Article(id=1322941955126211398, tenantId=1146029695717560320, journalId=1322258508890079423, issueId=1322941718441623734, articleNumber=null, orderNo=null, doi=10.13809/j.cnki.cn32-1825/te.2025051, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1745510400000, receivedDateStr=2025-04-25, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793343541175, onlineDateStr=2026-10-30, pubDate=1779724800000, pubDateStr=2026-05-26, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793343541175, onlineIssueDateStr=2026-10-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793343541175, creator=13701087609, updateTime=1793343541175, updator=13701087609, issue=Issue{id=1322941718441623734, tenantId=1146029695717560320, journalId=1322258508890079423, year='2026', volume='16', issue='3', pageStart='489', pageEnd='736', issueExtLink='null', onlineDate='null', pubDate='1779724800000', pubDateStr='2026-05-26', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793343484745, creator='13701087609', updateTime=1793344165564, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1322944574066402279, tenantId=1146029695717560320, journalId=1322258508890079423, issueId=1322941718441623734, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1322944574070596584, tenantId=1146029695717560320, journalId=1322258508890079423, issueId=1322941718441623734, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=675, endPage=683, ext={EN=ArticleExt(id=1322941955344315207, articleId=1322941955126211398, tenantId=1146029695717560320, journalId=1322258508890079423, language=EN, title=Inversion method for fiber optic monitoring of two-phase flow production profiles in horizontal wells, columnId=1322941693024141328, journalTitle=Petroleum Reservoir Evaluation and Development, columnName=Oil and Gas Development, runingTitle=null, highlight=
Distributed temperature sensing (DTS) technology is widely applied in intelligent monitoring of production dynamics in oil and gas wells. To address the challenges in quantitatively analyzing oil-water two-phase flow profile in horizontal wells, a temperature profile prediction model applicable to oil-water two-phase flow in horizontal wells was constructed, comprehensively considering multiple micro-thermal effects, including the Joule-Thomson effect. Simulation and sensitivity analyses of the temperature profile of a reservoir horizontal well were conducted. Meanwhile, the particle swarm optimization (PSO) algorithm was used to establish a DTS data inversion model, innovatively enabling the inversion of multi-dimensional unknown downhole parameters based on a single DTS data source, thereby achieving a quantitative interpretation of the oil-water two-phase flow production profile in horizontal wells. The results showed that: (1) The main influencing factors of the temperature profile in oil-water two-phase horizontal wells, ranked by impact degree from high to low, were single-well production (Q)> permeability (k)> water cut (FW)> wellbore radius (Rw)> crude oil density (ρo)> damage zone radius (Rd)> reservoir thermal conductivity (Kt). (2) Single-well production, permeability, and water cut were the key dominant factors affecting the temperature profile. When inverting measured DTS data, formation permeability could be prioritized as the core target parameter for inversion, and secondary factors could be set as fixed values or assigned reasonable ranges to simplify the problem. (3) By using the PSO inversion model to invert the DTS temperature data of the field well, the production positions of the two-phase fluids could be accurately identified. The interpreted liquid production profile obtained from inversion showed high consistency with field production logging tool (PLT) test results, with a mean absolute error of the average liquid production per section of less than 10%, fully verifying the reliability of the PSO inversion model. Future research can focus on enhancing the model’s depiction of complex flows and expand toword multiphase flow application.
