MODELING, SIMULATION AND MULTI-OBJECTIVE OPTIMIZATION OF INDUSTRIAL HYDROCRACKERS NAVEEN BHUTANI NATIONAL UNIVERSITY OF SINGAPORE 2007 MODELING, SIMULATION AND MULTI-OBJECTIVE OPTIMIZATION OF INDUSTRIAL HYDROCRACKERS NAVEEN BHUTANI (M.Tech, Indian Institute of Technology, Delhi, India) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2007 ACKNOWLEDGEMENTS With all respect and gratitude, I wish to express my sincere thanks to my research advisors, Prof G P Rangaiah and Prof A K Ray, for their encouragement and invaluable suggestions with kind support for the last few years Foremost, I wish to thank them for providing a friendly and non-pressuring environment, very much essential for academic research I would also like to thank the members of my supervisory committee, Prof Rajagopalan Srinivasan and Prof George Zhao, for their many useful suggestions and comments that enhanced the quality of this work I would like to thank Prof Laksh, Prof Farooq, Prof Karimi for their invaluable feedback and suggestions and educating me on various aspects of chemical engineering fundamentals and advanced topics I would also wish to thank other professors in the chemical and bimolecular engineering department who have contributed, directly or indirectly, to this thesis Many thanks to technical and non-technical staff of the department and the SVU team for their kind assistance in providing the necessary laboratory facilities and computational resources A special tribute to all my colleagues and friends, both in Singapore and abroad, for the encouragement and technical support I will always relish the warmth and affection that I received from my present and past colleagues My family members deserve the most, for all their sacrifices, boundless love, encouragement, moral support and dedication, which gave me hopes and will to reach my goals I sincerely acknowledge the financial support and excellent research facilities from the National University of Singapore i TABLE OF CONTENTS Acknowledgements i Table of Contents ii Summary v viii List of Tables List of Figures x Nomenclature xv Introduction 1.1 1.2 Hydrocracking mechanism and catalysts 1.3 Modeling and optimization 1.4 Motivation and scope of work 1.5 Hydrocracking and its significance Organization of thesis 10 Literature Review 2.1 Introduction 11 2.2 Reaction kinetics of hydrocracking and its catalysts 12 2.3 Property estimation 19 2.4 Hydrocracker configuration and Trickle-bed reactor 20 hydrodynamics 2.5 Modeling approaches and reactor model 26 2.6 Genetic algorithms: Working principle and multi-objective 31 optimization 2.7 Summary 36 Modeling, Simulation and Optimization of an Industrial Hydrocracking Unit 3.1 Introduction 38 3.2 Process description 39 3.3 First Principles Model development 40 3.3.1 Assumptions 40 3.3.2 Mass balances 42 3.3.3 Energy balance 43 3.3.4 Correlations for kinetics and product distribution 43 ii 3.3.5 Characterization and property prediction 45 3.4 Model solution and validation 49 3.5 Multi-objective optimization 56 3.5.1 Two-objective optimization using NSGA 57 3.5.2 Problem formulation 58 3.5.3 Sensitivity analysis 61 3.5.4 NSGA parameters and objectives definition 61 3.5.5 Optimization results and discussion 63 3.6 Summary 67 Modeling, Simulation and Optimization of an Industrial Hydrocracking Unit in the Local Refinery 4.1 69 4.2 Process description 69 4.3 Hydrocracking kinetics and modeling 73 4.4 Modeling and simulation of the hydrocracking unit 75 4.5 Feed and product characterization and property prediction 81 4.6 Model calibration: fine tuning of model parameters 86 4.7 Sensitivity analysis 93 4.8 Multi-objective optimization using elitist NSGA 98 4.9 Optimization results and discussion 101 4.10 Introduction Summary 114 Hybrid Modeling and Optimization of an Industrial Hydrocracking Unit 5.1 Introduction 116 5.2 Modeling approaches 118 5.2.1 119 First principles, data based and hybrid models 5.3 Development of neural network models 122 5.3.1 Data pretreatment and analysis 123 5.3.2 Architecture, training and selection 126 5.4 Development of hybrid models of hydrocracking unit 129 5.5 Model results and discussion 127 5.5.1 132 5.6 Model testing and performance assessment Operation optimization of hydrocracker 137 iii 5.7 Summary 145 A Multi-platform, Multi-language Environment for Process Modeling, Simulation and Optimization 6.1 Introduction 6.2 146 Development of multi-platform, multi-language