Equivalent Permeability Tensor Research Articles

REV and Three-Dimensional Permeability Tensor of Fractured Rock Masses with Heterogeneous Aperture Distributions

This study performed a representative elementary volume (REV) and 3D equivalent continuum study of rock fractures based on fluid simulations of 3D discrete fracture networks (DFNs). A series of 3D DFNs with heterogeneous aperture distributions (the DFN-H model) and uniform apertures (the DFN-I model) were established, in which the fractures were oriented according to the geological field mapping of a high-level radioactive waste candidate site in China. The 3D DFNs of the different model sizes were extracted and rotated in a number of directions to check whether there was a tensor quality of the permeability at a certain scale. The results show that aperture heterogeneity increases the REV size and results in a necessarily larger model size to reach an equivalent continuum behavior, and this effect is more obvious when the fracture density is smaller. The shape of the 2D permeability contour is irregular, with some breaks when the model size is small. As the model size increases, its shape gradually tends to become smooth and approaches an ellipse. The shape of the permeability contours of the DFN-H model is slender compared to the DFN-I model, indicating a larger difference between the minimum and maximum values of the permeability. For the DFN-H model, there is no appropriate approximation for the equivalent permeability tensor over the studied model size range, whereas a good fit of the permeability ellipsoid is obtained for the DFN-I model, and the 3D directional permeability is calculated at this model scale. The corresponding magnitude and direction of the principal permeability are obtained, which can be viewed as the equivalent permeability tensor for the approximated continuum medium.

On quantification of equivalent permeability tensor in sparsely fractured rock masses

The work presented in this paper is focused on the assessment of hydraulic conductivity in sparsely fractured rocks. Different simplified methodologies are used, including Oda's notion of permeability tensor as well as pipe network models, and the results are compared with those generated by a more accurate approach, which incorporates a constitutive law with embedded discontinuity (CLED). Several numerical examples involving fluid flow in the presence of discrete fracture networks are provided, and the estimates of principal values as well as eigenvectors of the equivalent conductivity tensor are compared for all methodologies employed. It is demonstrated that the predictions corresponding to pipe-network model, enhanced by the graph theory algorithm, are fairly consistent with CLED approach, particularly in terms of assessing the orientation of principal directions of permeability. A simple pragmatic procedure is therefore suggested for defining the anisotropic equivalent hydraulic conductivity operator.

Dependence of connectivity dominance on fracture permeability and influence of topological centrality on the flow capacity of fractured porous media

The influence of fracture permeability and fracture network connectivity on the equivalent permeability tensor of the fractured rock mass is investigated and compared. 70 discrete three-dimensional fracture networks with various connectivity are generated. By constructing a graph of each fracture network based on intersection judgment between fractures, two types of connected subnetworks (subgraphs) are extracted according to their potential contribution to flow. The equivalent permeability tensors of the fractured porous media containing the full fracture network and its subnetworks under eight fracture permeability are calculated, respectively. Results demonstrate: (1) the fracture permeability determines the upper and lower bounds of the magnitude of the equivalent permeability tensor of the fractured rock mass. (2) The dominance of the connectivity of a percolating fracture network on the equivalent permeability tensor is dependent on the ratio of matrix permeability to fracture permeability. When the ratio of fracture permeability to matrix permeability is less than 1 × 105, even high fracture network connectivity cannot exert control over the ensemble flow response and the equivalent permeability of the fractured rock mass is limited by the fracture permeability and intensity. (3) As the ratio exceeds 1 × 105, the number of percolating dimensions of the connected subnetworks plays a critical role in the shape of the equivalent permeability ellipsoid of the fractured porous media. Moreover, the average of the three principal values of the equivalent permeability tensor has a negative exponent relationship with the mean of nodes’ normalized betweenness centrality of the connected subnetwork and increases exponentially as the mean of nodes’ degree centrality of the connected subnetwork increases.

