基于PB设计和响应面法的CPS硫黄回收装置能量优化

doi:10.16085/j.issn.1000-6613.2025-1010

化工进展 ›› 2025, Vol. 44 ›› Issue (S1): 124-133.DOI: 10.16085/j.issn.1000-6613.2025-1010

• 能源加工与技术 • 上一篇

基于PB设计和响应面法的CPS硫黄回收装置能量优化

尹晓云¹^,²(), 朱进³, 刘春艳³, 张锦涛¹^,², 徐源⁴, 朱英如⁵, 苏明¹^,², 孙月¹^,², 孙杰⁶, 袁颖⁷

^1.中国石油西南油气田分公司安全环保与技术监督研究院，四川成都 610041
^2.页岩气评价与开采四川省重点实验室，四川成都 610041
^3.中国石油西南油气田公司，四川成都 610051
^4.中国石油油气和新能源公司，北京 100007
^5.中国石油规划总院，北京 100083
^6.西南石油大学石油与天然气工程学院，四川成都 610500
^7.西安石油大学石油工程学院，陕西西安 710065

收稿日期:2025-07-14 修回日期:2025-07-26 出版日期:2025-10-25 发布日期:2025-11-24
通讯作者: 尹晓云
作者简介:尹晓云（1995—），女，博士，研究方向为油气集输多相流、油气田节能低碳。E-mail：yinxy0122@163.com。
基金资助:
四川省中央引导地方科技发展专项(2024ZYD0123);陕西省自然科学基础研究计划(2024JC-YBQN-0380);中国石油西南油气田公司博士后科技项目(20230307-07)

Energy optimization of CPS sulfur recovery unit based on Plackett-Burman design and response surface methodology

YIN Xiaoyun¹^,²(), ZHU Jin³, LIU Chunyan³, ZHANG Jintao¹^,², XU Yuan⁴, ZHU Yingru⁵, SU Ming¹^,², SUN Yue¹^,², SUN Jie⁶, YUAN Ying⁷

^1.Safety, Environment and Technology Supervision Research Institute of PetroChina Southwest Oil and Gas Field Company, Chengdu 610041, Sichuan, China
^2.Shale Gas Evaluation and Exploitation Key Laboratory of Sichuan Province, Chengdu 610041, Sichuan, China
^3.PetroChina Southwest Oil and Gas field Company, Chengdu 610051, Sichuan, China
^4.Oil, Gas and New Energy Company, PetroChina, Beijing 100007, China
^5.Planning and Engineering Institute, PetroChina, Beijing 100083, China
^6.School of Oil & Natural Gas Engineering, Southwest Petroleum University, Chengdu 610500, Sichuan, China
^7.College of Petroleum Engineering, Xi’an Shiyou University, Xi’an 710065, Shaanxi, China

Received:2025-07-14 Revised:2025-07-26 Online:2025-10-25 Published:2025-11-24
Contact: YIN Xiaoyun

摘要/Abstract

摘要：

针对天然气净化厂硫黄回收装置能量产出较低的问题，本文提出了一种结合工艺过程模拟和数据统计分析的优化方法。首先，利用Plackett-Burman（PB）试验设计筛选出对硫黄回收装置能量产出影响显著的关键因素，再通过Box-Behnken design（BBD）响应面试验对硫黄回收工艺进行优化，最后通过模拟分析验证了BBD响应面优化方法的有效性。结果表明：①酸气流量、酸气中H₂S含量和分流比对硫黄回收装置能量产出的影响最为显著，各因素的影响显著程度由大到小依次为酸气中H₂S含量>酸气流量>分流比；②确定的最佳工艺条件为，酸气流量90kmol/h、酸气中H₂S质量分数42%、分流比0.1，在此优化条件下，硫黄回收装置的能量产出可提高25.11%；③软件模拟值与模型预测值的相对误差仅为0.01%，所建立的硫黄回收装置能量产出模型预测准确可靠；④最优工艺参数经现场装置使用后的效果为，硫黄回收率为99.94%，平均能量产出达到2051.14kW。经过工艺参数优化后，硫黄回收装置的能量产出得到显著提升。

关键词: 硫黄回收, 酸气流量, 酸气中H₂S含量, 分流比, PB设计, BBD响应面法, 能量优化

Abstract:

To address the issue of low energy production in sulfur recovery units of natural gas purification plants, this research proposed an optimization method that combined process simulation with statistical data analysis. Initially, the Plackett-Burman (PB) experimental design was employed to identify the key factors that significantly affected the energy production of sulfur recovery unit. Subsequently, the Box-Behnken design (BBD) response surface methodology was used to optimize the sulfur recovery process. Finally, the effectiveness of the BBD optimization method was validated through simulation analysis. The results showed that acid gas flow rate, H₂S content in acid gas, and split ratio were the most significant factors affecting the energy production of sulfur recovery unit, and the order of significance of these factors was as follows: H₂S content in acid gas>acid gas flow rate>split ratio. The optimal process conditions determined were acid gas flow rate of 90kmol/h, H₂S content in acid gas of 42%, and split ratio of 0.1. Under the optimized conditions, the energy production of sulfur recovery unit could be increased by 25.11%. The relative error between the software simulation value and the model prediction value was only 0.01%, confirming the accuracy and reliability of the established energy production model for the sulfur recovery unit. The results of the optimal process parameters after being used by on-site equipment showed that the sulfur recovery rate was 99.94% and the energy production reached 2051.14kW. In conclusion, through the optimization of process parameters, the energy production of the sulfur recovery unit has been significantly improved.

Key words: sulfur recovery, acid gas flow rate, H₂S content in acid gas, split ratio, Plackett-Burman (PB) design, Box-Behnken design (BBD) response surface methodology, energy optimization

中图分类号:

TE644

尹晓云, 朱进, 刘春艳, 张锦涛, 徐源, 朱英如, 苏明, 孙月, 孙杰, 袁颖. 基于PB设计和响应面法的CPS硫黄回收装置能量优化[J]. 化工进展, 2025, 44(S1): 124-133.

YIN Xiaoyun, ZHU Jin, LIU Chunyan, ZHANG Jintao, XU Yuan, ZHU Yingru, SU Ming, SUN Yue, SUN Jie, YUAN Ying. Energy optimization of CPS sulfur recovery unit based on Plackett-Burman design and response surface methodology[J]. Chemical Industry and Engineering Progress, 2025, 44(S1): 124-133.

图/表 14

图1 天然气净化厂硫黄回收装置工艺流程

图2 硫黄回收装置工艺流程稳态模拟模型

表1 模型模拟结果与现场实际运行数据对比

名称	项目	实际值	模拟值	相对误差/%
酸气	温度/℃	32.14	32.14	0.00
	压力/kPa	170	170	0.00
	流量/kmol·h^-1	72.52	72.52	0.00
	CH₄摩尔分数/%	0.9	0.9	0.00
	H₂S摩尔分数/%	41.06	41.06	0.00
	CO₂摩尔分数/%	53.77	53.77	0.00
过程气S31	温度/℃	120	120	0.00
	压力/kPa	120	120	0.00
	流量/kmol·h^-1	138.23	137.10	-0.82
	H₂S摩尔分数/%	0.029	0.028	-3.45
	CO₂摩尔分数/%	30.56	31.97	4.61
	SO₂摩尔分数/%	0.015	0.014	-6.67
液硫	温度/℃	119.85	121.30	1.21
	压力/kPa	120	120	0.00
	流量/kg·h^-1	964.88	967.24	0.24
	S摩尔分数/%	≥99.95	99.97	—
	H₂S含量/mg·m^-3	≤15	11	—
尾气	SO₂含量/mg·m^-3	≤400	150.58	—
余热锅炉	能量产出/kW	1184.57	1200.93	1.38
硫黄回收装置	硫回收率/%	≥99.80	99.94	—

表2 PB试验的因素及水平

因素	编码	低水平（-1）	高水平（1）
酸气流量/kmol·h^-1	A	70	90
酸气中H₂S摩尔分数/%	B	30	42
酸气温度/℃	C	172	180
空气温度/℃	D	96	104
分流比	E	0.1	0.5
热段冷凝器温度/℃	F	148	154
克劳斯反应器入口温度/℃	G	278	284