, articleAbstract=null, authors=HANLAN XIONG1, HONGWEN LUO1, HAITAO LI1, WENBIN AI2, YANI HUANG1, JIALIN MA1, BINGQI CHEN1, FEIFEI RAN1, XIAOYI PAN1, authorsList=HANLAN XIONG, HONGWEN LUO, HAITAO LI, WENBIN AI, YANI HUANG, JIALIN MA, BINGQI CHEN, FEIFEI RAN, XIAOYI PAN, authorCompany=null, correspAuthors=HONGWEN LUO, 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, fund=null), CN=ArticleExt(id=1322941958179664726, articleId=1322941955126211398, tenantId=1146029695717560320, journalId=1322258508890079423, language=CN, title=水平井两相流产出剖面光纤监测反演方法, columnId=1322941693259022355, journalTitle=油气藏评价与开发, columnName=油气开发, runingTitle=null, highlight=
分布式光纤温度传感(Distributed Temperature Sensing,DTS)技术在油气井生产动态的智能化监测中应用广泛。针对水平井油水两相流产出剖面定量解析难题,本文构建了综合考虑焦耳-汤姆逊效应(Joule-Thomson effect)等多种微热效应、适用于水平井油水两相流的温度剖面预测模型,并对某油藏中的水平井温度剖面进行了模拟与敏感性分析。同时,本文采用粒子群优化(Particle Swarm Optimization,PSO)算法建立了DTS数据反演模型,创新性地实现了基于单一DTS数据源的井下多维未知参数反演,进而完成水平井两相流产出剖面的定量解释。研究表明:①油水两相流水平井温度剖面主要影响因素及其影响程度排序为,单井产量(Q)>渗透率(k)>含水率(Fw)>井筒半径(Rw)>原油密度(ρo) >伤害带半径(Rd)>储层导热系数(Kt);②单井产量、渗透率和含水率是影响温度剖面的关键主导因素,在对实测DTS数据进行反演时,可优先将地层渗透率作为核心目标参数进行反演,次要因素可设定为固定值或合理范围以简化问题;③利用PSO反演模型对现场井DTS温度数据进行反演,能够精准识别两相流体的产出位置,反演得到的产液剖面解释结果与现场生产测井(PLT)测试结果高度吻合,各产出段平均产液量的平均绝对误差低于10%,充分验证了PSO反演模型的可靠性。未来可从提升模型对复杂流动的刻画精度、拓展至多相流等方向深入研究。
, articleAbstract=null, authors=熊瀚澜1, 罗红文1, 李海涛1, 艾文斌2, 黄雅妮1, 马佳林1, 陈柄杞1, 冉飞飞1, 潘晓艺1, authorsList=熊瀚澜, 罗红文, 李海涛, 艾文斌, 黄雅妮, 马佳林, 陈柄杞, 冉飞飞, 潘晓艺, authorCompany=null, correspAuthors=罗红文, authorNote=
熊瀚澜(2001—),男,在读硕士研究生,主要从事井下分布式光纤监测解释及物理模拟实验方向的研究。地址:四川省成都市新都区新都大道8号,邮政编码:610500。E-mail:18883078943@163.com
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罗红文(1990—),男,博士,讲师,硕士研究生导师,主要从事油气井分布式光纤监测(DTS/DAS/DSS)解释、注采动态评价及完井优化方面的研究工作。地址:四川省成都市新都区新都大道8号,邮政编码:610500。E-mail:
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熊瀚澜(2001—),男,在读硕士研究生,主要从事井下分布式光纤监测解释及物理模拟实验方向的研究。地址:四川省成都市新都区新都大道8号,邮政编码:610500。E-mail:18883078943@163.com
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熊瀚澜(2001—),男,在读硕士研究生,主要从事井下分布式光纤监测解释及物理模拟实验方向的研究。地址:四川省成都市新都区新都大道8号,邮政编码:610500。E-mail:18883078943@163.com
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1 State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation , Southwest Petroleum University, Chengdu, Sichuan 610500, China), AuthorCompanyExt(id=1322941958464877401, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, companyId=1322941958443905879, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=
