岩石裂隙的非饱和渗透特性及其演化规律研究

岩石裂隙的非饱和渗透特性是岩土、能源和环境等领域科学研究中的热点问题。采用三维激光扫描获取花岗岩裂隙的表面形貌特征,分析裂隙微观形貌特征对非饱和渗透特性的影响。研究在张拉、压缩、剪切等复杂荷载作用下裂隙开度分布的演化规律,建立复杂荷载作用下岩石裂隙非饱和毛细压力曲线演化模型。基于裂隙的微观形貌特征推导了岩石裂隙非饱和相对渗透系数模型,通过与试验数据对比,验证了模型的准确性和有效性,并在此基础上建立了复杂荷载作用下岩石裂隙非饱和相对渗透系数演化模型。研究成果对非饱和条件下裂隙岩体的水-力耦合机制研究具有一定指导意义。     

Polyaxial stress-dependent permeability of a three-dimensional fractured rock layer

A study about the influence of polyaxial (true-triaxial) stresses on the permeability of a three-dimensional (3D) fractured rock layer is presented. The 3D fracture system is constructed by extruding a two-dimensional (2D) outcrop pattern of a limestone bed that exhibits a ladder structure consisting of a “through-going” joint set abutted by later-stage short fractures. Geomechanical behaviour of the 3D fractured rock in response to in-situ stresses is modelled by the finite-discrete element method, which can capture the deformation of matrix blocks, variation of stress fields, reactivation of pre-existing rough fractures and propagation of new cracks. A series of numerical simulations is designed to load the fractured rock using various polyaxial in-situ stresses and the stress-dependent flow properties are further calculated. The fractured layer tends to exhibit stronger flow localisation and higher equivalent permeability as the far-field stress ratio is increased and the stress field is rotated such that fractures are preferentially oriented for shearing. The shear dilation of pre-existing fractures has dominant effects on flow localisation in the system, while the propagation of new fractures has minor impacts. The role of the overburden stress suggests that the conventional 2D analysis that neglects the effect of the out-of-plane stress (perpendicular to the bedding interface) may provide indicative approximations but not fully capture the polyaxial stress-dependent fracture network behaviour. The results of this study have important implications for understanding the heterogeneous flow of geological fluids (e.g. groundwater, petroleum) in subsurface and upscaling permeability for large-scale assessments.     

Analysis of Stress-dependent Permeability in Nonorthogonal Flow and Deformation Fields

Summary The stress-dependent permeability of porous-fractured media is examined where principal stresses do not coincide with the principal permeabilities. This condition is the norm, and may arise when either flow is controlled at the local level due to the presence of inclined bedding partings or oblique fractures, or as a result of the evolving loading environment. Permeability response is controlled by shear and normal stiffnesses of fractures, frictional dilation coefficients, skeletal and grain modulii, initial permeabilities and stress state. For parameters representative of intact and fractured rocks, hydrostatic loading modes are shown to have the greatest effect in the pre-failure regime. Shear dilation effects are small, primarily controlled by the selected magnitudes of shear stiffnesses and dilation coefficients. The resulting stress-permeability relationships, which cover both fractured and intact media, are examined in a numerical study of fluid flow injected across the diameter of a cylindrical core with inclined fabric, subjected to various loading configurations. This is used to produce relationships that allow one to reduce flow test data in non-standard specimen geometries, where effective stress changes are simultaneously applied. These results confirm the significant impact of inclination of the rock fabric with respect to both flow and loading geometry on the evolving permeability field.     

