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摘要:
以页岩油气为代表的低品位油气资源勘探与开发不断取得重大突破，已经成为中国重要的接替性资源。开展页岩气渗流机理和数值模拟模型研究有助于实现页岩气藏开发的动态变化过程，为认识页岩气渗流规律、优化数学模型、产能评价和预测奠定技术基础。围绕页岩气多尺度多流态多重介质下的运移机理，系统地阐述了页岩气数值模拟模型的研究进展，页岩气数值模拟模型可分为等效连续介质模型、离散裂缝网络模型和混合模型，总结了这3类数值模拟模型的优缺点。等效连续介质模型原理简单，追求宏观尺度的等效，忽略了储层内部真实流态，适用于裂缝发育程度低的均质页岩气藏；离散裂缝网络模型准确反映复杂裂缝网络的渗流特征，可以描述高度离散裂缝的形态规律，适用于勘探程度高且裂缝高度发育的页岩气藏；混合模拟模型结合两者的优点，能够准确反映复杂裂缝网络和流体运移规律，在满足计算精度的同时又节约了大量的计算资源，随着计算处理能力的增强，混合模拟模型是今后的发展趋势。最后分析了页岩气藏数值模拟模型中存在的问题，并指出了发展方向。
Abstract:The exploration and development of low grade oil and gas resources which have become important alternative resources in China have made great breakthrough. Research on numerical simulation of shale gas is helpful to realizing the dynamic process of shale gas development, laying a technical foundation for understanding seepage law of shale gas, optimizing mathematical model and evaluating as well as predicting productivity. Based on intensive investigation of literature from China and abroad, this paper systematically expounds the research progress of numerical simulation methods of shale gas and summarizes advantages and disadvantages of these methods. Shale gas numerical simulation models can be divided into equivalent continuous medium model, discrete fracture network model and mixed simulation model. The equivalent continuum model is simple in principle, pursues the macroscopic equivalent, neglects the true flow mechanism inside the reservoir, and is hence suitable for homogeneous shale gas reservoirs with low development of fractures. The discrete fracture network model accurately can reflect the porous flow characteristics of complex fracture networks and describe the objective regularity of highly discrete fractures and is hence suitable for shale gas reservoirs with completed exploration and high fracture development. The mixed simulation model combines the advantages of these two models to accurately reflect the complex fracture network and fluid migration law, meet the calculation accuracy, and save a lot of computing resources. With the improvement of computing and processing capabilities, the mixed simulation model is the future development trend. Finally, various problems in the numerical simulation model of shale gas reservoir are analyzed, and the development trends of shale gas numerical simulation are pointed out.
