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.     

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.     

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.     

基于开挖的增强型地热系统概述

地热能赋存于地球内部岩土体、流体和岩浆体中,是一种永久的、可再生的、储量丰富的清洁能源。地热能的开发,尤其是干热岩的开发利用,有可能成为解决人类未来能源危机的重要途径。目前采用的干热岩开采方法被称为增强型地热系统(EGS)。热储地质环境的复杂性和水力化措施对天然裂隙的依赖性,造成多数的EGS项目存在热储体积和换热面积不足、工质流量小、终端温度低,以及诱发地震风险等局限性,致使干热岩开发始终未能大规模商业化。基于开挖的增强型地热系统(EGS-E)的提出为突破传统EGS的技术弊端和规模局限提供了新思路。文章在其概念模型的基础上,从系统原理、工程构想、技术优势等方面对EGS-E进行了更详尽的阐述。EGS-E采用开挖、爆破、崩落等采矿技术,形成了独特的热储致裂系统和热能交换系统,能够大幅度降低地质环境对热储质量的限制,具备构建定制的热储空间、形成充足的换热面积,维持稳定的工质流量与温度及减少诱发地震风险等优势,为干热岩开发的商业化提供了新的解决方案。     

增强型地热系统在碳酸盐岩型深层地热能开发利用中的应用进展

地热能是一种储量大、分布范围广、清洁环保的可再生能源,其中深层干热岩地热能最具开发潜力。增强型地热系统是开发深层干热岩地热能的有效手段,在碳酸盐岩热储区已广泛应用,取得了良好的经济社会效益。系统总结了国内外增强型地热系统在碳酸盐岩型地热开发中的进展和经验,分析了国内发展现状,认为加强基础理论研究、核心技术攻关和工程示范,尽快形成具有中国特色的深部地热能开采方案,是今后工作的重点方向之一。     

Thermal recovery from a fractured medium in local thermal non‐equilibrium

Thermal recovery from a hot dry rock (HDR) reservoir viewed as a deformable fractured medium is investigated with a focus on the assumption of local thermal non‐equilibrium (LTNE). Hydraulic diffusion, thermal diffusion, forced convection and deformation are considered in a two‐phase framework, the solid phase being made by impermeable solid blocks separated by saturated fractures. The finite element approximation of the constitutive and field equations is formulated and applied to obtain the response of a generic HDR reservoir to circulation tests. A change of time profile of the outlet fluid temperature is observed as the fracture spacing increases, switching from a single‐step pattern to a double‐step pattern, a feature which is viewed as characteristic of established LTNE. A dimensionless number is proposed to delineate between local thermal equilibrium (LTE) and non‐equilibrium. This number embodies local physical properties of the mixture, elements of the geometry of the reservoir and the production flow rate. All the above properties being fixed, the resulting fracture spacing threshold between LTNE and LTE is found to decrease with increasing porosity or fluid velocity. The thermally induced effective stress is tensile near the injection well, illustrating the thermal contraction of the rock, while the pressure contribution of the fracture fluid is negligible during the late period. Copyright © 2012 John Wiley & Sons, Ltd.     

增强型地热系统:潜力大、开发难

文中讨论了为什么要开发干热岩地热资源?什么是干热岩系统和增强型地热系统?中国干热岩系统的潜力,如何发展中国的EGS以及我们可供考虑的建议。随着常规能源的不断消耗,可再生能源日益受到人类的青睐。在可再生能源中,地热能的容量最大,地热发电提供的是基本负荷,但是由于诸多因素,开发滞后。尤其是对潜力大、开发难的增强型地热系统,中国更是从研究到开发,都刚刚起步。如果地热发电的规模要超过风能及太阳能等其他新能源,不能仅靠水热型地热系统的开发利用,而必须重视和利用干热岩资源,大力研发增强型地热系统。中国干热岩系统的潜势如何呢?中国科学院地质地球物理研究所利用921个大地热流数据编制了《中国大陆地区新版热流图》以及3~10km深处不同深度温度分布图,计算了不同深度干热岩地热资源量,总数为2.09×107 EJ;其中主要分布在青藏高原,占全国总资源量的五分之一。作者们认为,干热岩资源的开发和增强型地热系统的建立是一个系统工程,地热资源的开发是一项风险投资,亚经济型的EGS风险更甚。国家必须统一安排和投资。工程项目必须学习国外的经验和吸取开发的教训。要选择关键地区进行试验和研究。作者们建议可考虑选择羊八井地热田的北部作为试验地区。     

