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.     

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.

     

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part I: theory and formulation

Reservoir depletion results in rock failure, wellbore instability, hydrocarbon production loss, oil sand production, and ground surface subsidence. Specifically, the compaction of carbonate reservoirs with soft rocks often induces large plastic deformation due to rock pore collapse. On the other hand, following the compaction of reservoirs and failure of rock formations, the porosity and permeability of formations will, in general, decrease. These bring a challenge for reservoir simulations because of high nonlinearity of coupled geomechanics and fluid flow fields. In this work, we present a fully implicit, fully coupled, and fully consistent finite element formulation for coupled geomechanics and fluid flow problems with finite deformation and nonlinear flow models. The Pelessone smooth cap plasticity model, an important material model to capture rock compaction behavior and a challenging material model for implicit numerical formulations, is incorporated in the proposed formulation. Furthermore, a stress-dependent permeability model is taken into account in the formulation. A co-rotational framework is adopted for finite deformation, and an implicit material integrator for cap plasticity models is consistently derived. Furthermore, the coupled field equations are consistently linearized including nonlinear flow models. The physical theories, nonlinear material and flow models, and numerical formulations are the focus of part I of this work. In part II, we verify the proposed numerical framework and demonstrate the performance of our numerical formulation using several numerical examples including a field reservoir with soft rocks undergoing serious compaction.     

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.     

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。     

The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks

We present a discussion of the state-of-the-art on the use of discrete fracture networks (DFNs) for modelling geometrical characteristics, geomechanical evolution and hydromechanical (HM) behaviour of natural fracture networks in rock. The DFN models considered include those based on geological mapping, stochastic generation and geomechanical simulation. Different types of continuum, discontinuum and hybrid geomechanical models that integrate DFN information are summarised. Numerical studies aiming at investigating geomechanical effects on fluid flow in DFNs are reviewed. The paper finally provides recommendations for advancing the modelling of coupled HM processes in fractured rocks through more physically-based DFN generation and geomechanical simulation.     

Grain boundaries as microreactors during reactive fluid flow: experimental dolomitization of a calcite marble

Limestone dolomitization is an example of a fluid-induced mineralogical transformation that commonly affects extensive rock volumes. To understand the mechanisms enabling these efficient replacement reactions, we investigated experimentally the dolomitization of a fractured calcite marble under flow-through conditions at mild hydrothermal conditions. Contrary to most earlier studies of coupled dissolution reprecipitation reactions that were conducted using small, individual grains, in this study, the integrity of the rock was preserved, so that the experiment explored the links between flow in a fracture and fluid–rock interaction. In these experiments, grain boundaries acted as microreactors, in which a Mg-poor ‘protodolomite’ formed initially, and then transformed into dolomite. The difficulty in nucleating dolomite played a key role in controlling the evolution of the porosity, by allowing for (1) initial dissolution along grain boundaries, and (2) formation of coarse porosity at the reaction interface. This porosity evolution not only enabled the reaction to progress efficiently, but also controlled the mineralogy of the system, as shown by brucite replacing calcite near the fracture once the fluid along calcite grain boundaries became sufficiently connected to the fluid flowing through the fracture. This study illustrates the role of grain boundaries, porosity evolution and nucleation in controlling reaction progress as well as the nature and textures of the products in pervasive mineralogical transformations.     

构造-流体-成矿体系的反应-输运-力学耦合模型和动力学模拟

建立了一个综合的构造流体成矿体系的反应输运力学耦合动力学模型。利用有限元方法求解岩石变形、断裂作用和断裂网络统计动力学、流体流动、有机和无机地球化学反应及成岩成矿作用、压力溶液和其它压实力学、热迁移的方程组 ,可以对构造流体成矿体系的动力学演化过程进行 1～ 3维数值模拟。模拟的主要内容是在各种过程耦合作用下描述构造流体成矿体系的主要变量的时空演化 :( 1)与成矿流体的形成和性质有关的变量 ,如地层中矿物 (包括成矿物质 )的溶解速率、流体中各组分的浓度与饱和度、流体温度、压力、离子强度等 ;( 2 )与构造变形和流体运移有关的各变量 ,如应力与变形速率、岩石孔隙度、构造 (断裂 )渗透率等 ;( 3 )与沉淀成矿有关的变量 ,如矿物 (金属矿物和脉石矿物 )的成核速率、各矿物的沉淀量等 ;( 4 )上述各有关变量间的时空耦合关系 ,如断裂渗透率时空演化与流体流动、汇聚和成矿的耦合关系等。以湖南沃溪金锑钨矿床为例 ,应用该模型和方法对成矿动力学过程和动力学机制进行了初步的模拟与分析。     

岩体水力学基础（四）：岩体渗流场与应力场耦合的等效连续介质模型

本文把裂隙岩体看作等效连续介质，用渗透系数张量描述岩体的渗透性能；用应力张量描述岩体的力学性能。介绍岩体渗流场与应力场耦合的等效连续介质模型。     

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。     

A fracture mapping and extended finite element scheme for coupled deformation and fluid flow in fractured porous media

This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Modelling of fluid expulsion and deformation behaviour of dewatering sediments

A finite element model is developed for modelling coupled fluid expulsion/deformation behaviour of dewatering sediments subjected to external loadings under isothermal conditions. The non-linear deformation behaviour of the sediment (soil) skeleton is based on the force equilibrium equation in which the constitutive relationship of stress and strain is implemented by the modified Cam-Clay model in soil plasticity. The fluid flow behaviour in the model is described by the generalized porous media flow equation. The model allows temporal and spatial variations of porosity and permeability. The fluid viscosity and density are assumed to be temperature-dependent. The model also allows the development of single and multiple faults, depending upon the material (sediment and fluid) properties, loading and boundary conditions. Procedures are implemented for (1) updating the material properties such as porosity, permeability, fluid density and viscosity and (2) the development of faults which allow the formation of high-permeability conduits for fluid flow. The solution algorithm for displacements of the sediments and the excess pore (fluid) pressure is based on a residual load technique to handle the non-linear (elastic-plastic) deformation behaviour of the sediment skeleton. The model can be applied to one- and two-dimensional problems. Examples of a plane strain saturated sediment layer subjected to stepwise horizontal tractions versus time are given.     