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1. 引言
在资源枯竭、经济发展和环境保护的三重压力下，寻找并开发利用新型清洁能源是关系国计民生和社会可持续发展的紧迫任务。推动绿色发展，构建清洁、安全、高效的能源体系已成为时代的要求。地热资源作为清洁能源的重要组成部分被寄予厚望。
天津市地热资源条件优越，地热开发利用水平一直处于全国前列。天津地热勘查研究工作开始于20世纪70年代，李四光同志主导的天津地热会战掀起了全国地热勘查研究的第一个春天，并发现了新近系和奥陶系两个热储。80年代以来，在市政府和原地矿部的支持以及联合国开发计划署的援助下，地热勘查开始向深部基岩热储发展，先后完成王兰庄、山岭子、塘沽地区三个地热田的勘查工作。自此之后，天津的地热研究与开发工作一直处于中国前列。先后发现地热田8个，已发现两大类6个热储，即孔隙型热储(新近系明化镇组、馆陶组热储和古近系东营组)和裂隙溶隙型热储(奥陶系、寒武系和蓟县系雾迷山组三、四段热储)，3000 m以浅年可开采地热流体为7606×104 m3。其中，蓟县系雾迷山组三、四段热储是天津地热开发的主力储层。随着开发强度不断增大，部分地区开采潜力已达极限(天津地热勘查开发设计院, 2000；Wang, 2008；王继革等，2013)。
随着钻探技术的不断进步和清洁能源需求的持续增长，向地球深部进军，探测深部地热资源、开辟深部热储第二空间、增加可开采资源量，成为保障天津地区地热可持续开发的有效途径之一。为此，2017年以来，中国地质调查局在天津东丽湖地区部署了深部地热探测工作，并在主力储层下部探获雾迷山组二段高产能新储层。本文主要介绍天津东丽湖深部岩溶热储探测和高产能地热井参数研究取得的新成果、新进展。
2. 研究区概况
2.1 地热地质背景
天津市地处Ⅰ级构造单元华北地台北缘，以宁河—宝坻断裂为界分为北部山区和南部平原区。其中，南部平原区属Ⅱ级构造单元华北断坳区，是中、新生代断陷、坳陷盆地。区内Ⅲ级构造单元包括一隆两坳即沧县隆起、冀中坳陷和黄骅坳陷。隆起和坳陷及其间分布的诸多Ⅳ级构造单元凸起、凹陷的延伸方向和较大断裂的走向均呈北北东(NNE)向，形成雁行式相间排列的构造格局(陈墨香, 1988)(图 1)。
宝坻—宁河断裂以南为天津南部平原区，总面积8700 km2，地热资源条件优越。发育有王兰庄、山岭子、滨海、武清、潘庄—芦台、宁河—汉沽、万家码头和周良庄等8个地热田，年可开采地热流体7606×104 m3(图 2)。各地热田均位于华北断坳范围内，地面均为第四系松散沉积物覆盖，厚度可达数百米。其下是巨厚的新生界陆相碎屑岩沉积，是一套半胶结的砂岩和泥岩地层，沉积厚度在沧县隆起相对较薄，在冀中坳陷和黄骅坳陷沉积较厚，最大厚度可达近万米。在新生界的巨大不整合覆盖之下，主要是古生界和中上元古界的基底地层，在坳陷中还有局部中生界分布。区内地热资源主要赋存于两大类6个储层中：一类为孔隙型热储，包括新近系明化镇组、馆陶组和古近系东营组热储；一类为裂隙溶隙型热储，包括奥陶系、寒武系和蓟县系雾迷山组热储(张百鸣等, 2006; Wang, 2008)(图 3)。
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图 3 天津市地热田主要热储及储盖结构Figure 3. The vertical structure of geothermal reservoirs in Tianjin东丽湖地区位于天津市东部，隶属于天津市东丽区，位于Ⅳ级构造单元潘庄凸起上，发育有著名的山岭子地热田。依据研究区内地热井的钻探资料，揭露的地层从新到老为：新生界(第四系和新近系)、古生界(奥陶系和寒武系)、中新元古界(青白口系和蓟县系)(表 1)。区内已发现新近系明化镇组、新近系馆陶组、奥陶系和蓟县系雾迷山组三、四段4个热储。其中，雾迷山组三、四段为当前主力储层，沧县隆起上钻孔揭露顶板埋深为1752~2016 m，揭露厚度为480~1032 m，单井出水量为70~120 m3/h，最大可达204 m3/h，出水温度为88~102℃，孔隙度1%~5.8%，渗透率5.52×10-14 m2，水化学类型为Cl · HCO3·SO4-Na或Cl·SO4·HCO3-Na型，总矿化度为1670~2200 mg/L，总硬度为120~240 mg/L(以CaCO3计)，pH值为7.3~8.4(林黎等, 2007; 王继革等, 2013)。从区域地质资料看(高昌，2003；赵苏民等, 2006)，区内雾迷山组厚度约3500 m，岩石组合为一套富镁碳酸盐岩，岩性主要为白云岩。燧石条带白云岩、硅质白云岩夹2~5层棕红、紫红色泥岩和页岩，可作为雾迷山组三、四段和一、二段的分界线。从岩性组合的相似性可以推测，雾迷山组一、二段可作为未来深部热储探测的重要方向，也是本次研究的重点。
表 1 天津东丽湖地区综合地层简表Table 1. The simplified table of geological strata in Donglihu area, Tianjin
2.2 开发利用现状
