裂隙岩体不稳定温度场的复合单元算法研究

基于复合单元法,结合三维热传导-对流方程和“充填模型”,提出了裂隙岩体不稳定温度场的复合单元模型。该模型前处理简便快捷,计算网格生成时无需考虑裂隙的存在,网格剖分不受限制,随后利用复合单元前处理程序,依据裂隙的位置和方位将其自动离散在单元内。对常规热传导-对流方程进行自伴随性调整,应用变分原理,推导出裂隙岩体不稳定温度场的复合单元算法,该算法可分别计算出岩块子单元和裂隙的温度值,且可真实反映裂隙中水流与相邻岩块间的热能量交换规律。将复合单元数值模型计算的不稳定温度场结果与相应的实测数据进行对比分析可知,数值计算结果与实测数据基本一致,验证了裂隙岩体不稳定温度场复合单元算法的可靠性与有效性。算例分析表明,裂隙中水流与相邻岩块间有明显的热传导和热对流作用。     

Numerical modelling of fluid flow tests in a rock fracture with a special algorithm for contact areas

The fluid flow in rock fractures during shear processes has been an important issue in rock mechanics and is investigated in this paper using finite element method (FEM), considering evolutions of aperture and transmissivity with shear displacement histories under different normal stress and normal stiffness conditions as measured during laboratory coupled shear-flow tests. The distributions of fracture aperture and its evolution during shearing were calculated from the initial aperture, based on the laser-scanned sample surface roughness results, and shear dilations measured in the laboratory tests. Three normal loading conditions were adopted in the tests: simple normal stress and mixed normal stress and normal stiffness to reflect more realistic in situ conditions. A special algorithm for treatment of the contact areas as zero-aperture elements was used to produce more accurate flow field simulations, which is important for continued simulations of particle transport but often not properly treated in literature. The simulation results agree well with the measured hydraulic apertures and flow rate data obtained from the laboratory tests, showing that complex histories of fracture aperture and tortuous flow fields with changing normal loading conditions and increasing shear displacements. With the new algorithm for contact areas, the tortuous flow fields and channeling effects under normal stress/stiffness conditions during shearing were more realistically captured, which is not possible if traditional techniques by assuming very small aperture values for the contact areas were used. These findings have an important impact on the interpretation of the results of coupled hydro-mechanical experiments of rock fractures, and on more realistic simulations of particle transport processes in fractured rocks.     

水平井中多条裂缝同步扩展时裂缝竞争机制

水平井中多条水力裂缝间的应力干扰行为,造成了压裂液排量的非均匀分配,影响了水力裂缝的几何形态。采用边界元法研究岩体在压裂液作用下的变形程度,以幂律流体泊肃叶平板流动方程来研究水力裂缝内部的压裂液流场,考虑了多条裂缝间应力干扰和压裂液流量分配,建立了流-固耦合的水平井多条水力裂缝同步扩展模型。模型可模拟水平井多条水力裂缝几何形态、应力干扰情况和压裂液排量的分配情况,可解释水力裂缝之间的竞争机制。多条裂缝同步扩展时,压裂液排量并非均等地分配到各个裂缝之中,进入到内部裂缝的压裂液流量最小,内部裂缝宽度最小;内部的水力裂缝增长一定长度后,停止增长,并且在应力干扰下逐渐闭合。     

Numerical Simulation of 3D Hydraulic Fracturing Based on an Improved Flow-Stress-Damage Model and a Parallel FEM Technique

The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress–axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures.     