environment (MPMLE) 6.2.1 Integration of Visual Basic with HYSYS 151 6.2.2 Integration of Visual Basic with Visual C++ 153 6.2.3 Integration of Visual Basic with Visual FORTRAN 159 6.2.4 6.3 149 Integration of Visual C++ with Visual FORTRAN 162 Multi-objective optimization of styrene production using 165 MPMLE 6.3.1 6.4 The interface of MPMLE Modeling and simulation of styrene reactor unit and styrene 167 168 plant 6.5 170 6.6 Results and discussion 171 6.7 Multi-objective optimization problem Summary 187 Conclusions and Recommendations 189 7.1 Conclusions 189 7.2 Recommendations and further study 191 195 References Appendices A Genetic algorithm and non-dominated sorting genetic 219 algorithms A.1 Genetic algorithms 219 A.2 Non-dominated sorting genetic algorithms 220 B Peng-Robinson Equation of State 223 C Characterization of feed and products to pseudo- 225 components D Problem formulation for model fine tuning 229 iv SUMMARY Hydrocracking is a catalytic process of significant importance in petroleum refineries As the name suggests, hydrocracking involves the cracking of relatively heavy oil fractions into lighter products in the presence of hydrogen For example, heavy gas oils and vacuum gas oils are converted into high-quality middle distillates and lighter products, i.e diesel, kerosene, naphtha, butane, propane etc with higher value and demand The hydrocracker (HC) feed is a complex mixture and often a common process variable which affects reaction kinetics and ultimately the operation of the overall unit Hence, these impose various challenges to refiners to operate the HC unit optimally and meet products demand Several molecular schemes and pseudocomponent approaches are studied for developing hydrocracking kinetics and mechanistic models but their reported implementation on industrial units is limited The data-based and hybrid models are practically non-existent for HCs in the open literature Further, no work in the open literature discusses single or multi-objective optimization (MOO) of HC unit though multiple objectives are relevant to overall optimum operation The availability of powerful computational resources and robust evolutionary techniques further motivate MOO of industrial units like HCs The broad objective of the present research is to model and simulate HC units in two different refineries, and to optimize their operation for multiple objectives of importance under various operating scenarios In detail, it includes (a) simulation and MOO of the HC unit (a two-stage configuration with intermediate separation) in a refinery using the first principle model (FPM) of Mohanty et al (1991) and nondominated sorting genetic algorithm (NSGA), (b) improvements in the FPM and its v subsequent implementation on a local HC unit with series-flow configuration for simulation and corresponding MOO using the elitist NSGA (Bhutani et al., 2006a), (c) development of data-based and hybrid models for the local industrial HC unit followed by optimization (Bhutani et al., 2006b), and (d) development of a generic modeling and optimization package by integrating the recent MOO technique: elitist NSGA with a process simulator, and its subsequent validation on a styrene plant (Bhutani et al., 2006c) The FPMs for industrial HCs are based on lumped kinetics The FPM used for simulation of the HC with two-stage configuration and intermediate separation, is improved by increasing the number of pseudo-components and fined tuned for its model parameters using design and operating data for its implementation on the HC in the local refinery The models are validated against independent data taken from the literature or from a local refinery These models can adequately predict product flow rates, temperature profiles in the reactor(s) and hydrogen makeup requirements, and are suitable for optimization of industrial HC units NSGA and elitist NSGA are employed to obtain Pareto optimal solutions for various multi-objective constrained optimization problems of industrial importance The FPMs have limited usage because of common process variations Hence, databased models (DBMs) are developed using industrial data and artificial neural networks The FPMs are then combined with DBMs to develop three hybrid models (series, parallel and series-parallel) All these models are evaluated and tested for their prediction performances on industrial hydrocracking unit for a number of days of vi future