An Integrated Numerical Modelling–Discrete Fracture Network Approach Applied to the Characterisation of Rock Mass Strength of Naturally Fractured Pillars

Naturally fractured mine pillars provide an excellent example of the importance of accurately determining rock mass strength. Failure in slender pillars is predominantly controlled by naturally occurring discontinuities, their influence diminishing with increasing pillar width, with wider pillars failing through a combination of brittle and shearing processes. To accurately simulate this behaviour by numerical modelling, the current analysis incorporates a more realistic representation of the mechanical behaviour of discrete fracture systems. This involves realistic simulation and representation of fracture networks, either as individual entities or as a collective system of fracture sets, or a combination of both. By using an integrated finite element/discrete element–discrete fracture network approach it is possible to study the failure of rock masses in tension and compression, along both existing pre-existing fractures and through intact rock bridges, and incorporating complex kinematic mechanisms. The proposed modelling approach fully captures the anisotropic and inhomogeneous effects of natural jointing and is considered to be more realistic than methods relying solely on continuum or discontinuum representation. The paper concludes with a discussion on the development of synthetic rock mass properties, with the intention of providing a more robust link between rock mass strength and rock mass classification systems.     

裂缝诱导双相HTI介质模型及其弹性波传播方程

将Biot双相介质理论与Gurevich裂缝各向异性理论相结合,建立了能够同时考虑实际裂缝性储层孔隙性和各向异性的裂缝诱导双相HTI介质模型。从本构方程、动力学方程和动力学达西定律出发,推导出了裂缝诱导双相HTI介质中弹性波传播的一阶速度-应力方程,并针对方程的刚性问题,给出了利用显式二阶时间积分法数值求解该方程时所需要满足的稳定性条件。该方程能够定量地给出双相HTI介质的波场特征与裂缝参数、背景孔隙介质参数之间的关系,描述弹性波在这种介质中的传播机理。     

Boundary element analysis of contaminant transport in fractured porous media

A two-dimensional boundary integral method to analyse the flow of contaminant in fractured media having a two- or three-dimensional orthogonal fracture network is presented. The method assumes that the fractures provide the paths of least resistance for transport of contaminants while the matrix, because of its low permeability, acts as ‘storage blocks’ into which the contaminant diffuses. Laplace transform is used to eliminate the time variable in the governing equation in order to facilitate the formulation of a boundary integral equation in the Laplace transform space. Conventional boundary element techniques are applied to solve for the contaminant concentrations at specified locations in the spatial domain. The concentration in the time domain is then obtained by using an efficient inversion technique developed by Talbot. The method is able to analyse the behaviour of waste repositories which have diminishing concentration due to the mass transport of the contaminant into the surrounding fractured media.     

Coping with uncertainties through an automated workflow for 3D reservoir modelling of carbonate reservoirs

Reliable 3D modelling of underground hydrocarbon reservoirs is a challenging task due to the complexity of the underground geological formations and to the availability of different types of data that are typically affected by uncertainties.In the case of geologically complex depositional environments,such as fractured hydrocarbon reservoirs,the uncertainties involved in the modelling process demand accurate analysis and quantification in order to provide a reliable confidence range of volumetric estimations.In the present work,we used a 3D model of a fractured carbonate reservoir and populated it with different lithological and petrophysical properties.The available dataset also included a discrete fracture network(DFN)property that was used to model the fracture distribution.Uncertainties affecting lithological facies,their geometry and absolute positions(related to the fault system),fracture distribution and petrophysical properties were accounted for.We included all different types of uncertainties in an automated approach using tools available in today's modelling software packages and combining all the uncertain input parameters in a series of statistically representative geological realizations.In particular,we defined a specific workflow for the definition of the absolute permeability according to an equivalent,single porosity approach,taking into account the contribution of both the matrix and the fracture system.The results of the analyses were transferred into a 3D numerical fluid-dynamic simulator to evaluate the propagation of the uncertainties associated to the input data down to the final results,and to assess the dynamic response of the reservoir following a selected development plan.The"integrated approach"presented in this paper can be useful for all technicians involved in the construction and validation of 3D numerical models of hydrocarbon-bearing reservoirs and can potentially become part of the educational training for young geo-scientists and engineers,since an integrated and well-constructed workflow is the backbone of any reservoir study.     

