Optimization of distillation column based on trust region algorithm

doi:10.11949/0438-1157.20220036

Abstract

Abstract:

In this paper, a mixed integer nonlinear programming (MINLP) model for distillation columns optimization is established from the perspective of structural optimization. In order to eliminate integer variables, the bypass efficiency model is introduced to transform the MINLP problem into a nonlinear programming (NLP) problem. An optimization method is proposed to solve the NLP problem. In this method, the trust region optimization algorithm which commonly used in structural optimization is used and the pseudo-transient continuation model is used to assist the steady-state simulation in optimization. The optimization method proposed in this paper is used to optimize three distillation cases. All the cases can get satisfactory optimization results starting from different initial points. The results show that the proposed optimization method has good robustness and can still effectively solve the complex partial thermal coupling distillation process. The trust region algorithm also shows good convergence in the optimization of distillation column.

Key words: optimization, distillation, algorithm, trust region, bypass efficiency model

摘要：

从结构优化角度建立精馏塔优化的混合整数非线性规划(MINLP)模型，为了消除整数变量，引入绕流效率将MINLP问题转化为非线性规划(NLP)问题。针对得到的NLP问题提出一种优化方法，在该方法中采用结构优化中常用的信赖域优化算法进行求解，并应用虚拟瞬态连续性方程辅助优化中的稳态模拟。采用提出的优化方法对3个精馏系统进行设计优化，以不同初始值开始，均可得到令人满意的优化结果，表明所提优化方法具有良好的稳健性，对于较复杂的部分热耦合精馏过程仍然可以有效优化求解；信赖域算法在精馏塔优化中也表现出良好的收敛性。

关键词: 优化, 蒸馏, 算法, 信赖域, 绕流效率模型

CLC Number:

TQ 028.3

Xingwei LIU, Shengkun JIA, Yiqing LUO, Xigang YUAN. Optimization of distillation column based on trust region algorithm[J]. CIESC Journal, 2022, 73(5): 2031-2038.

刘星伟, 贾胜坤, 罗祎青, 袁希钢. 基于信赖域算法的精馏塔优化[J]. 化工学报, 2022, 73(5): 2031-2038.

Figures/Tables 11

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绕流效率的初值	N₁	N₂	RR/ (kmol/kmol)	V_f/ (kmol/kmol)	TAC/ (10⁴ USD/a)
0.1	20	19	6.30	0.8348	325.445
0.3	20	19	6.30	0.8348	325.445
0.5	21	20	6.15	0.8323	327.789
0.7	20	20	6.22	0.8334	326.351
0.9	21	20	6.15	0.8323	327.789

绕流效率的初值	N₁	N₂	RR/ (kmol/kmol)	V_f/ (kmol/kmol)	TAC/ (10⁴ USD/a)
0.1	20	19	6.30	0.8348	325.445
0.3	20	19	6.30	0.8348	325.445
0.5	21	20	6.15	0.8323	327.789
0.7	20	20	6.22	0.8334	326.351
0.9	21	20	6.15	0.8323	327.789

绕流效率的初始值	N₁	N₂	N₃	N₄	RR₁/(kmol/kmol)	V_f1/(kmol/kmol)	RR₂/(kmol/kmol)	V_f2/(kmol/kmol)	TAC/（10⁴ USD/a)
0.1	9	14	12	13	1.41	0.6124	1.50	0.7535	544.851
0.3	8	15	11	12	1.42	0.6142	1.52	0.7551	544.371
0.5	8	14	11	12	1.44	0.6142	1.53	0.7555	544.024
0.7	8	14	12	12	1.43	0.6137	1.52	0.7546	544.207
0.9	8	14	11	12	1.44	0.6142	1.53	0.7556	544.024

绕流效率的初始值	N₁	N₂	N₃	N₄	RR₁/(kmol/kmol)	V_f1/(kmol/kmol)	RR₂/(kmol/kmol)	V_f2/(kmol/kmol)	TAC/（10⁴ USD/a)
0.1	9	14	12	13	1.41	0.6124	1.50	0.7535	544.851
0.3	8	15	11	12	1.42	0.6142	1.52	0.7551	544.371
0.5	8	14	11	12	1.44	0.6142	1.53	0.7555	544.024
0.7	8	14	12	12	1.43	0.6137	1.52	0.7546	544.207
0.9	8	14	11	12	1.44	0.6142	1.53	0.7556	544.024

绕流效率的初始值	N₁	N₂	N₃	N₄	RR₁/(kmol/kmol)	S_f/(kmol/kmol)	RR₂/(kmol/kmol)	V_f/(kmol/kmol)	TAC/(10⁴ USD/a)
0.1	8	17	11	11	2.53	0.4507	2.53	0.6611	224.098
0.3	7	17	11	11	2.56	0.4476	2.52	0.6620	224.189
0.5	7	18	10	11	2.56	0.4485	2.54	0.6631	224.328
0.7	8	18	11	11	2.51	0.4508	2.52	0.6605	224.206
0.9	7	18	10	11	2.56	0.4485	2.54	0.6631	224.328