The role of hydromechanical coupling in fractured rock engineering

This paper provides a review of hydromechanical (HM) couplings in fractured rock, with special emphasis on HM interactions as a result of, or directly connected with human activities. In the early 1960s, the coupling between hydraulic and mechanical processes in fractured rock started to receive wide attention. A series of events including dam failures, landslides, and injection-induced earthquakes were believed to result from HM interaction. Moreover, the advent of the computer technology in the 1970s made possible the integration of nonlinear processes such as stress–permeability coupling and rock mass failure into coupled HM analysis. Coupled HM analysis is currently being applied to many geological engineering practices. One key parameter in such analyses is a good estimate of the relationship between stress and permeability. Based on available laboratory and field data, it was found that the permeability of fractured rock masses tends to be most sensitive to stress changes at shallow depth (low stress) and in areas of low in-situ permeability. In highly permeable, fractured rock sections, fluid flow may take place in clusters of connected fractures which are locked open as a result of previous shear dislocation or partial cementation of hard mineral filling. Such locked-open fractures tend to be relatively insensitive to stress and may therefore be conductive at great depths. Because of the great variability of HM properties in fractured rock, and the difficulties in using laboratory data for deriving in-situ material properties, the HM properties of fractured rock masses are best characterized in situ. Electronic Publication     

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.     

Cubic law with aperture-length correlation: implications for network scale fluid flow

Previous studies have computed and modeled fluid flow through fractured rock with the parallel plate approach where the volumetric flow per unit width normal to the direction of flow is proportional to the cubed aperture between the plates, referred to as the traditional cubic law. When combined with the square root relationship of displacement to length scaling of opening-mode fractures, total flow rates through natural opening-mode fractures are found to be proportional to apertures to the fifth power. This new relationship was explored by examining a suite of flow simulations through fracture networks using the discrete fracture network model (DFN). Flow was modeled through fracture networks with the same spatial distribution of fractures for both correlated and uncorrelated fracture length-to-aperture relationships. Results indicate that flow rates are significantly higher for correlated DFNs. Furthermore, the length-to-aperture relations lead to power-law distributions of network hydraulic conductivity which greatly influence equivalent permeability tensor values. These results confirm the importance of the correlated square root relationship of displacement to length scaling for total flow through natural opening-mode fractures and, hence, emphasize the role of these correlations for flow modeling.     

Permeability tensor and representative elementary volume of fractured rock masses

Based on a simulation of three-dimensional fracture networks and a superposition principle of liquid dissipation energy for fractured rock masses, a model of the fracture permeability tensor is proposed. An elastic constitutive model of rock fractures, considering fracture closure and dilation during shearing, is also proposed, based on the dilation angle of the fracture. Algorithms of flow-path searching and calculation of the effective flow coefficients for fracture networks are presented, together with a discussion on the influence of geometric parameters of the fractures (trace length, spacing, aperture, orientation and the number of fracture sets) on magnitude, anisotropy of hydraulic permeability and the size of a representative elementary volume (REV). The anisotropy of hydraulic permeability of fractured rock masses is mainly affected by orientation and the number of fracture sets, and the REV size is mainly influenced by trace length, spacing and the number of fracture sets. The results of studies on REV size and the influence of in-situ stress on hydraulic conductivity of the rock mass on the slope of Jinping-I hydropower station, China, are presented using the developed models and methods. The simulation results agreed well with the results obtained from field water-pressure measurements, with an error of less than 10 %.     

页岩储层裂隙渗透率模型和试验研究

页岩储层的裂隙渗透率是评价页岩气开采的重要参数,基于裂隙法向刚度的概念,考虑页岩储层变形过程中裂隙系统和基质系统之间的相互作用以及页岩气解吸引起的体应变,提出了与有效应力相关的页岩储层的渗透率模型。然后分别分析了页岩气藏在单轴应变和常体积条件下的渗透率模型,分析表明,单轴应变和常体积条件下（3个方向的总应变都为0）的裂隙渗透率模型完全一致。采用脉冲衰减渗透率仪测试了煤系页岩的裂隙渗透率,当有效应力从0.7 MPa增加到14.5 MPa时,渗透率从41.81×10-17 m2降到5.43×10-17 m2。为了阐述渗透率模型的有效性,利用煤系页岩的渗透率数据对有效应力-渗透率模型进行拟合。结果表明,当裂隙的法向刚度、张开度和煤系页岩的初始渗透率分别为57 922.5 MPa/m、0.000 17 m和50.15×10-17 m2时,有效应力-渗透率模型和煤系页岩的渗透率拟合程度较好。然后利用现场渗透率数据对该模型进行拟合,结果表明,当裂隙的法向刚度和张开度的关系符合反比例函数时,拟合程度非常好。该渗透率模型适合于单轴应变、常体积和常围压条件,可用于描述页岩气开采过程中页岩储层裂隙渗透率随孔隙压力的变化规律。同时,该渗透率模型和P&M模型以及S&D模型进行了比较,结果表明,该渗透率模型的拟合结果与S&D模型基本一致,但与P&M模型存在一定的差别。     

