FDEM-TH3D: A three-dimensional coupled hydrothermal model for fractured rock

This paper proposes a three-dimensional coupled hydrothermal model for fractured rock based on the finite-discrete element method to simulate fluid flow and heat transport. The 3D coupled hydrothermal model is composed of three main parts: a heat conduction model for the rock matrix, a heat transfer model for the fluid in the fractures (including heat conduction and heat convection), and a heat exchange model between the rock matrix and the fluid in the fractures. Four examples with analytical solutions are provided to verify the model. A heat exchange experiment of circulating water in a cylindrical granite sample with one fracture is simulated. The simulation results agree well with the experimental results. The effects of the fracture aperture, fluid viscosity, and pressure difference on the heat exchange between the fluid and rock are studied. Finally, an application concerned with heat transport and fluid flow in fractured rock is presented. The simulation results indicate that the 3D fully coupled hydrothermal model can capture the fluid flow and temperature evolution of rocks and fluids.     

分布热源作用下裂隙岩体渗流-传热的拉氏变换-格林函数半解析计算方法

以裂隙岩体高放射性核废物地下处置库性能评估为目标,提出了分布热源作用下单裂隙岩体渗流-传热的简化概念模型、控制微分方程和拉氏变换-格林函数半解析法,为进一步采用半解析法计算分布热源作用下多裂隙岩体的渗流-传热问题奠定了基础。针对单裂隙岩体的渗流-传热问题,建立考虑岩石内热源和二维热传导的控制微分方程,利用拉氏变换域微分方程的基本解建立格林函数积分方程,采用解析法处理其中的奇点,通过数值积分和拉氏数值逆变换求解,计算任意时刻裂隙水和岩石的温度分布。通过算例,与基于岩石一维热传导假定的解析解进行了对比,并计算分析了分布热源作用下单裂隙岩体的渗流-传热特征及其对裂隙开度、岩石热传导系数和热流集度的敏感度。算例表明,（1）就裂隙水温度而言,由于考虑了岩石的二维热传导,拉氏变换-格林函数半解析解小于基于岩石一维热传导假定的解析解;（2）裂隙水温度和岩石温度对裂隙开度和热流集度的敏感度较大,对岩石热传导系数的敏感度较小。     

Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion

Quantification of mass and heat transport in fractured porous rocks is important to areas such as contaminant transport, storage and release in fractured rock aquifers, the migration and sorption of radioactive nuclides from waste depositories, and the characterization of engineered heat exchangers in the context of enhanced geothermal systems. The large difference between flow and transport characteristics in fractures and in the surrounding matrix rock means models of such systems are forced to make a number of simplifications. Analytical approaches assume a homogeneous system, numerical approaches address the scale at which a process is operating, but may lose individual important processes due to averaging considerations. Numerical stability criteria limit the contrasts possible in defining material properties. Here, a hybrid analytical–numerical method for transport modeling in fractured media is presented. This method combines a numerical model for flow and transport in a heterogeneous fracture and an analytical solution for matrix diffusion. By linking the two types of model, the advantages of both methods can be combined. The methodology as well as the mathematical background are developed, verified for simple geometries, and applied to fractures representing experimental field conditions in the Grimsel rock laboratory.     

裂隙岩体不稳定温度场的复合单元算法研究

基于复合单元法,结合三维热传导-对流方程和“充填模型”,提出了裂隙岩体不稳定温度场的复合单元模型。该模型前处理简便快捷,计算网格生成时无需考虑裂隙的存在,网格剖分不受限制,随后利用复合单元前处理程序,依据裂隙的位置和方位将其自动离散在单元内。对常规热传导-对流方程进行自伴随性调整,应用变分原理,推导出裂隙岩体不稳定温度场的复合单元算法,该算法可分别计算出岩块子单元和裂隙的温度值,且可真实反映裂隙中水流与相邻岩块间的热能量交换规律。将复合单元数值模型计算的不稳定温度场结果与相应的实测数据进行对比分析可知,数值计算结果与实测数据基本一致,验证了裂隙岩体不稳定温度场复合单元算法的可靠性与有效性。算例分析表明,裂隙中水流与相邻岩块间有明显的热传导和热对流作用。     