Fracture closure modes during flowback from hydraulic fractures

Flowback analysis recently has been considered as a potential tool for assessing induced fractures through corresponding pressure analyses and rate transient analysis. In this paper, we study fracture closure mechanisms during the flowback of fracturing fluid after hydraulic fracturing treatments. Although it is known that flowback can be significantly affected by the geometry of the fractures and closure stress, there has not been any effort to understand the problem from the geomechanical point of view; rather, available studies assume that a fracture closes uniformly with constant fracture compressibility. The coupled geomechanics and fluid flow model presented in this paper help to elucidate how geostresses may affect fracturing fluid recovery under different conditions. We perform a scaling analysis to formulate the occurrence of different fracture closure modes and then use numerical analyses to verify our scaling parameters. The factors governing the flowback process include the mechanical and petrophysical properties of the rock as well as preexisting discontinuities such as natural fractures. Three different closure modes for fracture networks are described and numerically verified. The occurrence of each mode can dramatically affect fracturing fluid recovery. The role of fluid leakoff into the formation, fractures conductivity, and drawdown strategy are examined for each fracture closure scenario.     

Finite element modeling of hydraulic fracturing in 3D

A procedure based on the finite element method is suggested for modeling of 3D hydraulic fracturing in the subsurface. The proposed formulation partitions the stress field into the initial stress state and an additional stress state caused by pressure buildup. The additional stress is obtained as a solution of the Biot equations for coupled fluid flow and deformations in the rock. The fluid flow in the fracture is represented on a regular finite element grid by means of “fracture” porosity, which is the volume fraction of the fracture. The use of the fracture porosity allows for a uniform finite element formulation for the fracture and the rock, both with respect to fluid pressure and displacement. It is demonstrated how the fracture aperture is obtained from the displacement field. The model has a fracture criterion by means of a strain limit in each element. It is shown how this criterion scales with the element size. Fracturing becomes an intermittent process, and each event is followed by a pressure drop. A procedure is suggested for the computation of the pressure drop. Two examples of hydraulic fracturing are given, when the pressure buildup is from fluid injection by a well. One case is of a homogeneous rock, and the other case is an inhomogeneous rock. The fracture geometry, well pressure, new fracture area, and elastic energy released in each event are computed. The fracture geometry is three orthogonal fracture planes in the homogeneous case, and it is a branched fracture in the inhomogeneous case.     

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.     

稀疏非正交填充裂隙岩体水流—传热—应力模型与离散元模拟

为研究填充裂隙水流速度对岩体温度和应力的影响，选取甘肃北山地区的花岗岩，制作了稀疏非正交裂隙岩体模 型，采用河砂填充裂隙后进行模型试验；并对模型试验进行离散元数值模拟，分析了模型试验所测岩体温度和热应力与数 值模拟结果的差异和原因。结果显示：填砂裂隙强化了裂隙介质的热导能力，无填充时岩体温度和热应力比填砂时低；模 型试验和离散元模拟均表明，岩体温度和岩体应力随裂隙水流速度增大而减小，但是系统达到稳态所需要的时间变短；模 型试验中斜裂隙水流对温度场起主要作用；由于现有3DEC软件不能考虑水的热物性参数随温度的变化，进而产生自然对 流换热，斜裂隙水流和靠近热源侧的竖裂隙水流对温度场起主要作用。     

稀疏非正交填充裂隙岩体水流—传热—应力模型与离散元模拟

为研究填充裂隙水流速度对岩体温度和应力的影响,选取甘肃北山地区的花岗岩,制作了稀疏非正交裂隙岩体模 型,采用河砂填充裂隙后进行模型试验;并对模型试验进行离散元数值模拟,分析了模型试验所测岩体温度和热应力与数 值模拟结果的差异和原因。结果显示：填砂裂隙强化了裂隙介质的热导能力,无填充时岩体温度和热应力比填砂时低;模 型试验和离散元模拟均表明,岩体温度和岩体应力随裂隙水流速度增大而减小,但是系统达到稳态所需要的时间变短;模 型试验中斜裂隙水流对温度场起主要作用;由于现有3DEC软件不能考虑水的热物性参数随温度的变化,进而产生自然对 流换热,斜裂隙水流和靠近热源侧的竖裂隙水流对温度场起主要作用。     

