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。     

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.     

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.     

Robust algorithms for polyhedral modelling of fractured rock mass structure

This paper presents robust algorithms for application in polyhedral modelling of rock mass structure based on discrete fracture networks. The algorithms improve the robustness of current polyhedral modellers to challenging or degenerate geometries and geometrical errors. These issues are inevitably encountered when the fracture network realisations incorporate large numbers of fractures, or regions of densely packed fractures are modelled, or when the number of fracture network realisations interrogated is large. Several stages in the polyhedral modelling process which are sensitive to geometrical errors are reviewed and algorithms which are robust and capable of handling topological errors in the input fracture network geometry are presented.     

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.     

Fracture in a heterogeneous medium: a network approach

Fracture in a heterogeneous medium is simulated by a network model. Heterogeneity is introduced by randomly distributing an initial population of cracks on a triangular network of bonds. Each ruptured bond represents a crack. External stresses are applied onto the network and the evolution of the crack population is analysed when the stresses are increased. A crack will propagate to an intact bond if the critical crack extension force is reached. This propagation leads to the coalescence of bonds: crack clusters are formed. When their shapes are complex we approximate them by simpler ones to compute a crack extension force. Crack interactions are introduced by adding for a given bond the contributions of all adjacent dusters. By using this kind of approach combining fracture mechanics and network modelling, we are able to simulate the rupture of a rock specimen under compression/ traction or shear stresses and to give some characteristics of the macroscopic fracture.     

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.     

结构面网络模拟结果后处理研究

结构面网络模拟是获取岩体结构模型的主要手段。基于网络模拟结果建立岩体力学或水力学分析模型,然后开展精细数值模拟研究,是岩石力学领域具有良好前景的发展方向。但目前尚没有成熟的分析软件能够将网络模拟结果转化为能用于力学或水力学计算的单元网格,针对这一现状,开发了一整套结构面网络模拟结果后处理程序,利用该程序,可以方便地将网络模拟结果转化为能用于水力学计算的连通水力网络,以及能用于力学分析的包含节理单元的有限元网格。并对相关的程序算法和实现过程作了详尽的介绍,希望能够对从事该领域研究工作的同行有参考价值。     

3D model of fracture zones at Soultz-sous-Forêts based on geological data,image logs,induced microseismicity and vertical seismic profiles

This study presents a new deterministic 3D model of the fracture zones observed in the granitic reservoir of the Soultz European geothermal project. The major fracture zones encountered around 6 wells (4550, EPS1, GPK1, GPK2, GPK3 and GPK4) consist in 53 main structures that are located and characterized in terms of size and orientation: 39 fracture zones, 8 microseismic structures and 6 structures derived from vertical seismic profiles are represented in the 3D model using Discrete Fracture Network tools of the gOcad modelling platform (Paradigm?, Earth Decision?). This work illustrates the complexity of 3D fracture zone correlation and interpretation in crystalline rock masses characterized at meter scale (borehole) and at the reservoir scale (kilometer) thanks to geophysical imaging techniques.     

Finite element simulation of fluid flow in fractured rock media

Fluid dynamics models are used by the petroleum industry to model single- and/or multi-phase flow within fractured rock formations, in order to facilitate extraction of fluids such as oil and natural gas, and in other areas of engineering to study groundwater flow, as well as to estimate contaminant seepage and transport. In this paper, the numerical modelling software Comsol is used to simulate air and water flow through a specimen of granite with a single vertical fracture subjected to triaxial loading conditions. The intent of the model is to simulate triaxial test findings on a rock specimen with a natural fracture. Fluid flow is simulated at various confining and inlet pressures using the cubic law. Model results were in good agreement with laboratory findings. Pressure distribution along the fracture and across the specimen are as expected with a near linear pressure distribution along the length of the fracture. A drawdown effect on pressure distribution across the specimen in the vicinity of the fracture is also observed. Pressure gradient was largely uniform; however, some localised zones of high gradient along the fracture are observed.     

油气藏水力压裂计算模拟技术研究现状与展望

水力压裂技术是油气藏尤其是页岩气开发中的核心技术,利用数值模拟方法进行压裂优化和产能预测又是水力压裂成功的关键。本文首先介绍了水力压裂技术的发展历程。然后从计算模型(二维模型、拟三维模型和全三维模型)和数值模拟方法(基于连续介质和基于非连续介质)两方面对油气藏开发领域的水力压裂计算模拟技术进行较全面的总结。最后,从以下3个方面指出现今研究的不足并提出了进一步的研究建议:(1)全三维模型的完善-全三维模型应当与真实的工程参数和监测数据结合,用于校正模型本身,而校正后的全三维模型又可预测和优化新的现场水力压裂作业; (2)数值模拟方法的选用-已有的水力压裂数值模拟方法种类繁多,需要针对各种方法的适用范围、计算效率和模拟效果等,进行全面的比较和优化; (3)页岩储层中天然裂缝网络的数值模拟-天然裂隙网络加剧了页岩储层力学性质的各向异性,同时水力裂缝沟通天然裂缝活化扩展是有利于储层的增渗增产,对压裂缝网的形态、尺寸和连通率等起着至关重要的作用。因此,数值计算过程中综合考虑页岩储层中天然裂缝与水力裂缝的相互作用,将是未来水力压裂模拟的热点。     

