地热回灌示踪技术及热储模拟实验研究
|
摘要
在能源与环境形势日趋严峻的今天,清洁的地热资源无疑具有广阔的应用前景。然而,由于开采的严重无序化,造成热储压力和温度降低、资源枯竭等问题,影响了地热资源的永续利用。国内外实践证明,地热回灌是解决问题的首要途径。因此,通过地热回灌试验与数值模拟技术,研究温度场演化与热响应机制,探索热突破时间与地热地质环境的关系,对保护地热资源、确保地热资源的可持续利用、延长地热田的开发利用寿命具有重大的理论和现实意义。
北京城区热田,地处华北平原北部,属于断陷盆地中低温传导型地热系统。本文以北京城区热田122号-123号深层地下热水井为研究对象,在总结北京城区热田的热储分布特征、地热地质、水文地质资料和研究成果的基础上开展模拟试验研究取得如下认识和成果：
二元回灌示踪试验成功取得高质量成果数据,参数求解准确度较高。接收点信号捕获分辨率高,无背景干扰,铝元素浓度峰值曲线线形清晰,可以明确断定示踪剂突破时间68.66h,计算得渗流速度为3.35 m/h。结合抽水试验资料,利用抽水试验三次降深数据构造高斯——塞德尔迭代方程组,编制计算程序求解渗透系数K,反向代入示踪试验实测数据,获取重要参数——高渗性含水层厚度4.81m,由此求算得研究区域热储岩石裂隙率。充分利用示踪试验计算参数服务于热储温度场模拟研究,对采暖中期和末期热储温度场进行模拟分析,发现采暖前期至中期,冷锋面推移始终受阻,与大地热流增温加热和周围热水环境影响有关,后期井间热储资源大量循环开采,冷锋面逐渐向抽水井方向推进,冷热锋面对峙于中轴附近,地温梯度值大,温度等值线分布密集。纵观整个过程,并没有发生热突破现象,但趋势性变化仍为下一步研究指明了方向。
左家庄观测站不同时间尺度范围内水位、水温变化数据表明,热水资源量的补给与自然降水过程密切相关,长期开采地热资源,热储温度显示波动变化,无明显下降趋势。研究区122号——123号地热对系统采用热储法对地下热储资源进行评价,整合计算得可采热水资源量为8.8×106m3,地热资源量为2.73×1010KJ,折合933吨标准煤热量。鉴于系统热储影响范围远远大于计算范围,可采热储量完全满足供暖需求。单纯从热能角度出发在保证热水资源量供给前提下,热储所蕴藏的地热能量再生性强,可长期开采利用。
In the increasingly serious energy and environmental situation of today, no doubt that the clean geothermal resources have broad application prospects. However, because the mining is seriousiy disorder, reservoir pressure and temperature come down and resource depletion affecting the sustainable use of geothermal resources. Proved at home and abroad, geothermal water reinjection is the primary way to solve the problem. Therefore, through the geothermal reinjection experiment and simulation, study the effects heat recharge thermal response mechanism to explore the relationship between thermal breakthrough time and and geothermal geological environment.There will be significant for protection of geothermal resources, sustainable use of geothermal resources and geothermal field to extend the life of the development and utilization.
Geothermal fields in Beijing urban area located in the North China plain. It is classified as rift basin medium-low conduction geothermal system. Taking 122#-123# geothermal double-wells as the research object, Summary Beijing City geothermal field distribution of the thermal storage, geothermal geological, hydrogeological data and other research results.Through reinjection tracer test and numerical simulation techniques, study on the evolution of geothermal reservoir simulation of temperature field.Understanding and results achieved as follows:
From dual tracer test, the results showed that the signal receivers to capture high resolution, no background interference.We could see clear linear concentration curve peak of MO.Tracer breakthrough time can be clearly concluded that 68.66h, calculated flow rate of 3.35 m/h. Combination of pumping test data, the data structure used three descending deep Gauss-Seidel iterative equations.Then computer program solving the permeability coefficient K, reverse generation of measured data into the tracer test,getting the permeability of the aquifer thickness is 4.81m.Full use of tracer test calculation parameters serving temperature field simulation from medium-term to the final phase.The cold front is blocked from prophase to medium-term. In the final phase, mass exploitation of thermal energy storage resources made the cold front gradually advance to the pumping direction and located near the central axis, which is affected by heat flow heating and environmental temperature.Then the geothermal gradient value increases and the temperature contours intensive. Throughout the entire process there is no heat breakthrough phenomenon, but the trend of change still point out the direction of further research.