Radon modelling and the heat transfer surface area of the British hot dry rock geothermal reservoir

A simple thermal model is developed to evaluate the heat exchange surface area of a hot dry rock geothermal reservoir. This model, in conjunction with the Rn model of Andrews and coworkers, is applied to RH12/RH15 system of the British HDR reservoir. Results suggest that although the estimated Rn transfer surface area represents the actual swept surface area, it is between 25 and 45 times larger than the heat transfer surface area. The difference is explained as due to clustering of several fractures within a range of thermal interaction, over the duration of the circulation. It is also shown that the decline in the measured temperatures of circulation fluids since 1985 to the present is consistent with the heat exchange surface area going through a maximum in 1987.     

干热岩资源和增强型地热工程:国际经验和我国展望

干热岩（HDR）是一种没有水或含有少量水的高温岩体,保守估计地壳中3~10 km深处干热岩所蕴含的能量相当于全球所有石油、天然气和煤炭所蕴藏能量的30倍。增强型地热系统（EGS）是指通过水力压裂等工程手段在地下深部低渗透性干热岩体中形成人工地热储层,采出相当数量热能的人工地热系统。EGS的研究与开发已有40年的历史,但早期只局限在美国、英国、法国、日本、澳大利亚等国家,我国这方面的研究于近几年起步。目前干热岩的开发面临诸多挑战,如大体积人工裂隙热储的建造、实现EGS商业化需要进一步研究和技术开发等。本文回顾分析了国际上重要EGS示范场地建设和研究过程中所取得的经验和积累的教训,讨论了我国近几年的研究进展,希望为我国今后EGS研究和工程化示范提供参考和借鉴。     

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.     

Interaction of a cylindrical thin‐walled pile with an inhomogeneous isotropic elastic medium

This paper presents a rigorous analysis for the static interaction of a cylindrical thin‐walled pile with an inhomogeneous isotropic elastic half‐space under vertical, horizontal, and torsional forces individually applied at the top of pile. The inhomogeneity is specified with the exponential variation of shear modulus along depth of the embedding medium, and the Poisson's ratio is assumed to be constant. By means of a set of Green's functions for pile and soil medium and satisfying the compatibility conditions between the 2 interacting media, the formulation is reduced to coupled Fredholm integral equations. Using the adaptive‐gradient elements, capable of capturing the singular stress transfer at both ends of the pile, a numerical procedure is developed and utilized for evaluating the relevant integral equations and studying the inhomogeneity effect on the soil‐pile interaction responses. The analysis results have been validated for different soil‐pile modulus ratios under axial load and for a Poisson's ratio of 0.3 under lateral load. The procedure does not consider the nonlinear behavior of the soil medium or plastic yielding in the pile section, and the impact of the unreliable results for the case of high Poisson's ratio is not examined.     

热应力影响下干热岩水压致裂数值模拟

干热岩水压致裂过程中低温诱导热应力与注入水压共同影响裂缝的萌生与扩展。首先通过THM耦合分析了低温压裂液注入过程中注入水压与热应力的相互作用及其对裂缝萌生的影响,随后建立描述岩石细观结构的THMD耦合模型对热应力影响下高温岩石水压致裂过程进行初探。结果表明：低温压裂液注入高温岩石产生的热应力包括岩石自身温度梯度形成的热应力与岩石颗粒非均匀膨胀导致的热应力,并在井筒周围呈现为拉应力。高注入压力将抑制热应力导致的多裂缝萌生,井筒附近热应力的存在对注入压力也具有削弱作用。基岩温度升高,裂缝萌生阶段更多裂缝在井筒附近起裂,缝网沿最大地应力方向的扩展速度减慢,但改造规模增加,同时多裂缝的存在也使得裂缝延伸压力增加。     

Rigid cylinder in a transversely isotropic half‐space under lateral loads

A boundary integral equation method is presented for a rigid cylindrical pipe‐pile of finite length embedded in a transversely isotropic half‐space under lateral loads. In the framework of three‐dimensional elastostatics, the complicated soil‐structure interaction problem is shown to be reducible to three coupled Fredholm integral equations. Through an analysis of the associated Cauchy singular kernels, the intrinsic singular characteristics of the radial, angular, and vertical interfacial load transfers are rendered explicit. By means of a complicated numerical procedure, detailed results on the three‐dimensional load–transfer process are provided for benchmark comparison and practical applications. Copyright © 2011 John Wiley & Sons, Ltd.     

