质量交换网络的质-能系统比拟与平行进化

doi:10.11949/0438-1157.20241337

摘要/Abstract

摘要：

基于质量和能量交换过程、设备和网络的比拟关系，采用质-能网络比拟优化可将小尺度特征的质量交换网络比拟为广义换热网络，有效地扩大求解域，提升全局优化质量。然而，该方法尚未充分考虑广义换热网络的不同个体在不同进化时期的最优网络结构，其全局和局部优化性能仍有较大的提升空间。为此，建立了广义换热网络和质量交换网络的同步比拟和平行进化策略，实现广义换热网络的局部最优结构实时回归至质量交换网络，并至平行进化层实施进一步的全局和局部优化。空气除氨和废水脱酚算例的应用结果表明，质-能系统比拟与平行进化可充分发挥广义换热网络在更大求解域内的全局搜索能力，并通过平行进化兼顾局部最优精度，为质量交换网络综合提供更有效的方法。

关键词: 质量交换网络, 质-能比拟, 广义换热网络, 全局优化

Abstract:

Based on the analogy between mass and heat exchange processes, devices and networks, the mass-energy network analogy optimization can be used to analogize the mass exchange network with small-scale characteristics to the generalized heat exchange network, effectively expanding the solution domain and improving the global optimization quality. However, this method has not yet fully considered the optimal network structures of different individuals of the generalized heat exchange network in different evolutionary periods, and there is still much room for improvement of its global and local optimization performance. To this end, a synchronous analogy and parallel evolution strategy for the generalized heat exchange network and the mass exchange network was established to achieve the real-time regression of the local optimal structure of the generalized heat exchange network to the mass exchange network, and further global and local optimization was implemented in the parallel evolution layer. The analysis of the results of phenol removal and ammonia removal shows that the mass-heat analogy and parallel evolution can give full play to the global search capability of the generalized heat exchanger network in a larger solution domain, and take into account the local optimum accuracy through parallel evolution, providing a more effective method for mass exchange network synthesis.

Key words: mass exchange network, mass-heat analogy, generalized heat exchanger network, global optimization

中图分类号:

TQ 021.8

陈怡, 肖媛, 崔国民. 质量交换网络的质-能系统比拟与平行进化[J]. 化工学报, 2025, 76(6): 2755-2769.

Yi CHEN, Yuan XIAO, Guomin CUI. Parallel evolutionary and mass-heat analogy optimization method of mass exchange network[J]. CIESC Journal, 2025, 76(6): 2755-2769.

图/表 24

图1 质量交换网络示意图

Fig.1 Mass exchange network diagram

图2 单个质量交换器内部的传质过程

Fig.2 Mass transfer process inside a mass exchanger

表1 不同传质设备的比拟关系

Table 1 The analogy of different mass transfer equipment

传质设备	比拟关系Ⅰ	比拟关系Ⅱ
填料塔	$\frac{A}{a m_{p}} = \frac{1}{ρ} C_{1}$	$K_{m, p} = \frac{K_{w}}{a}$
板式塔	$\frac{A}{μ_{0} N} = \frac{1}{ρ} C_{1}$	$K_{m, t} = \{\begin{matrix} \frac{G_{i} L_{j} l n (\frac{L_{j}}{m_{i, j} G_{i}})}{(L_{j} - m_{i, j} G_{i}) μ_{0}}, \frac{L_{j}}{m_{i, j} G_{i}} \neq 1 \\ \frac{G_{i}}{μ_{0}}, \frac{L_{j}}{m_{i, j} G_{i}} = 1 \end{matrix}$

表1 不同传质设备的比拟关系

Table 1 The analogy of different mass transfer equipment

传质设备	比拟关系Ⅰ	比拟关系Ⅱ
填料塔	$\frac{A}{a m_{p}} = \frac{1}{ρ} C_{1}$	$K_{m, p} = \frac{K_{w}}{a}$
板式塔	$\frac{A}{μ_{0} N} = \frac{1}{ρ} C_{1}$	$K_{m, t} = \{\begin{matrix} \frac{G_{i} L_{j} l n (\frac{L_{j}}{m_{i, j} G_{i}})}{(L_{j} - m_{i, j} G_{i}) μ_{0}}, \frac{L_{j}}{m_{i, j} G_{i}} \neq 1 \\ \frac{G_{i}}{μ_{0}}, \frac{L_{j}}{m_{i, j} G_{i}} = 1 \end{matrix}$