Fluid flow and mass transport in fractured media with curved fractures and varying apertures: A 3D modeling approach

AbstractFractured media have been extensively studied due to their significant impact on hydraulic properties of subsurface systems. However, accurately modeling and simulating flow and transport in complex 3D fractured media still remains a challenge. For this purpose, this work aims to develop a new 3D modeling approach and investigate flow and mass transport in fractured media. First, a modeling approach is presented for generating 3D complex structures and high quality finite element grids. This approach allows for the presence of a range of complex geometries, including curved fracture, multiple fractures and the coexistence of fracture‐inclusions. The resulting models and grids are of high quality, enabling accurate simulation and analysis of complex systems. Furthermore, stress‐dependent aperture and roughness are integrated in the computational scheme using Barton–Bandis law. The Galerkin finite element method is used for numerical discretization, then pressure and concentration are calculated in a unified formulation. Later, numerical tests are performed to analyze the role of 3D fractures in flow and mass transport. Simulation results show that fractures have a larger impact on pressure distribution and flow rate compared to inclusions. Fracture roughness increases the aperture then the effective conductivity is improved as well. Curved fractures may reduce flow rate more than planar fractures due to the tortuosity effect. The variation of equivalent permeability tensor is analyzed with varying orientation, roughness, and number of fractures. The impact of stress and fracture roughness causes a variation of fracture permeability and a high pressure gradient on the fracture‐matrix interface, resulting in different patterns of concentration evolution. Overall, this investigation provides insights into the role of 3D fractures in subsurface flow and transport, with implications for various applications.

Computed-tomography-based discrete fracture-matrix modeling: An integrated framework for deriving fracture networks

Investigating the topology of natural fractures and associated flow properties allow for better understanding of fluid flow patterns and mechanical response in fractured reservoirs, key points in the energy supply through geothermal systems, or in the reduction of net CO2 emissions through carbon capture and storage (CCS) practices. However, limited information on the fracture networks is available from seismic data, which poses as a challenge in the accurate modeling of fractured reservoirs. This work proposes an integrated framework for obtaining fracture networks with real aperture distributions, based on X-ray computed tomography (CT) images of core plugs from naturally fractured rock formations. We adapt and employ segmentation, skeletonization and geometry generation algorithms that are available in open-source libraries and licensed software. In addition, we investigate the contributions of fractures and porous matrix to the equivalent permeability tensor through fluid flow simulations considering three different scenarios for the matrix permeability. This work is novel in the coordination of the steps involved in the generation of discrete fracture-matrix (DFM) models from CT-scans of core plugs.

Numerical simulating of pre-grouting in multi-jointed rock mass in deep coalmine roadway excavated via TBM

Tunnel Boring Machines (TBMs) have been used in many underground coal mines in China in recent years, most of which are open-type. The open-type TBM is unfavorable to advance in complex geological conditions, especially in heavily jointed rock mass. When the TBM advance in multi-jointed soft rock mass, the surrounding rock frequently damages and deforms around the tunneling face uncontrollably, which brings risk for the workers and reduces the advance rate. Pre-grouting the rock mass ahead before excavating is a common measure used to handle the above-mentioned condition. However, it is difficult to evaluate how the slurry diffuses and how it enhances the rock mass. Therefore, it is short of guidance to determine the parameters of the pre-grouting. In the present research, a 3D Ubiquitous-Multiple-Joint (UMJ) model was first proposed to simulate the mechanical behavior of rock mass affected by multiple sets of joints around the excavating face of TBM. Then, a seepage model with an equivalent anisotropic permeability tensor was proposed to simulate the diffusion of slurry in the jointed rock mass for pre-grouting. Following the in-situ action, the numerical model was first excavated using the UMJ model and then grouted according to the equivalent permeability tensor. After that, the grouted rock mass was enhanced by improving the mechanical parameters of joints. The effect of pre-grouting reinforcement could thus be simulated. Using the method, this paper studied the effect of grouting parameters and proposed some suggestions for TBM tunneling in multi-jointed rock mass.

The Seepage Tensor of the Multiparameter Model of Pipe Element in Fractured Rock Mass

Based on the measured fracture production of the rock body in the field, the disc fracture hypothesis is used to generate three groups of fractures to form a fracture network by the Monte-Carlo method. The three-dimensional fracture network is simplified into a spatial one-dimensional pipe element model based on the hypothesis of water channel flow in the fractures, and the equivalent pipe diameter of the pipe element is considered to be linearly related to the fracture width. The equivalent permeability tensor is obtained by using a genetic algorithm to obtain the ratio of the equivalent pipe diameter to aperture size for each group of fissures, and compared with the equivalent permeability tensor obtained by the overall single-parameter model and direct algorithm. In comparison with the measured permeability tensor, it is concluded that the multiparameter model can better characterize the permeability tensor than the single-parameter model.

