455 1006 654

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -08 -05 -10 -09 -10 -08 -10 -06 -09


33


degC)

C1 C2 C3 C4 C5 C6 C7 C8 C9

Condition

2

Case 1 439 787 485 582 530 584 430 991 631

Optimisation 450 766 500 595 545 592 441 982 644

Difference 10 -23 14 12 14 07 10 05 -01

Condition

3

Case 1 454 798 505 599 550 599 450 1003 650

Optimisation 450 795 500 595 545 595 445 1000 645

Difference -04 -03 -05 -04 -05 -04 -05 -03 -05











Table 9











34





























35







convection


conditions


36




Cooling

towers

Make-up water

flowrate (th)

1 231 241 10 217 207 -10 220 226 06

2 189 195 06 176 168 -08 180 183 03



(MW) 097 071 -026 352 385 033 217 201 -016

Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045

Pumps Power

consumption (kW)

1 2173 2469 296 2173 2307 134 2173 2197 24

2 1657 1951 294 1657 1769 112 1657 1723 66

Total 3830 4420 590 3830 4076 246 3830 3920 90

Fans Power

consumption (kW)

1 460 639 179 444 305 -139 452 597 145

2 419 538 119 405 239 -166 412 496 84

Total 879 1177 298 849 544 -305 864 1093 229


Cost (poundh)

Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027

Power 4709 5597 888 4679 4620 -059 4694 5013 319

Total 5969 6905 936 5858 5745 -113 5894 6240 346


37

5 Conclusions

























in the base case








38





cost increases









Nomenclature

Sets


k set of coolers

q set of coolers

Parameters













C)


39







C W)


C W)













a1-a3 coefficients

b1-b3 coefficients

Variables










degC

-1)





40
























(degC)













41









C)



Greek Symbols

α coefficients

β coefficients

γ coefficients


s-1

)









Subscripts

a air

db dry bulb

f fans

i insideinlet

o outsideoutlet

p pumps

s1-s6 nodes

w cooling water

wb wet bulb


42

References








2209


Cooling Towers


128












914-923



pp 1-7











43












1033-1043




InTech





Science 56(12) pp 3641-3658





pp 117ndash195



pp 540ndash551









44







134 pp 88-93


York USA



Appendix

Appendix A Models



( ) ( ) ( )

( ) (A1)





( ) ( ( ) ( )) ( ) ( ( ) ) ( )

( ) (A2)






45


respectively


( ) ( ) ( ) ( ) ( )

( ( ) ) (A3)




bulb temperature



method


( ) ( ) ( ) ( ( ) ) (A4)


( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)






respectively


46


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)





( ) 0 ( ) ( )

1 (A8)



flowrate



( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)







47


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)






( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (B3)







( ) ( ) ( )

h ( ) ( ) (B4)

S( ) h ( ) h ( )

( ) ( ) (B5)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



48


Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(B8)




respectively


( ) w( )

( ) ( )

w ( ) μw( )

w( )

(B9)






( ) 7 ( ) R ( ) 8 ( ) w( ) w( )

( ) ( ( ) ) ( ) ( )

( ) ( ( ) ( )

) (B10)







49


( ) ( ) ( )

w( ) ( ) ( ) (B11)






( ) ( )

w( ) n( ) (B12)





( ) ( )

w( ) ut( ) (B13)











50




No 1 2 3 4 5

ht

(W(m2 K))

Wang 12072 57689 14026 15846 75662

HTRI 12993 56440 14700 16169 73632

Relative error () -709 221 -459 -200 276

∆Pt

(kPa)

Wang 688 287 886 693 261

HTRI 712 297 868 735 268

Relative error () -337 -337 207 -571 -261



( ) ( ) ( ) ( ) (C1)




( ) ( ( ) ) (C2)



( ) ( ) w ( )

( ) (C3)


51








No 1 2 3 4 5


Specific heat

(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223

Thermal

conductivity

(WmK)

0137 0133 0633 0623 0123 0106 0089 0091 0087 0675

Viscosity

(mPa s) 040 360 062 071 289 120 033 110 180 030

Density

(kgm3) 785 850 991 994 820 790 702 801 786 957

Flow rate

(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390

Inlet

temperature

(degC)

2000 380 480 330 517 2100 2270 1120 1700 770

Fouling

resistance (10-4

m2KW)

