Stochastic Representation of Sedimentary Geology

Discrete fracture network representations of discontinuities in rock masses have been shown to be useful in capturing heterogeneity in rock mass properties. Providing computational efficiency in the resulting simulations and analyses is attained, these fracture representations can be combined with structural modelling and sampling algorithms. Multiple fracture network realisations can be generated and the resulting rock mass properties interrogated. Statistical analyses based on fracture connectivity, block size distribution and slope stability can be performed and provide results defined in terms of confidence intervals. For sedimentary geology consisting of dense bedding, equivalent medium continuum methods have traditionally been used in preference to discrete fracture representations due to the large numbers of structures involved and resulting computational complexity. In this paper, it is shown that stochastic representation of these layers can be employed. An analytical solution to accommodate bedding given an assumed block size distribution has been derived. Using this formulation, polyhedral modelling has been used to investigate the influence of bedding on block formation and block size distributions using field data. It is shown that the analysis is both computationally efficient and can capture truncation of size distribution by such layers without numerical methods.     

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.     

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.     

高陡岩质斜坡的结构面非接触式采集技术与三维裂隙网络模拟研究

本文分别以非接触式测量与三维裂隙网络模拟技术对汶川县绵虒镇大溪沟沟口高陡斜坡的结构面系统进行了深入研究。以无人机、数字近景摄影测量与三维激光扫描方法建立了现场斜坡的三维DEM模型并识别与解译了斜坡的结构面系统。尤其是采用无人机与近景摄影测量技术,识别并解译了整体斜坡的长大控制性结构面与坡面上的6663条随机构造结构面。基于以上数据,本文提出了一种适用于高陡斜坡分析的超大窗口三维裂隙网络模拟方法,采用概率统计与空间几何推导的方法,建立了岩体三维结构面的直径、产状与密度计算方法。这种方法更加简便且针对性强,现场验证也表明其具有较高的模拟精度。     

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.     

Fracture network versus single fractures: Measurement of fracture geometry with X-ray tomography

Several long-standing questions concerning fluid transport in fractured rock involve the geometrical properties of the connected void space within a fracture network. We present experimental results that compare the geometrical properties of a fracture network to those of the individual fractures in the network. To image and quantify the aperture distribution of natural fracture networks in coal, a Wood's metal injection method is combined with X-ray computerized tomography and image analysis. We find that the aperture distribution of the networks is spatially anisotropic and dependent on the number and geometry of the individual fractures. Void area in the individual fractures ranged between 45%–58%. A three-dimensional auto-correlation analysis on the fracture network and a two-dimensional analysis on the individual fractures found that the apertures were correlated over distances of 10 mm to 20 mm in the direction of flow.     

An enhanced stochastic optimization in fracture network modelling conditional on seismic events

This paper presents an approach to modelling fracture networks in hot dry rock geothermal reservoirs. A detailed understanding of the fracture network within a geothermal reservoir is critically important for assessments of reservoir potential and optimal production design. One important step in fracture network modelling is to estimate the fracture density and the fracture geometries, particularly the size and orientation of fractures. As fracture networks in these reservoirs can never be directly observed there is significant uncertainty about their true nature and the only feasible approach to modelling is a stochastic one. We propose a global optimization approach using simulated annealing which is an extension of our previous work. The fracture model consists of a number of individual fractures represented by ellipses passing through the micro-seismic points detected during the fracture stimulation process, i.e. the fracture model is conditioned on the seismic points. The distances of the seismic points from fitted fracture planes (ellipses) are, therefore, important in assessing the goodness-of-fit of the model. Our aims in the proposed approach are to formulate an appropriate objective function for the optimal fitting of a set of fracture planes to the micro-seismic data and to derive an efficient modification scheme to update the model parameters. The proposed objective function consists of three components: orthogonal projection distances of the seismic points from the nearest fitted fractures, the amount of fracturing (fitted fracture areas) and the volumes of the convex hull of the associated points of fitted fractures. The functions used in the model update scheme allow the model to achieve an acceptable fit to the points and to converge to acceptable fitted fracture sizes. These functions include two groups of proposals: one for updating fracture parameters and the other for determining the size of the fracture network. To increase the efficiency of the optimization, a spatial clustering approach, the Distance-Directional Transform, was developed to generate parameters for newly proposed fractures. A simulated dataset was used as an example to evaluate our approach and we compared the results to those derived using our previously published algorithm on a real dataset from the Habanero geothermal field in the Cooper Basin, South Australia. In a real application, such as the Habanero dataset, it is difficult to determine definitively which algorithm performs better due to the many uncertainties but the number of association points, the number of final fractures and the error are three important factors that quantify the effectiveness of our algorithm.     

