Methodologies, applications and performance assessment

PLANT-WIDE CONTROL: METHODOLOGIES, APPLICATIONS AND PERFORMANCE ASSESSMENT SURAJ VASUDEVAN NATIONAL UNIVERSITY OF SINGAPORE 2010 PLANT-WIDE CONTROL: METHODOLOGIES, APPLICATIONS AND PERFORMANCE ASSESSMENT SURAJ VASUDEVAN 2010 PLANT-WIDE CONTROL: METHODOLOGIES, APPLICATIONS AND PERFORMANCE ASSESSMENT SURAJ VASUDEVAN (B.Eng.(Hons.), National University of Singapore) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2010 To My Late Father and Maternal Grandfather Acknowledgements I would like to express my sincere gratitude to my thesis advisor, Prof G.P Rangaiah for his valuable guidance, close supervision and positive criticism during the course of my PhD research I greatly value the thought-provoking discussions during the weekly meetings with him that have immensely contributed to the worth of the research work presented in this thesis; my thanks to him for devoting his valuable time and effort for the same I also like the way Prof Rangaiah stimulates the thought process by putting forward questions that would lead us to think and come up with new findings and ideas One more particular thing that I admire about him is the immense effort and care that he takes in reviewing drafts of manuscripts, presentations and other materials In fact, I think I have greatly improved my writing and presentation skills under him Besides the above aspects related to work, I would also like to express my heartfelt thanks to Prof Rangaiah for the care and kind understanding that he has shown to me during all the ups and downs that I have experienced on the personal front during the course of my doctoral research, such as the illness of my mother (for which he kindly supported one-year leave of absence) and the unexpected passing away of my father In this aspect, I consider myself blessed to have him as my supervisor Finally, I will never forget all the moments that I spent with Prof Rangaiah during the informal get-togethers and dinners that he has arranged for our research group I would like to thank my thesis panel members, Dr R Gunawan and A/Prof S Laksh for their constructive and helpful comments when I defended my thesis proposal, the majority of which I believe I have incorporated or addressed in this thesis I would like to make special mention of A/Prof Laksh for always being a i source of inspiration since my undergraduate days My respect and appreciation to the late Prof Krishnaswamy for teaching me the basics of process control during my undergraduate studies at NUS In fact, I began to like process control because of him and consequently pursued control-related research for my doctoral studies My sincere acknowledgment to Prof W.L Luyben of Lehigh University for his useful comments on some of my works I would also like to acknowledge Mr Lim (of Tanglin Secondary School) and Ms Lee (of Raffles Junior College), the wonderful Chemistry teachers I have been fortunate to have Special thanks to Mr K.H Boey and Ms Samantha Fam for taking care of the lab and equipment related issues, and also to Ms Doris How for taking care of academic and administrative matters for research students I am thankful to my senior, (Dr.) N.V.S.N Murthy Konda for his unselfish assistance and help when I joined Prof Rangaiah’s research group Special mention must be made of the detailed and useful comments that he gave for some of my initial works He has been and still is a very good buddy and guide My past lab-mates: M Srinivas and Elaine Lee have been my chatting companions and are still good friends