Mathematical Modeling and Global Optimization Approach for Entire Petrochemical Planning Operations

Mathematical Modeling
and Global Optimization Approach for Entire Petrochemical Planning Operations

Jie Li,^1,2
Fani Boukouvala,¹ Xin Xiao,² Yong Qiao,³ Baoguo
Zhao,⁴ Guangming Du,⁴ Xin Su,⁴ Hongwei Liu,⁴
and Christodoulos A. Floudas¹

¹Artie McFerrin Department of
Chemical Engineering

Texas A & M
University

College Station,
TX 77843

²State Key Laboratory
of Multiphase Complex Systems

Institute of
Process Engineering

Chinese Academy
of Sciences

Beijing, China
100190

³Science,
Technology and Information Department, PetroChina Refining and Chemical
Company, PetroChina Company Limited, Beijing, China 100007

⁴Dushanzi
Petroleum and Petrochemical Complex, PetroChina

Dushanzi,
Xinjiang, China 833600

Abstract

The petrochemical
industry has succeeded by creating markets and supplying them with suitable
products such as gasoline, diesel, jet fuel, naphtha, light naphtha, and top
oil that used to create goods such as plastics, cosmetics, lubricants, and
paints in the last twenty years. The tighter competition, strict environmental
regulations, and lower-margin profits driving provide an impetus for new
technologies to improve their planning operations.

The
entire petrochemical operations consist of refinery and chemical production
operations. The refinery operations can be divided into three components
including crude oil blending and processing, production unit operations, and product
blending and distribution[1-2]. The entire petrochemical planning operations involve
crude blending and distillation, production processing, production mode
selection, 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, pooling and blending
operations introduces bilinear, quadratic, polynomial, signomial, exponential, and
higher order terms. On the other hand, the selection of parallel production
units and production modes introduces binary variables. Hence, the entire
problem is a large-scale non-convex mixed integer nonlinear optimization
(MINLP) problem.

Commercial
software such as RPMS (Refinery and Petrochemical Modeling System),[3] PIMS
(Process Industry Modeling System),[4] and GRTMPS (Haverly Systems)[5] have
been developed for optimization of entire petrochemical planning operations.
However, they use non-rigorous models and approximate algorithms, which often
lead to inaccuracies and generate solutions with suboptimal profitability or sacrificing
product quality. Moreover, global optimality is not guaranteed. Nonlinear
models and specialized algorithms [6-9] have also been developed, but have been
restricted to refinery planning problems. A comprehensive review on refinery planning
can be found in [1].

In this presentation,
we propose mathematical modeling and global optimization framework to address
the entire petrochemical planning problem. In our proposed framework, we first develop
detailed models to predict product yields and properties in production units
including crude distillation units, coking units, hydrocracking units,
catalytic cracking units, reforming units, ethylene-cracking units and other
processing units. The yield and property prediction models for crude
distillation units are developed using swing cut theory based on crude assay
data. Models for the remaining processing units are developed by postulating
surrogate approximations for the yield and property predictions and globally
solving a non-linear parameter estimation problem for each unit, which includes
all of the postulated equations and mass balance equations. These models
involve bilinear, quadratic, polynomial, and exponential terms. The property
indices in pooling and blending units are linearly additive and calculated on
weight or volume basis, which introduces bilinear and trilinear terms. We also
introduce binary variables to denote the selection of several parallel units
and operation modes in some production units. The entire planning model is a large-scale
non-convex mixed integer nonlinear optimization (MINLP) model. To solve this large-scale
MINLP 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 the commercial
solver ANTIGONE[10] to obtain e-global optimality.
Finally, we have developed a user-friendly platform allowing the user to modify
the planning model by updating model parameters when new data is available,
product demands and specifications, and cost parameters. Several large-scale
industrial examples are solved to illustrate the effectiveness of our proposed modeling
and global optimization approach. The computational results show that all
examples can be solved to global optimality within 30 minutes. Most
importantly, we achieve at least 30% significant profit increase compared to the
reported profit.

Key words: refinery, planning, nonlinear programming,
non-convex, global optimality

References

[1] Shah, N. K.;
Li, Z.; Ierapetritou, M. G. Petroleum Refining Operations: Key Issues,
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[2] Shah, N. K.;
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[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.

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