稀疏不规则裂隙岩体模型三维水流-传热对温度和应力影响的试验研究

选取高放射核废物处置库重要预选场区甘肃北山地区的花岗岩,制作750 mm（宽）×300 mm（厚）×1 000 mm（高）的稀疏不规则裂隙岩体模型,该模型由18块花岗岩和竖向与斜向各两条裂隙组成,在裂隙及岩石内部埋置温度传感器、水压计、直角应变花,并在模型一侧设置局部热源,研究热源温度和裂隙水流速对岩石温度和应力的影响。结果表明,竖裂隙水主要从顶部进水口流向底部出水口,斜裂隙水主要从侧部进水口流向侧部出水口,竖裂隙与斜裂隙在交汇处存在微小流量交换;由于热源处在两条斜裂隙进水口之间,并且斜裂隙长度小于竖裂隙,岩石热传导与斜裂隙水流对岩石温度分布起控制作用,竖裂隙水流对岩石横向热传导起阻滞作用;由于热传导和水流传热的不规则性,上层岩石形成从左向右为主的传热路径,中层和下层岩石形成从上向下为主的传热路径;由于上、下层岩石温度梯度较小,岩石收缩受热拉应力,而中层岩石温度梯度较大,岩石膨胀受热压应力,大主应力的方向大致垂直于斜裂隙面与竖裂隙面的交线,岩石应力增量随斜平面方向的温度梯度增大而增大;热源温度越高,裂隙水流速越低,岩石温度越高、岩石应力越大,系统达到稳态需要的时间越长。     

壁面局部接触裂隙岩体水流-传热的一种理论模型及计算分析

核废物地质处置、地热开发、石油开采等工程领域都可能涉及稀疏裂隙岩体中的水流-传热过程。现有的裂隙岩体水流-传热理论模型和计算方法基本上都是以平行光滑壁面裂隙模型为基础的,没有考虑裂隙的壁面局部接触对水流、水-岩热交换以及岩体传热的影响。针对粗糙壁面裂隙水流过程,阐述了基于Stokes方程的Reynolds润滑方程及Hele-Shaw裂隙模型,采用MATLAB软件中的PDE工具求解,并与Walsh的等效水力开度公式进行对比;分析壁面局部接触裂隙水流-传热与填充裂隙水流-传热的相似性,提出了瞬时局部热平衡假设的适用条件,并在裂隙局部接触体传热满足Biot数条件的前提下,计算分析裂隙局部接触体与水流之间的局部热平衡时间及其影响因素;在裂隙局部接触体与水流之间满足瞬时热平衡假设的前提下,利用填充裂隙水流-传热的解析解,计算了壁面局部接触裂隙水及两侧岩石的温度分布,并分析了裂隙局部接触面积率、裂隙开度、裂隙水平均流速对岩石温度和裂隙水温度的影响特征,结果表明：（1）在设定条件下,由于裂隙局部接触体与裂隙水流之间的热交换,裂隙水流对其两侧岩石温度的影响范围随接触面积率的增大而减小,裂隙两侧岩石对裂隙水流温度的影响程度随接触面积率的增大而增大;（2）裂隙开度和裂隙水流速对岩石温度和裂隙水温度的影响方式的影响是一致的,即由于裂隙水流量随裂隙开度和裂隙水流速的增大而增大,裂隙水流对其两侧岩石温度的影响范围随裂隙开度和裂隙水流速的增大而增大,裂隙两侧岩石对裂隙水流温度的影响程度随裂隙开度和裂隙水流速的增大而减小。     

分布热源作用下单裂隙岩体三维水流-传热的半解析计算方法

针对高放射性核废物地下处置库近场饱和裂隙岩体环境,提出一种由分布热源、饱和单裂隙和两侧无限大岩石构成的三维水流-传热简化模型,建立了控制微分方程和基于拉氏变换域格林函数的积分方程;采用矩形单元把裂隙面域离散化,利用极坐标下的解析方法计算包含奇点的单元积分,利用数值方法计算分布热源和不包含奇点的单元积分,建立拉氏变换域的线性代数方程组,求解后,利用拉氏数值逆变换,计算任意时刻裂隙水和岩石的温度分布。对两个无内热源、流场确定的计算模型进行了计算,与仅考虑岩石沿裂隙面法向一维热传导的解析解进行了对比。计算分析了分布热源作用下饱和单裂隙岩体的三维水流-传热特征及其对裂隙水流速、岩石热传导系数和热源热流集度的敏感度。计算结果表明：与直接采用高斯数值积分相比,提出的解析法奇异积分精度较高;就裂隙水温度而言,单裂隙岩体三维水流-传热半解析计算方法与解析法得到的结果基本一致,但由于半解析计算方法考虑了岩石的三维热传导,使得裂隙水的上游温度较低,而下游温度较高;无分布热源作用时,岩石热传导系数越大,裂隙水温度越低;裂隙水流速越大,裂隙进水温度对裂隙水和岩石温度分布的影响越明显;由于受到裂隙水流动传热的作用,分布热源对裂隙水温度和岩石温度的影响在裂隙水流的下游区域比较显著。     