35 53 70 40 35 35 53 53 88 53


52


No 1 2 3 4 5

Tube pitch (m) 003175 002500 002540 003125 002500

Number of tubes 124 3983 528 1532 582


Tube length L (m) 4270 9000 5422 9000 7100



Tube pattern





nozzle (m) 01023 04380 01280 03370 01540


nozzle (m) 01023 04380 01280 03370 01540


19

Chapter 4







1



Condensing Turbines



Abstract


























2

Highlights




considered


performance

1 Introduction

























3



































4


































5


































6

2 Model Development

















( ) n( ) ut( )

n( ) ( ) (1)






equation (1)


7

( ) ( ) ( ( ) ( )) ( ) (2)



of steam is given












(2) Saturated steam





S ( ) ( ) S ( ) ( ( )) S ( ) (3)






8



( ) ( ) ( ) ( ( )) ( ) (4)







( ) ut( ) ( )

( ) ( ) (5)









( ) ( ) ( ) ( ( ) ( )) (6)





9















( ) ( ) (7)














10











( ) ( ut( ) ( )) ( ( ) ( ))

ut( ) t ( )

( ) t ( )

(8)

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(9)




( ) ( ) ( ) (10)



turbine i







11

( ) ( ( ) ( )) ( ( ) ( ))

( ) t ( )

( ) t ( )

(11)







Max (12)





sum ( ) (13)




sum ( ) sum ( ( ) ( )) (14)




12

3 Solution Method



















4 Case Studies











13



entering coolers

degC

Temperature leaving

coolers degC

Heat capacity

flowrate

kWdegC

Heat transfer

coefficient

W(m2degC)

Fouling

resistance


C1 998 650 600 735 1864 000035

C2 847 600 550 1167 2375 000035

C3 781 650 600 4367 3625 000035

C4 787 600 550 3356 4747 000035

C5 951 600 550 669 2106 000035

C6 952 600 550 2159 4747 000035

C7 637 450 400 2492 7036 000018

C8 676 450 400 1612 7347 000018

C9 642 500 450 3050 4686 000018

C10 742 500 450 2198 3903 000018

C11 635 450 400 2955 8277 000018

C12 696 500 450 2201 4820 000018



Coolers Number of

tubes

Tube

passes

Tube

diameter

(mm)

Tube

length

(m)

Cross sectional

area (m2)

Heat transfer

area (m2)

C1 1234 2 19times2 6 01090 4346

C2 742 2 25times2 9 01285 5184

C3 1452 2 19times2 9 01290 7642

C4 1452 2 19times2 9 01290 7642

C5 588 2 25times2 9 01018 4108

C6 1452 2 19times2 9 01290 7642

C7 1424 4 19times2 9 00745 7495

C8 988 2 19times2 9 00873 5249

C9 1234 2 19times2 9 01090 6556

C10 1452 2 19times2 9 01290 7642

C11 1452 2 19times2 9 01290 7642

C12 860 4 25times2 9 00745 5956


14



provided


Inlet steam


Pressure (bara) 40


Turbine





Condenser

Area (m2) 1984


Tube passes 1


Tube length (m) 836

Tube pitch (m) 0032





Ambient air

conditions







Power(poundkWh) 01



15



Cooling towers

Water mass flowrate

(th)

Upper bound 9000

Lower bound 5000

Air mass flowrate

(th)

Upper bound 12600

Lower bound 5000



Upper bound 15

Lower bound 07



Coolers



Lower bound 05






respectively

41 Base case









16




1

Case

2

Case

3

Cooling

water system

Operation

Circulating water

flowrate (th) 7560 6047 9000 6414

Air flowrate (th) 8237 7267 12053 7258


cooling water into

the cooling tower

(degC)

430 456 405 449

Outlet temperature

of cooling water

from the cooling

tower (degC)

320 319 313 321

Water

consumption

Make-up water

(th) 183 181 187 181

Power

consumption

Fans (kW) 398 351 582 350

Pumps (kW) 1568 1372 1877 1411

Total (kW) 1966 1723 2459 1762


Condensing

turbine






17


Base

case

Case

1

Case

2

Case

3

C1 640 650 648 650

C2 592 600 600 600

C3 643 650 650 650

C4 592 600 600 600

C5 590 600 600 600

C6 592 600 600 600

C7 450 450 450 450

C8 440 450 450 450

C9 500 500 500 500

C10 500 500 500 500

C11 445 450 450 450

C12 500 500 500 500


42 Case study 1




Unit Models

Cooling tower


( ) times ( ))

7

7

( )

Pump

( )

Fan

( )

