基于简化相平衡关联式的高效简捷精馏塔模型

doi:10.11949/0438-1157.20241007

摘要/Abstract

摘要：

化工单元的准确快速模拟是化工数字孪生成功实施的关键之一。精馏塔作为最复杂和应用最广泛的化工单元之一，其高效准确求解对于实现化工装置数字孪生具有重要意义。传统精馏塔模型则由于规模较大和热力学性质计算耗时等原因，形成了制约其数字孪生的瓶颈。为此，在简捷精馏塔模型基础上，引入了组分相平衡常数与温度间关联式，以简化相平衡计算，并基于此提出了烃类精馏塔的高效简捷精馏塔模型。最后，通过实际工业中的精馏塔进行验证，结果表明所提出的高效简捷精馏塔模型能有效减少计算耗时，为精馏塔的数字孪生建模奠定了基础。

关键词: 模型简化, 过程系统, 计算机模拟, 数字孪生, 简捷精馏塔模型

Abstract:

Accurate and rapid simulation of chemical engineering units is crucial to the success of chemical process digital twins. As one of the most complex and widely used units in chemical engineering, the efficient and accurate solution of distillation columns is essential for the implementation of digital twins in chemical plants. However, traditional distillation column model has become a bottleneck restricting its digital twin due to its large scale and time-consuming calculation of thermodynamic properties. To address this, a efficient and short-cut distillation column model for hydrocarbon systems was developed based on the short-cut distillation column model by introducing the correlation between component equilibrium constants and temperature, thereby simplifying the phase equilibrium calculations. The model was validated by using a distillation column from an actual industrial process. The results show that the proposed efficient and short-cut distillation column model significantly reduces computation time, laying a solid foundation for digital twin modeling of distillation columns.

Key words: model reduction, process systems, computer simulation, digital twin, short-cut distillation column model

中图分类号:

TQ 021.8

王宗廷, 王丽丽, 孙晓岩, 夏力, 陶少辉, 项曙光. 基于简化相平衡关联式的高效简捷精馏塔模型[J]. 化工学报, 2025, 76(3): 1133-1142.

Zongting WANG, Lili WANG, Xiaoyan SUN, Li XIA, Shaohui TAO, Shuguang XIANG. Simplified phase equilibrium correlation-based efficient and short-cut distillation column model[J]. CIESC Journal, 2025, 76(3): 1133-1142.

图/表 14

图1 Edmister模型发展历程

Fig.1 Development process of edmister model

图2 高效AEM模型示意图

Fig.2 Efficient AEM model

图3 全塔区域划分图

Fig.3 Zoning map of the whole column

图4 气分装置流程示意图

Fig.4 Schematic diagram of gas separation device flow

表 1 参数回归值

Table 1 Parameter regression value

物质	$Δ C 0, i$	$Δ C 1, i$
C₃	11.4165	-10.8881
C₃=	11.0834	-11.0999
i-C₄	17.0333	-13.7702
n-C₄	16.7055	-13.1724
C₄=	16.3690	-13.4467
i-C₄=	16.1458	-13.2884
t-C₄=	16.5793	-13.4199
cis-C₄=	17.4739	-14.0764

表 1 参数回归值

Table 1 Parameter regression value

物质	$Δ C 0, i$	$Δ C 1, i$
C₃	11.4165	-10.8881
C₃=	11.0834	-11.0999
i-C₄	17.0333	-13.7702
n-C₄	16.7055	-13.1724
C₄=	16.3690	-13.4467
i-C₄=	16.1458	-13.2884
t-C₄=	16.5793	-13.4199
cis-C₄=	17.4739	-14.0764

图5 简化相平衡结果对比

Fig.5 Comparison of simplified phase equilibrium

图6 气分装置主要组成对比

Fig.6 Comparison of the main components of the gas separation device

图7 气分装置塔顶塔底温度对比

Fig.7 Comparison of temperature at the top and bottom of the air separation device

图8 模型计算效率对比

Fig.8 Comparison of model calculation efficiency

图9 原油物质的TBP曲线

Fig.9 TBP curve of crude oil

图10 初馏塔塔段示意图

Fig.10 Schematic diagram of primary distillation column

图11 真实组分和虚拟组分的相平衡计算结果

Fig.11 Calculation results of phase equilibrium between real and virtul components

图12 塔顶真实组分与虚拟组分流率

Fig.12 Flow rate of real and virtual components of column top

表2 初馏塔塔顶塔底温度对比

Table 2 Temperature of the primary column

塔	温度/K			相对误差%
塔	严格精馏塔	原始AEM	高效AEM	原始AEM	高效AEM
塔顶	417.58	419.70	420.10	-0.51	-0.60
塔底	501.77	505.64	506.42	-0.77	-0.93

