An integral equation solution for three‐dimensional heat extraction from planar fracture in hot dry rock

In the numerical simulation of heat extraction by circulating water in a fracture embedded in geothermal reservoir, the heat conduction in the reservoir is typically assumed to be one‐dimensional and perpendicular to the fracture in order to avoid the discretization of the three‐dimensional reservoir geometry. In this paper we demonstrate that by utilizing the integral equation formulation with a Green's function, the three‐dimensional heat flow in the reservoir can be modelled without the need of discretizing the reservoir. Numerical results show that the three‐dimensional heat conduction effect can significantly alter the prediction of heat extraction temperature and the reservoir life as compared to its one‐dimensional simplification. Copyright © 2003 John Wiley & Sons, Ltd.     

A three‐dimensional integral equation model for calculating poro‐ and thermoelastic stresses induced by cold water injection into a geothermal reservoir

Poro‐mechanical and thermo‐mechanical processes change the fracture aperture and thus affect the water flow pattern in the fracture during the cold water injection into enhanced geothermal systems (EGS). In addition, the stresses generated by these processes contribute to the phenomenon of reservoir seismicity. In this paper, we present a three‐dimensional (3D) partially coupled poro‐thermoelastic model to investigate the poroelastic and thermoelastic effects of cold water injection in EGS. In the model, the lubrication fluid flow and the convective heat transfer in the fracture are modeled by the finite element method, while the pore fluid diffusion and heat conductive transfer in the reservoir matrix are assumed to be 3D and modeled by the boundary integral equation method without the need to discretize the reservoir. The stresses at the fracture surface and in the reservoir matrix are obtained from the numerical model and can be used to assess the variation of in situ stress and induced seismicty with injection/extraction. Application of the model shows that rock cooling induces large tensile stresses and increases fracture conductivity, whereas the rock dilation caused by fluid leakoff decreases fracture aperture and increases compressive total stresses around the injection zone. However, increases in pore pressure reduce the effective stresses and can contribute to rock failure, fracture slip, and microseismic activity. Copyright © 2009 John Wiley & Sons, Ltd.     

Integral equation solution of heat extraction from a fracture in hot dry rock

In the study of heat extraction by circulating water in a fracture embedded in geothermal reservoir, the heat conduction in the reservoir is typically assumed to be one dimensional and perpendicular to the fracture. In this paper, we demonstrate that by an integral equation formulation utilizing Green's function, the multi‐dimensional heat flow in the reservoir can be modelled. In the resulting numerical solution system, the discretization of reservoir geometry is entirely eliminated, leading to a much more efficient scheme. The multi‐dimensional heat conduction effect as compared to its one‐dimensional simplification is studied. Copyright © 2001 John Wiley & Sons, Ltd.     

Integral equation solution for three-dimensional heat transfer in multiple-fracture enhanced geothermal reservoirs

For the prediction of energy production from multiple-fractured geothermal reservoirs, previous models basically focused on the one-dimensional conduction in the rock containing evenly distributed fractures of equal scale. Here, a novel model is described to numerically investigate the three-dimensional heat transfer in geothermal reservoirs with unevenly spaced disc fractures of various sizes including the aperture and radius. In terms of the water flow through each fracture, an approximate analytical solution is obtained on the assumption that the water pressure disturbances, induced by the fracture margin and extraction (injection) operation, at the injection (extraction) well center and at different locations within the injection (extraction) well range were approximately equal. By the integral equation scheme for two-dimensional planar fractures, the three-dimensional problem of heat exchange is simulated without the reservoir discretization. The singular integral is analytically calculated in polar coordinates whereas the nonsingular integrand is numerically estimated by the Gaussian quadrature method in Cartesian coordinates. Compared with the one-dimensional simplification, the three-dimensional heat conduction remarkably alters the prediction of extraction temperature. In addition, the reservoir temperature field is also significantly influenced by the spacings and dimensions of fractures. The present model may be used for the estimation, design, and optimization of a geothermal reservoir.     