A Spatial Clustering Approach for Stochastic Fracture Network Modelling

Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for  fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach followed by a real 3D case study of the Habanero reservoir in the Cooper Basin, Australia.     

The Development of a new Numerical Modelling Approach for Naturally Fractured Rock Masses

Summary. An approach for modelling fractured rock masses has been developed which has two main objectives: to maximise the quality of representation of the geometry of existing rock jointing and to use this within a loading model which takes full account of this style of jointing. Initially the work has been applied to the modelling of mine pillars and data from the Middleton Mine in the UK has been used as a case example. However, the general approach is applicable to all aspects of rock mass behaviour including the stress conditions found in hangingwalls, tunnels, block caving, and slopes. The rock mass fracture representation was based on a combination of explicit mapping of rock faces and the synthesis of this data into a three-dimensional model, based on the use of the FracMan computer model suite. Two-dimensional cross sections from this model were imported into the finite element computer model, ELFEN, for loading simulation. The ELFEN constitutive model for fracture simulation includes the Rotating Crack, and Rankine material models, in which fracturing is controlled by tensile strength and fracture energy parameters. For tension/compression stress states, the model is complemented with a capped Mohr-Coulomb criterion in which the softening response is coupled to the tensile model. Fracturing due to dilation is accommodated by introducing an explicit coupling between the inelastic strain accrued by the Mohr-Coulomb yield surface and the anisotropic degradation of the mutually orthogonal tensile yield surfaces of the rotating crack model. Pillars have been simulated with widths of 2.8, 7 and 14 m and a height of 7 m (the Middleton Mine pillars are typically 14 m wide and 7 m high). The evolution of the pillar failure under progressive loading through fracture extension and creation of new fractures is presented, and pillar capacities and stiffnesses are compared with empirical models. The agreement between the models is promising and the new model provides useful insights into the influence of pre-existing fractures. Further work is needed to consider the effects of three-dimensional loading and other boundary condition problems.     

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.     

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。     

裂缝性储集层表征及建模方法研究进展

从目前裂缝性储层表征及建模研究现状入手,结合自身实践,详细介绍了裂缝性储层表征及建模研究中的各种方 法,分析了每种方法的优缺点。裂缝表征中主要使用的方法包括：野外露头分析法、岩心分析法、测井分析法、地震预测 分析法、动态响应分析法、岩石力学分析法。裂缝建模中主要使用离散裂缝网格模型和等效连续模型两种方法。其中,重 点介绍了分形理论在野外火山岩露头裂缝分析中的应用、数字岩心技术在微观裂缝表征中的应用、各种最新的地球物理及 岩石力学表征和预测裂缝的方法、动态裂缝在裂缝性油藏开发的作用、近年来国外学者所倡导的裂缝地层学理论、非常规 储层中的裂缝表征,以及上述两种裂缝地质建模方法。在此基础上,讨论了裂缝性储层表征及建模中存在的问题,最终指 出了该项研究未来发展的趋势。     

基于离散裂隙网络模型的核素粒子迁移数值模拟研究

高放废物地质处置过程中涉及的核素在围岩裂隙地下水中的迁移问题已引起广泛关注,数值模拟是研究核素粒子运移的重要方法。目前裂隙介质中渗流模型主要是等效连续介质模型、双重介质模型和离散裂隙网络模型。对于岩体尺度裂隙地下水的流动,离散裂隙网络模型能充分表现裂隙介质的各向异性、不连续性等特征。因此,针对裂隙介质准确概化及核素迁移模拟等难点,文章结合Monte Carlo随机生成裂隙方法、裂隙渗流有限元算法和高放射性核素衰变方程等方法,依据花岗岩深钻孔裂隙统计数据,采用离散裂隙网络模型对内蒙古阿拉善高放废物地质处置预选区展开了核素粒子迁移数值模拟研究,并讨论了实例预测分析结果。结果显示:针对设定的地质模型,核素粒子从中心运移到边界的迁移路径长度平均为1293.35 m,粒子运移到边界耗费的时间平均为1.70E+11 d。     

Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics

We propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a pruned DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. The method allows for the level of accuracy to be a user-controlled parameter.     

