离散裂隙渗流方法与裂隙化渗透介质建模

流体渗流模拟的连续介质方法通常适用于多孔地质体，并不一定适用于裂隙岩体，由于裂隙分布及其特征与孔隙差异较大。若流体渗流主要受裂隙的控制，对于一定尺寸的裂隙岩体，多孔介质假设则较难刻划裂隙岩体的渗流特征。离散裂隙渗流方法不但可直接用于模拟裂隙岩体非均质性和各向异性等渗流特征，而且可用其确定所研究的裂隙岩体典型单元体及其水力传导（渗透）张量大小。主要讨论了以下问题：（1）饱和裂隙介质中一般的离散流体渗流模拟；（2）裂隙岩体中的REV（典型单元体）及其水力传导（渗透）张量的确定；（3）利用离散裂隙网络流体渗流模型研究裂隙方向几何参数对水力传导系数和REV的影响；（4）在二维和三维离散裂隙流体渗流模型中对区域大裂隙和局部小裂隙的处理方法。调查结果显示离散裂隙流体渗流数学模型可用来评价不同尺度上的裂隙岩体的水力特征，以及裂隙方向对裂隙化岩体的水力特征有着不可忽视的影响。同时，局部小裂隙、区域大裂隙应当区别对待，以便据其所起的作用及水力特征，建立裂隙化岩体相应的流体渗流模型。     

裂隙岩体渗流概念模型研究

裂隙岩体中的渗流和传统的多孔介质渗流在机理上存在本质的差别,这种差别主要表现为裂隙岩体在各种尺度上存在的非均质性。模拟裂隙岩体渗流的主要困难在于描述这种非均质性。目前的概念模型,包括等效连续体模型、离散裂隙网络模型和混合模型使用了不同的技术来预测裂隙岩体中的渗流。这些模型基于不同的假设和概念框架,有着各自不同的优缺点。在实际应用时,应当根据研究域的具体特点和所要解决的问题的要求对其选择,此外,还讨论了单裂隙的概念模型。     

裂隙岩体渗透系数确定方法研究

裂隙岩体渗透系数以及渗透主方向的确定对研究岩体渗透性大小及各向异性具有重要意义。高放废物地质处置库介质岩体的渗透性能将直接影响其使用安全性。本文运用离散裂隙网络模拟的方法对我国高放废物处置库甘肃北山预选区3#钻孔附近裂隙岩体进行了渗透性质分析。通过对3#钻孔171.5~178.0m段压水试验数据的反演,标定了离散裂隙网络渗流模型中的裂隙渗透参数(导水系数T)。利用标定的离散裂隙网络模型对场区裂隙岩体进行了渗流模拟,确定了该区域裂隙岩体的渗流表征单元体(REV)的尺寸大小以及渗透主值和主渗透方向。运用离散裂隙网络模型计算得出的渗透主值的几何均值与现场压水试验计算结果较接近,证明了计算结果的有效性。     

裂隙岩体渗透系数确定方法综述

总结了近年来裂隙岩体渗透系数的确定方法,主要有现场水力试验法、裂隙测量法和离散裂隙网络渗流数值试验法。每种方法都有自己的适用性和测量尺度。裂隙岩体渗透系数存在尺度效应,针对不同尺度的研究对象,应尽量选取与渗流模型网格剖分尺度匹配的测量方法。裂隙的延伸具有方向性,测试点的布设应合理科学,不同测量方法需要结合起来才能得到裂隙岩体真实的渗透系数。     

Stochastic continuum modeling of flow and transport in a crystalline rock mass: Fanay-Augères,France, revisited

