Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

Mathematical Geosciences - We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic...     

岩体三维不连续裂隙网络及其逆建模方法

通过拟合实测的二维裂隙编录图和钻孔裂隙编录图，优化裂隙三维大小和密度参数，使模型能够准确再现野外所观测到的实际现象，包括开挖面和钻孔上不同裂隙的数量、密度和长度，通过计算实例验证了方法的可行性。     

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

ＩＮＴＲＯＤＵＣＴＩＯＮＧｒｏｕｎｄｗａｔｅｒｏｒｆｌｕｉｄｆｌｏｗｍｏｄｅｌｉｎｇｉｎｆｒａｃｔｕｒｅｄｒｏｃｋｓｉｓａｃｏｍｐｌｉｃａｔｅｄｔｈｅｏｒｅｔｉｃａｌａｎｄａｐｐｌｉｅｄｔｏｐｉｃ.Ｂｏｔｈｔｈｅｏｒｅｔｉｃａｌｌｙａｎｄｏｐｅｒａｔｉｏｎａｌｌｙ ,ｉｔｉｓｉｍｐｏｒｔａｎｔｉｎｍａｎｙｆｉｅｌｄｓｓｕｃｈａｓｇｅｏｌｏｇｉｃａｌａｎｄｈｙｄｒｏｇｅｏｌｏｇｉｃａｌｅｎｇｉｎｅｅｒｉｎｇ ,ｅｎｖｉｒｏｎｍｅｎｔａｌｅｎｇｉｎｅｅｒｉｎｇａｎｄｐｅｔｒｏｌｅｕｍｅｎｇｉｎｅｅｒｉｎ…     

Sensitivity Analysis of Discrete Fracture Network Connectivity Characteristics

Mathematical Geosciences - This paper presents the results of a sensitivity analysis of the characteristics of discrete fracture network (DFN) connectivity. The sizes of the maximum and mean...     

裂缝密度约束的离散裂缝网络建模方法与实现

如何高效地用多种类型资料(如地震、测井、岩芯等)所得到的裂缝信息对离散裂缝网络建模至关重要。为此本文提出一种裂缝密度约束的离散裂缝网络建模方法,将多种裂缝先验信息转换为裂缝密度,通过密度约束裂缝网络模型。方法对裂缝位置的确定方法进行改进,从编程的角度对二维和三维实现进行了分析,同时讨论了方法的适用性及参数设定。为验证方法效果,实例分析部分选用鄂尔多斯盆地延河剖面附近的一井区数据进行裂缝建模,并与实际生产资料进行比对,结果表明该方法所建立的裂缝模型与实际生产数据吻合。     

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。     

A Connectivity Index for Discrete Fracture Networks

Connectivity is an important measure for assessing flow transport in rock, especially through fractures. In this paper, rock fracture systems are modelled by a discrete fracture model simulated by a marked point process. A connectivity index is then introduced to quantify the connectivity between any two points in space. Monte Carlo simulation is used to evaluate the connectivity index for stationary cases and relationships between the connectivity index and the parameters of the discrete fracture model are analysed. The average number of intersections per fracture, X_f, and the fracture intensity, P12 (P32), are calculated and the relationships between these parameters and the connectivity index are investigated, concluding that X_f is the more suitable parameter for the classification of rock mass flow properties. The relationships between the connectivity index and the percolation state of the fractured medium are also discussed. An edge correction is briefly discussed and a practical example is used to demonstrate the method of computing the connectivity index.     

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.     

Use of an Integrated Discrete Fracture Network Code for Stochastic Stability Analyses of Fractured Rock Masses

The paper presents the Discrete Fracture Network code RESOBLOK, which couples geometrical block system construction and a quick iterative stability analysis in the same package. The deterministic or stochastic geometry of a fractured rock mass can be represented and interactively displayed in 3D using two different fracture generators: one mainly used for hydraulic purposes and another designed to allow block stability evaluation. RESOBLOK has downstream modules that can quickly compute stability (based on limit equilibrium or energy-based analysis), display geometric information and create links to other discrete software. The advantage of the code is that it couples stochastic geometrical representation and a quick iterative stability analysis to allow risk-analysis with or without reinforcement and, for the worst cases, more accurate analysis using stress–strain analysis computer codes. These different aspects are detailed for embankment and underground works.     

基于离散裂缝网络模型裂缝储层的随机模拟——以王窑区块为例

在燕山期、喜山期构造活动作用下,王窑区块发育北东向和南北向共轭剪切裂缝。针对该裂缝进行了统计分析,并利用离散裂缝网络模型对裂缝进行了随机模拟。模拟结果表明:研究区共轭裂缝北东向较为显著,且以高角度裂缝为主。裂缝对渗透率影响较为明显,将研究区的渗透率提高到20×10-3μm2,孔隙度增加约2%。     

稀疏非正交填充裂隙岩体水流—传热—应力模型与离散元模拟

为研究填充裂隙水流速度对岩体温度和应力的影响，选取甘肃北山地区的花岗岩，制作了稀疏非正交裂隙岩体模 型，采用河砂填充裂隙后进行模型试验；并对模型试验进行离散元数值模拟，分析了模型试验所测岩体温度和热应力与数 值模拟结果的差异和原因。结果显示：填砂裂隙强化了裂隙介质的热导能力，无填充时岩体温度和热应力比填砂时低；模 型试验和离散元模拟均表明，岩体温度和岩体应力随裂隙水流速度增大而减小，但是系统达到稳态所需要的时间变短；模 型试验中斜裂隙水流对温度场起主要作用；由于现有3DEC软件不能考虑水的热物性参数随温度的变化，进而产生自然对 流换热，斜裂隙水流和靠近热源侧的竖裂隙水流对温度场起主要作用。     

