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Title: Integration of process design and controller design forchemical processes using model-based methodology
Authors: Mohd Kamaruddin Abd Hamid, Gurkan Sin, Rafiqul
Gani
PII: S0098-1354(10)00029-3
DOI: doi:10.1016/j.compchemeng.2010.01.016
Reference: CACE 3966
To appear in: Computers and Chemical Engineering
Received date: 3-9-2009
Revised date: 7-1-2010
Accepted date: 21-1-2010
Please cite this article as: Hamid, M. K. A., Sin, G., & Gani, R.,
Integration of process design and controller design for chemical processes
using model-based methodology, Computers and Chemical Engineering (2008),
doi:10.1016/j.compchemeng.2010.01.016
This is a PDF file of an unedited manuscript that has been accepted for publication.
As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proof
before it is published in its final form. Please note that during the production process
errors may be discovered which could affect the content, and all legal disclaimers that
apply to the journal pertain.
http://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/doi:10.1016/j.compchemeng.2010.01.016http://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.compchemeng.2010.01.016http://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.compchemeng.2010.01.016http://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/doi:10.1016/j.compchemeng.2010.01.016 -
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Integration of process design and controller design for chemical1
processes using model-based methodology2
3
Mohd Kamaruddin Abd Hamid, Grkan Sin
and Rafiqul Gani4
5
Computer Aided Process-Product Engineering Center (CAPEC), Department of Chemical and6
Biochemical Engineering, Technical University of Denmark, DK-2800, Kgs. Lyngby,7
Denmark.8
9
10
Abstract11
In this paper, a novel systematic model-based methodology for performing integrated12
process design and controller design (IPDC) for chemical processes is presented. The13
methodology uses a decomposition method to solve the IPDC typically formulated as a14
mathematical programming (optimization with constraints) problem. Accordingly the15
optimization problem is decomposed into four sub-problems (i) pre-analysis, (ii) design16
analysis, (iii) controller design analysis, and (iv) final selection and verification, which are17
relatively easier to solve. The methodology makes use of thermodynamic-process insights and18
the reverse design approach to arrive at the final process design-controller design decisions.19
The developed methodology is illustrated through the design of: (a) a single reactor, (b) a20
single separator, and (c) a reactor-separator-recycle system and shown to provide effective21
solutions that satisfy design, control and cost criteria. The advantage of the proposed22
Corresponding author. Tel.: +45 45 252 806; Fax: +45 45 932 906; Email: [email protected]
nuscript
http://ees.elsevier.com/cace/viewRCResults.aspx?pdf=1&docID=2720&rev=1&fileID=53639&msid={7402F0FB-6A49-4B76-AF81-8D1788E58EB4} -
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methodology is that it is systematic, makes use of thermodynamic-process knowledge and23
provides valuable insights to the solution ofIPDCproblems in chemical engineering practice.24
25
Keywords: Model-based methodology; process design, controller design; decomposition26
method; graphical method, integration.27
28
29
1. Introduction30
31
Traditionally, process design and controller design are two separate problems that are32
dealt with sequentially. The process is designed first to achieve the design objectives, and33
then, the operability and control aspects are analyzed and resolved to obtain the controller34
design. This traditional sequential approach is often inadequate since many process control35
challenges arise because of poor design of the process and may lead to overdesign of the36
process, dynamic constraint violations, and may not guarantee robust performance (Malcom et37
al., 2007). Another drawback has to do with how process design decisions influence the38
controllability of the process. To assure that design decisions give the optimum economic and39
the best control performance, controller design issues need to be considered simultaneously40
with the process design issues. The research area of combining process design and controller41
design considerations is referred here as integrated process design and controller design42
(IPDC). One way to achieveIPDCis to identify variables together with their target values that43
have roles in process design (where the optimal values of a set of design variables are obtained44
to match specification on a set of process variables) and controller design (where the same set45
of design variables serve as the actuators or manipulated variables and the same set of process46
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variables become the controlled variables). Also, the optimal design values become the set-47
points for the controlled and manipulated variables. Using model analysis, controllability48
issues are incorporated to pair the identified actuators with the corresponding controlled49
variables. The integrated design problem is therefore reduced to identifying the dual purpose50
design-actuator variables, the process-controlled variables, their sensitivities, their target-51
setpoint values, and their pairing.52
The importance of an integrated process-controller design approach, considering53
operability together with the economic issues, has been widely recognized (Allgor and Barton,54
1999; Bansal et al., 2000; Bansal et al., 2003; Kookos and Perkins, 2001; Luyben, 2004;55
Meeuse and Grievink, 2004; Patel et al., 2008; Ricardez Sandoval et al., 2008; Schweiger and56
Floudas, 1997). The objective has been to obtain a profitable and operable process, and control57
structure in a systematic manner. The IPDC has advantage over the traditional-sequential58
method because the controllability issues are resolved together with the optimal process59
design issues. Meeuse and Grievink (2004) used the Thermodynamic Controllability60
Assessment (TCA) technique to incorporate controllability issues into the design problem. The61
IPDC problem, however, involved multi-criteria optimization and needed trade-off between62
conflicting design and control objectives. For example, the process design issues point to63
design of smaller process units in order to minimize the capital and operating costs, while,64
process control issues point to larger process units in order to smooth out disturbances65
(Luyben, 2004).66
A number of methodologies have been proposed for solvingIPDCproblems (Sakizlis et67
al., 2004; Seferlis and Georgiadis, 2004). In these methodologies, a mixed-integer non-linear68
optimization problem (MINLP) is formulated and solved with standard MINLP solvers. The69
continuous variables are associated with design variables (flow rates, heat duties) and process70
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variables (temperatures, pressures, compositions), while binary (decision) variables deal with71
flowsheet structure and controller structure. When anMINLPproblem represents anIPDC, the72
process model considers only steady state conditions, while a MIDO(mixed-integer dynamic73
optimization) problem represents an IPDCwhere steady state as well as dynamic behaviour74
are considered.75
A number of algorithms have been developed to solve the MIDO problem. From an76
optimization point of view, the solution approaches for MIDOproblems can be divided into77
simultaneous and sequential methods, where the originalMIDOproblem is reformulated into a78
mixed-integer nonlinear program (MINLP) problem (Sakizlis et al., 2004). The former79
method, also called complete discretization approach, transforms the original MIDOproblem80
into a finite dimensional nonlinear program (NLP) by discretization of the state and control81
variables. Avraam et al. (1999), Flores-Tlacuahuac and Biegler (2007) and Mohideen et al.82
(1996) applied this complete discretization approach and solved the resulting MINLPproblem83
using outer approximation (OA) and generalized Benders decomposition (GBD) frameworks.84
However, this method typically generates a very large number of variables and equations,85
yielding large NLPs that may be difficult to solve reliably (Exler et al., 2008; Patel et al.,86
2008), depending on the complexity of the process models.87
As regards the sequential method, also called control vector parameterization approach,88
only control variables are discretized. TheMIDOalgorithm is decomposed into a sequence of89
primal problems (nonconvex DOs) and relaxed master problems (Bansal et al., 2003;90
Mohideen et al., 1997; Schweiger and Floudas, 1997; Sharif et al., 1998). Because of91
nonconvexity of the constraints inDOproblems, such solution methods are possibly excluding92
large portions of the feasible region within which an optimal solution may occur, leading to93
the suboptimal solutions (Chachuat et al., 2005).94
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In order to overcome convergence to the suboptimal solution inDOorMIDOproblems,95
stochastic and deterministic global optimization (GO) methods have also been proposed.96
Regarding stochastic GOmethods, a number of works have shown that the region of global97
solutions can be located with relative efficiency (Banga et al., 2003; Moles et al., 2003; Sendin98
