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Article(id=1261262692644434268, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1261262687258985194, articleNumber=null, orderNo=null, doi=10.12404/j.issn.1671-1815.2405914, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1722873600000, receivedDateStr=2024-08-06, revisedDate=1745337600000, revisedDateStr=2025-04-23, acceptedDate=null, acceptedDateStr=null, onlineDate=1778638059053, onlineDateStr=2026-05-13, pubDate=1752768000000, pubDateStr=2025-07-18, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1778638059053, onlineIssueDateStr=2026-05-13, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1778638059053, creator=13701087609, updateTime=1778638059053, updator=13701087609, issue=Issue{id=1261262687258985194, tenantId=1146029695717560320, journalId=1146123166801305609, year='2025', volume='25', issue='20', pageStart='8317', pageEnd='8759', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1778638057769, creator=13701087609, updateTime=1778753106634, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1261745237240722095, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1261262687258985194, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1261745237240722096, tenantId=1146029695717560320, journalId=1146123166801305609, issueId=1261262687258985194, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=8508, endPage=8513, ext={EN=ArticleExt(id=1261262695970517361, articleId=1261262692644434268, tenantId=1146029695717560320, journalId=1146123166801305609, language=EN, title=Heat Extraction Performance of Medium-depth Coaxial Geothermal Wells Based on Orthogonal Experiments, columnId=1156264600770302582, journalTitle=Science Technology and Engineering, columnName=Papers·Energy and Power Engineering, runingTitle=null, highlight=null, articleAbstract=

Medium-depth coaxial geothermal wells, as an efficient way to utilize geothermal energy, are now being vigorously promoted by many regions in China. In order to study its heat extraction performance and its influencing factors, COMSOL Multiphysics was used for modeling and orthogonal experimental analysis. The results show that the effects of all influencing factor on the heat extraction from geothermal wells are listed in the following order: ground temperature gradient, inlet flow rate, thermal conductivity of the backfill material, inlet temperature, and thermal conductivity of the inner tube. When designing geothermal wells, it is necessary to consider multiple factors to determine the optimal operating conditions. The radial temperature influence range of geothermal wells is about 10 m, which is a reference for the arrangement of multiple wells in the same area.

, correspAuthors=Ling-hong TANG, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Si-yuan LIU, Ling-hong TANG), CN=ArticleExt(id=1261262706619855339, articleId=1261262692644434268, tenantId=1146029695717560320, journalId=1146123166801305609, language=CN, title=基于正交实验下的中深层同轴套管式地热井取热性能, columnId=1156264600912908920, journalTitle=科学技术与工程, columnName=论文·能源与动力工程, runingTitle=null, highlight=null, articleAbstract=

中深层同轴套管式地热井作为一种高效的地热能利用方式,目前受到中国许多地区的大力推广。为了研究其取热性能及其影响因素,采用COMSOL Multiphysics进行建模,并进行正交实验分析。结果表明:各因素对地热井取热功率影响程度的大小依次为:地温梯度、入口流量、回填材料导热系数、入口温度、内管导热系数;在设计地热井时需综合多因素考虑,以确定最佳运行工况;地热井径向温度影响范围约为10 m,对于同一区域多井布置有一定参考。

, correspAuthors=唐凌虹, authorNote=null, correspAuthorsNote=
* 唐凌虹(1979—),男,汉族,湖北襄阳人,博士,副教授。研究方向:强化传热与节能技术。E-mail:。
, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=eBgXnEAYxbwnGkMM06CdDQ==, magXml=0x7pAI1xfh8aM72bIR1XGQ==, pdfUrl=null, pdf=vMk7a8VTvvgzV/+XDFTIvQ==, pdfFileSize=5434292, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=iqRdg6vg2SgJuQE0GSQaLA==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=S7pLlRigGvx6q4xUGyd7EQ==, mapNumber=null, authorCompany=null, fund=null, authors=