Mechanical and hydraulic properties of rocks related to induced seismicity

Witherspoon, P.A. and Gale, J.E., 1977. Mechanical and hydraulic properties of rocks related to induced seismicity. Eng. Geol., 11(1): 23–55.The mechanical and hydraulic properties of fractured rocks are considered with regard to the role they play in induced seismicity. In many cases, the mechanical properties of fractures determine the stability of a rock mass. The problems of sampling and testing these rock discontinuities and interpreting their non-linear behavior are reviewed. Stick slip has been proposed as the failure mechanism in earthquake events. Because of the complex interactions that are inherent in the mechanical behavior of fractured rocks, there seems to be no simple way to combine the deformation characteristics of several sets of fractures when there are significant perturbations of existing conditions. Thus, the more important fractures must be treated as individual components in the rock mass.In considering the hydraulic properties, it has been customary to treat a fracture as a parallel-plate conduit and a number of mathematical models of fracture systems have adopted this approach. Non-steady flow in fractured systems has usually been based on a two-porosity model, which assumes the primary (intergranular) porosity contributes only to storage and the secondary (fracture) porosity contributes only to the overall conductivity. Using such a model, it has been found that the time required to achieve quasi-steady state flow in a fractured reservoir is one or two orders of magnitude greater than it is in a homogeneous system. In essentially all of this work, the assumption has generally been made that the fractures are rigid.However, it is clear from a review of the mechanical and hydraulic properties that not only are fractures easily deformed but they constitute the main flow paths in many rock masses. This means that one must consider the interaction of mechanical and hydraulic effects. A considerable amount of laboratory and field data is now available that clearly demonstrates this stress-flow behavior. Two approaches have been used in attempting to numerically model such behavior: (1) continuum models, and (2) discrete models. The continuum approach only needs information as to average values of fracture spacing and material properties. But because of the inherent complexity of fractured rock masses and the corresponding decrease in symmetry, it is difficult to develop an equivalent continuum that will simulate the behavior of the entire system. The discrete approach, on the other hand, requires details of the fracture geometry and material properties of both fractures and rock matrix. The difficulty in obtaining such information has been considered a serious limitation of discrete models, but improved borehole techniques can enable one to obtain the necessary data, at least in shallow systems. The possibility of extending these methods to deeper fracture systems needs more investigation. Such data must be considered when deciding whether to use a continuum or discrete model to represent the interaction of rock and fluid forces in a fractured rock system, especially with regard to the problem of induced seismicity. When one is attempting to alter the pressure distribution in a fault zone by injection or withdrawal of fluids, the extent to which this can be achieved will be controlled in large measure by the behavior of the fractures that communicate with the borehole. Since this is essentially a point phenomenon, i.e., the changes will propagate from a relatively small region around the borehole, the use of a discrete model would appear to be preferable.     

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.     

低温裂隙岩体水-热耦合模型研究及数值分析

裂隙渗流会引起裂隙周围岩体中的温度场变化,在低温岩体中其影响更为明显;此外,裂隙水与周围低温岩石介质发生热交换会引起裂隙中的水冰相变过程发生,而裂隙水冻结将阻碍裂隙渗流,引起裂隙渗流场的变化。因此,低温下的裂隙岩体水-热相互作用是一个强耦合过程。考虑裂隙中的水冰相变过程和渗流作用,建立了低温冻结条件下裂隙岩体水-热耦合模型;以冻结法施工为例,考察了低温冻结过程中裂隙水渗流对裂隙冻结交圈的影响。研究结果表明：由于裂隙渗流的存在,距裂隙较远处岩石先冻结,裂隙冻结所需时间远大于周围岩石;裂隙宽度和裂隙水压力差都会影响冻结交圈时间,裂隙越宽、水压力差越大,裂隙冻结需要时间越长;随着冻结时间的推进,裂隙水渗流速度逐渐降低,当裂隙冻结后裂隙渗流停止。最后通过构建随机裂隙网络模型,利用所建立的水-热耦合模型考察了裂隙网络渗流对冻结交圈的影响,说明了在冻结法施工中考虑裂隙的重要性。     