Geothermal water level and temperature data processing as different time scales showed that thermal water supply quantity is closely related with the natural process of precipitation. Long-term exploitation of geothermal resources, thermal reservoir temperature display fluctuation with no significant downward trend.Geothermal double-well system(122#-123#) using underground thermal energy storage calculation method to evaluate resources.Through Integration calculating,the recoverable amount of hot water is 8.8×106m3 and geothermal resources is 2.73×1010KJ, equivalent to 933 tons of standard coal heat. In view of the fact that the system scope is much larger than thermal energy storage of calculating, recoverable reserves could satisfy heating demand for hot. If providing enough hot water, thermal reservoir energy storage will renew quickly and can be long-term exploited.
北京城区热田,地处华北平原北部,属于断陷盆地中低温传导型地热系统。本文以北京城区热田122号-123号深层地下热水井为研究对象,在总结北京城区热田的热储分布特征、地热地质、水文地质资料和研究成果的基础上开展模拟试验研究取得如下认识和成果：
二元回灌示踪试验成功取得高质量成果数据,参数求解准确度较高。接收点信号捕获分辨率高,无背景干扰,铝元素浓度峰值曲线线形清晰,可以明确断定示踪剂突破时间68.66h,计算得渗流速度为3.35 m/h。结合抽水试验资料,利用抽水试验三次降深数据构造高斯——塞德尔迭代方程组,编制计算程序求解渗透系数K,反向代入示踪试验实测数据,获取重要参数——高渗性含水层厚度4.81m,由此求算得研究区域热储岩石裂隙率。充分利用示踪试验计算参数服务于热储温度场模拟研究,对采暖中期和末期热储温度场进行模拟分析,发现采暖前期至中期,冷锋面推移始终受阻,与大地热流增温加热和周围热水环境影响有关,后期井间热储资源大量循环开采,冷锋面逐渐向抽水井方向推进,冷热锋面对峙于中轴附近,地温梯度值大,温度等值线分布密集。纵观整个过程,并没有发生热突破现象,但趋势性变化仍为下一步研究指明了方向。
左家庄观测站不同时间尺度范围内水位、水温变化数据表明,热水资源量的补给与自然降水过程密切相关,长期开采地热资源,热储温度显示波动变化,无明显下降趋势。研究区122号——123号地热对系统采用热储法对地下热储资源进行评价,整合计算得可采热水资源量为8.8×106m3,地热资源量为2.73×1010KJ,折合933吨标准煤热量。鉴于系统热储影响范围远远大于计算范围,可采热储量完全满足供暖需求。单纯从热能角度出发在保证热水资源量供给前提下,热储所蕴藏的地热能量再生性强,可长期开采利用。
In the increasingly serious energy and environmental situation of today, no doubt that the clean geothermal resources have broad application prospects. However, because the mining is seriousiy disorder, reservoir pressure and temperature come down and resource depletion affecting the sustainable use of geothermal resources. Proved at home and abroad, geothermal water reinjection is the primary way to solve the problem. Therefore, through the geothermal reinjection experiment and simulation, study the effects heat recharge thermal response mechanism to explore the relationship between thermal breakthrough time and and geothermal geological environment.There will be significant for protection of geothermal resources, sustainable use of geothermal resources and geothermal field to extend the life of the development and utilization.
Geothermal fields in Beijing urban area located in the North China plain. It is classified as rift basin medium-low conduction geothermal system. Taking 122#-123# geothermal double-wells as the research object, Summary Beijing City geothermal field distribution of the thermal storage, geothermal geological, hydrogeological data and other research results.Through reinjection tracer test and numerical simulation techniques, study on the evolution of geothermal reservoir simulation of temperature field.Understanding and results achieved as follows:
From dual tracer test, the results showed that the signal receivers to capture high resolution, no background interference.We could see clear linear concentration curve peak of MO.Tracer breakthrough time can be clearly concluded that 68.66h, calculated flow rate of 3.35 m/h. Combination of pumping test data, the data structure used three descending deep Gauss-Seidel iterative equations.Then computer program solving the permeability coefficient K, reverse generation of measured data into the tracer test,getting the permeability of the aquifer thickness is 4.81m.Full use of tracer test calculation parameters serving temperature field simulation from medium-term to the final phase.The cold front is blocked from prophase to medium-term. In the final phase, mass exploitation of thermal energy storage resources made the cold front gradually advance to the pumping direction and located near the central axis, which is affected by heat flow heating and environmental temperature.Then the geothermal gradient value increases and the temperature contours intensive. Throughout the entire process there is no heat breakthrough phenomenon, but the trend of change still point out the direction of further research.