青海共和盆地地热资源热源机制与聚热模式

青海共和盆地东侧贵德扎仓热田是探讨共和盆地地热资源成因的关键地区。本文综合区域地质、岩石热物性、同位素年代学、水文地球化学和地球物理测量等方法,重点分析了共和盆地的构造背景和热源机制,深入研究了共和盆地地热能系统的关键环节。研究发现:①识别出盆地地壳15 km以下深度发育高导体,并可与新生代青藏高原东部中-下地壳发育的层状低速高导层对比;②近NW-NS向的瓦里贡左旋走滑逆冲断裂是扎仓热田重要的控热和导热断裂;③晚中生代花岗岩与上覆围岩具有显著的热导率;④温泉氢氧同位素指示水源以地表水补给为主;⑤存在浅层新生界碎屑岩中-低温热储和深层花岗岩中-高温热储,发育四层两类地热资源。综合分析提出了共和盆地干热岩三元聚热模式:即新生代中-下地壳发育的高温低速高导层是主要热源,中晚三叠世花岗岩是良好的导热和储热体,既是干热岩母岩,也是热储,新生代低热导率沉积岩是良好的盖层。研究对于青藏高原地热成因、资源预测、开发规划等具有参考意义。     

Experiments and Analysis of the Hydraulic Fracture Propagation Behaviors of the Granite with Structural Planes in the Gonghe Basin

Hydraulic fracture (HF) propagation behavior is signi?cant when building enhanced geothermal systems (EGS). HF geometry is closely related to the structural planes (SPs) in hot dry rock (HDR), such as natural fractures (NFs), quartz veins (QVs) and lithologic interfaces (LIs). However, the HF behaviors in HDR have not been well understood, especially the influence of multiple SPs on the HF geometry. To clarify this mechanism, several groups of physical simulation experiments of hydraulic fracturing were conducted to investigate the intersection relationship between the HFs and the SPs. Results show that the HF geometry shows great differences when intersecting with different SPs. In summary, the HF geometry displays four basic patterns, namely, propagation along the SPs, branching, capture, penetration/non-dilation. The fluctuation degree of the pressure-time curve and the HF complexity show a positive correlation. The cementing strength of the SP and their different mechanical properties from rock matrix influence the HF behaviors significantly. Therefore, the HF shows diverse geometries when intersecting with the NFs and LIs, while propagating along the QV when intersecting with it. For the complex networks, it is favorable for the HF to penetrate through and dilate several SPs, rather than simply cross or propagate along the SP.     

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。     

渤海湾盆地中南部干热岩选区方向

渤海湾盆地是我国华北油气开发的主战场,多年的油气勘探开发积累了大量钻井、测录井及测温数据。通过对区内深钻井测温数据的分析研究,发现中南部的冀中坳陷、黄骅坳陷、临清坳陷和济阳坳陷是干热岩地热资源的主要富集区,温度≥180 ℃的热储主要发育在基岩潜山或斜坡区,埋深适宜,温度较高,有一定的天然孔渗条件。4个主要坳陷区4 000 m以深钻井平均地温梯度范围为3.07~3.32 ℃/100 m,5 000 m以深钻井平均地温梯度范围为2.96~3.27 ℃/100 m,埋深越大,地温梯度越低。坳陷区埋深在4 309~6 261 m时相继达到180 ℃温度,为干热岩目标埋深范围。不同坳陷、区块和井区达到180 ℃干热岩温度界限的深度相差较大。下古生界、中元古界和太古宇三套热储是渤海湾盆地中南部最具开发利用潜力的干热岩热储类型。冀中坳陷主要发育奥陶系灰岩、寒武系白云岩和中元古界白云岩热储,黄骅坳陷以奥陶系灰岩热储为主,济阳坳陷发育寒武系-奥陶系灰岩和太古宇变质岩热储,临清坳陷主要为奥陶系灰岩热储。坳陷区的凹中和凹边凸起区,顶面埋深3 000~5 000 m的前中生界潜山是主要的勘探方向,冀中坳陷河西务、长洋淀等潜山,黄骅坳陷南大港、千米桥等潜山,济阳坳陷桩西孤北等潜山,临清坳陷马场、文留等潜山是干热岩勘探开发有利区。干热岩勘探可与深层油气勘探开发相结合,进行不同类型资源的兼探和综合开发利用。     

