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UC engineering

University of Carabobo

[email protected]

ISSN (print): 1316-6832

VENEZUELA

2003

Aida Perez R. / Eliana T. Pea /

Pascual Aljibes D.

MODELING, SIMULATIONAND CONTROL OF

A REACTOR exothermic

Batches using MATLAB-SIMULINK

UC Engineering, August, yr

/ vol. 10, number 002

University of Carabobo

Valencia, Venezuela

pp. 7-17

Network of Scientific Journals of Latin America and the Caribbean, Spain and

Portuguese

Autonomous University of Mexico State

http://redalyc.uaemex.mx


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Aida R. Perez, Eliana T. Pea, D. Pascual Aljibes

Research Unit in Industrial Automation, School of ElectricalEngineering, University of Carabobo, Venezuela, E-

mail: [email protected], pad@net_uno.net

Department of Physics, Faculty of Engineering, University

of Carabobo, E-mail: [email protected]

Summary

This paper aims to study a batch exothermic reactor from its mathematical

model. It defines the equations describing the dynamic behavior of the

reactor studied and selected parameter that represent it. Analyses are

performed in open loop system modeling and design your control scheme,

based on the traditional algorithm proportional - integral - derivative (PID).

Keywords:Chemical reactor, simulation in Matlab-Simulink, nonlinear

model, phases of operation, PID algorithm.

Modeling, simulation and control of a reactor

exothermic batch using Matlab-Simulink

Modeling, simulation and control of a reactor

exothermic batch using Matlab-Simulink1. INTRODUCTION

A chemical reactor can be defined as a

equipment which is a substance or

product from other call reactant through

a series of chemical transformation

Batch processing is a sector importantchemical process industry. This type of

process is used in the production

of chemical use highly specialized

monkeys, pharmaceuticals, polymers

and other related field of biotechnology.

Batch processes require a strategy

different from control continuous

processes as they do not operate at

steady state.

The objective control is to make the system

output follows a desired trajectory.

The batch reactor operation are intermittent

rather complex since they require

procedures such as filling, mixing, heating,

control of the endpoint, adding power,

cooling products, removal and emptying. Ifyou also have an exothermic reaction, the it

is often unstable steady state.

Because of the importance of these

units and often costly process that would

involve the study from pilot plant at the

undergraduate level his article focuses

on the design of a control scheme

for an exothermic batch reactor, with the

mathematical modeland computer

simulation as supports for the whole

development of the design, and using the


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Academic scientific software Matlab Simulinktool and programming elements.

2. DESCRIPTION OF THE PROCESS

The batch reactor model studied is limited tothe stages of heating, filling the cooling

jacket, which occurs during exothermic

reaction in the tank and the desired products

is formed from a reactant, he reactant has

been previously loaded and mixed in the

reactor, so the same volume remains

constant. To star the reaction mixture is

injected into the steam jacket. This raises the

temperature of the mixture to certain limit

value. After reaching this value, the valve

closes the steam injection. After the reaction,

begin, it begins to release heat, which will be

removed by opening the cold water valve, in

order to maintain the reactor temperature

within the operating range established by the

process.

The original control objective is to achieve

a proper conversion of the product formed,

minimizing the presence of the product. This

is achieved by controlling the temperatureinside the reactor, to be the variable that

provides more information on the dynamics of

the reaction.

The manipulated variables are the steam and

water flows entering the reactor, thus forming

the heating-cooling system of the reactor.

This system will operate with heat transfer

coefficients up, in order to provide or remove

(depending on the phase of operation of the

model) as much heat as possible. The

mechanism of movement isa single pass, ie,

the flow of steam and water pass through

the coat once. The disturbance applied to the

process is the temperature of cold water for

filling and cooling stages only.

BATCH REACTOR MODELING

The nonlinear dynamic model of the batch

reactor was obtained from the differential

equations describe its operation.

Please note that this is an intermittent

and self-regulatory process. The following

considerations were made:

The reaction is exothermic, irreversible and

first order, the type A => B => C, where A isthe reactant, B and C the main product the

product unwanted side.

The downtime is not modeled

Reactant, product and product are liquid

phase

The density and heat capacity of the

mixture remain constant and other

thermodynamic properties of reactant andproduct.

Only the energetic effects are modeled to

occur in the wall of the tank and are

considered negligible effects on the walls of

the jacket.

The volume of the mixture is constant.