参考文献 31

1	Singh M, Fuenmayor E, Hinchy E P, et al. Digital twin: origin to future[J]. Applied System Innovation, 2021, 4(2): 36.
2	陶飞, 张贺, 戚庆林, 等. 数字孪生十问: 分析与思考[J]. 计算机集成制造系统, 2020, 26(1): 1-17.
	Tao F, Zhang H, Qi Q L, et al. Ten questions towards digital twin: analysis and thinking[J]. Computer Integrated Manufacturing Systems, 2020, 26(1): 1-17.
3	Pan Y H, Qu T, Wu N Q, et al. Digital twin based real-time production logistics synchronization system in a multi-level computing architecture[J]. Journal of Manufacturing Systems, 2021, 58: 246-260.
4	Jana A K. Chemical Process Modelling and Computer Simulation[M]. PHI Learning Pvt. Ltd., 2018: 3-33.
5	Schäfer P, Caspari A, Schweidtmann A M, et al. The potential of hybrid mechanistic/data-driven approaches for reduced dynamic modeling: application to distillation columns[J]. Chemie Ingenieur Technik, 2020, 92(12): 1910-1920.
6	Zendehboudi S, Rezaei N, Lohi A. Applications of hybrid models in chemical, petroleum, and energy systems: a systematic review[J]. Applied Energy, 2018, 228: 2539-2566.
7	张梦轩, 刘洪辰, 王敏, 等. 化工过程的智能混合建模方法及应用[J]. 化工进展, 2021, 40(4): 1765-1776.
	Zhang M X, Liu H C, Wang M, et al. Intelligence hybrid modeling method and applications in chemical process[J]. Chemical Industry and Engineering Progress, 2021, 40(4): 1765-1776.
8	Ghosh D, Hermonat E, Mhaskar P, et al. Hybrid modeling approach integrating first-principles models with subspace identification[J]. Industrial & Engineering Chemistry Research, 2019, 58(30): 13533-13543.
9	Mcbride K, Sanchez Medina E I, Sundmacher K. Hybrid semi-parametric modeling in separation processes: a review[J]. Chemie Ingenieur Technik, 2020, 92(7): 842-855.
10	Sansana J, Joswiak M N, Castillo I, et al. Recent trends on hybrid modeling for Industry 4.0[J]. Computers & Chemical Engineering, 2021, 151: 107365.
11	Kremser A. Theoretical analysis of absorption process[J]. National Petroleum News, 1930, 22(21): 43-49.
12	Edmister W C. Absorption and stripping-factor functions for distillation calculation by manual-and digital-computer methods[J]. AIChE Journal, 1957, 3(2): 165-171.
13	Kamath R S, Grossmann I E, Biegler L T. Aggregate models based on improved group methods for simulation and optimization of distillation systems[J]. Computers & Chemical Engineering, 2010, 34(8): 1312-1319.
14	Ecker A M, Thomas I, Häfele M, et al. Development of a new column shortcut model and its application in process optimisation[J]. Chemical Engineering Science, 2019, 196: 538-551.
15	Kender R, Stops L, Krespach V, et al. Reduced order modeling of a pressure column of an air separation unit using the dynamic edmister method[J]. Computers & Chemical Engineering, 2023, 174: 108250.
16	Lemmon E W, Jacobsen R T. A generalized model for the thermodynamic properties of mixtures[J]. International Journal of Thermophysics, 1999, 20(3): 825-835.
17	Zhang T, Zhang Y H, Katterbauer K, et al. Phase equilibrium in the hydrogen energy chain[J]. Fuel, 2022, 328: 125324.
18	Nichita D V. A reduction method for phase equilibrium calculations with cubic equations of state[J]. Brazilian Journal of Chemical Engineering, 2006, 23(3): 427-434.
19	Kamath R S, Biegler L T, Grossmann I E. An equation-oriented approach for handling thermodynamics based on cubic equation of state in process optimization[J]. Computers & Chemical Engineering, 2010, 34(12): 2085-2096.
20	Fan J Y, Pan J Y. An improved trust region algorithm for nonlinear equations[J]. Computational Optimization and Applications, 2011, 48(1): 59-70.
21	Ghafoori M J, Aghamiri S F, Talaie M R. A new empirical K-value equation for reservoir fluids[J]. Fuel, 2012, 98: 236-242.
22	Ahmed T. Reservoir Engineering Handbook[M]. Gulf Professional Publishing, 2018: 1109-1218.
23	Hoffman A E, Crump J S, Hocott C R. Equilibrium constants for a gas-condensate system[J]. Journal of Petroleum Technology, 1953, 5(1): 1-10.
24	Michelsen M L. Simplified flash calculations for cubic equations of state[J]. Industrial & Engineering Chemistry Process Design and Development, 1986, 25(1): 184-188.
25	Leibovici C, Stenby E H, Knudsen K. A consistent procedure for pseudo-component delumping[J]. Fluid Phase Equilibria, 1996, 117(1/2): 225-232.
26	Rabeau P, Gani R, Leibovici C. An efficient initialization procedure for simulation and optimization of large distillation problems[J]. Industrial & Engineering Chemistry Research, 1997, 36(10): 4291-4298.
27	Westerberg A W, Berna T J. Decomposition of very large-scale Newton-Raphson based flowsheeting problems[J]. Computers & Chemical Engineering, 1978, 2(1): 61-63.
28	Dennis Jr J E, El-Alem M, Williamson K. A trust-region approach to nonlinear systems of equalities and inequalities[J]. SIAM Journal on Optimization, 1999, 9(2): 291-315.
29	Edmister W C. Design for hydrocarbon absorption and stripping[J]. Industrial & Engineering Chemistry, 1943, 35(8): 837-839.
30	Wächter A, Biegler L T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming[J]. Mathematical Programming, 2006, 106(1): 25-57.
31	Wilson G M. A modified Redlish-Kwong equation of state, application to general physical data calculation[C]// 65th National AICHE Metting. Cleveland, 1969.