刘思远(1999—),男,汉族,甘肃平凉人,硕士研究生。研究方向:中深层地热利用。E-mail:。

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刘思远(1999—),男,汉族,甘肃平凉人,硕士研究生。研究方向:中深层地热利用。E-mail:。

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刘思远(1999—),男,汉族,甘肃平凉人,硕士研究生。研究方向:中深层地热利用。E-mail:。

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Probability theory and mathematical statistics[M]. Nanjing: Nanjing University Press, 2019., articleTitle=null, refAbstract=null)], funds=[Fund(id=1261377074984509779, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, awardId=2023-JC-YB-350, language=CN, fundingSource=陕西省自然科学基础研究计划(2023-JC-YB-350), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1261377025982455809, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, xref=null, ext=[AuthorCompanyExt(id=1261377025995038722, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, companyId=1261377025982455809, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=New Energy College, Xi’an Shiyou University, Xi’an 710065, China), AuthorCompanyExt(id=1261377026305417220, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, companyId=1261377025982455809, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=西安石油大学新能源学院, 西安 710065)])], figs=[ArticleFig(id=1261377050242310308, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Fig.1, caption=Schematic diagram of a medium-depth coaxial cased geothermal well, figureFileSmall=9ZXI9N3ABQdjXEIzTNOTSQ==, figureFileBig=fCFZENkdxkMY4296IgOsxA==, tableContent=null), ArticleFig(id=1261377052784058542, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=图1, caption=中深层同轴套管式地热井原理简图, figureFileSmall=9ZXI9N3ABQdjXEIzTNOTSQ==, figureFileBig=fCFZENkdxkMY4296IgOsxA==, tableContent=null), ArticleFig(id=1261377054457585854, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Fig.2, caption=Diagram of grids, figureFileSmall=bGXEFqbubpJVK4VC4XfCIQ==, figureFileBig=7VlALSVfaw142l5OTxDJoQ==, tableContent=null), ArticleFig(id=1261377056995139785, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=图2, caption=网格划分示意图, figureFileSmall=bGXEFqbubpJVK4VC4XfCIQ==, figureFileBig=7VlALSVfaw142l5OTxDJoQ==, tableContent=null), ArticleFig(id=1261377058182127820, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Fig.3, caption=Variation of grid independence, figureFileSmall=DCb+cX7AvJVLXEcADEBXaQ==, figureFileBig=wtQwdu3683jCyE1mZB6Edw==, tableContent=null), ArticleFig(id=1261377059100680402, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=图3, caption=网格无关性验证, figureFileSmall=DCb+cX7AvJVLXEcADEBXaQ==, figureFileBig=wtQwdu3683jCyE1mZB6Edw==, tableContent=null), ArticleFig(id=1261377060786790619, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Fig.4, caption=Validation of simulation results, figureFileSmall=KF5lxIJ41rCDW/V6bmUgEg==, figureFileBig=8lVSf1suEbt9LIzz7EB7KQ==, tableContent=null), ArticleFig(id=1261377061646622946, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=图4, caption=模拟结果验证, figureFileSmall=KF5lxIJ41rCDW/V6bmUgEg==, figureFileBig=8lVSf1suEbt9LIzz7EB7KQ==, tableContent=null), ArticleFig(id=1261377062397403364, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Fig.5, caption=Average heat extraction power and average temperature of each factor, figureFileSmall=sfSSbFFdhjSytGOCKPAQlg==, figureFileBig=rEInH2rL8ELEWy3PAs1cuA==, tableContent=null), ArticleFig(id=1261377063655694575, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=图5, caption=各因素下影响下的平均取热功率与平均温度, figureFileSmall=sfSSbFFdhjSytGOCKPAQlg==, figureFileBig=rEInH2rL8ELEWy3PAs1cuA==, tableContent=null), ArticleFig(id=1261377065320833268, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Fig.6, caption=Outlet temperature and heat extraction power versus operating time under the optimum working condition, figureFileSmall=IYW3hYQTJbMD0J4UTHRGPA==, figureFileBig=UM9Au9/F2gNSDYh5vyr4XQ==, tableContent=null), ArticleFig(id=1261377065740263674, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=图6, caption=最佳工况出口温度和取热功率随时间变化趋势, figureFileSmall=IYW3hYQTJbMD0J4UTHRGPA==, figureFileBig=UM9Au9/F2gNSDYh5vyr4XQ==, tableContent=null), ArticleFig(id=1261377066616873217, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Fig.7, caption=Geotechnical temperature distributions, figureFileSmall=f6Gz/3kOtPObbRy8vYOSWQ==, figureFileBig=F+39r5JJ1bKj08T7E40O5w==, tableContent=null), ArticleFig(id=1261377067409596682, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=图7, caption=岩土温度云图, figureFileSmall=f6Gz/3kOtPObbRy8vYOSWQ==, figureFileBig=F+39r5JJ1bKj08T7E40O5w==, tableContent=null), ArticleFig(id=1261377067841610001, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Table 1, caption=

