Simulation of multiphase flow in fractured reservoirs using a fracture-only model with transfer functions

We present a fracture-only reservoir simulator for multiphase flow: the fracture geometry is modeled explicitly, while fluid movement between fracture and matrix is accommodated using empirical transfer functions. This is a hybrid between discrete fracture discrete matrix modeling where both the fracture and matrix are gridded and dual-porosity or dual-permeability simulation where both fracture and matrix continua are upscaled. The advantage of this approach is that the complex fracture geometry that controls the main flow paths is retained. The use of transfer functions, however, simplifies meshing and makes the simulation method considerably more efficient than discrete fracture discrete matrix models. The transfer functions accommodate capillary- and gravity-mediated flow between fracture and matrix and have been shown to be accurate for simple fracture geometries, capturing both the early- and late-time average behavior. We verify our simulator by comparing its predictions with simulation results where the fracture and matrix are explicitly modeled. We then show the utility of the approach by simulating multiphase flow in a geologically realistic fracture network. Waterflooding runs reveal the fraction of the fracture–matrix interface area that is infiltrated by water so that matrix imbibition can occur. The evolving fraction of the fracture–matrix interface area turns out to be an important characteristic of any particular fracture system to be used as a scaling parameter for capillary driven fracture–matrix transfer.     

采用复合单元法模拟裂隙多孔介质变饱和流动

采用复合单元法建立了模拟裂隙多孔介质变饱和流动的数值模型。该模型具有以下特点:裂隙不需要离散成特定单元,而是根据几何位置插入到孔隙基质单元中形成复合单元;在复合单元中,分别建立裂隙流和孔隙基质流的计算方程,二者通过裂隙-基质界面产生联系并整合成复合单元方程;复合单元方程具有和常规有限单元方程相同的格式,因此,可以使用常规有限单元方程的求解技术。采用欠松弛迭代、集中质量矩阵以及自适应时步调节等技术,开发了裂隙多孔介质变饱和流动计算程序。通过模拟一维干土入渗和复杂裂隙含水层内的流动问题,验证了该模型的合理性和适用性。模拟结果为进一步认识非饱和裂隙含水层地下水流动特性提供了理论依据。     

核废料贮存裂隙岩体中THM耦合过程的有限元分析

本文首先给出了核废料贮存裂隙岩体中THM耦合作用的数学模型,然后用加权残数法,建立了以结点位移、水压力和温度为求解量的有限元计算格式,提出了数值模拟渗流、附加应力和热载耦合作用的有限元分析方法,最后给出了一个BMT1问题的算例.     

裂隙岩体溶质运移模型综述

本文综述了裂隙岩体系统中溶质运移的概念模型和数学模型。分析了目前各种裂隙岩体系统中溶质运移的数学模型的适用性和优缺点，为选取合理的数学模型求解具体的问题提供了参考依据。最后提出了有待进一步研究的问题。     

基于边界模型和广义耦合马尔可夫链模型的地层变异性模拟方法

地层变异性对岩土结构物的性能评价影响显著,地层变异性的准确表征对工程实际具有重要意义.为此,提出了一种有效的地层变异性模拟方法,在概率框架内,将边界模型和广义耦合马尔可夫链模型相结合形成一种组合模型,以综合利用两者的优势.首先,通过贝叶斯方法识别边界模型参数,进而采用条件随机场对地层边界进行模拟.然后,将边界模型模拟结...     

米尺度裂隙岩体模型水流-传热试验的数值模拟分析

为了研究高放射性核废物地下处置库近场的水流-传热耦合问题,采用国内高放废物地下处置库预选场址--甘肃北山地区的花岗岩石块体,加工组合成米尺度的规则裂隙岩体模型,设置边界热源和裂隙水流,试验模拟裂隙水水流与传热之间的相互作用。作为该室内模型试验的前期理论研究,采用等效孔隙介质数值模型,着重分析了裂隙开度、裂隙流量和热源功率对流场和温度场的影响。在设定条件下,计算分析表明：热传导和裂隙水水流由热源作用初期的不耦合很快转化为耦合;不流动的裂隙水主要表现为热存储和热传导,而流动的裂隙水还引起流动传热和水与岩石之间的对流换热,使岩体温度场明显不同于单纯热传导的情况;如果保持裂隙水流量不变,则裂隙开度的变化对水流-传热影响不大;如果保持裂隙水流速不变,则裂隙开度的变化对水流-传热影响显著;热源功率越大,通过裂隙水的热流量越大,裂隙水压强越大,而当温度超过100 ℃时,裂隙水会因汽化而压强显著增大;加热7 d时,热量的输入和输出几乎相等,裂隙水流带走的热量接近热源供给的热量,模型系统基本达到了热平衡。     

地下水流模型识别的分步解法

地下水流模型识别问题是综合的水文地质分析与计算过程,但常常被片面理解为反求水文地质参数问题,这种片面的认识大大妨碍了对水文地质条件的认识及对水文地质过程的理解,并由此导致一些不应有的错误结论。简要论述了地下水流模型识别的概念及问题类型,利用模型分解的方法指出地下水流模型的识别可分2步完成:一是利用附加水头场(或附加降深场)求参数;二是利用初始水头场确定边界条件及源汇项。除参数外,源汇项、初始条件、边界条件也是地下水流模型识别的重要内容。     

