(736c) Mathematical Modeling and Global Optimization for Entire Petrochemical Planning Operations

In the last twenty years, the petrochemical industry has succeeded by creating markets and supplying them with suitable products used to create goods such as plastics, cosmetics, lubricants, and paints. Petrochemical production begins in a refinery that separates crude oils mainly into lighter components such as naphtha, light naphtha, top oil, and liquid fuels including gasoline, diesel and jet fuel. The lighter components are further processed into various petrochemicals such as ethylene, propylene, butadiene, benzene, toluene, xylol and some other high-valued products via cracking, butadiene extraction, hydrotreating, etherification, and polymerization processes. Nowadays, tighter competition, strict environmental regulations, and lower-margin profits, drive the petrochemical industry to apply new technologies to improve their planning operations.

Integrated petrochemical operations include both refinery and chemical production operations, such as crude oil blending and processing, production unit operations, and product blending and distribution [1-2]. Planning of integrated petrochemical operations involves optimization of crude blending, processing amounts for production units, unit production modes, flow connections between production units, and pooling and blending operations to satisfy quality requirements of production units, intermediates and final products. Mathematical modeling of production units, pooling and blending operations introduces bilinear, trilinear terms, and higher order terms, which result to a mixed integer non-convex nonlinear optimization problem.

The refinery planning problem has received considerable attention since the introduction of linear programming in 1950s. Research focused on developing different models and algorithms to solve large-scale industrial problems, leading to commercial software such as RPMS (Refinery and Petrochemical Modeling System) [3], PIMS (Process Industry Modeling System) [4], and GRTMPS (Haverly Systems) [5]. Commercially available software can be extended to model and optimize integrated petrochemical processes, however, inaccuracy caused by non-rigorous linear models and approximate algorithms may reduce the overall profitability or sacrifice product quality. Moreover, no global optimality can be guaranteed. On the other hand, nonlinear models and specialized algorithms have also been proposed for refinery planning problems. For instance, Pinto and Moro [6] developed a nonlinear planning model for production planning which allows the implementation of nonlinear process models as well as blending relations. Li et al.[7] presented a refinery planning model that utilizes simplified empirical nonlinear process models with considerations for crude characteristics, product yields, and qualities. Alhajri et al.[8] developed a nonlinear model to address the refinery planning problem. Alattas et al. [9] developed a fractionation index based nonlinear model for crude distillation units and integrated it into the linear refinery planning model, solving it with NLP solvers without guaranteeing global optimality. A comprehensive review on refinery planning can be found in Shah et al. [1]. It can be concluded that very few theoretical developments and results have been reported for global optimization of integrated refinery and petrochemical planning problems.

In this presentation, we first propose detailed nonlinear models to predict product yields and properties in production units including crude distillation unit, vacuum distillation unit, hydrocracking units, catalytic cracking units, ethylene-cracking units and other processing units present in a petrochemical plant. The yield and property prediction models for crude distillation and vacuum distillation units are developed using swing cut theory based on crude assay data. Empirical non-linear models are developed for other processing units, including bilinear, trilinear, quadratic, polynomial, and exponential terms. Parameter estimation for all of the developed models is performed by globally minimizing the least squares error between the parametric models and real production data. Moreover, property indices in blending units are linearly additive and calculated on weight or volume basis, which introduce bilinear and trilinear terms. We also introduce binary variables to denote different operation modes for several production units.

The entire planning model is a non-convex mixed integer nonlinear optimization model (MINLP). To solve this large-scale nonlinear model, we propose an optimization-based procedure to obtain the tightest lower and upper bounds for variables especially the variables involving nonlinear terms. Then, we incorporate those tightest lower and upper bounds into commercial solver ANTIGONE [10] to obtain e-global optimality. Finally, a user-friendly platform is developed to allow the user to modify the planning model by updating model parameters when new data is available, product demands and specifications, cost parameters and many more. Several large-scale industrial examples are solved to illustrate the efficiency of our proposed model and global optimization approach.

References

[1] Shah, N. K.; Li, Zu; Ierapetritou, M. G. Petroleum Refining Operations: Key Issues, Advances, and Opportunities, Industrial and Engineering Chemistry Research, 2011, 50, 1161-1170.

[2] Shah, N. K.; Ierapetritou, M. G. Short-Term Scheduling of a Large-Scale Oil-Refinery Operaitons: Incorporating Logistics Details. AIChE Journal2011, 57, 1570-1584.

[3] RPMS (Refinery and Petrochemical Modeling Systems): A System Description; Bonner and Moore: Houston, TX, 1979.

[4]  Aspen PIMS System Reference (v7.2), Aspen Technology Inc.; Burlington, MA, 2010.

[5] GRTMPS (Haverly Systems), http://www.haverly.com/main-products/13-products/9-grtmps.

[6] Pinto, J. M.; Moro, L. F. L. A Planning Model for Petroleum Refineries. Braz. J. Chem. Eng. 2000, 17, 575-585.

[7] Li, W. K.; Hui, C. W.; Li, A. X. Integrating CDU, FCC, and Product Blending Models into Refinery Planning. Computers and Chemical Engineering 2005, 29, 2010-2028.

[8] Alhajri, I.; Elkamel, A.; Albahri, T.; Douglas, P. L. A Nonlinear Programming Model for Refinery Planning and Optimization with Rigorous Process Models and Product Quality Specifications. International Journal of Oil, Gas, and Coal Technology 2008, 1, 283-307.

[9] Alattas, A. M.; Grossmann, I. E.; Palou-Rivera, I. Integration of Nonlinear Crude Distillation Unit Models in Refinery Planning Optimization. Industrial and Engineering Chemistry Research 2011, 50, 6860-6870.

[10] Misener, R.; Floudas, C. A. ANTIGONE: Algorithms for continuous/Integer Global Optimization of Nonlinear Equations. Journal of Global Optimization, In press, 2014.