et al., 2004), but they tend to be computationally expensive and have difficulties with highly99
constrained problems. Most importantly, their major drawback is that global optimality cannot100
be guaranteed. While deterministic GOmethods can guarantee that the optimal performance101
has been found (Esposito & Floudas; 2000), however their applicability is limited only to102
problems with medium complexity (Moles et al., 2003).103
The objective of this paper is to present an alternative systematic model-based IPDC104
approach that is simple to apply, easy to visualize and efficient to solve. Here, the IPDC105
problem is solved by the so-called reverse approach (reverse design algorithm) by106
decomposing it into four sequential hierarchical sub-problems: (i) pre-analysis, (ii) design107
analysis, (iii) controller design analysis, and (iv) final selection and verification (Hamid and108
Gani, 2008). Using thermodynamic and process insights, a bounded search space is first109
identified. This feasible solution space is further reduced to satisfy the process design and110
controller design constraints in sub-problems 2 and 3, respectively, until in the final sub-111
problem all feasible candidates are ordered according to the defined performance criteria112
(objective function). The final selected design is verified through rigorous simulation. In the113
pre-analysis sub-problem, the concepts of attainable region (AR) and driving force (DF) are114
used to locate the optimal process-controller design solution (see section 2.4) in terms of115
optimal condition of operation from design and control viewpoints. While other optimization116
methods may or may not be able to find the optimal solution, depending on the performance of117
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their search algorithms and computational demand, the use of ARandDFconcepts is simple118
and able to find at least near-optimal designs (if not optimal) toIPDCproblems.119
This paper is organized as follows. First the new model-based IPDC methodology120
together with the decomposition into sub-problems and the methods used within the sub-121
problems are introduced in Section 2. Then, in Section 3, the application of the IPDC122
methodology in solving process design-controller design problems related to of a single123
reactor, a single separator, and a reactor-separator-recycle system are presented and discussed.124
Finally, future perspectives and conclusions are presented.125
126
127
2. The IPDCMethodology128
129
2.1 Problem formulation130
131
TheIPDCproblem is typically formulated as a generic optimization problem in which a132
performance objective in terms of design, control and cost is optimized subject to a set of133
constraints: process (dynamic and steady state), constitutive (thermodynamic states) and134
conditional (process-control specifications)135
136
m
i
n
j jji
wPJ1 1 ,
(1)137
s.t.138
Process (dynamic and/or steady state) constraints139
tYfdtd ,,,,, dxux (2)140
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Constitutive (thermodynamic) constraints141
xv, )(0 1g (3)142
Conditional (process-control) constraints143
xu,0 1h (4)144
dxu ,,h20 (5)145
YCS ux (6)146
147
In the above equations, x is the set of process (controlled) variables; usually148
temperatures, pressures and compositions. u is the set of design (manipulated) variables. d is149
the set of disturbance variables, is the set of constitutive variables (physical properties,150
reaction rates), v is the set of chemical system variables (molecular structure, reaction151
stoichiometry, etc.) and t is the independent variable (usually time). The performance152
function, Eq. (1) includes design, control and cost, where i indicates the category of the153
objective function term and j indicates a specific term of each category. jw is the weight154
factor assigned to each objective term jiP, (i= 1, 3;j= 1, 2).155
Eq. (2) represents a generic dynamic process model from which the steady state model is156
obtained by setting 0dtdx . Eq. (3) represents constitutive equations which relate the157
constitutive variables to the process and chemical system variables. Eqs. (4) (5) represent158
sets of equality and inequality constraints (such as product purity, chemical ratio in a specific159
stream) that must be satisfied for feasible operation - they can be linear or non-linear. In Eq.160
(6), Yis the set of binary decision variables for the controller structure selection (corresponds161
to whether a controlled variable is paired with a particular manipulated variable or not).162
Different optimization scenarios can be generated as follows:163
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164
Maximize jP,1 to achieve process design objectives. Here, maximize 1,1P the165
performance criteria for reactor design and maximize 2,1P the performance criteria for166
separator design.167
Minimize-maximize jP ,2 to achieve the control objectives. Here, 1,2P is minimized by168
minimizing ( dx dd ) the sensitivity of controlled variables x with respect to disturbances169
d , and 2,2P is maximized by maximizing ( xu dd ) the sensitivity of manipulated170
variables u with respect to controlled variables x for the best controller structure171
(controlled-manipulated pairing).172
Minimize jP,3 to achieve the economic objectives. Here, 1,3P is minimized by173
minimizing the capital cost and 2,3P is minimized by minimizing the operating costs.174
175
The multi-objective function in Eq. (1) is reformulated as,176
177
2,1)1()1( ,3,32,22,21,21,2,1,1 jPwPwPwPwJ jjjj (7)178
179
180
2.2 Decomposition-based solution strategy181
182
In most ofIPDCproblems, the feasible solutions to the problems may lie in a relatively183
small portion of the search space due to the large number of constraints involved. The ability184
to solve such problems depends the effectiveness of the method of solution in identifying and185
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locating the feasible solutions (one of these is the optimal solution). Hence, one approach to186
solve thisIPDCproblem is to apply a decomposition method as illustrated in Fig. 1. The basic187
idea here is that in optimization problems with constraints, the search space is defined by the188
constraints within which all feasible solutions lie and the objective function helps to identify189
one or more of the optimal solutions. In the simultaneous approach, all the constraint190
equations are solved together with the objective function to determine the values of the191
optimization variables (design-manipulated and decision variables) that satisfy the constraints192
and lead to the optimal objective function value. In the decomposition-based approach193
(Karunanithi et al., 2005) the constraint equations are solved in a pre-determined sequence194
such that after every sequential sub-problem, the search space for feasible solutions is reduced195
and a sub-set of design-manipulated and/or decision variables are fixed. When all the196
constraints are satisfied, it remains to calculate the objective function for all the identified197
feasible solutions to locate the optimal.198
The IPDC problem is decomposed into four hierarchical stages: (1) pre-analysis, (2)199
design analysis, (3) controller design analysis, and (4) final selection and verification. As200
shown in Fig. 1, the set of constraint equations in theIPDCproblem is decomposed into four201
sub-problems which correspond to four hierarchical stages (see Figs. 1 2). In this way, the202
solution of the decomposed set of sub-problems is equivalent to that of the original problem.203
As each sub-problem is being solved, a large portion of the infeasible solution of the search204
space is identified and eliminated, thereby leading to a final sub-problem that is significantly205
smaller, which can be solved more easily. Therefore, while the sub-problem complexity may206
increase with every subsequent stage, the number of feasible solutions is reduced at every207
stage, as illustrated in Fig. 2.208
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Stage 1: Pre-analysis. The objective of this stage is to define the operational window and209
set the targets for the design-controller solution. First, all x and u are analyzed and the210
important ones with respect to the multi-objective function, Eq. (7) are shortlisted. The211
operational window is defined in terms of x and u (note that d is known). Choice is made212
for x based on thermodynamic-process insights and Eq. (3) (also defines the optimal solution213
targets). Then Eqs. (4)(5) are solved (for u ) to establish the operational window. For each214
reactor task, an attainable region (AR) is drawn and the location of the maximum in theARis215
selected as the reactor design target. This point gives the highest selectivity of the reaction216
product with respect to the limiting and/or a selected reactant. Similarly, for each separation217
task, the design target is selected at the highest driving force (DF). Note that, both plots ofAR218
andDFhave a well defined maximum.219
Stage 2: Design analysis.The search space within the operational window identified in220
stage 1 is further reduced in this stage. The objective is to validate the targets defined in stage221
1 by finding acceptable values (candidates) of x and u by considering Eq. (2) the steady222
state process model. If the acceptable values cannot be found or the solution is located outside223
the operational window, then a new target is selected and the procedure is repeated until a224