Geothermal water level and temperature data processing as different time scales showed that thermal water supply quantity is closely related with the natural process of precipitation. Long-term exploitation of geothermal resources, thermal reservoir temperature display fluctuation with no significant downward trend.Geothermal double-well system(122#-123#) using underground thermal energy storage calculation method to evaluate resources.Through Integration calculating,the recoverable amount of hot water is 8.8×106m3 and geothermal resources is 2.73×1010KJ, equivalent to 933 tons of standard coal heat. In view of the fact that the system scope is much larger than thermal energy storage of calculating, recoverable reserves could satisfy heating demand for hot. If providing enough hot water, thermal reservoir energy storage will renew quickly and can be long-term exploited.
引文
[1]蔡义汉.地热直接利用.天津：天津大学出版社,2004,23-25.
[2]刘时彬.中国地热资源开发利用现状以及发展趋势分析,北京地热国际研讨会论文集.北京：地质出版社,2002,25-30.
[3]徐军祥.我国地热资源与可持续开发利用.中国人口资源与环境,2005,15(2)：139-140.
[4]李志茂,朱彤.世界地热发电现状,太阳能产业论坛,2007.
[5]北京市水文地质公司,北京市平原区地热普查地质报告,1990,91-92.
[6]孔凡军,李永浮.北京市地热资源开发的时空变化.资源开发与市场,2005(2)：117-118.
[7]陈墨香,汪集,邓孝,等.中国地热资源—分布特点与潜力估算.北京：科学出版社,1994.
[8]郑克梭.地热为北京2008奥运会作贡献：2002北京地热国际研讨会综述[J].水文地质工地质,2003,(2)：109-110.
[9]刘久荣.地热回灌的发展现状,水文地质工程地质,2003,3：100-102.
[10]Liu J,X Pan,Y Yang,et al.Potential assessment of the Urban Geothermal Field,Beijing,China [A].Edited by Liu,l.et al.Proceedings of 2002 Beijing International Geothermal Symposium[C]. Beijing,China:Geological Publishing House,2002,211-2181.
[11]戴文育,北京城区地热形成机理及开采动态研究：[硕士学位论文]北京：中国地质大学(北京),2007.
[12]Axelsson G, O Flovenz,A Hjartarson,et al.A. Arnasson and R. Bodvarsson. Thermal energy extraction by reinjection from the Laugaland geothermal system in N-Iceland [A].Proceedings of the World Geothermal Congress2000 [C].Kyushu Tohoku,Japan:2000,3027-30321.
[13]M J O Sullivan,Geothermal Reservoir Engineering,天津地热研究培训中心教材1988.
[14]Campbell,M.D.,1986.Overview of Well Testing, Testing of Geothermal Well, Geothermal Resources Council Short Course, Palm Springs, CA.
[15]Pruess,K.,Bodvarsson,GS.,1983.Thermal Effects of Reinjection in Geothermal Reservoir with Major Vertical Fractures, Society of Petroleum Engineers 58th Annual Technical Conference, San Francisco, California.
[16]Goyal KP. Injection recovery factors in various areas of the Southeast Geysers,California. Geothermics,1995,24(2):167-186.
[17]Axelsson G, Stefansson V. Reinjection and geothermal reservoir management2associated benefits. Proceedings of the International Workshop on Direct Use of Geothermal Energy,Ljubjana,Slovenia, 1999,21.
[18]Stefansson V. Geothermal reinjection experience [J].Geothermics,1997,26(1):992139.
[19]刘道选,孙启邦等.德国砂岩热储层地热水回灌实验,GEOTHERMAI ENERGY,2009,5.
[20]白铁珊,贡美珍.北京城区热田地下热水弃水回灌试验阶段总结报告[R].北京：北京市水文地质工程地质公司,1984.
[21]陈宗宇.天津市塘沽低温热储回灌的水-岩相互作用地球化学模拟[J].地球科学,1998,23(5)：513-515
[22]王贵玲,刘志明等.西安地热田地热弃水回灌数值模拟研究[J].地球学报,2002,23(2)： 183-186.