中国深层地热能开采的地质条件评价

深层地热能是指深度大于3 000 m的地热能。我国深层地热能资源丰富,但是开采条件怎么样呢?本文基于地热地质学原理,结合岩石力学等相关学科的理论,提出一种对深层地热能开采条件进行评价的指标体系,对各单一指标采用专家打分的方法赋值,继而采用模糊数学定量计算和评估深层地热能资源开发的难易程度。该方法考虑了深层地热能开发利用中的增强地热系统(EGS)的环境安全问题,即传统的“刚性造储”可能带来的诱发地震等不利于地热能行业健康发展的因素,倡导“柔性造储”和广义EGS理念,强调储层属性和地物理场的整合,针对我国地热能分布与构造活动关系密切、地壳总体上活动性强、地应力高、地震频发等构造型地热特点,是对以往评价方法的补充和拓展。该方法充分利用了专家知识,发挥了模糊数学综合评估作用,给出的量化结果易于对比和使用,可以更好地支持决策。本文基于新的评估方法,利用现有的深部地热研究及勘探成果,评估了中国大陆地区九个区域深层地热能开发的难易程度,评价区包括西藏南北地堑系、云南西部火山型地热区、青海东部共和盆地以及东北、华北等。从本文的结果可以看出,我国深层地热能开采的地质条件复杂,开采难度较大。     

Numerical prediction of blast‐induced stress wave from large‐scale underground explosion

This paper presents a numerical model for predicting the dynamic response of rock mass subjected to large‐scale underground explosion. The model is calibrated against data obtained from large‐scale field tests. The Hugoniot equation of state for rock mass is adopted to calculate the pressure as a function of mass density. A piecewise linear Drucker–Prager strength criterion including the strain rate effect is employed to model the rock mass behaviour subjected to blast loading. A double scalar damage model accounting for both the compression and tension damage is introduced to simulate the damage zone around the charge chamber caused by blast loading. The model is incorporated into Autodyn3D through its user subroutines. The numerical model is then used to predict the dynamic response of rock mass, in terms of the peak particle velocity (PPV) and peak particle acceleration (PPA) attenuation laws, the damage zone, the particle velocity time histories and their frequency contents for large‐scale underground explosion tests. The computed results are found in good agreement with the field measured data; hence, the proposed model is proven to be adequate for simulating the dynamic response of rock mass subjected to large‐scale underground explosion. Extended numerical analyses indicate that, apart from the charge loading density, the stress wave intensity is also affected, but to a lesser extent, by the charge weight and the charge chamber geometry for large‐scale underground explosions. Copyright © 2004 John Wiley & Sons, Ltd.     

世界干热岩地热资源开发进展与地质背景分析

干热岩资源指内部不存在或仅存在少量流体,温度高于180℃的异常高温岩体,是一种极具潜力的地热资源类型。自20世纪70年代美国Fenton Hill项目实施以来,已在全球14个国家实施了41个干热岩开发项目,以干热岩储层建造和连通的目标地层周围或上部是否存在水热型储层为标准,25个属于传统意义的干热岩开发项目,16个属于增强型地热系统(Enhanced Geothermal System或Engineered Geothermal System,缩写为EGS)。从板块构造角度分析,这些干热岩开发项目主要分布在欧亚板块板内地热域、印澳板块板内地热域、东太平洋离散—汇聚板缘型地热域、西太平洋汇聚板缘型地热域和加勒比海火山活动岛弧区。按照盆地类型划分,全球干热岩开发项目所处的大地构造背景包括克拉通盆地、前陆盆地、裂谷盆地、弧前盆地、弧后盆地、近现代火山(火山带)和褶皱带地区,其中以欧洲阿尔卑斯褶皱带磨拉石盆地为代表的前陆盆地,和以欧洲阿尔卑斯褶皱带上莱茵地堑、北美新生代科迪勒拉造山带内华达盆地为代表的裂谷盆地是全球干热岩开发项目最为集中的两种盆地类型。考虑我国干热岩资源分布情况,上莱茵地堑、内华达盆地的干热岩开发历程对我国干热岩资源的勘探和开发具有一定的借鉴作用。