1 西南石油大学油气藏地质及开发工程全国重点实验室,四川 成都 610500)]), AuthorCompany(id=1322941958557152090, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, xref=2, ext=[AuthorCompanyExt(id=1322941958569735003, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, companyId=1322941958557152090, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=
2 PetroChina Changqing Oilfield Company, Shaanxi, Xi’an 710021, China), AuthorCompanyExt(id=1322941958578123612, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, companyId=1322941958557152090, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=
2 中国石油长庆油田分公司,陕西 西安 710021)])], figs=[ArticleFig(id=1322941963615482774, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Fig.1, caption=
Schematic diagram of box-shaped oil reservoir horizontal well structure, figureFileSmall=Bra6vVb2M+BqvE19z0iIgg==, figureFileBig=9jifn2aHtoYgaWJfN3GlCQ==, tableContent=null), ArticleFig(id=1322941963699368855, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=CN, label=图1, caption=
箱型油藏水平井结构示意图, figureFileSmall=Bra6vVb2M+BqvE19z0iIgg==, figureFileBig=9jifn2aHtoYgaWJfN3GlCQ==, tableContent=null), ArticleFig(id=1322941963934249880, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Fig.2, caption=
Schematic diagram of fluid flow within horizontal wellbore, figureFileSmall=YbwPaSkqK5wgnAbfSFBkKg==, figureFileBig=aXL0jVm/fktxghYYaVtJjQ==, tableContent=null), ArticleFig(id=1322941964060079001, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=CN, label=图2, caption=
水平井井筒内流体流动示意图注:R为井筒半径,单位m;θ为井筒与垂直方向的夹角,单位(°)。
, figureFileSmall=YbwPaSkqK5wgnAbfSFBkKg==, figureFileBig=aXL0jVm/fktxghYYaVtJjQ==, tableContent=null), ArticleFig(id=1322941964135576474, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Fig.3, caption=
Solution process of oil-water two-phase temperature profile prediction model for horizontal well, figureFileSmall=3mL3A+xy8CTuDQsLLeBWNQ==, figureFileBig=A8UM3sH5xeHGQuYzHJX+Sg==, tableContent=null), ArticleFig(id=1322941964206879643, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=CN, label=图3, caption=
水平井油水两相流温度剖面预测模型求解流程注:t为时间,单位min;t0为0次迭代的时间步长;tmax为允许的最大时间步长;Twb为井筒的温度,单位℃; n为第n次迭代;下标k为第k次计算更新的井筒温度剖面;ε为设定可接受的最大误差值;Y为判断成立;N为判断条件不成立。
, figureFileSmall=3mL3A+xy8CTuDQsLLeBWNQ==, figureFileBig=A8UM3sH5xeHGQuYzHJX+Sg==, tableContent=null), ArticleFig(id=1322941964278182812, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Fig.4, caption=
