This article was downloaded by: [Indian Institute of Petroleum]On: 20 June 2012, At: 01:48Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Mathematical and Computer Modellingof Dynamical Systems: Methods, Toolsand Applications in Engineering andRelated SciencesPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/nmcm20

CO2 removal by absorption: challengesin modellingL.E. Øi aa Department of Technology, Telemark University College, PO Box203, N-3901, Porsgrunn, Norway

Available online: 15 Jul 2010

To cite this article: L.E. Øi (2010): CO2 removal by absorption: challenges in modelling,Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications inEngineering and Related Sciences, 16:6, 511-533

To link to this article: http://dx.doi.org/10.1080/13873954.2010.491676

PLEASE SCROLL DOWN FOR ARTICLE

Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representationthat the contents will be complete or accurate or up to date. The accuracy of anyinstructions, formulae, and drug doses should be independently verified with primarysources. The publisher shall not be liable for any loss, actions, claims, proceedings,demand, or costs or damages whatsoever or howsoever caused arising directly orindirectly in connection with or arising out of the use of this material.

CO2 removal by absorption: challenges in modelling

L.E. Øi*

Department of Technology, Telemark University College, PO Box 203, N-3901 Porsgrunn, Norway

(Received 4 September 2009; final version received 5 May 2010)

The traditional method for large-scale CO2 removal is by absorption in a mixture of anamine and water. The tasks of modelling this process can be divided into descriptions ofabsorption and reaction kinetics, gas/liquid equilibrium, gas and liquid flows and pressuredrop. Process simulation tools containing models for most of these tasks are commerciallyavailable, and the calculated results can be used as a basis for equipment dimensioning andeconomical optimization. A flowsheet calculation in the program Aspen HYSYS® is usedas an example. Calculation convergence is important, especially the column convergence iscritical. For some simplified conditions, calculation of stage efficiencies can give asatisfactory description of the absorption process. Computational fluid dynamics is anefficient tool for calculating flow conditions, pressure drop and temperature profiles,especially for one-fluid phase. An unsolved problem when using computational fluiddynamics for gas/liquid processes is the description of the gas/liquid interfacial area. Amajor challenge is to combine different models and calculation tools. An improved modelfor a specific task must be available and possible to combine with other calculation tools tobe utilized by other programs. In an example, models for equilibrium and mass transferefficiency are used in a flowsheet calculation including CO2 absorption and desorption,followed by economical optimization. The example illustrates some possibilities,limitations and challenges.

Keywords: CO2; amine; absorption; simulation; modelling; efficiency

1. Introduction

CO2 has been removed from process streams at an industrial scale since about 1930. The mostimportant removal processes have been from natural gas and in the removal of CO2 fromindustrial gases at high pressures for ammonia and methanol production. The main process isabsorption in amixture of an amine andwater. Other solvents like carbonate salt solutions havealso been used. An overview of processes can be found in Kohl and Nielsen [1].

CO2 removal from exhaust gases has received much interest because of the environ-mental need for reducing CO2 emissions to the atmosphere. Many processes for removal ofCO2 from power plants or other exhaust gases have been suggested. The emphasis here isput on post-combustion absorption in an amine-based solvent. This is the most relevantmethod for gas-based power plants in the near future. The technology is relatively matureand can be utilized by existing plants with little modification. Absorption is traditionallyperformed in a column with plates, random packing or structured packing; CO2-containinggas flows upwards and the absorption liquid flows downwards. The absorbed CO2 isregenerated in a desorption column, and the solvent is recirculated to the absorption

Mathematical and Computer Modelling of Dynamical SystemsVol. 16, No. 6, December 2010, 511–533

*Email: lars.oi@hit.no

ISSN 1387-3954 print/ISSN 1744-5051 online© 2010 Taylor & FrancisDOI: 10.1080/13873954.2010.491676http://www.informaworld.com

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

column. A removal process consisting of absorption, desorption, heat exchangers andauxiliary equipment is shown in Figure 1.

The main challenges in modelling the CO2 removal are in the absorption and desorptionprocesses. The absorption column is the largest and most expensive unit, and the mostimportant chemical reactions take place in this column. The main energy consumption is inthe reboiler connected to the desorption column. Equipment units like heat exchangers andpumps in the CO2 removal process are little different from similar equipment in otherchemical processes.

In CO2 absorption and desorption, the modelling challenges can be divided into thefollowing tasks:

� Absorption and reaction kinetics� Gas/liquid equilibrium� Gas and liquid flows� Pressure drop

Calculation methods for most of these tasks have been available for a long time.Danckwerts and Sharma [2] wrote a review as early as in 1966. When computers wereintroduced for chemical engineering calculations, computer programs were made to performthese calculations. The calculations can also be extended to comprise tools for, for example,mechanical equipment dimensioning, cost estimation and economical optimization.

Several commercial process simulation programs have included models especially forthe amine/water/CO2 system. Examples of such programs are Aspen HYSYS®, AspenPlus®, Pro/II® and ProMax®. These programs have built-in models especially for vapour/liquid equilibrium and calculation tools especially for column solving. Some of them alsohave kinetic models available. Most of the tasks in the list above can be handled in a processsimulation program.

Computational fluid dynamics (CFD) modelling can be used to calculate the flow phe-nomena in absorption and desorption columns. This can then be used to calculate liquid hold-up, pressure drop and capacity. Fluent® and CFX® are examples of commercial CFDprograms. An optimistic aim for CFD modelling of absorption and desorption is to contributeto a complete, detailed and quantitative description of the absorption/desorption process.

Desorber

Amine cooler

Reboiler

Condenser

Amine/amine exchangerExhaust gas

Purified gas

Product CO2

CO2 absorber

Figure 1. A general CO2 absorption and desorption process.

512 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

This article first gives an overview of process simulation tools that have been usedfor CO2 removal. Then some details of the chemistry, kinetics and equilibrium for theprocess are presented. An overview of models describing the mechanisms of absorp-tion combined with chemical reaction is presented. Traditional design methods forcalculating pressure drop, interfacial area and mass transfer are presented, followed bysimilar calculation methods using CFD. The last part of this article discusses thecombination of different models. In an example, a flowsheet calculation is performedwhich combines models for equilibrium and mass transfer efficiency with calculationtools for column solving and cost optimization. This example illustrates some possi-bilities, limitations and challenges.

The models for solving specific tasks of the CO2 absorption process differ in accuracy,complexity and robustness. The main purpose of this article is to give an overview and topinpoint areas where further modelling can lead to important improvements. A majorchallenge is to combine different models and calculation tools.

2. Flowsheet calculation of CO2 removal using process simulation tools

2.1. Use of process simulation programs for absorption and desorption

Process simulation programs such as Aspen HYSYS®, Aspen Plus®, Pro/II® and ProMax®

have been used to calculate CO2 removal by absorption, mainly at steady-state conditions. Themain advantages of these process simulation programs are that a large number of models forvapour/liquid equilibrium and also different calculation tools for unit operations are available.

Simulation of CO2 removal from flue gas in a monoethanol amine (MEA)/water systemhas been performed by Desideri and Paolucci [3] and by Alie et al. [4]. Both have used thesimulation program Aspen Plus® with the MEA property insert, which is based on the Chen/Austgen electrolyte-non-random two-liquid (NRTL) equilibrium model [5,6]. Desideri andPaolucci used a specified number of theoretical stages in the absorption and desorptioncolumn. Tobiesen et al. [7] and Aroonwilas et al. [8] have made Fortran® programs to performsimilar calculations. All of the above-mentioned references calculate steady-state solutions.Kvamsdal et al. [9] have simulated the absorption part of the process dynamically (as afunction of time) using gPROMS® as a modelling tool. At Telemark University College,Matlab® has also been used to model CO2 absorption and desorption dynamically [10].