suitable match is found.225
Stage 3: Controller design analysis. The search space is further reduced by considering226
now the feasibility of the process control. This sub-problem considers the process model227
constraints, Eq. (2) (dynamic and steady state forms) to evaluate the controllability228
performance of feasible candidates, and Eq. (6) for the selection of the controller structure. In229
this respect, two criteria are analyzed: (a) sensitivity ( dx dd ) of controlled variables x with230
respect to disturbances d , which should be low, and (b) sensitivity ( xu dd ) of manipulated231
variables u with respect to controlled variables x , which should be high. Lower value of232
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dx dd means the process has lower sensitivity with respect to disturbances, hence the process233
is more robust in maintaining its controlled variables against disturbances. On the other hand,234
higher value of xu dd will determine the best pair of the controlled-manipulated variables (to235
satisfy Eq. (6)) and also the optimal control action. It is assumed by this methodology that the236
best set-point values of the controller are actually those already defined as design targets. It237
should be noted that, the objective of this stage is not to find the optimal value of controller238
parameters or type of controller, but to generate the feasible controller structures.239
Stage 4: Final selection and verification. The final stage is to select the best candidates240
by analyzing the value of the multi-objective function, Eq. (7). The best candidate in terms of241
the multi-objective function will be verified using rigorous simulations or by performing242
experiments. It should be noted that, the rigorous simulation will be easy because very good243
estimates of x and u are obtained from stages 1 3. For controller performance verification244
is made through open or closed loop simulations. For closed loop simulation, the standard245
Cohen-Coon tuning method (Cohen and Coon, 1953) or any other tuning methods can be used246
to determine the value of controller parameters.247
248
2.3 The algorithm of decomposition-based methodology249
250
Stage 1: Pre-analysis251
a. Variables analysis252
Analyze all x and u , and shortlist the important ones with respect to the multi-253
objective functions, Eq. (7).254
b. Operational window identification255
Define the operational window in terms of x and u variables by solving Eqs. (4)(5).256
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c. Design-control target identification257
DrawARandDFdiagrams using Eq. (3) and identify design-control target by locating258
the maximum points on theARandDFdiagrams.259
260
Stage 2: Design analysis261
Calculate the acceptable values (candidates) of x and u variables using steady state262
process model of Eq. (2).263
a. For reactor design: at the maximum point of AR, identify the corresponding value of264
concentrations. Then find all other values of design (manipulated) and process265
variables i.e., volume, flow rates.266
b. For separator design: at the maximum point of DF and given desired product267
composition, then find all other value of design (manipulated) and process variables268
i.e., feed stage, reflux ratio, reboil ratio, reboiler and condenser duties.269
270
Stage 3: Controller design analysis271
a. Sensitivity analysis272
Calculate dx dd using Eq. (2) to determine the process sensitivity with respect to273
disturbances.274
b. Controller structure selection275
Calculate xu dd using Eq. (2) to determine the best pair of the controlled-manipulated276
variables to satisfy Eq. (6).277
278
Stage 4: Final selection and verification279
a. Final selection: verification of design280
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Evaluate the multi-objective function for the feasible candidates using Eq. (7) to select281
the optimal.282
b. Dynamic rigorous simulations: verification of controller performance283
Perform open or closed loop rigorous simulations. Solve Eqs. (2)(5).284
285
2.4 Defining design targets286
287
TheARconcept is used in this methodology to find the optimal (design target) values of288
the process variables for any reaction system. Glasser et al., (1987, 1990) considered a reactor289
as a system where the only processes occurring are reaction and mixing. For given kinetics290
and given feeds, it might be possible to find the set of outputs from all possible reactor291
systems. They have also shown that once the ARis found the optimization of the problem is292
straightforward. If one knows theAR, one can then search all over the entire region (often the293
boundary) to find the output conditions that maximize an objective function. In this paper, the294
AR-concept is used to determine the maximum of the objective function ( 1,1P ) (for reactor295
design) in terms of selectivity or maximum concentration of the reaction product.296
Similarly, theDFconcept is used in this methodology to find the optimal (design target)297
values of the process variables for separation systems. Gani and Bek-Pedersen, (2000)298
proposed a design method based on identification of the largestDF, defined as the difference299
in composition of a component i between the vapor phase and the liquid phase, which is300
caused by the difference in the volatilities of component i and all other components in the301
system. This DF is calculated for a binary mixture or a binary pair of key components of a302
multi component mixture. As the DF approaches zero, separation of the corresponding key303
component i from the mixture becomes more difficult. On the other hand, as the DF304
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approaches a maximum, separation becomes easier and the energy necessary to maintain the305
two-phase system is a minimum. Therefore, if the separation design is based on maximizing306
theDF, it naturally leads to a highly energy efficient design and the optimal objective function307
value ( 2,1P ).308
For each reactor design problem, theARis drawn and the location of the maximum in the309
ARis selected as the reactor design target. Similarly, for each separation design problem, the310
DFis drawn and the design target is selected at the highestDF. From a process design point of311
view, at these targets give the highest selectivity of the product with respect to limiting and/or312
selected reactant for a reactor, and the lowest energy required for the separation. From a313
controller design point of view, at these targets the controllability of the process is best314
satisfied. At these targets, the value of dx dd is minimum and the value of xu dd is315
maximum. According to Russel et al. (2002), the value of dx dd will determine process316
sensitivity and flexibility with respect to disturbances. If dx dd is small, the process317
sensitivity is low and process flexibility is high. This means that, at these targets the process is318
more robust in maintaining its controlled variables at optimal set points in the presence of the319
disturbances. On the other hand, the maximum value of xu dd will determine the best pair of320
the controlled-manipulated variables and also the optimal control action. At these targets, the321
best controller structure can be selected with the optimal control action. Therefore, by locating322
the maximum point of the AR and DF as design targets, insights can be gained in terms of323
controllability, and the optimal solution of theIPDCproblems can be obtained in a systematic324
manner.325
326
327
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3. Applications328
329
In this section, the solution of the IPDCproblems through the proposed decomposition330
methodology is presented for the design of: (i) a single reactor system, (ii) a single separator331
system, and (iii) a reactor-separator-recycle system, involving the ethylene glycol production332
process.333
334
3.1 Application to a single reactor design335
336
In this section we consider a simple case study that is related to IPDC problem. We337
consider the following situation. In a continuous stirred tank reactor (CSTR), the product338
ethylene glycol (EG) is to be produced from ethylene oxide (EO) and water (W). The339
production of EG involves an isothermal, irreversible liquid phase reactions and can be340
represented as follows:341
342
O k1+ H2O HO OH
(8)343
HO OH k2 OHHO O
O +
(9)344
k3OHHO OO + OHO O OH
(10)345
346
where,EOand Wreact to produceEGin Eq. (8). Eqs. (9) - (10) are the side-reactions where347
EGreacts with EO to produce diethylene glycol (DEG), and DEGreacts with the remaining348
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EO to produce triethylene glycol (TEG), respectively. The production of further glycols is349
comparatively small and is therefore neglected.350
351
)10583163.30exp(238.51 Tk ; 12 1.2 kk ; 13 2.2 kk (11)352
353
EOand Ware considered to be premixed at the same ratio of 1:1 (for justification, see section354
3.1.2), and other component concentrations are zero in the given feed. The kinetic data in Eq.355
(11) for the above reactions are taken from Parker and Prados (1964). The objective is then to356
determine the design-control solution in which the multi-objective function, Eq. (7) is optimal.357
A schematic of the process is depicted in Fig. 4.358
359
3.1.1 Problem formulation360
361
The IPDCproblem for the EGproduction process described above is defined in terms of a362