A stochastic discrete-fracture model was used by Cacas et al.^a,b to interpret flow measurements and transport experiments in a fractured crystalline rock mass at Fanay-Augères. They considered continuum models to be incapable of properly interpreting small-scale measurements or tracer tests in fractured systems, which, in their view, require three-dimensional modeling of numerous discrete channels; in their opinion, continuum modeling applies only to average flow on a relatively large scale. Cacas et al. considered their discrete fracture model to have been validated by its demonstrated ability to reproduce selected experimental results. In this paper, flow and transport at Fanay-Augères are modeled by viewing the fractured rock as a stochastic continuum in a manner originally proposed by Neuman^c,d. The stochastic continuum approach obviates the need for detailed information about fracture geometry or assumptions about how individual fractures control flow and transport. All it requires is the delineation of a few dominant features, which can be embedded into the stochastic continuum model as heterogeneous porous slabs. Though a fault zone has been identified at the Fanay-Augères experimental site, it has been modeled neither by Cacas et al. nor in this paper. In fact, in this paper, a larger selection of experimental results than those considered by Cacas et al. are reproduced merely by modeling the rock as a statistically homogeneous continuum in two dimensions. These results demonstrate that a continuum approach may be well suited for the analysis of flow and transport in fractured rock. This does not constitute a validation of the continuum approach, just as the results of Cacas et al. fall short of validating the discrete fracture approach. Instead, the two sets of results illustrate jointly the well-established principle that an open system, especially one as complex as fractured hydrogeologic environments tend to be, cannot be described uniquely on the basis of sparse data and need not be described in great detail to capture its salient behavior by a model.^a Cacas MC, Ledoux E, de Marsily G, Barbreau A, Calmels P, Gaillard B, Margritta R (1990a) Modelling fracture flow with a stochastic discrete fracture network: calibration and validation. 1. The flow model. Water Resour Res 26(3):479–489^b Cacas MC, Ledoux E, de Marsily G, Barbreau A, Calmels P, Gaillard B, Margritta R (1990b) Modelling fracture flow with a stochastic discrete fracture network: calibration and validation. 2. The transport model. Water Resour Res 26(3):491–500^c Neuman SP (1987) Stochastic continuum representation of fractured rock permeability as an alternative to the REV and fracture network concepts, in Rock Mechanics. In: Farmer IW, Daemen JJK, Desai CS, Glass CE, Neuman SP (eds) Proceedings of the 28th U.S. Symposium, Tucson, Arizona. Balkema, Rotterdam, pp 533–561^d Neuman SP (1988) A proposed conceptual framework and methodology for investigating flow and transport in Swedish crystalline rocks. SKB Swedish Nuclear Fuel and Waste Management Co., Stockholm, September, Arbetsrapport 88–37, 39 pp     

A hybrid modeling approach to evaluate the groundwater flow system at the low- and intermediate-level radioactive waste disposal site in Gyeong-Ju, Korea

The development and implementation of a hybrid discrete fracture network/equivalent porous medium (DFN/EPM) approach to groundwater flow at the Gyeong-Ju low- and intermediate-level radioactive waste (LILW) disposal site in the Republic of Korea is reported. The geometrical and hydrogeological properties of fractured zones, background fractures and rock matrix were derived from site characterization data and implemented as a DFN. Several DFN realizations, including the deterministic fractured zones and the stochastic background fractures, whose statistical properties were verified by comparison with in-situ fracture and hydraulic test data, were suggested, and they were then upscaled to continuums using a fracture tensor approach for site-scale flow simulations. The upscaled models were evaluated by comparison to in-situ pressure monitoring data, and then used to simulate post-closure hydrogeology for the LILW facility. Simulation results demonstrate the importance of careful characterization and implementation of fractured zones. The study highlighted the importance of reducing uncertainty regarding the properties and variability of natural background fractures, particularly in the immediate vicinity of repository emplacement.     

裂隙岩体的多孔介质水力等效性研究

工程岩体中数量众多的裂隙面限制了离散裂隙网络模型在岩体渗流中的应用,迫使人们寻找能够用理论上成熟的等效连续介质模型替代,这就要求进行岩体多孔介质的水力等效性研究。在野外大量实测裂隙的基础上,进行裂隙密度、方位、大小、延续性、开度等几何参数的统计分析,以Enhanced Baecher模型建立离散裂隙网络随机模型,采用Monte-Carlo随机模拟方法进行三维裂隙网络随机模拟。在所生成的一定尺度的三维裂隙网络图基础上,给出计算研究域REV的方法,通过判断REV是否存在,确定能否用等效连续介质模型分析岩体渗流。     

Numerical estimation of REV and permeability tensor for fractured rock masses by composite element method

The Monte Carlo method is used to generate parent stochastic discrete fracture network, from which a series of fractured rock samples of different sizes and orientations are extracted. The fracture network combined with a regular grid forms composite element mesh of the fractured rock sample, in which each composite element is composed of sub‐elements incised by fracture segments. The composite element method (CEM) for the seepage is implemented to obtain the nodal hydraulic potential as well as the seepage flow rates through the fractured rock samples. The application of CEM enables a large quantity of stochastic tests for the fractured rock samples because the pre‐process is facilitated greatly. By changing the sizes and orientations of the samples, the analysis of the seepage characteristics is realized to evaluate the variation of the permeability components, the existence of the permeability tensor and the representative element volume. The feasibility and effectiveness are illustrated in a numerical example. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Fully coupled simulation of a hydraulic fracture interacting with natural fractures with a hybrid discrete‐continuum method