Thanks to Zhang Chi, for the thought-provoking discussions on research-related issues that I have had with her Thanks also to Tay Wee Hwa and Ee Kai, who Prof Rangaiah gave me the opportunity to work with for their final year projects, and who made important contributions towards two of my publications Thanks to my pals Satya, Sreenivas, Kong Fei, Ravi, Sundar and Shangari Finally, thanks to my current lab-mates Haibo, Krishna (the most jovial), Vaibhav, Shivom, Naviyn (the most hardworking) and Sumit for their camaraderie and support that I value I dedicate this thesis to my late father, who aspired that I should successfully complete my doctoral research I terribly miss him as I complete this thesis I guess he ii would be happy now and blessing me from His abode I am always grateful to my mother for her endless love, patience and support My parents’ upbringing and the values they have instilled in me are the main factors behind my achievements Thanks to my brother for his everlasting love and generous support with computer-related issues at home Finally, I would like to profusely thank NUS for providing the opportunity and funding for my doctoral research iii Table of Contents Acknowledgements i Table of Contents iv Summary viii Nomenclature x List of Figures xv List of Tables Chapter xviii Introduction 1.1 Plant-Wide Control (PWC) 1.2 Motivation and Scope of Work 1.2.1 Control Degrees of Freedom (CDOF) 1.2.2 Dynamic Simulation and PWC of Styrene Monomer Plant 1.2.3 Performance Assessment of PWC Systems 1.2.4 Reactor-Separator-Recycle (RSR) Network 1.2.5 Integrated Framework of Simulation, Heuristics and Optimization 1.3 Chapter Organization of the Thesis Literature Review 10 2.1 Classification of PWC Methodologies 10 2.2 Processes Studied in PWC Applications 24 2.3 Review of Control Methodologies based on RSR Processes 28 2.4 Summary 37 iv Chapter Control Degrees of Freedom Using the Restraining Number: Further Evaluation 38 3.1 Introduction 38 3.2 Summary of the Procedure 40 3.3 Clarifications and Improvements 41 3.4 Restraining Number of Additional Units 44 3.5 Application to Three-Phase Distillation 48 3.6 Application to Four Complex Industrial Processes 51 3.7 Summary 57 Chapter A Comparative Study on Plant-Wide Control of a Styrene Plant 58 4.1 Introduction 59 4.2 Overview and Simulation of the Styrene Process 64 4.3 Application of Luyben’s Heuristics Procedure 67 4.4 Application of the Integrated Framework 76 4.5 Application of Self-Optimizing Control Procedure 86 4.6 Evaluation of the Control Systems 107 4.7 Summary 115 Chapter Criteria for Performance Assessment of Plant-Wide Control Systems 116 5.1 Introduction 116 5.2 Performance Measures for PWC Systems 121 5.2.1 Overall Process Settling Time 122 5.2.2 Dynamic Disturbance Sensitivity 123 5.2.3 Unit-Wise Dynamic Disturbance Sensitivity 124 v 5.2.4 Total Variation in the Manipulated Variables 125 5.2.5 Net Variation in the Plant Operating Profit 5.2.6 Deviation from the Production Target 126 5.2.7 Integral Absolute Error in Product Purity 5.3 125 128 Application to the Styrene Monomer Plant 129 5.3.1 Dynamic Simulation of the Selected Control Structures 5.3.2 Chapter Results and Discussion 133 5.3.3 5.4 129 General Assessment of the Performance Measures 143 Summary 149 Guidelines from Reactor-Separator-Recycle Studies for Plant-Wide Control 150 6.1 Introduction 150 6.2 Gas-Phase RSR 153 6.3 Case Study 1: HDA Process 156 6.3.1 Control of Inert Composition 159 6.3.2 Control of System Pressure 162 6.3.3 Fresh Feed vs Total Feed Case Study 2: Ammonia Process 167 