Well parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 数值
埋管深度/m 2 500
计算深度/m 2 700
计算半径/m 50
内管外径/mm 110
内管壁厚/mm 13
外管外径/mm 177.8
外管壁厚/mm 9.19
回填材料厚度/mm 100
), ArticleFig(id=1261377069573857558, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=表1, caption=

井身参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 数值
埋管深度/m 2 500
计算深度/m 2 700
计算半径/m 50
内管外径/mm 110
内管壁厚/mm 13
外管外径/mm 177.8
外管壁厚/mm 9.19
回填材料厚度/mm 100
), ArticleFig(id=1261377069917790492, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Table 2, caption=

Material property parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
材料 密度/
(kg·m-3)		 比热容/
(J·kg-1·K-1)		 导热系数/
(W·m-1·K-1)
循环水 1 000 4 200 0.62
内管 7 850 2 300 0.40
外管 7 850 400 44.50
回填材料 2 000 2 200 1.80
), ArticleFig(id=1261377070433689890, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=表2, caption=

材料物性参数

, figureFileSmall=null, figureFileBig=null, tableContent=
材料 密度/
(kg·m-3)		 比热容/
(J·kg-1·K-1)		 导热系数/
(W·m-1·K-1)
循环水 1 000 4 200 0.62
内管 7 850 2 300 0.40
外管 7 850 400 44.50
回填材料 2 000 2 200 1.80
), ArticleFig(id=1261377070815371557, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Table 3, caption=

Orthogonal experimental factors and level settings

, figureFileSmall=null, figureFileBig=null, tableContent=
编号 因素 水平
1 2 3
A 入口流量/(m3·h-1) 20 40 60
B 入口温度/℃ 7 10 13
C 内管导热系数/(W·m-1·K-1) 0 0.2 0.4
D 回填材料导热系数/(W·m-1·K-1) 1 2 3
E 地温梯度/(℃·km-1) 25 30 35
), ArticleFig(id=1261377071343853869, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=表3, caption=

正交实验因素水平设置

, figureFileSmall=null, figureFileBig=null, tableContent=
编号 因素 水平
1 2 3
A 入口流量/(m3·h-1) 20 40 60
B 入口温度/℃ 7 10 13
C 内管导热系数/(W·m-1·K-1) 0 0.2 0.4
D 回填材料导热系数/(W·m-1·K-1) 1 2 3
E 地温梯度/(℃·km-1) 25 30 35
), ArticleFig(id=1261377071796838703, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Table 4, caption=