Laboratory investigation of hydraulic fracture propagation using real-time ultrasonic measurement in shale formations with random natural fractures

The significance of natural fractures in unconventional shale hydrocarbon formations has opened new research frontiers in hydraulic fracturing. Among many of its unique contributions to gas production, the interaction between natural fractures and hydraulic fractures has long been experimentally and computationally investigated. Here, we experimentally investigated the evolution of the fracturing network with a self-developed ultrasonic testing system. Laboratory experiments are proposed to study the propagation of hydraulic fracture in naturally fractured model blocks that contain random micro-fractures. Our analysis suggests that the total fracture width obtained by ultrasonic pulse velocity (UPV) can reflect the dynamic evolution of the fracturing network. The nonlinear fracturing network evolution process is closely related to the variation of the total fracture width. It is suggested from the total fracture width that the maximum fracture network can be realized with greater natural fracture density, large injection rate, and smaller stress ratio. The study presents a better insight into the response of random naturally fractured shale formation under hydraulic fracturing treatment by analyzing the variation of UPV in real time.     

可变倾角单裂隙动水注浆模型试验研究

突涌水灾害对地下工程危害严重,实践表明,注浆是治理突涌水灾害的有效方法。近年来,裂隙岩体注浆理论的研究成为热点,但裂隙动水注浆理论发展缓慢,不能有效指导工程实践。在水平裂隙动水注浆U型扩散理论基础上,研发可变倾角小比例裂隙动水注浆模型试验系统,开展多组室内模型试验,研究倾角对裂隙动水注浆扩散规律的影响机制,同时,利用COMSOL软件对一定倾角的裂隙动水注浆扩散进行数值模拟。研究表明：当裂隙水平时,满足U型扩散形态;当裂隙存在倾角时,在动水水头差和浆液自身重力因素作用下,浆液呈现彗星状扩散形态;相同扩散效果下,注浆速率随裂隙倾角的增加呈抛物线型增长规律,增加注浆速率可以保持注浆孔附近相对于其周边区域的浓度梯度优势。该研究结论对于目前裂隙动水注浆理论是一种重要补充,对指导突涌水灾害治理有一定的实践意义。     

Modeling of subsidence and stress-dependent hydraulic conductivity for intact and fractured porous media

Summary This study investigates the changes in deformation and stress dependent hydraulic conductivities that occur as a result of underground mining in intact and fractured porous media. The intact porous medium is assumed to be comprised of regularly packed spherical grains of uniform size. The variation in grain size or pore space due to the effect of changing intergranular stresses results in a change in rock hydraulic conductivity. A model is developed to describe the sensitivity of hydraulic conductivity to effective stresses through Hertzian contact of spherical grains. The fractured porous medium is approximated as an equivalent fracture network in which a single fracture is idealized as a planar opening having a constant equivalent thickness or aperture. Changes in fracture aperture as a result of changes in elastic deformation control the variation of hydraulic conductivity. A model is presented to illustrate the coupling between strain and hydraulic conductivity. Subsidence induced deformations that result from mining induced changes in hydraulic conductivity in both intact and fractured media. These changes are examined and compared with results from a mining case study.     

Heterogeneity preserving upscaling for heat transport in fractured geothermal reservoirs

In simulation of fluid injection in fractured geothermal reservoirs, the characteristics of the physical processes are severely affected by the local occurence of connected fractures. To resolve these structurally dominated processes, there is a need to develop discretization strategies that also limit computational effort. In this paper, we present an upscaling methodology for geothermal heat transport with fractures represented explicitly in the computational grid. The heat transport is modeled by an advection-conduction equation for the temperature, and solved on a highly irregular coarse grid that preserves the fracture heterogeneity. The upscaling is based on different strategies for the advective term and the conductive term. The coarse scale advective term is constructed from sums of fine scale fluxes, whereas the coarse scale conductive term is constructed based on numerically computed basis functions. The method naturally incorporates the coupling between solution variables in the matrix and in the fractures, respectively, via the discretization. In this way, explicit transfer terms that couple fracture and matrix solution variables are avoided. Numerical results show that the upscaling methodology performs well, in particular for large upscaling ratios, and that it is applicable also to highly complex fracture networks.     