Inversion interpretation process of production profile of oil-water two-phase flow in horizontal well, figureFileSmall=+CKGas0Qslso7Mc3mtrujw==, figureFileBig=BOQLVqVemO8PjIMh+hQ8uw==, tableContent=null), ArticleFig(id=1322941964341097373, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=CN, label=图4, caption=
油水两相流水平井产出剖面反演解释流程注:I为初始粒子群中的粒子总数量;c1为个体加速常数;c2为群体加速常数;T*为最大迭代次数;为第t次迭代优化中第i个粒子的位置;为第t次迭代优化中第i个粒子的速度;为第t+1次迭代优化中第i个粒子的位置;第t+1次迭代优化中第i个粒子的速度;为经过t次迭代优化后第i个粒子的适应度值;为经过t+1次迭代优化后第i个粒子的适应度值;为第t次迭代优化中第i个粒子的个体极值;为第t+1次迭代优化中第i个粒子的个体极值;为第t次迭代优化中粒子群的全局极值;为第t+1次迭代优化中粒子群的全局极值。
, figureFileSmall=+CKGas0Qslso7Mc3mtrujw==, figureFileBig=BOQLVqVemO8PjIMh+hQ8uw==, tableContent=null), ArticleFig(id=1322941964416594846, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Fig.5, caption=
Measured DTS data of well X1, figureFileSmall=9Etm6JoDtZrwNnIgppVDgw==, figureFileBig=97K+0vabpHmjOmUCM0QZDg==, tableContent=null), ArticleFig(id=1322941966052373407, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=CN, label=图5, caption=
X1井实测DTS数据, figureFileSmall=9Etm6JoDtZrwNnIgppVDgw==, figureFileBig=97K+0vabpHmjOmUCM0QZDg==, tableContent=null), ArticleFig(id=1322941966148842400, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Fig.6, caption=
Inversion fitting results of DTS data, figureFileSmall=as0VfjxJInHKQ3OwOdgM3g==, figureFileBig=S/4qUJctPGdgoXxfJotG6Q==, tableContent=null), ArticleFig(id=1322941966220145569, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=CN, label=图6, caption=
DTS数据反演拟合结果, figureFileSmall=as0VfjxJInHKQ3OwOdgM3g==, figureFileBig=S/4qUJctPGdgoXxfJotG6Q==, tableContent=null), ArticleFig(id=1322941966320808866, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Fig.7, caption=
Inversion interpretation results of well X1, figureFileSmall=a2d2Iq/OrnzG67rtTXsjoA==, figureFileBig=hA1NGE38UsXD9UPAPZMdnA==, tableContent=null), ArticleFig(id=1322941966396306339, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=CN, label=图7, caption=
X1井反演解释结果, figureFileSmall=a2d2Iq/OrnzG67rtTXsjoA==, figureFileBig=hA1NGE38UsXD9UPAPZMdnA==, tableContent=null), ArticleFig(id=1322941966475998116, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Table 1, caption=
Basic parameters of horizontal well, figureFileSmall=null, figureFileBig=null, tableContent=