Orthogonal experimental results of factors affecting heat extraction power

, figureFileSmall=null, figureFileBig=null, tableContent=
工况 因素 取热功
率/kW
A B C D E 空白
1 1 1 1 1 1 1 372.9
2 1 1 2 2 3 3 492.5
3 1 2 1 3 3 2 544.6
4 1 2 3 1 2 3 337.3
5 1 3 2 3 2 1 394.5
6 1 3 3 2 1 2 290.3
7 2 1 1 3 2 3 556.7
8 2 1 3 1 3 2 506.0
9 2 2 2 2 2 2 483.2
10 2 2 3 3 1 1 416.8
11 2 3 1 2 3 1 550.9
12 2 3 2 1 1 3 336.7
13 3 1 2 3 1 2 491.1
14 3 1 3 2 2 1 535.5
15 3 2 1 2 1 3 441.2
16 3 2 2 1 3 1 514.8
17 3 3 1 1 2 2 424.4
18 3 3 3 3 3 3 564.8
), ArticleFig(id=1261377071956222257, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=表4, caption=

取热功率影响因素正交实验结果

, figureFileSmall=null, figureFileBig=null, tableContent=
工况 因素 取热功
率/kW
A B C D E 空白
1 1 1 1 1 1 1 372.9
2 1 1 2 2 3 3 492.5
3 1 2 1 3 3 2 544.6
4 1 2 3 1 2 3 337.3
5 1 3 2 3 2 1 394.5
6 1 3 3 2 1 2 290.3
7 2 1 1 3 2 3 556.7
8 2 1 3 1 3 2 506.0
9 2 2 2 2 2 2 483.2
10 2 2 3 3 1 1 416.8
11 2 3 1 2 3 1 550.9
12 2 3 2 1 1 3 336.7
13 3 1 2 3 1 2 491.1
14 3 1 3 2 2 1 535.5
15 3 2 1 2 1 3 441.2
16 3 2 2 1 3 1 514.8
17 3 3 1 1 2 2 424.4
18 3 3 3 3 3 3 564.8
), ArticleFig(id=1261377072123994423, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Table 5, caption=

Heat extraction power range analysis

, figureFileSmall=null, figureFileBig=null, tableContent=
项目 取热功率/kW
A B C D E
K1 2 432.0 2 954.7 2 890.7 2 492.0 2 348.9
K2 2 850.2 2 737.8 2 712.7 2 793.6 2 731.6
K3 2 971.9 2 561.7 2 650.7 2 968.5 3 173.6
k1 405.3 492.4 481.8 415.3 391.5
k2 475.0 456.3 452.1 465.6 455.3
k3 495.3 426.9 441.8 494.7 528.9
R 90.0 65.5 40.0 79.4 137.4
), ArticleFig(id=1261377072430178623, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=表5, caption=

取热功率极差分析

, figureFileSmall=null, figureFileBig=null, tableContent=
项目 取热功率/kW
A B C D E
K1 2 432.0 2 954.7 2 890.7 2 492.0 2 348.9
K2 2 850.2 2 737.8 2 712.7 2 793.6 2 731.6
K3 2 971.9 2 561.7 2 650.7 2 968.5 3 173.6
k1 405.3 492.4 481.8 415.3 391.5
k2 475.0 456.3 452.1 465.6 455.3
k3 495.3 426.9 441.8 494.7 528.9
R 90.0 65.5 40.0 79.4 137.4
), ArticleFig(id=1261377074107900227, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=EN, label=Table 6, caption=

Heat extraction power variance analysis

, figureFileSmall=null, figureFileBig=null, tableContent=
因素 离差平方和 自由度 均方 F值 显著性
A 26 728.0 2 13 364.0 36.2 ***
B 12 916.6 2 6 458.3 17.5 ***
C 5 173.4 2 2 586.7 7.0 **
D 19 365.8 2 9 682.9 26.2 ***
E 56 766.9 2 28 383.5 76.9 ***
空白 2 582.5 7 368.9 — —
), ArticleFig(id=1261377074363752774, tenantId=1146029695717560320, journalId=1146123166801305609, articleId=1261262692644434268, language=CN, label=表6, caption=