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。     

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。     

A semi‐analytical modeling approach for three‐dimensional heat transfer in sparsely fractured rocks with water flow and distributed heat source

A semi‐analytical approach is developed for modeling 3D heat transfer in sparsely fractured rocks with prescribed water flow and heat source. The governing differential equations are formulated, and the corresponding integral equations over the fracture faces and the distributed heat source are established in the Laplace transformed domain using the Green function method with local systems of coordinates. The algebraic equations of the Laplace transformed temperatures of water in the fractures are formed by dividing the integrals into elemental ones; in particular, the fracture faces are discretized into rectangular elements, over which the integrations are carried out either analytically for singular integrals when the base point is involved or numerically for regular integrals when otherwise. The solutions of the algebraic equations are inverted numerically to obtain the real‐time temperatures of water in the fractures, which may be employed to calculate the temperatures at prescribed locations of the rock matrix. Three example calculations are presented to illustrate the workability of the developed approach. The calculations found that water flux in the fractures may decrease the rate of temperature rise in regions close to the distributed heat source and increase the rate of temperature rise in regions downstream away from the distributed heat source and that the temperature distribution and evolvement in a sparsely fractured rock mass may be significantly influenced by water flow exchange at intersection of fractures. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical simulation of two-phase flow in conceptualized fractures

Two-phase flow in fractured rock is an important phenomenon related to a range of practical problems, including non-aqueous phase liquid contamination of groundwater. Although fractured rocks consist of fracture networks, the study of two-phase flow in a single fracture is a pre-requisite. This paper presents a conceptual and numerical model of two-phase flow in a variable fracture. The void space of the fracture is conceptualized as a system of independent channels with position-dependent apertures. Fundamental equations, governing two-phase displacement in each channel, are derived to represent the interface positions and fractional flows in the fracture. For lognormal aperture distributions, simple approximations to fractional flows are obtained in analytical form by assuming void occupancy based on a local capillary allowability criterion. The model is verified by analytical solutions including two-phase flow in a parallel-plate fracture, and used to study the impacts of aperture variation, mobility ratio and fracture orientation on properties of two-phase flow. Illustrative examples indicate that aperture variation may control the distribution of wetting and non-wetting fluids within the fracture plane and hence the ability of the fracture to transmit these fluids. The presence of wetting fluid does little to hinder non-wetting fluid flow in fractures with large aperture variations, whereas a small volume of non-wetting fluid present in the fracture can significantly reduce wetting fluid flow. Large mobility ratios and high fracture slope angles facilitates the migration of non-wetting fluid through fractures.     

岩体水力学基础(二)─—岩体水力学的基础理论

单裂隙水流立方定律是岩体水力学中最基本的．也是最重要的定理。本文从不变形平直等宽单裂隙水流运动定理开始，讨论了受应力作用岩体单裂隙、一组平行裂隙、一组正交裂隙以及岩体裂隙系统中水流运动规律，分析了单裂隙中水流渗透压力与裂隙变形之关系。运用水力学原理推导了岩溶单管道流定理，为岩体水力学模型研究奠定了基础。     

A hybrid modeling approach to evaluate the groundwater flow system at the low- and intermediate-level radioactive waste disposal site in Gyeong-Ju, Korea

The development and implementation of a hybrid discrete fracture network/equivalent porous medium (DFN/EPM) approach to groundwater flow at the Gyeong-Ju low- and intermediate-level radioactive waste (LILW) disposal site in the Republic of Korea is reported. The geometrical and hydrogeological properties of fractured zones, background fractures and rock matrix were derived from site characterization data and implemented as a DFN. Several DFN realizations, including the deterministic fractured zones and the stochastic background fractures, whose statistical properties were verified by comparison with in-situ fracture and hydraulic test data, were suggested, and they were then upscaled to continuums using a fracture tensor approach for site-scale flow simulations. The upscaled models were evaluated by comparison to in-situ pressure monitoring data, and then used to simulate post-closure hydrogeology for the LILW facility. Simulation results demonstrate the importance of careful characterization and implementation of fractured zones. The study highlighted the importance of reducing uncertainty regarding the properties and variability of natural background fractures, particularly in the immediate vicinity of repository emplacement.     