盆地地热场模拟在地热资源勘探中的应用

地热资源是一种新型无污染能源,具有极高的开采价值,已经受到世界各国的关注.盆地因其特殊的地质条件,内部往往蕴涵着丰富的地热资源,且具有易开采、利用的特点.但目前地热资源勘探的手段和研究方法单一,制约着地热资源的开采与开发.而盆地地热场模拟技术已经较为成熟,并在油气成藏模拟中广泛应用.我们可以在已有的技术手段下结合盆地地热模拟技术来提高勘探的精度.本文还探讨了以地温控制方程与地下热水水流方程相结合来建立模型,模拟盆地地热资源.     

Semianalytical modeling on 3D stress redistribution during hydraulic fracturing stimulation and its effects on natural fracture reactivation

The hydraulic fracturing technique has been widely applied in many fields, such as the enhanced geothermal systems (EGS), the improvement of injection rates for geologic sequestration of CO₂, and for the stimulations of oil and gas reservoirs. The key points for the success of hydraulic fracturing operations in unconventional resources are to accurately estimate the redistribution of pore pressure and stresses around the induced fracture and predict the reactivations of preexisting natural fractures. The pore pressure and stress regime around hydraulic fracture are affected by poroelastic and thermoelastic phenomena as well as by fracture opening compression. In this work, a comprehensive semi-analytical model is used to estimate the stress and pore pressure distribution around an injection-induced fracture from a single well in an infinite reservoir. The model allows the leak-off distribution in the formation to be three-dimensional with the pressure transient moving ellipsoidically outward into the reservoir from the fracture surface. The pore pressure and the stress changes in three dimensions at any point around the fracture caused by poroelasticity, thermoelasticity, and fracture compression are investigated. With Mohr-Coulomb failure criterion, we calculate the natural fracture reactivations in the reservoir. Then, two case studies of constant water injection into a hydraulic fracture are presented. This work is of interest in the interpretation of microseismicity in hydraulic fracturing and in the estimation of the fracture spacing for hydraulic fracturing operations. In addition, the results from this study can be very helpful for the selection of stimulated wells and further design of the refracturing operations.     

A shear‐dilation‐based model for evaluation of hydraulically stimulated naturally fractured reservoirs

The role of shear dilation as a mechanism of enhancing fluid flow permeability in naturally fractured reservoirs was mainly recognized in the context of hot dry rock (HDR) geothermal reservoir stimulation. Simplified models based on shear slippage only were developed and their applications to evaluate HDR geothermal reservoir stimulation were reported. Research attention is recently focused to adjust this stimulation mechanism for naturally fractured oil and gas reservoirs which reserve vast resources worldwide. This paper develops the overall framework and basic formulations of this stimulation model for oil and gas reservoirs. Major computational modules include: natural fracture simulation, response analysis of stimulated fractures, average permeability estimation for the stimulated reservoir and prediction of an average flow direction. Natural fractures are simulated stochastically by implementing ‘fractal dimension’ concept. Natural fracture propagation and shear displacements are formulated by following computationally efficient approximate approaches interrelating in situ stresses, natural fracture parameters and stimulation pressure developed by fluid injection inside fractures. The average permeability of the stimulated reservoir is formulated as a function of discretized gridblock permeabilities by applying cubic law of fluid flow. The average reservoir elongation, or the flow direction, is expressed as a function of reservoir aspect ratio induced by directional permeability contributions. The natural fracture simulation module is verified by comparing its results with observed microseismic clouds in actual naturally fractured reservoirs. Permeability enhancement and reservoir growth are characterized with respect to stimulation pressure, in situ stresses and natural fracture density applying the model to two example reservoirs. Copyright © 2002 John Wiley & Sons, Ltd.     