取热功率方差分析

, figureFileSmall=null, figureFileBig=null, tableContent=
因素 离差平方和 自由度 均方 F值 显著性
A 26 728.0 2 13 364.0 36.2 ***
B 12 916.6 2 6 458.3 17.5 ***
C 5 173.4 2 2 586.7 7.0 **
D 19 365.8 2 9 682.9 26.2 ***
E 56 766.9 2 28 383.5 76.9 ***
空白 2 582.5 7 368.9 — —
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基于正交实验下的中深层同轴套管式地热井取热性能
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刘思远 , 唐凌虹 *
科学技术与工程 | 论文·能源与动力工程 2025,25(20): 8508-8513
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科学技术与工程 | 论文·能源与动力工程 2025, 25(20): 8508-8513
基于正交实验下的中深层同轴套管式地热井取热性能
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刘思远 , 唐凌虹*
作者信息
  • 西安石油大学新能源学院, 西安 710065

    • 刘思远(1999—),男,汉族,甘肃平凉人,硕士研究生。研究方向:中深层地热利用。E-mail:。

通讯作者:

* 唐凌虹(1979—),男,汉族,湖北襄阳人,博士,副教授。研究方向:强化传热与节能技术。E-mail:。
Heat Extraction Performance of Medium-depth Coaxial Geothermal Wells Based on Orthogonal Experiments
Si-yuan LIU , Ling-hong TANG*
Affiliations
  • New Energy College, Xi’an Shiyou University, Xi’an 710065, China
出版时间: 2025-07-18 doi: 10.12404/j.issn.1671-1815.2405914
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摘要
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中深层同轴套管式地热井作为一种高效的地热能利用方式,目前受到中国许多地区的大力推广。为了研究其取热性能及其影响因素,采用COMSOL Multiphysics进行建模,并进行正交实验分析。结果表明:各因素对地热井取热功率影响程度的大小依次为:地温梯度、入口流量、回填材料导热系数、入口温度、内管导热系数;在设计地热井时需综合多因素考虑,以确定最佳运行工况;地热井径向温度影响范围约为10 m,对于同一区域多井布置有一定参考。

中深层地热能  /  同轴套管  /  正交实验  /  COMSOL Multiphysics

Medium-depth coaxial geothermal wells, as an efficient way to utilize geothermal energy, are now being vigorously promoted by many regions in China. In order to study its heat extraction performance and its influencing factors, COMSOL Multiphysics was used for modeling and orthogonal experimental analysis. The results show that the effects of all influencing factor on the heat extraction from geothermal wells are listed in the following order: ground temperature gradient, inlet flow rate, thermal conductivity of the backfill material, inlet temperature, and thermal conductivity of the inner tube. When designing geothermal wells, it is necessary to consider multiple factors to determine the optimal operating conditions. The radial temperature influence range of geothermal wells is about 10 m, which is a reference for the arrangement of multiple wells in the same area.