performance objective (Eq. (7)) and the three sets of constraints (process, constitutive and363
conditional).364
365
Process constraints:366
NC,iVRCFCFdtdC ii,i,i, 122112 (12)367
RRi QHVRHFHFdtdH 2221112 (13)368
Rcoutout,cout,c
cinin,cin,c
cout QHFHFdtdH (14)369
370
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Eq. (12) is the mass balance for the reactor for component i (there are i= 1, NC equations,371
whereNCis the total number of components), Eqs. (13) (14) represent the energy balances372
for the reactor and jacket, respectively. Assuming that the volume and density are constant for373
both reactor and jacket, 21 FFF and out,cin,cc FFF . The steady state process is374
obtained by setting the right hand side of Eqs. (12)(14) equal to zero.375
376
Constitutive constraints:377
NC,iCTkR i,i 10 2 (15)378
210 ,jTH jj (16a)379
out,injTH jccj 0 (16b)380
381
Eqs. (15)(16) represent the phenomena models for the reaction rate and enthalpies (reactor382
and jacket), respectively. The reactor temperature, T is assumed to be equal to the reactor383
effluent stream temperature, i.e., 2TT .384
385
Conditional (process-control specifications) constraints:386
Sizing equations387
FV0 (17)388
V.VVR 1030 (18a)389
V.VVR 103 (18b)390
NC
i
*ii
opt PxPP1
(19)391
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i
bii
i
mii TxKTTx )( (20)392
Controller structure selection (Eq. (6))393
Eqs. (17) (19) are the sizing equations for a single reactor. Eq. (17) represents the394
reactor volume as a function of the flow residence time. Eqs. (18a) (18b) represent the real395
reactor volume, RV by summing the reaction volume, V with the head space, where the396
headspace is calculated from 10% of the reaction volume. The acceptable value of RV for a397
jacketed reactor is 303 RV m2 (as defined in Table 6.2 of Sinnott (2005) as a relation398
between capacity and cost for estimation of purchased equipment costs). The reactor optimal399
pressure is calculated by analyzing the vapour pressure for all components at the optimal400
operating temperature using Eq. (19). The optimal pressure optP that is greater than the401
operating pressure P is selected in order to have all components in the liquid phase. The402
allowable operating temperature is calculated using Eq. (20) where, ix is the mole fraction of403
component i, and miT andb
iT are the melting and boiling points, respectively, of component i.404
The initial conditions of the process are given in Table 1.405
406
3.1.2 Decomposition-based solution strategy407
408
The summary of the decomposition-based solution strategy for this problem is tabulated in409
Table 2. It can be seen that the constraints in the problem are decomposed into four sub-410
problems which correspond to the four hierarchical stages. In this way, the solution of the411
decomposed set of sub-problems is equal to that of the original problem.412
413
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Stage 1: Pre-analysis414
415
a. Variables analysis416
All design/manipulated and process/controlled variables are tabulated in Table 3. From417
Table 3, the important design/manipulated and process/controlled variables are identified and418
tabulated in Table 4. Design/manipulated variables ],[ cm FVu are selected since they are419
unknown variables and their values are directly related to the capital and operating costs.420
Process/controlled variables ],,,[ 2,2,2, EGWEOm CCCTx , on the other hand, are the important421
intensive variables that need to be monitored and controlled.422
423
b. Operational window identification424
Operational window is identified based on reactor volume for mu and operating425
temperature constraints for mx . For a single reactor, its volume should satisfy the sizing and426
costing constraints as defined in Eqs. (18a)(18b). The temperature range is defined between427
the minimum melting point and maximum boiling point of components, Eq. (20). Therefore,428
the operational window (feasible solutions) within which the optimal solution is likely to exist,429
is given by 30)(3 3 mV and 562)(161 KT .430
431
c. Design-control target identification432
TheARis drawn from the feed points using Eqs. (21a) (21d), which are derived from433
Eq. (15). Detailed derivation can be obtained from the authors.434
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1112
1
0
0
.C
C.
C
C
C
C
W
W
W
W
W
EG
(21a)435
2.12.2
11.2
0
0
W
W
W
W
W
EG
W
DEG
C
C
C
C
C
C
C
C (21b)436
122
0
W
W
W
DEG
W
TEG
C
C
C
C.
C
C (21c)437
122121
000
W
W
W
DEG
W
EG
W
W
W
EO
W
EO
C
C
C
C.C
C.C
C
C
C
C
C (21d)438
439
Solving Eqs. (29a) (29d) for specified values of WC with0WC = 1.00 kmol/m
3and 0EOC =440
1.00 kmol/m3, values for EGC , DEGC , TEGC and EOC are calculated. Then, theARis created441
by plotting the concentration of EGC with respect to concentration of WC as shown in Fig. 5.442
The location of the maximum point in theAR(Point A) is selected as the reactor design target.443
It can easily be seen from Fig. 5 that a maximum of 0.1667 kmol/m3of EGC can be achieved444
using a CSTRwith effluent of 0.59 kmol/m3of WC . The calculation is repeated for different445
ratios of initial concentration of EO and W of 1:2, 1:10, and 1:20. It was found that by446
increasing ratio of WC in the feed, concentration of EGC is also increasing. This is because by447
adding more WC , the side reactions are suppressed and make the main reaction more active,448
thus more EGC is produced. However, the normalized value of EGC with respect to0WC is still449
the same as shown in Fig. 5 for all ratios. Besides, it was found that there is an operation450
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constraint of WC for all ratios as shown in Fig. 5. For ratio of 1:1, the range of operation with451
respect to WC was 0.54 WC (kmol/m3) 1.0. When WC 0.54, EOC was all exhausted,452
thereby, turning off the operation. For other ratios, the operation ranges of WC were 0.72 453
WC (kmol/m3) 1.0 for ratio 1:2, 0.92 WC (kmol/m
3) 1.0 for ratio 1:10, and 0.96 454
WC (kmol/m3) 1.0 for ratio 1:20. For ratio higher than 1:1, the maximum point (point A) was455
located outside the operation range (see Fig. 5). The initial design of the reactor is made at the456
maximum point ofAR for WEO CC : of 1:1.457
458
Stage 2: Design analysis459
460
In this stage, the search space defined in Stage 1 is further reduced using design analysis.461
The established target (Point A) in Fig. 6(a) is now matched by finding the acceptable values462
(candidates) of the design/manipulated and process/controlled variables. If feasible values463
cannot be obtained or the variable values are lying outside of the operational window, a new464
target is selected and variables are recalculated until satisfactory matching is obtained. At465
Point A, the allowable operating temperature is calculated using Eq. (30). The feasible466
solution search space for temperature is now reduced to 406)(251 KT from467
562)(161 KT . At this range, a feasible pressure range of 8.5)(0.1 atmP is predicted468
using Eq. (19).469
With this new range, the feasible solution range for the volume470
(11.78< RV (m3)
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is further reduced to 406)(394 KT . After Stage 2, the region of the feasible solutions is474
now between 406)(394 KT and 89.26)(78.11 3 mV with feasible pressure of475
8.5)(5.4 atmP . Within the feasible solutions for temperature 406)(394 KT , different476
feasible candidates can be enumerated. For illustration purposes, only four feasible candidates477
are considered with the scale of temperature decreasing by 4K. Candidates of478
design/manipulated and process/controlled variables for stage 2 are tabulated in Table 5. In479
principle, if the design is repeated for higher amounts of WC and fixed EOC , the pressure480
would decrease but the size parameters would increase.481
482
Stage 3: Control analysis483
484
a. Sensitivity analysis485
The search space is further reduced by considering feasibility of the process control. The486
feasible candidates from stage 2 are evaluated in terms of controllability performance. The487
process sensitivity is analyzed by calculating the derivative of the controlled variables with488
respect to disturbances. In this case, WC and 1T are potential sources of disturbance in the489
reactor feed while EGC is the controlled variable which needs to be maintained at its optimal490
value (set point). Fig. 6(b) shows plots of derivative of EGC with respect to WC and feed491
temperature 1T . It can be seen that the derivative values are smaller at the maximum ARpoint492
(point A). Smaller value of derivative to disturbances means process sensitivity is lower,493
hence process is more robust with respect to feed concentration and temperature variations. As494
shown in Fig. 6(b), the value of 0 WEGWEG dCdTdTdCdCdC and495
011 dTdTdTdCdTdC EGEG , thus from a control perspective, concentration and496
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temperature control are feasible. However, since value of 1dTdCEG is smaller than497
WEG dCdC , thereby, temperature control should have better performance than concentration498
control. By selecting temperature as a controlled variable rather than EGC at the highest AR499
point, the controller performance should be the best. At this point, any big changes to the500
temperature will result in smaller changes in the EGC (see Fig. 6(b)). Therefore, by501
maintaining (controlled) temperature at its optimal value (set point) at the highest AR point,502
EGC can more easily be controlled.503
504
b.