An Elastic Stress–Strain Relationship for Porous Rock Under Anisotropic Stress Conditions

A stress–strain relationship within porous rock under anisotropic stress conditions is required for modeling coupled hydromechanical processes associated with a number of practical applications. In this study, a three-dimensional stress–strain relationship is proposed for porous rock under elastic and anisotropic stress conditions. This relationship is a macroscopic-scale approximation that uses a natural-strain-based Hooke’s law to describe deformation within a fraction of pores and an engineering-strain-based Hooke’s law to describe deformation within the other part. This new relationship is evaluated using data from a number of uniaxial and triaxial tests published in the literature. Based on this new stress–strain relationship, we also develop constitutive relationships among stress, strain, and related stress-dependent hydraulic/mechanical properties (such as compressibility, shear modulus, and porosity). These relationships are demonstrated to be consistent with experimental observations.     

Mechanical and transport constitutive models for fractures subject to dissolution and precipitation

Transient changes in the permeability of fractures in systems driven far‐from‐equilibrium are described in terms of proxy roles of stress, temperature and chemistry. The combined effects of stress and temperature are accommodated in the response of asperity bridges where mineral mass is mobilized from the bridge to the surrounding fluid. Mass balance within the fluid accommodates mineral mass either removed from the flow system by precipitation or advection, or augmented by either dissolution or advection. Where the system is hydraulically closed and initially at equilibrium, reduction in aperture driven by the effects of applied stresses and temperatures will be augmented by precipitation on the fracture walls. Where the system is open, the initial drop in aperture may continue, and accelerate, where the influent fluid is oversaturated with respect to the equilibrium mineral concentration within the fluid, or may reverse, if undersaturated. This simple zero‐dimensional model is capable of representing the intricate behavior observed in experiments where the feasibility of fracture sealing concurrent with net dissolution is observed. This zero‐order model is developed as a constitutive model capable of representing key aspects of changes in the transport parameters of the continuum response of fractured media to changes in stress, temperature and chemistry. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

A coupled compressible flow and geomechanics model for dynamic fracture aperture during carbon sequestration in coal

This paper presents the development of a discrete fracture model of fully coupled compressible fluid flow, adsorption and geomechanics to investigate the dynamic behaviour of fractures in coal. The model is applied in the study of geological carbon dioxide sequestration and differs from the dual porosity model developed in our previous work, with fractures now represented explicitly using lower-dimensional interface elements. The model consists of the fracture-matrix fluid transport model, the matrix deformation model and the stress-strain model for fracture deformation. A sequential implicit numerical method based on Galerkin finite element is employed to numerically solve the coupled governing equations, and verification is completed using published solutions as benchmarks. To explore the dynamic behaviour of fractures for understanding the process of carbon sequestration in coal, the model is used to investigate the effects of gas injection pressure and composition, adsorption and matrix permeability on the dynamic behaviour of fractures. The numerical results indicate that injecting nonadsorbing gas causes a monotonic increase in fracture aperture; however, the evolution of fracture aperture due to gas adsorption is complex due to the swelling-induced transition from local swelling to macro swelling. The change of fracture aperture is mainly controlled by the normal stress acting on the fracture surface. The fracture aperture initially increases for smaller matrix permeability and then declines after reaching a maximum value. When the local swelling becomes global, fracture aperture starts to rebound. However, when the matrix permeability is larger, the fracture aperture decreases before recovering to a higher value and remaining constant. Gas mixtures containing more carbon dioxide lead to larger closure of fracture aperture compared with those containing more nitrogen.     