medium-depth geothermal energy  /  coaxial casing  /  orthogonal experiments  /  COMSOL Multiphysics
刘思远, 唐凌虹. 基于正交实验下的中深层同轴套管式地热井取热性能. 科学技术与工程, 2025 , 25 (20) : 8508 -8513 . DOI: 10.12404/j.issn.1671-1815.2405914
Si-yuan LIU, Ling-hong TANG. Heat Extraction Performance of Medium-depth Coaxial Geothermal Wells Based on Orthogonal Experiments[J]. Science Technology and Engineering, 2025 , 25 (20) : 8508 -8513 . DOI: 10.12404/j.issn.1671-1815.2405914
正文
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地热能作为一种可再生清洁能源,具有分布广泛,稳定开采等优点。中国地热能储量丰富,特别是在华北平原、松辽盆地、关中平原、山东半岛等地拥有十分优秀的中低温地热资源[1]。由于地热能是来源于地球内部的热量,所以地热能不受昼夜、季节、气候等因素影响,在这方面优于太阳能、风能、潮汐能等其他可再生能源[2]。
中深层同轴套管式地热井作为一种高效的地热能利用形式,因其“取热不取水”的特点及高效换热的优点,得到学者们的广泛关注[3-10]。杜甜甜等[3]利用Fortran程序编译软件对多土层的不同物性参数条件下的中深层同轴套管地热井的名义取热量进行了计算分析,结果表明,其名义取热量会随着年平均环境温度、大地热流、井孔深度、循环水流量的增大而增大。宋先知等[4]对雄安新区一口中深层同轴套管地热井进行具体测量和分析,并建立数值模型,对地热储层最大产能、井下换热系统取热效率及关键参数的影响规律进行研究,优选出现场试验所需的工艺参数。赵阳[5]利用MATLAB建立了数值模型,采用隐式差分算法求解,并与实际测量结果进行对比,具有较高的精度。黄奕斌[6]对吉林松原地区一口中深层同轴套管地热井进行具体测量和分析,并建立数值模型,对多通道及多孔介质热储强化进行研究,发现雷诺数的增加和固体颗粒温度的升高可以强化传热。王硕等[7]测量并分析青岛一口2 605 m深的地热井,其井底温度为83.2 ℃,同时利用Fluent建立数值模型,发现地热井换热能力随运行时间的增加而减弱,地埋管取热量过大会导致供暖后期地埋管进水温度过低。张丰琰等[8]对不同温度下固井水泥导热系数进行研究,通过测试地热井纯水泥和空心玻璃微珠水泥的导热系数,分析不同孔隙度和测试温度下固井水泥石导热系数的变化规律。韩元红等[9]对中深层同轴套管地热井的取热能力及热影响半径进行研究,结果表明,2 500 m地热井30年可持续取热功率为350 kW,30 年最大热影响半径为110 m。王卫莲等[10]对中深层同轴套管地热井热储恢复进行研究,结果表明,人为干预的蓄热恢复可以在非供暖季结束时完成良好的恢复。
上述研究根据建立的数值模型,可以有效分析各个影响因素对地热井性能的影响效果及变化趋势,然而,无法定量分析出各个影响因素对地热井性能的影响程度。鉴于此,利用COMSOL Multiphysics中的流体流动传热模块及多物理场中的非等温流动,建立同轴套管式地热井的传热模型,基于瞬态求解,采用实测数据进行验证,结合正交实验综合分析各因素对中深层同轴套管式地热井取热性能的影响程度,研究成果可对中深层同轴套管式地热井的设计和运行维护提供一定指导。
1 模型建立
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1.1 物理模型
中深层同轴套管式地热井的原理如图1所示。循环水通过水泵从同轴套管的外管流入井底,在此过程中与岩土区域完成井下的热量交换,之后从同轴套管的内管流出地面,经热泵机组提取热量后向建筑供暖,供暖完成后的冷却水通过循环泵再次流入井内,完成循环[11]。
1.2 模型假设
中深层同轴套管式地热井的井下传热受地下水渗流、回填材料与岩土热接触等因素的影响,为简化模型,做出以下假设:①假设此过程为纯导热问题,忽略传热过程中地下水渗流的影响;②假设回填材料与井壁及岩土之间无接触热阻;③假设地表温度恒定不变;④假设传热过程中只有径向导热,忽略轴向导热;⑤假设岩土的热物性参数不随岩土温度变化而变化;⑥假设流体、管道及回填材料初始温度与同深度岩土温度相同;⑦假设地热井为完全竖直结构;⑧假设岩土边界温度为恒定温度梯度。
1.3 参数设置及边界条件
基于COMSOL Multiphysics中的流体传热与湍流模块(湍动能k-耗散率ε)进行二维轴对称仿真计算。该模型自定义参数包括井身参数和材料物性参数,具体数值如表1和表2所示。
岩土区域顶端和底端为绝热边界条件,岩土区域顶端温度为15 ℃,地温梯度25 ℃/km。流体速度为入口边界条件,压力出口为出口边界条件。
1.4 网格划分及模型验证
1.4.1 网格划分及无关性验证
在网格划分阶段,采用结构化网格,并对近井区域网格进行加密,以在确保计算精度的情况下,有效节约计算时间,提升计算效率。在COMSOL Multiphysics中采用映射分布的方法对网格进行划分,网格在水平方向的分布采用预定义的分布类型,其中增长率选择为指数,单元数为100,单元大小比为10(单元大小比表示中间单元与最后单元的大小比值);在竖直方向采用均匀分布的形式,单元数为500。网格划分结果如图2所示。
在开始计算前进行网格无关性验证,分别计算网格数量为33 585、39 834、51 053、76 503的模型出口温度,如图3所示。网格数量为51 053的出口温度与网格数量为39 834的出口温度相差为0.14%,与网格数量为76 503的出口温度相差为0.11%,因此,采用网格数量为51 053的网格进行计算。
1.4.2 模型验证
为确保本模型的准确性,采用郭海明等[12]的实验数据作为验证,模型求解瞬态求解,结果如图4所示。
取热功率的计算公式为