表2 R5S3算例的流股参数

Table 2 Stream data in case R5S3

流股	流量上限/ (kg/s)	入口浓度/ (kg/kg)	出口浓度/ (kg/kg)	m_i,j	b_i,j	C₀_j
K_w=0.02 kg NH₃/(s∙kg)；f_C,p=139.05；α=0.66
R1	2.00	0.0050	0.0010	—	—	—
R2	4.00	0.0050	0.0025	—	—	—
R3	3.50	0.0110	0.0025	—	—	—
R4	1.50	0.0100	0.0050	—	—	—
R5	0.50	0.0080	0.0025	—	—	—
S1	1.80	0.0017	0.0071	1.20	0	0
S2	1.00	0.0025	0.0085	1.00	0	0
S3	∞	0	0.0170	0.50	0	0.001

表3 H5C3算例的流股参数和比拟参数

Table 3 Stream data and analogy data in case H5C3

流股		热容流率上限/[J/(kg/s)]	入口温度/ ℃	出口温度/℃
H1		20.00	200.00	40.00
H2		40.00	200.00	100.00
H3		35.00	440.00	100.00
H4		15.00	400.00	200.00
H5		5.00	320.00	100.00
C1		18.00	81.60	340.80
C2		10.00	100.00	340.00
C3		50.00	0	340.00
比拟参数
C_max	T_max	a	c_p	ρ	C₀
0.0100	400.00	100	10	1000	1.4

表4 RWCE算法的关键进化参数

Table 4 The parameters of the RWCE for optimizing GHEN and MEN

Problem	X	∆L_X	X_min	Φ_e_X	X_g	Φ_g_,X	δ	NP
GHEN	Q	100.0000	5.00000	0.2850	100.000	0.001	0.010	10
	SP	0.0300	0.01000	0.0150	1.000
	Fc_p	0.0500	0.00100	0.0001	1.000
MEN	M	0.0003	0.00005	0.2400	0.002	0.005	0.001	10
	SPM	0.0300	0.01000	0.0600	1.000
	L	0.0300	0.02000	0.1000	0.500

图3 质量交换网络结构

Fig.3 The structure diagram of mass exchange network

图4 不同迭代步数下相同个体的优化结果对比

Fig.4 Comparison of optimization results for the same individuals at different iteration steps

图5 质量交换网络结构

Fig.5 The structure diagram of mass exchange network

图6 不同个体的相同迭代步数下的优化结果对比

Fig.6 Comparison of optimization results at the same number of iteration steps for different individuals

图7 质量交换网络结构图

Fig.7 The structure diagram of mass exchange network

图8 质-能系统比拟与平行进化方法的概念示意图

Fig.8 The conceptual diagram of mass-heat analogy and parallel evolution method

图9 质-能系统比拟与平行进化方法流程图

Fig.9 Mass-heat analogy and parallel evolution method flowchart

表5 R2S3算例的流股数据

Table 5 Stream data in case R2S3

流股	流量上限/ (kg/s)	入口浓度/ (kg/kg)	出口浓度/ (kg/kg)	m_i.j	b_i.j	C₀_j
f_C,N=4552 USD/(块·a)
R1	2.00	0.0500	0.0100	—	—	—
R2	1.00	0.0300	0.0060	—	—	—
S1	5.00	0.0050	0.0150	2.00	0	0
S2	3.00	0.0100	0.0300	1.53	0	0
S3	∞	0.0013	0.0150	0.71	0.001	0.010

表6 H2C3算例的流股参数和比拟参数

Table 6 Stream data and analogy data in case H2C3

流股	热容流率上限/(J/(kg·s))	入口温度/℃		出口温度/℃
H1	20.00	1000.00		200.00
H2	10.00	600.00		120.00
C1	50.00	200.00		600.00
C2	30.00	306.00		918.00
C3	10.00	38.46		233.00
比拟参数
C_max	T_max	μ₀	c_p	ρ	C₀
0.0100	200.00	10000	10	1000	0.8

表7 RWCE算法的关键进化参数

Table 7 Parameters of the RWCE for optimizing GHEN and MEN

Problem	X	∆L_X	X_min	Φ_e_X	X_g	Φ_g,_X	δ
GHEN	Q	100.0000	10.00000	0.4000	100.000	0.005	0.020
	SP	0.0300	0.01000	0.1000	1.000
	$F C_{p N_{S}}$	0.5000	0.00100	0.0001	1.000
MEN	M	0.0003	0.00005	0.2400	0.002	0.005	0.002
	SPM	0.0300	0.01000	0.0600	1.000
	$L_{N_{S}}$	0.0500	0.02000	0.0001	0.500