Processes


Cases


18



















19


cooling requirement

43 Case study 2
















20






02 degC

44 Case study 3






Table 6 and Table 7



21

















45 Discussion

















22









5 Conclusions
























23












Nomenclature

Sets



k q set of coolers

Parameters















C)




24












C W)


C W)









a1-a3 coefficients

b1-b3 coefficients

Variables







C)



C)








25






























(oC)










26












C)


C)


C)







Greek Symbols



s-1

)


s-1

)












Subscripts

a air


27

db dry bulb

f fans

i insideinlet

m n nodes

o outsideoutlet

p pumps

w cooling water

wb wet bulb

m mean value

cn condensing zone


References


Water Systems





2209












781







28


128















134 pp 88-93


Appendix




follows










29


( ) ( ) ( ) ( ( ) ) (A1)

( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)


( ) ( ) ( )

( ) (A3)

( ) ( ( ) ( )) ( ) ( ( ) )

( ) ( )

(A4)

( ) ( ) ( ) ( ) ( )

( ( ) ) (A5)


( ) ( ) ( ( ) ) (A6)


( ) ( )

(A7)




( ) 0 ( ) ( )

1 (A8)


30


A21 Cooler modeling











shell


( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)


( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)


( )

( )

h ( ) ( )

R ( ) ( )

( )

h ( ) ( )

( )

( )

( )

( ) (A11)


( ) ( ) ( )

h ( ) ( ) (A12)


31

S( ) h ( ) h ( )

( ) ( ) (A13)

For S( )

( ) radic ( ) (( ( )) ( ( ) ( ))frasl )


For S( )

( ) radic (q)

(q)



Δ ( ) ( h ( ) ( )) ( h ( ) ( ))

th (q) t (q)

th (q) t (q)

(A16)


(A17) [15]

( ) w( )

( ) ( )

w( ) μw( )

w( )

(A17)


( ) ( ) ( ) ( ) ( ) ( )

( ) ( ( ) ) ( )

( ) ( ) ( ( ) ( )

)

(A18)


( ) ( ) ( )

w( ) ( ) ( ) (A19)


32

( ) ( )

w( ) n( ) (A20)

( ) ( )

w( ) ut( ) (A21)






( ) sum ( ) (A22)

( ) sum ( ) (A23)

( ) sum ( ) (A24)

( ) sum ( ) (A25)

( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) (A26)

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)



equation

( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)


33


( ) sum ( ) ( ) (A29)

( ) sum ( ) sum ( ) ( ) (A30)

( ) sum ( ) ( ) (A31)

( ) sum ( ) sum ( ) ( ) (A32)

( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)

( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )

( )) ( ) (A34)










( ) ( )

( )

w( ) ( )

( )

( )

w( ) ( ) (A35)





34

( ) ( ) ( ) ( ) (A36)

( ) ( ( ) ) (A37)

( ) ( ) w ( )

( ) (A38)




S ( ) (

( ) ((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B1)




( ) ((sum

( )

) (sum ( ( ))

( )

)) (B2)



35

( ) ((sum

ut ( )

) (sum ( ( ))

ut ( )

)) (B3)




S ( ) (

( )

((sum

( )

) (sum ( ( ))

( )

)) (( ( ) sum

( )

) (sum ( ( ))

( )

))) (B4)


S ( ) (

( )

(sum ut( )

( )

)

sum ut( )

( )

) (B5)



( ) ((sum

( )

) (sum ( ( ))

( )

)) (B6)


36

( ) (sum ut( )

( )

) (B7)


in Appendix B)

( ) ( ( )

( ) ( ( ) ( ) ( )) )

(B8)

( ) ( )

( )

( )

( )

(B9)

( ) ( )

( )

( )

( )

(B10)

( ) ( )

( )

7 ( )

( )

(B11)

Where



Assumptions








equations [13]


( ) ( ) ( ) (C1)


37


( ) ( )

( ) ( ) (C2)

( ) n( )

( ) n ( ) (C3)

( ) ( ) ( ) ( ) (C4)

( ) ( ) ( ) ( ) (C5)




( ) ( ) ( )

( ) ( )

μ ( ) ( )

( )

(C6)

( ) ( )

( ) (C7)

( ) n( )

( ) ( ) (C8)





20


51 Conclusions






cooling requirement

























21


















52 Future work




areas listed below









22














cost







23

References





2209














Science 56(12) pp 3641-3658



pp 117ndash195






pp 49-54







modelling, integration and optimisation for recirculating

Documents