An important feature of commercial process simulation programs is the available tools forachieving convergence of the process flowsheet (containing unit operations and streams). Theearly process simulation programs (Pro/II® and Aspen Plus®) were sequential modular andhad to be solved in a forward manner. A traditional way to calculate the flowsheet is to userecycle convergence blocks to compare updated streams with earlier calculated streams. Somesimulation programs (like Aspen HYSYS®) can calculate the flowsheet backwards, butbecause of limitations especially in the column units, flowsheet convergence is normallyachieved as if the program was sequential modular. For flowsheet convergence, the programscan make use of recycle blocks, nested or simultaneous calculation sequences and differentacceleration methods like Wegstein or dominant eigenvalue methods. Convergence of thecolumns is particularly important and was the core technology in the early steady-state processsimulation programs. Because the CO2/amine/water system is highly non-ideal, the need forefficient and robust column solvers is of major importance. Column solver methods availablein addition to the default Hysim Inside-Out method in the Aspen HYSYS® program are

Mathematical and Computer Modelling of Dynamical Systems 513

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

� Modified Hysim Inside-Out� Newton Raphson Inside-Out� Sparse Continuation Solver� Simultaneous Correction� OLI Solver� Fixed or adaptive damping factor

An Aspen HYSYS® flowsheet from Øi [11] is shown in Figure 2. Specifications for thecalculation are given in Table 1. The Aspen HYSYS® version 2004.2 was used with the KentEisenberg equilibriummodel [12], which is extended in Aspen HYSYS by Li and Shen [13].If there are too many stages specified in the columns, they tend to diverge, which istraditional for column stage calculations. It was found that the Modified Hysim Inside-Outmethod with adaptive damping gives the best convergence [11].

The base case calculated a CO2 removal rate of 85%with a heat consumption of 3.67MJ/kg CO2. Figure 3 shows the calculated CO2 removal efficiency and heat consumption whenthe amine circulation rate is varied in the Aspen HYSYS® flowsheet calculation. Thecalculation shows a minimum heat consumption at a certain circulation rate.

2.2. Rigorous simulation in process simulation programs

Most of the column models in commercial process simulation programs are based onequilibrium stages or stages with a stage efficiency. More rigorous column models, whichinclude kinetic expressions, are available. Some of these are able to calculate the concentra-tion profiles of all the diffusing components through the liquid film near the gas/liquidsurface. This kind of approach is based on solving the differential equations describing thediffusion and chemical kinetics in the liquid film. An approach for rigorous modelling withresulting differential equations is presented in Section 5.5.

Recycle

MIX-100

Sweet gasRich MEA to rich/lean heat

exchanger

Rich/lean

heat

exchanger

Rich MEA to

desorber

Lean

pumpDesorber

Sour

gas Rich

MEA

Lean MEA to rich/lean heat exchanger

Q-Rich

pimp

Q-Lean pump

Lean MEA

from

desorber

Q-Reboiler

Q-CondenserCO

2

Rich

pump

Lean

MEA

Absorber

SPRDSHT-1

Make

up MEA

RCY-1

Lean MEA recycle

Lean MEA to lean

cooler

Lean

cooler

Q-Lean

cooler

Make

up

water

Figure 2. Aspen HYSYS® flowsheet for a CO2 removal process (from Øi [11]).

514 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

The program Aspen Plus® has possibilities to include such calculations, contrary to, forexample, Aspen HYSYS®. Al-Baghli et al. [14] have made a rate-based model for the designof gas absorbers for the removal of CO2 and H2S using aqueous solutions of MEA anddiethanol amine (DEA). Freguia and Rochelle [15] used a Fortran® subroutine integratedinto Aspen Plus® to perform a rate-based calculation of CO2 absorption into MEA. Kuckaet al. [16] have used the Aspen Custom Modeler® tool in Aspen Plus® to model the liquidfilm by dividing the film into a number of segments. The mentioned examples in AspenPlus® have been performed at steady state.

Table 1. Specifications for base case CO2 removal.

Inlet gas temperature 40�CInlet gas pressure 1.1 bar (abs)Inlet gas flow 85,000 kmol/hCO2 in inlet gas 3.73 mol%Water in inlet gas 6.71 mol%Lean amine temperature 40�CLean amine pressure 1.1 bar (abs)Lean amine rate 120,000 kmol/ha

MEA content in lean amine 29 mass%a

CO2 in lean amine 5.5 mass%a

Number of stages in absorber 10Murphree efficiency in absorber 0.25Rich amine pump pressure 2 barHeated rich amine temperature 104.5�Ca

Number of stages in stripper 6 (3 + 3)Murphree efficiency in stripper 1.0Reflux ratio in stripper 0.3Reboiler temperature 120�CLean amine pump pressure 2 barMinimum delta T in heat exchange 10�C

Note: aIn first iteration.

90

80

(0)

CO

2 re

mov

al (

%)

(*)

Hea

t con

sum

ptio

n (M

J/kg

CO

2)

85

752.5 2.6 2.7 2.8

Circulation rate (1000 ton/h)2.9 3 3.1 3.2

3.6

3.8

4

4.2

Figure 3. CO2 removal grade and heat consumption as a function of amine circulation rate (fromØi [11]).

Mathematical and Computer Modelling of Dynamical Systems 515

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

2.3. Difficulties and challenges using process simulation tools for CO2 absorption

Dynamic simulations are of interest for regulation, for start-up and shut-down analysis andfor evaluation of emergency situations. Most of the process simulation calculations of CO2

removal from atmospheric exhaust in the open literature are simplified processes at steadystate. The unit operation modules in the process simulation programs Aspen HYSYS®,Aspen Plus® and Pro/II® are traditionally based on the solving of algebraic equations for asteady-state solution. All these programs have the possibility to calculate a flowsheet as afunction of time by performing time steps. There are many challenges met when trying toextend steady-state simulations to dynamic conditions. Reducing computer time andincreasing calculation robustness are two challenges.

There are of course challenges to improve the different models in a process simulationprogram. There is perhaps a more important challenge on how to combine the differentmodels. Because process simulation programs utilize many rigorous models, calculationconvergence can be a problem. Alie et al. [4] use a flowsheet decomposition approach,dividing the calculation of the absorption column and desorption column, to overcome thisproblem.

Detailed absorption kinetics models can be complex and can involve nonlinear equili-brium models and the solving of partial differential equations. It is doubtful whether suchcalculations should be performed for each iteration when a flowsheet involving absorptionand desorption columns is calculated several times.

3. Chemistry of CO2 removal with amines

3.1. Primary, secondary and tertiary amines

A general amine has the formula NR1R2R3 where R1, R2 and R3 are organic groups orhydrogen directly bonded to the central nitrogen atom. An amine with only one organicgroup directly bonded to nitrogen is a primary amine, with two organic groups it is asecondary amine and with three it is a tertiary amine. If an organic group contains an OHgroup, the amine is called an alkanolamine. MEA (H2NC2H4OH) is a primary alkanolamineoften used for CO2 removal. DEA is a simple secondary amine andN-methyldiethanolamine(MDEA), with R1 and R2 as C2H4OH-groups and R3 as a CH3-group, is probably the mostused tertiary amine for CO2 removal. When used as solvents, the amines are typically20–40 wt.% solutions in water.

3.2. Absorption of CO2 into amine solutions including chemical reactions

The absorption of CO2 into an amine solution with MEA can be described by the followingequations: Equation (1) describes the transfer of CO2 from gas to an aqueous liquid,Equation (2) describes the reaction to a protonated amine ion (HMEA+) and a carbamateion, and bicarbonate ðHCO�

3 Þ formation according to Equation (3) is also occurring. (Acarbamate ion is a reaction product formed by CO2 and an amine, and if the amine is MEA,the carbamate ion has the formula HN(C2H4OH)COO

-.) In the case of other amines thanMEA, a reaction equivalent to Equation (3) can be more important than the reaction inEquation (2).

CO2ðgÞ $ CO2ðaqÞ (1)

CO2 þ 2MEA $ HMEAþ þ Carbamate� (2)

516 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

CO2 þMEAþ H2O $ HMEAþ þ HCO�3 (3)

CO2 in an aqueous solution can be in the form of free (or molecular) CO2 or asbicarbonate or carbonate ions (HCO�

3 or CO2�3 ). When an amine is added, carbamate can

be formed according to Equation (2). The total concentration of CO2 (at a molar basis) is thesum of all the concentrations of the different forms:

CCO2;TOT ¼ CCO2 þ CHCO�3þ CCO2�

3þ CCARBAMATE

� (4)

The amine MEA can be in the form of free MEA, protonated MEA (HMEA+) or as a partof a carbamate, The total concentration of MEA is the sum of the concentrations of thedifferent forms:

CMEA;TOT ¼ CMEA þ CHMEAþ þ CCARBAMATE� (5)

3.3. Reaction kinetics for MEA (and other primary and secondary amines) with CO2

The detailed reaction kinetics for the reaction between even simple amines and CO2 are quitecomplicated. However, for the simple amines, for example MEA, the kinetics are nowregarded as well known. Overviews can be found in the review articles by Danckwertsand Sharma [2] and Versteeg et al. [17]. The mass transfer kinetics of MEA absorption inlaboratory absorption equipment under controlled conditions can be explained by traditionalmass transfer models [17].