Accurate modeling and simulation of seepage in 3D heterogeneous fractured porous media with complex structures

The past decades have witnessed an increasing interest in numerical simulation for flow in fractured porous media. To date, most studies have focused on 2D or pseudo-3D computational models, where the impact of 3D complex structures on seepage has not been fully addressed. This work presents a method for modeling seepage in 3D heterogeneous porous media. The complex structures, typically the stochastic discrete fractures and inclusions, are able to be simulated. A mesh strategy is proposed to discretize the complex domain. In particular, a treatment on the intersected elements is developed to ensure a conforming mesh. Then, numerical discretization is provided, in which the flux interactions of fractures, inclusions and surrounding rock matrix are included. Numerical tests are performed to analyze the hydraulic characteristics of 3D fractured media. First, the developed framework is validated by comparing numerical solutions with the results of embedded discrete fracture model. Next, the effects of orientation, aperture and radius of fractures on fluid flow and equivalent permeability tensor are analyzed. The variations of pressure distribution are studied in heterogeneous and homogeneous media. Finally, the hydraulic properties of a medium with complex structures are investigated to show the difference of hydraulic feature between fractures and inclusions.

Equivalent Permeability Tensor of Heterogeneous Media: Upscaling Methods and Criteria (Review and Analyses)

When conducting numerical upscaling, either for a fractured or a porous medium, it is important to account for anisotropy because in general, the resulting upscaled conductivity is anisotropic. Measurements made at different scales also demonstrate the existence of anisotropy of hydraulic conductivity. At the “microscopic” scale, the anisotropy results from the preferential flatness of grains, presence of shale, or variation of grain size in successive laminations. At a larger scale, the anisotropy results from preferential orientation of highly conductive geological features (channels, fracture families) or alternations of high and low conductive features (stratification, bedding, crossbedding). Previous surveys of homogenization techniques demonstrate that a wide variety of approaches exists to define and calculate the equivalent conductivity tensor. Consequently, the resulting equivalent conductivities obtained by these different methods are not necessarily equal, and they do not have the same mathematical properties (some are symmetric, others are not, for example). We present an overview of different techniques allowing a quantitative evaluation of the anisotropic equivalent conductivity for heterogeneous porous media, via numerical simulations and, in some cases, analytical approaches. New approaches to equivalent permeability are proposed for heterogeneous media, as well as discontinuous (composite) media, and also some extensions to 2D fractured networks. One of the main focuses of the paper is to explore the relations between these various definitions and the resulting properties of the anisotropic equivalent conductivity, such as tensorial or non-tensorial behavior of the anisotropic conductivity; symmetry and positiveness of the conductivity tensor (or not); dual conductivity/resistivity tensors; continuity and robustness of equivalent conductivity with respect to domain geometry and boundary conditions. In this paper, we emphasize some of the implications of the different approaches for the resulting equivalent permeabilities.

A framework for upscaling and modelling fluid flow for discrete fractures using conditional generative adversarial networks

Scaling up highly heterogeneous aperture distributions of fractures into equivalent permeability tensors enables a substantial reduction in the computational cost of simulating fluid flow in fractured porous media by allowing the employment of coarser grids while keeping the accuracy of an explicit model. This work proposes the adaptation and application of conditional generative adversarial networks (CGAN) for upscaling the permeability of single fractures. Three different types of aperture distributions are used as input in this work: layered media, Zinn & Harvey transformations and self-affine fractals. As output, the model predicts the pressure inside the fracture which is used for calculation of the equivalent permeability tensor. Our results show that the framework employing CGAN provides equivalent tensors that can capture accurately both the permeability angle and anisotropy of discrete fractures, with a substantial reduction of the computational time when compared to traditional frameworks that rely on the numerical simulations.

Interdisciplinary fracture network characterization in the crystalline basement: a case study from the Southern Odenwald, SW Germany