| 储层参数 | 数值 | 井筒参数 | 数值 | 流体物性 | 数值 |
|---|
| 储层深度/m | 3 000 | 水平井长度/m | 1 000 | 原油密度/(kg/m3) | 950 |
| 水平渗透率/10-3 μm2 | 200 | 井筒直径/m | 0.24 | 原油黏度/(mPa·s) | 22 |
| 垂向渗透率/10-3 μm2 | 20 | 套管外径/m | 0.177 8 | 原油热容/[J/(kg·K)] | 2 000 |
| 孔隙度/% | 18 | 套管内径/m | 0.159 4 | 原油膨胀系数/(10-4/K) | 4 |
| 饱和度 | 0.2 | 井壁粗糙度/m | 0.000 1 | 原油体积系数/(m3/m3) | 1.37 |
| 供给半径/m | 500 | 套管导热系数/[W/(m·K)] | 53 | 原油热导率/[W/(m·K)] | 0.14 |
| 地面温度/℃ | 20 | 水泥环导热系数/[W/(m·K)] | 0.933 | 地层水密度/(kg/m3) | 1 001 |
| 地温梯度/(℃/m) | 0.03 | 储层岩石热力学参数/[W/(m·K)] | 2.5 | 地层水黏度/(mPa·s) | 0.14 |
| 储层温度/℃ | 50 | 岩石密度/(kg/m3) | 2 377 | 地层水热容/[J/(kg·K)] | 4 234 |
| 地层压力/MPa | 12 | 岩石热容/[J/(kg·K)] | 845 | 地层水热膨胀系数/(10-4/K) | 2.02 |
| 产层数量 | 10 | 总导热系数/W/(m·K) | 4.46 | 地层水体积系数/(m3/m3) | 1.02 |
), ArticleFig(id=1322941966543106981, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=CN, label=表1, caption=
水平井基础参数
, figureFileSmall=null, figureFileBig=null, tableContent=
| 储层参数 | 数值 | 井筒参数 | 数值 | 流体物性 | 数值 |
|---|
| 储层深度/m | 3 000 | 水平井长度/m | 1 000 | 原油密度/(kg/m3) | 950 |
| 水平渗透率/10-3 μm2 | 200 | 井筒直径/m | 0.24 | 原油黏度/(mPa·s) | 22 |
| 垂向渗透率/10-3 μm2 | 20 | 套管外径/m | 0.177 8 | 原油热容/[J/(kg·K)] | 2 000 |
| 孔隙度/% | 18 | 套管内径/m | 0.159 4 | 原油膨胀系数/(10-4/K) | 4 |
| 饱和度 | 0.2 | 井壁粗糙度/m | 0.000 1 | 原油体积系数/(m3/m3) | 1.37 |
| 供给半径/m | 500 | 套管导热系数/[W/(m·K)] | 53 | 原油热导率/[W/(m·K)] | 0.14 |
| 地面温度/℃ | 20 | 水泥环导热系数/[W/(m·K)] | 0.933 | 地层水密度/(kg/m3) | 1 001 |
| 地温梯度/(℃/m) | 0.03 | 储层岩石热力学参数/[W/(m·K)] | 2.5 | 地层水黏度/(mPa·s) | 0.14 |
| 储层温度/℃ | 50 | 岩石密度/(kg/m3) | 2 377 | 地层水热容/[J/(kg·K)] | 4 234 |
| 地层压力/MPa | 12 | 岩石热容/[J/(kg·K)] | 845 | 地层水热膨胀系数/(10-4/K) | 2.02 |
| 产层数量 | 10 | 总导热系数/W/(m·K) | 4.46 | 地层水体积系数/(m3/m3) | 1.02 |
), ArticleFig(id=1322941966614410150, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Table 2, caption=
Basic parameters of each section of horizontal well, figureFileSmall=null, figureFileBig=null, tableContent=
| 产层序号 | 顶深/m | 底深/m | 渗透率/10-3 μm2 | 孔隙度/% | 含水饱和度 | 平均压力/MPa |
|---|
| 1 | 3 000 | 3 100 | 50 | 12 | 0.2 | 19.7 |
| 2 | 3 100 | 3 200 | 100 | 13 | 0.4 | 19.7 |
| 3 | 3 200 | 3 300 | 500 | 11 | 0.3 | 19.7 |
| 4 | 3 300 | 3 400 | 200 | 13 | 0.3 | 19.7 |
| 5 | 3 400 | 3 500 | 400 | 13 | 0.3 | 19.7 |
| 6 | 3 500 | 3 600 | 1 000 | 13 | 0.3 | 19.7 |
| 7 | 3 600 | 3 700 | 400 | 13 | 0.3 | 19.7 |
| 8 | 3 700 | 3 800 | 800 | 13 | 0.3 | 19.7 |
| 9 | 3 800 | 3 900 | 50 | 13 | 0.3 | 19.7 |