化学刺激法提高花岗岩类岩石裂隙渗透性的实验研究

增强型地热系统(EGS)用于通过人工形成地热储层的方法从深部低渗透性岩体中开采地热能;国际上常采用水力压裂辅以化学刺激的方法改造EGS 储层以提高其渗透率。本文以采自青海共和盆地的花岗闪长岩样品为对象,选用3种不同化学刺激剂(氢氧化钠、盐酸和土酸),在3组不同注入流速条件下开展了系统化学刺激实验。结果表明:注入盐酸和土酸后样品渗透率均有提高,且采用土酸时渗透率提高幅度明显大于盐酸;但注入氢氧化钠后,样品渗透率反而降低。在3类化学刺激剂中,土酸对长石类矿物的溶蚀能力最强,而氢氧化钠溶液对石英的溶蚀能力最强,但氢氧化钠溶液在溶解岩石样品裂隙表面矿物后极易形成非定形态二氧化硅或非定形态铝硅酸盐蚀变矿物并阻塞裂隙,反而对化学刺激效果造成负面影响。总体来看,土酸是青海共和盆地干热岩体的最佳化学刺激剂。在中等注入速度(3 mL·min^-1)条件下,土酸对岩石样品的溶蚀程度就可达到最高;在此基础上进一步降低流速,则可能使溶解组分更易从液相中沉淀而充填于样品裂隙,导致样品渗透率有所下降。     

青海共和盆地地热资源分布特征兼述CSAMT在地热勘查中的作用

青海共和盆地为一新生代断陷盆,具有良好地热地质背景与其东、西两侧构造岩浆带断裂型地热分布,构成秦昆接合部SN向地热带。另据CSAMT在海南州首府共和县恰卜恰镇地热勘查推断出一小型拉分盆地,兼有盆地传导型层状热储和断裂对流型带状热储的特征,提出拟建地热井位钻孔布置构造有利部位,建议孔深1200m。经钻探打出全省第一口水温高、水量大、水质优的地热井,发挥了CSAMT在地热勘查中的指导作用。     

贵州省安顺市开发区地热地质勘查

安顺市市区由于其所处的地质构造位置,被认为是地热开发的盲区。2008年7月28日,该区成功地打出一口井口水温54.0℃、水量530.87m3/d的热水井,证明在该区内有地热井田存在。研究认为：该区的热储构造与深大断裂有关,热矿水主要赋存在断裂与背斜的联合蓄水构造中,北东向的头铺逆断层F11为主要的导水构造;主要热储层为上石炭统马平群及黄龙组的石灰岩及白云岩,主要隔热保温盖层为二叠系长兴组、大隆组、龙潭组的砂岩及砂质泥岩,热水埋藏深度为1300～2200m。该区的热矿水可作为天然饮用矿泉水及天然医疗矿泉水进行开发利用。     

Evaluating the stress intensity factors of anisotropic bimaterials using boundary element method

This paper presents a boundary element method (BEM) procedure for a linear elastic fracture mechanics analysis in two‐dimensional anisotropic bimaterials. In this formulation, a displacement integral equation is only collocated on the uncracked boundary, and a traction integral equation is only collocated on one side of the crack surface. A fundamental solution (Green's function) for anisotropic bimaterials is also derived and implemented into the boundary integral formulation so that except for the interfacial crack part, the discretization along the interface can be avoided. A special crack‐tip element is introduced to capture the exact crack‐tip behavior. A computer program using FORTRAN has been developed to effectively calculate the stress intensity factors of an anisotropic bimaterial. This BEM program has been verified to have a good accuracy with previous studies. In addition, a central cracked bimaterial Brazilian specimen constituting cement and gypsum is prepared to conduct the Brazilian test under diametral loading. The result shows that the numerical analysis can predict relatively well the direction of crack initiation and the path of crack propagation. Copyright © 2007 John Wiley & Sons, Ltd.     