It has been known for a long time that the main reaction described by Equation (2) ofprimary amines like MEA and CO2 is a second-order reaction under normal conditions:

rCO2 ¼ k2 � CCO2 � CMEA (6)

In Equation (6), rCO2 is the reaction rate (in mole CO2 reacted per volume and time), k2 isthe reaction rate constant (which is temperature dependent) and CCO2 and CMEA are theconcentrations of free CO2 andMEA. Versteeg et al. [17] give temperature-dependent valuesfor the reaction rate constant. Caplow [18] gives a detailed description of the reactionkinetics, introducing the so-called zwitterion mechanism. This has later been generallyaccepted as the actual mechanism [17]. The mechanism is similar for simple primary andsecondary amines.

3.4. Kinetics for MDEA (and other tertiary amines) and sterically hindered amines

MDEA is a tertiary amine and does not react with CO2 according to the carbamate formationreaction in Equation (2). The absorption of CO2 is in this case instead followed by an acid/base reaction as in Equation (3). The reaction is described in Blauwhoff et al. [19] and Rinkeret al. [20]. The mechanism is similar for many of the tertiary amines. Because tertiary aminesdo not form carbamates, they normally have lower desorption energy compared to primaryamines.

Not all primary and secondary amines react with CO2 to form carbamate. Because ofbulky groups close to the nitrogen atom in the amine group, some primary and secondary

Mathematical and Computer Modelling of Dynamical Systems 517

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

amines do not react with CO2 to form carbamates. These are so-called sterically hinderedamines. One example is 2-amino-2-methyl-1-propanol (AMP). The sterically hinderedamines perform in contact with water and CO2 in many ways like tertiary amines. Theidea of using sterically hindered amines is described by Sartori and Savage [21]. The solventKS-1 (which is based on sterically hindered amines) is used by Mitsubishi Heavy Industriesin their commercial process for CO2 removal from flue gases. The KS-1 process is claimed tohave much lower energy consumption than an MEA-based process [22].

3.5. Reaction kinetics for mixtures of amines with CO2

Using mixtures of amines for CO2 removal is first described by Chakrawarty et al. [23]. Oneidea is to combine the high reactivity of one amine (e.g. MEA) with the low desorptionenergy of another amine (e.g. MDEA). The reaction kinetics can normally be described bythe kinetics of the single amines. The combination of reaction kinetics with mass transferwill however be much more complicated in the case of mixed amines. The combination ofreaction kinetics, diffusion and equilibrium is treated in more detail in Section 5.

4. Equilibrium description of mixtures of water, CO2 and amines

4.1. Gas/liquid equilibrium

Equilibrium between the CO2 content in the gas and the concentration of free CO2 in theliquid phase can be described by a Henry’s constant (He), which is temperature dependent:

pCO2 ¼ He � CCO2 (7)

pCO2 is the partial pressure of CO2 and CCO2 is the concentration (on a molar basis) of freeCO2 in the liquid. Under atmospheric conditions, gas non-idealities are normally negligible,and the ideal gas law is sufficient to describe the gas phase. An equation of state like PengRobinson [24] can also be used to take care of the minor gas non-idealities. In that case, thepartial pressure of CO2 is replaced by the fugacity of CO2.

A water/amine/CO2 mixture can be specified by the total concentrations of CO2 andamine. The gas/liquid equilibrium can be expressed by the equilibrium between the partialpressures of CO2 in the gas above a specified solution at a given temperature as indicated inEquation (8):

pCO2 ¼ f ðCCO2;TOT;CAMINE;TOT; TÞ (8)

Experimental gas/liquid equilibrium data for amine systems are often measured as partialpressures of CO2 in the gas above a specified solution, and the data will then be in the form ofEquation (8).

4.2. General chemical equilibrium models

Simple models which empirically fit measured data, for example, according to Equation (8)are available. Such models will, however, not give any information about the actualcomposition of the liquid.

Kent and Eisenberg [12] gave an equilibrium description based on literature values forHenry’s constants and equilibrium constants for the water/carbonate/bicarbonate system. Thewater, carbonate and bicarbonate system is a widely studied and well-described system [2].

518 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

Then the equilibrium constants for the amine/carbamate equilibrium and the amine/protonatedamine (Equations (2) and (3)) were fitted to experimental data. A modified version of thismodel, Li/Shen [13], is used by the simulation program Aspen HYSYS®.

4.3. Activity-based equations/electrolyte models

Amore detailed description can be done by expressing the activities (or chemical potentials)of all the ionic and molecular components as a function of liquid concentrations andtemperature. The Chen/Austgenmodel [6], for simple amine systems, is based on the generalelectrolyte-NRTL model of Chen and Evans [5]. This model is available in the simulationprogram Aspen Plus®. This is a rigorous model and has a high complexity, many adjustableparameters and high accuracy. Liu et al. [25] have adjusted the parameters for the MEA/water system from the Chen/Austgen model to make the heat of vapourization to be moreaccurate.

Li/Mather [26] is a similar model available in Aspen HYSYS®, using an electrolyte-Margules model. Aspen HYSYS® is in principle not a program suitable for describingelectrolytic systems. It does not calculate the resulting concentrations of ionic species in thesolution. When the Li/Mather model is calculated in Aspen HYSYS®, the result is theconcentrations of the constituting components of the solution (e.g. CCO2TOT and CMEA,TOT).The calculation based on ionic species is kept inside the subroutine containing the model.

Kaewsichan et al. [27] gave an overview over equilibrium models in amine systems andalso presented a model based on an electrolyte UNIversal-QUAsi-Chemical (UNIQUAC)model. An extended UNIQUACmodel has also been used to describe the CO2/amine systemat Technical University of Denmark [28]. The statistical associating fluid theory – variablerange (SAFT-VR) [29] has been used by Imperial College [30] to model the equilibrium andkinetics in amine/water/CO2 systems. This has been implemented in the program packagegPROMS®. The use of such a molecular approach is especially interesting for modellingkinetic and equilibrium properties for new solvents with limited available equilibrium data.

The accuracy of models for amine mixtures is often limited by the accuracy in theavailable equilibrium data. Equilibrium models often have a trade-off between a complexmodel with high accuracy and a simpler model with less accuracy. There is a challenge tofind equilibrium models that are simple, accurate and achieve convergence easily.

5. Models for absorption of CO2 followed by chemical reaction

5.1. Description of the absorption process followed by chemical reaction

A schematic overview of typical partial pressure and concentration profiles at a certaincolumn height in the absorber is given in Figure 4. The figure is based on the two-filmconcept. Absorption of a gas is described by transport from the bulk gas to the liquid surface,the assumption of gas/liquid equilibrium at the interface and then transport of absorbed gasto the liquid bulk. After absorption, CO2 can either react directly in the liquid close to theinterface or be transported into the bulk liquid. In the bulk liquid, CO2 or other species canreact further, limited by either equilibrium or chemical kinetics.

The concentration of amine decreases from the bulk to the liquid film as shown inFigure 4 because it reacts with CO2 mainly in the film. Amine also evaporates to some extentto the gas phase. This is, however, not important for the CO2 absorption and reactionmechanisms. The rate of amine evaporation is important for the study of amine emissionsfrom the absorption column and the possibility to reduce amine emissions to the atmosphere.

Mathematical and Computer Modelling of Dynamical Systems 519

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

5.2. Mass transfer models

Popular mass transfer models are the two-film theory by Lewis and Whitman [31] and thepenetration model and surface renewal model developed by Higbie [32] and Danckwerts[33], respectively. The two-film model is based on the concept of thin gas and liquid filmswith a constant thickness and transport rate based on molecular diffusion. This model resultsin mass transfer proportional to diffusivity ðDCO2Þ. The penetration and the surface renewalmodels are regarded to be more realistic models for the liquid film. They are based on theidea of continuous transport of volume elements from the interface to the liquid bulk. Thedifference between the models is that the penetration model assumes equal contact time forthe elements, whereas the surface renewal model assumes a contact time distribution. Bothof these models result in mass transfer proportional to the square root of the diffusivity. Theboundary layer theory has also been used to calculate mass transfer from basic laws of fluiddynamics, mainly for simple geometries [34].