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.     

岩体裂隙系统渗流场与应力场耦合模型

岩体系统具有复杂的结构。一般认为，岩体系统是非均质各向异性不连续的多相介质体系。当岩体以裂隙为主，且其分布较密集时，可将岩体系统看作等效连续多相介质体系。本文运用等效连续介质理论，提出了两种岩体裂隙系统渗流场与应力场耦合模型：一是以渗透水压力与隙变形关系、应力与渗透系统数关系为基础，建立渗透系数张量计算公式，进而建立等效效连续介质渗流为数学模型。以裂隙岩体应变张量分析为基础，建立裂隙岩体效应力张量     

渗流-化学溶解耦合作用下岩石单裂隙渗透特性研究

为揭示在渗流-化学溶解耦合作用下单裂隙渗透特性的变化规律,建立了描述二维渗流-化学溶解耦合作用的偏微分方程组,并利用COMSOL Multiphysics软件成功地求解该方程组。首先,模拟了文献[1]中的盐岩渗流-溶解耦合渗流试验结果,数值模拟结果与试验结果较为吻合,验证了数学模型的正确性和有效性。然后,利用分形理论生成了一个粗糙的裂隙面数字模型,着重分析了二维石灰岩粗糙裂隙面在水流、矿物溶解和输运过程中其渗透特性的变化规律。数值分析显示,（1）溶质浓度对裂隙面的溶解具有非常重要的作用,从而水流进口端的溶解厚度比出口端大得多。（2）裂隙的整体渗透性在初始时刻增加较慢,随着裂隙开度的增大和贯通,溶解速度会逐渐增大,是一个加速的过程。     

计算流体地球化学研究的进展

成矿作用的化学机理可以通过实验和计算机模拟进行研究。随着计算机运算能力的不断增强 ,在地球化学中正在形成一门新兴学科———计算地球化学。其中热质输运模拟、化学质量迁移数值模拟和流体输运化学反应耦合动力学研究取得了显著进展。建立在Darcy定律和守恒方程基础上的多孔介质热质输运模拟通过流函数图、等温线图及速率矢量图等 ,从古水文学和流体地球化学方面高度动态研究成矿作用。根据化学和热力学原理进行的化学质量迁移数值模拟则通过矿物和流体中化学物种的热力学数据 ,预测多组分体系中发生的流体岩石相互作用 ,定量揭示经历了复杂化学反应进程的成矿作用的化学行为。将上述两方面结合的流体输运化学反应耦合动力学 ,可以从时间和空间上模拟真实成矿流体系统复杂的动力学行为 ,是计算流体地球化学的发展方向。     

油井开采过程中油层变形的流固耦合分析

在油气开采过程中,随着油气的不断采出,必然造成孔隙流体压力的逐渐降低,由此导致储层岩石骨架的有效应力增大,使得油层产生变形或压实。当油层产生变莆或压实时,对油气生产将造成不利影响。比如：使得油藏的渗透率降低,继而使油井的产能降低,同时,油层的变形直接影响着油井和套管的变形与破坏等等。敢开采过程中油层的变形可以描述为三维变形与三维流体流动场的耦合问题,利用可变形多孔介质中流体渗流的流固耦合有限元数值     

Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method

This paper presents a coupled hydro‐mechanical formulation for the simulation of non‐planar three‐dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non‐planar three‐dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three‐dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

Review and classification of structural controls on fluid flow during regional metamorphism

Mechanisms for kilometre-scale, open-system fluid flow during regional metamorphism remain problematic. Debate also continues over the degree of fluid flow channellization during regional metamorphism, and the mechanisms for pervasive fluid flow at depth. The requirements for pervasive long-distance fluid flow are an interconnected porosity and a large regional gradient in fluid pressure and hydraulic head (thermally or structurally controlled) that dominates over local perturbations in hydraulic head due to deformation. In contrast, dynamic or transient porosity interconnection and fluid flow accompanying deformation of heterogeneous rock suites should result in moderately to strongly channellized flow at a range of scales, of which there are many examples in the literature. Classification of fluid flow types based on scale and degree of equilibration between fluid and rock, wallrock permeability, and mode of fluid transport contributes to an understanding of key factors that control fluid flow. Closed-system fluid behaviour, with restricted fluid flow in microcracks or cracks and limited fluid–rock interaction, occurs over a range of strains and crustal depths, but requires low permeabilities and/or small fluid fluxes. Long-distance, open-system fluid flow in channels is favoured in heterogeneous rocks at high strains, moderate (but variable) permeabilities, and moderate to high fluid fluxes. Long-distance, broad, pervasive fluid flow during regional metamorphism requires that the rocks are not accumulating high strains and have high permeabilities, low permeability contrasts, and high fluid fluxes. The ideal situation for such fluid flow is in situations where the rocks are undergoing stress relaxation immediately after a major deformation phase. In the mid-crust, fairly specific conditions are thus required for pervasive fluid flow. During active orogenesis, structurally controlled fluid flow (with focused open systems surrounding regions of closed-system behaviour) predominates in most, but not all, regional metamorphic situations, at a range of scales.