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Invasion percolation (IP) models of dense non‐aqueous phase liquid (DNAPL) invasion into saturated horizontal fractures typically neglect viscous and gravity forces, as it is assumed that capillarity dominates in many situations. An IP model simulating DNAPL invasion into saturated horizontal fractures was modified to include gravity as a local effect. The model was optimized using a genetic algorithm, and demonstrated that the inclusion of gravity is important for replicating the architecture of the DNAPL invasion pattern. The optimized gravity‐included simulation showed the DNAPL invasion pattern to be significantly more representative of the experimentally observed pattern (80% accuracy) than did the optimized gravity‐neglected simulation (70% accuracy). Additional simulations of DNAPL invasion in 360 randomly generated fractures were compared with and without gravity forces. These simulations showed that with increasing fracture roughness, the minimum difference between simulations with and without gravity increases to 35% for a standard deviation of the mid‐aperture elevation field (SDz) of 10 mm. Even for low roughness (SDz = 0.1 mm), the difference was as high as 30%. Furthermore, a scaled Bond Number is defined which includes data regarding DNAPL type, media type and statistical characteristics of the fracture. The value of this scaled Bond Number can be used to determine the conditions under which gravity should be considered when simulating DNAPL invasion in a macroscopically horizontal fracture. Finally, a set of equations defining the minimum and maximum absolute percentage difference between gravity‐included and gravity‐neglected simulations is presented based on the fracture and DNAPL characteristics. 相似文献
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Numerical Study on Behavior of Groundwater Flow in Single Rough Fractures Under Mechanical Effect 
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下载免费PDF全文 Woochang Jeong 《Ground water》2017,55(1):38-50
This paper numerically investigates the characteristics of groundwater flow in spatially correlated variable aperture fractures under the mechanical effect. Spatially correlated aperture distributions are generated using the geostatistical method (i.e., turning bands algorithm in this study). To represent a nonlinear relationship between the effective normal stress and the fracture aperture, a simple mechanical formula is combined with a local flow model. Numerical results indicate that the groundwater flow is significantly affected by the geometry of aperture distribution, varying with the applied effective normal stress as well as the spatial correlation length of aperture distribution. Moreover, using the flow results simulated in this study, two empirical formulae are proposed: (1) the first one (modified Louis formula) is to represent the relationship between the effective normal stress and the effective permeability of fracture and (2) the second one is to represent the relationship between relative roughness and effective permeability. 相似文献
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Experiments on the immiscible displacement of water by air were performed in two horizontal artificial open rough-walled fractures with different correlation structures. The aperture field of the first fracture has a Gaussian variogram with a finite correlation length, while that of the second one has a power-law variogram, for which no finite correlation length can be assigned. We simulated the displacement process using an invasion percolation model, which takes the in-plane curvature of the interface between water and air into account. The correlation structure of the aperture field has no effect on the irregularity of the shape of the air clusters. However, the correlation structure in combination with the in-plane curvature influences the density of the air clusters and thus has an impact on characteristic properties of the flow. We analyze the model parameters and properties with respect to the fracture properties. The stochastic average of the air clusters for models with different curvature numbers and fields with different correlation lengths is then calculated in order to analyze their influence on continuum approach models. 相似文献
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Modeling fracture porosity development using simple growth laws 总被引：2，自引：0，他引：2
A model of porosity development has been developed to investigate general relationships between simple fracture aperture growth laws and fracture porosity in evolved fracture arrays in aquifers. The growth of fracture apertures in two-dimensional orthogonal arrays with initially spatially uncorrelated lognormal aperture distributions has been studied, where aperture growth rate is proportional to an exponent of the flow rate through each fracture. The evolved arrays show geometrical phase changes as a function of the aperture growth rate exponent, e, and the standard deviation of the initial aperture distribution, sigma(z). Low values of e and sigma(z) lead to bimodal aperture distributions, where apertures parallel to flow are preferentially enlarged. At moderate values of e and sigma(z), there is a transition to a regime of more complex geometries consisting of networks of channel-like structures of preferentially enlarged apertures. At larger values of e, array-spanning channel-like paths of preferentially enlarged apertures develop, where the tortuosity of the channel-like paths is a linear function of sigma(z). Following an initial growth phase, during which dynamically stable aperture configurations develop, arrays undergo simple amplification. The geometry of the evolved aperture fields is diverse and they can be highly complex; consequently, parameterization and prediction of their evolution in terms of the initial aperture distributions and growth rate laws is not trivial. 相似文献