基于T2WELL的U型地热井供暖潜力数值模拟

为了了解U型井式闭循环地热系统的可持续利用能力,探究场地内利用U型井式闭循环地热系统开发地热能用于供暖的可行性,以及地热井长期运行下的产能状态和不同影响因素的作用规律,设计合理的地热能开采方案。采用数值模拟方法,以邯郸东部平原地区试验井的短期实测数据为基础,以多相多组分井筒-储层耦合流动模拟程序T2WELL为工具,开展场地尺度U型井长期换热数值模拟。研究结果显示：U型井式闭循环地热系统水平井段长度为400～500 m,循环流速和注入温度分别设置为80 m3/h和20 ℃左右时,可以实现地热能的可持续开采,20 a平均提热功率能满足供暖需求,采用该种方式进行供暖具备较高的可行性。      

鄂尔多斯盆地南缘延安地区中深层地热能特征研究

近年来水热型、浅层地热能发展产生的缺点问题日益突出,以取热不取水为原则,中深层U型水平对接换热技术成为新的技术方向。通过对鄂尔多斯盆地南缘延安地区地层岩性、地温梯度特征、热储层特征等特征研究,分析了研究区中深层地热资源潜力,研究结果表明鄂尔多斯盆地南缘奥陶系马家沟组为良好的热传导型热储,深部地温梯度为3.05℃/100m。当马家沟组深度在3157m时,对应温度达到110.67℃。测井及注水试验结果表明,奥陶系马家沟组为极弱含水层,几乎没有流体,属于良好的干热岩型地热资源,具有较高的开采价值。充分确定了该区地热地质条件良好、地热资源潜力巨大。为合理、高效开发利用该区地热资源提供了科学依据,对进一步开发利用该区的地热能具有重要意义。     

岸上襄郏断层中段地热地质特征

通过对岸上襄郏断层的地热地质条件分析,表明该断层在研究区可分为三部分,且以南部地热异常最为明显;热储盖层为其上覆二叠系含煤地层和第四系砂泥岩,主要热储层为寒武系固山组白云质灰岩;热水的水质类型为HCO3SO4—NaCa,大气降水是热水的主要来源,地下热水的垂直运移是形成热水主要原因。根据注水试验资料评价了断层带的地热资源量,按照地热资源利用率为15%,初步估算了断层带地热资源量为2 491.735万t标准煤,认为采用注采结合的方法开采地热资源是较为合理的。最后建议加强中部地区地热资源的进一步勘查研究,以获得更多的地热资源。     

章丘市枣园桃花山地热田地质特征分析

章丘市枣园桃花山地区蕴藏着丰富的地热资源。根据煤矿勘探和地热普查成果,对桃花山地热田的地质背景、热储特征、地球物理化学特征等进行综合分析,认为桃花山地热田属于典型的带状兼层状、对流兼传导型地热田,热储层为奥陶纪马家沟组灰岩,该区地温梯度主要受断裂控制,断裂导热是形成该地温场的一个重要因素,地热水水源主要为渗入的溶滤水。     

沧县隆起中段献县凸起和阜城凹陷岩溶型地热资源特征

为探究华北平原的岩溶热储分布规律,以及如何高效开发利用献县凸起和阜城凹陷地热田的地热资源,结合前人研究成果与已有地热井的测井、地震、水化学等资料,分析了岩溶热储分布规律以及献县凸起和阜城凹陷地热田的四大要素即“源、储、通、盖”等地热地质条件,建立了地热田概念模型,并精细评价了地热资源量。研究表明地热田是形成于渤海湾盆地新生代伸展断陷背景下的受深大断裂控制的传导型地热田,主要以大气降水为补给水源,深大断裂和岩溶不整合面为水运移通道。来自太行山和燕山的水再补给、汇聚,在献县凸起及阜城凹陷岩溶热储中富集,形成中-低温传导型地热系统,具有良好的盖层以及高达3.63~5.31 ℃/100 m的地温梯度。蓟县系岩溶热储顶板埋深1 400~1 500 m,有效厚度累计336.1 m;奥陶系岩溶热储顶板埋深2 000~2 500 m,有效厚度累计55.3 m。献县凸起地热田蓟县系岩溶热储可采资源量3.75×10⁹ GJ,折合标煤1.28×10⁸ t,年开采地热资源量可满足供暖面积4 523×10⁴ m²;阜城凹陷奥陶系岩溶储可采资源量0.80×10⁹ GJ,折合标煤0.27×10⁸ t,年开采地热资源量可满足供暖面积954×10⁴ m²。献县凸起及阜城凹陷地热田开发潜力巨大。     

