基于非线性规划的三氟化硼-11分离工艺优化

doi:10.16085/j.issn.1000-6613.2024-1430

摘要/Abstract

摘要：

化学交换法分离三氟化硼-11工艺过程因变量间存在强相互作用难题，导致工艺过程无法满足精准优化，本文提出了一种基于非线性规划的求解模型，在稳态数学模型的基础上完成了三氟化硼-11分离工艺的参数优化。分析了3个关键工艺参数对三氟化硼-11同位素丰度的影响关系，得出络合塔温度降低、回流比及理论板数增加均有利于丰度富集的结论。在研究确定的工艺参数优化范围内，分析了双因素中各工艺参数对三氟化硼-11同位素丰度富集的显著影响关系。分别以成本费用与丰度为目标，构建了目标值与络合塔温度、回流比以及理论板数之间的函数关系。以达到设计丰度值为约束条件，以成本费用最低为优化目标，建立了非线性规划问题，使用非线性规划算法求解得到了工艺参数值，并借助Aspen Plus软件对获得的工艺参数值进行了实验验证。研究结果显示，当络合塔温度为10.03℃、回流比为94.17、理论板数为567时，三氟化硼-11模型丰度值为99.90%，软件丰度值为99.94%，在满足设计要求的前提下，成本费用价格低。本文提出的非线性规划求解思想对三氟化硼-11及其他同位素分离工艺的参数优化具有重要的科学意义和实际应用价值，能够为产业化设计提供更加准确的理论支持。

关键词: 非线性规划, 三氟化硼-11, 化学交换法, 分离, 优化, Aspen Plus数值模拟

Abstract:

In the separating boron isotopes process by chemical exchange method, due to the problem of strong interaction between variables, which leads to the difficulty in precise optimization, a solution model based on nonlinear programming was proposed, and the parameters of the boron-11 trifluoride separation process were optimized on the basis of the steady-state mathematical model. The effects of three key process parameters on the isotope abundance of boron-11 trifluoride were analyzed, and the results showed that the decrease of the complex tower temperature, the increase of the reflux ratio and the theoretical plates number were conducive to the abundance enrichment. Within the scope of optimization of process parameters determined, the significant influence of each process parameter on the isotope abundance of boron-11 in the two factors was analyzed. The functional relationships between the target value and the complex tower temperature, the reflux ratio and the theoretical plates numbers were constructed with the cost and abundance as the targets, respectively. With the design abundance value as the constraint and the lowest cost as the optimization goal, the nonlinear programming problem was established, and the process parameter values were solved by using the nonlinear programming algorithm, and the obtained process parameter values were experimentally verified by using Aspen Plus software. The results showed that when the complex tower temperature was 10.03℃, the reflux ratio was 94.17, and the theoretical plates numbers was 567, the abundance value of boron-11 trifluoride model was 99.90%, and the abundance value of software was 99.94%. The cost was low under the premise of meeting the design requirements. The nonlinear programming solution proposed in this paper had important scientific significance and practical application value for the separation processes parameters optimization of boron-11 trifluoride and other isotope, and can provide more accurate theoretical support for industrial design.

Key words: nonlinear programming, boron-11 trifluoride, chemical exchange method, separation, optimization, Aspen Plus numerical simulation

中图分类号:

TQ028

任倩倩, 吴高胜, 杨军, 宗睿, 包春凤, 刘陈真, 许保云, 艾波, 李瑜哲. 基于非线性规划的三氟化硼-11分离工艺优化[J]. 化工进展, 2025, 44(10): 5599-5608.

REN Qianqian, WU Gaosheng, YANG Jun, ZONG Rui, BAO Chunfeng, LIU Chenzhen, XU Baoyun, AI Bo, LI Yuzhe. Optimization of boron-11 trifluoride separation process based on nonlinear programming[J]. Chemical Industry and Engineering Progress, 2025, 44(10): 5599-5608.

图/表 15

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因素	因素变化范围
络合塔温度（X₁）	10~30℃
回流比（X₂）	48.95~400
理论板数（X₃）	184~800

因素	因素变化范围
络合塔温度（X₁）	10~30℃
回流比（X₂）	48.95~400
理论板数（X₃）	184~800

序号	理论板数	三氟化硼-11丰度/%		三氟化硼-11丰度变化的相对偏差/%	三氟化硼-11丰度变化的相对偏差平均值/%
序号	理论板数	络合塔温度30℃	络合塔温度10℃	三氟化硼-11丰度变化的相对偏差/%	三氟化硼-11丰度变化的相对偏差平均值/%
1	184	93.27	95.63	2.53	2.67
2	250	94.42	96.88	2.61
3	300	95.03	97.53	2.63
4	350	95.48	98.01	2.65
5	400	95.82	98.38	2.67
6	450	96.10	98.68	2.68
7	500	96.32	98.90	2.69
8	550	96.50	99.10	2.70
9	600	96.64	99.25	2.70
10	650	96.76	99.38	2.71
11	700	96.86	99.49	2.72
12	800	97.00	99.65	2.73

序号	理论板数	三氟化硼-11丰度/%		三氟化硼-11丰度变化的相对偏差/%	三氟化硼-11丰度变化的相对偏差平均值/%
序号	理论板数	络合塔温度30℃	络合塔温度10℃	三氟化硼-11丰度变化的相对偏差/%	三氟化硼-11丰度变化的相对偏差平均值/%
1	184	93.27	95.63	2.53	2.67
2	250	94.42	96.88	2.61
3	300	95.03	97.53	2.63
4	350	95.48	98.01	2.65
5	400	95.82	98.38	2.67
6	450	96.10	98.68	2.68
7	500	96.32	98.90	2.69
8	550	96.50	99.10	2.70
9	600	96.64	99.25	2.70
10	650	96.76	99.38	2.71
11	700	96.86	99.49	2.72
12	800	97.00	99.65	2.73

序号	络合塔温度/℃	三氟化硼-11丰度/%		三氟化硼-11丰度变化的相对偏差/%	三氟化硼-11丰度变化的相对偏差平均值/%
序号	络合塔温度/℃	理论板数184	理论板数800	三氟化硼-11丰度变化的相对偏差/%	三氟化硼-11丰度变化的相对偏差平均值/%
1	10	95.63	99.65	4.20	4.26
2	15	94.96	99.20	4.47
3	20	94.35	98.52	4.42
4	25	93.77	97.73	4.23
5	30	93.27	97.00	4.00