Control structure selection505
Next, the controller structure is selected by calculating the derivative value of the506
manipulated variable u with respect to the controlled variable x . Since there is only one507
actuator ( cF ) available for controlled variable ( T), therefore, T can be controlled by508
manipulating cF . The derivative value of dTdFc is calculated and plotted in Fig. 6(c). It can509
be seen that value of dTdFc at the maximumARpoint is higher. The big value of dTdFc 510
means the process gain is high (Russel et al., 2002). Suppose that disturbance move our511
controlled variable away from its optimal set point. If the process has a high gain, then the512
controlled variable is very sensitive to the changes in the manipulated variable and the513
controller should make small action to correct the error. Conversely, if the process has a small514
gain, then the controller needs to make large action to correct the same error (high control515
cost).516
0
c
W
W
EG
c
EG
dF
dT
dT
dC
dC
dC
dF
dC (22)517
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From Eq. (22), since 0cEG dFdC as shown in Fig. 6(c), it makes sense to control518
reactor temperature by manipulating cF in order to maintain EGC at its optimal value (set-519
point). Therefore, the concentration-to-temperature cascade control is proposed. In this520
structure, the concentration EGC controller is the primary (master or outer loop) controller,521
while the reactor temperature controller is the secondary (slave or inner loop) controller. This522
is effective because the reactor temperature controller is less sensitive than concentration523
controller (see Fig. 6(b)). An inner-loop disturbance, such as feed temperature, will be524
sensed by the reactor temperature before it has a significant effect on the concentration525
EGC . This inner-loop controller then adjusts the manipulated variable before a substantial526
effect on the primary output has occurred. With this control structure, the robust performance527
of a controller in order to maintain desired product EGC at its optimal set point in the presence528
of disturbance can be assured. Thus, the proposed controller structure is as follows:529
530
Primary controlled variable :EG
C 531
Secondary controlled variable : T532
Manipulated variable : cF 533
Primary setpoint : 0.1667 kmol/m3534
Secondary set point : 406 K535
536
The proposed control structure for an ethylene glycol process is shown in Fig. 7.537
538
Stage 4: Final selection and verification539
540
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a. Final selection: Verification of design541
The multi-objective function Eq. (7) is calculated by summing up each term of the542
objective function value using equal weights. This is given in Table 6. s,P11 corresponds to the543
scaled value of the concentration ofEG. s,P 12 and s,P 22 are the scaled value of 1dTdCEG and544
dTdFc , represent process sensitivity and process gain, respectively. Whereas, s,P 13 and s,P 23 545
are the scaled value of reactor volume and cooling water flow rate, respectively, which546
represent capital and operating costs. Since all candidates in Table 6 are at the maximum point547
of AR (point A), values for s,P11 , s,P 12 and s,P 22 are the same. It can be seen that, value of548
Jfor Candidate 1 is higher than other candidates. Therefore, it is verified that Candidate 1 is549
the optimal solution to integrated design and control of ethylene glycol reaction process which550
satisfies the design, control and cost criteria. It should also be noted that a qualitative analysis551
(Jhighest for point A) is sufficient for the purpose of controller structure selection.552
553
b. Open loop dynamic simulation: Verification of controller performance554
As explained in the section 2.4, when a reactor is designed corresponding to the555
maximum point of the AR (point A), the controllability of the system is also best satisfied.556
This is verified by selecting two but sub-optimal points in the AR (see Fig. 6(a)). From a557
design point of view, they are not feasible since points B and C generate lower EG558
concentrations. From control point of view, the derivative values of the desired product EGC 559
with respect to disturbances ( WC and 1T ) at Point A is smaller than those at points B and C, as560
shown in Fig. 6(b). This in turn means that any changes in WC and 1T will give smaller561
changes in EGC at Point A compared to points B or C.562
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In order to further verify the controllability aspects, a disturbance (+10% step change in563
feed temperature 1T ) moves reactor temperature Taway from its set points (points A, B, C).564
According to Fig. 6(b), any changes in the 1T at points B and C will easily move the desired565
product EGC away from its steady state value in a big scale and as a result, it will be more566
difficult to maintain the EGC at these points than at Point A.567
Fig. 8 shows the open-loop output response of Tand EGC when +10% step changes in568
feed temperature 1T is applied at points A, B, and C. One observes that the effect of569
disturbance to the EGC is negligible at Point A, whereas for points B and C are quite570
significant (see Fig. 8(a)). This means that, process sensitivity at Point A is lower than other571
points. As a result, Point A offers better robustness in maintaining its desired product572
concentration EGC against disturbance. Therefore, it can be verified (albeit empirically) that,573
designing a reactor at the maximum point of ARleads to a process with lower sensitivity with574
respect to disturbance.575
As a summary, the results demonstrate the potential use of the decomposition method in576
solving a simpleIPDCproblems particularly its ability to reduce the dimension of the feasible577
solutions and locate the optimal solution. It was confirmed that in each subsequent stage the578
search space for temperature and volume are reduced until in the final stage only a small579
number of the remaining feasible candidates are evaluated. It was also confirmed that580
designing a reactor at the maximum point of the ARleads to a process with lower sensitivity581
with respect to disturbance. All in all, this application demonstrates that the developed582
methodology is viable and effective tool in solvingIPDCproblems for a single reactor system.583
584
585
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3.2 Application to a single separator design586
587
The application of the decomposition-based methodology is illustrated for the separation588
system of an ethylene glycol process. We consider the following situation. The effluent stream589
from the reactor in the previous case study is now fed to a distillation column where it is split590
into two streams of specified purity - bottom product (stream B with mainly EG, DEG and591
TEG) and distillate product (stream D containing 99.5% of unreacted Wand 100% EO). The592
objective is then to determine the design-control solution in which the multi-objective function593
Eq. (7) is optimal. The process is operated at a nominal operating point as specified in Table 7.594
A schematic of the process is depicted in Fig. 9.595
596
3.2.1 Detailed formulation of the problem597
The IPDC problem consists of a performance objective function (Eq. (7)) and a set of598
constraints: process (dynamic and steady state), constitutive (thermodynamic states) and599
conditional (process-control specifications).600
601
Process constraints:602
We assume potential feeds on all of the stages and adopt the following set notation. The603
number of stages in the column is assumed to be N inclusive of both the reboiler and604
condenser, with stages numbered from the bottom. The set STAGES:= {1, ..., N) will denote605
the numbered stages and index, j subscripted to a quantity associated with stage, j. The set606
COMPdenotes the components in the column. The superscripts land vrefer to the quantities607
associated with the liquid and vapor phases, respectively.608
Total mass balance on each stage609
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11121 FLVL
dt
dM (23)610
jjjjj
jFLVLV
dt
dM 11 N,\STAGESj 1 (24)611
NNNNN FLDVV
dt
dM 1 (25)612
where Mj, Lj, Vj, Fj are the holdup, liquid flowrate, vapor flowrate and feed rate on the jth613
stage, respectively.614
Component balance on each stage615
For each component COMPi , we have:616
111111221
,i,i,i,i,i zFxLyVxL
dt
dM (26)617
j,ijj,ijj,ijj,ijj,ijj,i
zFxLyVxLyVdt
dM 1111 N,\STAGESj 1 (27)618
N,iNN,iNN,iN,iNN,iNN,i
zFxLDxyVyVdt
dM
11 (28)619
whereMi,j, zi,j,xj,i,yi,jrepresent the hold-up, feed, liquid and vapor composition of component620
ion thejth stage, respectively.621
Energy balance on each stage622
In the following jjjj T,y,xU , jjlj T,xh and jjvj T,yh define the stage holdup internal623
energy and the specific heat content of liquid and vapor emanating from stage j. These are624
functions of composition of the mixture and stage temperature.625
rflvl
QhFhLhVhLdt
dU 11111122
1 (29)626
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fjj
ljj
vjj
ljj
vjj
jhFhLhVhLhV
dt
dU 1111 N,\STAGESj 1 (30)627
cfNN
lNN
lN
vNN
vNN
N QhFhLDhhVhVdt
dU 11 (31)628
with fjh representing the specific enthalpy of the feed stream to stage jand Qrand Qcare the629