[23]潘小平.科学开发中国地热资源,科学开发中国地热资源高层研讨会论文集,2008.
[24]Axelsson G,2003:Simple modelling of geothermal system,UNU G. T. P.,Iceland,unpu-blished lecture notes.
[25]Fuchinp H.Status of geothermal power generation in Japan [A] Proceedings of the world geothermal Congress 2000[C].Kyushu Tohoku,Japan:2000,193198.
[26]曾梅香.同位素示踪技术在地热对井回灌系统中的运用,全国地热产业可持续发展学术研讨会论文集,2005.
[27]D.P. Bullivant,M. J. O'Sullivan. Travel-time analysis of tracer tests in two geothermal fields [J]. Transport in Porous Media.1991,3:241-259.
[28]D. P. Bullivant,M. J. O'Sullivan. Calculation of tracer travel times in fractured geothermal reservoirs [J].Transport in Porous Media.1991,3:261-280.
[29]张远东,魏加华.冰岛Laugaland地热田示踪试验与回灌温度模拟,中国科学院研究生院学报[J],2005,22(6)：761-765.
[30]孙宝成,曾梅香等.天津地热对井回灌系统中的同位素示踪技术,地质调查与研究[J],2005,28(3)：187-191.
[31]Bear J.1972.Dynamics of Fluids in Porous Media.American Elsevier Publishing Company,Inc.
[32]周训,陈明佑等.地下热水运移数学模型简介,地质科技情报[J],2002,21(1)：47-49.
[33]陈墨香,张菊明等.井口水温与热储层温度关系的有限元模拟及实例剖析,地质科学[J],1992,1：55-58.
[34]薛禹群,谢春红等.三维非稳定流含水层储能的数值模拟研究,地质评论[J],1994,40(1)：74-80.
[35]薛传东,刘星等.昆明市地热田越流含水系统中地下热水的数值模拟,地球科学进展[J].2003,18(6)：9.
[36]林黎.天津地区雾迷山组热储地下热水资源可持续开发利用研究：[博士学位论文],北京：中国地质大学(北京),2006.
[37]樊秀峰,吴振祥等.福州温泉区地下热水有限元数值模拟研究,福州大学学报[J],200533(2)：226-229.
[38]RECENT STUDY ON GEOTHERMAL RESOURCESASSESSMENT IN JAPAN,1981,GEOLOGICAL SURVEY OF JAPAN,NEW ENERGY DEVELOPMENT OGARNIZATION.
[39]Renner,J.L.,White,D.E.and Williams,D.L.:Hydrothermal convection systems,In Assessment of Geothermal Resources of the United States,5-57,1975.
[40]颜英军.蒙特卡罗法在中国典型地热资源评价中的应用：[硕士学位论文],北京：中国地质大学(北京)，2009.
[41]柳志国,徐魏,郑克棪.北京市小汤山地热田地热资源评价报告,北京：北京市地质工程勘察院地热工程研究所,2005.
[42]施尚明,朱焕来等.沉积盆地型地热水资源定量评价体系的建立及应用[J],大庆石油学院学报,2004,28(5)：4-9
[43]于湲,北京城区地热田地下热水的水化学及同位素研究：[硕士学位论文],北京：中国地质大学(北京),2006.
[44]朱家玲,张启.天津静海团泊风景区地下热水资源评价数值模拟[J].太阳能学报,1996,17(4)：336-343.
[45]北京城区地下热水勘探年度报告,北京市水文一大队,1974.
[46]吕金波,车用太等.京北地区热水水文地球化学特征与热系统的成因模式[J],地震地质,2006,28(3)：419-428.
[47]颜世强,潘懋,邹祖光等.山东德州凹陷地下热水地球化学特征及成因[J].中国地质,2007,34(1)：150-151.
[48]贾秀梅,刘满杰等.万家寨水库右岸岩溶渗漏试验研究[J].地质学报,2005,26(2)：179-182.
[49]薛禹群.地下水动力学原理[M].地质出版社,1986.
[50]龙熙华等.数值分析[M].陕西省科学技术出版社,2000.
[51]张凤娥.北京、天津低温热田对井开发效应的预测研究：[硕士学位论文],北京：中国地质科学院,1992.
[52]FEFLOW5.1 user's manual. WASY Software.
[53]周训,深层地下热水运移的三维数值模拟[M],地质出版社,2001.
[54]Bear,J,Hydraulics of Groundwater.McGraw-Hill.INC.,New York,1979.