6.4.1 Control of Inert Composition 169 6.4.2 6.4 165 Control of System Pressure 171 6.5 Case Study 3: Styrene Process 177 6.6 Discussion and Proposed Guidelines 180 6.7 Summary 189 vi Ricker, N.L Decentralized Control of The Tennessee Eastman Challenge Problem J Proc Cont., 6, pp.205-221 1996 Riggs, J.B Improve Distillation Column Control Chem Eng Prog., 94(10), pp.3147 1998 Robertson, M.W.; Watters, J.C.; Deshpande, P.B.; Assef, J.Z.; Alatiqi, I.M ModelBased Control for Reverse Osmosis Desalination Processes Desalination, 104, pp.59-68 1996 Robinson, D.; Chen, R.; McAvoy, T.; Schnelle, P.D An Optimal Control Based Approach to Designing Plant-Wide Control System Architectures J Proc Cont., 11, pp.223-236 2001 Sagale, A.A and Pushpavanam, S A Comparison of Control Strategies for a NonLinear Reactor-Separator Network Sustaining an Autocatalytic Isothermal Reaction Ind Eng Chem Res., 41, pp.2005-2012 2002 Seborg, E.; Edgar, T.F.; Mellichamp, D.A Process Dynamics and Control New Jersey: Wiley 2004 Seferlis, P and Grievink, J Process Design and Control Structure Screening Based on Economic and Static Controllability Criteria Comput Chem Eng., 25, pp.177188 2001 Seider, W.D.; Seader, J.D.; Lewin, D.R Product and Process Design Principles: Synthesis, Analysis and Evaluation New York: Wiley 2004 Seki, H and Naka, Y A Hierarchical Controller Design for a Reactor/Separator System with Recycle Ind Eng Chem Res., 45, pp.6518-6524 2006 Seki, H and Naka, Y Optimizing Control of CSTR/Distillation Column Processes with One Material Recycle Ind Eng Chem Res., 47, pp.8741-8753 2008 248 Seki, H.; Ogawa, M.; Itoh, T.; Ootakara, S.; Murata, H.; Hashimoto, Y.; Kano, M Plant-Wide Control System Design of the Benchmark Vinyl Acetate Monomer Production Plant Comput Chem Eng., 34, pp.1282-1295 2010 Semino, D and Giuliani, G Control Configuration Selection in Recycle Systems by Steady-State Analysis Comput Chem Eng., 21, pp.S273–S278 1997 Sheel, J.C.P and Crowe, C.M Simulation and Optimization of an Existing Ethyl Benzene Dehydrogenation Reactor Can J Chem Eng., 47, pp.183-187 1969 Shen, Y.; Cai, W.J.; Li, S Multivariable Process Control: Decentralized, Decoupling, or Sparse? Ind Eng Chem Res., 49, pp.761-771 2010 Skogestad, S Plant-Wide Control: The Search for the Self-Optimizing Control Structure J Proc Cont., 10, pp.487-507 2000a Skogestad, S Self-Optimizing Control: The Missing Link Between Steady-State Optimization and Control Comput Chem Eng., 24, pp.569-575 2000b Skogestad, S Simple Analytic Rules for Model Reduction and PID Controller Tuning J Proc Cont., 13, pp.291-309 2003 Skogestad, S Control Structure Design for Complete Chemical Plants Comput Chem Eng., 28, pp.219-234 2004 Sliger, H and Quinn, R Treatment of Sewage Effluent by Reverse Osmosis for Boiler Feed Makeup at the Wyodak Wyoming Station of the Black Hills Power and Light Desalination, 23, pp.37-47 1977 Stephanopoulos, G Synthesis of Control Systems for Chemical Plants – A Challenge for Creativity Comput Chem Eng., 7, pp.331-365 1982 Stephanopoulos, G Chemical Process Control New Jersey: Prentice Hall 1984 Subramanian, S and Georgakis, C Methodology for the Steady-State Operability Analysis of Plant-Wide Systems Ind Eng Chem Res., 44, pp.7770-7786 2005 249 Sundaram, K.M.; Sardina, H.; Fernandez-Baujin, J.M.; Hildreth, J.M Styrene Plant Simulation and Optimization Hydrocarbon Processing, 70(1), pp.93-97 1991 Tarafder, A.; Rangaiah, G.P.; Ray, A.K Multi-Objective Optimization of an Industrial Styrene Monomer Manufacturing Process Chem Eng Sci., 60, pp.347363 2005 Tian, Z.H and