P=cm(T2-T1)

式(1)中:P为取热功率,kW;c为循环水的比热容,J/(kg·K);m为循环流量,kg/h;T2和T1分别为出口温度和入口温度,℃。
实验平均出口温度为22.1 ℃,模拟平均出口温度为22.6 ℃,实验平均功率为496.5 kW,模拟平均功率为527.0 kW,误差分别为2.3%与6.2%,可以有效验证本文模型的准确性。
2 正交实验
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由于中深层同轴套管式地热井取热功率的影响因素较多,因此采用无交互作用的正交实验对部分影响因素进行分析[13]。选取入口流量(A)、入口温度(B)、内管导热系数(C)、回填材料导热系数(D)、地温梯度(E)共5项作为影响因素,以实验时间为连续运行500 h内的平均取热功率作为研究结果,其中每个因素选取3个水平,具体实验因素水平设置如表3所示。
本实验采用正交表L18(36)进行实验,共实验18次,其中因素部分由5项影响因素和空白组作为误差分析构成,如表4所示。实验完成后进行极差分析与方差分析,最终确定各个因素对取热功率的影响。
3 结果与讨论
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3.1 极差分析
正交实验结果如表4所示。极差分析是通过计算每个因素在不同水平上平均值的极差来发现该因素对结果的影响程度。极差是指同一列中数值最大的数与最小的数之差,极差越大说明该因素对实验指标的影响越大,因此可以从中找出最好的组合搭配[14]。
根据实验结果(表4),计算出各个因素影响下的取热功率,计算结果如表5所示。
由表5可知,R由大到小依次为地温梯度(E)、入口流量(A)、回填材料导热系数(D)、入口温度(B)、内管导热系数(C),其中地温梯度(E)和入口流量(A)为主要影响因素,综合考虑,最优组合工况为A3B1C1D3E3。
3.2 方差分析
方差分析用于分析各个因素对结果影响,并确定哪些因素对结果具有显著性影响,在一定程度上可以弥补极差分析的不足。
根据实验结果,可以计算出各个因素影响下的取热功率,计算结果如表6所示。
由表6可知,入口流量(A)、入口温度(B)、回填材料导热系数(D)、地温梯度(E)的F值均大于F0.01(2,7),表明这4个因素对取热功率均有非常显著性影响,内管导热系数(C)的F值在[F0.05(2,7), F0.01(2,7)],表明内管导热系数(C)对取热功率有显著性影响。根据F值判断各因素对取热功率影响的先后顺序为:地温梯度(E)、入口流量(A)、回填材料导热系数(D)、入口温度(B)、内管导热系数(C)。
极差分析下各个因素水平取热功率所示结果一致,验证了极差分析得到的最优组合方案的准确性。
3.3 综合分析
3.3.1 影响因素
根据3.1节、3.2节分析可知,取热功率与入口流量(A)、回填材料导热系数(D)、地温梯度(E)具有正相关性,与入口温度(B)、内管导热系数(C)具有负相关性。各因素下影响下的平均取热功率与平均温度如图5所示,产生该结果的原因如下。
(1)入口流量(A)增大,系统出口温度减小,取热功率增加。由于流量增大,努塞尔数增加,传热效果加强,取热功率呈现上升趋势。在实际工程中,入口流量的增大对于地热井管材、封堵结构、循环水泵等要求随之提高,因此在设计过程中需要综合考虑。
(2)入口温度(B)增大,系统出口温度增大,取热功率减小。根据取热功率的计算公式,由于出入口温差减小,取热功率呈现下降趋势。在实际工程中,入口温度取决于环境温度、热泵与建筑侧消耗热量,在设计之初应综合考虑其影响,确定合适的入口温度。
