Temperature inferential control of compound distillation sequences

doi:10.16085/j.issn.1000-6613.2025-0138

Abstract

Abstract:

The compound distillation sequence (CDS) combines simple distillation columns with dividing-wall columns into an integrated system for multi-component mixture separation. This integration not only reduces capital investment costs and operational energy consumption, but also facilitates industrial implementation. However, the inherent nonlinear characteristics of dividing-wall columns and strong coupling effects from material flow connections between distillation units pose significant challenges for stable operation and effective control of CDS. To overcome these challenges, three temperature inferential control schemes were developed, including a temperature control scheme, a temperature difference control scheme, and a double temperature difference control scheme. Closed-loop simulation demonstrated that all three schemes could ensure the stable operation and effective control of the CDS. Furthermore, as the control scheme evolved from the simpler temperature control to the more complex double temperature difference control, although the complexity of control scheme increased, the steady-state deviations in product purity were significantly reduced. The implementation of these control schemes addressed the operational and control challenges of the CDS, providing a solid foundation for their industrial application.

Key words: compound distillation sequence, temperature inferential control, temperature difference, process control, multi-component separation

摘要：

复合精馏序列（CDS）通过将简单精馏塔与隔壁塔整合成一个系统来分离多元混合物，不仅能够实现较低的设备投资成本与操作能耗，还能有效降低系统的工业实施难度。但是，由于隔壁塔单元固有的高度非线性特性，以及各精馏单元间因物料流连接而产生的强烈耦合效应，实现CDS的稳定操作与有效控制面临显著挑战。为解决这一问题，本文提出了3种温度推断控制方案，包括温度控制方案、温差控制方案以及双温差控制方案。闭环仿真验证表明，这3种方案均能保证CDS的平稳运行与有效控制，并且，随着控制策略从简单的温度控制逐步演进到更为复杂的双温差控制，虽然控制复杂度有所增加，但被控产品纯度的稳态偏差能够被有效降低。3种温度推断控制策略的提出有助于解决CDS的操纵与控制难题，为推动CDS的工业应用奠定基础。

关键词: 复合精馏序列, 温度推断控制, 温差, 过程控制, 多元混合物分离

CLC Number:

TQ021.8

WANG Guochao, DING Huidian, SHI Li, LI Qiang, XIA Tao, YUAN Yang. Temperature inferential control of compound distillation sequences[J]. Chemical Industry and Engineering Progress, 2025, 44(8): 4720-4731.

汪国超, 丁晖殿, 师丽, 李强, 夏涛, 苑杨. 复合精馏序列的温度推断控制[J]. 化工进展, 2025, 44(8): 4720-4731.

Figures/Tables 14

TC			TDC			DTDC
控制器	K_C	t_i /min	控制器	K_C	t_i /min	控制器	K_C	t_i /min
TC1	0.48	9.24	TDC1	0.59	9.24	TDC1	0.55	9.24
TC2	3.54	17.16	TDC2	0.46	18.48	TDC2	0.46	17.16
TC3	0.25	7.92	TC1	0.33	7.92	TC1	0.29	7.92
TC4	2.54	11.88	TDC3	0.83	9.24	TDC3	0.92	9.24
TC5	6.35	13.20	TDC4	0.54	15.84	DTDC1	0.16	17.16
TC6	1.98	6.60	TC2	2.05	5.28	TC2	1.99	5.28
TC7	7.32	13.20	TDC5	0.95	11.88	TDC4	0.87	13.20
TC8	20.77	14.52	TDC6	1.08	15.84	DTDC2	0.42	13.20
TC9	3.86	6.60	TDC7	0.16	13.20	DTDC3	0.04	13.20
TC10	13.57	18.48	TDC8	0.81	14.52	DTDC4	0.07	17.16