Hoo, K.A Multiple Model-Based Control of the Tennessee Eastman Process Ind Eng Chem Res., 44, pp.3187-3202 2005 Turkay, M.; Gurkan, T.; Ozgen, C Synthesis of Regulatory Control Structures for a Styrene Plant Comput Chem Eng., 17, pp.601-608 1993 Turton, R.; Bailie, R.C.; Whiting, W.B.; Shaeiwitz, J.A Analysis, Synthesis, and Design of Chemical Processes New Jersey: Prentice Hall 2003 Ulrich, J and Morari, M Influence of Impurities on the Control of Heterogeneous Azeotropic Distillation Columns Ind Eng Chem Res., 41, pp.230-250 2002 Vasbinder, E.M and Hoo, K.A Decision-Based Approach to Plant-Wide Control Structure Synthesis Ind Eng Chem Res., 42, pp.4586-4598 2003 Vasbinder, E.M.; Hoo, K.A.; Mann, U Synthesis of Plant-Wide Control Structures using a Decision-Based Methodology In The Integration of Process Design and Control, ed by Seferlis, P and Georgiadis, M.C., pp.375-400 Amsterdam: Elsevier 2004 Vasudevan, S.; Rangaiah, G.P.; Konda, N.V.S.N.M.; Tay, W.H Application and Evaluation of Three Methodologies for Plant-Wide Control of the Styrene Monomer Plant Ind Eng Chem Res., 48, pp.10941-10961 2009 Wang, P and McAvoy, T Synthesis of Plant-Wide Control Systems Using a Dynamic Model and Optimization Ind Eng Chem Res., 40, pp.5732-5742 2001 250 Ward, J.D.; Mellichamp, D.A.; Doherty, M.F Insight from Economically Optimal Steady-State Operating Policies for Dynamic Plant-Wide Control Ind Eng Chem Res., 45, pp.1343-1353 2006 Woodle, G.B Styrene In Encyclopedia of Chemical Processing, ed by Lee, S., pp.2859-2869 New York: Taylor and Francis 2006 Wu, K.L and Yu, C.C Reactor/Separator Processes with Recycle – Candidate Control Structure for Operability Comput Chem.Eng., 20, pp.1291-1316 1996 Wu, K.L.; Yu, C.C.; Luyben, W.L.; Skogestad, S Reactor/Separator Processes with Recycles – Design for Composition Control Comput Chem.Eng., 27, pp.401421 2002 Xiong, Q.; Cai, W.J.; He, M.J A Practical Loop Pairing Criterion for Multivariable Processes J Proc Cont., 15, pp.741-747 2005 Ye, N.; McAvoy, T.J.; Kosanovich, K.A.; Piovoso, M.J Optimal Averaging Level Control for the Tennessee Eastman Problem Can J Chem Eng., 73, pp.234-240 1995 Yi, C.K and Luyben, W.L Evaluation of Plant-Wide Control Structures by SteadyState Disturbance Sensitivity Analysis Ind Eng Chem Res., 34, pp.2393-2405 1995 Zhang, C.; Rangaiah, G.P.; Vasudevan, S Plant-Wide Control System Design for Ammonia Synthesis Process by the Integrated Framework Presented at PSE Asia 2010, Singapore, July 2010a Zhang, C.; Vasudevan, S.; Rangaiah, G.P Plant-Wide Control System Design and Performance Evaluation for Ammonia Synthesis Process Ind Eng Chem Res., 49, pp.12538-12547 2010b 251 Zheng, A and Mahajanam, R.V A Qualitative Controllability Index Ind Eng Chem Res., 38, pp.999-1006 1999 Zheng, A.; Mahajanam, R.V.; Douglas, J.M Hierarchical Procedure for Plant-Wide Control System Synthesis AIChE J., 45, pp.1255-1265 1999 Zhu, G.Y.; Henson, M.A.; Ogunnaike, B.A A Hybrid Model Predictive Control Strategy for Non-Linear Plant-Wide Control J Proc Cont., 10, pp.449-458 2000 Zhu, G.Y and Henson, M.A Model Predictive Control of Inter-connected Linear and Non-Linear Processes Ind Eng Chem Res., 41, pp.801-816 2002 252 Appendix A Summary of LS Control Structure for the Styrene Plant During the course of review of the publication Vasudevan et al (2009) that has been detailed in Chapter 4, an alternative control structure was proposed by Prof W.L Luyben (Lehigh University) for the styrene plant This control structure is summarized in Table A.1 together with the tuning parameters The tuning parameters