| 10 | 3 900 | 4 000 | 500 | 13 | 0.3 | 19.7 |
), ArticleFig(id=1322941966681519015, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=CN, label=表2, caption=
水平井各层段基础参数
, figureFileSmall=null, figureFileBig=null, tableContent=
| 产层序号 | 顶深/m | 底深/m | 渗透率/10-3 μm2 | 孔隙度/% | 含水饱和度 | 平均压力/MPa |
|---|
| 1 | 3 000 | 3 100 | 50 | 12 | 0.2 | 19.7 |
| 2 | 3 100 | 3 200 | 100 | 13 | 0.4 | 19.7 |
| 3 | 3 200 | 3 300 | 500 | 11 | 0.3 | 19.7 |
| 4 | 3 300 | 3 400 | 200 | 13 | 0.3 | 19.7 |
| 5 | 3 400 | 3 500 | 400 | 13 | 0.3 | 19.7 |
| 6 | 3 500 | 3 600 | 1 000 | 13 | 0.3 | 19.7 |
| 7 | 3 600 | 3 700 | 400 | 13 | 0.3 | 19.7 |
| 8 | 3 700 | 3 800 | 800 | 13 | 0.3 | 19.7 |
| 9 | 3 800 | 3 900 | 50 | 13 | 0.3 | 19.7 |
| 10 | 3 900 | 4 000 | 500 | 13 | 0.3 | 19.7 |
), ArticleFig(id=1322941966748627880, tenantId=1146029695717560320, journalId=1322258508890079423, articleId=1322941955126211398, language=EN, label=Table 3, caption=
Design of factors and their level values for orthogonal experimental analysis, figureFileSmall=null, figureFileBig=null, tableContent=
| 因素名 | Q/(m3/d) | k/10-3 μm2 | Kt/[W/(m·K)] | Fw | ρo/(kg/m3) | Rw/m | Rd/m |
|---|
| 水平1 | 100 | 300 | 3 | 0.1 | 750 | 0.10 | 0 |
| 水平2 | 300 | 400 | 4 | 0.2 | 850 | 0.14 | 1.5 |
| 水平3 | 500 | 500 | 5 | 0.3 | 950 | 0.18 | 2.0 |
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正交试验分析因素及其取值水平设计
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| 因素名 | Q/(m3/d) | k/10-3 μm2 | Kt/[W/(m·K)] | Fw | ρo/(kg/m3) | Rw/m | Rd/m |
|---|
| 水平1 | 100 | 300 | 3 | 0.1 | 750 | 0.10 | 0 |
| 水平2 | 300 | 400 | 4 | 0.2 | 850 | 0.14 | 1.5 |
| 水平3 | 500 | 500 | 5 | 0.3 | 950 | 0.18 | 2.0 |
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Schemes and results of orthogonal experiments, figureFileSmall=null, figureFileBig=null, tableContent=
| 试验编号 | Q | k | Rw | Fw | Kt | ρo | Rd | 平均温度差/℃ |
|---|
| 1 | 水平1 | 水平1 | 水平1 | 水平1 | 水平1 | 水平1 | 水平1 | 2.578 8 |
| 2 | 水平1 | 水平2 | 水平2 | 水平2 | 水平2 | 水平2 | 水平2 | 2.924 0 |
| 3 | 水平1 | 水平3 | 水平3 | 水平3 | 水平3 | 水平3 | 水平3 | 3.159 4 |
| 4 | 水平2 | 水平1 | 水平1 | 水平2 | 水平2 | 水平3 | 水平3 | 3.018 3 |
| 5 | 水平2 | 水平2 | 水平2 | 水平3 | 水平3 | 水平1 | 水平1 | 3.238 0 |
| 6 | 水平2 | 水平3 | 水平3 | 水平1 | 水平1 | 水平2 | 水平2 | 3.959 3 |
| 7 | 水平3 | 水平1 | 水平2 | 水平1 | 水平3 | 水平2 | 水平3 | 3.882 6 |
| 8 | 水平3 | 水平2 | 水平3 | 水平2 | 水平1 | 水平3 | 水平1 | 4.344 7 |
| 9 | 水平3 | 水平3 | 水平1 | 水平3 | 水平2 | 水平1 | 水平2 | 3.395 9 |
