复合精馏序列的温度推断控制

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

摘要/Abstract

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

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

中图分类号:

TQ021.8

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.

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.

图/表 14

图1 用于分离正丁烷、正戊烷、苯、甲苯、邻二甲苯和2,4-二甲基苯六元混合物的最优CDS设计及其温度分布

图2 温度控制方案

图3 CDS各精馏单元的灵敏度分析结果

表1 CDS温度推断控制系统的控制器参数

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

图4 对进料流量施加±10%阶跃扰动时被控产品纯度的动态响应曲线

图5 对进料中的A组分施加±10%阶跃扰动时被控产品纯度的动态响应曲线

图6 CDS各精馏单元的SVD分析结果

表2 TDC的控制回路全部使用温差时的RGA

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

表2 TDC的控制回路全部使用温差时的RGA

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

图7 温差控制方案

表3 TDC的控制回路部分使用温差时的RGA

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

表3 TDC的控制回路部分使用温差时的RGA

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

图8 双温差控制方案

表4 TC、TDC和DTDC方案在面对±10%进料流量和组分扰动时被控产品纯度的IAE

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

表4 TC、TDC和DTDC方案在面对±10%进料流量和组分扰动时被控产品纯度的IAE

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

表5 TC、TDC和DTDC方案在面对±10%进料流量和组分扰动时再沸器热负荷变化

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

表5 TC、TDC和DTDC方案在面对±10%进料流量和组分扰动时再沸器热负荷变化

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

表6 TC、TDC和DTDC方案的抗干扰能力测试结果

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%]

表6 TC、TDC和DTDC方案的抗干扰能力测试结果

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%]

参考文献 23

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