Abstract. The crystalline basement is considered a ubiquitous and almost inexhaustible source of geothermal energy in the Upper Rhine Graben (URG) and other regions worldwide. The hydraulic properties of the basement, which are one of the key factors in the productivity of geothermal power plants, are primarily controlled by hydraulically active faults and fractures. While the most accurate in situ information about the general fracture network is obtained from image logs of deep boreholes, such data are generally sparse and costly and thus often not openly accessible. To circumvent this problem, an outcrop analogue study was conducted with interdisciplinary geoscientific methods in the Tromm Granite, located in the southern Odenwald at the northeastern margin of the URG. Using light detection and ranging (lidar) scanning, the key characteristics of the fracture network were extracted in a total of five outcrops; these were additionally complemented by lineament analysis of two different digital elevation models (DEMs). Based on this, discrete fracture network (DFN) models were developed to calculate equivalent permeability tensors under assumed reservoir conditions. The influences of different parameters, such as fracture orientation, density, aperture and mineralization, were investigated. In addition, extensive gravity and radon measurements were carried out in the study area, allowing fault zones with naturally increased porosity and permeability to be mapped. Gravity anomalies served as input data for a stochastic density inversion, through which areas of potentially increased open porosity were identified. A laterally heterogeneous fracture network characterizes the Tromm Granite, with the highest natural permeabilities expected at the pluton margin, due to the influence of large shear and fault zones.

2D modeling and simulation of deformation bands’ effect on fluid flow: Implications for hydraulic properties in siliciclastic reservoirs

Deformation bands can influence fluid flow within reservoirs, mainly acting as flow barriers. This study aims to characterize deformation bands and evaluate the influence of these structures on fluid flow through 2D modeling and numerical simulation using the equivalent permeability tensor computed numerically through a flow-based upscaling procedure in siliciclastic reservoirs. To do so, we analyze arkosic sandstones of the Antenor Navarro Formation in the Rio do Peixe Basin, NE Brazil. The characterization of deformation bands involved: 1) acquisition of aerial imagery using a drone; 2) conducting direct field-based structural analysis along one scanline (frequency of deformation bands/m); and 3) collection of samples in the field to perform petrophysical (porosity and permeability) tests. After the characterization phase, we built a 2D geological model using the previously acquired parameters and performed a single-phase numerical flow simulation of water using finite element code. We simulated four different horizontal and vertical flow scenarios for both measured and exaggerated host rock permeability. Our structural analysis demonstrated that the deformation bands preferentially strike NE–SW, with secondary E–W– to N–S–orientations. Our petrophysical analysis showed that samples affected by deformation bands have lower porosity (by up to two orders of magnitude) and permeability (by up to four orders of magnitude) values than samples collected in the host rocks. The numerical fluid flow simulation allowed us to conclude that the deformation bands act as partial flow barriers where the hydraulic head can indicate the barrier effect intensity. Pressure drops between host rock regions separated by deformation bands reached values from 10 to 40%, depending on the fluid flow direction, especially for cases with a high contrast between the permeability values (three orders of magnitude) of the deformation bands and the host rock. The results of this study focus on the importance of contrasts in permeability measurements between deformation bands and host rocks, which could help to enhance understanding of the behavior of the deformation bands as partial fluid flow barriers, as well as their implications for hydraulic properties in deformed siliciclastic reservoirs.

Equivalent Permeability Distribution for Fractured Porous Rocks: The Influence of Fracture Network Properties

Equivalent fracture models are widely used for simulations of groundwater exploitation, geothermal reservoir production, and solute transport in groundwater systems. Equivalent permeability has a great impact on such processes. In this study, equivalent permeability distributions are investigated based on a state-of-the-art numerical upscaling method (i.e., the multiple boundary method) for fractured porous rocks. An ensemble of discrete fracture models is created based on power law length distributions. The equivalent permeability is upscaled from discrete fracture models based on the multiple boundary method. The results show that the statistical distributions of equivalent permeability tensor components are highly related to fracture geometry and differ from each other. For the histograms of the equivalent permeability, the shapes of k x x and k y y change from a power law-like distribution to a lognormal-like distribution when the fracture length and the number of fractures increase. For the off-diagonal component k x y , it is a normal-like distribution and its range expands when the fracture length and the number of fractures increase. The mean of diagonal equivalent permeability tensor components increases linearly with the fracture density. The analysis helps in generating stochastic equivalent permeability models in fractured porous rocks and reduces uncertainties when applying equivalent fracture models.