温差	$L D 1$	$L S 1$	$Q R 1$	$β L 1$	$L D 2$	$Q R 2$	$L D 3$	$L S 3$	$Q R 3$	$β L 2$
C1塔： $T C 1,5$ - $T C 1,2$	0.86	0.05	-0.01	0.1	0	0	0	0	0	0
C1塔： $T C 1,20$ - $T C 1,14$	-0.45	1.46	0.42	-0.43	0	0	0	0	0	0
C1塔： $T C 1,28$ - $T C 1,25$	0.15	0.01	1.47	-0.63	0	0	0	0	0	0
C1塔： $T C 1, P 5$ - $T C 1, P 2$	0.44	-0.52	-0.88	1.96	0	0	0	0	0	0
C2塔： $T C 2,7$ - $T C 2,2$	0	0	0	0	0.86	0.14	0	0	0	0
C2塔： $T C 2,17$ - $T C 2,22$	0	0	0	0	0.14	0.86	0	0	0	0
C3塔： $T C 3,7$ - $T C 3,2$	0	0	0	0	0	0	1	0.04	-0.06	0.02
C3塔： $T C 3,28$ - $T C 3,18$	0	0	0	0	0	0	0	0.83	0.17	0
C3塔： $T C 3,38$ - $T C 3,46$	0	0	0	0	0	0	0.02	0.2	0.96	-0.18
C3塔： $T C 3, P 10$ - $T C 3, P 2$	0	0	0	0	0	0	-0.02	-0.07	-0.07	1.16

温差	$L D 1$	$L S 1$	$Q R 1$	$β L 1$	$L D 2$	$Q R 2$	$L D 3$	$L S 3$	$Q R 3$	$β L 2$
C1塔： $T C 1,5$ - $T C 1,2$	0.86	0.05	-0.01	0.1	0	0	0	0	0	0
C1塔： $T C 1,20$ - $T C 1,14$	-0.45	1.46	0.42	-0.43	0	0	0	0	0	0
C1塔： $T C 1,28$ - $T C 1,25$	0.15	0.01	1.47	-0.63	0	0	0	0	0	0
C1塔： $T C 1, P 5$ - $T C 1, P 2$	0.44	-0.52	-0.88	1.96	0	0	0	0	0	0
C2塔： $T C 2,7$ - $T C 2,2$	0	0	0	0	0.86	0.14	0	0	0	0
C2塔： $T C 2,17$ - $T C 2,22$	0	0	0	0	0.14	0.86	0	0	0	0
C3塔： $T C 3,7$ - $T C 3,2$	0	0	0	0	0	0	1	0.04	-0.06	0.02
C3塔： $T C 3,28$ - $T C 3,18$	0	0	0	0	0	0	0	0.83	0.17	0
C3塔： $T C 3,38$ - $T C 3,46$	0	0	0	0	0	0	0.02	0.2	0.96	-0.18
C3塔： $T C 3, P 10$ - $T C 3, P 2$	0	0	0	0	0	0	-0.02	-0.07	-0.07	1.16

温差	$L D 1$	$L S 1$	$Q R 1$	$β L 1$	$L D 2$	$Q R 2$	$L D 3$	$L S 3$	$Q R 3$	$β L 2$
C1塔： $T C 1,5$ - $T C 1,2$	0.99	0.04	-0.03	0	0	0	0	0	0	0
C1塔： $T C 1,20$ - $T C 1,14$	0	1	0.32	-0.32	0	0	0	0	0	0
C1塔： $T C 1,28$	0.02	0.12	0.87	-0.01	0	0	0	0	0	0
C1塔： $T C 1, P 5$ - $T C 1, P 2$	-0.01	-0.16	-0.16	1.33	0	0	0	0	0	0
C2塔： $T C 2,7$ - $T C 2,2$	0	0	0	0	0.97	0.03	0	0	0	0
C2塔： $T C 2,17$	0	0	0	0	0.03	0.97	0	0	0	0
C3塔： $T C 3,7$ - $T C 3,2$	0	0	0	0	0	0	1	0.04	-0.06	0.02
C3塔： $T C 3,28$ - $T C 3,18$	0	0	0	0	0	0	0	0.83	0.17	0
C3塔： $T C 3,38$ - $T C 3,46$	0	0	0	0	0	0	0.02	0.2	0.96	-0.18
C3塔： $T C 3, P 10$ - $T C 3, P 2$	0	0	0	0	0	0	-0.02	-0.07	-0.07	1.16