Numerical modeling of stress-permeability coupling in rough fractures

A numerical model is described for coupled flow and mechanical deformation in fractured rock. The mechanical response of rock joints to changes in hydraulic pressure is strongly influenced by the geometric characteristics of the joint surfaces. The concept of this work is to combine straightforward finite element solutions with complex and realistic fracture surface geometry in order to reproduce the non-linear stress-deformation-permeability coupling that is commonly observed in fractures. Building on the numerous studies that have expanded the understanding of the key parameters needed to describe natural rough-walled fractures, new methods have been developed to generate a finite element mesh representing discrete fractures with realistic rough surface geometries embedded in a rock matrix. The finite element code GeoSys/Rockflow was then used to simulate the coupled effects of hydraulic stress, mechanical stress, and surface geometry on the evolving permeability of a single discrete fracture. The modeling concept was experimentally verified against examples from the literature. Modeling results were also compared to a simple interpenetration model.     

基于DDA方法一种流-固耦合模型的建立及裂隙体渗流场分析和应用

以非连续变形分析方法（DDA）为基础并采用稳态流体计算方法将二者结合进行裂隙岩体流-固耦合分析。利用DDA方法生成裂隙岩体模型,在此基础上采用矩阵搜索等方法形成新的裂隙水通网络模型。采用稳态迭代算法和立方定律求得裂隙水压力,并把裂隙水压力作为线载荷施加到块体边界,在DDA算法中每个迭代步完成后更新裂隙开度和水压值,与DDA算法结合研究裂隙水与块体之间相互作用关系。利用以上裂隙岩体流-固耦合计算方法研究了某水封油库开挖和运行过程洞室围岩流量和密封性,为该工程预测水封效果提供了有益的主要依据,也是国内首次采用DDA方法做大型工程的流-固耦合模型分析。     

Stress-Dependent Fluid Flow and Permeability in Fractured Media: from Lab Experiments to Engineering Applications

Summary. Permeability is a physical property in rocks of extreme importance in energy engineering, civil and environmental engineering, and various areas of geology. Early on, fractures in fluid flow models were assumed to be rigid. However, experimental research and field data confirmed that stress-deformation behavior in fractures is a key factor governing their permeability tensor. Although extensive research was conducted in the past, the three-dimensional stress-permeability relationships, particularly in the inelastic deformation stage, still remain unclear. In this paper, laboratory experiments conducted on large concrete blocks with randomly distributed fractures and rock core samples are reported to investigate fluid flow and permeability variations under uniaxial, biaxial and triaxial complete stress-strain process. Experimental relationships among flowrate, permeability and fracture aperture in the fractured media are investigated. Results show that the flowrate and stress/aperture exhibit “cubic law” relationship for the randomly distributed fractures. A permeability-aperture relationship is proposed according to the experimental results. Based on this relationship, stress-dependent permeability in a set of fractures is derived in a three-dimensional domain by using a coupled stress and matrix-fracture interactive model. A double porosity finite element model is extended by incorporating such stress-dependent permeability effects. The proposed model is applied to examine permeability variations induced by stress redistributions for an inclined borehole excavated in a naturally fractured formation. The results indicate that permeability around underground openings depends strongly on stress changes and orientations of the natural fractures.     

An Approach for Modeling Rock Discontinuous Mechanical Behavior Under Multiphase Fluid Flow Conditions

In this paper, the two computer codes TOUGH2 and RDCA (for “rock discontinuous cellular automaton”) are integrated for coupled hydromechanical analysis of multiphase fluid flow and discontinuous mechanical behavior in heterogeneous rock. TOUGH2 is a well-established code for geohydrological analysis involving multiphase, multicomponent fluid flow and heat transport; RDCA is a numerical model developed for simulating the nonlinear and discontinuous geomechanical behavior of rock. The RDCA incorporates the discontinuity of a fracture independently of the mesh, such that the fracture can be arbitrarily located within an element, while the fluid pressure calculated by TOUGH2 can be conveniently applied to fracture surfaces. We verify and demonstrate the coupled TOUGH–RDCA simulator by modeling a number of simulation examples related to coupled multiphase flow and geomechanical processes associated with the deep geological storage of carbon dioxide—including modeling of ground surface uplift, stress-dependent permeability, and the coupled multiphase flow and geomechanical behavior of fractures intersecting the caprock.     