Pseudofaults resulting from compartmentalized Liesegang bands: update

Abstract Liesegang bands with apparent offset along fractures are common in some calcisiltite beds. Thin sections show, however, that primary laminations are not offset along the fractures. Following the development of fracture sets in the calcisiltite, the fractures were cemented by calcite. This formed polyhedral compartments of low‐permeability calcisiltite bounded by impermeable walls of calcite. Liesegang bands formed when oxygen in ground water diffused into polyhedra containing soluble ferrous iron in pore water. Each joint‐bounded polyhedral compartment behaved as an independent diffusion cell. Liesegang bands with nearly the same pattern and thickness tended to develop in adjacent compartments, but not at the same stratigraphic level; this resulted in the formation of pseudofaults.     

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.     

Rockfall Hazard Analysis From Discrete Fracture Network Modelling with Finite Persistence Discontinuities

Developing an accurate representation of the rock mass fabric is a key element in rock fall hazard analysis. The orientation, persistence and density of fractures control the volume and shape of unstable blocks or compartments. In this study, the discrete fracture modelling technique and digital photogrammetry were used to accurately depict the fabric. A volume distribution of unstable blocks was derived combining polyhedral modelling and kinematic analyses. For each block size, probabilities of failure and probabilities of propagation were calculated. A complete energy distribution was obtained by considering, for each block size, its occurrence in the rock mass, its probability of falling, its probability to reach a given location, and the resulting distribution of energies at each location. This distribution was then used with an energy–frequency diagram to assess the hazard.     

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。     

Explicit Fracture Network Modelling: From Multiple Point Statistics to Dynamic Simulation

This paper addresses the problem of explicit fractured media modelling in an operational case. On one side, realistic fracture models are mainly used for research purposes in order to investigate better the flow behaviour impacted by the complex multi-scale fracture network. Often, a very fine grid and hence an increased computation time are needed. On the other hand, an operational fractured reservoir is still generally modelled using an implicit fracture media representation. The upscaled petrophysical properties and dual media are defined on a coarse grid to limit the computational time of dynamic simulation. The challenge of this work is to demonstrate that an explicit fracture modelling is not reserved only for the research domain, but can be applied to an operational case study. The static model is constructed using a multiple point statistics approach in order to represent complex interaction patterns of fractures and faults observed at the analogue outcrop. The dynamic behaviour is simulated based on this spatial fracture network representation.     

不同水力加载条件下非均质储层缝网扩展规律研究

水力压裂可显著提高页岩气等致密储层岩体的渗透性以增加油气产量,然而受多因素影响,水力压裂形成缝网结构的机理和压裂优化设计一直是研究的焦点和难点。本研究基于渗流-应力-破坏耦合计算模拟方法,对不同水力加载条件下的非均质储层水力压裂过程进行了模拟和对比研究。研究结果表明:水力压裂过程中起始注水压力和增量大小对水力压裂缝网扩展和改造区域形态有着显著的影响。当起始注水压力小于等于模型材料体抗拉强度,并缓慢增压致裂时,压裂过程可近似视为稳态应力-破坏-渗流耦合作用过程的不同阶段,这种情况下仅在压裂井孔周围形成两组对称式的伞状水力裂缝带。当对模型体施加高于模型材料体破裂压力的注水压力时,相当于对压裂孔快速施加高动水压力,水力裂缝沿压裂孔全方位迅速萌生并快速扩展,当注水压力值高于破裂压力一定幅值时,压裂改造可形成围绕压裂井全方位的放射状裂缝网络,使压裂储层得以最大范围改造。在拟静力和拟动力两种加载条件下,不同水岩相互作用机理是造成不同水力加载条件出现不同缝网结构的力学机制,而对于实际的页岩气储层改造,压裂产生围绕压裂井全方位放射状的缝网结构则是一种最优的体积压裂改造。     