| 10 | 水平1 | 水平1 | 水平3 | 水平3 | 水平2 | 水平2 | 水平1 | 2.975 6 |
| 11 | 水平1 | 水平2 | 水平1 | 水平1 | 水平3 | 水平3 | 水平2 | 2.776 2 |
| 12 | 水平1 | 水平3 | 水平2 | 水平2 | 水平1 | 水平1 | 水平3 | 2.923 2 |
| 13 | 水平2 | 水平1 | 水平2 | 水平3 | 水平1 | 水平3 | 水平2 | 3.255 0 |
| 14 | 水平2 | 水平2 | 水平3 | 水平1 | 水平2 | 水平1 | 水平3 | 3.756 9 |
| 15 | 水平2 | 水平3 | 水平1 | 水平2 | 水平3 | 水平2 | 水平1 | 3.181 0 |
| 16 | 水平3 | 水平1 | 水平3 | 水平2 | 水平3 | 水平1 | 水平2 | 4.086 8 |
| 17 | 水平3 | 水平2 | 水平1 | 水平3 | 水平1 | 水平2 | 水平3 | 3.353 8 |
| 18 | 水平3 | 水平3 | 水平2 | 水平1 | 水平2 | 水平3 | 水平1 | 4.199 0 |
| 均值1 | 2.891 | 3.051 | 3.300 | 3.525 | 3.404 | 3.332 | 3.420 | |
| 均值2 | 3.401 | 3.405 | 3.399 | 3.415 | 3.378 | 3.379 | 3.400 | |
| 均值3 | 3.877 | 3.714 | 3.471 | 3.230 | 3.387 | 3.459 | 3.351 | |
| 极差 | 0.986 | 0.663 | 0.199 | 0.295 | 0.025 | 0.127 | 0.101 | |
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正交试验方案及试验结果
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| 试验编号 | Q | k | Rw | Fw | Kt | ρo | Rd | 平均温度差/℃ |
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| 1 | 水平1 | 水平1 | 水平1 | 水平1 | 水平1 | 水平1 | 水平1 | 2.578 8 |
| 2 | 水平1 | 水平2 | 水平2 | 水平2 | 水平2 | 水平2 | 水平2 | 2.924 0 |
| 3 | 水平1 | 水平3 | 水平3 | 水平3 | 水平3 | 水平3 | 水平3 | 3.159 4 |
| 4 | 水平2 | 水平1 | 水平1 | 水平2 | 水平2 | 水平3 | 水平3 | 3.018 3 |
| 5 | 水平2 | 水平2 | 水平2 | 水平3 | 水平3 | 水平1 | 水平1 | 3.238 0 |
| 6 | 水平2 | 水平3 | 水平3 | 水平1 | 水平1 | 水平2 | 水平2 | 3.959 3 |
| 7 | 水平3 | 水平1 | 水平2 | 水平1 | 水平3 | 水平2 | 水平3 | 3.882 6 |
| 8 | 水平3 | 水平2 | 水平3 | 水平2 | 水平1 | 水平3 | 水平1 | 4.344 7 |
| 9 | 水平3 | 水平3 | 水平1 | 水平3 | 水平2 | 水平1 | 水平2 | 3.395 9 |
| 10 | 水平1 | 水平1 | 水平3 | 水平3 | 水平2 | 水平2 | 水平1 | 2.975 6 |
| 11 | 水平1 | 水平2 | 水平1 | 水平1 | 水平3 | 水平3 | 水平2 | 2.776 2 |
| 12 | 水平1 | 水平3 | 水平2 | 水平2 | 水平1 | 水平1 | 水平3 | 2.923 2 |
| 13 | 水平2 | 水平1 | 水平2 | 水平3 | 水平1 | 水平3 | 水平2 | 3.255 0 |
| 14 | 水平2 | 水平2 | 水平3 | 水平1 | 水平2 | 水平1 | 水平3 | 3.756 9 |
| 15 | 水平2 | 水平3 | 水平1 | 水平2 | 水平3 | 水平2 | 水平1 | 3.181 0 |
| 16 | 水平3 | 水平1 | 水平3 | 水平2 | 水平3 | 水平1 | 水平2 | 4.086 8 |
| 17 | 水平3 | 水平2 | 水平1 | 水平3 | 水平1 | 水平2 | 水平3 | 3.353 8 |
| 18 | 水平3 | 水平3 | 水平2 | 水平1 | 水平2 | 水平3 | 水平1 | 4.199 0 |
| 均值1 | 2.891 | 3.051 | 3.300 | 3.525 | 3.404 | 3.332 | 3.420 | |
| 均值2 | 3.401 | 3.405 | 3.399 | 3.415 | 3.378 | 3.379 | 3.400 | |
| 均值3 | 3.877 | 3.714 | 3.471 | 3.230 | 3.387 | 3.459 | 3.351 | |
| 极差 | 0.986 | 0.663 | 0.199 | 0.295 | 0.025 | 0.127 | 0.101 | |
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