[1]	任超, 王凯, 韩洁, 阳春华. 事件-时间触发的慢时变工业过程动态调度方法[J]. 化工学报, 2025, 76(1): 256-265.
[2]	卢昕悦, 陈锐莹, 姜夏雪, 梁海瑞, 高歌, 叶正芳. 耦合LNG冷能的液态空气储能系统和液态CO₂储能系统对比分析[J]. 化工学报, 2024, 75(9): 3297-3309.
[3]	李洪瑞, 黄纯西, 洪小东, 廖祖维, 王靖岱, 阳永荣. 基于自适应变步长同伦法的循环流程收敛算法[J]. 化工学报, 2024, 75(7): 2604-2612.
[4]	黄志鸿, 周利, 柴士阳, 吉旭. 耦合加氢装置优化的多周期氢网络集成[J]. 化工学报, 2024, 75(5): 1951-1965.
[5]	文一如, 付佳, 刘大欢. 基于机器学习的MOFs材料研究进展：能源气体吸附分离[J]. 化工学报, 2024, 75(4): 1370-1381.
[6]	王浩, 王振雷. 基于自适应谱方法的裂解炉烧焦模型化简策略[J]. 化工学报, 2023, 74(9): 3855-3864.
[7]	陈哲文, 魏俊杰, 张玉明. 超临界水煤气化耦合SOFC发电系统集成及其能量转化机制[J]. 化工学报, 2023, 74(9): 3888-3902.
[8]	刘远超, 关斌, 钟建斌, 徐一帆, 蒋旭浩, 李耑. 单层XSe₂（X=Zr/Hf）的热电输运特性研究[J]. 化工学报, 2023, 74(9): 3968-3978.
[9]	郑玉圆, 葛志伟, 韩翔宇, 王亮, 陈海生. 中高温钙基材料热化学储热的研究进展与展望[J]. 化工学报, 2023, 74(8): 3171-3192.
[10]	文兆伦, 李沛睿, 张忠林, 杜晓, 侯起旺, 刘叶刚, 郝晓刚, 官国清. 基于自热再生的隔壁塔深冷空分工艺设计及优化[J]. 化工学报, 2023, 74(7): 2988-2998.
[11]	李贵贤, 曹阿波, 孟文亮, 王东亮, 杨勇, 周怀荣. 耦合固体氧化物电解槽的CO₂制甲醇过程设计与评价研究[J]. 化工学报, 2023, 74(7): 2999-3009.
[12]	邵远哲, 赵忠盖, 刘飞. 基于共同趋势模型的非平稳过程质量相关故障检测方法[J]. 化工学报, 2023, 74(6): 2522-2537.
[13]	刘尚豪, 贾胜坤, 罗祎青, 袁希钢. 基于梯度提升决策树的三组元精馏流程结构最优化[J]. 化工学报, 2023, 74(5): 2075-2087.
[14]	贠程, 王倩琳, 陈锋, 张鑫, 窦站, 颜廷俊. 基于社团结构的化工过程风险演化路径深度挖掘[J]. 化工学报, 2023, 74(4): 1639-1650.
[15]	王子宗, 索寒生, 赵学良. 数字孪生智能乙烯工厂研究与构建[J]. 化工学报, 2023, 74(3): 1175-1186.