Integral equation solution for three-dimensional heat transfer in multiple-fracture enhanced geothermal reservoirs

For the prediction of energy production from multiple-fractured geothermal reservoirs, previous models basically focused on the one-dimensional conduction in the rock containing evenly distributed fractures of equal scale. Here, a novel model is described to numerically investigate the three-dimensional heat transfer in geothermal reservoirs with unevenly spaced disc fractures of various sizes including the aperture and radius. In terms of the water flow through each fracture, an approximate analytical solution is obtained on the assumption that the water pressure disturbances, induced by the fracture margin and extraction (injection) operation, at the injection (extraction) well center and at different locations within the injection (extraction) well range were approximately equal. By the integral equation scheme for two-dimensional planar fractures, the three-dimensional problem of heat exchange is simulated without the reservoir discretization. The singular integral is analytically calculated in polar coordinates whereas the nonsingular integrand is numerically estimated by the Gaussian quadrature method in Cartesian coordinates. Compared with the one-dimensional simplification, the three-dimensional heat conduction remarkably alters the prediction of extraction temperature. In addition, the reservoir temperature field is also significantly influenced by the spacings and dimensions of fractures. The present model may be used for the estimation, design, and optimization of a geothermal reservoir.     

基于RJM断续节理岩体强度与破坏特征的数值模拟研究

裂隙结构的存在对于工程岩体的强度和稳定性具有重要影响,岩石宏观裂隙的产生源自于微破裂的积累。针对岩体裂隙的粗糙特性,通过Matlab建立考虑粗糙度的节理模型（Roughness Joint Model）,采用简化的正弦曲线来表示粗糙节理,并将其导入到颗粒流试验模型中进行单轴压缩试验。对比完整岩体、直线型裂隙岩体、RJM岩体三者破坏的应力-应变曲线,改变裂隙倾角（与水平方向夹角）α,岩桥倾角β,裂隙密度γ,建立不同裂隙分布的断续节理岩体数值试样,开展一系列数值模拟试验。研究结果发现:（1）裂隙的存在明显降低了岩体的抗压强度,RJM模型峰值强度和峰值应变均高于直线型裂隙岩体;（2）岩体抗压强度总体上随裂隙倾角增大而增加,随裂隙密度增加而减小,但随岩桥倾角的改变呈非线性变化,岩桥倾角45°时峰值强度最低,峰值应变最小;（3）裂隙分布会影响岩体的破裂模式,微裂隙的扩展反映了岩体力学性质的各向异性;（4）不同倾角下增加裂隙密度,岩体强度下降程度不同,倾角75°时密度对强度影响最小,30°和60°时影响最大。     

Influence of flow velocity on conservative solute transport in sets of parallel fractures with fracture skin

Analysis of contaminant transport through fractured crystalline rocks has received considerable attention, particularly with regard to subsurface nuclear waste repositories. Most of the studies have employed the dual continuum approach, with the fractures and the rock matrix as the two continuums, assuming that fractures control the overall conductivity of the rock and the porous matrix just provides storage. However, field observations of rock fractures have shown that the real situation can be very complex. Based on some recent investigations, it has been reported that the portion of the rock matrix adjacent to many open fractures is physically and chemically altered. These alterations, referred to as the fracture skin, can have different sorption and diffusion properties compared to those of the undisturbed rock matrix and this may influence the transport of solutes through such formations. In the present study, a numerical model is developed to simulate conservative solute transport in a fractured crystalline rock formation using the triple continuum approach ?? with the fracture, fracture skin and the rock matrix as the three continuums. The model is solved using a fully implicit finite difference scheme. Contaminant migration in the fractured formation with and without skin has been simulated. It is observed that contaminant penetration along the fracture is enhanced at large flow velocities. The effect of flow velocity on conservative solute transport is investigated for different fracture apertures and fracture skin thicknesses. The influence of flow velocity on contaminant transport is demonstrated to be more with change in fracture aperture than with change in skin thickness.