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.     

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.     

徐家围子断陷深层火石岭组致密火山岩储层地应力分布规律研究

徐家围子断陷位于松辽盆地北部,其深层中生代火石岭组为致密火山岩气藏,天然裂缝发育,地应力分布非均质性强。结合诱导裂缝法与井径崩落法进行单井现今地应力方向分析,利用声波测井法计算现今地应力大小的纵向分布。依据火石岭组构造顶底面图、火山岩相组及断层分布特征建立非均质三维地质模型;在动、静态岩石物理参数拟合校正的基础上,结合实验测试及已有研究成果,确定不同岩相组和断层岩石物理参数,建立三维力学模型;利用Ansys有限元数值模拟软件建立火石岭组三维数学模型并进行相关运算获得三维现今地应力分布模型。计算结果表明在火石岭组地层中,水平最大主应力方向主要为东西向,应力值范围在86~110 MPa;水平最小主应力方向主要为南北向,应力值范围在67~84 MPa。分析模拟结果可知火山岩相、断层和构造起伏三者对火石岭组现今地应力分布影响较大。其中水平主应力的方向主要受断层和近火山口相分布的影响,而水平主应力的大小则是受三者综合作用。在构造低部位,近火山口相组发育处,断层上盘及断层端部皆为主应力的集中区域。依据现今地应力研究成果可为徐家围子断陷下一步开发井网部署、压裂改造方案和水平井的设计以及注水管理提供重要指导。      

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.     

裂缝性储层裂缝的阵列侧向测井响应数值模拟

为了研究裂缝性储层裂缝的阵列侧向测井响应, 采用裂缝组平板裂缝模型, 利用三维有限元方法, 进行不同裂缝参数条件下的高分辨率阵列侧向测井响应数值模拟.表明阵列侧向视电导率和裂缝孔隙度与裂缝流体电导率成线性关系; 低角度裂缝的阵列侧向深浅视电阻率呈现负差异特征, 高角度缝呈现正差异; 相同裂缝孔隙度下, 裂缝密度增加可使得阵列侧向视电阻率增加, 当裂缝密度足够大时, 测井响应特征基本不随裂缝密度发生变化; 交叉缝的测井响应与具有相同角度的平行裂缝组差异明显, 且不同倾角组合的交叉缝的测井响应之间差异明显.阵列侧向测井对裂缝有较强的敏感性, 根据其测井视电阻率大小可以评价裂缝孔隙度, 根据深浅视电阻率的幅度差异可以研究裂缝的产状, 这些为将阵列侧向测井用于裂缝性储层裂缝评价有指导意义.      

裂隙岩体的多孔介质水力等效性研究

工程岩体中数量众多的裂隙面限制了离散裂隙网络模型在岩体渗流中的应用,迫使人们寻找能够用理论上成熟的等效连续介质模型替代,这就要求进行岩体多孔介质的水力等效性研究。在野外大量实测裂隙的基础上,进行裂隙密度、方位、大小、延续性、开度等几何参数的统计分析,以Enhanced Baecher模型建立离散裂隙网络随机模型,采用Monte-Carlo随机模拟方法进行三维裂隙网络随机模拟。在所生成的一定尺度的三维裂隙网络图基础上,给出计算研究域REV的方法,通过判断REV是否存在,确定能否用等效连续介质模型分析岩体渗流。     

Influence of three-dimensional roughness of rock fracture on seepage characteristics based on the digital image technology

Digital image processing technology can objectively reflect the surface roughness of coal and rock mass fractures and turn physical properties such as fluctuation height to physical data of the rock fracture surface to be used for numerical analyses; thus, it can effectively be applied to the seepage flow analysis of rock fractures. First, clear digital images of the fracture surface height are obtained under the same camera conditions, and then characteristic function values specific to various structure are normalized. Subsequently, the fluctuation height distribution of the rock surface is restored according to the measured fluctuation heights of local points. Finally, according to the surface fluctuation of fractures, invasive restructuring is carried out for three-dimensional fractures in the same coordinate system. Obtained physical parameters on the three-dimensional fractures of the rock are inputted into the COMSOL Multiphysics software to obtain the characteristic three-dimensional model of the rock fracture surface. The numerical analysis results are compared with experimental data on fracture seepage obtained from a seepage coupling true triaxial test system, and the relevance between the simulated result and the physical experiment is higher than 90%, which confirms that the integration of the digital image technology and the numerical analysis method can effectively simulate seepage in rough fractures. The hydraulic gradient of rough fractures and seepage velocity are also consistent with Forchheimer flow characteristics.     

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.      

