Simultaneous optimization of pressure operating path and heat exchange matches in work and heat integration

doi:10.11949/0438-1157.20250743

Abstract

Abstract:

Traditional optimization design methods for work and heat exchange networks often first determine the pressure adjustment processes and then conduct heat exchanger network design. Superstructure-based simultaneous optimization methods for work and heat networks can achieve better overall system performance because they can consider the coupling and interactions between work and heat. However, this type of simultaneous optimization model is usually highly non-convex and non-linear, leading to solution difficulties, especially when facing large-scale industrial problems. To address this difficulty, this study proposes a deterministic optimization design method based on a dynamic transportation model. This method leverages the characteristics of the transportation model to efficiently determine the pressure operating path and heat exchange matching scheme under optimal work and heat integration. It ensures linear constraints for the heat integration model and provides guidance for the detailed design of the work and heat exchange network. A case study of power and heat integration involving 14 heat exchange streams was conducted. The proposed method generated a new pressure operating path and corresponding heat exchange matching within 1000 s. The total cost target for this solution was 8761480.49 USD·a^-1, which is highly close to the cost-optimal solution found in the literature, validating the accuracy and effectiveness of the proposed method.

Key words: work and heat integration, mathematical programming, dynamic transportation model, optimal design, process system

摘要：

传统的功热网络优化设计方法往往先确定变压过程，随后进行换热网络设计。基于超结构的功热网络同步优化方法因其能考虑功热间的耦合与相互影响，可实现更优的系统整体性能。然而，此类同步优化模型通常高度非凸非线性，导致求解困难，尤其是面向大规模工业问题时。为应对这一难题，本研究提出了一种基于动态运输模型的确定性优化设计方法。该方法利用运输模型的特性，在保证热集成模型线性约束下，实现最优功热集成下系统压力操作路径与换热匹配方案的高效确定，并为功热网络的详细设计提供指导。针对一个包含14条换热流股的功热集成案例进行研究，提出的方法在1000 s内得到了一个新的压力操作路径以及相应的换热匹配，该方案的总费用目标值为8761480.49 USD·a^-1，与文献中已知费用最优解高度逼近，验证了所提方法的准确性和有效性。

关键词: 功热集成, 数学规划, 动态运输模型, 优化设计, 过程系统

CLC Number:

TQ 021.8

Wenjin ZHOU, Yatong ZHANG, Zhitong ZHAO, Wei ZHANG. Simultaneous optimization of pressure operating path and heat exchange matches in work and heat integration[J]. CIESC Journal, 2025, 76(12): 6477-6485.

周文晋, 张雅桐, 赵志仝, 张玮. 功热集成中压力操作路径和换热匹配的同步优化[J]. 化工学报, 2025, 76(12): 6477-6485.

Figures/Tables 10

Fig.1 Schematic diagram of multi-stage compression process for low-pressure stream

Fig.2 Schematic diagram of proposed work-heat integration optimization superstructure

Fig.3 Schematic diagram of transportation model

Fig.4 Relative position of temperature interval k and temperature range of hot stream

Fig.5 Two-stage membrane separation process for carbon capture

Table 1 Stream data

流股	$T s I n$ /K	$T s O u t$ /K	$P s I n$ / bar	$P s O u t$ / bar	CP/ (kW·K^-1)	h/ (kW·m^-2·K^-1)
1(LP-Fe1)	298.15	298.15	1	8	37.49	0.1
2(LP-Fe2)	298.15	298.15	1	8	10.09	0.1
3(Flue gas)	650.15	348.15	—	—	43.77	0.1
4(HP-Re1)	298.15	298.15	8	1	27.40	0.1
5(HP-Re2)	298.15	298.15	8	1	4.40	0.1
6(Cold air)	288.15	600.15	—	—	34.70	0.1
HU	650.00	649.00	—	—	—	1.0
CU	288.15	289.15	—	—	—	1.0

Table 1 Stream data

流股	$T s I n$ /K	$T s O u t$ /K	$P s I n$ / bar	$P s O u t$ / bar	CP/ (kW·K^-1)	h/ (kW·m^-2·K^-1)
1(LP-Fe1)	298.15	298.15	1	8	37.49	0.1
2(LP-Fe2)	298.15	298.15	1	8	10.09	0.1
3(Flue gas)	650.15	348.15	—	—	43.77	0.1
4(HP-Re1)	298.15	298.15	8	1	27.40	0.1
5(HP-Re2)	298.15	298.15	8	1	4.40	0.1
6(Cold air)	288.15	600.15	—	—	34.70	0.1
HU	650.00	649.00	—	—	—	1.0
CU	288.15	289.15	—	—	—	1.0

Table 2 Other parameters

参数	数值	参数	数值
Coem/(USD·kW^-1·a^-1)	455.04	Af	0.18
Coge/(USD·kW^-1·a^-1)	364.03	$γ$	1.4
HU/(USD·kW^-1·a^-1)	400	$η C$	0.85
CU/(USD·kW^-1·a^-1)	100	$η T$	0.9
压缩机投资费/(USD·a^-1)	51104.85w^0.62	Rc 范围	1.1~8
膨胀机投资费/(USD·a^-1)	2585.47w^0.81	Rt 范围	0.125~0.8
电动机或发电机投资费/(USD·a^-1)	985.47w^0.62	变压流股温度范围/K	150~600
离散化后温度误差允许的上界值/K	2	换热器投资费用/(USD·a^-1)	93500.12+602.96area+0.149(area)²

Table 2 Other parameters

参数	数值	参数	数值
Coem/(USD·kW^-1·a^-1)	455.04	Af	0.18
Coge/(USD·kW^-1·a^-1)	364.03	$γ$	1.4
HU/(USD·kW^-1·a^-1)	400	$η C$	0.85
CU/(USD·kW^-1·a^-1)	100	$η T$	0.9
压缩机投资费/(USD·a^-1)	51104.85w^0.62	Rc 范围	1.1~8
膨胀机投资费/(USD·a^-1)	2585.47w^0.81	Rt 范围	0.125~0.8
电动机或发电机投资费/(USD·a^-1)	985.47w^0.62	变压流股温度范围/K	150~600
离散化后温度误差允许的上界值/K	2	换热器投资费用/(USD·a^-1)	93500.12+602.96area+0.149(area)²

Fig.6 Optimization results of work network

Table 3 Heat exchange matches determined through optimization

项目	(ts1, m1)	(ts1, m2)	(ts2, m1)	(ts2, m2)	cps1	cus1
(cs1, m1)	1	1	1	1
(cs1, m2)					1	1
(cs2, m1)		1
(cs2, m2)						1
hps1		1		1	1	1

Table 4 Comparison of integrated optimization results of work and heat in this article and literatures

项目	Pavão等^[31]	Santos等^[18]	Lin 等^[19]	本研究^①
TAC/(USD·a^-1)	9011115.00	8919187.84	8829551.00	8761480.49
回收热量/kW	14648.90	14721.10	14777.70	15000.19
回收功/kW	3822.40	3870.40	3951.10	3930.15
热公用工程消耗/kW	0	0	0	0
冷公用工程消耗/kW	8935.50	8818.30	8473.00	7945.28
电力消耗/kW	6544.30	6426.10	6082.90	5908.83
电力产生/kW	0	0	0	0
换热器数量	10	9	14	12
变压单元数量	4	5	5	6

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