煤岩水力压裂裂缝扩展形态试验研究

通过室内水力压裂物理模拟试验系统,对大尺寸原煤进行了水力压裂模拟试验,根据水力裂缝的空间展布形态分析了煤岩储层水力裂缝的延伸规律,揭示了网状裂缝的形成机制。结果表明：水力裂缝易在弱层理处分叉和转向,发育的层理和裂缝系统等结构面为压裂形成裂缝网络提供了前提条件。泵压曲线呈现出的频繁波动是煤岩内产生网状裂缝的一个显著特征。水力裂缝的起裂与延伸有4种基本模式,裂缝网络的形成多为这4种基本模式的组合。地应力差异系数和泵注排量对煤层水力裂缝形态有较大影响。较小的地应力差异系数更利于网状裂缝的形成;较高的压裂液排量易形成相对简单的裂缝形态,导致压裂改造效果较差。该试验方法和试验结果可为现场水力压裂参数设计和优化提供参考和依据。     

Numerical simulation of fracture flow with a mixed-hybrid FEM stochastic discrete fracture network model

We introduce a discrete fracture network model of stationary Darcy flow in fractured rocks. We approximate the fractures by a network of planar circle disks, which is generated on the basis of statistical data obtained from field measurements. We then discretize this network into a mesh consisting of triangular elements placed in three-dimensional space. We use geometrical approximations in fracture planes, which allow for a significant simplification of the final triangular meshes. We consider two-dimensional Darcy flow in each fracture. In order to accurately simulate the channeling effect, we assign to each triangle an aperture defining its hydraulic permeability. For the discretization we use the lowest order Raviart-Thomas mixed finite element method. This method gives quite an accurate velocity field, which is computed directly and which satisfies the mass balance on each triangular element. We demonstrate the use of this method on a model problem with a known analytical solution and describe the generation and triangulation of the fracture network and the computation of fracture flow for a particular real situation.     

Can tensile stress develop in fractured multilayers under compressive strain conditions?

To contribute to the understanding of how opening-mode fractures (joints) form and open or close at depth in layered rocks, we present a 2D numerical study aiming to determine whether tensile stress can develop in pre-fractured elastic multilayers submitted to biaxial compressive strain conditions.First, we investigate the role of the elastic and geometrical properties of the layers on the development of tensile stress in models with five bonded layers and containing one open fracture in the central layer. Our results indicate that, in absence of elastic contrast (in Young's modulus) between the layers, no tensile stress develops in the models. However, when the fractured layer is stiffer than the two adjacent layers directly above and below, a lobe of horizontal tensile stress develops centered on the pre-existing fracture. The creation of this tensile stress is contingent upon the partial closing of the fracture. The levels of tensile stress and the thickness of the lobe of tensile stress increase logarithmically with an increase in the elastic contrast and are systematically larger for a larger Soft/Stiff ratio (ratio of the total thickness of the soft layers with the total thickness of the stiff layers).Second, we investigate the role of fracture interaction in the development of tensile stress in models containing a pair of open fractures. We observe that the levels of tensile stress in the region between the fractures are systematically higher than those observed in identical models containing a single fracture. This increase in tensile stress is very large for small elastic contrasts between the layers but diminishes when the elastic contrast increases. Furthermore, the spacing between the pre-existing fractures plays an important role in the stress distribution in the region between them. When the fracture spacing is equal to or lower than 1.15 times the height of the fractured layer for the experimental conditions chosen, the lobes of tensile stress centered on the fractures coalesce. This results in the formation of vast areas of tensile stress in models under remote compressive loading conditions. Such tensile areas are likely to allow the initiation and propagation of subsequent opening-mode fractures.The results obtained provide new insights into the formation of joints in layered rocks in compressive environments, with important consequences on fluid flow.     

