综合评价模型联合遗传算法的混合工质ORC系统性能研究

doi:10.11949/0438-1157.20221492

摘要/Abstract

摘要：

采用R601a/R600作为工质回收工业余热，并以系统的热力学性能（输出功率W_net、热效率η_th、㶲效率ε_ex）、经济性能（投资成本回收周期ICPP、单位输出功率所需换热面积APR）、环境影响（CO₂当量排放ECE、环境㶲代价E_xc）为评价指标，采用AHP-和积法确定不同评价指标的权重并结合遗传算法对系统进行综合分析。结果表明，综合评价指标F₁的目标函数的权重大小依次为：环境影响>经济性能>热力学性能。当R601a/R600工质配比为0.33%/99.67%，蒸发温度为137.2℃时，W_net、η_th、ε_ex、APR、ICPP、ECE和E_xc分别为62.9 kW、15.8%、48.7%、4.3 m²/kW、6.6 a、25.0 t、4.0 W。得到的ECE和E_xc与平衡权重的TOPSIS相比，分别降低了45.9%和57.0%。这说明F₁对环境影响更为重视，能根据不同权重给予实际工程更多的参考方案，比传统TOPSIS更有指导意义。

关键词: 非共沸混合工质, 有机朗肯循环, AHP-和积法, 综合评价

Abstract:

The system uses R601a/R600 as the working fluid to recover industrial waste heat. It uses the thermodynamic performance (output power W_net, thermal efficiency η_th and exergy efficiency ε_ex), economic performance (investment cost payback period ICPP, heat exchanger area per unit power output APR), and environmental impact (emissions of CO₂ equivalent ECE, environmental exergy cost E_xc) as evaluation indicators, and the weights of different evaluation indicators are determined by the AHP-sum-product method and combined with the genetic algorithm to conduct comprehensive analysis and optimization of the system. The results show that when the weight of the objective functions of the comprehensive evaluation index F₁ is in the following order: environmental impact > economic performance > thermodynamic performance. When the mass fraction ratio of R601a/R600 is 0.33%/99.67% and the evaporation temperature is 137.2℃, W_net, η_th, ε_ex, APR, ICPP, ECE and E_xc are 62.9 kW, 15.8%, 48.7%, 4.3 m²/kW, 6.6 a, 25.0 t, and 4.0 W, respectively. The ECE and E_xc obtained are reduced by 45.9% and 57.0%, respectively, compared with those obtained by TOPSIS based on balanced weight. This shows that F₁ pays more attention to environmental impact, and can give more reference plans for actual projects according to different weights, which is more instructive than traditional TOPSIS.

Key words: zeotropic mixtures, organic Rankine cycle, AHP-sum-product method, comprehensive evaluation

中图分类号:

TK 11⁺.2

党玉荣, 莫春兰, 史科锐, 方颖聪, 张子杨, 李作顺. 综合评价模型联合遗传算法的混合工质ORC系统性能研究[J]. 化工学报, 2023, 74(5): 1884-1895.

Yurong DANG, Chunlan MO, Kerui SHI, Yingcong FANG, Ziyang ZHANG, Zuoshun LI. Comprehensive evaluation model combined with genetic algorithm for the study on the performance of ORC system with zeotropic mixture[J]. CIESC Journal, 2023, 74(5): 1884-1895.

图/表 12

图1 ORC系统的结构和温熵图

Fig.1 The structure and T-S diagram of ORC

表 1 工质的基本物性［21］

Table 1 Physical properties of working fluids［21］

工质	化学式	M/(kg/kmol)	T_cri/℃	p_cri/MPa	GWP(100 a)	ODP	TLV_TWA
R601a（异戊烷）	C₅H₁₂	72.15	187.2	3.38	20	0	600
R600（丁烷）	C₄H₁₀	58.12	152.0	3.80	20	0	800

