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。     

A 2D coupled hydro-thermal model for the combined finite-discrete element method

Based on the combined finite-discrete element method (FDEM), a two-dimensional coupled hydro-thermal model is proposed. This model can simulate fluid flow and heat transfer in rock masses with arbitrary complex fracture networks. The model consists of three parts: a heat conduction model of the rock matrix, a heat-transfer model of the fluid in the fracture (including the heat conduction and convection of fluid), and a heat exchange model between the fluid and rock at the fracture surface. Three examples with analytical solutions are given to verify the correctness of the coupled model. Finally, the coupled model is applied to hydro-thermal coupling simulations of a rock mass with a fracture network. The temperature field evolution, the effect of thermal conductivity of the rock matrix thermal conductivity and the fracture aperture on the outlet temperature are studied. The coupled model presented in this paper will enable the application of FDEM to study rock rupture driven by the effect of hydro-thermo-mechanical coupling in geomaterials such as in geothermal systems, petroleum engineering, environmental engineering and nuclear waste geological storage.

     

Simulation of heat transfer performance using middle-deep coaxial borehole heat exchangers by FEFLOW

Due to its large heat transfer area and stable thermal performance,the middle-deep coaxial borehole heat exchanger (CBHE) has become one of the emerging technologies to extract geothermal energy. In this paper,a numerical modeling on a three-dimensional unsteady heat transfer model of a CBHE was conducted by using software FEFLOW,in which the model simulation was compared with the other studies and was validated with experimental data. On this basis,a further simulation was done in respect of assessing the influencing factors of thermal extraction performance and thermal influence radius of the CBHE. The results show that the outlet temperature of the heat exchanger decreases rapidly at the initial stage,and then tended to be stable; and the thermal influence radius increases with the increase of borehole depth. The heat extraction rate of the borehole increases linearly with the geothermal gradient. Rock heat capacity has limited impact on the heat extraction rate,but has a great influence on the thermal influence radius of the CBHE. When there is groundwater flow in the reservoir,the increase of groundwater velocity will result in the rise of both outlet temperature and heat extraction rate. The heat affected zone extends along with the groundwater flow direction; and its influence radius is increasing along with flow velocity. In addition,the material of the inner pipe has a significant effect on the heat loss in the pipe,so it is recommended that the material with low thermal conductivity should be used if possible.     

Two－Dimensional Model of Hydraulic Fracturing in Geosciences：Effects of Fluid Buoyancy

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Elastic wave velocities and permeability of cracked rocks

Cracks play a major role in most rocks submitted to crustal conditions. Mechanically, cracks make the rock much more compliant. They also make it much easier for fluid to flow through any rock body. Relying on Fracture Mechanics and Statistical Physics, we introduce a few key concepts, which allow to understand and quantify how cracks do modify both the elastic and transport properties of rocks. The main different schemes, which can be used to derive the elastic effective moduli of a rock, are presented. It is shown from experimental results that an excellent approximation is the so-called non-interactive scheme. The main consequences of the existence of cracks on the elastic waves is the development of elastic anisotropy (due to the anisotropic distribution of crack orientations) and the dispersion effect (due to microscopic local fluid flow). At a larger scale, macroscopic fluid flow takes place through the crack network above the percolation threshold. Two macroscopic fluid flow regimes can be distinguished: the percolative regime close to the percolation threshold and the connected regime well above it. Experimental data on very different rock types show both of these behaviors.     

不连续面在双重介质热-水-力三维耦合分析中的有限元数值实现

在建立双重介质热-水-力耦合微分控制方程的基础上,提出了裂隙岩体热-水-力耦合的三维力学模型,对不同介质分别建立以节点位移、水压力和温度为求解量的三维有限元格式,开发了双重介质热-水-力耦合分析的的三维有限元计算程序,在有限元数值分析中不连续面应力计算采用等厚度空间8节点节理单元进行离散,而不连续面渗流和热能计算时采用平面4节点等参单元进行离散,这样保证了不同介质之间的水量、热量交换和两类模型接触处节点水头、温度和位移相等。通过高温岩体地热开发算例,揭示了在热-水-力耦合作用下不连续面处于低应力区,其张开度随运行时间的延长呈非线性增加,非稳定渗流阶段不连续面显著地控制着渗流场的整体分布,它的水头远高于拟连续岩体介质的水头,而进入稳定渗流阶段不连续面的控渗作用不明显,由于高温岩体地热开发系统中存在大规模的热量补给,不连续面对岩体温度场分布的影响并不显著。     