A mass transfer number for the liquid film, kL, can be defined by Equation (9). The gas/liquid interfacial area per volume has symbol a, and the interface and bulk positions areshown in Figure 4. RCO2 is used as the symbol for the absorption rate of CO2 per totalvolume. The reaction rate rCO2 of CO2 in Equation (4) is per liquid volume. At steady-stateconditions, and assuming that the amount of unreacted CO2 is negligible compared to thereacted CO2, the rate of reaction equals the rate of absorption for CO2:

RCO2 ¼ NCO2 � a ¼ kL � a � ðCCO2;INTERFACE � CCO2;BULKÞ: (9)

The gas transport of CO2 to the interface is normally not rate-limiting [2]. The gas sidemass transfer can often be neglected or it can be described by a simple empirical correlation.

5.3. Simplified models for absorption followed by chemical reaction

These kinds of processes have been treated by, for example, Van Krevelen and Hoftijzer[35]. They used an enhancement factor which is the ratio of the actual absorption rate divided

Liquid filmGas film Liquid bulk

CAmine

PCO2

CCO2

Distance (m)

Con

cent

ratio

n or

par

tial p

ress

ure

(mol

/m3 )

or

(Pa)

CCO2, Interface

PCO2, Interface

Gas bulk

Figure 4. Typical concentration profiles in liquid film with absorption and chemical reaction,assuming equilibrium between partial pressure and concentration of CO2 at interface.

520 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

by the absorption rate by pure mass transfer. This can be expressed as the ratio between themass transfer number with and without reaction:

EENH ¼ kLkL;WITHOUT REACTION

: (10)

In the case where the rate expression can be assumed to be independent of the amineconcentration, the pseudo-first-order conditions occur. In that case, the rate expressionbecomes [35]

RCO2 ¼ CCO2; INTERFACE � a �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik2 � DCO2 � CMEA

p(11)

where DCO2 is the molecular diffusivity of CO2 in the liquid. With this rate expression, it ispossible to calculate a Murphree efficiency for a tray or a packed section at the given flowconditions. The Murphree efficiency for a tray or a packing section can be defined as shownin Figure 5.

Aspen HYSYS® has a model for calculating Murphree efficiencies in plate columnsbased on a pseudo-first-order expression. This model is based on the work by Tomkejet al. [36].

For the conditions in Table 1, Aspen HYSYS® calculates a Murphree efficiency thatvaries slightly from top to bottom with an average value of approximately 0.09. If a platedistance of 0.6 m is assumed, this is equivalent to a Murphree efficiency of 0.15/m ofpacking. The Murphree efficiency increases slightly with temperature.

There has been much work on calculation methods for enhancement factors and evalua-tions of the conditions for when to use approximate expressions. DeCoursey [37] developed

y

yn–1

Tray n(or section n)

Tray n–1

y*

Figure 5. Definition of Murphree efficiency, EMURPHREE ¼ (y - yn-1)/(y* - yn-1), where y is molefraction (CO2) in the gas phase leaving tray (or section) n, and y* is in equilibrium with the liquid ontray (or section) n.

Mathematical and Computer Modelling of Dynamical Systems 521

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

an explicit approximate expression for the case of absorption followed by a second-orderirreversible reaction. Later, this was extended to reversible reactions [38], like CO2 absorp-tion in an amine solution. Tobiesen and Svendsen [39] have calculated enhancement factorsfor CO2 absorption into MEA for both simple models and a rigorous model and compared itwith pilot scale experiments. In a temperature range between 50 and 70�C, the deviationusing a pseudo-first-order approximation was in the order of magnitude area between 5%and 50%. The deviation increased with CO2 concentration and temperature. For the case ofCO2 absorption into MEA solutions at atmospheric conditions, it is not clear under whichconditions the pseudo-first-order approximation is valid.

5.4. Models for CO2 absorption into mixed amines

In the case of mixed amines, the combined reaction and mass transfer kinetics might be quitecomplicated. One model is the shuttle mechanism from Astarita et al. [40], which tries tomodel absorption into a mixture of a reactive amine (e.g. MEA) in small amounts and a lessreactive amine (e.g. MDEA) in larger amounts. The idea is that CO2 first reacts with MEA inthe film close to the surface and is transferred into the bulk liquid. In the bulk liquid, CO2 isreleased from MEA and reacts with MDEA, so that the MEA can be shuttled back to theliquid film. Hagewiesche et al. [41] have modelled absorption into blends of MEA andMDEA. The absorption mechanism was shown to follow the shuttle mechanism proposedby Astarita.

5.5. Rigorous simulation

There have been several attempts to calculate the concentration profiles through the liquidfilms based on available mass transfer and kinetic models. De Leye and Froment [42], Al-Baghli et al. [14] and Kucka et al. [16] are examples. Equations (12) and (13) are fromDeCoursey [37] for the case of a second-order irreversible reaction between an absorbedcomponent (e.g. CO2) and a liquid component (e.g. MEA). Mass transfer is based on asurface renewal model [33]. The equations represent a time-dependent material balance forCO2 and MEA:

DCO2

@2CCO2

@x2� @CCO2

@t� k2 � CCO2 � CMEA ¼ 0 (12)

DMEA@2CMEA

@x2� @CMEA

@t� 2 � k2 � CCO2 � CMEA ¼ 0: (13)

The boundary conditions are that for t ¼ 0 and x > 0 and for t > 0 and x ¼1, CCO2 andCMEA are equal to the bulk concentrations; and for t > 0 and x ¼ 0, CCO2 is the interfaceconcentration and ∂CMEA/∂x¼ 0. The boundary condition that ∂CMEA/∂x¼ 0 at the interfaceis based on no transport of amine into the gas [37]. The solution of these equations gives theconcentration profiles through the liquid film at a given time t. The accuracy is of courselimited to the accuracy of the data used and the assumptions taken.

Such models can be applied in steady-state flowsheet calculations if a contact time τ orcontact time distribution (as in the surface renewal model) is assumed. In that case, the fluxNCO2 at the gas/liquid interface is calculated by Equation (14) from the solution of thedifferential equations. The average absorption rate per volume is then calculated as the meanflux as shown by Equation (15):

522 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

NCO2 ¼ �DCO2 �@CCO2

@x

� �x¼0

(14)

RCO2 ¼ NCO2 � a ¼ a

τ

Zτ

0

NCO2dt: (15)

5.6. Rigorous simulation of reversible reactions

For the case of reversible reactions, the description of the reactions becomes more compli-cated. One new equation is necessary for each relevant reaction product, the rate expressionin Equation (6) must be extended and the equilibrium must be taken into consideration. Asimple way to describe the equilibrium is to specify an equilibrium constant based onconcentrations.

There is a challenge to combine rigorous kinetic models with rigorous equilibriummodels. The most accurate equilibrium models are based on activities. A consistencyproblem may occur if the kinetic expressions used are based on concentrations and theequilibrium expressions are based on activities.

6. Pressure drop, interfacial area, mass transfer, gas and liquid distributionin columns

6.1. Traditional design methods for random and structured packing

Design of packed columns is generally based on empirical correlations for liquid hold-up,pressure drop, gas/liquid interfacial area and mass transfer. The resistance to absorption isoften divided into gas side and liquid side resistance. These methods are described in, forexample, Kohl and Nielsen [1].

Structured packing columns will probably be the primary choice in case of a large-scaleCO2 removal process from atmospheric exhaust. Structured packing is very efficient andgives a very low pressure drop. Plate columns will probably not be practical for columnswith large diameters (more than 15 m). Large plates will need extensive mechanical support,and horizontally flowing liquid will need very long flow paths for each plate. Randompacking will have lower investment than structured packing and might be an economicalalternative.

The gas flow (or gas capacity) in an absorption column is limited by pressure drop,loading or flooding. The loading point can be defined as the point where mass transferefficiency drops significantly, and the flooding point can be defined as the condition ofrestricted liquid downward flow leading to liquid filling of the column. To calculate flooding(capacity) and pressure drop in random packing, empirical charts or equations as inSherwood et al. [43] and Eckert [44] are traditional methods. They are based on correlationsfrom dimensional analysis which are fitted to performance data. The empirical Onda [45]and Bravo and Fair [46] correlations are standard methods to calculate mass transfer inrandom packing. They have different correlations for calculating the gas side and liquid sidemass transfer.