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。     

煤层气储层裂隙阵列侧向测井响应数值模拟与分析

裂隙是煤层气储层重要的流体渗流通道,是煤层气有效储集体形成的重要条件。研究裂隙的测井响应特征是确定煤层裂隙参数的关键。利用三维有限元方法,确定不同裂隙条件的阵列侧向测井响应。研究表明:阵列侧向测井修正的视电导率与裂隙孔隙度、裂隙流体电导率基本为线性关系;随裂隙倾角增大,阵列侧向视电阻率升高;随基块电阻率增大,阵列侧向视电阻率增加;高角度裂隙(组)的阵列侧向测井深浅视电阻率呈现正差异,而基块电阻率较大的低角度裂隙(组)的响应可呈现负差异特征;相同裂隙孔隙度下,裂隙密度增加可能使裂隙组的阵列侧向视电阻率增加,当裂隙密度足够大时,测井响应基本不随裂隙密度发生变化;交叉裂隙的测井响应与平行裂隙组差异明显,且不同倾角组合的交叉裂隙的测井响应之间差异明显。      

Interpreting Dual Laterolog Fracture Data in Fractured Carbonate Formation

The estimation of fractures is key to evaluating fractured carbonate reservoirs. It is difficult to evaluate this kind of reservoir because of its heterogeneously distributed fractures and anisotropy, A three-dimensional numerical model was used to simulate the responses of the dual laterolog （DLL） in a fractured formation based on a macro-isotropic anisotropic model, Accordingly, a fast fracture computing method was developed. First, the apparent conductivity of the DLL is linearly related to the porosity of the fracture and the conductivity of pore fluid. Second, the amplitude difference of the deep and shallow apparent resistivity logs is mainly dependent on the dip angle of the fracture. Then the response of the DLL to a formation with dip angle fractures is approximately depicted as a function of the bulk resistivity of the rock, the porosity of the fractures and the conductivity of fracture fluid. This function can be used to compute the porosity of fracture quickly. The actual data show that the fracture parameters determined by the DLL closely coincide with the formation micro imager log.     

三维交叉裂隙渗流传质特性数值模拟

对交叉裂隙渗流传质特性的定量描述是研究整个裂隙网络渗透传质特性的基础。为真实模拟水流及溶质在三维交叉裂隙中的运移过程,首先通过三维轮廓仪获取天然岩石裂隙表面的形貌数据,再应用三维重构技术生成相应的三维交叉裂隙模型,随后求解Navier-Stokes方程,假定溶质运移满足Fick定律,模拟水流和溶质在三维交叉裂隙中的运移过程。通过对比粗糙裂隙模型与平行平板模型的模拟结果发现：粗糙度对流体的分布及流动状态存在显著的影响;不同进、出口工况下的流体流动及溶质运移状态亦表明：裂隙交叉的几何形貌会显著地影响溶质混合行为。这些结果表明,目前被广泛采用的平行平板模型在评估岩体内特别是交叉口的物质运移特性时将导致较大的偏差,在将来的研究中有必要针对裂隙交叉口的几何特征建立修正的模型以提高评估的准确性。     

裂缝性碳酸盐岩裂缝的双侧向测井响应特征及解释方法

裂缝评价是裂缝性碳酸盐岩储层评价的关键, 其常规评价方法受到裂缝发育的不均匀性及储层各向异性的影响而存在诸多困难.采用三维数值算法, 利用宏观各向异性地层模型, 研究不同的裂缝参数条件下双侧向测井响应特征, 由此导出一种用于裂缝孔隙度计算的快速算法.分析表明, 裂缝的双侧向响应同裂缝孔隙度与孔隙流体电导率之间存在明显的线性关系, 裂缝的倾角造成双侧向测井曲线幅度差异的变化; 不同倾斜情况下, 将双侧向测井响应近似表示为岩石基岩电阻率、裂缝孔隙度、裂缝流体电导率的函数, 用于裂缝孔隙度的快速计算.实际资料处理表明, 利用双侧向依据该方法确定的裂缝参数同成像测井资料具有良好的对应性.      

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。     

基于连续损伤的水平井射孔-近井筒三维破裂模拟

射孔作为井筒与储层之间的液流通道,是水力压裂过程中的重要可控性参数。为研究水平井射孔-近井筒破裂机制,采用岩层变形-流体渗流方程描述应力状态变化,应用连续损伤破裂单元表征三维破裂位置与形态演化,并开发有限元求解程序模拟分析了射孔对水平井初始破裂压力、破裂位置及近井筒裂缝复杂性的调控作用。通过与解析模型及射孔压裂物理模型试验结果对比,验证了模型及有限元程序的有效性;水平井破裂压力数值分析结果与现场测试数据吻合较好。研究表明：射孔可调控水平井破裂压力与初始破裂位置,同时对近井筒区域裂缝扩展形态影响显著。通过优化射孔参数可以引导初始破裂向最优破裂面扩展、有效降低破裂压力,减小由于螺旋射孔空间排布引起的水平井近井筒裂缝迂曲与复杂程度,提高致密油气藏压裂改造效果。     