Thermo-hydro-mechanical modeling of fracturing porous media with two-phase fluid flow using X-FEM technique

In this paper, a fully coupled thermo-hydro-mechanical model is presented for two-phase fluid flow and heat transfer in fractured/fracturing porous media using the extended finite element method. In the fractured porous medium, the traction, heat, and mass transfer between the fracture space and the surrounding media are coupled. The wetting and nonwetting fluid phases are water and gas, which are assumed to be immiscible, and no phase-change is considered. The system of coupled equations consists of the linear momentum balance of solid phase, wetting and nonwetting fluid continuities, and thermal energy conservation. The main variables used to solve the system of equations are solid phase displacement, wetting fluid pressure, capillary pressure, and temperature. The fracture is assumed to impose the strong discontinuity in the displacement field and weak discontinuities in the fluid pressure, capillary pressure, and temperature fields. The mode I fracture propagation is employed using a cohesive fracture model. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. It is shown that the effect of thermal expansion on the effective stress can influence the rate of fracture propagation and the injection pressure in hydraulic fracturing process. Moreover, the effect of thermal loading is investigated properly on fracture opening and fluids flow in unsaturated porous media, and the convective heat transfer within the fracture is captured successfully. It is shown how the proposed computational model is capable of modeling the fully coupled thermal fracture propagation in unsaturated porous media.     

随机裂隙岩体渗流-应力耦合分析的块体单元法

视岩石裂隙为一种“充填介质”,进而将有填充物和无填充物的裂隙统一处理,推导了裂隙面的刚度系数、导水系数和法向应力之间的关系式。在此基础上,根据块体单元法的应力、渗流分析的基本原理,即认为岩块为刚体、变形集中发生于裂隙面,假定岩块不透水、渗流仅通过裂隙面进行,并考虑了法向应力和裂隙面刚度、导水系数的关系式,运用两场交叉迭代法,提出了三维随机裂隙岩体渗流与应力耦合分析的块体单元模型。编写了相应的Fortran程序,该程序将块体元的应力、渗流两个分析模块整合在一起,计算效率较高。该模型的最大优势是能考虑大规模复杂的节理、裂隙,且前、后处理简单。通过沙沱重力坝的分析,验证了方法的准确性和有效性     

Simulations of hydro-fracking in rock mass at meso-scale using fully coupled DEM/CFD approach

The paper deals with two-dimensional (2D) numerical modelling of hydro-fracking (hydraulic fracturing) in rocks at the meso-scale. A numerical model was developed to characterize the properties of fluid-driven fractures in rocks by combining the discrete element method (DEM) with computational fluid dynamics (CFD). The mechanical behaviour of the rock matrix was simulated with DEM and the behaviour of the fracturing fluid flow in newly developed and pre-existing fractures with CFD. The changes in the void geometry in the rock matrix were taken into account. The initial 2D hydro-fracking simulation tests were carried out for a rock segment under biaxial compression with one injection slot in order to validate the numerical model. The qualitative effect of several parameters on the propagation of a hydraulic fracture was studied: initial porosity of the rock matrix, dynamic viscosity of the fracking fluid, rock strength and pre-existing fracture. The characteristic features of a fractured rock mass due to a high-pressure injection of fluid were realistically modelled by the proposed coupled approach.

     

剪胀对复杂裂隙岩体渗透性影响的离散元分析

裂隙岩体流固耦合问题是目前国内外研究热点之一,采用离散元软件UDEC对裂隙岩体发生节理剪胀的渗透性变化规律进行了模拟分析。基于现场调查的裂隙信息统计生成裂隙网络岩体模型。 通过固定垂直应力、不断增加应力比RS(RS=水平应力/垂直应力)使岩体出现剪胀,采用库伦滑移节理模式对岩体在剪胀过程中的渗透性变化情况进行模拟。结果发现:当应力比较小(RS3.1)时,节理水力隙宽、流速、渗透系数等参数都随着应力比的增加表现出明显的降低; 而当岩体出现剪胀现象之后(应力比大于3.1),发生剪切滑移和剪胀现象的节理控制着裂隙岩体的总体渗流行为,与不考虑节理剪胀的计算结果相比,岩体渗透能力出现了显著增长。这一结果表明,剪胀对裂隙岩体渗透性的影响是显著而不可忽视的。     