Design methods for structured packing are based on the same type of correlations asfor random packing, for example Rocha et al. [47,48], Billet and Schultes [49] and DeBrito et al. [50]. Most of these methods are limited to the flow regime below the loadingpoint. Droplet formation (which occurs above the loading point), and its influence on

Mathematical and Computer Modelling of Dynamical Systems 523

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

interfacial area and mass transfer, is difficult to predict. Review articles for mass transferin structured packing are written by Brunazzi et al. [51], Valluri et al. [52] and Wanget al. [53].

The semi-empirical calculation methods for mass transfer are traditionally based on thefollowing calculation steps [51]:

� liquid hold-up� gas/liquid interfacial area� mass transfer coefficient for gas side� mass transfer coefficient for liquid side

The deviation between the estimation methods is especially large for the calculatedeffective interfacial area. This is an important parameter because the absorption rate isnormally proportional to this entity, for example as in Equation (11). There is a largepotential in improving the estimation methods for the effective interfacial area.

6.2. Non-empirical modelling of absorption in structured packing

In their review, Valluri et al. [52] have one section for non-empirical modelling of thedesign parameters. They refer to Shetti and Cerro [54] as the first complete model of thiskind. One of their aims was to estimate design parameters in structured packing withoutany adjustable parameters. An idea was to establish the equations for the fluid flow patternand mass transfer through the films and then solve the equations to achieve the designparameters for heat and mass transfer. The equations to be solved are typically a set ofalgebraic and differential equations. Another early presentation of a mechanistic modelfor mass transfer in structured packing is by Nawrocki et al. [55]. Figure 6 is an illustration ofimportant factors in modelling flow in structured packings. The liquid flows downwards,normally covering most of the solid surface area. The liquid velocity is largest close tothe gas/liquid interface area. The gas flows upwards in the space not occupied by solid andliquid. The gas velocity is lowest close to the liquid (or solid) surface. In some models, itis assumed that the liquid (and possibly also the gas) is perfectly mixed at certain mixingpoints.

At Delft University, models for columns with structured packing have been studied.Olujic et al. [56,57] distinguish between modelling at a geometric macro-level (channel

Liquid flowGas flow

Solid surface

Mixing points Gas/liquid interfacial area

Solid sheets(possibly withcorrugationand holes)

Figure 6. Illustration of important factors in modelling flow in structured packing.

524 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

dimensions) and micro-level (film and surface texture dimensions). Models for film flow,gas side mass transfer and liquid side mass transfer are suggested. Their prediction methoddoes not require packing specific constants. It is stated that a reliable prediction of theeffective interfacial area is the key to the success of a prediction method.

Shilkin and Kenig [58], from the University of Dortmund, have made a model forstructured packing columns giving a set of differential equations. The concept is based ontwo phases which are totally mixed at regular intervals as indicated in Figure 6. Theequations are solved numerically. The results are the velocity profiles, the concentrationprofiles and the temperature profiles through the column.

Iliuta and Larachi [59], at the Laval University in Quebec, have made a mechanisticmodel for structured packing columns, calculating pressure drop, liquid hold-up and wettedarea. The model is based on a double-slit mechanistic approach. In a channel, the liquid filmflows downwards in one slit and the gas upwards in another slit. The resulting model givesthree coupled algebraic equations to be solved. The model requires no adjustable parameters.Their work has been developed further into CFD modelling.

6.3. CFD modelling of separation columns with structured packing

A CFD program divides a fluid flow geometry into a grid of small volumes and then solvesthe fundamental equations for mass, energy and momentum conservation for each volume.Modelling of turbulence is an important part of a CFD program. Equations for chemicalkinetics and equilibrium can be included. Because a CFD simulation consists of a largenumber of equations, CFD simulation consumes much computer memory and time. Fluent®

and CFX® are commercial CFD programs.Valluri et al. [52] state that very few publications have been presented in the field of

using CFD for structured packings. Most of them are about catalytic reactors. However,mass transfer both in gas and liquid in structured packing was also covered. Klöker et al. [60]have tried to integrate CFD and process simulation for reactive distillation in structuredpacking.

Petre et al. [61], from the Laval group in Quebec, calculated dry pressure drop instructured packing for large-scale absorption with 3D CFD. The CFD program Fluent®

was used with the ReNormalized-Group (RNG) k-" turbulence model. Larachi et al. [62]and Iliuta et al. [63] calculated the pressure drop for two-phase flow using CFD. The types ofstructured packing studied were MellaPak®, GemPak®, Sulzer BX® and Montz-Pak®.

Raynal et al. [64] wrote an article called ‘Liquid holdup and pressure drop determinationin structured packing with CFD simulations’. Dry pressure drop was calculated in 3D CFDusing Fluent® with the k-" turbulence model and the RNG k-" model. Hold-up wascalculated using a 2D laminar model. The calculations were compared with experimentsfrom an air/water system. Raynal et al. [65] have also written an article called ‘Use of CFDfor CO2 absorbers optimum design: from local scale to large industrial scale’.

CFD modelling of packed columns may be used for the calculation of total pressure dropand for the modelling of different mechanisms resulting in pressure drop. This may be used forpredicting performance and for optimizing operation conditions. The information gained canalso be used for improving the packing. CFD is obviously suitable for simulating flowdistribution and calculating pressure drop in auxiliary column equipment like liquid and gasdistributors.

There seems to be no attempts in the literature to simulate an overall model for anabsorption process with CFD. A major challenge is how to model the gas/liquid interface.

Mathematical and Computer Modelling of Dynamical Systems 525

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

7. Combination of models and calculation tools

7.1. User-defined components in process simulation tools

In process simulation programs, there are normally possibilities to include user-definedcomponents. In Pro/II®, it is possible to write routines in Fortran® that can be linked to Pro/II®. User-defined subroutines in Fortran® can also be linked to Aspen Plus®. In AspenHYSYS®, new routines can be written in C++® or in Visual Basic®. And in AspenHYSYS®, it is possible to introduce Excel®-like spreadsheets which can both import andexport data to other parts of the flowsheet calculation. An example where spreadsheets areused in Aspen HYSYS® is given in Section 7.4.

7.2. Process simulation programs and Cape-Open

Process simulation programs are specialized in combining many types of components likeequilibrium models and calculation tools for columns and other unit operations. Theobjective of the projects Cape-Open from 1997 to 1999 and Global Cape-Open from 1999to 2001 was to define standard interfaces between the major components of a processsimulation program. The contributors to these projects were mainly vendors of majorprocess simulator programs and major chemical companies. One result of these programswas a set of interface standards between process modelling components and programs. Theorganization Cape-Open Laboratory Network (http://www.colan.org) is now maintainingthe Cape-Open interface standards.

7.3. Cost estimation of CO2 removal from flue gas with amines

Most cost estimation work is performed within commercial companies and is not published.Mariz [66] has given some background for cost estimation of an Econamine® process(MEA-based process from Fluor Daniel) for CO2 removal from flue gas. In the CO2

Capture Project (CCP), Choi et al. [67] performed a study with title: ‘CO2 Removal fromPower Plant Flue Gas – Cost Efficient Design and Integration Study’.

The process simulation programs like Aspen Plus®, Pro/II® and Aspen HYSYS® havedimensioning and cost estimation tools that can cost estimate the equipment after the processcalculations.

In several student projects at Telemark University College, Aspen HYSYS® has beenused for process simulation of a CO2 removal process followed by mechanical equipmentdimensioning, cost estimation of the installed equipment and estimation of energy cost as themost important operating cost. This has normally been done by utilizing spreadsheets.Parameter variation makes it possible to find the most economical temperatures, circulationrates and column heights [68].

7.4. Example of combination of models and calculation tools for economicaloptimization using HYSYS®

A cost estimation of the base case in Figure 2 has been performed [69], using the AspenHYSYS® version 7.0. The base case specifications from Table 1 were used, except for theMurphree efficiency, which was set to 0.15 for 1 m of packing height. Equipment cost wascalculated using an open available cost estimator available on the internet by Peters et al.[70]. Installed cost (for all the equipment) was calculated using a type- and cost-dependentinstallation factor [69]. These dimensioning and cost estimation calculations were performed

526 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

in spreadsheets connected to the process simulation program. The installed cost of theequipment was estimated to 160 mill. USD, and the energy cost for 10 years was estimatedto 370 mill. USD. The absolute value of the total estimate was not regarded as very accurate,but it was expected to include most of the factors varying with size and capacity.