表3 BBD响应面试验的因素及水平

因素	编码	水平
因素	编码	-1	0	1
酸气流量/kmol·h^-1	X₁	70	80	90
酸气中H₂S摩尔分数/%	X₂	30	36	42
分流比	X₃	0.1	0.3	0.5

表4 PB试验设计方案及结果

试验编号	A/kmol·h^-1	B/%	C/℃	D/℃	E	F/℃	G/℃	硫回收率/%	尾气中SO₂含量/mg·m^-3	能量产出/kW
1	-1	-1	-1	1	-1	1	1	99.94	151.23	1153.09
2	-1	1	1	1	-1	-1	-1	99.94	152.07	1606.78
3	1	1	-1	-1	-1	1	-1	99.94	152.13	2067.05
4	-1	1	-1	1	1	-1	1	99.94	149.75	1586.39
5	-1	-1	-1	-1	-1	-1	-1	99.94	151.80	1153.51
6	1	-1	-1	-1	1	-1	1	99.96	149.73	1441.59
7	1	1	1	-1	-1	-1	1	99.94	151.56	2067.14
8	-1	1	1	-1	1	1	1	99.94	149.75	1586.48
9	-1	-1	1	-1	1	1	-1	99.94	149.73	1120.75
10	1	1	-1	1	1	1	-1	99.96	149.72	2039.84
11	1	-1	1	1	-1	1	1	99.94	151.23	1481.55
12	1	-1	1	1	1	-1	-1	99.96	149.73	1440.70

表5 PB试验模型方差分析

来源	自由度	平方和	均方	F值	P值	显著性
合计	1.306×10⁶	11
模型	1.300×10⁶	7	1.858×10⁵	125.86	0.0002	**
酸气流量	4.527×10⁵	1	4.527×10⁵	306.75	<0.0001	**
酸气中H₂S含量	8.334×10⁵	1	8.334×10⁵	564.68	<0.0001	**
酸气温度	1588.50	1	1588.50	1.08	0.3581
空气温度	1368.53	1	1368.53	0.9272	0.3901
分流比	8183.53	1	8183.53	5.54	0.0781
热段冷凝器温度	1941.54	1	1941.54	1.32	0.3154
克劳斯反应器入口温度	1052.60	1	1052.60	0.7132	0.4459
误差	5903.86	4	1475.97

图3 标准化效应的正态概率图（α=0.05，α为显著性水平）

图4 标准化效应的Pareto图（α=0.05）

表6 BBD响应面试验方案及结果

试验编号	X₁/kmol·h^-1	X₂/%	X₃	硫回收率/%	尾气中SO₂含量/mg·m^-3	能量产出/kW
1	-1	1	0	99.94	149.92	1596.35
2	0	-1	1	99.94	149.76	1280.99
3	1	0	-1	99.94	154.65	1772.27
4	0	0	0	99.94	150.43	1560.82
5	0	0	0	99.94	150.43	1560.82
6	-1	-1	0	99.94	150.10	1138.48
7	-1	0	-1	99.95	150.99	1380.12
8	-1	0	1	99.94	149.75	1354.02
9	0	1	1	99.95	149.88	1813.63
10	0	0	0	99.94	150.43	1560.82
11	1	0	1	99.95	149.69	1740.63
12	0	1	-1	99.94	153.15	1836.52
13	1	1	0	99.94	150.50	2051.55
14	1	-1	0	99.94	151.81	1463.06
15	0	0	0	99.94	150.43	1560.82
16	0	-1	-1	99.95	151.88	1317.72
17	0	0	0	99.94	150.43	1560.82

表7 BBD响应面试验模型方差分析

方差来源	平方和	自由度	均方	F值	P值	显著性
模型	8.598×10⁵	9	9.553×10⁴	1.762×10⁵	<0.0001	**
X₁	3.036×10⁵	1	3.036×10⁵	5.600×10⁵	<0.0001	**
X₂	5.501×10⁵	1	5.501×10⁵	1.015×10⁶	<0.0001	**
X₃	1722.03	1	1722.03	3175.97	<0.0001	**
X₁X₂	4265.94	1	4265.94	7867.78	<0.0001	**
X₁X₃	7.67	1	7.67	14.14	0.0071	**
X₂X₃	47.97	1	47.97	88.48	<0.0001	**
$X 12$	1.23	1	1.23	2.26	0.1765
$X 22$	4.18	1	4.18	7.71	0.0274	*
$X 32$	0.66	1	0.66	1.21	0.3073
残差	3.80	7	0.54
总和	8.598×10⁵	16

