Optimal scheduling of refinery crude oil operations

Carnegie Mellon University Research Showcase Dissertations Theses and Dissertations 12-1-2010 Optimal Scheduling of Refinery Crude-Oil Operations Sylvain Mouret Carnegie Mellon University Follow this and additional works at: http://repository.cmu.edu/dissertations Recommended Citation Mouret, Sylvain, "Optimal Scheduling of Refinery Crude-Oil Operations" (2010) Dissertations Paper 23 This is brought to you for free and open access by the Theses and Dissertations at Research Showcase It has been accepted for inclusion in Dissertations by an authorized administrator of Research Showcase For more information, please contact research-showcase@andrew.cmu.edu Optimal Scheduling of Refinery Crude-Oil Operations A DISSERTATION Submitted to the Graduate School in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy in Chemical Engineering by Sylvain Mouret Carnegie Mellon University Pittsburgh, Pennsylvania December, 2010 Acknowledgments First of all, I would like to express my most sincere gratitude to my advisor Professor Ignacio E Grossmann for his inestimable guidance and support over the course of my Ph.D He has managed to create a productive yet friendly environment and proved to be an abundant source of knowledge for myself I cannot thank him enough for his confidence in me and his deep implication in my studies and in my life Besides my advisor, I would like to thank my thesis committee members – Professors Lorenz Biegler, Nikolaos Sahinidis, John Hooker, and Willem-Jan van Hoeve for their time and valuable comments I would like to thank Pierre Pestiaux, my supervisor at Total, whose strong commitment to the project and never-ending enthusiasm has made this thesis possible I would also like to thank Philippe Bonnelle for bringing his experience and his insightful suggestions into the project as well as other collaborators at SOG and CReG, for their useful feedback on my work and friendly support Furthermore, I am grateful to Total Refining & Marketing for financial support of this project I wish to express my thankfulness for all my past and present workmates in the PSE group for setting a productive mood in the office and a diverting atmosphere out of work Among them I would like to specifically mention Rosanna Franco, Gonzalo Guill´en Gos´albez, Ricardo Lima, Rodrigo L´ opez-Negrete de la Fuente, Mariano Martin, Roger Rocha, Sebastian Terrazas, and Victor Zavala with whom I share many unforgettable memories I would also like to thank my fellow football and tennis teammates, Tarot card players, French speaking lunchers, barbecue grillers, etc who made my Pittsburgh experience a very enjoyable one I want to express my gratitude to my family who has always been there when I needed them, and to my 18-month-old niece Anna for being so cute and joyful Acknowledgments ii Last but not least, I cannot thank enough my beloved fianc´ee Charlotte for her patience and for standing by me during the past three and a half years Her unconditional love is never to be forgotten Acknowledgments iii Abstract This thesis deals with the development of mathematical models and algorithms for optimizing refinery crude-oil operations schedules The problem can be posed as a mixed-integer nonlinear program (MINLP), thus combining two major challenges of operations research: combinatorial search and global optimization First, we propose a unified modeling approach for scheduling problems that aims at bridging the gaps between four different time representations using the general concept of priority-slots For each time representation, an MILP formulation is derived and strengthened using the maximal cliques and