Different parameter values were then varied to find the optimum process parameters[69]. Equipment cost change from base case to new conditions was calculated by multi-plying with the capacity ratio raised to 0.65. Optimum parameters were found by performingseveral simulations, and optimum was found at minimum net present value (installed costplus energy cost for 10 years with full operation). Figure 7 shows the net present (negative)value as a function of minimum temperature difference with the optimum temperaturedifference at 19�C. This value has high uncertainty, especially due to the uncertainty inthe cost connected to the heat exchanger. Other calculated optimums were 16 m of packingheight (each with Murphree efficiency 0.15) and 35�C in absorber inlet gas temperature. Forthe inlet temperature optimization, the Murphree efficiency was specified to be temperaturedependent, varying linearly from 0.14 to 0.16 between 30�C and 50�C. These calculationswere performed with much trial and error, especially due to divergence problems in thecolumn calculations.

The optimization calculation using the Optimizer tool in Aspen HYSYS® [69] was alsotried. A variable (here the temperature difference) was automatically varied in repeatedsimulations to achieve the minimum criteria function (here the net present value). For thecase of minimum temperature difference, it was calculated to 17.7�C, close to the value of19�C found in Figure 7 by specifying the parameter in each simulation. The figure shows aflat minimum between 16�C and 21�C.

However, the Optimizer tool in Aspen HYSYS® has some limitations, especially inoptimizing column parameters. The column height cannot be optimized by Optimizer,because the number of column stages is an integer value. And the absorber inlet temperaturecannot be optimized using the Optimizer tool, because the Murphree efficiencies in the

520

530

540

550

560

570

580

590

5 10 15 20 25

Delta T (C)

Net

pre

sen

t valu

e (

millio

n U

SD

)

Figure 7. Net present (negative) value of CO2 removal plant as a function of minimum ΔT in amine/amine heat exchanger (from Øi et al. [69]).

Mathematical and Computer Modelling of Dynamical Systems 527

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

column cannot be specified as temperature-dependent variables. It is an obvious challenge tomake such automatic optimizations possible. There are many challenges in making robustmodels combining complex equilibrium models, kinetic models, column solving and opti-mization tools.

7.5. When is the use of rigorous models doubtful?

There is in general a trade-off between complex and accurate models compared to simplerand more robust models. The purpose of the calculation will of course influence on what ismost important. Calculation time is not a very important factor any longer. A more importantproblemwith a too rigorous model is when the model leads to divergence. Another drawbackwith a too complicated model is that it can lead to confusion and make the model moredifficult to specify.

An example of an unnecessary complicated model is the use of differential equations (asin Equations (12) and (13)) to calculate the absorption rate when the absorption is in thepseudo-first-order regime and can be calculated by Equation (11). Trying to solve thedifferential equations does not increase the accuracy and increases computing time anddivergence tendency.

When column calculations are in a flowsheet network, the columns are calculated severaltimes. In process simulation programs for steady-state calculations, the column solvermethods, for example the methods mentioned in Section 2.1, traditionally consist of onlyalgebraic equations. The columns are then modelled as stages representing each plate in aplate column or a specified packing height in a packed column. More rigorous modelsinvolving differential equations describing concentration and temperature profiles in bothaxial and radial directions are also possible. However, a rigorous column model combinedwith a complex description of the equilibrium and kinetics is doubtful if this leads toflowsheet divergence. In the case of time-dependent simulation, the robustness of the modelsis probably more important than the accuracy. It is important to find a good balance in eachflowsheet to obtain a fast, robust and accurate calculation.

For direct use in mass transfer calculations, rigorous fluid flow models like CFD areprobably too rigorous. Mass transfer models normally need parameters like mass transfernumbers and effective gas/liquid interfacial area, and these are traditionally not calculated inCFD calculations. More specific correlations for mass transfer numbers and interfacial areaare normally more relevant. But for the future, it is of course a challenge to combine CFDwith mass transfer calculations.

7.6. Validation of the flowsheet calculations containing differentmodels and calculation tools

Avalidation of the process flowsheet calculations against reality is difficult because there areno plants in operation at large scale (1 mill. ton CO2/yr). Data from smaller plants are noteasily available. An article for validation of simulation codes against pilot plants for CO2

removal was presented in 2009 by Luo et al. [71]. Most programs (with different equilibriummodels) show reasonable results compared to pilot plant data. Aspen Plus® gives slightlyhigher heat of desorption results compared to other programs and pilot plant data.

Validation of flowsheet calculations can be done by comparing with other calculations.The flowsheet calculation in Section 2.1 gives 85% CO2 removal with an energy consump-tion of 3.67 MJ/kg CO2 at base case conditions. When changing equilibrium model from

528 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

Kent Eisenberg to Li/Mather in the Aspen HYSYS® flowsheet calculation the CO2 removalwas reduced to 82% and the heat consumption was reduced to 3.4MJ/kg CO2 [11]. There areliterature values for similar processes between 3.9 and 4.9 MJ/kg CO2 from Desideri andPaolucci [3] and Alie et al. [4]. Most of these energy consumption values are calculatedusing Aspen Plus® with the Chen/Austgen model. In Liu et al. [25], it is claimed that theoriginal electrolytic NRTL model of Chen/Austgen tends to overpredict the heat consump-tion and suggests new parameter values to correct this.

Validation of cost estimation calculations is difficult because there are no exact costvalues. The cost estimates calculated in Section 7.4 are not claimed to be very accurate. Theinvestment cost estimate is, however, expected to include most of the cost factors that varywith size and capacity. Because of this, the calculated optimum process values like 16 mpacking height, 35�C inlet temperature and 18�C in heat exchanger temperature differenceare assumed to be reasonable.

There are no calculated optimum values in the literature to compare with. There are,however, typical values available in the literature. In the CO2 Capture Project [67], a totalabsorber height of 28 m was used, where the packing height is only a part. This compares wellwith our calculated optimum of 16m packing height. In the same project, the gas to the absorberwas cooled to 47�C compared to our calculated optimum of 35�C. There is a high uncertainty inthe optimum value of this temperature. The gas cooling cost is very dependent on localconditions. In the calculations, there is a high uncertainty in the temperature dependency ofthe absorption efficiency. TheCO2Capture Project uses aminimumheat exchanger temperaturedifference of 11�C. This is lower than our calculated optimum at 18�C. Tobiesen et al. [7] haveshown in process simulations that there is little energy to save by reducing this temperaturedifference. This indicates that the optimum temperature difference is higher than 11�C. A mainaim with this work is to show the possibility to calculate such optimum process values.

8. Summary

The tasks of modelling the CO2 removal process can be divided into descriptions ofabsorption and reaction kinetics, gas/liquid equilibrium, gas and liquid flows and pressuredrop. Process simulation tools containing models for most of these tasks are commerciallyavailable, and the calculated results can be used as a basis for equipment dimensioning andeconomical optimization. A flowsheet calculation in the program Aspen HYSYS® is used asan example. Calculation convergence is important, especially the column convergence iscritical. For some simplified conditions, calculation of stage efficiencies can give a satisfac-tory description of the absorption process.

There is still a challenge to search for improved vapour/liquid equilibriummodels. Thereis need for improved accuracy, and the models should be robust and easy to use incombination with kinetic models.

There is serious deviation between different estimation methods for mass transfer instructured packing. The deviation is especially large for the different prediction methods foreffective gas/liquid interfacial area.

CFD is an efficient tool for calculating flow conditions, pressure drop and temperatureprofiles, especially for one fluid phase. CFD is obviously suitable for simulating flowdistribution and for calculating pressure drop in auxiliary equipment like liquid and gasdistributors. It is a challenge to make more use of CFD for gas/liquid processes. An unsolvedproblem is the description of the gas/liquid interfacial area, and especially combined withabsorption.