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Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law 下载免费PDF全文
下载免费PDF全文 Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls. 相似文献
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A quasi-static scheme based on pore space spatial statistics is presented to simulate pore-scale two-phase capillary-dominant displacement processes. The algorithm is coupled with computational fluid dynamics in order to evaluate saturation functions. Wettability heterogeneity in partial and fractional/mixed-wet media is implemented using a contact angle map. The simulation process is pixel-wised and performed directly on binary images. Bypassing and snap-off are tackled as non-wetting phase trapping mechanisms. Post-processing results include residual saturations, effective permeability and capillary pressure curves for drainage and imbibition scenarios. The primary advantages of the proposed workflow are eliminating pore space skeletisation/ discretization, superior time efficiency and minimal numerical drawbacks when compared to other direct or network-based simulation techniques. 相似文献
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M. C. Tom Kuo 《Ground water》2022,60(4):510-517
Few published data are available for two-phase flow in fractures from field studies. All measurements of relative permeability reported in the literature were done in laboratory-scale. The in situ water saturations are normally not known for multiphase flow in natural fractures; therefore, the direct measurements of relative permeability are difficult in field-scale. With the help of a case study before and after the 2008 Mw 5.4 Antung earthquake, groundwater radon was used as a tracer to determine the gas and water saturations in a small naturally fractured aquifer. Well tests were also conducted to estimate aquifer transmissivity before and after the 2008 Antung earthquake. Anomalous declines in both groundwater radon concentration and transmissivity were observed precursory to the 2008 Antung earthquake. Both declines are two precursory phenomena having a common effect of gas bubbles. Using the data from well tests and radon tracer, one data point of water relative permeability can be obtained for in situ fractures. This data point reveals strong phase interference between water and gas bubbles for multiphase flow in natural fractures. Both the data of well tests and radon tracer are essential to gain an improved understanding of mass transfer behavior of groundwater-dissolved gases between water and gas phases. 相似文献
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In the current paper, the effect of the geometrical characteristics of 2-D porous media on the relative permeability in immiscible two-phase flows is studied. The generation of the different artificial porous media is performed using a Boolean model based on a random distribution of overlapping circles/ellipses, the size and shape of which are chosen to satisfy the specific Minkowski functionals (i.e. volume fraction, solid line contour length, connectivity). The study aims to identify how each different Minkowski functional affects the relative permeability of each phase at various saturations of the non-wetting phase. A 2-D multi-relaxation time (MRT) lattice Boltzmann model (LBM) that can handle high density ratios is employed in the simulation. The relationship between the driving forces G and the relative permeabilities of the two phases for every artificial structure is quantified. It is found that for high non-wetting phase saturations (fully connected flow), a non-linear relationship exists between the non-wetting phase flow rate and the driving force, whilst this relationship becomes linear at higher magnitudes of the latter. The force magnitude required to approach the linear region is highly influenced by the pore size distribution and the connectivity of the solid phase. For lower non-wetting phase saturation values, its relative permeability in the linear regime decreases as the fraction of small pores in the structure increases and the non-wetting phase flow becomes disconnected. A strong influence of the solid phase connectivity is also observed. 相似文献
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由于水平油水两相流局部流速及局部相含率沿管径方向存在复杂分布,致使其流量及相含率测量非常困难.本文利用伞集流涡轮流量计、电导传感器、过流式电容传感器构成的生产测井组合仪,在水平油水两相流模拟井中开展了动态实验,分析了流动特性及管子角度倾斜对涡轮流量计及含水率传感器响应特性的影响.根据电容及电导传感器在不同总流量及含水率范围的响应分辨特性,分别采用变系数漂移模型及统计模型预测分相流量,发现变系数漂移模型能够自适应调整模型中的流型参数,且对油水两相分相流量具有较高预测精度. 相似文献