岩溶热储井间连通性的示踪研究

岩溶热储储层的不均匀性强,采灌井之间的连通性不易确定。示踪技术可以将运移参数量化,有效刻画储层流体的特征,研究回灌井和开采井之间的水力联系,包括导水通道,流体流速等信息,对长期回灌可能引起的开采井的冷却进行预测,是岩溶热储井间连通性研究十分有效的技术。本文以华北牛驼镇地热田雄县地区为例,针对蓟县系雾迷山组岩溶热储,采用荧光素钠示踪剂,进行了1口井注入,10口井观测的群井示踪试验。采用裂隙介质溶质运移模型,对示踪试验数据进行了解释,得到优势通道的长度、渗透流速、纵向弥散度、回收率等储层性质,获得了试验区内采灌井之间的连通特征。对调整采灌井布局提出了建议。     

山东省曹县城区地热资源地质条件综合研究

曹县城区地处鲁西南黄泛平原地区,该区地表被巨厚的第四系和新近系松散层覆盖,区域断裂构造十分发育,地热成矿地质条件有利。可被利用的热储层主要有2个,分别为新近纪明华镇组热储和奥陶纪热储,二个热储层地热资源各具特点。对该区可利用热储层地热资源地质条件进行了分析研究,为下一步曹县城区地热资源的开发利用提供参考性地质依据。     

Large‐scale poroelastic fractured reservoirs modeling using the fast multipole displacement discontinuity method

An effective approach to modeling the geomechanical behavior of the network and its permeability variation is to use a poroelastic displacement discontinuity method (DDM). However, the approach becomes rather computationally intensive for an extensive system of cracks, particularly when considering coupled diffusion/deformation processes. This is because of additional unknowns and the need for time‐marching schemes for the numerical integration. The Fast Multipole Method (FMM) is a technique that can accelerate the solution of large fracture problems with linear complexity with the number of unknowns both in memory and CPU time. Previous works combining DDM and FMM for large‐scale problems have accounted only for elastic rocks, neglecting the fluid leak‐off from the fractures into the matrix and its influence on pore pressure and stress field. In this work we develop an efficient geomechanical model for large‐scale natural fracture networks in poroelastic reservoirs with fracture flow in response to injection and production operations. Accuracy and computational performance of the proposed method with those of conventional poroelastic DDM are compared through several case studies involving up to several tens of thousands of boundary elements. The results show the effectiveness of the FMM approach to successfully evaluate field‐scale problems for the design of exploitation strategies in unconventional geothermal and petroleum reservoirs. An example considering faults reveals the impact of reservoir compartmentalization because of sealing faults for both geomechanical and flow variables under elastic and poroelastic rocks. Copyright © 2015 John Wiley & Sons, Ltd.     

山东孤岛潜山凸起区裂隙岩溶热储资源综合评价与发电潜力研究

山东孤岛潜山凸起区是以古生界为基底的披覆背斜,发育巨厚的寒武纪—奥陶纪碳酸盐岩,具备形成大型裂隙岩溶热储的条件。为研究该区热储的开发利用前景及发电潜力,在深入分析该区地质背景的基础上,以Gg2孔为例,查明寒武系—奥陶系以碳酸盐岩为主,其中奥陶纪八陡组、五阳山组、北庵庄组,寒武纪—奥陶纪三山子组及寒武纪张夏组以灰岩和白云岩为主,可形成良好的裂隙岩溶热储,累计厚度约480 m。以热储中点处温度为平均温度,以中、低温双循环地热发电为利用方向,下限温度按70 ℃估算,该区裂隙岩溶热储可供发电的热量为804×10¹⁶ J,当服务年限设为30 a、热效率系数设为7%时,估算的发电潜力为595 MW,为大型地热田。