reboiler and condenser heat duties, respectively.630
631
Constitutive constraints:632
For each stage STAGESj 633
634
jijii xyFD ,, (32)635
11
jk,ij,i
j,ijk,i
j,ix
xy COMPi (33)636
k,j
j,ijk,i
K
K (34)637
jjij,i P,TKK (35)638
639
Conditional constraints:640
Product quality, 05.0Wx (36)641
Controller structure selection, Eq. (6)642
643
3.2.2 Decomposition-based solution strategy644
645
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The summary of the decomposition-based solution strategy is tabulated in Table 8. It can be646
seen that the constraints in the problem are decomposed into four sub-problems which647
correspond to the four hierarchical stages. In this way, the solution of the decomposed set of648
sub-problems is equal to that of the original problem.649
650
Stage 1: Pre-analysis651
a. Variables analysis652
All design and control variables involve in this process are tabulated in Table 9. From653
Table 9, the important variables are identified and tabulated in Table 10. Design/manipulated654
variables ],,,,,,[ crFm QQDBRBRRNu are selected since they are unknown variables and655
have a potential to be manipulated variables except for FN . Beside that, values of rQ and cQ 656
are directly proportional to the operating cost. On the other hand, process/controlled variables657
],,,,,[ TEGWBEGWm TyyTxxx are important since they are potential candidates to be658
controlled for the bottom and top composition.659
660
b. Operational window identification661
The operational window is identified based on bottom and top products purity. Since662
desired product is recovered in the bottom, for that reason, its quality should be monitored and663
controlled. On the other hand, since most of the unreacted reactants are recovered at the top,664
its purity will not be monitored and controlled because it is going to be recycled back to the665
reactor. In order to satisfy product quality, the bottom water composition Wx should be less666
than 0.05.667
668
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c. Design-control target identification669
The step-by-step algorithm for a simple distillation column proposed by Gani and Bek-670
Pedersen (2000) are implemented here. The DFdiagram for a W-EG(the key-components of671
binary pair) system at P = 5.8 atm is drawn as shown in Fig. 10(a). DF is a measure of the672
relative ease of separation. The larger the driving force, the easier the separation is. In this673
graphical method, the target for the optimal process-controller design solution for distillation674
is identified at the maximum point of the DF (point D). In Fig. 10(a) also, two other points675
which are not at the maximum are identified as candidate alternative designs. From a process676
design point of view, they are not optimal since at points E and F the value of driving force is677
smaller hence separation at this point is more difficult. Therefore, from a design perspective678
point D is the optimal solution for distillation (this claim will be tested/verified in stage 4).679
680
Stage 2: Design analysis681
682
The established targets (points D, E and F) in Fig. 10(a) are now matched by finding the683
acceptable values of the design/manipulated variables (e.g. feed stage, reflux ratio, etc.). The684
values of the design variables are determined graphically as shown in Fig. 11. Table 11685
summarizes the results with respect to design/manipulated variables at three different design686
alternatives. With the values of N, FN , RR , product purity, and feed condition are specified,687
the design of a distillation column can be verified through rigorous simulation. Results of the688
steady-state simulation at different design alternatives are tabulated in Table 12. It can be689
noted that design at the maximum point of DF (Point D) corresponds to the minimum with690
respect to energy consumption than other points, as also confirmed by Gani and Bek-Pedersen691
(2000).692
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693
Stage 3: Control analysis694
695
a.
Sensitivity analysis696
In this stage, the controllability of the selected design candidates (column designs D, E,697
F) is analyzed. In this respect, two criteria are considered: (a) process sensitivity with respect698
to disturbances, which should be low and (b) sensitivity of manipulated variable with respect699
to controlled variable, which should be high. The process sensitivity is analyzed by calculating700
the derivative of the controlled variables with respect to disturbances. In this case, bottom701
composition of W ( Wx ) is the most important variable that need to be monitored and702
controlled whereas, feed composition of W( Wz ) and feed temperature are potential sources of703
disturbance. Fig. 10(b) shows plots of derivative ofDFwith respect to composition of Wand704
temperature. It can be seen that derivative values are smaller at the maximum point of DF.705
Hence, at this point the process is more robust in maintaining its product purity against feed706
composition and temperature variations. As shown in Fig. 10(b), the value of707
0 iBBiii dxdTdTdFDdxdFD and 0 dTdTdTdFDdTdFD BBii , thus from a708
control perspective, composition and temperature control are feasible. However, since value of709
dTdFDi is smaller than ii dxdFD , thereby, temperature control has better performance than710
composition control. By selecting bottom temperature as a controlled variable rather than Wx 711
at the highest DF point, the controller performance will be the best. At this point, any big712
changes to the bottom temperature will result in smaller changes in the Wx (see Fig. 10(b)).713
Therefore, by maintaining (controlled) bottom temperature at its optimal value (set point) at714
the highestDFpoint, Wx can more easily be controlled.715
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716
b. Control structure selection717
Next the controller structure is selected by calculating the derivative value of the718
manipulated variable u with respect to the controlled variable x . Since column bottom level,719
bh and condenser level, dh are controlled by manipulating distillate flow rate, D and bottom720
flow rate, B , respectively, there are two available manipulated variables (vapour boilup, V 721
and reflux rate, L ) to be paired with bottom and distillate composition of W ( Wx and Wy ).722
Since V is directly related to Wx and L is directly related to Wy , it is possible to pair WxV 723
and WyL . For bottom composition controller, the derivative value of BdTdV is calculated724
and plotted in Fig. 10(c). It can be seen that value of BdTdV at the maximum DFpoint is725
slightly higher at column design D and other designs. Therefore, control action at column726
design D is better than in column designs E and F. Since 0dVdxW as shown in Fig. 10(c)727
and from Eq. (37), it makes sense to control bottom temperature by manipulating V , in order728
to maintain Wx at its optimal value (set point).729
0
dV
dT
dT
dFD
dFD
dx
dV
dx B
B
i
i
WW (37)730
Therefore, the composition-to-temperature cascade control is proposed. In this structure, the731
composition Wx controller is the primary controller, while the bottom column temperature732
controller is the secondary controller. With this control structure, the robust performance of a733
controller in order to maintain desired bottom product purity at its optimal set point in the734
presence of disturbance can be assured. Similarly the control structure for the distillate735
composition control is also identified. The proposed control structure for an ethylene glycol736
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column designs when 5K step changes in feed temperature is applied. One can clearly see760
that the response of Wx manages to maintain to its set point at column design A in the761
presence of disturbance whereas for column design F is most sensitive (see Fig. 13). This762
means that, process sensitivity with respect to disturbance at column design D is lower than763
other designs. As a result, column design D offers better robustness in maintaining its desired764
composition Wx against disturbance. Therefore, it can be verified that, designing a distillation765
column at the maximum point of DFleads to a process with better robustness with respect to766
disturbance.767
As a summary, the results reveal the potential use of the decomposition andDFmethods768
in solving IPDC problem of a single distillation column. It was confirmed that designing a769
distillation column at the maximum point of the DF leads to a process with lower energy770
required and more robust in maintaining its product purity than any other points. In general,771
this application has shown that the proposed methodology is viable and provides valuable772
insights to the solution of theIPDCproblem for a single separator system.773
774
3.3 Application to a reactor-separator-recycle design775
776
This section demonstrates the use of decomposition methodology in solving integrated777
design and control of a RSR system as illustrated in Fig. 14. We consider the following778
situation. The effluent stream from the CSTR (reactor case study) is fed to the distillation779
column (distillation case study) where it is split into two streams of specified purity. The780