Mathematical and Computer Modelling of Dynamical Systems 529

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

There is a traditional trade-off between complex and accurate models compared tosimpler and more robust models. Under some conditions, a non-rigorous model is accuratelyenough. There is a challenge to find out under which conditions a simplified method issatisfactory. In time-consuming calculations like optimization and time-dependent simula-tions, it can be advantageous to avoid complex models that may lead to divergence, forexample complex equilibrium models and models involving the solving of differentialequations. In such cases a more rigorous model can be used in a separate calculation.

A major challenge is the combination of different models and calculation tools. In thecase of process simulation programs, Cape-Open is an example of a standard interface forintroducing a new component into an existing program package. An improved model for aspecific task must be available and possible to combine with other calculation tools to beutilized by other programs.

In an example, models for equilibrium and mass transfer efficiency are used in aflowsheet calculation including CO2 absorption and desorption, followed by economicaloptimization. The example illustrates some possibilities, limitations and challenges.

References[1] A. Kohl and R. Nielsen, Gas Purification, 5th ed., Gulf Publications, Houston, 1997.[2] P.V. Danckwerts and M.M. Sharma, The absorption of carbon dioxide into solutions of alkalis

and amines (with some notes on hydrogen sulphide and carbonyl sulphide), The ChemicalEngineer, October (1966), pp. 244–280.

[3] U. Desideri and A. Paolucci, Performance modelling of a carbon dioxide removal system forpower plants, Energy Conversion Manage. 40 (1999), pp. 1899–1915.

[4] C. Alie, P. Backham, E. Croiset, and P.L. Douglas, Simulation of CO2 capture using MEAscrubbing: a flowsheet decomposition method, Energy Conversion Manage. 46 (2005), pp.475–487.

[5] C. Chen and L.B. Evans, A local composition model for the excess Gibbs energy of aqueouselectrolyte systems, AICHE J. 32 (1986), pp. 444–454.

[6] D.M. Austgen, G.T. Rochelle, X. Peng, and C. Chen, Model of vapor–liquid equilibria foraqueous acid gas-alkanolamine systems using the electrolyte-NRTL equation, Ind. Eng. Chem.Res. 28 (1989), pp. 1060–1073.

[7] F.A. Tobiesen, H.F. Svendsen, and K.A. Hoff, Desorber energy consumption amine basedabsorption plants, Int. J. Green Energy 2 (2005), pp. 201–215.

[8] A. Aroonwilas, A. Chakma, P. Tontiwachwuthikul, and A. Veawab, Mathematical modelling ofmass-transfer and hydrodynamics in CO2 absorbers packed with structured packings, Chem.Eng. Sci. 58 (2003), pp. 4037–4053.

[9] H.M. Kvamsdal, J.P. Jacobsen, and K.A. Hoff, Dynamic modelling and simulation of a CO2

absorber column for post-combustion CO2 capture, Chem. Eng. Process: Process Intensification48 (2009), pp. 135–144.

[10] T. Greer, S.A. Jayarathna, M. Alic, M.C. Melaaen, and B. Lie, Dynamic model for removal ofcarbon dioxide from a post combustion process with monoethanolamine, 6th Vienna Conferenceon Mathematical Modelling (MATHMOD 09), Vienna, Austria, 2009.

[11] L.E. Øi, Aspen HYSYS simulation of CO2 removal by amine absorption from a gas based powerplant, The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007), Gøteborg,Sweden, 2007.

[12] R.L. Kent and B. Eisenberg, Better data for amine treating, Hydrocarbon Process. 76 (1976),pp. 87–90.

[13] M.H. Li and K.P. Shen, Calculation of equilibrium solubility of carbon dioxide in aqueousmixtures of monoethanolamine with methyldiethanolamine, Fluid Phase Equilib. 85 (1993),pp. 129–140.

[14] N.A. Al-Baghli, S.A. Pruess, V.F. Yesavage, andM.S. Selim, A rate-based model for the design ofgas absorbers for the removal of CO2 and H2S using aqueous solutions of MEA and DEA, FluidPhase Equilib. 185 (2001), pp. 31–43.

530 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

[15] S. Freguia and G.T. Rochelle,Modelling of CO2 capture by aqueous monoethanolamine, AICHEJ. 49 (2003), pp. 1676–1686.

[16] L. Kucka, I. Müller, E.Y. Kenig, and A. Gorak, On the modelling and simulation of sour gasabsorption by aqueous amine solutions, Chem. Eng. Sci. 58 (2003), pp. 3571–3578.

[17] G.F. Versteeg, L.A.J. Van Dijck, and W.P.M. Van Swaaij, On the kinetics between CO2 andalkanolamines both in aqueous and non-aqueous solutions: an overview, Chem. Eng. Comm.144 (1996), pp. 113–158.

[18] M. Caplow, Kinetics of carbamate formation and breakdown, J. Am. Chem. Soc. 90(24) (1968),pp. 6795–6803.

[19] P.M.M. Blauwhoff, G.F. Versteeg, and P.M. Van Swaaij, A study on the reaction between CO2 andalkanolamines in aqueous solutions, Chem. Eng. Sci. 39 (1984), pp. 207–225.

[20] E.B. Rinker, H.A. Ashour, and O.C. Sandall, Kinetics and modelling of carbon dioxide absorp-tion into aqueous solutions of N-methyldiethanolamine, Chem. Eng. Sci. 50 (1995), pp. 755–768.

[21] G. Sartori and D.W. Savage, Sterically hindered amines for CO2 removal from gases, Ind. Eng.Chem. Fund. 22 (1983), pp. 239–249.

[22] T. Mimura, S. Shimojo, T. Suda, M. Iijma, and S.Mitsuoka, Research and development on energysaving technology for flue gas carbon dioxide recovery and steam system in power plant, EnergyConversion Manage. 36 (1995), pp. 397–400.

[23] T. Chakravarty, U.K. Phukan, and R.H. Weiland, Reaction of acid gases with mixtures of amines,Chem. Eng. Prog. 81 (1985), pp. 32–36.

[24] D. Peng and D.B. Robinson, A new two-constant equation of state, Ind. Eng. Chem. Fundam.15(1) (1976), pp. 59–64.

[25] Y. Liu, L. Zhang, and S.Watanasiri, Representing vapor–liquid equilibrium for an aqueousMEA-CO2 system using the electrolyte nonrandom-two-liquid model, Ind. Eng. Chem. Res. 38 (1999),pp. 2080–2090.

[26] Y. Li and A.E. Mather, Correlation and prediction of the solubility of carbon dioxide in a mixedalkanol solution, Ind. Eng. Chem. Res. 33 (1994), pp. 2006–2015.

[27] L. Kaewsichan, O. Al-Bofersen, V.F. Yesavage, and M. Sami Selim, Predictions of the solubilityof acid gases in monoethanolamine (MEA) and methyldiethanolamine (MDEA) solutions usingthe electrolyte-UNIQUAC model, Fluid Phase Equilib. 183–184 (2001), pp. 159–171.

[28] L. Faramarzi, G.M. Kontogorgis, K. Thomsen, and E.H. Stenby, Extended UNIQUAC model forthermodynamic modeling of CO2 absorption in aqueous alkanolamine solutions, Fluid PhaseEquilib. 282 (2009), pp. 121–132.

[29] A. Gil-Villegas, A. Galindo, P.J. Whitehead, S.J. Mills, G. Jackson, and A.N. Burgess, Statisticalassociating fluid theory for chain molecules with attractive potentials of variable range, J. Chem.Phys. 106 (1997), pp. 4168–4186.

[30] N. Mac Dowell, A. Galindo, C.S. Adjiman, and G. Jackson,Modelling the phase behaviour of theCO2+H2O+amine mixtures using transferable parameters with SAFT-VR, Presentation at AIChEAnnual Meeting, Nashville, Tennessee, 8–13 November 2009.

[31] W.K. Lewis and W.G. Whitman, Principles of gas absorption, Ind. Eng. Chem. 16 (1924), pp.1215–1220.

[32] R. Higbie, The rate of absorption of a pure gas into a still liquid during short periods of exposure,Trans. Am. Inst. Chem. Eng. 31 (1935), pp. 365–383.

[33] P.V. Danckwerts, Significance of liquid-film coefficients in gas absorption, Ind. Eng. Chem. 43(1951), pp. 1460–1467.

[34] W. Kays, M. Crawford, and B. Weigand, Convective heat and mass transfer, 4th ed.,McGrawHill, Boston, 2005.