天津地热资源开发利用水平在全国居于较高地位，也是全国中低温地热直接利用规模最大的城市，是全国第一批“中国温泉之都”。自20世纪30年代以来，经过80多年的发展，天津地热资源开发利用从浅到深、从无序到有序、从粗放到精细，逐渐形成了规模化、产业化，在中国地热勘查开发利用史上具有举足轻重的作用。截至2017年，天津市共有地热开采井466眼，年开采总量为5181.08×104 m3，其中，蓟县系雾迷山组三、四段约占开采总量的54%。地热资源主要应用于供暖、洗浴、理疗、旅游、养殖等。其中，供暖是最主要的利用方式，占年总开采量的81.5%。建有地热供暖小区及公建项目496个，全市地热供暖总面积达3500×104 m2，占全市集中供暖面积的8%，是中国利用水热型地热资源供暖规模最大的城市。
东丽湖地区现有地热井34眼。其中，新近系明化镇组4眼，新近系馆陶组2眼，奥陶系3眼，蓟县系雾迷山组三、四段25眼。年开采地热流体约395.44×104 m3，采用梯级、综合利用和群井联动回灌的开发模式，达到资源的优化配置和实时调控，地热利用率和回灌率达到95%以上，实现了资源的统一规划、统一开发和统一管理。地热资源广泛应用于供暖、温泉洗浴、养生理疗、康乐旅游、矿泉水开发等领域，建有东丽湖温泉旅游度假区，在发展温泉旅游产业，促进地区经济发展，保护生态环境方面取得了显著的成效。2008年12月25日和2011年12月30日，分别被中国矿业联合会和国土资源部命名为“中国温泉之乡”。
3. 深部热储探测方法
本次研究主要基于地质综合分析，采用地球物理探测、地热钻探、地球物理测井和热储试验相结合的方法开展探测研究。
3.1 地球物理探测
为满足深部储层探测需要，本次地球物理探测的主要目标确定为5 km以浅地层的结构探测，为地热钻探提供依据。由于探测深度大，且存在高压线、铁路等城市干扰源，本次地球物理探测采用了二维地震和时频电磁相结合的勘查方法，其中，时频电磁方法首次应用到地热勘查领域。时频电磁方法是通过大功率人工场源激发信号，测量研究区测线的电磁场分量，分析频率域信号的振幅和相位特征，来获得介质的地电参数(电阻率和极化率)，把信号转换到时间域，建立高分辨的电法勘探的时间断面。较传统电磁方法，在应对强电磁干扰方面具有一定的优势(Dong et al., 2008; 周印明等, 2013, 2015)。
本次工作部署时频电磁法完成测线4条，剖面24.4 km，点距200 m，物理点128个；二维地震完成剖面3条，8.25 km，测点254个(图 4)。
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图 4 二维地震与时频电磁法工作部署图Figure 4. Location of seismic and time-frequency electromagnetic survey sections地球物理探测结果初步揭示了天津东丽湖地区雾迷山组二段的分布。从TFEM-1测线地质剖面解译图(图 5)可以看出，F1沧东断裂西侧，电阻率异常特征从上至下依次为“低—高—低—高—次高—高”，表层低阻和浅层高、低阻分别是第四系、新近系明化镇组与馆陶组地层响应特征，电阻率过渡连续，无明显的错断。第二套高阻层为寒武系(Є) 与青白口系(Qb)的反映，深部的次高阻为蓟县系雾迷山组4段(Jxw4)的反映，深部的高阻为蓟县系雾迷山组2、3段(Jxw2-3)的反映。蓟县系雾迷山组四段埋深2300~3000 m，下部发育雾迷山组二段和三段地层，埋深在3000 m以下。因缺乏雾迷山组二、三段电性参数，不易进一步细分。从二维地震DZ01剖面解释图(图 6)可以看出，区内4000 m以浅揭示的地层分别为第四系、新近系明化镇组、新近系馆陶组、寒武系、青白口系和蓟县系雾迷山组。新近系馆陶组底界以上主要标准反射界面清晰可辨，以下反射界面呈断续分布。推测第四系底界埋深341~363 m；新近系明化镇组底界埋深1123~1160 m，馆陶组底界埋深1347~1500 m；寒武系张夏组底界埋深1758~2033 m，馒头组底界埋深1786~2113 m，昌平组底界埋深1856~2164 m；青白口系底界埋深2196~2444 m；蓟县系雾迷山组四段底界埋深2802~3004 m，三段底界二段顶界埋深3552~3726 m。4000 m探测深度范围内未揭示蓟县系雾迷山组底界。
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图 5 TFEM 1测线时频电磁二维反演电阻率剖面图Figure 5. Time-frequency electromagnetic method profile in the line TFEM 13.2 地热科学钻探
在天津东丽湖部署地热科学钻探CGSD-01井，目标层位为蓟县系雾迷山组二段。2017年11月20日开钻，2018年11月19日完钻。成井深度4051.68 m，3715 m进入雾迷山组二段储层，是当时天津最深的地热井。