reactant-rich stream Y is recycled back to the reactor, to increase the process economy when781
the conversion in the reactor is low. The objective here is to solve sub-problems 1 2 of the782
generalIPDCproblemthat is, to only identify a feasible window of operation within which783
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the so-called snowball effect will not appear and the reaction product composition will he784
high.785
As Luyben and Floudas (1994) have shown, the RSR system shown in Fig. 14 exhibits786
the snowball effect when a small disturbance in the fresh feed rate causes a very large787
disturbance to the recycle flow rate. However, according to Kiss et al. (2007), the control788
problems created by snowball effects can be avoided through reactor (volume) design.789
Consequently, instead of managing the snowball effect using some control strategy, it is790
possible to avoid it through an appropriate reactor design. Therefore, it is important to define791
the feasible range of operation with respect to manipulated (design) and controlled (process)792
variables where the snowball effect can be avoided.793
For sub-problems (stages 12) we only need the process model and Eq. (4), i.e., the set of794
conditional constraints. Eq. (4) is derived for the RSR system under the following795
assumptions:796
797
A0. Steady-state condition using a CSTR,798
A1. Complete recovery ofEOrecycled back to the reactor ( 1 S,Y ),799
A3. No recycle ofEG,DEGand TEG( 0,,, SYSYSY ),800
A4. Equimolar feed flowrate of reactants ( F,WF,EO FF ),801
A5. Isothermal reaction in CSTR.802
803
Through manipulation of the mass balance equations, the following set of conditional804
constraints are obtained in terms of dimensionless variables , S,Y , Da and variables EOm ,805
Wf . The detailed derivation for these equations can be obtained from the authors.806
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807
1321110 WEOS,Y fm (38)808
809
12132112 11210 WS,YEOS,Y f.m (39)810
811
213232123 12220 ..mEO (40)812
with813
2321 1
S,YWEO fm
Da814
815
In this IPDC problem, we want to identify the feasible range of operation in terms of816
dimensionless design variable ( FEOFEO FVCkDa ,2
,1 ) and within which the highest817
composition of productEG )( ,SEGz can be obtained and the snowball effect can be eliminated.818
Eqs. (38)(40) can be written in compact form as,819
820
0 = f u, (41)821
where822
WEOSY fmDa ,,, ,u 823
Vector u represents the set of design variables. Once the vector uhas been determined, Eq.824
(41) is solved for and using Eqs. (42)(47) (representing the steady state process model)825
the values of the important process variables are obtained.826
321
1
S,Y
WEO
fmS (42)827
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38
321
321
1
S,YWEO
EOS,EO
fm
mz (43)828
321
1
1
1
S,YWEO
S,YWS,W
fm
fz (44)829
32121
1
S,YWEO
S,EGfm
z (45)830
32132
1
S,YWEO
S,DEGfm
z (46)831
3213
1
S,YWEO
S,TEGfm
z (47)832
833
The responses of the product composition of EG ( SEGz , ) and the reactor effluent flow834
rate, Sare plotted in Fig. 15 (ab). In Fig. 15(a), it can be observed that the maximum value835
of SEGz , is within the range of 103 Da . But, when 5Da , the Sincreases significantly836
indicating a possible snowball effect, as shown in Fig. 15(b). In order to avoid the snowball837
effect, the system should be operated at a higher value of Da (for example 4Da ) (see Fig.838
15(b)). Therefore, for the maximum values for the production of EGand also to eliminate the839
snowball effect, the feasible range for Da is identified within 105 Da and 5.5Da .840
Once the feasible range of Da has been established, design-control targets identified earlier at841
the maximum points ofARandDF, for reactor and separator designs, respectively are used to842
determine the remaining design variables and controller structure design.843
As a summary, the results demonstrate the potential use of the decomposition-based844
method in solving IPDC problem of RSR systems. It was confirmed that by applying the845
developed methodology, the nonlinearity such as the snowball effect in this process is avoided846
while maintaining higher productivity and controllable process. All in all, this application847
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demonstrates that the developed methodology has advantages that it is systematic, makes used848
of thermodynamic-process knowledge and provides valuable insights to the solution of IPDC849
problems forRSRsystems.850
851
852
4. Future perspectives853
854
An important issue with model-based process design and controller design is the effect of855
uncertainties such as those related to the operating conditions (i.e. feed flowrates and856
concentrations, catalyst activity etc.), model parameters (i.e. heat transfer coefficients, kinetic857
constants, etc.) and the costs or prices of the materials. It is possible that an optimal design858
under nominal conditions would show poor operability performances under uncertainties.859
IPDCunder uncertainty has been discussed by others, which have shown that it is important to860
develop an optimal process for the entire range of uncertainties to ensure robust operability861
(Bansal et al., 2000; Malcom et al., 2007; Moon et al., 2009; Ricardez Sandoval et al., 2008).862
However, adding the uncertainties significantly increases the complexity of these problems863
and leads to massive optimization models (Sahinidis, 2004). Therefore, as future perspectives864
the effect of uncertainties will be incorporated during the analysis (sub-problems 1 3) to865
ensure robust operability of the optimal designed process.866
867
868
5. Conclusions869
870
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This paper presents a novel systematic model-based methodology for solving IPDC871
problems in chemical processes. The main idea is to decompose the complexity of the IPDC872
problem by following four hierarchical stages (sub-problems) (i) pre-analysis, (ii) design873
analysis, (iii) controller design analysis, and (iv) final selection and verification, which are874
relatively easier to solve. The developed methodology incorporates thermodynamic-process875
insights to determine a priori, the optimal values of the process variables and then through876
them, all other design and decision variables are obtained. TheARandDFconcepts have been877
used to define the design targets and then matching these targets through a decomposed search878
technique. The application of this methodology has been illustrated with the help of three case879
studies. In the first case study, an optimal solution was found with respect to design, control880
and cost criteria of a single reactor system for EGproduction. In the second case study, the881
design-control problem of a single separator system was addressed. Finally, an optimal882
solution was identified with respect to design, control and cost of a reactor-separator-recycle883
system in the third case study, where the designed system is able to produce higher884
productivity without experiencing nonlinearity problem. In general, all results from three case885
studies indicate the viability and effectiveness of the developed methodology. The886
methodology has advantages that it is systematic, makes use of thermodynamic-process887
knowledge and provides valuable insights to the solution ofIPDCproblem.888
889
Acknowledgements890
891
The financial support for this PhD project provided by the Malaysian Ministry of Higher892
Education (MoHE) and Universiti Teknologi Malaysia (UTM) is gratefully acknowledged.893
894
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41
Nomenclature895
B Bottom flowrate896
0EOC , F,EOC Feed concentration of Ethylene Oxide897
0WC Feed concentration of Water898
DEGC Concentration of Diethylene Glycol899
EGC Concentration of Ethylene Glycol900
EOC Concentration of Ethylene Oxide901
TEGC Concentration of Triethylene Glycol902
WC Concentration of Water903
pcp CC , Heat capacity for component and coolant904
D Distillate flowrate905
Da Damkhler number906
d Set of disturbance variables907
iFD Driving force908
cF Coolant flowrate909
jF Feed flowrate on thejth stage910
F,EOF Ethylene Oxide feed flowrate911
F,WF Water feed flowrate912
Wf Dimensionless Water feed flowrate913
RH Heat of reaction914
jH Reactor enthalpy of streamj915
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cjH Jacket enthalpy of streamj916
ljh Specific heat content of liquid emanating from stagej917
vjh Specific heat content of vapor emanating from stagej918
J Objective function919
ik Reaction kinetic of reaction i920
j,iK Equilibrium constant of component ion thejth stage921
jL Liquid flowrate on thejth stage922
j,iM Holdup of component ion thejth stage923
jM Holdup on thejth stage924
EOm Dimensionless Ethylene Oxide mixer flowrate925
N No. of stage926
FN Feed stage927
optP Optimal pressure928
*iP Partial pressure of component i929
P Pressure930
jP,1 Design objective term931
jP ,2 Control objective term932
jP ,3 Economic objective term933
cQ Condenser duty934
rQ Reboiler duty935
RQ Heat transfer between the jacket and the reactor936
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ir Reaction rate of component i937
iR Net reaction rate of reaction i938