温差	$L D 1$	$L S 1$	$Q R 1$	$β L 1$	$L D 2$	$Q R 2$	$L D 3$	$L S 3$	$Q R 3$	$β L 2$
C1塔： $T C 1,5$ - $T C 1,2$	0.99	0.04	-0.03	0	0	0	0	0	0	0
C1塔： $T C 1,20$ - $T C 1,14$	0	1	0.32	-0.32	0	0	0	0	0	0
C1塔： $T C 1,28$	0.02	0.12	0.87	-0.01	0	0	0	0	0	0
C1塔： $T C 1, P 5$ - $T C 1, P 2$	-0.01	-0.16	-0.16	1.33	0	0	0	0	0	0
C2塔： $T C 2,7$ - $T C 2,2$	0	0	0	0	0.97	0.03	0	0	0	0
C2塔： $T C 2,17$	0	0	0	0	0.03	0.97	0	0	0	0
C3塔： $T C 3,7$ - $T C 3,2$	0	0	0	0	0	0	1	0.04	-0.06	0.02
C3塔： $T C 3,28$ - $T C 3,18$	0	0	0	0	0	0	0	0.83	0.17	0
C3塔： $T C 3,38$ - $T C 3,46$	0	0	0	0	0	0	0.02	0.2	0.96	-0.18
C3塔： $T C 3, P 10$ - $T C 3, P 2$	0	0	0	0	0	0	-0.02	-0.07	-0.07	1.16

干扰类型	$x D 1, A$ /10^-2			$x S 1, B$ /10^-2			$x D 2, A B C$ /10^-2			$x D 3, A B C D /$ 10^-2			$x S 3, E$ /10^-2			$x B 3, F$ /10^-2
干扰类型	TC	TDC	DTDC	TC	TDC	DTDC	TC	TDC	DTDC	TC	TDC	DTDC	TC	TDC	DTDC	TC	TDC	DTDC
+10% $F$	0.473	0.350	0.349	1.756	0.848	0.837	0.350	0.352	0.660	1.103	0.943	0.699	3.176	1.799	0.550	4.545	1.384	0.804
-10% $F$	0.421	0.343	0.345	1.737	0.828	0.803	0.293	0.315	0.468	0.715	0.852	0.640	2.716	1.935	0.513	2.614	0.951	0.297
+10% $x F, A$	1.650	1.629	1.636	1.697	0.093	0.100	0.061	0.052	0.054	0.163	0.171	0.127	0.568	0.375	0.109	0.615	0.207	0.045
-10% $x F, A$	1.658	1.345	1.351	1.619	0.555	0.561	0.062	0.062	0.058	0.174	0.173	0.126	0.577	0.369	0.110	0.680	0.222	0.049
+10% $x F, B$	1.429	1.083	1.081	0.392	3.482	3.491	0.056	0.082	0.090	0.163	0.170	0.126	0.569	0.373	0.108	0.615	0.206	0.045
-10% $x F, B$	1.634	1.421	1.418	0.411	1.643	1.643	0.057	0.077	0.081	0.175	0.172	0.127	0.579	0.368	0.108	0.680	0.222	0.050
+10% $x F, C$	0.361	0.376	0.377	1.360	1.309	1.313	0.260	0.588	0.164	0.101	0.189	0.166	0.376	0.311	0.103	0.602	0.262	0.063
-10% $x F, C$	0.382	0.430	0.431	1.726	1.764	1.769	0.303	0.626	0.167	0.107	0.229	0.201	0.371	0.320	0.110	0.663	0.284	0.071
+10% $x F, D$	0.104	0.064	0.065	0.148	0.151	0.149	1.027	1.211	0.589	1.881	1.754	1.615	4.884	1.185	0.444	0.666	0.348	0.188
-10% $x F, D$	0.110	0.068	0.069	0.154	0.158	0.155	1.285	1.570	0.698	1.929	1.416	1.331	3.200	0.924	0.343	1.244	0.350	0.186
+10% $x F, E$	0.166	0.128	0.129	0.343	0.067	0.064	0.432	0.334	0.439	1.344	1.053	1.084	1.987	0.502	0.159	0.795	1.214	0.532
-10% $x F, E$	0.169	0.129	0.129	0.332	0.052	0.050	0.435	0.355	0.398	1.377	1.328	1.353	1.817	0.436	0.129	0.351	1.463	0.547
+10% $x F, F$	0.051	0.029	0.030	0.200	0.410	0.410	0.574	0.433	0.234	0.828	0.819	0.588	2.656	2.034	0.701	2.440	1.361	0.670
-10% $x F, F$	0.050	0.031	0.032	0.228	0.452	0.452	0.550	0.433	0.222	0.934	1.023	0.664	4.340	3.398	0.835	1.999	1.221	0.685