bicliques of the non-overlapping graph Additionally, we present three solution methods to obtain global optimal or near-optimal solutions The scheduling approach is applied to single-stage and multi-stage batch scheduling problems as well as a crude-oil operations scheduling problem maximizing the gross margin of the distilled crude-oils In order to solve the crude-oil scheduling MINLP, we introduce a two-step MILP-NLP procedure The solution approach benefits from a very tight upper bound provided by the first stage MILP while the second stage NLP is used to obtain a feasible solution Next, we detail the application of the single-operation sequencing time representation to the crude-oil operations scheduling problem As this time representation displays many symmetric solutions, we introduce a symmetry-breaking sequencing rule expressed as a deterministic finite automaton in order to efficiently restrict the set of feasible solutions Furthermore, we propose to integrate constraint programming (CP) techniques to the branch & cut search to dynamically improve the linear relaxation of a crude-oil operations scheduling problem minimizing the total logistics costs expressed as a bilinear objective CP is used to derived tight McCormick convex envelopes for each node subproblem thus reducing the optimality gap for the MINLP Abstract iv Finally, the refinery planning and crude-oil scheduling problems are simultaneously solved using a Lagrangian decomposition procedure based on dualizing the constraint linking crude distillation feedstocks in each subproblem A new hybrid dual problem is proposed to update the Lagrange multipliers, while a simple heuristic strategy is presented in order to obtain feasible solutions to the full-space MINLP The approach is successfully applied to a small case study and a larger refinery problem Abstract v Contents Acknowledgments ii Abstract iv Contents vi List of Tables x List of Figures Introduction 1.1 Single-Stage and Multi-Stage Batch Scheduling 1.2 Optimization of Oil Refineries 1.2.1 Refinery Planning 1.2.2 Crude-Oil Operations Scheduling 1.3 Mixed-Integer Optimization Tools 1.3.1 Mixed-Integer Linear Programming 1.3.2 Mixed-Integer Nonlinear Programming 1.3.3 Constraint Programming 1.3.4 Lagrangian Relaxation 1.3.5 Symmetry-Breaking Approaches 1.4 Overview of Thesis 1.4.1 Chapter 1.4.2 Chapter 1.4.3 Chapter 1.4.4 Chapter 1.4.5 Chapter 1.4.6 Chapter xii Time Representations and Mathematical Models Problems 2.1 Introduction 2.2 Case Study 2.3 Time Representations 2.4 Mathematical Models 2.4.1 Sets and Parameters 2.4.2 Variables 2.4.3 MOS Model Contents 5 10 12 13 14 16 16 16 16 17 17 18 18 for Process Scheduling 19 19 21 22 28 28 29 30 vi 32 32 33 33 33 34 36 37 38 39 39 40 41 42 44 51 52 53 55 57 59 62 63 64 65 Short-Term Scheduling of Crude-Oil Operations 3.1 Introduction 3.2 Problem Statement 3.2.1 General Description 3.2.2 Case Study 3.3 Mathematical Models 3.3.1 Sets 3.3.2 Parameters 3.3.3 Variables 3.3.4 Objective Function 3.3.5 General Constraints 3.3.6 Strengthened Constraints 3.3.7 Symmetry-Breaking Constraint for MOS Models 3.3.8 Full Models 3.4 Solution Method 3.5 Computational Results 3.5.1 Scheduling Results 67 67 68 68 70 72 72 74 74 75 75 78 79 80 80 82 82 2.5 2.6 2.7 2.8 2.9 2.4.4 MOS-SST Model 2.4.5 MOS-FST Model 2.4.6 SOS Model Strengthened Reformulations 2.5.1 Non-overlapping Graph Properties 2.5.2 MOS Model 2.5.3 MOS-SST Model 2.5.4 MOS-FST Model 2.5.5 SOS Model Solution Methods 2.6.1 Additive Approach 2.6.2 Multiplicative Approach 2.6.3 Direct Approach Single-Stage Batch Scheduling Problem 2.7.1 MOS Model 2.7.2 MOS-SST Model 2.7.3 MOS-FST Model 2.7.4 SOS Model 2.7.5 Models Comparison