A hybrid discrete‐continuum numerical scheme is developed to study the behavior of a hydraulic fracture crossing natural fractures. The fully coupled hybrid scheme utilizes a discrete element model for an inner domain, within which the hydraulic fracture propagates and interacts with natural fractures. The inner domain is embedded in an outer continuum domain that is implemented to extend the length of the hydraulic fracture and to better approximate the boundary effects. The fracture is identified to propagate initially in the viscosity‐dominated regime, and the numerical scheme is calibrated by using the theoretical plane strain hydraulic fracture solution. The simulation results for orthogonal crossing indicate three fundamental crossing scenarios, which occur for various stress ratios and friction coefficients of the natural fracture: (i) no crossing, that is, the hydraulic fracture is arrested by the natural fracture and makes a T‐shape intersection; (ii) offset crossing, that is, the hydraulic fracture crosses the natural fracture with an offset; and (iii) direct crossing, that is, the hydraulic fracture directly crosses the natural fracture without diversion. Each crossing scenario is associated with a distinct net pressure history. Additionally, the effects of strength contrast and stiffness contrast of rock materials and intersection angle between the hydraulic fracture and the natural fracture are also investigated. The simulations also illustrate that the level of fracturing complexity increases as the number and extent of the natural fractures increase. As a result, we can conclude that complex hydraulic fracture propagation patterns occur because of complicated crossing behavior during the stimulation of naturally fractured reservoirs. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

A finite element method for modeling coupled flow and deformation in porous fractured media

Modeling the flow in highly fractured porous media by finite element method (FEM) has met two difficulties: mesh generation for fractured domains and a rigorous formulation of the flow problem accounting for fracture/matrix, fracture/fracture, and fracture/boundary fluid mass exchanges. Based on the recent theoretical progress for mass balance conditions in multifractured porous bodies, the governing equations for coupled flow and deformation in these bodies are first established in this paper. A weak formulation for this problem is then established allowing to build a FEM. Taking benefit from recent development of mesh‐generating tools for fractured media, this weak formulation has been implemented in a numerical code and applied to some typical problems of hydromechanical coupling in fractured porous media. It is shown that in this way, the FEM that has proved its efficiency to model hydromechanical phenomena in porous media is extended with all its performances (calculation time, couplings, and nonlinearities) to fractured porous media. Copyright © 2015 John Wiley & Sons, Ltd.     

REV and its properties on fracture system and mechanical properties,and an orthotropic constitutive model for a jointed rock mass in a dam site in China

Fracture data available for one of the rock masses (limestone) in the dam site of Yujian River Reservoir were used to build and validate a stochastic 3-D fracture network model, and to perform a REV and equivalent continuum study in 3-D. A number of relations are developed in the paper between the rock mass mechanical parameters and fracture tensor components in 3-D. Based on the mechanical parameter values obtained in every 45° direction in 3-D, the principal parameter values, principal directions and tensors are developed for rock mass mechanical parameters to represent the REV block size properties. An incrementally linear elastic, orthotropic constitutive model is suggested to represent the equivalent continuum pre-failure mechanical behavior of the jointed rock mass by incorporating the effect of joint geometry network by the fracture tensor components.     

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.     