(3)内管导热系数(C)增大,系统出口温度减小,取热功率减小。根据物理模型,内管为出口管,内管导热系数越大,其导热性能越好,在流出过程的热量损失就越多,取热功率越小。在实际工程中,为减少热量损失,需尽可能选择导热系数小的内管。
(4)回填材料导热系数(D)增大,系统出口温度增大,取热功率增大。根据物理模型,回填材料与岩土区域直接接触,其导热系数越大,热传导效率越高,更有利于提高换热量。在实际工程中,为提高换热量,需尽可能选择导热系数大的回填材料。
(5)地温梯度(E)增大,系统出口温度增大,取热功率增大。根据物理模型,更高的地温梯度可以实现更高的取热量。在实际工程中,需提前勘探该区域的地质条件,为地热井选择合适的位置。
3.3.2 最佳工况分析
根据上述分析,计算出最佳工况为A3B1C1D3E3,该工况下平均出口温度为16.5 ℃,平均取热功率为663.8 kW,出口温度和取热功率随时间变化如图6所示。
系统运行前后岩土温度云图如图7所示。可以看出,在运行500 h后,地热井温度径向影响范围约为10 m,在越靠近岩土区域顶端,其影响范围越大,对于同一区域多井布置有一定参考。距顶端约400 m的以上区域岩土温度稍有升高,原因是浅层岩土区域温度较低,当流体经井底加热后,其温度将稍高于浅层岩土温度,管内流体会向浅层岩土区域逆向传热,产生一定的热量损失。在实际工程中,可以在该部分选取导热系数较小的内管以降低该部分热量损失。
4 结论
收起
利用COMSOL Multiphysics建立中深层同轴套管地热井模型,设计18个工况进行正交实验,得出如下结论。
(1)地热井取热功率受多因素综合影响,各因素对其影响程度由大到小依次为:地温梯度、入口流量、回填材料导热系数、入口温度、内管导热系数。
(2)设计地热井最佳工况需综合考虑多因素影响作用及循环泵、热泵等性能要求,以确定地热井最佳运行工况。
(3)地热井在运行500 h后,径向温度影响范围约为10 m,对于同一区域多井布置有一定参考。
基金
收起
  • 陕西省自然科学基础研究计划(2023-JC-YB-350)
文献
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2025年第25卷第20期
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doi: 10.12404/j.issn.1671-1815.2405914
  • 接收时间：2024-08-06
  • 首发时间：2026-05-13
  • 出版时间：2025-07-18
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  • 收稿日期：2024-08-06
  • 修回日期：2025-04-23
基金
陕西省自然科学基础研究计划(2023-JC-YB-350)
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    西安石油大学新能源学院, 西安 710065

通讯作者:

* 唐凌虹(1979—),男,汉族,湖北襄阳人,博士,副教授。研究方向:强化传热与节能技术。E-mail:。
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
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红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
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