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。     

A comparative simulation study of coupled THM processes and their effect on fractured rock permeability around nuclear waste repositories

This paper presents an international, multiple-code, simulation study of coupled thermal, hydrological, and mechanical (THM) processes and their effect on permeability and fluid flow in fractured rock around heated underground nuclear waste emplacement drifts. Simulations were conducted considering two types of repository settings (1) open emplacement drifts in relatively shallow unsaturated volcanic rock, and (2) backfilled emplacement drifts in deeper saturated crystalline rock. The results showed that for the two assumed repository settings, the dominant mechanism of changes in rock permeability was thermal–mechanically induced closure (reduced aperture) of vertical fractures, caused by thermal stress resulting from repository-wide heating of the rock mass. The magnitude of thermal–mechanically induced changes in permeability was more substantial in the case of an emplacement drift located in a relatively shallow, low-stress environment where the rock is more compliant, allowing more substantial fracture closure during thermal stressing. However, in both of the assumed repository settings in this study, the thermal–mechanically induced changes in permeability caused relatively small changes in the flow field, with most changes occurring in the vicinity of the emplacement drifts.     

三轴应力下不同粒径破碎砂岩渗透特性试验

地下工程中破碎岩体往往处于三向应力状态,此类岩体具有孔隙率大、渗透性高等特点,在地应力与高水头作用下易发生渗流失稳破坏,诱发突水灾害。为研究三轴应力下破碎砂岩的渗透特性,运用自主研发的破碎岩石三轴渗流试验系统,采用稳态渗透法进行5种粒径破碎砂岩的渗流试验,得到了三轴应力下破碎砂岩渗透特性变化规律,推导了有效应力与渗流速度之间的关系。试验结果表明：三轴应力下破碎砂岩的有效应力与渗流速度呈线性关系,且轴向位移越大时,随有效应力的增加渗流速度减小的幅度越小;三轴应力下5种粒径破碎砂岩的孔压梯度与渗流速度服从Forchheimer关系,两者之间的相关系数达0.95以上;轴向位移恒定时,随着围压的增大,破碎砂岩渗透率k减小,非Darcy流β因子增大,各级轴向位移下,破碎砂岩的渗透率与围压之间呈指数函数关系;随着孔隙率的减小,5种粒径的破碎砂岩渗透率呈减小趋势,非Darcy流β因子整体增大,且渗透率量级为10-14～10-11 m2,非Darcy流β因子的量级为106～1012 m-1。     

Flow–stress coupled permeability tensor for fractured rock masses

In this paper a new analytical model is proposed to determine the permeability tensor for fractured rock masses based on the superposition principle of liquid dissipation energy. This model relies on the geometrical characteristics of rock fractures and the corresponding fracture network, and demonstrates the coupling effect between fluid flow and stress/deformation. This model empirically considers the effect of pre‐peak shear dilation and shear contraction on the hydraulic behavior of rock fractures and can be used to determine the applicability of the continuum approach to hydro‐mechanical coupling analysis. Results of numerical analysis presented in this paper show that the new model can effectively describe the permeability of fractured rock masses, and can be applied to the coupling analysis of seepage and stress fields. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical simulation of two-phase flow in conceptualized fractures