operation Under limited extrapolation, DBM is found to be better and is successfully employed for optimizing the industrial unit The FPMs of HC were developed in F90, partly due to lack of proper interface between HYSYS and elitist NSGA Hence, a generic multi-platform, multi-language environment (MPMLE) is developed to integrate HYSYS with elitist NSGA for simulating and optimizing industrial processes realistically and quickly As an example, the styrene reactor unit and the overall manufacturing plant are successfully simulated in HYSYS and then optimized using the MPMLE Considering the very limited works on HC modeling, simulation and optimization in the open literature, results and findings of the above works as well as the MPMLE will be valuable to both researchers and practitioners vii LIST OF TABLES Table 2.1 Examples of commercial processes involving trickle-bed reactors 22 Table 3.1 Plant data for VGO hydrocracking unit 51 Table 3.2 Characterization of feed 52 Table 3.3 Comparison of simulated values with the industrial data (Mohanty et al., 1991) 54 Table 3.4 Industrial products and reactants cost details 58 Table 3.5 Effect of 5% increase in decision variables on products, recycle and H2 flow rates 62 Table 3.6 Values of NSGA optimization studies multi-objective 62 Table 4.1 Characterization of feed and products to pseudo-components 83 Table 4.2 Experimental data for feed and products obtained from the refinery 87 Table 4.3 Data on catalyst in the hydrocracker beds 87 Table 4.4 A set of operating data for hydrotreater and hydrocracker 88 Table 4.5 Comparison of fine tuned parameter values obtained in this study with the reported values (Mohanty et al., 1991) 91 Table 4.6 % Error between industrial data and predictions by the HC unit model fine tuned using average data of day 93 Table 4.7 Sensitivity analysis - effect of different variables on HC unit performance 96 Table 4.8 Multi-objective optimization problems solved 97 Table 4.9 Values of NSGA optimization studies multi-objective 99 Table 5.1 Correlation coefficients of the given property (IBP and FBP) with product flow rate 121 Table 5.2 Average performance and computational time (in minutes) for training ANN models using “trainbr” algorithm 128 parameters parameters for for viii Tan, W.W., F Lu, A.P Loh and K.C Tan Modeling and control of a pilot pH plant using genetic algorithm, Engineering Applications of Artificial Intelligence, 18(4), pp 485-494, 2005 Tarafder, A., A.K Ray and G.P Rangaiah Application of non-dominated sorting genetic algorithms for multi-objective optimization of an industrial styrene reactor, The second international conference on computational intelligence, Robotics and autonomous systems, CIRAS, Singapore 2003 Tarafder, A., G.P Rangaiah and A.K Ray Multiobjective optimization of an industrial styrene monomer manufacturing process, Chem Eng Sci., 60(2), pp 347-363, 2005 Tarafder, A., B.C.S Lee, A.K Ray and G.P Rangaiah Multi-objective optimization of an industrial ethylene reactor using a non-dominated sorting genetic algorithm, Ind Eng Chem Res., 44, pp 124-141, 2004 Teh, Y.S and G.P Rangaiah Tabu search for global optimization of continuous functions with application to phase equilibrium calculations, Comp and Chem Eng., 27, pp 1665-1679, 2003 Temeng, K.O., P.D Schnelle and T.J McAvoy Model predictive control of an industrial packed bed reactor using neural networks, J Proc Cont., 5(1), pp 1927, 1995 Tendulkar, S.B., S.S Tambe, I Chandra, P.V Rao, R.V Naik and B.D Kulkarni Hydroxylation of phenol to dihydroxybenzenes: Development of artificial neural network-based process identification and model predictive control strategies for a pilot plant scale reactor, Ind Eng Chem Res., 37, pp 2081, 1998 215 Thakur, D.S and M.G Thomas Catalyst deactivation in heavy petroleum and synthetic crude processing: a review, Applied Catalysis, 15, pp 197-225, 1985 Thompson, M.L and M.A Kramer Modeling chemical processes using prior knowledge and neural networks, AIChE J., 40, pp 1328-1340, 1994 Topsoe, H., B.S Clausen and F.E Massoth in Catalysis, Science and Technology, J Anderson, M Boudart (Eds.), vol 11, pp 1, Springer, 1996 Trambouze, P., Engineering of hydrotreating processes, in Chemical reactor technology for environmentally safe reactors and products, De Lasa H I., Dogu G., Ravella A., NATO Advanced Study Institute Series E, Plenium, New York, pp 425, 1992 Vadapalli, A and J.D Seader, A