for all the major loops like temperature and composition are the same as those given by Prof Luyben 253 Table A.1: Controllers with their Parameters for LS Control Structure for the Styrene Plant CV Total EB flow Total EB/LP2 ratio Total EB/LP1 ratio PFR-1 inlet T Q1/total EB ratio (cascade) PFR-2 inlet T V-1 T V-1 P V-1 liquid % level V-1 aqueous % level Condenser P Condenser level Reboiler level Reflux/feed flow ratio Reflux flow (cascade) Stage 59 EB composition Vent/feed flow ratio Vent flow (cascade) Condenser P Condenser level Reboiler level Stage T Distillate/reflux flow ratio (cascade) Stage 29 toluene composition MV Reaction Section EB feed flow (TPM) LP2 flow LP1 flow Q1/Total EB ratio SP Furnace duty Intermediate heater duty Cooling water flow Lights flow Organic flow Water flow Product Column (T-1) Condenser duty Distillate flow Bottoms flow Reflux flow SP Reflux flow Reboiler duty Vent flow SP Compressor duty Recycle Column (T-2) Condenser duty Reflux flow Bottoms flow Distillate/reflux ratio SP Distillate flow Reboiler duty Controller Parameters [Kc (%/%), Ti (min)] 0.5, 0.3 0.36, 0.035 0.1, 0.018 0.21, 22 0.1, 0.96, 24 0.13, 0.14 2, 10 18.8, 0.45 1.31, 0.12 2, 10 1.2 2.2 1, 0.5, 0.3 0.23, 54 0.47, 0.025 0.5, 0.3 1.8, 30 1.2 6.7, 41 0.42, 0.026 0.13, 36 254 Appendix B Summary of Control Structure Decisions for HS, IF and SOC Control Structures for the Styrene Plant Table B.1: Control Structure Decisions for HS Control Structure at each Level Level Steady-state gain analysis PFR-2 T Intermediate heater duty Most direct manipulator Total EB feed flow Fresh EB feed flow Most direct manipulator Reboiler duty Steam/EB ratio at PFR-1 inlet Steam feed flow T-1 P Condenser duty Cooling water flow Split steam flow Lights flow T-2 P Condenser duty V-1 liquid level Organic flow V-1 aqueous level Water flow T-1 condenser level Distillate flow T-1 reboiler level Bottoms flow T-2 condenser level Reflux flow T-2 reboiler level Bottoms flow T-2 distillate EB composition Distillate flow Follows from selection made for T-2 condenser level in Level T-1 reflux T-1 reflux Heuristics Overhead vent flow Furnace duty V-1 P PFR-1 T Split steam flow Reason for Selection V-1 T Selected MVs T-1 bottoms EB composition Selected CVs Compressor duty Most direct manipulator Reboiler duty Follows from selection made for T-2 reboiler level in Level T-2 bottoms toluene composition Best manipulator based on heuristics Richardson’s Rule 255 Table B.2: Control Structure Decisions for IF Control Structure at each Level Level Selected CVs Selected MVs Reason for Selection 3.1 EB fresh feed flow EB fresh feed flow Heuristics 3.2 T-1 bottoms EB composition Reboiler duty RGA analysis Split steam flow Split steam flow Steam/Total EB ratio at PFR-1 inlet Steam feed flow PFR-1 T Furnace duty PFR-2 T Intermediate heater duty V-1 T Cooling water flow T-1 P Condenser duty V-1 P Lights flow T-2 P Condenser duty V-1 liquid level Organic flow V-1 aqueous level Water flow T-1 condenser level Distillate flow T-1 reboiler level Bottoms flow T-2 condenser level Reflux flow T-2 reboiler level Bottoms flow T-1 distillate styrene composition Reflux flow T-2 distillate EB composition Distillate flow T-2 bottoms toluene composition Reboiler duty Vent flow Compressor duty Simulation EB conversion PFR-1 T SP Most promising manipulator 4.1 4.2 Best manipulator based on simulation Most direct manipulator Heuristics with simulation Follows from selections made in Level 4.2 256 Table B.3: Control Structure Decisions for SOC Control Structure at each Level Level Reason