Development of a numerical groundwater flow model using SRTM elevations

Remotely-sensed elevation data are potentially useful for constructing regional scale groundwater models, particularly in regions where ground-based data are poor or sparse. Surface-water elevations measured by the Shuttle Radar Topography Mission (SRTM) were used to develop a regional-groundwater flow model by assuming that frozen surface waters reflect local hydraulic head (or groundwater potential). Drainage lakes (fed primarily by surface water) are designated as boundary conditions and seepage lakes and isolated wetlands (fed primarily by groundwater) are used as observation points to calibrate a numerical flow model of the 900 km² study area in the Northern Highland Lakes Region of Wisconsin, USA. Elevation data were utilized in a geographic information system (GIS) based groundwater-modeling package that employs the analytic element method (AEM). Calibration statistics indicate that lakes and wetlands had similar influence on the parameter estimation, suggesting that wetlands might be used as observations where open water elevations are unreliable or not available. Open water elevations are often difficult to resolve in radar interferometry because unfrozen water does not return off-nadir radar signals.     

Application of the two-stage Markov chain Monte Carlo method for characterization of fractured reservoirs using a surrogate flow model

In this paper, we develop a procedure for subsurface characterization of a fractured porous medium. The characterization involves sampling from a representation of a fracture’s permeability that has been suitably adjusted to the dynamic tracer cut measurement data. We propose to use a type of dual-porosity, dual-permeability model for tracer flow. This model is built into the Markov chain Monte Carlo (MCMC) method in which the permeability is sampled. The Bayesian statistical framework is used to set the acceptance criteria of these samples and is enforced through sampling from the posterior distribution of the permeability fields conditioned to dynamic tracer cut data. In order to get a sample from the distribution, we must solve a series of problems which requires a fine-scale solution of the dual model. As direct MCMC is a costly method with the possibility of a low acceptance rate, we introduce a two-stage MCMC alternative which requires a suitable coarse-scale solution method of the dual model. With this filtering process, we are able to decrease our computational time as well as increase the proposal acceptance rate. A number of numerical examples are presented to illustrate the performance of the method.     

Evaluation of regional fracture properties for groundwater development using hydrolithostructural domain approach in variably fractured hard rocks of Purulia district,West Bengal,India

Estimation of geohydrologic properties of fractured aquifers in hard crystalline and/or metamorphosed country rocks is a challenge due to the complex nature of secondary porosity that is caused by differential fracturing. Hydrologic potentiality of such aquifers may be assessed if the geological controls governing the spatial distribution of these fracture systems are computed using a software-based model. As an exemplar, the Precambrian metamorphics exposed in and around the Balarampur town of Purulia district, West Bengal (India) were studied to find out the spatial pattern and consistency of such fracture systems. Surfer and Statistica softwares were used to characterize these rock masses in terms of hydrological, structural and lithological domains. The technique is based on the use of hydraulically significant fracture properties to generate representative modal and coefficient of variance (Cν) of fracture datasets of each domain. The Cν is interpreted to obtain the spatial variability of hydraulically significant fracture properties that, in turn, define and identify the corresponding hydrolithostructural domains. The groundwater flow estimated from such a technique is verified with the routine hydrological studies to validate the procedure. It is suggested that the hydrolithostructural domain approach is a useful alternative for evaluation of fracture properties and aquifer potentiality, and development of a regional groundwater model thereof.     

基于地下水渗流方程的三维地面沉降模型

针对地下水抽取引起的大面积地面沉降的问题,提出了一种计算方法。该方法基于饱和与不饱和岩土介质中地下水渗流理论,计算出三维状态下的大面积地面沉降。提出的方法被结合到地下水渗流的三维有限元法分析中,计算时考虑了地层的可压缩性,并被用来分析软土的固结,将该法与太沙基理论及固结试验的结果进行比较,结果表明其误差小于2 %。该法还被用来分析单井抽取承压地下水引起的周围地基的沉降及承压水层由于挡水板的阻断作用而引起的下游侧的地基的沉降。     

Groundwater flow into underground openings in fractured crystalline rocks: an interpretation based on long channels

Rethinking an old tracer experiment in fractured crystalline rock suggests a concept of groundwater flow in sparse networks of long channels that is supported by results from an innovative lattice network model. The model, HyperConv, can vary the mean length of ‘strings’ of connected bonds, and the gaps between them, using two independent probability functions. It is found that networks of long channels are able to percolate at lower values of (bond) density than networks of short channels. A general relationship between mean channel length, mean gap length and probability of percolation has been developed which incorporates the well-established result for ‘classical’ lattice network models as a special case. Using parameters appropriate to a 4-m diameter drift located 360 m below surface at Stripa Mine Underground Research Laboratory in Sweden, HyperConv is able to reproduce values of apparent positive skin, as observed in the so-called Macropermeability Experiment, but only when mean channel length exceeds 10 m. This implies that such channel systems must cross many fracture intersections without bifurcating. A general relationship in terms of flow dimension is suggested. Some initial investigations using HyperConv show that the commonly observed feature, ‘compartmentalization’, only occurs when channel density is just above the percolation threshold. Such compartments have been observed at Kamaishi Experimental Mine (Japan) implying a sparse flow network. It is suggested that compartments and skin are observable in the field, indicate sparse channel systems, and could form part of site characterization for deep nuclear waste repositories.     