工质变物性对EGS热开采过程影响的数值模拟

增强型地热系统(EGS)热开采过程中循环工质的温度和压力会经历较大范围的变化,这会造成循环工质的热物性变化,从而影响流体工质的输运和岩石-流体热交换;数值模拟EGS热开采过程,预测EGS的寿命、出力等性能指标有必要考虑循环工质的热物性变化.笔者在EGS热开采过程三维数值模拟中考虑水和超临界二氧化碳的变物性,实现了热流双向耦合.针对水EGS分析了各物性变化对EGS采热性能的影响,并对变物性条件的水和超临界二氧化碳EGS的采热性能进行了对比研究.结果表明:工质在密度影响下开采寿命为9.0 a在密度和比定压热容共同影响下的开采寿命为7.5 a,说明密度和比定压热容越大则EGS开采寿命越短;在黏度系数影响下的开采寿命为18.0 a,说明黏度系数越大则EGS开采寿命越长;导热系数则对EGS采热性能无明显影响.注入压力一定的条件下以水为工质的EGS具有较长寿命,但相同时刻的质量流率和热开采率低于以临界二氧化碳为工质的EGS.     

套管式地埋管换热器热短路及换热性能

套管式地埋管换热器是深层地源热泵系统常用的换热装置。基于流体流动换热方程,建立套管式地埋管换热器与周围岩体之间的传热模型。以第一个供暖季为例,分析内管导热系数和循环水流量对换热性能的影响,并引入换热器效能对热短路现象进行评估,研究结果显示:内管导热系数越大,热短路现象越显著;热短路使内外管中循环水温差降低,管内出现热堆积,导致换热器换热功率降低;套管式地埋管换热器的换热功率随循环水流量的增大逐渐增大;内外管之间存在热短路时,出口水温随循环水流量的增大先升高后降低,随着流量增大,换热器效能增大。研究成果可为深层地源热泵系统中地埋管换热器的设计提供借鉴。      

Transport model of buoyant metamorphic fluid by hydrofracturing in leaky rock

Abstract Aqueous fluid released in metamorphism is transported upwards from depth to the Earth's surface. I propose a hydrofracturing model for the fluid transport. In the model, fluid is transported by the upward propagation of a two-dimensional vertical fluid-filled crack from a fluid reservoir (e.g. overpressured compartment under a seal) at depth to the Earth's surface; fluid is injected consecutively from the reservoir into the crack at a given (but not necessarily constant) injection rate; some of the injected fluid is lost by infiltration from the crack walls into the surrounding permeable rock. An approximate solution of the crack propagation is obtained using fluid dynamics for turbulent film flow and linear elastic fracture mechanics. The solution shows the transition from a regime in which the excess pressure of the fluid in the reservoir drives the propagation to a regime in which the buoyancy of the fluid in the crack drives the propagation. For example, if the net injection rate of H₂O is 1 m²/s, the regime transition occurs when the vertical crack length becomes 280 m; after the transition, the propagation velocity and average aperture are constant: 21 m/s and 4.8 cm. If the injection rate is lower than a critical value, hydrofracturing cannot be an effective mode for the fluid transport because of the significant fluid loss by infiltration from the crack walls into the surrounding permeable rock. Assuming a fluid-saturated crust with hydrostatic pore fluid pressure, a lower limit can be estimated for the injection rate required to transport H₂O by hydrofracturing without significant fluid loss. For example, the lower limit for transport from a depth of 15 km to the Earth's surface is estimated at 0.2 m²/s if the crustal permeability is 10^-17 m². The lower limit decreases with decreasing crustal permeability.     

A thermo-mechanical damage model for rock stiffness during anisotropic crack opening and closure

A thermodynamic framework is proposed to couple the effect of mechanical stress and temperature on crack opening and closure in rocks. The model is based on continuum damage mechanics, with damage defined as the second-order crack density tensor. The free energy of the damaged rock is expressed as a function of deformation, temperature, and damage. The damage criterion captures mode I crack propagation, the reduction in toughness due to heating, and the increase in energy release rate with cumulated damage. Crack closure is modeled through unilateral effects produced on rock stiffness. The model was calibrated and verified against published experimental data. Thermo-mechanical crack opening (resp. closure) was studied by simulating a triaxial compression test (resp. uniaxial extension test), including a thermal loading phase. The degradation of stiffness due to tensile stress and recovery of stiffness induced by both mechanical and thermo-mechanical unilateral effects are well captured. The thermo-mechanical energy release rate increases with thermal dilation and also decreases with ambient temperature. It was observed that there is a temperature threshold, below which the rock behaves elastically. A parametric study also showed that the model can capture hardening and softening during thermo-mechanical closure (for specific sets of parameters). These numerical observations may guide the choice of rock material used in geotechnical design, especially for nuclear waste disposals or compressed-air storage facilities.     

