Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter

doi:10.1016/j.cjche.2023.10.003

Chinese Journal of Chemical Engineering ›› 2024, Vol. 66 ›› Issue (2): 145-156.DOI: 10.1016/j.cjche.2023.10.003

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Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter

Xuepu Cao¹, Shengkun Jia², Xing Qian³, Yiqing Luo², Xigang Yuan²

1. College of Chemical and Pharmaceutical, Hebei University of Science & Technology, Shijiazhuang 050018, China;
2. School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China;
3. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China

Received:2023-04-19 Revised:2023-10-08 Online:2024-04-20 Published:2024-02-28
Contact: Shengkun Jia,E-mail:jiask@tju.edu.cn;Xigang Yuan,E-mail:yuanxg@tju.edu.cn
Supported by:
Support by the National Natural Science Foundation of China (22308251, 22178247, 22378304) and the Natural Science Foundation of Hebei Province (B2021208026) are acknowledged.

Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter

Xuepu Cao¹, Shengkun Jia², Xing Qian³, Yiqing Luo², Xigang Yuan²

1. College of Chemical and Pharmaceutical, Hebei University of Science & Technology, Shijiazhuang 050018, China;
2. School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China;
3. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China

通讯作者: Shengkun Jia,E-mail:jiask@tju.edu.cn;Xigang Yuan,E-mail:yuanxg@tju.edu.cn
基金资助:
Support by the National Natural Science Foundation of China (22308251, 22178247, 22378304) and the Natural Science Foundation of Hebei Province (B2021208026) are acknowledged.

Abstract

Abstract: Optimizing multistage processes, such as distillation or absorption, is a complex mixed-integer nonlinear programming (MINLP) problem. Relaxing integer into continuous variables and solving the easier nonlinear programming (NLP) problem is an optimization idea for the multistage process. In this article, we propose a relaxation method based on the efficiency parameter. When the efficiency parameter is 1 or 0, the proposed model is equivalent to the complete existence or inexistence of the equilibrium stage. And non-integer efficiency represents partial existence. A multi-component absorption case shows a natural penalty for non-integer efficiency, which can assist the efficiency parameter converging to 0 or 1. However, its penalty is weaker than the existing relaxation models, such as the bypass efficiency model. In a simple distillation case, we show that this property can weaken the nonconvexity of the optimization problem and increase the probability of obtaining better optimization results.

Key words: Mathematical modeling, Absorption, Distillation, Optimization

摘要： Optimizing multistage processes, such as distillation or absorption, is a complex mixed-integer nonlinear programming (MINLP) problem. Relaxing integer into continuous variables and solving the easier nonlinear programming (NLP) problem is an optimization idea for the multistage process. In this article, we propose a relaxation method based on the efficiency parameter. When the efficiency parameter is 1 or 0, the proposed model is equivalent to the complete existence or inexistence of the equilibrium stage. And non-integer efficiency represents partial existence. A multi-component absorption case shows a natural penalty for non-integer efficiency, which can assist the efficiency parameter converging to 0 or 1. However, its penalty is weaker than the existing relaxation models, such as the bypass efficiency model. In a simple distillation case, we show that this property can weaken the nonconvexity of the optimization problem and increase the probability of obtaining better optimization results.

关键词: Mathematical modeling, Absorption, Distillation, Optimization

Xuepu Cao, Shengkun Jia, Xing Qian, Yiqing Luo, Xigang Yuan. Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter[J]. Chinese Journal of Chemical Engineering, 2024, 66(2): 145-156.

Xuepu Cao, Shengkun Jia, Xing Qian, Yiqing Luo, Xigang Yuan. Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter[J]. 中国化学工程学报, 2024, 66(2): 145-156.

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Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter

Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter

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