[55]肖占山.注水井井下温度场数值模拟：[硕士学位论文],大庆石油学院,2002.
[56]孙颖,刘久荣等.北京市地热资源开发利用状况[J],安徽农业科学,2009,37(16)：7564-7566.
[57]北京市国土资源局.北京市地热资源可持续利用规划(2006-2020)[Z].2006：16.
[58]车用太,刘喜兰等.首都圈地区井水温度的动态类型及其成因分析[J],地震地质,2003,25(3)：403-418.①地热资源地质勘查规范
[2]刘时彬.中国地热资源开发利用现状以及发展趋势分析,北京地热国际研讨会论文集.北京：地质出版社,2002,25-30.
[3]徐军祥.我国地热资源与可持续开发利用.中国人口资源与环境,2005,15(2)：139-140.
[4]李志茂,朱彤.世界地热发电现状,太阳能产业论坛,2007.
[5]北京市水文地质公司,北京市平原区地热普查地质报告,1990,91-92.
[6]孔凡军,李永浮.北京市地热资源开发的时空变化.资源开发与市场,2005(2)：117-118.
[7]陈墨香,汪集,邓孝,等.中国地热资源—分布特点与潜力估算.北京：科学出版社,1994.
[8]郑克梭.地热为北京2008奥运会作贡献：2002北京地热国际研讨会综述[J].水文地质工地质,2003,(2)：109-110.
[9]刘久荣.地热回灌的发展现状,水文地质工程地质,2003,3：100-102.
[10]Liu J,X Pan,Y Yang,et al.Potential assessment of the Urban Geothermal Field,Beijing,China [A].Edited by Liu,l.et al.Proceedings of 2002 Beijing International Geothermal Symposium[C]. Beijing,China:Geological Publishing House,2002,211-2181.
[11]戴文育,北京城区地热形成机理及开采动态研究：[硕士学位论文]北京：中国地质大学(北京),2007.
[12]Axelsson G, O Flovenz,A Hjartarson,et al.A. Arnasson and R. Bodvarsson. Thermal energy extraction by reinjection from the Laugaland geothermal system in N-Iceland [A].Proceedings of the World Geothermal Congress2000 [C].Kyushu Tohoku,Japan:2000,3027-30321.
[13]M J O Sullivan,Geothermal Reservoir Engineering,天津地热研究培训中心教材1988.
[14]Campbell,M.D.,1986.Overview of Well Testing, Testing of Geothermal Well, Geothermal Resources Council Short Course, Palm Springs, CA.
[15]Pruess,K.,Bodvarsson,GS.,1983.Thermal Effects of Reinjection in Geothermal Reservoir with Major Vertical Fractures, Society of Petroleum Engineers 58th Annual Technical Conference, San Francisco, California.
[16]Goyal KP. Injection recovery factors in various areas of the Southeast Geysers,California. Geothermics,1995,24(2):167-186.
[17]Axelsson G, Stefansson V. Reinjection and geothermal reservoir management2associated benefits. Proceedings of the International Workshop on Direct Use of Geothermal Energy,Ljubjana,Slovenia, 1999,21.
[18]Stefansson V. Geothermal reinjection experience [J].Geothermics,1997,26(1):992139.
[19]刘道选,孙启邦等.德国砂岩热储层地热水回灌实验,GEOTHERMAI ENERGY,2009,5.
[20]白铁珊,贡美珍.北京城区热田地下热水弃水回灌试验阶段总结报告[R].北京：北京市水文地质工程地质公司,1984.
[21]陈宗宇.天津市塘沽低温热储回灌的水-岩相互作用地球化学模拟[J].地球科学,1998,23(5)：513-515
[22]王贵玲,刘志明等.西安地热田地热弃水回灌数值模拟研究[J].地球学报,2002,23(2)： 183-186.
[23]潘小平.科学开发中国地热资源,科学开发中国地热资源高层研讨会论文集,2008.
[24]Axelsson G,2003:Simple modelling of geothermal system,UNU G. T. P.,Iceland,unpu-blished lecture notes.
[25]Fuchinp H.Status of geothermal power generation in Japan [A] Proceedings of the world geothermal Congress 2000[C].Kyushu Tohoku,Japan:2000,193198.
[26]曾梅香.同位素示踪技术在地热对井回灌系统中的运用,全国地热产业可持续发展学术研讨会论文集,2005.