Theoretical study on the stability of a reservoir created by the intersection of a fluid-filled crack with an oblique joint for the extraction of geothermal heat

On the basis of the two-dimensional theory of elasticity, the theoretical analysis of a vertical, fluid-filled crack intersecting and oblique joint has been made for the extraction of geothermal heat from hot, dry rock masses, where the opening of the joint near a point of intersection and the frictional resistance against slips along the joint are taken into account. The stress intensity factors are evaluated for discussing crack kinking at the upper joint tip, and the sufficient conditions on theinclination of the joint and on the length between the upper joint tip and the point of intersection are obtained for keeping a fluid-filled crack stable just beneath a joint. It is also shown that the volume of the stable reservoir created by using a joint is much larger than that of a fluidfilled crack in a jointless rock mass, even if the joint is oblique and is opened up by the fluid pressure.     

节理岩体单孔抽注水渗流研究

为了研究工程中在节理岩体内抽水和注水的渗流问题,通过应用UDEC建立单孔抽注水离散元模型进行数值模拟,对比分析不同水位边界条件、不同抽注水速率下的流体的流速和流向等流动状态及孔隙压力分布与变化曲线.表明流体的流动状态和孔隙压力分布受边界水位和抽注水速率直接影响,UDEC进行节理岩体抽注水渗流研究是可行的.     

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.     

稀疏不规则裂隙岩体模型三维水流-传热对温度和应力影响的试验研究

选取高放射核废物处置库重要预选场区甘肃北山地区的花岗岩,制作750 mm（宽）×300 mm（厚）×1 000 mm（高）的稀疏不规则裂隙岩体模型,该模型由18块花岗岩和竖向与斜向各两条裂隙组成,在裂隙及岩石内部埋置温度传感器、水压计、直角应变花,并在模型一侧设置局部热源,研究热源温度和裂隙水流速对岩石温度和应力的影响。结果表明,竖裂隙水主要从顶部进水口流向底部出水口,斜裂隙水主要从侧部进水口流向侧部出水口,竖裂隙与斜裂隙在交汇处存在微小流量交换;由于热源处在两条斜裂隙进水口之间,并且斜裂隙长度小于竖裂隙,岩石热传导与斜裂隙水流对岩石温度分布起控制作用,竖裂隙水流对岩石横向热传导起阻滞作用;由于热传导和水流传热的不规则性,上层岩石形成从左向右为主的传热路径,中层和下层岩石形成从上向下为主的传热路径;由于上、下层岩石温度梯度较小,岩石收缩受热拉应力,而中层岩石温度梯度较大,岩石膨胀受热压应力,大主应力的方向大致垂直于斜裂隙面与竖裂隙面的交线,岩石应力增量随斜平面方向的温度梯度增大而增大;热源温度越高,裂隙水流速越低,岩石温度越高、岩石应力越大,系统达到稳态需要的时间越长。     

地热储层单裂隙岩体渗流传热数值模拟研究

研究地热储层裂隙岩体中的渗流传热过程对干热岩地热资源的开采具有重要的意义。本文以干热岩地热工程为背景,采用COMSOL Multiphysics数值模拟软件对地热储层单裂隙岩体中渗流传热机理进行了研究,并分析了流体注入速度和温度对岩体温度场的影响及其对干热岩地热工程的影响。研究发现流体参数对岩体温度场的影响主要体现在两个方面：一方面是对岩体温度场受扰动区域以及幅度的影响,另一方面是对岩体温度场达到稳态所需要时间的影响。流体注入速度的提升会降低系统的寿命和寿命期的出口法向总热量值,当考虑出口法向总热通量时,存在最佳流体注入速度,本研究中最佳流体注入速度为0.011m/s。流体注入温度的提升会增加系统的寿命和系统的出口法向总热通量和总热量。研究为干热岩自热资源的开发与利用提供了理论依据,为工程运行参数的设计提供了参考依据。     

流动环境中圆孔水平热射流三维数值模拟

根据计算流体动力学理论,采用Realizable k-ε紊流模型和SIMPLEC算法,考虑浮力作用,利用有限体积法来离散求解流动环境中圆孔水平热射流的流动与传热控制方程,对流动环境中圆孔水平热射流进行了三维数值模拟,比较了不同流速比和不同射流出口温度条件下的流动特性和温度分布特性,得到了热射流轨迹的速度和温度衰减规律,分析了流速比和射流出口温度对热射流轨迹温度分布的影响。     

The influence of paleoclimatic events on the functioning of an alpine thermal system (France): the contribution of hydrodynamic–thermal modeling