The volume of the jacket is constant during

the heating and cooling phases

In the Figure 1 shows an illustrative drawing

process, accompanied by the heating

system cooling jacket type

Figure 1


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Below are the equations describing the

operation of the batch reactor under study:

Component balance on the reactant:

Where:

(T): final concentration of reactant

lbmol/pie3

K (T): specific reaction rate of the reaction

major, min. (depends on the temperature of

the mixture).

Balance on the product component

Where:

(t): the final product concentration

lbmol/pie3

(T): specific reaction rate of the

secondary reaction, min.

Equations for reaction rates specific

Where:

, : pre-exponential factor or frequency

Arrhenius for primary and secondary

reactions, respectively, min.

, activation energies of the

respective primary and secondary reactions,

Btu / lbmol.

R: universal gas constant, Btu / lbmol. R.

T (t): temperature inside the reactor, F.

Energy balance in the reactor:

Where:

: density of the reaction mixture, lbm/ft3.

CP: average heat capacity of the mixture,

Btu / lbm. F.

V: volume of the reaction mixture, ft3.

me: film coefficient of internal heat transfer,

Btu / F.ft2.s.: internal area of heat transfer, ft2.

TM (t): temperature of the walls of the tank,

F.

, : exothermic heat of the main reactions

and secondary, respectively, Btu / lbmol.

Energy balance in the tank walls

Two coefficients are defined external heat

transfer: one for the heating phase (vapor of

water) and one for filling and cooling phases

(cool water).

Energy balance in the tank walls

during the calentamient

Where:

: density of the metal walls of the tank,

lbm/pie3.

: heat capacity of the tank walls,

Btu/ lbm. F.

: volume of the tank walls, ft3.

MOS film transfer coefficient external heat of

steam,Btu / F.ft2.

: External area of heat transfer, ft2.

(t): temperature inside the jacket, F.


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Energy balance in the tank walls duringfilling and cooling stages:

Where:

mow: film coefficient of heat transfer

External cold water, Btu / F.pie2.s.

Mass balance in the jacket to the heating

step:

Where:

: Constant volume of the jacket, ft3.

: vapor density inside and at the exit of the

jacket, lbm/pie3.

Fs (t): flow rate of water vapor, pie3/min.

: density of vapor entering the jacket,

lbm/pie3.

WC (t): rate of condensation of vapor massflow water, lbm / min.

Equation of state of water vapor:

Where:

: enthalpy difference between inletand vapor outlet enthalpy.

Equation for vapor pressure:

Where:

: Constant pressure of water vapor, R.

: Constant pressure of water vapor,dimensionless.

Equation for calculating vapor density

depending on pressure and temperature:

Where:

M: Molecular weight of the vapor,

M=18lbm/mol.

Mass balance in the jacket to the stage of

filling:

Where:

: Constant volume of the jacket, ft3.

=flow rato of water supply Cold

Energy balance in the jacket to the stage

filling:

Where:

: Density of water coming out of the jacket,

lbm/.

: Heat capacity of water in the jacket,

Btu/lbm. F.

: Power flow temperature of the jacket.

F.

Film coefficient of heat transfer

external Btu/ F..s.

: External area of heat transfer, .

Equation for the variation of transfer area in

the external heat:


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Expression for the calculation of the

temperature in the jacket:

Energy balance in the jacket to the stage

cooling:

4. CHARACTERISTICS PARAMETERS andInitial Conditions

Operating Condition:

=200F

Table 2. Constants Used.

Table 3. Initial Conditions

5. DESCRIPTION OF THE SCHEME

INSTRUMENTATION AND CONTROL

The following are aspects with theinstrumentation and control scheme for

exothermic batch reactor under study.

5.1 Transmitter

There is only one variable to be measured

the temperature, the reactor. To measure a

transmitter is used a standard output 4 to

20mA. The same range was selected

according to the maximum values obtained

by temperature-loop closed.


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The equation to represent the transmitter iszero order, consist only of a gain for convert

mA temperature and delay is considered

negligible compared with the constant

processing time. The equation of the output

signal of the transmitter follows:

Where:

TT(t): Output signal of the transmitter mA.

: Temperature signal input to the

transmitter. F.

: Minimum value of the transmitter range,

50F.: Maximum output signal of the

transmitter, 20 mA.

: Minimum transmitter output. 4mA.

The equation (17-A) indicates that the

relationship between the input signal and the

output of the transmitter is a straight linewhose, slope a represents the gain of the

transmitter:

5.2. Controller

The output signals of the temperature

controller go to two valves that will operate inrange match, one of steam and other cold

water. The input and electrical output of the

controller are in the range standard 4 to 20

mA. The controller is of action inverse. This

action is selected according to the position

must have the valves to a fault safe. The

strategy employed will be the basis of

proportional, integral and derivative (PID).