干扰类型	$x D 1, A$ /10^-2			$x S 1, B$ /10^-2			$x D 2, A B C$ /10^-2			$x D 3, A B C D /$ 10^-2			$x S 3, E$ /10^-2			$x B 3, F$ /10^-2
干扰类型	TC	TDC	DTDC	TC	TDC	DTDC	TC	TDC	DTDC	TC	TDC	DTDC	TC	TDC	DTDC	TC	TDC	DTDC
+10% $F$	0.473	0.350	0.349	1.756	0.848	0.837	0.350	0.352	0.660	1.103	0.943	0.699	3.176	1.799	0.550	4.545	1.384	0.804
-10% $F$	0.421	0.343	0.345	1.737	0.828	0.803	0.293	0.315	0.468	0.715	0.852	0.640	2.716	1.935	0.513	2.614	0.951	0.297
+10% $x F, A$	1.650	1.629	1.636	1.697	0.093	0.100	0.061	0.052	0.054	0.163	0.171	0.127	0.568	0.375	0.109	0.615	0.207	0.045
-10% $x F, A$	1.658	1.345	1.351	1.619	0.555	0.561	0.062	0.062	0.058	0.174	0.173	0.126	0.577	0.369	0.110	0.680	0.222	0.049
+10% $x F, B$	1.429	1.083	1.081	0.392	3.482	3.491	0.056	0.082	0.090	0.163	0.170	0.126	0.569	0.373	0.108	0.615	0.206	0.045
-10% $x F, B$	1.634	1.421	1.418	0.411	1.643	1.643	0.057	0.077	0.081	0.175	0.172	0.127	0.579	0.368	0.108	0.680	0.222	0.050
+10% $x F, C$	0.361	0.376	0.377	1.360	1.309	1.313	0.260	0.588	0.164	0.101	0.189	0.166	0.376	0.311	0.103	0.602	0.262	0.063
-10% $x F, C$	0.382	0.430	0.431	1.726	1.764	1.769	0.303	0.626	0.167	0.107	0.229	0.201	0.371	0.320	0.110	0.663	0.284	0.071
+10% $x F, D$	0.104	0.064	0.065	0.148	0.151	0.149	1.027	1.211	0.589	1.881	1.754	1.615	4.884	1.185	0.444	0.666	0.348	0.188
-10% $x F, D$	0.110	0.068	0.069	0.154	0.158	0.155	1.285	1.570	0.698	1.929	1.416	1.331	3.200	0.924	0.343	1.244	0.350	0.186
+10% $x F, E$	0.166	0.128	0.129	0.343	0.067	0.064	0.432	0.334	0.439	1.344	1.053	1.084	1.987	0.502	0.159	0.795	1.214	0.532
-10% $x F, E$	0.169	0.129	0.129	0.332	0.052	0.050	0.435	0.355	0.398	1.377	1.328	1.353	1.817	0.436	0.129	0.351	1.463	0.547
+10% $x F, F$	0.051	0.029	0.030	0.200	0.410	0.410	0.574	0.433	0.234	0.828	0.819	0.588	2.656	2.034	0.701	2.440	1.361	0.670
-10% $x F, F$	0.050	0.031	0.032	0.228	0.452	0.452	0.550	0.433	0.222	0.934	1.023	0.664	4.340	3.398	0.835	1.999	1.221	0.685