Numerical models of the Aix-les-Bains thermal aquifer (France) were used to investigate the influence of Quaternary paleoclimatic events on the current thermal state of the groundwater. Initial numerical tests were successful in that present-day fluid flows (heads and flow rates) and the resulting velocities were compatible with residence time data. Water flowing through an aquifer cools the rock mass; therefore, the rate of water flow governs the outlets temperature. For the Aix-les-Bains aquifer, applying present-day flow rates to the entire history of the aquifer leads to much more substantial cooling of the rock mass than is indicated by the outlets temperature (i.e. present-day flow rates are 10 times too high). This suggests that the aquifer may have gone through alternating functioning phases, during which the rock mass cooled, and blocked phases, during which the aquifer reheated. Other results indicate that the main parameters affecting thermal behavior during a functioning phase are the total inflow volume, rather than individual inflow rates, and the initial heat field. As phenomena linked to glaciation can lead to the blocking of infiltration zones and aquifer outlets, the findings suggest that the hypothesis of intermittent aquifer functioning related to glaciations is compatible with the current thermal field.     

Capturing the two‐way hydromechanical coupling effect on fluid‐driven fracture in a dual‐graph lattice beam model

Fluid‐driven fractures of brittle rock is simulated via a dual‐graph lattice model. The new discrete hydromechanical model incorporates a two‐way coupling mechanism between the discrete element model and the flow network. By adopting an operator‐split algorithm, the coupling model is able to replicate the transient poroelasticity coupling mechanism and the resultant Mandel‐Cryer hydromechanical coupling effect in a discrete mechanics framework. As crack propagation, coalescence and branching are all path‐dependent and irreversible processes, capturing this transient coupling effect is important for capturing the essence of the fluid‐driven fracture in simulations. Injection simulations indicate that the onset and propagation of fractures is highly sensitive to the ratio between the injection rate and the effective permeability. Furthermore, we show that in a permeable rock, the borehole breakdown pressure, the pressure at which fractures start to grow from the borehole, depends on both the given ratio between injection rate and permeability and the Biot coefficient.     

FDEM-TH3D: A three-dimensional coupled hydrothermal model for fractured rock

This paper proposes a three-dimensional coupled hydrothermal model for fractured rock based on the finite-discrete element method to simulate fluid flow and heat transport. The 3D coupled hydrothermal model is composed of three main parts: a heat conduction model for the rock matrix, a heat transfer model for the fluid in the fractures (including heat conduction and heat convection), and a heat exchange model between the rock matrix and the fluid in the fractures. Four examples with analytical solutions are provided to verify the model. A heat exchange experiment of circulating water in a cylindrical granite sample with one fracture is simulated. The simulation results agree well with the experimental results. The effects of the fracture aperture, fluid viscosity, and pressure difference on the heat exchange between the fluid and rock are studied. Finally, an application concerned with heat transport and fluid flow in fractured rock is presented. The simulation results indicate that the 3D fully coupled hydrothermal model can capture the fluid flow and temperature evolution of rocks and fluids.     

Mechanical controls on fluid flow during regional metamorphism: some numerical models

The control of fluid flow by plastic deformation during metamorphism is critical to our understanding of metamorphic processes. Various geological observations and field studies demonstrate the consequences of fluid flow control by deformation, so that the concept appears to be accepted, at least for small-scale PUBLIC (for example faults and vein PUBLIC). However, the concept appears to be less well recognized at regional scales. Considered here are examples of simple, conceptual models based on fully coupled mechanical–fluid flow concepts; they include deformation of a section of fluid-saturated crust containing a block or a layer of material of different properties from its surrounds. In particular, rheological and permeability contrasts between rock types during deformation associated with regional metamorphism are sufficient to control the form of fluid flow over the range of a few kilometres. Low contrasts and small strains allow pervasive fluid flow, whereas greater contrasts and increasing strains cause focusing of the flow. Such focusing is generally associated with localization of the deformation, especially for a strongly dilatant elastic–plastic material. However, a rate of fluid flow much greater than the rate of deformation may result in pervasive flow, although for most models pervasive flow is difficult to attain over regional distances. Furthermore, lateral and downward fluid flow may occur, demonstrated here by simple models for folding and for deformation of regions containing plutons. Therefore, such modelling may be used as a means of testing the various hypotheses concerning the volumes of fluid predicted to have passed through some rock volumes. Numerical models of the future will become increasingly complex and powerful, allowing greater coupling of thermal, mechanical, chemical and fluid flow effects, and based more on the physical processes involved. Combined field and laboratory studies will provide correspondingly greater understanding and will permit the determination of the timing of fluid flow and structural controls on fluid flow patterns.