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— A numerical fracture flow simulation based on the lubrication approximation is used to investigate the influence of roughness on the flow inside a rough fracture, at low Reynolds number. Facing surfaces are described as self-affine topographies with identical roughness magnitude. Resolution of the Reynolds equation is achieved using two distinct numerical schemes, with consistency. Fracture closure is studied assuming perfect plastic contact between facing surfaces. Long-range correlations are shown to exist in the local aperture field due to the fracture geometry and subsequently in the local fluxes inside the fracture. Flow channeling is the result of these correlations in terms of spatial distribution of the flow, and is responsible for either flow-enhancing or flow-inhibiting behavior of the fracture. Matching between the two surfaces at scales larger than a mismatch scale is studied. The mismatch scale is the upper limit scale for the local apertures scale invariance. It appears to control flow channeling and the related dispersion of the possible behaviors over a large statistics of fractures with identical statistical features. Hydraulic anisotropy of a given fracture is investigated: the dependence of the fracture transmittivity on the pressure drop orientation is proved to be sinusoidal, with an amplitude that is controlled by the mismatch scale. 相似文献
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Fluid conductivity and elastic properties in fractures depend on the aperture geometry – in particular, the roughness of fracture surfaces. In this study, we have characterized the surface roughness with a log-normal distribution and investigated the transport and flow behaviour of the fractures with varying roughness characteristics. Numerical flow and transport simulations have been performed on a single two-dimensional fracture surface, whose aperture geometry changes with different variances and correlation lengths in each realization. We have found that conventional measurement of hydraulic conductivity alone is insufficient to determine these two parameters. Transient transport measurements, such as the particle breakthrough time, provide additional constraints to the aperture distribution. Nonetheless, a unique solution to the fracture aperture distribution is still under-determined with both hydraulic conductivity and transport measurements. From numerical simulations at different compression states, we have found that the flow and transport measurements exhibit different rates of changes with respect to changes in compression. Therefore, the fracture aperture distribution could be further constrained by considering the flow and transport properties under various compression states. 相似文献
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We propose a novel computational method for the efficient simulation of two-phase flow in fractured porous media. Instead of refining the grid to capture the flow along the faults or fractures, we represent the latter as immersed interfaces, using a reduced model for the flow and suitable coupling conditions. We allow for non matching grids between the porous matrix and the fractures to increase the flexibility of the method in realistic cases. We employ the extended finite element method for the Darcy problem and a finite volume method that is able to handle cut cells and matrix-fracture interactions for the saturation equation. Moreover, we address through numerical experiments the problem of the choice of a suitable numerical flux in the case of a discontinuous flux function at the interface between the fracture and the porous matrix. A wrong approximate solution of the Riemann problem can yield unphysical solutions even in simple cases. 相似文献
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Numerical experiments are conducted to examine the effects of gravity on monodisperse and polydisperse colloid transport in water-saturated fractures with uniform aperture. Dense colloids travel in water-saturated fractures by advection and diffusion while subject to the influence of gravity. Colloids are assumed to neither attach onto the fracture walls nor penetrate the rock matrix based on the assumptions that they are inert and their size is larger than the pore size of the surrounding solid matrix. Both the size distribution of a colloid plume and colloid density are shown to be significant factors impacting their transport when gravitational forces are important. A constant-spatial-step particle-tracking code simulates colloid plumes with increasing densities transporting in water-saturated fractures while accounting for three forces acting on each particle: a deterministic advective force due to the Poiseuille flow field within the fracture, a random force caused by Brownian diffusion, and the gravitational force. Integer angles of fracture orientation with respect to the horizontal ranging from ±90° are considered: three lognormally distributed colloid plumes with mean particle size of 1 μm (averaged on a volumetric basis) and standard deviation of 0.6, 1.2 and 1.8 μm are examined. Colloid plumes are assigned densities of 1.25, 1.5, 1.75 and 2.0 g/cm3. The first four spatial moments and the first two temporal moments are estimated as functions of fracture orientation angle and colloid density. Several snapshots of colloid plumes in fractures of different orientations are presented. In all cases, larger particles tend to spread over wider sections of the fracture in the flow direction, but smaller particles can travel faster or slower than larger particles depending on fracture orientation angle. 相似文献
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Numerical investigation of alternative fracture stiffness measures and their respective scaling behaviours 下载免费PDF全文