min,RBRB Real reboil ratio, minimum reboil ratio939
min,RRRR Real reflux ratio, minimum reflux ratio940
S Reactor effluent flowrate941
t Time942
jT Temperature of streamj943
cco TT , Coolant temperature (input and output)944
bi
mi TT , Melting and boiling point of component i945
iU Holdup internal energy on thejth stage946
u Set of design/manipulated variables947
v Set of chemical system variables948
V Reactor volume949
jV Vapor flowrate on thejth stage950
RV Real reactor volume951
jw Weight factor assigned to each objective term952
x Set of process/controlled variables953
j,ix Liquid mole fraction for component ion thejth stage954
Y Binary decision variables955
j,iy Vapor mole fraction for component ion thejth stage956
j,iz Feed composition for component ion thejth stage957
Greek symbols958
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Bansal, V., Perkins, J. D., Pistikopoulos, E. N., Ross, R., & Van Schijndel, J. M. G. (2000).981
Simultaneous design and control optimization under uncertainty. Computers and982
Chemical Engineering, 24, 261-266.983
Bansal, V., Sakizlis, V., Ross, R., Perkins, J. D., & Pistikopoulos, E. N. (2003). New984
algorithms for mixed-integer dynamic optimization. Computers and Chemical985
Engineering, 27, 647-668.986
Chachuat, B., Singer, A. B., and Barton, P. I. (2005). Global mixed-integer dynamic987
optimization.AIChE Journal, 51(8), 2235-2253.988
Cohen, G. H., and Coon, G. A. (1953). Theoretical considerations of retarded control. Trans.989
ASME, 75, 827-834.990
Esposito, W. R., Floudas, C. A. (2000). Deterministic global optimization in nonlinear optimal991
control problems.Journal of Global Optimization, 17, 245-255.992
Exler, O., Antelo, L. T., Egea, J. A., Alonso, A. A., & Banga, J. R. (2008). A Tabu search-993
based algorithm for mixed-integer nonlinear problems and its application to integrated994
process and control system design. Computers and Chemical Engineering, 32, 1877-995
1891.996
Flores-Tlacuahuac, A., and Biegler, L. t. (2007). Simulatenous mixed-integer dynamic997
optimization for integrated design and control. Computers and Chemical Engineering,998
31, 588-600.999
Gani, R., & Bek-Pedersen, E. (2000). A simple new algorithm for distillation column design.1000
AIChE Journal, 46(6), 1271-1274.1001
Glasser, D., Hildebrandt, D., & Crowe, C. (1987). A geometric approach to steady flow1002
reactors: The attainable region and optimization in concentration space. Industrial and1003
Engineering Chemistry Research, 26(9), 1803-1810.1004
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Glasser, D., Hildebrandt, D., & Crowe, C. (1990). Geometry of the attainable region generated1005
by reaction and mixing: With and without constraints. Industrial and Engineering1006
Chemistry Research, 29(1), 49-58.1007
Hamid, M. K. A., & Gani, R. (2008). A model-based methodology for simultaneous process1008
design and control for chemical processes. In: Proceedings of the FOCAPO 2008,1009
Massachusetts, USA, 205-208.1010
Karunanithi, A. P. T., Achenie, L. E. K., and Gani, R (2005). A new decomposition-based1011
computer-aided molecular/mixture design methodology for the design of optimal solvents1012
and solvent mixtures,Industrial and Engineering Chemistry Research, 44, 4785-4797.1013
Kiss, A. A., Bildea, C. S., and Domian, A. C. (2007). Design and control of recycle systems1014
by non-linear analysis, Computers and Chemical Engineering,31, 601-611.1015
Kookos, I. K., & Perkins, J. D. (2001). An algorithm for simultaneous process design and1016
control.Industrial and Engineering Chemistry Research, 40, 4079-4088.1017
Luyben, W. L. (2004). The need for simultaneous design education, in: Seferlis, P. and1018
Georgiadis, M. C. (Eds.). The integration of process design and control. Amsterdam:1019
Elsevier B. V., 10-41.1020
Luyben, M. L., & Floudas, C. A. (1994). Analyzing the interaction of design and control 2.1021
reactor-separator-recycle system. Computers and Chemical Engineering, 18(10), 971-1022
993.1023
Malcom, A., Polam, J., Zhang, L., Ogunnaike, B. A., & Linninger, A. A. (2007). Integrating1024
system design and control using dynamic flexibility analysis. AIChE Journal, 53(8),1025
2048-2061.1026
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Meeuse, F. M., & Grievink, J. (2004). Thermodynamic controllability assessment in process1027
synthesis, in: Seferlis, P. and Georgiadis, M. C. (Eds.). The integration of process design1028
and control.Amsterdam: Elsevier B. V., 146-167.1029
Mohideen, M., Perkins, J. D., & Pistikopoulos, E. N. (1996). Optimal design of dynamic1030
systems under uncertainty.AIChE Journal, 42(8), 2251-2272.1031
Mohideen, M., Perkins, J. D., & Pistikopoulos, E. N. (1997). Towards an efficient numerical1032
procedure for mixed integer optimal control. Computers and& Chemical Engineering,1033
21(Suppl), S457-S462.1034
Moles, C. G., Gutierrez, G., Alonso, A. A., & Banga, J. R. (2003). Integrated process design1035
and control via global optimization: A wastewater treatment plant case study. Chemical1036
Engineering Research and Design, 81, 507-517.1037
Moon, J., Kim, S., Ruiz, G. J., and Linninger, A. A. (2009). Integrated design and control1038
under uncertaintyalgorithms and applications. In: M. M. El-Hawagi & A. A. Linninger,1039
Design for energy and the environment, CRC Press, 659-668.1040
Parker, W. A., & Prados, J. W. (1964). Analog computer design of an ethylene glycol system.1041
Chemical Engineering Progress, 60(6), 74-78.1042
Patel, J., Uygun, K., & Huang, Y. (2008). A path constrained method for integration of1043
process design and control. Computers and Chemical Engineering, 32, 1373-1384.1044
Ricardez Sandoval, L. A., Budman, H. M., & Douglas, P. L. (2008). Simultaneous design and1045
control of process under uncertainty.Journal of Process Control, 18, 735-752.1046
Russel, B. M., Henriksen, J. P., Jrgensen, S. B., & Gani, R. (2002). Integration of design and1047
control through model analysis. Computers and Chemical Engineering, 26, 213-225.1048
Sahinidis, N. V. (2004). Optimization under uncertainty: state-of-the-art and opportunities.1049
Computers and Chemical Engineering, 28, 971-983.1050
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Sakizlis, V., Perkins. J. D., & Pistikopoulos, E. N. (2004). Recent advances in optimization-1051
based simultaneous process design and control design. Computers and Chemical1052
Engineering, 28, 2069-2086.1053
Schweiger, C. A., & Floudas, C. A. (1997). Interaction of design and control: optimization1054
with dynamic models, in: W. Hager & P. Pardalos (Eds.), Optimal Control: Theory,1055
Algorithms and Applications, Kluver Academic Publishers, Gainesville, USA, 388-435.1056
Seferlis, P., & Georgiadis, M. C. (2004). The integration of process design and control.1057
Amsterdam: Elsevier B. V.1058
Sendin, O. H., Moles, C. G., Alonso, A. A., & Banga, J. R. (2004). Multiobjective integrated1059
design and control using stochastic global optimization methods. In: P. Seferlis & M.1060
Georgiadis (Eds.), The integration of process design and control.Amsterdam: Elsevier B.1061
V., 555-581.1062
Sharif, M., Shah, N., & Pantelides, C. C. (1998). On the design of multicomponent batch1063
distillation columns. Computers and Chemical Engineering, 22 (Suppl), S69-S76.1064
Sinnott, R. K. (2005). Chemical Enginering, Volume 6, Fourth edition, Chemical Engineering1065
Design, Elsevier Butterworth-Heinemann.1066
1067
1068
1069
1070
1071
1072
1073
1074
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List of Figures1075
1076
Fig. 1. Decomposition method forIPDCproblem (Hamid and Gani, 2008).1077
1078
Fig. 2. The number of feasible solution is reduced to satisfy constraints at every sub-1079
problems.1080
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1081
Fig. 3. Determination of optimal solution of design-control for a reactor using AR diagram1082
(left) and a separator usingDFdiagram (right).1083
1084
Fig. 4. CSTRfor an ethylene glycol production.1085
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1086
Fig. 5. Normalized plot of the desired product concentration EGC and EOC with respect to1087
WC for different WEO CC : .1088
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1089
Fig. 6. (a) AR diagram for the desired product concentration EGC with respect to WC for1090
WEO CC : of 1:1, (b) Corresponding derivatives of EGC with respect to WC and T, (c)1091
Corresponding derivative of cF with respect to Tand derivative of EGC with respect to cF .1092
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1100
Fig. 9. Distillation column for an ethylene glycol process.1101
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1102
Fig. 10. (a) DF diagram for the separation of water-ethylene glycol by distillation, (b)1103
Corresponding derivatives of the DF with respect to composition and temperature, (c)1104
Corresponding derivative of vapour boilup, V with respect to temperature and derivative of1105
composition of water with respect to vapour boilup, V .1106
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1107
1108
1109
Fig. 11. Driving force diagram with illustration of the distillation design parameters at (a)1110
point D; (b) point E; and (c) point F.1111
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