Two-phase flow in fractured rock is an important phenomenon related to a range of practical problems, including non-aqueous phase liquid contamination of groundwater. Although fractured rocks consist of fracture networks, the study of two-phase flow in a single fracture is a pre-requisite. This paper presents a conceptual and numerical model of two-phase flow in a variable fracture. The void space of the fracture is conceptualized as a system of independent channels with position-dependent apertures. Fundamental equations, governing two-phase displacement in each channel, are derived to represent the interface positions and fractional flows in the fracture. For lognormal aperture distributions, simple approximations to fractional flows are obtained in analytical form by assuming void occupancy based on a local capillary allowability criterion. The model is verified by analytical solutions including two-phase flow in a parallel-plate fracture, and used to study the impacts of aperture variation, mobility ratio and fracture orientation on properties of two-phase flow. Illustrative examples indicate that aperture variation may control the distribution of wetting and non-wetting fluids within the fracture plane and hence the ability of the fracture to transmit these fluids. The presence of wetting fluid does little to hinder non-wetting fluid flow in fractures with large aperture variations, whereas a small volume of non-wetting fluid present in the fracture can significantly reduce wetting fluid flow. Large mobility ratios and high fracture slope angles facilitates the migration of non-wetting fluid through fractures.     

Normal-stress dependence of fracture hydraulic properties including two-phase flow properties

A systematic approach has been developed for determining relationships between normal stress and fracture hydraulic properties, including two-phase flow properties. The development of a relationship between stress and fracture permeability (or fracture aperture and fracture closure) is based on a two-part Hooke’s model (TPHM) that captures heterogeneous elastic-deformation processes at a macroscopic scale by conceptualizing the rock mass (or a fracture) into two parts with different mechanical properties. The developed relationship was verified using a number of datasets in the literature for fracture closure versus stress, and satisfactory agreements were obtained. TPHM was previously shown to be able to accurately represent testing data for porous media as well. Based on the consideration that fracture–aperture distributions under different normal stresses can be represented by truncated-Gaussian distributions, closed-form constitutive relationships were developed between capillary pressure, relative permeability and saturation, for deformable horizontal fractures. The usefulness of these relationships was demonstrated by their consistency with a laboratory dataset.     

新场气田须二气藏天然裂缝有效性定量表征方法及应用

天然裂缝是地层中广泛分布的一种地质构造现象,当其在油气开发过程中保持一定有效性时具有重要作用,其有效程度高低是裂缝性油气藏高产富集的关键.本次研究以川西新场气田须二气藏裂缝特征及成因认识为基础,利用气藏各类动静态资料对裂缝张开度、裂缝渗透率、裂缝孔隙度等参数进行解释和评价,明确了不同资料计算获取裂缝参数的物理含义及相互之间的关系,为裂缝有效性评价奠定了基础.文中以井筒附近、地质模型网格单元体内裂缝网络系统作为裂缝有效性定量表征对象,通过裂缝网络系统裂缝参数的分布特征,选取并组合了参数分布的特征变量从而建立了裂缝有效性定量表征指标;基于裂缝有效性定量表征方法和建立的定量表征指标对新场气田须二气藏单井产层段裂缝的有效性及气藏裂缝有效性的纵横变化规律进行了研究和评价,其评价结果与区域构造、应力场分布、井下监测、生产动态具有很好的一致性.本文对油气藏中天然裂缝有效性的认识和定量表征方法为裂缝性油气藏地质建模中裂缝有效参数场的建立和数值模拟工作奠定了基础,为裂缝性油气藏的描述和生产动态研究提供了方向和思路.     

Semi-empirical equations for the systematic decrease in permeability with depth in porous and fractured media

Permeability loss with depth is a general trend in geological media and plays an essential role in subsurface fluid flow and solute transport. In the near surface zone where groundwater movement is active, the decrease in permeability with depth is dominated by the mechanical compaction of deformable media caused by the increase in lithostatic stress with depth. Instead of using empirical equations from statistical analysis, by considering the well-defined relationships among permeability, porosity, fracture aperture and effective stress under lithostatic conditions, new semi-empirical equations for the systematic depth-dependent permeability are derived, as well as the equations for the depth-dependent porosity in a porous medium and the depth-dependent fracture aperture in a fractured medium. The existing empirical equations can be included in the new equations as special cases under some simplification. These new semi-empirical equations perform better than previous equations to interpret the depth-dependent permeability of the Pierre Shale (with a maximum depth of approximately 4,500 m) and the granite at Stripa, Sweden (with a maximum depth of about 2,500 m).