下载免费PDF全文 We study the mechanical deformation of fractures under normal stress, via tangent and specific fracture stiffnesses, for different length scales using numerical simulations and analytical insights. First, we revisit an equivalent elastic layer model that leads to two expressions: the tangent stiffness is the sum of an “intrinsic” stiffness and the normal stress, and the specific stiffness is the tangent stiffness divided by the fracture aperture at current stress. Second, we simulate the deformation of rough fractures using a boundary element method where fracture surfaces represented by elastic asperities on an elastic half‐space follow a self‐affine distribution. A large number of statistically identical “parent” fractures are generated, from which sub‐fractures of smaller dimensions are extracted. The self‐affine distribution implies that the stress‐free fracture aperture increases with fracture length with a power law in agreement with the chosen Hurst exponent. All simulated fractures exhibit an increase in the specific stiffness with stress and an average decrease with increase in length consistent with field observations. The simulated specific and tangent stiffnesses are well described by the equivalent layer model provided the “intrinsic” stiffness slightly decreases with fracture length following a power law. By combining numerical simulations and the analytical model, the effect of scale and stress on fracture stiffness measures can be easily separated using the concept of “intrinsic” stiffness. We learn that the primary reason for the variability in specific stiffness with length comes from the fact that the typical aperture of the self‐affine fractures itself scales with the length of the fractures. 相似文献
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裂缝诱导的双相具有水平对称轴的横向各向同性(HTI)介质模型是由一组平行排列的垂直裂缝嵌入到统计各向同性的流体饱和多孔隙岩石中而组成的,它综合考虑了裂缝型储层岩石的各向异性和孔隙性.高精度的地震波场数值模拟技术是研究该介质中地震波传播规律的主要方法.本文结合错格伪谱法和时间分裂法,求解描述该介质中地震波传播的一阶速度-应力方程.模拟了单层和双层模型中的地震波场,并对其进行了特征分析.研究结果表明:错格伪谱法能有效消除标准网格伪谱法波场模拟结果中出现的数值伪影现象,与时间分裂法结合能够获得稳定的、高精度的模拟结果;裂缝诱导双相HTI介质中的地震波场兼具裂缝各向异性介质和双相介质中传播的地震波的波场特征. 相似文献
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The migration of five dense nonaqueous phase liquids (DNAPLs) through a single fracture in a clay aquitard was numerically simulated with the use of a compositional simulator. The effects of fracture aperture, fracture dip, matrix porosity, and matrix organic carbon content on the migration of chlorobenzene, 1,2-dichloroethylene, trichloroethylene, tetra-chloroethylene, and 1,2-dibromoethane were examined. Boundary conditions were chosen such that DNAPL entry into the system was allowed to vary according to the stresses applied. The aperture is the most important factor of those studied controlling the migration rate of DNAPL through a single fracture embedded in a clay matrix. Loss of mass to the matrix through diffusion does not significantly retard the migration rate of the DNAPL, particularly in larger aperture fractures (e.g., 50 microm). With time, the ratio of diffusive loss to the matrix to DNAPL flux into the fracture approaches an asymptotic value lower than unity. The implication is that matrix diffusion cannot arrest the migration of DNAPL in a single fracture. The complex relationships between density, viscosity, and solubility that, to some extent, govern the migration of DNAPL through these systems prevent accurate predictions without the use of numerical models. The contamination potential of the migrating DNAPL is significantly increased through the transfer of mass to the matrix. The occurrence of opposite concentration gradients within the matrix can cause dissolved phase contamination to exist in the system for more than 1000 years after the DNAPL has been completely removed from the fracture. 相似文献
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In this study, a numerical manifold method (NMM) model is developed to analyze flow in porous media with discrete fractures in a non-conforming mesh. This new model is based on a two-cover-mesh system with a uniform triangular mathematical mesh and boundary/fracture-divided physical covers, where local independent cover functions are defined. The overlapping parts of the physical covers are elements where the global approximation is defined by the weighted average of the physical cover functions. The mesh is generated by a tree-cutting algorithm. A new model that does not introduce additional degrees of freedom (DOF) for fractures was developed for fluid flow in fractures. The fracture surfaces that belong to different physical covers are used to represent fracture flow in the direction of the fractures. In the direction normal to the fractures, the fracture surfaces are regarded as Dirichlet boundaries to exchange fluxes with the rock matrix. Furthermore, fractures that intersect with Dirichlet or Neumann boundaries are considered. Simulation examples are designed to verify the efficiency of the tree-cutting algorithm, the calculation's independency from the mesh orientation, and accuracy when modeling porous media that contain fractures with multiple intersections and different orientations. The simulation results show good agreement with available analytical solutions. Finally, the model is applied to cases that involve nine intersecting fractures and a complex network of 100 fractures, both of which achieve reasonable results. The new model is very practical for modeling flow in fractured porous media, even for a geometrically complex fracture network with large hydraulic conductivity contrasts between fractures and the matrix. 相似文献
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以水平裂缝分布的孔隙介质模型为基础,建立了水平裂缝面的平行裂缝分布和带粗糙表面的点接触裂缝模型,导出了两类裂缝模型的水平和垂直电阻率响应关系,分析了两类裂缝模型在没有围压和存在围压条件下的水平电阻率、垂直电阻率变化规律和电各向异性系数的变化特征.讨论了裂缝开度、裂缝密度和裂缝粗糙度等裂缝特征参数对裂缝性储层电各向异性的影响.为简化讨论,所有电性响应特征的分析都忽略了裂缝和孔隙表面的导电性和极化的影响.利用平行分布水平裂缝面模型和带粗糙面的裂缝模型,考察了围压条件下的裂缝性岩石的电各向异性响应特征,得到了对实际应用有意义的结果. 相似文献