5.3. I/P Converter

They use two currents to pressure converter

I/P to convert a electrical signal from the

controller a pneumatic signal to the valve inlet

a respective governing steam and water

flows cold. The equation of the converter

output signal is as follows:

Where:

Y (t): Output signal of the converter, psig.

TC (t): Output signal of the controller, mA.

: Maximum output of the converter, 15

psig.

: Minimum converter output signal, 3psig.

The equation (18-A) represents a straight

line, slope:

5.4. Valves

5.4.1. Type of action

The valve action is selected according the

characteristics of the process for action of the

fail safe: the steam valve is closed fault or air

to open, as in case of supply failure air, it

remains closed, preventing that the

unregulated input of energy delivered by the

steam. The cold water valve is open or air

failure to close, to keep it open in case failure

so we can remove the maximum amount ofheat exothermic reaction possible and also

ensure the system security.

5.4.2. Flow characteristics of valves

Two were selected for linear valves manage

the flow of steam and cold water respectively.

For the steam valve, the mass flow that was

enters in the jacket is:


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Where:

: Coefficient of valve sizing steam lbm/min.

.

: Opening the steam valve.

: Feed pressure steam, psia.

Vapor pressure inside the jacket, psia.

For the cold water valve volumetric flow

that going inside the jacket is:

Where:

: Coefficient of valve sizing water,

lbm/min.

: Fraction of valve opening of cold

water.

: Head cold water pressure, psig.

This flow characteristic chosen for valves not

take into account aspects installation of the

pipes themselves, because the study is

limited to the simulation of the process

through of his mathematical equations, in

isolation, without include the effect of other

processes which would interacting with a

reactor in a real operation.

5.4.3 Operating Range Equations

The valves must be adjusted so that thesteam valve is fully open when the controller

output signals is at maximum value (20mA),

and is closed when its output is in half the

total range (12mA). The cold water valve is

closed when the controller output is 12mA

and completely open for a driver output signal

of 4mA (minimum range). The action of the

valves can be represented as follows:

Steam valve

Valve for cold water

Where:

Y (t): output of the converter I/P, Psig.

: Value of half the range of converter, 9

Psig.

: Maximum output of the converter, 15

Psig.

Minimum inverter output signal, 3 Psig.

5.4.4. Coefficient for Sizing

Coefficient for valve sizing steam:

: 112lbm/(min. .

Coefficient for valve sizing cold water:

: 100gpm/(.

The justification for the selection of thesevalues is detailed in this article, but appears

in the work of Perez and Pea.

5.5 Control Scheme

5.5.1. Open-Loop Tests

The reactor modeling can not operate in open

loop by requiring a system to regulate the

amount of heat added initially and then

remove that occurs as a result of thechemical reaction.

To demonstrate the accuracy of the above

statement, simulations were performed in

open loop leaving the reactor, keeping fixed

the valve openings respective governing

steam and water flows cold.

The simulations were performed on the

model built in Matlab-Simulink. Some of the

results obtained are presented in figures 2and 3 where shows the temperature

response of the reactor and concentration of


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the product when leaving the steam valvefully open and close the cold water valve.

Figure 2 shows how the temperature rises

without any restriction, reaching a peak value

becomes more than double its set point

which should be avoided with the controlscheme.

Temperature inside of reactor

Time in seconds

Figure 2. Simulation with the steam valve open.

Concentration of Products

Time in seconds

Figure 3. Simulation with open steam valve

100% and the water valve completely closed.

Concentration of the product.

Both temperature and concentration have an

inverse response due to the same increase

disproportionate temperature, which favors

secondary reaction and wastes part of theconversion initially achieved.

5.5.2 Criteria for selection as most

appropriate control

To control the batch reactor were performed

several simulations with different modes or

actions.

That allowed the end to reach an adequate

response within the constraints of the type of

controller and selected (traditional), taking

into account several aspects. Produce a

proper conversion of reactant to product,

about 50%.

Reduce the overshoot in temperature.

Achieve a good rejection to small

perturbations of the 10% and 20% inthe temperature cold water inlet.

Avoid continuous saturation and

oscillation controller and valves within

the limitations imposed by the

dynamics of the process.

5.5.3. Control Act.

We used a classical control law by feedback,

using a control scheme based on a PID. The

simplest formula for the controller PID is

written as follows:

Where:

: Controller gain.

Full time.

: Derivate time.