裂隙岩体渗流场分析及其三维有限元程序设计

针对水工建筑物裂隙岩基渗流场计算,采用双重介质解法编制了三维有限元裂隙渗流计算程序,用水量交换项耦合主干裂隙网络及裂隙岩块,自由面位置的确定使用自由面虚点法迭代逼近,得到了合理的计算结果。计算使用ANSYS建立渗流模型并剖分网格,相应的前处理子程序降低了裂隙渗流计算的复杂性,提高了裂隙渗流理论计算方法的可用性。     

Adaptive finite element analysis of mode I fracture in cement‐based materials

Microscopic studies using advanced experimental techniques have provided better insight into the fracture mechanisms in cement‐based materials. A clear understanding of fracture mechanisms is critical for the development of rigorous computational models for analysing fracture. Fracture analysis is usually carried out by finite element method. Accuracy of FE analysis depends upon the choice of mesh and for the predictions to be reliable, discretization errors are to be minimized. In cohesive crack approach, the non‐linearity is limited to the boundary conditions along the geometric discontinuity while the bulk of the material retains its elastic nature. The paper presents a mesh‐adaptive strategy based on ZZ error estimator to model discrete crack propagation in cement‐based materials. Examples of simulations have demonstrated the potential of the mesh‐adaptive technique in modelling the evolution of the localized strain profiles as well as failure of concrete test specimen. Copyright © 2001 John Wiley & Sons, Ltd.     

Permeability and stress in crystalline rocks

Groundwater from crystalline rocks is a significant resource in many areas of the world. It is also an important medium for contaminant transport from, for example, deep nuclear waste repositories. Stress distributions in fractured rocks are important in controlling groundwater flow in several ways: (i) palaeostress fields are responsible for the evolution of fracture systems which transmit groundwater; (ii) current in situ stress fields will influence the shape and aperture of fractures; (iii) humans can influence the natural stress field in a rock mass to enhance fracture flows. The significance of stresses for groundwater flow can be investigated by field techniques (hydraulic fracturing), laboratory techniques (stress cells) or by numerical modelling.     

岩体裂隙三维可视化新方法及其应用

快速准确地识别岩体裂隙的三维分布特征是西南山区铁路防灾减灾的关键.本研究提出了一套岩体裂隙可视化新方法,基于测窗调查的裂隙数据,依托球坐标及极射赤平投影进行数字化处理及降维,利用K-Means++聚类算法、Fisher分布模型和蒙特卡洛模拟,完成裂隙产状数据的自动分组和模拟,最后运用Python及圆盘模型实现岩体裂隙三维可视化.本研究采用坐标变换和三角网格曲面的方式,更有利于与其他三维建模软件嵌套分析.水电站工程的先行应用研究表明产状数据服从Fisher分布,本文的模型相对于传统玫瑰花图和施密特图有着一定的优势.因此,本文建立的岩体裂隙模型具有直观快速反映区域裂隙网络三维分布特征的优点,研究成果可以直接服务于西南山区铁路施工阶段隧道掌子面及洞壁的节理裂隙三维识别以及防灾减灾研究.      

岩体裂隙模拟的扩展有限元法应用研究

岩体中普遍存在着断层﹑节理和裂隙等结构面,这些结构面的存在和发展对岩体的整体强度﹑变形及稳定性有极大的影响。因此,研究岩体中原生结构面的萌生﹑发展以及贯通演化过程对评估岩体工程安全性和可靠性具有非常重要的理论与现实意义。扩展有限元法（XFEM）作为一种求解不连续问题的有效数值方法,模拟裂隙时独立于网格,因此,在模拟岩体裂隙扩展﹑水力劈裂等方面具有独特优势。针对扩展有限元法的基本理论及其在岩体裂隙扩展模拟中的应用展开了研究,建立了扩展有限元法求解岩体裂隙摩擦接触、岩体裂隙破坏等问题的数值模型,并将计算模型应用于岩质边坡稳定性分析和重力坝坝基断裂破坏等工程问题。     

裂隙网络管道模型弥散试验

为了探求不同裂隙几何参数对裂隙网络溶质运移的影响,基于离散裂隙网络思想和优势流、沟槽流理论,建立裂隙管道网络概念模型,搭建不同管径、不同连通方式的管道网络试验装置,进行渗流和溶质运移实验。运用应用广泛的模拟软件CHEMFLO-2000建立等效多孔介质模型,拟合不同几何参数下等效弥散度,定量刻画不同管道网络几何参数对溶质运移的影响,讨论了不同管径、连通方式等与等效弥散度之间的关系。通过进一步分析得出:在连通方式相同的情况下,不同管径的管道网络等效弥散度存在差异,但是差异不大;溶质在小管径中的穿透时间短于大管径,穿透曲线缓和程度相差不大;管道网络连通方式越复杂,其等效弥散度越大、对溶质运移的影响越大、穿透曲线越缓和、路径越长,等效弥散度越大;用这种等效弥散度的方法表征管道网络对溶质运移的影响,与多孔介质弥散度具有相似性;管道数目、管道面数目与等效弥散度成正相关关系,且等效弥散度随尺度的增大而增加。