干扰类型	Q_R1+Q_R2+Q_R3/kW
干扰类型	TC	TDC	DTDC
+10% $F$	31.080	29.070	27.031
-10% $F$	-26.614	-27.299	-27.753
+10% $x F, A$	-2.762	-3.044	-3.755
-10% $x F, A$	4.943	2.977	2.660
+10% $x F, B$	-0.899	-2.529	-2.800
-10% $x F, B$	2.736	2.427	1.797
+10% $x F, C$	2.119	2.091	1.739
-10% $x F, C$	-1.935	-2.194	-2.339
+10% $x F, D$	1.487	0.892	-1.241
-10% $x F, D$	4.557	-0.968	-1.546
+10% $x F, E$	5.172	2.134	1.884
-10% $x F, E$	-1.858	-1.987	-3.042
+10% $x F, F$	1.823	1.018	-0.588
-10% $x F, F$	0.573	-1.264	-1.572

干扰类型	Q_R1+Q_R2+Q_R3/kW
干扰类型	TC	TDC	DTDC
+10% $F$	31.080	29.070	27.031
-10% $F$	-26.614	-27.299	-27.753
+10% $x F, A$	-2.762	-3.044	-3.755
-10% $x F, A$	4.943	2.977	2.660
+10% $x F, B$	-0.899	-2.529	-2.800
-10% $x F, B$	2.736	2.427	1.797
+10% $x F, C$	2.119	2.091	1.739
-10% $x F, C$	-1.935	-2.194	-2.339
+10% $x F, D$	1.487	0.892	-1.241
-10% $x F, D$	4.557	-0.968	-1.546
+10% $x F, E$	5.172	2.134	1.884
-10% $x F, E$	-1.858	-1.987	-3.042
+10% $x F, F$	1.823	1.018	-0.588
-10% $x F, F$	0.573	-1.264	-1.572

干扰类型	TC	TDC	DTDC
$F$	[-20%, +10%]	[-20%, +15%]	[-35%, +25%]
$x F, A$	[-10%, +20%]	[-30%, +25%]	[-30%, +25%]
$x F, B$	[-25%, +10%]	[-25%, +10%]	[-25%, +10%]
$x F, C$	[-20%, +30%]	[-20%, +30%]	[-20%, +30%]
$x F, D$	[-10%, +10%]	[-50%, +30%]	[-75%, +30%]
$x F, E$	[-20%, +10%]	[-25%, +30%]	[-55%, +30%]
$x F, F$	[-10%, +20%]	[-10%, +30%]	[-35%, +30%]

干扰类型	TC	TDC	DTDC
$F$	[-20%, +10%]	[-20%, +15%]	[-35%, +25%]
$x F, A$	[-10%, +20%]	[-30%, +25%]	[-30%, +25%]
$x F, B$	[-25%, +10%]	[-25%, +10%]	[-25%, +10%]
$x F, C$	[-20%, +30%]	[-20%, +30%]	[-20%, +30%]
$x F, D$	[-10%, +10%]	[-50%, +30%]	[-75%, +30%]
$x F, E$	[-20%, +10%]	[-25%, +30%]	[-55%, +30%]
$x F, F$	[-10%, +20%]	[-10%, +30%]	[-35%, +30%]