基于区域分解法的水文地质参数寻优研究

在建立地下水流模型的过程中,水文地质参数寻优一直是较为复杂的步骤之一,具体难点包括寻优方法的取用,为保持总体平衡所引起的参数峰值异常以及总体寻优需要大量的计算机时等问题.本文运用区域分解法(Domain Decomposition method,DDM)的基本思想,将整个区域的参数寻优问题分解为各参数分区内的子域问题求解,通过寻找整个区域上的Nash均衡最终获得各子域上的最优参数.实验算例及其结果证明应用该方法实现水文地质参数自动寻优,不但具有高度的可靠性,同时优化问题的规模减小.此举不但减少了求解过程所需要的CPU时间,而且提高了参数拟合度.     

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.     

Simulation of groundwater flow and contaminant transport at a landfill site using models

Numerical and analytical modelling studies were conducted for the analysis of groundwater flow and contaminant transport at the Innisfil landfill site in the Town of Innisfil, County of Simcoe, in Ontario, Canada. Previously conducted field studies categorized the upper stratigraphy at the site into three units: upper sand unit, upper silt/clay unit and Intermediate Sand unit. Essentially horizontal groundwater movement in the two sand units and vertical downward flow in the silt/clay unit were reported by the field hydrogeologists. In the following, application of three computer models (FLOWPATH, USGS MOC and POLLUTE) for the simulation of the groundwater flow and contaminant transport processes at the Innisfil landfill site is described. The paper focuses on the calibration of groundwater flow and contaminant transport systems, and demonstrates how the insight gained during the contaminant transport calibration was used to improve the initial groundwater flow characterization of the hydrogeological system.     

Elastoplastic analysis of jointed rocks using a coupled finite element and boundary element method

This paper presents a coupled, elastoplastic, finite element and boundary element method for the two-dimensional, non-linear analysis of anisotropic jointed rock. The non-linear and anisotropic behaviour of a jointed rock mass is simulated by representing the mass as an equivalent anisotropic, elastoplastic continuum, so that the influence of the jointing system is ‘smeared’ across the continuum, i.e. the individual joints are not modelled as discrete entities. Numerical examples have been solved to verify the capability, accuracy and efficiency of the present technique. The proposed technique has also been applied to the analysis of tunnel excavation problems in plane strain. The effects of anisotropy and non-linearity of the jointed rock mass during excavation have been investigated in some detail.     

含裂隙饱和多孔介质流-固耦合的扩展有限元分析

基于应力平衡方程、渗流连续性方程以及改进的Biot有效应力原理,建立了含裂隙可变形饱和多孔介质流-固全耦合问题的控制方程。流体在介质和裂隙中的流动均满足达西定律,得到的非线性全耦合方程不仅反映多孔介质内部物理量的耦合效应,还考虑介质与裂隙之间的耦合作用。扩展有限元法在处理含裂隙问题时具有独特的优势,采用普通有限元和扩展有限元法构建了数值计算体系。在进行空间离散时,介质内部的位移和孔隙压力均采用普通的有限元进行离散;裂隙处的位移模式引入扩展有限元中的两类附加位移函数,以反映裂隙面的位移强不连续性和裂隙端部的应力奇异性;引入孔隙压力加强函数,以体现裂隙法向孔隙压力的弱不连续特征。使用向后差分格式进行时间离散。算例验证了该模型和算法的正确性和有效性,分析了裂隙的存在对流体流动的延迟作用、裂隙中张开位移及孔隙压力等物理量的分布情况,讨论了渗透率、外部流量的改变对计算结果的影响。     

An analytical method for predicting the groundwater inflow to tunnels in a fractured aquifer

Hydrogeology Journal - Based on the fracture network model and the cubic law of a single fracture with laminar flow, a method suitable for calculating hydraulic-head distribution and flow behaviors...     

非饱和裂隙岩体渗流的统计模型研究方法

常规方法研究非饱和裂隙介质往往采用宏观连续体的概念,然而现场试验证明,非饱和裂隙岩体中的渗流具有相当的非均质性。天然裂隙岩体的非饱和渗流是发生在三维裂隙网络中的多场非等温流,要在不完整的信息基础上刻画和表现介质的不均匀性,通常借助随机模拟的手段。将三维裂隙系统近似为概化的二维非均匀多孔介质的二维平面裂隙。采用模拟退火法将取自各种来源的信息资料通过建立适当的目标函数汇集至模型之中,以此模拟裂隙的空间特征。