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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.

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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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415


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


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


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


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



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


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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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


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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35

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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36

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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37

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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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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42

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

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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

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Georgiadis (Eds.), The integration of process design and control.Amsterdam: Elsevier B.1061

V., 555-581.1062

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distillation columns. Computers and Chemical Engineering, 22 (Suppl), S69-S76.1064

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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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