Review: The state-of-art of sparse channel models and their applicability to performance assessment of radioactive waste repositories in fractured crystalline formations

Laboratory and field experiments done on fractured rock show that flow and solute transport often occur along flow channels. ‘Sparse channels’ refers to the case where these channels are characterised by flow in long flow paths separated from each other by large spacings relative to the size of flow domain. A literature study is presented that brings together information useful to assess whether a sparse-channel network concept is an appropriate representation of the flow system in tight fractured rock of low transmissivity, such as that around a nuclear waste repository in deep crystalline rocks. A number of observations are made in this review. First, conventional fracture network models may lead to inaccurate results for flow and solute transport in tight fractured rocks. Secondly, a flow dimension of 1, as determined by the analysis of pressure data in well testing, may be indicative of channelised flow, but such interpretation is not unique or definitive. Thirdly, in sparse channels, the percolation may be more influenced by the fracture shape than the fracture size and orientation but further studies are needed. Fourthly, the migration of radionuclides from a waste canister in a repository to the biosphere may be strongly influenced by the type of model used (e.g. discrete fracture network, channel model). Fifthly, the determination of appropriateness of representing an in situ flow system by a sparse-channel network model needs parameters usually neglected in site characterisation, such as the density of channels or fracture intersections.     

Application of Stochastic Fracture Network with Numerical Fluid Flow Simulations to Groundwater Flow Modeling in Fractured Rocks

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利用三维裂隙网络确定岩体渗透张量的方法

对于可统计的岩石结构面数据,采用结构面三维网络模拟技术研究节理岩体力学特性特别是岩石水力学性质的过程中,三维裂隙网络与多孔连续介质渗流各向异性的等效方法是研究岩石水力学应用中的重要环节。本文基于流量等效,边界条件相同,根据渗透张量的性质,利用计算机模拟三维裂隙网络的样本单元推导二阶渗透张量的求解方法。最后,通过一个圆形随机结构面形成的裂隙网络样本单元的计算实例,与张量法的计算结果作了对照,说明了有限大小结构面形成的裂隙网络,利用本文提出的方法求解得到的样本单元等效渗透性,具有相当的合理性。本文的方法对于岩石水力学中三维问题的研究具有重要的理论指导作用。     

Fully coupled hydro-mechanical numerical manifold modeling of porous rock with dominant fractures

Coupled hydro-mechanical (HM) processes are significant in geological engineering such as oil and gas extraction, geothermal energy, nuclear waste disposal and for the safety assessment of dam foundations and rock slopes, where the geological media usually consist of fractured rock masses. In this study, we developed a model for the analysis of coupled hydro-mechanical processes in porous rock containing dominant fractures, by using the numerical manifold method (NMM). In the current model, the fractures are regarded as different material domains from surrounding rock, i.e., finite-thickness fracture zones as porous media. Compared with the rock matrix, these fractured porous media are characterized with nonlinear behavior of hydraulic and mechanical properties, involving not only direct (poroelastic) coupling but also indirect (property change) coupling. By combining the potential energy associated with mechanical responses, fluid flow and solid–fluid interactions, a new formulation for direct HM coupling in porous media is established. For indirect coupling associated with fracture opening/closure, we developed a new approach implicitly considering the nonlinear properties by directly assembling the corresponding strain energy. Compared with traditional methods with approximation of the nonlinear constitutive equations, this new formulation achieves a more accurate representation of the nonlinear behavior. We implemented the new model for coupled HM analysis in NMM, which has fixed mathematical grid and accurate integration, and developed a new computer code. We tested the code for direct coupling on two classical poroelastic problems with coarse mesh and compared the results with the analytical solutions, achieving excellent agreement, respectively. Finally, we tested for indirect coupling on models with a single dominant fracture and obtained reasonable results. The current poroelastic NNM model with a continuous finite-thickness fracture zone will be further developed considering thin fractures in a discontinuous approach for a comprehensive model for HM analysis in fractured porous rock masses.     

Geometric modelling and object-oriented software concepts applied to a heterogeneous fractured network from the Grimsel rock laboratory

Discrete fracture network simulations are computationally intensive and usually time-consuming to construct and configure. This paper presents a case study with techniques for building a 3D finite element model of an inhomogeneous fracture network for modelling flow and tracer transport, combining deterministic and stochastic information on fracture aperture distributions. The complex intersected fractures represent a challenge for geometrical model design, mesh quality requirements and property allocations. For the integrated and holistic modelling approach, including the application of numerical and analytical simulation techniques, new object-oriented concepts in software engineering are implemented to ensure a resourceful and practicable software environment.