for Selection Furnace duty RGA analysis PFR-2 T Intermediate heater duty Most direct manipulator V-1 liquid level Organic flow Most direct manipulator V-1 aqueous level Water flow Most direct manipulator T-1 condenser level Distillate flow RGA analysis T-1 reboiler level Bottoms flow RGA analysis T-2 condenser level Distillate flow RGA analysis T-2 reboiler level Bottoms flow RGA analysis V-1 P Lights flow Most direct manipulator T-1 P Condenser duty Most direct manipulator T-2 P Condenser duty Most direct manipulator Furnace outlet T Steam split ratio SP RGA analysis V-1 T Cooling water flow Most direct manipulator T-2 stage T Reflux flow RGA analysis Total EB feed flow EB fresh feed flow Heuristics Steam feed flow Steam feed flow Most direct manipulator PFR-1 inlet EB composition Steam feed flow SP RGA analysis T-1 feed styrene composition PFR-2 T set-point RGA analysis T-1 distillate styrene composition Selected MVs PFR-1 T 5.1 Selected CVs Reflux flow RGA analysis T-1 bottoms EB composition Reboiler duty RGA analysis T-2 distillate EB composition T-2 stage T SP RGA analysis T-2 bottoms toluene composition Reboiler duty RGA analysis Vent flow Compressor duty Most direct manipulator 257 Appendix C Sample Computations for the Various Performance Measures The computation of the various measures presented in Chapter is illustrated for disturbance d3 for control structure IF Note that the data for the plots presented can be extracted from the Aspen HYSYS ‘Databook’ feature, which can be used to compile the data of the selected variables at specified regular intervals (e.g., 20 seconds) during the dynamic simulation of the process with the control structure Overall Process Settling Time The settling time based on styrene production rate is calculated as follows Initial production rate = 120.7 kmol/h Final steady state production rate = 96.5 kmol/h Effective step-change in production rate = 120.7 – 96.5 = 24.2 kmol/h Cut-off point for settling time = ±5% of 24.2 kmol/h = ±1.21 kmol/h (i.e., between 95.3 and 97.7 kmol/h) From the production rate transient shown in Figure C.1, the point where the production rate falls between the above range is at 520 minutes Hence, settling time based on styrene production rate = 520 – 100 = 420 minutes since the disturbance is introduced at 100 minutes In a similar way, settling times based on styrene product quality and slowest control loop are calculated As for styrene product quality, the settling time based on a range of ±1% of the set point of 0.997 is The control loop with the slowest response for disturbance d3 is the recycle column EB distillate composition controller, and the 258 corresponding settling time based on a range of ±1% (i.e., between 0.0099 and 0.0101) of the set point (i.e., 0.01) is 740 minutes As for the settling time based on overall component accumulation, the settling time is the point where accumulation drops below 1.22 kmol/h (i.e., 1% of the steady-state styrene production rate) From Styrene Production Rate (kmol/h) Figure C.2, this point occurs at 555 minutes and hence settling time is 455 minutes 121 119 117 115 113 111 109 107 105 103 101 99 97 95 100 200 300 400 500 600 700 800 900 1000 Time (minutes) Overall Absolute Accumulation (kmol/h) Figure C.1: Styrene production rate transient for control structure IF in the presence of disturbance d3 10 0 100 200 300 400 500 600 700 800 900 1000 Time (minutes) Figure C.2: Transient profile of absolute accumulation of all components for control structure IF in the presence of disturbance d3 259 Dynamic Disturbance