该井井身结构为三开直井。其中，护壁段(0~76 m)采用Ф660.4 mm冲击钻钻头施工，下入Ф508 mm×8.0 mm无缝套管，总长度为74.42 m。一开井段(76~1469.53 m)采用Ф444.5 mm牙轮钻头钻进，入Ф339.7 mm×J55钢级套管，长度1469.84 m。二开井段(1469.53~2262.75 m)采用Ф311.2 mm牙轮钻头钻进，下入Ф244.5 mm×10.03 mm N80钢级套管，长度866.60 m，与一开套管重叠68.12 m。三开井段(2262.75~4051.68 m)采用Ф215.9 mm牙轮钻头钻进，下入Ф177.8 mm×9.19 mm N80钢级套管，长度1939.96 m，其中实管长度为1747.23 m，花管长度为192.73 m，与二开套管重叠151.03 m。钻进过程中，开展了岩屑和岩心采集工作。1500 m以浅每5 m捞取岩屑一次，1500 m以深每2 m捞取岩屑一次，全井共计捞取岩屑样1873个。500~4051.68 m井段采取定深分段采取岩心，累计取心37回次，进尺161.25 m，长度140.78 m，采取率85%。
3.3 地球物理测井
钻井过程中，对地热井开展了综合地球物理测井工作，主要包括温度测井、压力测井、井径测井、井斜测井、视电阻率测井、双感应测井、自然电位测井、自然伽马测井、声波测井、伽马-伽马测井和流体流量测井11项。
3.4 热储试验
钻探完成后，为获取蓟县系雾迷山组二段新储层热储参数，对地热井开展了3个落程的稳定流降压抽水试验。其中，大落程试验历时62 h，涌水量130.2 m3/h，水温度稳定在100℃，稳定时间39.5 h；中落程试验历时24 h，涌水量94.5 m3/h，水温度稳定在100℃，稳定时间16.5 h；小落程试验历时16 h，涌水量43.9 m3/h，水温度稳定在98℃，稳定时间8 h(图 7)。
4. 结果与讨论
4.1 热储结构特征
综合全井段地球物理测井、岩心与岩屑及区域地热地质等资料，CGSD-01井钻遇地层包括：第四系、新近系、寒武系、青白口系及蓟县系。钻遇主要储层5个，主要包括新近系明化镇组、馆陶组2个砂岩热储，寒武系昌平组灰岩热储，蓟县系雾迷山组三四段和一二段白云岩热储(表 2)。
表 2 天津东丽湖CGSD-01井钻遇地层表Table 2. Geological stratum of well CGSD-01 in the Tianjin
本次研究在地热井中实现雾迷山组四、三、二段精细划分，自上而下叙述如下。
雾迷山组四段(Jxw4)：深度段为2258~2896 m，地层厚度638 m。上部岩性主要为浅灰色细晶白云岩夹灰黑色泥晶白云岩，偶见少量深灰色厚层角砾状白云岩、灰白色硅质白云岩等；下部岩性主要为浅灰色细晶白云岩与灰黑色泥晶白云岩、泥质白云岩交互；底部主要发育灰黑色白云质泥岩夹细晶白云岩、泥晶白云岩、硅质白云岩。受原始沉积及沉积后多期次构造与岩溶作用等影响，雾迷山组四段白云岩层系整体较破碎，钻井岩心中裂隙和溶蚀孔洞极其发育，为地热水提供了良好的储集空间。
雾迷山组三段(Jxw3)：深度段为2896~3715 m，地层厚度819 m。上部岩性主要为深灰色细晶白云岩与灰黑色泥晶白云岩、泥质白云岩、白云质泥岩交互。电测曲线上，雾迷山组三段上部的GR值较雾迷山组四段底部低为特征，测井解释的泥质含量值也表现出类似特征；雾迷山组三段测井资料解释的孔隙度和渗透率值，下部整体较上部好(图 8)；下部岩性主要发育浅灰—灰黑色细晶白云岩夹灰黑色泥晶—泥质白云岩、灰质泥晶白云岩及白云质泥岩；底部以发育一套紫红色泥质白云岩夹浅灰色细晶白云岩为典型特征，厚度约73 m，裂隙不发育，具有隔水—弱透水性质，作为与下伏雾迷山组二段的分界。
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图 8 CGSD-01井蓟县系雾迷山组柱状图Figure 8. Comprehensive strata log diagram of well CGSD-01 in Wumishan Formation, Jixian Group雾迷山组二段(Jxw2)深度段为3715~4051 m，地层厚度336 m，未钻穿。与上覆雾迷山组三段相比，雾迷山组二段的岩性及电测特征存在明显的差别(图 8)。岩性特征上，雾迷山组二段上部主要发育浅灰色细晶白云岩夹浅灰色粉晶白云岩、灰黑色泥质白云岩，之上为雾迷山组三段底部紫红色泥质白云岩作为两者明显分界；雾迷山组二段下部主要为浅灰色粉晶白云岩与灰黑色泥质白云岩交互。电测曲线上，雾迷山组二段上部的GR值、自然电位值(SP)较雾迷山组三段底部低为特征，测井解释的泥质含量值也体现出类似特征；雾迷山组二段上部的深侧向、浅侧向电阻率较雾迷山组三段底部高为特征。雾迷山组二段内部，自下而上，GR值、自然电位值(SP)、深侧向电阻率、浅侧向电阻率及测井解释的泥质含量呈逐渐变小趋势；声波时差呈逐渐变大趋势，测井资料解释的孔隙度和渗透率呈逐渐变大趋势，指示雾迷山组二段上部的热储层较下部更为发育。
4.2 温度特征
2018年11月19日对CGSD-01井开展了稳态测温。从测温曲线(图 9)可以看出，CGSD-01井底温度105℃。井温总体呈凸型曲线特征，体现了储盖层热传导机制为总体传导型、层间对流型。总体地温梯度2.4℃/100 m。其中，0~400 m第四纪地层地温梯度最高，可达8℃/100 m；400~2300 m新近系与寒武系盖层地温梯度次之，为2.4℃/100 m；2300~3500 m雾迷山组三、四段主力储层受对流作用影响，地温梯度最小，为0.83℃/100 m；3500 m以下雾迷山组二段储层地温梯度为1.7℃/100 m，对流作用较主力储层稍弱。
岩石热物性分析表明，雾迷山组二段岩石热导率在4.33~7.96 W/(m · K)(10个样品，表 3)，平均值5.66 W/(m·K)，略高于雾迷山组三四段平均值4.37 W/(m·K)。