[35] D.W. Van Krevelen and P.J. Hoftijzer, Kinetics of gas–liquid reactions. Part 1: general theory,Rec. Trav. Chim. 67 (1948), pp. 563–568.

[36] R.A. Tomkej, F.D. Otto, H.A. Rangwala, and B.R. Morrell, Tray design for selective absorption,Gas Conditioning Conference, Norman, Oklahoma, 1987.

[37] W.J. DeCoursey, Absorption with chemical reaction: development of a new relation for theDanckwerts model, Chem. Eng. Sci. 29 (1974), pp. 1867–1872.

[38] W.J. DeCoursey, Enhancement factors for gas absorption with reversible reaction, Chem. Eng.Sci. 37 (1982), pp. 1483–1489.

[39] F.A. Tobiesen and H.F. Svendsen, Experimental validation of a rigorous absorber model for CO2

postcombustion capture, AICHE J. 53(4) (2007), pp. 846–865.

Mathematical and Computer Modelling of Dynamical Systems 531

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

[40] G. Astarita, D.W. Savage, and J.M. Longo, Promotion of CO2 mass transfer in carbonatesolutions, Chem. Eng. Sci. 36 (1981), pp. 581–588.

[41] D.P. Hagewiesche, H.A. Ashour, H.A. Al-Ghawas, and O.C. Sandall, Absorption of carbondioxide into aqueous blends of monoethanolamine and N-methyldiethanolamine, Chem. Eng.Sci. 50 (1995), pp. 1071–1079.

[42] L. De Leye and G.F. Froment, Rigorous simulation and design of columns for gas absorption andchemical reaction – I, Comput. Chem. Eng. 10(3) (1986), pp. 493–504.

[43] T.K. Sherwood, G.H. Shipley, and F.A.L. Holloway, Flooding velocities in packed columns, Ind.Eng. Chem. 30, No. 7 (1938), pp. 765–769.

[44] J.S. Eckert, No mystery in packed-bed design, Oil Gas J. 68(34) (1970), pp. 58–64.[45] K. Onda, H. Takeuchi, and Y. Okumoto,Mass transfer coefficients between gas and liquid phases

in packed columns, J. Chem. Eng. Jpn. 1 (1968), pp. 56–62.[46] J. Bravo and J. Fair,Generalized correlation for mass transfer in packed distillation columns, Ind.

Eng. Chem. Proc. Des. Dev. 21 (1982), pp. 162–170.[47] J.A. Rocha, J.L. Bravo, and J.R. Fair, Distillation columns containing structured packings: a

comprehensive model for their performance. 1. Hydraulic models, Ind. Eng. Chem. Res. 32(1993), pp. 641–651.

[48] J.A. Rocha, J.L. Bravo, and J.R. Fair, Distillation columns containing structured packings: acomprehensive model for their performance. 2. Mass-transfer model, Ind. Eng. Chem. Res. 35(1996), pp. 1660–1667.

[49] R. Billet and M. Schultes, Prediction of mass transfer columns with dumped and arrangedpackings, Trans. IChemE. 77 (1999), pp. 498–504.

[50] M.H. De Brito, U. von Stockar, and P. Bomio, Predicting the liquid phase mass transfercoefficient – kL-for the Sulzer structured packing Mellapak, ICHEME Symp. Ser. 128 (1992),pp. 137–144.

[51] E. Brunazzi, A. Paglianti, and L. Petarca,Design of absorption columns equipped with structuredpackings, La Chimica e l’Industria 78 (1996), pp. 459–467.

[52] P. Valluri, O.K. Matar, A. Mendes, and G.F. Hewitt,Modelling hydrodynamics and mass transferin structured packings – A review, Multiphase Sci. Tech. 14(4) (2002), pp. 303–348.

[53] G.Q. Wang, X.G. Yuan, and K.T. Yu, Review of mass-transfer correlations for packed columns,Ind. Eng. Chem. Res. 44 (2005), pp. 8715–8729.

[54] S. Shetti and R. Cerro, Fundamental liquid flow correlations for the computation of designparameters for ordered packings, Ind. Eng. Chem. Res. 36 (1997), pp. 771–783.

[55] P.A. Nawrocki, Z.P. Xu, and K.T. Chuang,Mass transfer in structured corrugated packing, Can.J. Chem. Eng. 69 (1991), pp. 1336–1343.

[56] Z. Olujic, Development of a complete simulation model for prediction the hydraulic and separa-tion performance of distillation columns equipped with structured packing, Chem. Biochem.Eng. Q. 11, No. 1 (1997), pp. 31–46.

[57] Z. Olujic, A.B. Kamerbeek, and J. de Graauw, A corrugation geometry based model for efficiencyof structured distillation packing, Chem. Eng. Process. 38 (1999), pp. 683–695.

[58] A. Shilkin and E.Y. Kenig, A new approach to fluid separation modelling in the columnsequipped with structured packings, Chem. Eng. J. 110 (2005), pp. 87–100.

[59] I. Iliuta and F. Larachi,Mechanistic model for structured-packing-containing columns: irrigatedpressure drop, liquid holdup, and packing fractional wetted area, Ind. Eng. Chem. Res. 40(2001), pp. 5140–5146.

[60] M. Klöker, E.Y. Kenig, and A. Górak, On the development of new column internals for reactiveseparations via integration of CFD and process simulation, Catal. Today 79–80 (2003), pp. 479–485.

[61] C.F. Petre, F. Larachi, I. Iliuta, and B.P.A. Grandjean, Pressure drop through structured packings:breakdown into the contributing mechanisms by CFD modelling, Chem. Eng. Sci. 58 (2003), pp.163–177.

[62] F. Larachi, C.F. Petre, I. Iliuta, and B. Grandjean, Tailoring the pressure drop of structuredpackings through CFD simulations, Chem. Eng. Process. 42 (2003), pp. 535–541.

[63] I. Iliuta, C.F. Petre, and F. Larachi, Hydrodynamic continuum model for two-phase flowstructured-packing-containing columns, Chem. Eng. Sci. 59 (2004), pp. 879–888.

[64] L. Raynal, C. Boyer, and J. Ballaguet, Liquid holdup and pressure drop determination instructured packing with CFD simulations, Can. J. Chem. Eng. 82 (2004), pp. 871–879.

[65] L. Raynal, F.B. Rayana, and A. Royon-Lebeaud,Use of CFD for CO2 absorbers optimum design:from local scale to large industrial scale, GHGT-9, Energy Procedia. 1 (2009), pp. 917–924.

532 L.E. Øi

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012

[66] C.L. Mariz, Carbon dioxide recovery: large scale design trends, J. Can. Petrol. Tech. 37(7)(1998), pp. 42–47.

[67] G.N. Choi, R. Chu, B. Degen, H.Wen, P.L. Richen, and D. Chinn,CO2 removal from power plantflue gas – cost efficient design and integration study, in CO2 Capture Project, Vol. 1, D.C.Thomas, ed., Elsevier, Oxford, 2005, pp. 99–116.

[68] T.G. Amundsen, C.H. Arntsen, E.A. Blaker, and A.M. Morland, Aspen HYSYS simulation andcost estimation of CO2 removal, MSc Project, Telemark University College, Porsgrunn, Norway,2007.

[69] L.E. Øi, E.A. Blaker, and N.H. Eldrup, Cost optimization of process parameters for CO2 removalby absorption in MEA using aspen HYSYS, Poster Presentation at 5th Trondheim Conference onCO2 Capture, Transport and Storage, NTNU, Trondheim, Norway, 16–17 June 2009.

[70] M.S. Peters, K.D. Timmerhaus, and R.E.West, Internet Estimator. Available at http://www.mhhe.com/engcs/chemical/peters/data/ (Accessed 4 June 2008).

[71] X. Luo, J.N. Knudsen, D. de Montigny, T. Sanpasertparnich, R. Idem, D. Gelowitz, R. Notz, S.Hoch, H. Hasse, E. Lemaire, P. Alix, F.A. Tobiesen, O. Juliussen, M. Köpcke, and H.F. Svendsen,Comparison and validation of simulation codes against sixteen sets of data from four differentpilot plants, GHGT-9, Energy Procedia 1, 2009, pp. 1249–1256.

Mathematical and Computer Modelling of Dynamical Systems 533

Dow

nloa

ded

by [

Indi

an I

nstit

ute

of P

etro

leum

] at

01:

48 2

0 Ju

ne 2

012