generalized framework for computing bifurcation diagrams using process simulation programs, Comp and Chem Eng., 25, pp 445-464, 2001 Van Can H.J.L., C Hellinga, K.C.A.M Luyben, J Heijnen and H.A.B Braake Strategy for dynamic process modeling based on neural networks and macroscopic balances, AIChE J., 42, pp 3403-3418, 1996 Walas, S H., Phase equilibria in chemical engineering, Butterworth Publishers, 1985 Wang, C., H Quan and X Xu Optimal design of multiproduct batch chemical process using tabu search, Comp and Chem Eng., 23, pp 427- 437, 1999 Wauquier, J P., Petroleum refining, Chap 4, vol 1, Paris: Editions Technip, 2000 Weekman, V.W and D.M Nace Kinetics of catalytic cracking selectivity in fixed, moving and fluid bed reactors, AIChE J., 16, pp 397, 1970 Weikamp, J., Hydrocracking and hydrotreating by John W Ward and Shai A Qader, ACS symposium series; 20, 1975 Weir, H.M and G.L Eaton, Ind Eng Chem., 24, pp 211-218, 1932 216 Willis, M.J, C.D Massimo, G.A Montague, M.T Tham and A.J Morris AIChE Annual Mtg., Chicago, IL, 1990 Willis, M.J., G.A Montague, D.C Massimo, A.J Morris and M.T Tham Artificial neural networks and their application in process engineering in IEE Colloq Neural Networks for Systems: Principles and Applications, pp 71-74, 1991 Wu J.L., A.M Agogino Automating keyphrase extraction with multi-objective genetic algorithms, Proceedings of the 37th Annual Hawaii International Conference on System Sciences (HICSS'04) - Track 4, pp 40104c, 2004 Yee, A.K.Y., A.K Ray, G.P Rangaiah Multiobjective optimization of an industrial styrene reactor, Comp and Chem Eng., 27, pp 111-130, 2003 Yoshimura, Y., T Sato, H Shimada, N Matsubayasi, M Imamura, A Nishijima, S Yoshitoni, T Kameoka and H Yanase Energy Fuels, 8, pp 435, 1994 Youssef, H., S.M Sait and H Adiche Evolutionary algorithms, simulated annealing and tabu search: a comparative study, Engineering Applications of Artificial Intelligence, 14, pp 167-181, 2001 Zahedi G., A Elkamel, A Lohi, A Jahanmiri and M.R Rahimpor Hybrid artificial neural network-First principle model formulation for the unsteady state simulation and analysis of a packed bed reactor for CO2 hydrogenation to methanol, Chem Eng J., 115, pp 113-120, 2005 Zbicinski I., P Strumillo and W Kaminski Hybrid model of thermal drying in a Fluidized Bed, Comp and Chem Eng., 20, pp 695-700, 1996 Zhang, C., H Shao, and Y Li Particle swarm optimisation for evolving artificial neural network, Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp 2487-2490, 2000 217 Zitzler, E and L Thiele Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Transactions on Evolutionary Computation, 3(4), pp 257-271, 1999 Zurada, J.M Introduction to artificial neural networks, Boston, MA: PWS-Kent, 1995 218 APPENDIX A GENETIC ALGORITHM AND NON-DOMINATED SORTING GENETIC ALGORITHMS A.1 Genetic Algorithms Genetic algorithms (GAs) are computerized search and optimization algorithms, which mimic the process of natural selection and genetics (Holland 1975) A typical GA starts with a population of random strings or chromosomes, representing values of the decision variables Each string is then evaluated to find the corresponding objective function and the fitness value The value of the objective function of any chromosome reflects its ‘fitness’ The Darwinian principle of ‘survival of the fittest’ is used to generate a new and improved gene pool (new generation) This is done by preparing a ‘mating pool’, comprising of copies of chromosomes, the number of copies of any chromosome being proportional to its fitness (Darwin's principle) via a selection step Pairs of chromosomes are then selected randomly, and pairs of daughter chromosomes are generated using operations similar to those in natural reproduction The gene pool evolves, with the fitness improving over the generations Three common operators: reproduction, crossover and mutation, are used in GA to obtain an improved (next) generation of chromosomes The entire process is repeated till some termination criterion is met (the specified maximum number of generations is attained, or the improvements in the values of the objective function become lower than a specified tolerance) Steps in GA are as follows Choose a coding scheme (binary, floating-point etc.) to represent decision variables, a selection operator, crossover operator and a mutation operator Choose population size, n, crossover probability, pc, mutation probability, pm 219 