表 3 CGSD-01井雾迷山组二段热储热导率测试值Table 3. Thermal conductivity test results of Wumishan Formation section 2 in well CGSD-01
4.3 热储参数
热储参数计算主要依据降压抽水试验计算。由于地热水密度与温度具有相关性，造成观测水位不能真实地反映地热井实际水位的变化，这种现象称之为“井筒效应”。资料整理过程中，以储层中部温度102.6℃作为储层温度对试验观测数据进行校准。校正后，做出的动水位埋深曲线如图 10。
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图 10 校正至热储温度降压抽水试验历时曲线Figure 10. Corrected duration curve of stable pumping test with reservoir temperature采用Dupuit公式与W.Sihart公式对试验数据进行分析计算CGSD-01井的热储参数。本次抽水试验目标热储层为蓟县系雾迷山组二段，厚度336.68 m(未穿透)，根据测井数据显示，裂隙厚度为123.1 m。根据降压抽水试验数据及相关校正，地热井基本参数见表 4。计算结果见表 5。依据降压抽水试验计算结果，取三个落程试验平均值可以得出，CGSD-01井单位涌水量1.53 m3/h · m，渗透系数0.40 m/d，导水系数48.69 m2/d。
表 4 CGSD-01井热储参数计算基本参数Table 4. Reservoir parameters of well CGSD-01
表 5 CGSD-01井地热热储参数计算结果Table 5. Interpretation results of pumping test for well CGSD-01
4.4 水化学特征
抽水试验过程中，采集样品对雾迷山组二段地热水进行了水化学、同位素和气体成分分析。
水化学分析表明，雾迷山组二段地热水水化学类型为Cl · SO4 · HCO3-Na型，矿化度1770.0 mg/L，总硬度124.6 mg/L(以CaCO3计)，pH值7.63。
结垢性和腐蚀性表明，地热水不生成碳酸钙垢，不生成硫酸钙垢，不生成硅酸盐垢，对管道及利用设施具有中等腐蚀性。
气体组分测试表明，溶解气体中以氮气和甲烷为主，分别占气体组分含量的66%和27%，还有少量乙烷、丙烷、异丁烷和异戊烷，指示储层处于还原环境。
同位素分析表明，地热水δD为-72‰~-72.7‰，δ18O为9.3‰~-9.5‰，δ13C为-3‰~-3.6‰，87Sr/86Sr为0.7113~0.7114。综合水化学和同位素特征，初步推断雾迷山组二段地热水来源于大气降水，主要发生混合、阳离子交替吸附、碳酸盐岩溶解、硫酸盐还原等作用，且未达到平衡。
4.5 开发利用潜力分析与建议
从区域地质背景和地层沉积序列看，雾迷山二段热储在潘庄凸起区全区均有分布，分布面积约604 km2，依据CGSD-01地热参数井信息，对潘庄凸起雾迷山组二段热储热量进行保守估算。年可开采热资源量按照100 a富水段可回收热量的0.01% 进行保守估算，其热量每年折合标煤250万t，初步估计可满足供暖面积6114×104 m2。
为了提高地热资源利用率，本文建议推广地热利用集约节约新技术，采用地热梯级利用联合水源热泵、地板辐射采暖、群井联动、地热与燃气或太阳能等多能源结合技术，降低尾水排放温度，实现地热资源利用最大化。
5. 结论
(1) 综合全井段地球物理测井、岩心与岩屑及区域地热地质等资料，CGSD-01井钻遇主要储层5个，主要包括新近系明化镇组、馆陶组2个砂岩热储，寒武系昌平组灰岩热储，蓟县系雾迷山组三四段和一二段白云岩热储。
(2) 雾迷山组二段上部单位涌水量1.53 m3/h · m，渗透系数0.40 m/d，导水系数48.69 m2/d，岩石热导率5.66 W/(m · K)，地热水类型为Cl · SO4 · HCO3-Na型，矿化度1.7 g/L，热储参数与潘庄凸起三、四段热储相近。
(3) CGSD-01井降压抽水试验结果表明，蓟县系雾迷山组二段单井最大涌水量可达130 m3/h，出水温度100 ℃，单井可满足约30万m2建筑物供暖需求；初步估计潘庄凸起雾迷山组二段热储热量可满足供暖面积6114×104 m2。
(4) 从区域地层沉积规律看，天津地区深部雾迷山组一段、杨庄组、高于庄组，厚度大、岩溶发育，与雾迷山组四、三、二段性质相似，均具有成为高产能新储层的可能性，加强深部地热探测研究意义重大。
致谢: 文章撰写过程中恩师王玉普院士对论文题目提出了建设性意见，指导老师李莉教授指导梳理了论文结构和内容，评审专家提出了宝贵的修改意见，在此一并表示诚挚的感谢。 -
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图 1 页岩气藏等效连续介质模拟模型(据Wu et al., 2009)
Figure 1. Schematic diagram of different conceptualizations for handling fracture-matrix interactions (after Wu et al., 2009)