表7 BBD响应面试验模型方差分析

方差来源	平方和	自由度	均方	F值	P值	显著性
模型	8.598×10⁵	9	9.553×10⁴	1.762×10⁵	<0.0001	**
X₁	3.036×10⁵	1	3.036×10⁵	5.600×10⁵	<0.0001	**
X₂	5.501×10⁵	1	5.501×10⁵	1.015×10⁶	<0.0001	**
X₃	1722.03	1	1722.03	3175.97	<0.0001	**
X₁X₂	4265.94	1	4265.94	7867.78	<0.0001	**
X₁X₃	7.67	1	7.67	14.14	0.0071	**
X₂X₃	47.97	1	47.97	88.48	<0.0001	**
$X 12$	1.23	1	1.23	2.26	0.1765
$X 22$	4.18	1	4.18	7.71	0.0274	*
$X 32$	0.66	1	0.66	1.21	0.3073
残差	3.80	7	0.54
总和	8.598×10⁵	16

图5 各因素交互作用对硫黄回收装置能量产出影响的响应面

表8 硫黄回收装置工艺参数优化前后对比

项目	酸气流量/kmol·h^-1	酸气中H₂S摩尔分数/%	分流比	硫回收率/%	尾气中SO₂含量/mg·m^-3	能量产出/kW
优化前	72.51	38.5	0.15	99.94	150.58	1650.53
优化后	90.00	42.0	0.10	99.94	154.97	2065.05

表9 硫黄回收装置工艺参数优化后近一个月生产及能量产出数据

时间	酸气流量/kmol·h^-1	酸气中H₂S摩尔分数/%	分流比	硫回收率/%	能量产出/kW
2025.6.01	90.26	42.10	0.11	99.94	2046.12
2025.6.02	90.18	43.05	0.10	99.94	2058.24
2025.6.03	92.31	41.85	0.12	99.94	2064.27
2025.6.04	91.45	43.93	0.10	99.95	2065.89
2025.6.05	90.24	42.01	0.09	99.94	2052.18
2025.6.06	89.49	41.99	0.09	99.94	2040.35
2025.6.07	90.21	41.85	0.12	99.94	2035.25
2025.6.08	91.26	44.02	0.11	99.94	2058.56
2025.6.09	90.98	40.96	0.10	99.94	2057.89
2025.6.10	88.31	42.94	0.09	99.94	2039.25
2025.6.11	90.22	42.51	0.09	99.94	2057.84
2025.6.12	92.08	40.92	0.12	99.94	2058.01
2025.6.13	89.77	42.00	0.11	99.94	2040.73
2025.6.14	90.22	40.84	0.10	99.94	2046.06
2025.6.15	90.18	41.72	0.12	99.94	2043.27
2025.6.16	87.36	42.65	0.10	99.94	2035.02
2025.6.17	90.11	40.29	0.09	99.94	2058.49
2025.6.18	90.22	42.85	0.08	99.95	2064.78
2025.6.19	89.87	40.12	0.12	99.94	2038.73
2025.6.20	90.34	41.46	0.09	99.94	2058.87
2025.6.21	90.55	42.93	0.12	99.94	2052.42
2025.6.22	88.22	40.97	0.11	99.93	2029.91
2025.6.23	90.73	42.11	0.10	99.94	2057.96
2025.6.24	92.31	41.75	0.09	99.94	2065.33
2025.6.25	90.42	40.84	0.09	99.94	2052.35
2025.6.26	89.58	41.38	0.12	99.93	2030.11
2025.6.27	89.61	42.47	0.11	99.94	2035.26
2025.6.28	90.29	43.41	0.10	99.94	2058.19
2025.6.29	91.18	42.29	0.12	99.94	2060.07
2025.6.30	90.05	44.07	0.08	99.95	2072.88
平均值	90.27	42.08	0.10	99.94	2051.14

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基于PB设计和响应面法的CPS硫黄回收装置能量优化

Energy optimization of CPS sulfur recovery unit based on Plackett-Burman design and response surface methodology

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