Permeability Tensors of Anisotropic Fracture Networks

Analytical models are presented to provide enhanced capabilities for modeling fluid flow through natural fractures nested in parallel plate type configurations. The modeled fractures may be arbitrarily positioned, but subgrouped according to the consistent parallel sequences. The derived analytical expressions for fracture permeability can be considered as an extension to those in which flow within fractures is uniform and isotropic. This modification offers a correction for the traditional permeability calculations whenever fractures are oblique to the flow orientation. For the fracture flow scenarios, the graphical solutions show the permeability envelope normal to any arbitrary planes within the calculated domain. Consideration of rock anisotropy may significantly improve the accuracy in determining the formation permeability in cases where natural fractures exhibit a dominant control in regional fluid flow.     

黄陵背斜南翼牛蹄塘组二段页岩岩心裂缝脉体成岩环境演化与页岩气保存

岩心观察鄂西黄陵背斜南翼下寒武统牛蹄塘组二段黑色页岩中发育构造挤压成因的高角度裂缝和顺层裂缝.选取不同产状的典型裂缝脉体样品,薄片镜下观察发现高角度裂缝中充填方解石脉,顺层裂缝中充填方解石-白云石复合脉.通过阴极发光、流体包裹体分析以及微区原位元素测定,开展了裂缝脉体成岩环境演化研究,分析了不同产状裂缝对页岩气层局部封闭性的影响.阴极发光结果表明,高角度方解石脉和顺层方解石-白云石复合脉均为2期流体活动形成.根据流体包裹体分析,高角度方解石脉早期成脉流体主要为变质较深的地层卤水,晚期成脉流体混入了低矿化度流体,而顺层方解石-白云石复合脉2期成脉流体均未受低矿化度流体的改造.利用不同阴极发光的裂缝脉体碳酸盐矿物的微区原位微量元素测定结果,对铁锰含量、稀土元素（REE）和氧化还原判别参数分析显示,高角度方解石脉成岩环境经历了由还原环境向氧化环境转化,而顺层方解石-白云石复合脉的成岩环境长期保持了较为还原的环境.因此认为,高角度裂缝对页岩气层的局部封闭条件可能产生破坏作用,从而造成页岩气一定程度的散失,而顺层裂缝对局部封闭条件的破坏作用相对有限,裂缝发育特征及其经历的成岩演化过程研究可为页岩气层自封闭和页岩气微观保存条件的评价提供依据.      

An embedded fracture modeling framework for simulation of hydraulic fracturing and shear stimulation

A numerical modeling framework is described that is able to calculate the coupled processes of fluid flow, geomechanics, and rock failure for application to general engineering problems related to reservoir stimulation, including hydraulic fracturing and shear stimulation. The numerical formulation employs the use of an embedded fracture modeling approach, which provides several advantages over more traditional methods in terms of computational complexity and efficiency. Specifically, the embedded fracture modeling strategy avoids the usual requirement that the discretization of the fracture domain conforms to the discretization of the rock volume surrounding the fractures. As fluid is exchanged between the two domains, conservation of mass is guaranteed through a coupling term that appears as a simple source term in the governing mass balance equations. In this manner, as new tensile fractures nucleate and propagate subject to mechanical effects, numerical complexities associated with the introduction of new fracture control volumes are largely negated. In addition, the ability to discretize the fractures and surrounding rock volume independently provides the freedom to choose an acceptable level of discretization for each domain separately. Three numerical examples were performed to demonstrate the utility of the embedded fracture model for application to problems involving fluid flow, mechanical deformation, and rock failure. The results of the numerical examples confirm that the embedded fracture model was able to capture accurately the complex and nonlinear evolution of reservoir permeability as new fractures propagate through the reservoir and as fractures fail in shear.