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图 2 Warren-Root双重介质模型(据Warren et al., 1963)
Figure 2. Schematic diagram of Warren-Root dual porosity model (after Warren et al., 1963)
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图 3 Kazemi层状双重介质模型(据Kazemi, 1969)
Figure 3. Schematic diagram of Kazemi laminar dual porosity model (after Kazemi, 1969)
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图 4 Deswaan双重介质模型(据Deswaan et al., 1976)
Figure 4. Schematic diagram of Deswaan dual porosity model (after Deswaan et al., 1976)
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图 5 多重连续介质（MINC）概念模型图(据Pruess et al., 1983)
Figure 5. Schematic diagram of MINC conceptual model (after Pruess et al., 1983)
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图 6 三重介质概念模型(据Wu et al., 2009, 有改动)
Figure 6. Basic conceptualization for triple-continuum approximation of three-dimensional large-fracture, small-fracture, and rock matrix systems (modified from Wu et al., 2009)
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图 7 页岩气三重介质扩散渗流模型(据程远方等, 2012)
Figure 7. Seepage mechanism of triple-continuum in shale gas reservoir (after Chen Yuanfang et al., 2012)
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图 8 页岩气四重介质概念模型
Figure 8. Scheme of conceptualization quadruple-media in shale gas reservoir
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图 9 二维离散裂缝孔隙介质示意图(据Sternolf et al., 2006)
Figure 9. Scheme of two-dimensional fracture porous media (after Stemolf et al., 2006)
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图 10 EDFM原理示意图(据Xu et al., 2017)
Figure 10. The working principle diagram for EDFM (after Xu et al., 2017)
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图 11 三孔双渗模型与双重介质模型流动示意图(据李泽沛等, 2016)
Figure 11. Flows in triple porosity-dual permeability model and dual porosity model (after Li Zepei et al., 2016)
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图 12 混合裂缝模拟模型示意图(据陈小凡等, 2018)
Figure 12. Scheme of mixed-fracture simulation model (after Chen Xiaofan et al., 2018)
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图 13 页岩基质与裂缝之间的物质传输(据Huang et al., 2019)
Figure 13. Mass transfer pyramid between different type of continua in shale matrix and fractures (after Huang et al., 2019)
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