Mechanical and hydraulic properties of rocks related to induced seismicity

Witherspoon, P.A. and Gale, J.E., 1977. Mechanical and hydraulic properties of rocks related to induced seismicity. Eng. Geol., 11(1): 23–55.The mechanical and hydraulic properties of fractured rocks are considered with regard to the role they play in induced seismicity. In many cases, the mechanical properties of fractures determine the stability of a rock mass. The problems of sampling and testing these rock discontinuities and interpreting their non-linear behavior are reviewed. Stick slip has been proposed as the failure mechanism in earthquake events. Because of the complex interactions that are inherent in the mechanical behavior of fractured rocks, there seems to be no simple way to combine the deformation characteristics of several sets of fractures when there are significant perturbations of existing conditions. Thus, the more important fractures must be treated as individual components in the rock mass.In considering the hydraulic properties, it has been customary to treat a fracture as a parallel-plate conduit and a number of mathematical models of fracture systems have adopted this approach. Non-steady flow in fractured systems has usually been based on a two-porosity model, which assumes the primary (intergranular) porosity contributes only to storage and the secondary (fracture) porosity contributes only to the overall conductivity. Using such a model, it has been found that the time required to achieve quasi-steady state flow in a fractured reservoir is one or two orders of magnitude greater than it is in a homogeneous system. In essentially all of this work, the assumption has generally been made that the fractures are rigid.However, it is clear from a review of the mechanical and hydraulic properties that not only are fractures easily deformed but they constitute the main flow paths in many rock masses. This means that one must consider the interaction of mechanical and hydraulic effects. A considerable amount of laboratory and field data is now available that clearly demonstrates this stress-flow behavior. Two approaches have been used in attempting to numerically model such behavior: (1) continuum models, and (2) discrete models. The continuum approach only needs information as to average values of fracture spacing and material properties. But because of the inherent complexity of fractured rock masses and the corresponding decrease in symmetry, it is difficult to develop an equivalent continuum that will simulate the behavior of the entire system. The discrete approach, on the other hand, requires details of the fracture geometry and material properties of both fractures and rock matrix. The difficulty in obtaining such information has been considered a serious limitation of discrete models, but improved borehole techniques can enable one to obtain the necessary data, at least in shallow systems. The possibility of extending these methods to deeper fracture systems needs more investigation. Such data must be considered when deciding whether to use a continuum or discrete model to represent the interaction of rock and fluid forces in a fractured rock system, especially with regard to the problem of induced seismicity. When one is attempting to alter the pressure distribution in a fault zone by injection or withdrawal of fluids, the extent to which this can be achieved will be controlled in large measure by the behavior of the fractures that communicate with the borehole. Since this is essentially a point phenomenon, i.e., the changes will propagate from a relatively small region around the borehole, the use of a discrete model would appear to be preferable.     

Regional fracture network permeability using outcrop scale measurements

Estimating the hydraulic properties of fractured aquifers is challenging due to the complexity of structural discontinuities that can generally be measured at a small scale, either in core or in outcrop, but influence groundwater flow over a range of scales. This modeling study uses fracture scanline data obtained from surface bedrock exposures to derive estimates of permeability that can be used to represent the fractured rock matrix within regional scale flow models. The model is developed using PETREL, which traditionally benefits from high resolution data sets obtained during oil and gas exploration, including for example seismic data, and borehole logging data (both lithological and geophysical). The technique consists of interpreting scanline fracture data, and using these data to generate representative Discrete Fracture Network (DFN) models for each field set. The DFN models are then upscaled to provide an effective hydraulic conductivity tensor that represents the fractured rock matrix. For each field site, the upscaled hydraulic conductivities are compared with estimates derived from pumping tests to validate the model. A hydraulic conductivity field is generated for the study region that captures the spatial variability of fracture networks in pseudo-three dimensions from scanline data. Hydraulic conductivities estimated using this approach compare well with those estimated from pumping test data. The study results suggest that such an approach may be feasible for taking small scale fracture data and upscaling these to represent the aquifer matrix hydraulic properties needed for regional groundwater modeling.     

非饱和带裂隙岩体渗流的特点和概念模型

非饱和带裂隙岩体中的渗流和饱和带相比有其不同的特点,包括毛细管流、薄膜流、优先流和裂隙-基质相互作用等。这些特点导致非饱和带裂隙岩体中的渗流具有相当的非均质性。笔者描述了裂隙岩体中非饱和渗流的这些特点,并简单讨论了目前所存在的模拟非饱和渗流的概念模型。     

Simulation of groundwater flow in fractured rocks using a coupled model based on the method of domain decomposition

Groundwater flow in fractured rocks is modeled using a coupled model based on the domain decomposition method. In the model, the fractured porous medium is divided into two non-overlapping sub-domains. One is the rock matrix, in which the medium is described using a continuum model. The other consists of deep fractures and fissure zones, where the medium is described using a discrete fracture network (DFN) model. The two models are coupled through the continuity of the hydraulic heads and fluxes on the common boundaries. The coupled model is used to simulate groundwater flow in a hydropower station. The results show that the model simulates groundwater levels that are in agreement with the measured groundwater levels. Furthermore, the model’s parameters relating to deep fractures and fissure zones are verified by comparing three different models (the continuum model, coupled model, and DFN model). The results show that the coupled model can capture and duplicate the hydrogeological conditions in the study domain, whereas the continuum model overestimates and the DFN model underestimates the measured hydraulic heads. A sensitivity analysis shows that fracture aperture has a considerable effect on the groundwater level. So, when the fracture aperture is large, the coupled model or DFN model is more appropriate than the continuum model in the fracture domain.     

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