稀疏非正交填充裂隙岩体水流—传热—应力模型与离散元模拟

为研究填充裂隙水流速度对岩体温度和应力的影响,选取甘肃北山地区的花岗岩,制作了稀疏非正交裂隙岩体模 型,采用河砂填充裂隙后进行模型试验;并对模型试验进行离散元数值模拟,分析了模型试验所测岩体温度和热应力与数 值模拟结果的差异和原因。结果显示：填砂裂隙强化了裂隙介质的热导能力,无填充时岩体温度和热应力比填砂时低;模 型试验和离散元模拟均表明,岩体温度和岩体应力随裂隙水流速度增大而减小,但是系统达到稳态所需要的时间变短;模 型试验中斜裂隙水流对温度场起主要作用;由于现有3DEC软件不能考虑水的热物性参数随温度的变化,进而产生自然对 流换热,斜裂隙水流和靠近热源侧的竖裂隙水流对温度场起主要作用。     

Simulation of the Steady-State Flow in Discrete Fracture Networks with Non-Conforming Meshes and Extended Finite Elements

In this paper a numerical method for the simulation of the steady-state fluid flow in discrete fracture networks is described. It is based on the use of non-conforming meshes, enrichment functions and an optimization procedure. The meshing process is performed on each fracture independently of the other fractures, i.e. without geometrical conformity at the intersections (traces). The slope discontinuities due to the flux exchange at the traces are then captured with the enrichment functions of the extended finite elements, and finally a functional is minimized by resorting to an optimization procedure. The method can be easily implemented for parallel computers being based on many small independent problems. In order to show the effectiveness of the method and the quality of the results, simulations of fluid flow in simple networks are illustrated.     

Correction to: Discrete dynamical Pareto optimization model in the risk portfolio for natural disaster insurance in China

Natural Hazards - The original article, Discrete dynamical Pareto optimization model in the risk portfolio for natural disaster insurance in China, in Natural Hazards (2018) 90: 445–460, was...     

碳酸盐岩油藏酸岩反应流动模拟研究进展

酸岩反应流动模拟可用于指导油藏酸化施工,优选注入参数,从而以最小的成本最大程度地改善地层.国内外很多学者基于不同的方法建立了不同的模型对碳酸盐岩油藏酸岩反应流进行了研究,但这些模型尚缺乏科学的归纳与整理.以研究对象的空间尺度为依据,将现有的碳酸盐岩油藏酸岩反应流模型分为孔隙尺度模型、岩心尺度模型及井筒尺度模型,简要概括了每类模型的适用条件及其在应用中的局限性.结合本课题组在酸岩反应流模拟方面所做的工作,重点论述了岩心尺度模型的最新研究进展和发展趋势,给出了岩心尺度模型下一步的研究方向,主要包括:建立更接近地层实际的数学模型,如考虑酸化过程中存在的非达西流和地应力的影响;发展高效的数值算法,将模型的计算区域扩大到油藏尺度;将岩心尺度模型进行尺度升级,得到可以指导油藏酸化施工的优化参数.      

求解岩体裂隙产状三维概率分布的数值方法

测线法是一种广泛使用的裂隙几何特征野外观测技术,但它获得的一维产状观测数据不能代表三维空间内的概率分布.在实测裂隙倾向和倾角之间相互独立的假设基础上,借用概率论和微积分建立了一维数据和三维分布的数值解关系式,进而提出一种由一维观测数据求解三维概率分布的方法.该方法的实现步骤是:(1)通过关系式数值求解产状的三维累积概率...     

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.     

A New Methodology for Singularity Modelling in Flow Simulations in Reservoir Engineering

In this paper, numerical methods for flow simulation in the well vicinity are discussed. Flux truncation errors are analyzed on gridblocks near the well. Due to the singularity of the well, standard numerical schemes are not efficient for near well flow simulations. To improve simulation accuracy, a new methodology, using a change of coordinates to make near well pressure linear, is presented for the singularity modelling. Based on this new approach, two numerical schemes, a two-point flux approximation scheme and a multi-point one, are proposed. These schemes are accurate for the near well modelling and are suitable for any kinds of gridblocks.     

基于嵌入离散裂缝的页岩气藏视渗透率模型

页岩储层具有不同类型的储集空间,但综合考虑不同储集空间,对页岩储层渗透率进行评价的模型未见报道.基于嵌入离散裂缝模型,建立的页岩气藏视渗透率模型包括4个步骤:（1）构建天然裂缝、有机质和无机质的空间分布模型;（2）筛选不同类型储集空间的渗透率计算方法;（3）基于嵌入离散裂缝模型,结合空间分布模型和渗透率计算方法,建立数值模拟模型;（4）在模型的入口和出口端施加压差,求得一定压差下通过该岩心的气体流量,采用达西定律得到该页岩气藏的视渗透率.其计算结果与文献报道的渗透率实验值吻合较好.通过对不同因素的探讨,结果表明,天然裂缝对页岩气藏视渗透率的贡献大于无机质和有机质孔隙.因此,计算页岩视渗透率时有必要对天然裂缝、有机质和无机质孔隙进行综合考虑.      

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.