References 23

[1]	WAIBEL Yannick, TRESCHER Lea, Lena-Marie RÄNGER, et al. First multiple dividing wall column: Design and operation[J]. Chemical Engineering Research and Design, 2023, 193: 132-144.
[2]	WANG Xiaohong, YU Xinshuai, XIE Li, et al. Energy-saving columns: Design and control of a Kaibel and a multi-sidestream column for separating hydrocarbon mixture[J]. Chemical Engineering and Processing-Process Intensification, 2018, 133: 66-82.
[3]	GUPTA Aayush, SINGH KUMAIYA Hemant, SRIVASTAVA Prakhar, et al. Single-pot extractive double divided wall column for acetonitrile, ethanol, and water separation: Design and control[J]. Separation and Purification Technology, 2025, 357: 130162.
[4]	ZHANG Tao, LI Min, PAN Hui, et al. Dynamic control of liquid-only transfer Kaibel dividing-wall column[J]. Chemical Engineering Science, 2023, 272: 118589.
[5]	KISS Anton A, IGNAT Radu M, FLORES LANDAETA Servando J, et al. Intensified process for aromatics separation powered by Kaibel and dividing-wall columns[J]. Chemical Engineering and Processing: Process Intensification, 2013, 67: 39-48.
[6]	ZHANG Yunlu, WANG Jingde, LIU Xiuyu, et al. Study on the distillation sequence with dividing wall column for five-component separations[J]. Computer Aided Chemical Engineering, 2018, 44: 1441-1446.
[7]	YUAN Yang, ZHANG Linlin, RANGAIAH Gade Pandu, et al. Design and optimization of compound distillation sequences comprising simple distillation and dividing-wall columns using genetic programming[J]. Chemical Engineering Science, 2024, 291: 119950.
[8]	ZHU Xiuyu, ZHAO Xiaoxiao, ZHANG Zhishan, et al. Optimal design and control of an energy-efficient triple-side-stream quaternary extractive distillation process[J]. Chemical Engineering and Processing: Process Intensification, 2021, 167: 108510.
[9]	LI Min, PENG Jiarui, CHENG Yan, et al. Dynamic control of an energy-saving process with two extractive dividing-wall columns for separation of acetone/methanol/butanone/tert-butyl alcohol mixtures[J]. Chemical Engineering Research and Design, 2023, 200: 281-291.
[10]	SYAUQI Ahmad, KIM Heehyang, Hankwon LIM. Optimizing olefin purification: An artificial intelligence-based process-conscious PI controller tuning for double dividing wall column distillation[J]. Chemical Engineering Journal, 2024, 500: 156645.
[11]	WAIBEL Yannick, Lena-Marie RÄNGER, FISCHER Melanie, et al. The start-up of a multiple dividing wall column—A theoretical and experimental study[J]. Chemical Engineering and Processing: Process Intensification, 2024, 201: 109798.
[12]	WALTERMANN Thomas, SIBBING Steffen, SKIBOROWSKI Mirko. Optimization-based design of dividing wall columns with extended and multiple dividing walls for three- and four-product separations[J]. Chemical Engineering and Processing: Process Intensification, 2019, 146: 107688.
[13]	PAN Hui, JU Feng, HE Guichun, et al. Numerical and experimental research on a Kaibel divided-wall column: Design and steady-state and dynamic operation[J]. Industrial & Engineering Chemistry Research, 2020, 59(27): 12557-12567.
[14]	LUYBEN William L. Distillation design and control using Aspen^TM simulation[M]. New York: John Wiley & Sons, 2013: 124-131..
[15]	WANG Zhujun, CAI Li. A class of inexact secant algorithms with line search filter method for nonlinear programming[J]. Mathematical Problems in Engineering, 2021: 6253424.
[16]	VILLEGAS-URIBE Cristopher A, Nancy MEDINA-HERRERA, HERNÁNDEZ-MAGALLANES Javier A, et al. Optimal design and control of three simplified Sargent four-product dividing-wall columns[J]. Chemical Engineering and Processing: Process Intensification, 2022, 174: 108860.
[17]	LING Hao, LUYBEN William L. Temperature control of the BTX divided-wall column[J]. Industrial & Engineering Chemistry Research, 2010, 49(1): 189-203.
[18]	DWIVEDI Deeptanshu, HALVORSEN Ivar J, SKOGESTAD Sigurd. Control structure selection for four-product Petlyuk column[J]. Chemical Engineering and Processing: Process Intensification, 2013, 67: 49-59.
[19]	MASEL Rebecca H, SMITH Dalton W, LUYBEN William L. Use of two distillation columns in systems with maximum temperature limitations[J]. Industrial & Engineering Chemistry Research, 2013, 52(14): 5172-5176.
[20]	HUNG Shih-Bo, LEE Ming-Jer, TANG Yeong-Tarng, et al. Control of different reactive distillation configurations[J]. AIChE Journal, 2006, 52(4): 1423-1440.
[21]	WU Ning, HUANG Kejin, LUAN Shujun. Operation of dividing-wall distillation columns. 2. A double temperature difference control scheme[J]. Industrial & Engineering Chemistry Research, 2013, 52(15): 5365-5383.
[22]	YUAN Yang, HUANG Kejin, CHEN Haisheng, et al. Configuring effectively double temperature difference control schemes for distillation columns[J]. Industrial & Engineering Chemistry Research, 2017, 56(32): 9143-9155.
[23]	PAN Hui, WU Xiang, QIU Jie, et al. Pressure compensated temperature control of Kaibel divided-wall column[J]. Chemical Engineering Science, 2019, 203: 321-332.