Sensitivity Based on the cut-off point of 1.22 kmol/h, the DDS for disturbance d3 is the area between the absolute accumulation curve and x-axis from 100 (i.e., when the disturbance sets in) to 555 minutes (see Figure C.2) This area (i.e., DDS), which can be easily computed using MATLAB, is 82 Unit-Wise Dynamic Disturbance Sensitivity The unit-wise DDS values are calculated in a similar way to the DDS values, except that the absolute accumulation profile now considered is for the individual units and not the entire plant The unitwise DDS values accordingly calculated are 7.2, 66.7 and 10.5 for the three-phase separator, styrene column and recycle column respectively Note that, as already explained in Section 5.2.3, the sum of unit-wise DDS (equal to 84.4) is slightly different from the overall plant DDS (equal to 82) Total Variation in the Manipulated Variables The MVs are all expressed in the form of percentage The values of the controller output are compiled at a regular time interval of 20 seconds over the simulation run of 2000 minutes The TV for each MV is then computed based on the following formula: TV  2000 u i0 (i 1 )  u i (C.1) The TV for the entire plant is then computed by summing up the TV for all the 21 control loops, and this is equal to 493% Net Variation in the Plant Operating Profit The net variation in the operating profit is equal to the net area indicated in Figure C.3 and is found to be +0.56 US$/(kg/hr) (note that the time units have been changed from minutes to hour) In this case, there is no negative area and hence the net area is just equal to the positive area The net variation in the profit per tonne of styrene is computed from equation 5.6 to be +16.8 US$/tonne 260 0.40 US$/kg Product Positive area 0.30 Steady-state profit 0.20 100 300 500 700 900 1100 1300 1500 1700 1900 Time (minutes) Figure C.3: Transient profile of profit per unit mass of product for control structure IF in the presence of disturbance d3 Deviation from the Production Target The DPT is equal to the area between the production rate curve and the target production rate line (which in this case is the final production rate) as shown in Figure C.4 This area is equal to +60.13 Styrene Production Rate (kmol/h) kmol of styrene, and hence the DPT is equal to +6263 kg of styrene 120 115 DPT 110 105 Target production rate 100 95 100 200 300 400 500 600 700 800 900 1000 Time (minutes) Figure C.4: Styrene production rate transient for control structure IF in the presence of disturbance d3 261 Integral Absolute Error in Product Purity The IAE in the product purity is calculated by summing up the absolute values of the areas A, B and C in Figure C.5 The absolute integral error is thus calculated to be 0.0084 Styrene Product Purity 0.999 Area A Area B 0.998 0.997 Required product purity 0.996 Area C 0.995 100 200 300 400 500 600 700 800 900 1000 Time (minutes) Figure C.5: Styrene product purity transient for control structure IF in the presence of disturbance d3 262 ...PLANT-WIDE CONTROL: METHODOLOGIES, APPLICATIONS AND PERFORMANCE ASSESSMENT SURAJ VASUDEVAN 2010 PLANT-WIDE CONTROL: METHODOLOGIES, APPLICATIONS AND PERFORMANCE ASSESSMENT SURAJ VASUDEVAN... et al (2004), Konda et al (2005 and 2006b), Araujo et al (2007a and 2007b), and Bouton and Luyben (2008) Luyben et al (1997 and 1998), Chen and McAvoy (2003) and Olsen et al (2005) have studied... (1997 and 1998), McAvoy (1999), Kookos and Perkins (2001), Wang and McAvoy (2001), Chen et al (2004), and Tian and Hoo (2005) The HDA plant has been considered by Stephanopoulos (1984), Ponton and