表7 RWCE算法的关键进化参数

Table 7 Parameters of the RWCE for optimizing GHEN and MEN

Problem	X	∆L_X	X_min	Φ_e_X	X_g	Φ_g,_X	δ
GHEN	Q	100.0000	10.00000	0.4000	100.000	0.005	0.020
	SP	0.0300	0.01000	0.1000	1.000
	$F C_{p N_{S}}$	0.5000	0.00100	0.0001	1.000
MEN	M	0.0003	0.00005	0.2400	0.002	0.005	0.002
	SPM	0.0300	0.01000	0.0600	1.000
	$L_{N_{S}}$	0.0500	0.02000	0.0001	0.500

图10 质量交换网络结构

Fig.10 The structure diagram of mass exchange network

表8 R2S3算例的优化结果对比

Table 8 Comparison results of case R2S3

文献	单元数	总塔板数	C $_{T A}^{M, t}$ /(USD/a)
[24]	6	28	345416
[8]	7	28	338168
[25]	7	28	333300
[18]	7	21	329503
[21]	6	24	321800
本文（图11）	6	21	318362
本文（图10）	6	22	317013

表8 R2S3算例的优化结果对比

Table 8 Comparison results of case R2S3

文献	单元数	总塔板数	C $_{T A}^{M, t}$ /(USD/a)
[24]	6	28	345416
[8]	7	28	338168
[25]	7	28	333300
[18]	7	21	329503
[21]	6	24	321800
本文（图11）	6	21	318362
本文（图10）	6	22	317013

表9 不同种群规模下R2S3算例的优化结果对比

Table 9 Comparison of optimization results for case R2S3 at different population sizes

算例	种群规模	C $_{T A}^{M, t}$ /(USD/a)	单元个数	总塔板数	迭代次数/步
R2S3	10	321086	6	22	4.17×10⁷
	20	321623	6	22	2.78×10⁷
	40	321766	7	27	1.39×10⁷
	60	325406	7	22	9.43×10⁶
	80	318362	6	21	6.88×10⁶
	100	334429	6	24	4.92×10⁶

表9 不同种群规模下R2S3算例的优化结果对比

Table 9 Comparison of optimization results for case R2S3 at different population sizes

算例	种群规模	C $_{T A}^{M, t}$ /(USD/a)	单元个数	总塔板数	迭代次数/步
R2S3	10	321086	6	22	4.17×10⁷
	20	321623	6	22	2.78×10⁷
	40	321766	7	27	1.39×10⁷
	60	325406	7	22	9.43×10⁶
	80	318362	6	21	6.88×10⁶
	100	334429	6	24	4.92×10⁶

图11 质量交换网络结构图

Fig.11 The structure diagram of mass exchange network

表10 不同接受差解概率下R2S3算例的优化结果

Table 10 The optimization results for R2S3 case study with different accepting imperfect solution

δ_M	单元数	总塔板数	C $_{T A}^{M, t}$ /(USD/a)	优化时间/s
0	5	24	334660	431764
0.100	7	22	321536	436478
0.010	6	23	319785	434416
0.001	6	24	321136	430204
0.002	6	22	317073	374296

表10 不同接受差解概率下R2S3算例的优化结果

Table 10 The optimization results for R2S3 case study with different accepting imperfect solution

δ_M	单元数	总塔板数	C $_{T A}^{M, t}$ /(USD/a)	优化时间/s
0	5	24	334660	431764
0.100	7	22	321536	436478
0.010	6	23	319785	434416
0.001	6	24	321136	430204
0.002	6	22	317073	374296

图12 不同接受差解概率下MEN优化过程最优TAC下降曲线

Fig.12 The optimal TAC decline curve for MEN optimization process with different accepting imperfect solution

图13 质量交换网络结构图

Fig.13 The structure diagram of mass exchange network

表11 R5S3算例的优化结果对比

Table 11 Comparison results of case R5S3

文献	单元数	C $_{T O}^{M, p}$ /(USD/a)	C $_{T C}^{M, p}$ /(USD/a)	C $_{T A}^{M, p}$ /(USD/a)
[27]	8	85203	48797	134000
[8]	7	82410	50913	133323
[28]	9	—	—	132101
[29]	9	81301	48599	129900
[30]	8	73350	47367	120717
[26]	9	77508	50299	127807
本文（图7）	9	78338	47823	126161
本文（图13）	9	78338	47773	126148

表11 R5S3算例的优化结果对比

Table 11 Comparison results of case R5S3

文献	单元数	C $_{T O}^{M, p}$ /(USD/a)	C $_{T C}^{M, p}$ /(USD/a)	C $_{T A}^{M, p}$ /(USD/a)
[27]	8	85203	48797	134000
[8]	7	82410	50913	133323
[28]	9	—	—	132101
[29]	9	81301	48599	129900
[30]	8	73350	47367	120717
[26]	9	77508	50299	127807
本文（图7）	9	78338	47823	126161
本文（图13）	9	78338	47773	126148

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