Multi-Stage Batch Scheduling Problem 2.8.1 MOS Model 2.8.2 MOS-SST Model 2.8.3 MOS-FST Model 2.8.4 Models Comparison Conclusion Contents vii 3.6 3.5.2 Performance of the 3.5.3 Performance of the 3.5.4 Performance of the 3.5.5 Performance of the Conclusion MOS Model MOS-SST Model MOS-FST Model MILP-NLP Decomposition Strategy 85 87 88 89 90 Single-Operation Sequencing Model for Crude-Oil Operations Scheduling 92 4.1 Introduction 92 4.2 Strengthened Constraints 92 4.3 Symmetry-Breaking Constraints 95 4.3.1 Symmetric Sequences of Operations 95 4.3.2 A Sequencing Rule Based on a Regular Language 95 4.3.3 Rule Derivation for COSP1 97 4.3.4 Regular Constraint 99 4.4 Computational Results 100 4.4.1 Performance of the SOS Model 101 4.4.2 Effect of the Number of Priority-Slots 102 4.4.3 Remark on the Optimality of the Solution 103 4.4.4 Effect of Symmetry-Breaking Constraints 105 4.5 Comparison of Crude-Oil Scheduling Models 106 4.6 Conclusion 108 Tightening the Linear Relaxation of a Crude-Oil MINLP Using Constraint Programming 5.1 Introduction 5.2 MINLP Model 5.3 Reformulation and Linear Relaxation 5.4 McCormick Cuts 5.5 Computational Results 5.6 Conclusion Operations Scheduling 109 109 110 113 114 116 118 Integration of Refinery Planning and Crude-Oil Scheduling grangian Decomposition 6.1 Introduction 6.2 Problem Statement 6.2.1 Refinery Planning Problem 6.2.2 Crude-Oil Scheduling Problem 6.2.3 Full-Space Problem 6.3 Lagrangian Decomposition Scheme 6.4 Solution of the Dual Problem 6.5 Heuristic Solutions 6.6 Remarks 6.6.1 CDU Feedstocks and Lagrange Multipliers Contents using La120 120 121 121 125 127 127 130 134 136 136 viii 6.7 6.8 6.9 6.6.2 Multi-Period Refinery Planning 6.6.3 CDU Feedstocks Aggregation 6.6.4 Handling Nonlinearities in Crude-Oil Scheduling Model 6.6.5 Handling Nonlinearities in the Refinery Planning Model 6.6.6 Detailed Implementation Numerical Illustration Larger Refinery Problem Conclusion Conclusion 7.1 Time Representations and Mathematical Models 7.2 Short-Term Scheduling of Crude-Oil Operations 7.3 Single-Operation Sequencing Model for Crude-Oil Operations Scheduling 7.4 Tightening the Linear Relaxation of an MINLP Using CP 7.5 Integration of Refinery Planning and Crude-Oil Scheduling 7.6 Contributions of the Thesis 7.7 Recommendations for Future Work 137 138 139 140 140 142 148 154 156 156 159 160 161 163 164 165 Bibliography 168 Appendices 177 A On Tightness of Strengthened Constraints 179 B Crude-Oil Operations Scheduling Examples 181 C Mathematical Models for Crude-Oil Operations C.1 MOS Model C.2 MOS-SST Model C.3 MOS-FST Model C.4 SOS Model 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mathematical results on the tightness of strengthened constraints • Constraint (2.17) is at least as tight as constraint (2.4) Indeed, assume constraint (2.17) is satisfied for W such that v1 , v2 ∈ W : Ziv1 + Ziv2 ≤ Ziv ≤ v∈W • Constraint (2.6) is at least as tight as constraints (2.5) Indeed, assume constraint (2.6) is satisfied for v1 , v2 ∈ W : Ei1 v1 ≤ Ei1 v1 + Ei1 v2 ≤ Si2 v1 + Si2 v2 + H · (1 − Zi2 v1 − Zi2 v2 ) ≤ Si2 v2 + H · (1 − Zi2 v2 ) + Si2 v1 − H · Zi2 v1 ≤ Si2 v2 + H · (1 − Zi2 v2 ) • Constraint (2.18) is at least as tight as constraint (2.6) Indeed, assume constraint (2.18) is satisfied for W such that v1 , v2 ∈ W : Ei1 v1 + Ei1 v2 ≤ Ei1 v v∈W ≤ Si2 v + H · v∈W 1− Z i2 v v∈W ≤ Si2 v1 + Si2 v2 + H · (1 − Zi2 v1 − Zi2 v2 ) + (Si2 v − H · Zi2 v ) v∈W \{v1 ,v2 } ≤ Si2 v1 + Si2 v2 + H · (1 − Zi2 v1 − Zi2 v2 ) Appendix A On Tightness of Strengthened Constraints 179 • Constraint (2.19) is at least as tight as constraint (2.18) Indeed, assume constraint (2.19) is satisfied for W : Ei1 v ≤ v∈W Ei1 v + Div ≤ i∈T v∈W i1