基于块体化程度确定裂隙岩体表征单元体

表征单元体（REV,或典型单元体）的存在是应用连续介质方法研究岩体问题的前提,因此,裂隙岩体表征单元体研究是岩体力学及岩体水力学中的一个基础问题,表征单元体的存在与否可以从不同物理参数的角度进行分析。从岩体块体化程度的角度对其存在性进行了较系统的分析,把岩体中由裂隙圈闭形成的孤立块体的总体积在岩体中所占体积百分比定义为裂隙岩体的块体化程度。介绍了GeneralBlock软件的基本分析过程,利用软件建立了三维裂隙岩体模型。根据国际岩石力学学会的裂隙分级,针对5个延展性级别、7个间距级别建立了35种岩体结构模型。利用GeneralBlock对这35种岩体进行了块体识别,分别讨论了这35种岩体结构的块体化程度随着模型范围变化的波动情况。由于所建立的岩体结构模型是随机的,对每种结构的每个研究范围进行了5次随机实现。结果表明,对所有的35种岩体,表征单元体的尺寸在4～8倍间距之间,不超过8倍间距。     

FDEM-flow3D: A 3D hydro-mechanical coupled model considering the pore seepage of rock matrix for simulating three-dimensional hydraulic fracturing

A hydro-mechanical coupled model that can simultaneously consider the pore seepage of a rock matrix and the fracture seepage is proposed to simulate three-dimensional hydraulic fracturing. This model appropriately takes into account the fluid leak-off into the surrounding rock matrix from the fracture. Several examples are given to validate the seepage algorithms and the coupled model. The results suggest that this model can solve problems involving pore seepage and fracture seepage through simple pure fracture seepage. Moreover, it can reproduce the fluid pressure distribution and the crack initiation and propagation and consider the fluid loss during hydraulic fracturing.     

Permeability tensor and representative elementary volume of fractured rock masses

Based on a simulation of three-dimensional fracture networks and a superposition principle of liquid dissipation energy for fractured rock masses, a model of the fracture permeability tensor is proposed. An elastic constitutive model of rock fractures, considering fracture closure and dilation during shearing, is also proposed, based on the dilation angle of the fracture. Algorithms of flow-path searching and calculation of the effective flow coefficients for fracture networks are presented, together with a discussion on the influence of geometric parameters of the fractures (trace length, spacing, aperture, orientation and the number of fracture sets) on magnitude, anisotropy of hydraulic permeability and the size of a representative elementary volume (REV). The anisotropy of hydraulic permeability of fractured rock masses is mainly affected by orientation and the number of fracture sets, and the REV size is mainly influenced by trace length, spacing and the number of fracture sets. The results of studies on REV size and the influence of in-situ stress on hydraulic conductivity of the rock mass on the slope of Jinping-I hydropower station, China, are presented using the developed models and methods. The simulation results agreed well with the results obtained from field water-pressure measurements, with an error of less than 10 %.     

The Development of a new Numerical Modelling Approach for Naturally Fractured Rock Masses

Summary. An approach for modelling fractured rock masses has been developed which has two main objectives: to maximise the quality of representation of the geometry of existing rock jointing and to use this within a loading model which takes full account of this style of jointing. Initially the work has been applied to the modelling of mine pillars and data from the Middleton Mine in the UK has been used as a case example. However, the general approach is applicable to all aspects of rock mass behaviour including the stress conditions found in hangingwalls, tunnels, block caving, and slopes. The rock mass fracture representation was based on a combination of explicit mapping of rock faces and the synthesis of this data into a three-dimensional model, based on the use of the FracMan computer model suite. Two-dimensional cross sections from this model were imported into the finite element computer model, ELFEN, for loading simulation. The ELFEN constitutive model for fracture simulation includes the Rotating Crack, and Rankine material models, in which fracturing is controlled by tensile strength and fracture energy parameters. For tension/compression stress states, the model is complemented with a capped Mohr-Coulomb criterion in which the softening response is coupled to the tensile model. Fracturing due to dilation is accommodated by introducing an explicit coupling between the inelastic strain accrued by the Mohr-Coulomb yield surface and the anisotropic degradation of the mutually orthogonal tensile yield surfaces of the rotating crack model. Pillars have been simulated with widths of 2.8, 7 and 14 m and a height of 7 m (the Middleton Mine pillars are typically 14 m wide and 7 m high). The evolution of the pillar failure under progressive loading through fracture extension and creation of new fractures is presented, and pillar capacities and stiffnesses are compared with empirical models. The agreement between the models is promising and the new model provides useful insights into the influence of pre-existing fractures. Further work is needed to consider the effects of three-dimensional loading and other boundary condition problems.     

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.