[27]D.P. Bullivant,M. J. O'Sullivan. Travel-time analysis of tracer tests in two geothermal fields [J]. Transport in Porous Media.1991,3:241-259.
[28]D. P. Bullivant,M. J. O'Sullivan. Calculation of tracer travel times in fractured geothermal reservoirs [J].Transport in Porous Media.1991,3:261-280.
[29]张远东,魏加华.冰岛Laugaland地热田示踪试验与回灌温度模拟,中国科学院研究生院学报[J],2005,22(6)：761-765.
[30]孙宝成,曾梅香等.天津地热对井回灌系统中的同位素示踪技术,地质调查与研究[J],2005,28(3)：187-191.
[31]Bear J.1972.Dynamics of Fluids in Porous Media.American Elsevier Publishing Company,Inc.
[32]周训,陈明佑等.地下热水运移数学模型简介,地质科技情报[J],2002,21(1)：47-49.
[33]陈墨香,张菊明等.井口水温与热储层温度关系的有限元模拟及实例剖析,地质科学[J],1992,1：55-58.
[34]薛禹群,谢春红等.三维非稳定流含水层储能的数值模拟研究,地质评论[J],1994,40(1)：74-80.
[35]薛传东,刘星等.昆明市地热田越流含水系统中地下热水的数值模拟,地球科学进展[J].2003,18(6)：9.
[36]林黎.天津地区雾迷山组热储地下热水资源可持续开发利用研究：[博士学位论文],北京：中国地质大学(北京),2006.
[37]樊秀峰,吴振祥等.福州温泉区地下热水有限元数值模拟研究,福州大学学报[J],200533(2)：226-229.
[38]RECENT STUDY ON GEOTHERMAL RESOURCESASSESSMENT IN JAPAN,1981,GEOLOGICAL SURVEY OF JAPAN,NEW ENERGY DEVELOPMENT OGARNIZATION.
[39]Renner,J.L.,White,D.E.and Williams,D.L.:Hydrothermal convection systems,In Assessment of Geothermal Resources of the United States,5-57,1975.
[40]颜英军.蒙特卡罗法在中国典型地热资源评价中的应用：[硕士学位论文],北京：中国地质大学(北京)，2009.
[41]柳志国,徐魏,郑克棪.北京市小汤山地热田地热资源评价报告,北京：北京市地质工程勘察院地热工程研究所,2005.
[42]施尚明,朱焕来等.沉积盆地型地热水资源定量评价体系的建立及应用[J],大庆石油学院学报,2004,28(5)：4-9
[43]于湲,北京城区地热田地下热水的水化学及同位素研究：[硕士学位论文],北京：中国地质大学(北京),2006.
[44]朱家玲,张启.天津静海团泊风景区地下热水资源评价数值模拟[J].太阳能学报,1996,17(4)：336-343.
[45]北京城区地下热水勘探年度报告,北京市水文一大队,1974.
[46]吕金波,车用太等.京北地区热水水文地球化学特征与热系统的成因模式[J],地震地质,2006,28(3)：419-428.
[47]颜世强,潘懋,邹祖光等.山东德州凹陷地下热水地球化学特征及成因[J].中国地质,2007,34(1)：150-151.
[48]贾秀梅,刘满杰等.万家寨水库右岸岩溶渗漏试验研究[J].地质学报,2005,26(2)：179-182.
[49]薛禹群.地下水动力学原理[M].地质出版社,1986.
[50]龙熙华等.数值分析[M].陕西省科学技术出版社,2000.
[51]张凤娥.北京、天津低温热田对井开发效应的预测研究：[硕士学位论文],北京：中国地质科学院,1992.
[52]FEFLOW5.1 user's manual. WASY Software.
[53]周训,深层地下热水运移的三维数值模拟[M],地质出版社,2001.
[54]Bear,J,Hydraulics of Groundwater.McGraw-Hill.INC.,New York,1979.
[55]肖占山.注水井井下温度场数值模拟：[硕士学位论文],大庆石油学院,2002.
[56]孙颖,刘久荣等.北京市地热资源开发利用状况[J],安徽农业科学,2009,37(16)：7564-7566.
[57]北京市国土资源局.北京市地热资源可持续利用规划(2006-2020)[Z].2006：16.
[58]车用太,刘喜兰等.首都圈地区井水温度的动态类型及其成因分析[J],地震地质,2003,25(3)：403-418.①地热资源地质勘查规范