and maximum allowable generations, tmax Initialize a random population of size n, and set number of generations counter, t = Evaluate the objective function at each string in the population If t > tmax or other termination criterion is satisfied, terminate Perform reproduction on the population Perform crossover on random pairs of strings Perform mutation on every string Evaluate strings in the new population Set t = t + and go to step A.2 Non-dominated Sorting Genetic Algorithms Non-dominated sorting GA (NSGA) was first implemented by Srinivas and Deb (1995) for solving MOO problems This algorithm generates a set of solutions which are non-dominating over one another Two solution are non-dominating if moving from one point to another results in an improvement in at least one objective and deterioration in one (or more) of the other objective function(s) The final set of nondominating solutions is referred to as a Pareto-optimal set NSGA differs from the traditional GA in the way the selection operator works In the former, prospective solutions are sorted into fronts - an imaginary enclosure within which all chromosomes are mutually non-dominating and such fronts are ranked progressively until all chromosomes are accounted for Each chromosome is then assigned a fitness value obtained by sharing a dummy fitness value of the front by its niche count - a parameter proportional to the number of chromosomes in its neighborhood (in decision variables space) within the same front This helps to spread out the chromosomes while maintaining the diversity of the gene pool All other 220 operations performed are similar to those in the traditional GA A flowchart describing NSGA is shown in Figure A.1 Deb et al (2000) developed an elitist NSGA, also called as NSGA-II In this algorithm, the offspring population is first created by using the parent population through a crowded tournament selection, where the better individuals in the parent population, the “elites”, are selected in such a way that diversity is maintained in the population Selected individuals will then undergo crossover and mutation operations to form an offspring population Both offspring and parent populations are then combined and sorted into non-dominated fronts Among individuals in each front, there is no one single best solution; each one of them performs better in some objectives than other individuals, but worse in the remaining objectives However, individuals in worse fronts (i.e sub-optimal solutions) are dominated by all individuals in the better fronts The next generation is then filled with the individuals from the sorted fronts starting from the best If a front can only partially fill the next generation, crowded tournament selection is invoked again to ensure diversity This strategy is called “niching” Once the next generation population has been filled, the algorithm loops back to creating an offspring population from this new parent population A flow diagram for NSGA-II is given by Wu et al (2004) 221 Start Generate initial population randomly Set Ng = Evaluate objective functions front = Is population classified? No Identify non-dominated individuals Yes Reproduction according to dummy fitness values Perform Crossover Perform Mutation Yes Assign dummy fitness Share in the current front front = front + Is Ng < Maxgen? No Stop Figure A.1 Flowchart of NSGA technique (Mitra et al., 1998) 222 APPENDIX B PENG–ROBINSON EQUATION OF STATE (PENG AND ROBINSON, 1976) For a mixture of N components, Peng-Robinson (PR) equation of state (EOS) can be expressed as: P= RT a − v − b v( v + b) + b( v − b ) N (B.1) N where a = ∑∑ x i x j a ij (B.2) i =1 j=1 N b = ∑ x ibi (B.3) i =1 b i = 0.07880 RTc i Pc i a i = 0.445724α i [ ( (i = 1, …, N) (RTc i )2 Pc i (B.4) (i = 1, …, N) (B.5) )( α i = + − Tri0.5 0.37464 + 1.54226ω − 0.26992ω )] (i = 1, …, N) (B.6) A mixing rule is used to calculate aij: aij = (1–kij) a i a j (i, j = 1, …, N) (B.7) where kij is the binary interaction coefficient The mixing rule, equation (B.7) is used for aij The partial fugacity coefficient of component i in a mixture can be calculated from the following equation:   N  2∑ x j a ij  ∧ bi   Z + B +  bi A  j ln φ i = ( Z − 1) − ln(Z − B) − −  ln   b a b 2B  Z − B1−        ( ( ) ) (i = 1, 2…, N) (B.8) 223 where A and B are defined by equations (B.9) and (B.11) respectively, and Z is the root of the following equation: Z − (1 − B) Z + (A − 2B − 3B ) Z − (AB − B − B3 ) = aP where A = B= Bi = (B.10) (RT )2 Ai = aiP (RT )2 (i = 1, …, N) bP RT bi P RT (B.9) (B.11) (B.12) (i = 1, …, N) (B.13) Equation B.9 has three roots, the smallest real root is used for evaluation of liquid phase properties 224 APPENDIX C CHARACTERIZATION OF FEED AND PRODUCTS TO PSEUDO- COMPONENTS The characterization of feed and products to pseudo-components is automated by writing the code in Visual Basic Editor in Excel, which can call HYSYS for the characterization The experimental data for feed and products: liquid volume/mass % with ASTM D2887/ASTM D286 are input into the worksheet and the number of cuts within the boiling range are defined (Figure C.1) Figure C.1 A print screen preview of assay data worksheet (shown partly, only feed and one product for clarity) 225 The flow rates of feed and products are entered through the graphic user interface and the simulation can simply be run by pressing the “Oil Characterization” button (Figure C.2) The characterization results in properties and flow rates of pseudocomponents stored in separate Excel worksheets As an example, when the simulation is run, HVGO and other products are blended to pseudo-components Figure C.3 shows the properties of various pseudo-components generated by blending HVGO and Figure C.4 shows the overall composition of products mixture in terms of pseudocomponents flow The pseudo-component distribution chart is also generated by simulation for comparison of pseudo-components profile generated from experimental data with the simulation results All these outputs are useful for simulation and validation of the HC model Flow Rates HVGO (m3/hr) 1.0 Light Naphtha (m3/hr) 0.11 Heavy Naphtha (m3/hr) 0.22 Kerosene (m3/hr) 0.37 Light Diesel (m3/hr) 0.13 Heavy Diesel (m3/hr) 0.23 Unconverted Oil (m3/hr) 0.51 Oil Characterization Figure C.2 A Graphical User Interface between HYSYS and Excel (Products flow rates are normalized to hide actual operating data for proprietary reasons) 226 Figure C.3 A print screen preview of pseudo-components properties obtained by HVGO blending 227 Figure C.4 A print screen preview of characterization of products to pseudocomponents and corresponding pseudo-components distribution in HC product Note: The flow rate of pseudo-component1 is zero in Figure C.4 This is so, because the flow rate of pseudo-component1 is defined by light ends obtained by summation of flow rates of off-gases and subtracting the amount of H2S and NH3 contained in off-gases, and H2 losses (as described in Chapter 4), but not by characterization procedure described above 228 APPENDIX D PROBLEM FORMULATION FOR MODEL FINE TUNING In series and series-parallel structures, the model and kinetic parameters which determine conversion, temperature in the reactor and product distribution are fine tuned using the objective in eq D.1 subject to constraints including model equations Details of the model, kinetic parameters and their significance are already discussed in Chapter The upper and lower limits on the industrial operating variables are given by eqs D.2 and D.3 The bed outlet temperatures are expected to deviate from their actual values as temperature sensors are never 100% accurate Hence, these temperatures are bounded within ± 0.3% (eq D.2) Eq D.3 accounts for overall mass balance enclosure around the HC unit, which should be satisfied within 6% for industrial operation This error is acceptable because of measurement inaccuracies, loss of gases from distillation units to flare and ammonia in the downstream wash water separation   7 f k ,S      Objective = Minimize  ∑ 1 −  k =1  f k ,I       (D.1) Temperature constraints for outlet bed temperatures  Touti ,S   ≤ 0.003 − 0.003 ≤ 1 −  T  outi , I   for I = to (D.2) Overall mass balance enclosure  FT ,S   − 0.06 ≤ 1 −  F  ≤ 0.06 T ,I   (D.3) 229 ...MODELING, SIMULATION AND MULTI- OBJECTIVE OPTIMIZATION OF INDUSTRIAL HYDROCRACKERS NAVEEN BHUTANI (M.Tech, Indian Institute of Technology, Delhi, India) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF. .. two -objective optimization: (a) Maximization of DS* and KS* simultaneously; (b) Maximization of DS* and KS* and minimization of total H2 flow; (c) Maximization of (DS+KS)* and minimization of. .. interface of MPMLE Modeling and simulation of styrene reactor unit and styrene 167 168 plant 6.5 170 6.6 Results and discussion 171 6.7 Multi- objective optimization problem Summary 187 Conclusions and