表2 ORC系统部件的能量平衡等式

Table 2 Energy equations of ORC components

部件	能量平衡等式
蒸发器	$Q_{e v a} = m_{o r c} (h_{3} - h_{1}) = m_{g} C_{g} (T_{g i} - T_{g o})$
泵	$W_{p} = m_{o r c} (h_{1} - h_{6}) = m_{o r c} (h_{1 s} - h_{6}) / η_{p}$
汽轮机	$W_{t} = m_{o r c} (h_{3} - h_{4}) = m_{o r c} (h_{3} - h_{4 s}) η_{t}$
冷凝器	$W_{c o n} = m_{o r c} (h_{3} - h_{6}) = m_{w} C_{w} (T_{w o} - T_{w i})$

表2 ORC系统部件的能量平衡等式

Table 2 Energy equations of ORC components

部件	能量平衡等式
蒸发器	$Q_{e v a} = m_{o r c} (h_{3} - h_{1}) = m_{g} C_{g} (T_{g i} - T_{g o})$
泵	$W_{p} = m_{o r c} (h_{1} - h_{6}) = m_{o r c} (h_{1 s} - h_{6}) / η_{p}$
汽轮机	$W_{t} = m_{o r c} (h_{3} - h_{4}) = m_{o r c} (h_{3} - h_{4 s}) η_{t}$
冷凝器	$W_{c o n} = m_{o r c} (h_{3} - h_{6}) = m_{w} C_{w} (T_{w o} - T_{w i})$

表 3 本模型与文献模型［29］的比较

Table 3 Comparison of the present work with the literature［29］

Item	T₄/℃	T₁/℃	p₂/MPa	Q_eva/kW	W_net/kW	η_th/%
R134^[29]	49.63	28.08	2.076	177.77	14.83	8.30
simulation	49.62	28.08	2.076	203.76	15.62	8.36
error/%	0.02	0	0	0.11	0.34	0.72

图2 ORC系统层次结构图

Fig.2 Hierarchy diagram of the ORC system

表4 不同目标函数之间的成对比较

Table 4 Pairwise comparison between two sub goal objectives

参数	W_net	η_th	ε_ex	APR	ICPP	ECE	E_xc	权重
W_net	1	2	2	1/4	1/4	1/5	1/5	ω₁
η_th	1/2	1	1	1/3	1/3	1/7	1/7	ω₂
ε_ex	1/2	1	1	1/3	1/3	1/7	1/7	ω₃
APR	4	3	3	1	1	1/2	1/2	ω₄
ICPP	4	3	3	1	1	1/2	1/2	ω₅
ECE	5	7	7	2	2	1	1	ω₆
E_xc	5	7	7	2	2	1	1	ω₇

图3 ORC的计算流程图

Fig.3 Flow chart of ORC

图4 R601a/R600的滑移温度分析结果

Fig.4 Results of slip temperature analysis for R601a/R600

图5 ORC系统的热力学性能分析

Fig.5 Thermodynamic performance analysis of ORC system

图6 ORC系统的经济性能分析

Fig.6 Economic performance analysis of ORC system

图7 ORC系统的环境影响分析

Fig.7 Environmental impact analysis of ORC system

表 5 综合性能指标F与TOPSIS［7］优化结果对比

Table 5 Optimization results of comprehensive performance index F compared with TOPSIS［7］

参数	综合性能指标F₁	综合性能指标F₂	TOPSIS^[7]
权重(ω₁∶ω₂∶ω₃∶ω₄∶ω₅∶ω₆∶ω₇)	5.5∶4.1∶4.1∶14.6∶14.6∶28.6∶28.6	14.3∶14.3∶14.3∶14.3∶14.3∶14.3∶14.3	—
T₂/℃	137.2	119.1	112.3
mf /%	0.33	12.4	8.6
W_net /kW	62.9	101.1	108.3
η_th /%	15.8	14.8	14.0
ε_ex /%	48.7	48.9	47.6
APR /(m²/kW)	4.3	4.7	4.8
ICPP /a	6.6	6.1	6.3
ECE /t	25.0	42.1	46.2
E_xc /W	4.0	8.8	9.3

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