Prediction of water inflow into underground excavations in fractured rocks using a 3D discrete fracture network (DFN) model

Groundwater flow is a major issue in underground opening in fractured rocks. Because of finding the fracture connectivity, contribution of each fracture in flow, and fracture connectivity to excavation boundary, the prediction of water flow to underground excavations is difficult. Simulation of fracture characteristics and spatial distribution is necessary to obtain realistic estimation of inflow quantity to tunnel and underground excavations. In this research, a computer code for three-dimensional discrete fracture network modeling of water inflow into underground excavations was developed. In this code, the fractures are simulated as ellipsoid while geometrical properties of the fractures are reproduced using a stochastic method. Properties such as the size, orientation, and density of the fractures are modeled by their respective probability distributions, which are obtained from field measurements. According to the fracture condition, the flow paths in rock mass are determined. The flow paths are considered as channels with rectangular sections in which channel width and fracture aperture determine geometry of channel section. Inflow into excavation is predicted ignoring matrix permeability and considering the hydrogeological conditions. To verify presented model, simulation results were compared to a part of the Cheshmeh-Roozieh water transfer tunnel in Iran. The results obtained from this research are in good agreement with the field data. Thus, the average of the predicted inflow has just an approximation error equal to 17.8%, and its standard deviation is 8.6 l/s, which is equal to 21% of the observed value that demonstrates low dispersion of the predicted values.     

与挠曲作用相关的一种特殊裂缝形成机制

浙江省临安市上侏罗统劳村组火山凝灰岩露头中发育了很多与挠曲相关的裂缝, 地层构造简单、露头良好, 为研究与挠曲相关裂缝提供了良好的条件.通过对两处野外露头的精细测量, 发现裂缝面平直、且未被充填, 均为构造裂缝, 在剖面上裂缝的组合呈扇形.裂缝面与岩层层面夹角为44°~80°, 裂缝密度随着地层厚度的增加而增加.根据裂缝面与层面的交切关系, 将两组裂缝分别命名为: 锐夹角指示邻层相对运动方向的D裂缝和锐夹角指示本层相对运动方向的D’裂缝.通过对地层挠曲变形的几何分析, 发现两组裂缝的形成是为了调节核部地层在变形过程中产生缩短量和剩余剪切, 地层厚度与地层中产生剩余剪切成正比.结果表明, 地层厚度越大, 形成的裂缝也越多.      

Visualization of the El Berrocal granite: application to rock engineering

This paper outlines the visualization of the El Berrocal granite using a computer-based geological modelling system, EarthVision, and discusses the application of this visualization to engineering aspects of waste disposal in crystalline rocks. The El Berrocal Project was an international study with the aim of understanding and modelling the migration processes which have controlled the distribution of naturally occurring radionuclides in a fractured granitic environment. EarthVision was used to provide three-dimensional geological models of the site structure and properties. Modelling of the site structure concentrated on the development of visualizations of the main discontinuities in the granite. These included a model of the main mineralized structures, a model of the regional fracture network, models of local fracture networks between borehole clusters and a visualization of the mineralogy of the fractures in individual boreholes. These fracture models were visualized with the boreholes and access gallery to the mine. In addition, the fracture network in the region of a large scale tracer test was visualized with the injection and extraction zones for the tracer test. Three-dimensional interpolations of the rock and fluid structure were undertaken. A model of the hydraulic conductivity illustrated large-scale variations in hydraulic conductivity and channelling effects in the tracer test zone. A model of the sulphate concentrations in the groundwater illustrated the interpolation of spatial data based on structural domains. The visualizations of the geology of the El Berrocal granite illustrate that, despite limitations, geological modelling can be a powerful and graphic tool in rock engineering. The use of computer visualizations can be provide the three-dimensional structural framework for computations, can aid decision making during the construction phase of waste repositories and can be useful in understanding and analysing the results of numerical calculations.