: Manual reset

The equation (23) corresponds to a PID

controller Parallel or ideal, for the three

moods are in parallel. When using all three

modes, usually an approximation using a

progress-delayed is resulting in the followingfunction of transfer.


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The typical values are from 0.05 to 0.1, a on

the selected, it is varied and not on the signal

error.

5.5.4 Simulation results with control

parameters calculated from the method of

continuous variations.

Parameters were calculated controller

according to the formulas for optimal settings

according to the method of continuous

oscillations of Ziegler and Nichols for closed

chain. We applied the pure proportional

mode, proportional most derivatives with the

controlled variable derivative, proportional

plus integral and proportional plus more

integral derivative in order to observe theresults provided with the control parameters

given in the table 4.

The parallel simulation with PID schemeparameter in table 4, could not be completedas which caused difficulties in the calculationof the derivative, is therefore obviate theresults of the experiment.

The analysis of the simulations (not shown inthis study) shows the following:

*The proportional action alone leaves a stateerror considerable stationary.

* For the proportional case, there is muchoscillation in the steam valve after their

operation stage. In a real plant would involvea continuous transition between injection ofsteam and water.

*The derivate term is implemented ideal,either on the controlled variable or on theerror, the simulator program causes problemsin the calculation of derivatives by advancefeature or Prediction of behavior of thecontrolled variable, in addition to saturate thecontroller and thus the final control elements.

*The integral action causes a large overshootin the heating phase of the reactor, but isrequired for the cooling phase.

5.5.5 Simulation results with improvedcontrol schemes

To improve the schemes, the parameterswere adjusted above and applied thefollowing changes:

Use a proportional control duringphases warming and filling, andchange to a proportional plus integralscheme at this stage of cooling

Introduction of a unit in advance delayin order to improve theimplementation of derivative action inthe simulator program

Use of a proportional plus derivativecontrol for the phases of warming andfilling, and a scheme for proportionalplus integral final stage of operation.

Some results are illustrated in figures 4 and

5. They show that the integral action

decreases in each case the phase error

cooling. The PID control unit lead-lag shown

in figure 4 achieves a short response to

temperature oscillations around the point of

operation. The control PD-PI (Figure 5) is not

as ideal as above but also produces a

trajectory acceptable temperature, with

variations bellows.


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Temperature inside of the reactor

Time (Seconds)

4-a Reactor Temperature

Flow

Flow

4-b Opening Of The Valves

Figure 4. Simulation with PID controller anddevelopment unit-in the controlled variabledelay.

: 2,3 . : 4.2 :33.3

The variation of and made in otherssimulations, it appeared that it did notproduce much effect on product conversionachieved, but affected the temperatureovershoot and oscillations steam valve.


Figure 5. Simulation with a PD-PI controller

:2. : 16.7 :58.3


Tiempo (s)

Figure 6, PID controller response unit lead-lag in temperature shocks cold water inlet.

5.5.6. Behavior disturbances

Figure 6, shows the mode behavior PID withlead-lag unit shocks +20% and -20% in theinlet temperature cold water flowing throughthe jacket, the value of operation is 80F.

The advance unit-delayed rejection improvescontroller to disturbances which reflected inthe overshoot, whose increase (fordisturbances positive) is much less than theschemes without derivative action, as is thecase of P-PI control. The latter requires moretime to recover from shocks applied.

6. Conclusions

The use of simulink as a tool sub-block

programming was used to construct thenonlinear model and batch reactor divided


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according to their distinct phases ofoperation:

Warming, filling and cooling. Theprogramming Matlab was used to coordinate

the simulation of these stages.

Achieved a conversion of reactant to productabout 50% thus minimizing the presence ofproduct through temperature control. Theapplication of different combinations of thealgorithm PID allowed observing the effect ofeach of these variations on the dynamic of asingle reactor chemical study by its level of asingle chemical study by its level of controlcomplete. The selection of the controller gainand coefficient of the valve sizing cold water

() implies a compromise betweenparameter, since a higher gain () and a coefficients less than the design produce anovershoot higher initial temperature, whileoscillations of the valve is reduced whendecrementing , .

7. References

Smith, J.M. (1997). Kinetic

Engineering Chemistry, editorial

CECSA, Mexico.

Shinskey, F.G.(1988).Process

Control Systems (Application, Design

and Tuning).Mc Graw Hill, Third

Edition U.S.A.

Luyben, William (1990). ProcessModeling,Simulation and Control for ChemicalEngineers. Mc Graw Hill. SecondEdition. U.S.A.

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