Equivalent Permeability Distribution for Fractured Porous Rocks: Correlating Fracture Aperture and Length

Estimating equivalent permeability at grid block scale of numerical models is a critical issue for large-scale fractured porous rocks. However, it is difficult to constrain the permeability distributions for equivalent fracture models as these are strongly influenced by complex fracture properties. This study quantitatively investigated equivalent permeability distributions for fractured porous rocks, considering the impact of the correlated fracture aperture and length model. Two-dimensional discrete fracture models are generated with varied correlation exponent ranges from 0.5 to 1, which indicates different geomechanical properties of fractured porous rock. The equivalent fracture models are built by the multiple boundary upscaling method. Results indicate that the spatial distribution of equivalent permeability varied with the correlation exponent. When the minimum fracture length and the number of fractures increase, the process that the diagonal equivalent permeability tensor components change from a power law like to a lognormal like and to a normal-like distribution slows down as the correlation exponent increases. The average dimensionless equivalent permeability for the equivalent fracture models is well described by an exponential relationship with the correlation exponent. A power law model is built between the equivalent permeability of equivalent fracture models and fracture density of discrete fracture models for the correlated aperture-length models. The results demonstrate that both the fracture density and length-aperture model influence the equivalent permeability of equivalent fracture models interactively.

The impact of stress orientation and fracture roughness on the scale dependency of permeability in naturally fractured rocks

The equivalent permeability of layered fractured rocks plays an important role in hydrocarbon recovery, underground energy storage, waste disposal management, groundwater hydrology, and subsurface contaminant transport. Borehole data contain some uncertainties/sampling bias during collection and interpretation. This sampling effect may lead to an inaccurate characterization of the fractured media. Studies show that long fractures with high permeability, which are rarely seen in borehole images, dominate the flow pattern and affect the overall permeability of the fractured system. This means that samples taken at any scale smaller than the scale of interest result in imprecise permeability upscaling.To understand this sampling problem, we have established an efficient sampling method to study the existence of the representative elementary volume (REV) in naturally fractured rocks. We selected a collection of outcrop data represented by discrete fracture and matrix (DFM) models in which fracture apertures are mechanically constrained. A finite-element-finite-volume approach is utilized to characterize the flow behavior of DFM models. Multiscale random sampling is combined with flow-based upscaling to determine the equivalent permeability tensor and its anisotropy by considering the variable orientation of the stress state and fracture roughness.Our findings indicate a convergence towards a scale-invariant equivalent permeability and fracture density with increasing sample size, and the equivalent permeability itself has a multimodal distribution. The spatial variation of the permeability tensor and the change in the degree of anisotropy with sample size reflect the inhomogeneity of the fracture patterns.

Permeability of Three‐Dimensional Numerically Grown Geomechanical Discrete Fracture Networks With Evolving Geometry and Mechanical Apertures

AbstractFracture networks significantly alter the mechanical and hydraulic properties of subsurface rocks. The mechanics of fracture propagation and interaction control network development. However, mechanical processes are not routinely incorporated into discrete fracture network (DFN) models. A finite element, linear elastic fracture mechanics‐based method is applied to the generation of three‐dimensional geomechanical discrete fracture networks (GDFNs). These networks grow quasi‐statically from a set of initial flaws in response to a remote uniaxial tensile stress. Fracture growth is handled using a stress intensity factor‐based approach, where extension is determined by the local variations in the three stress intensity factor modes along fracture tips. Mechanical interaction between fractures modifies growth patterns, resulting in nonuniform and nonplanar growth in dense networks. When fractures are close, stress concentration results in the reactivation of fractures that were initially inactive. Therefore, GDFNs provide realistic representations of subsurface networks that honor the physical process of concurrent fracture growth. Hydraulic properties of the grown networks are quantified by computing their equivalent permeability tensors at each growth step. Compared to two sets of stochastic DFNs, GDFNs with uniform fracture apertures are strongly anisotropic and have relatively higher permeabilities at high fracture intensities. In GDFN models, where fracture apertures are based on mechanical principles, fluid flow becomes strongly channeled along distinct flow paths. Fracture orientations and interactions significantly modify apertures, and in turn, the hydraulic properties of the network. GDFNs provide a new way of understanding subsurface networks, where fracture mechanics is the primary influence on their geometric and hydraulic properties.

A NUMERICAL STUDY OF EQUIVALENT PERMEABILITY OF 2D FRACTAL ROCK FRACTURE NETWORKS

This paper presents a numerical study on the equivalent permeability of a fractured rock. A series of two-dimensional discrete fracture network (DFN) models for the calculation of equivalent permeability are generated based on discrete element method (DEM). A sufficient large “parent” DFN model is generated based on the data obtained from a site investigation result of Three Gorges Project in China. Smaller DFN models are extracted from the large “parent” DFN model to calculate the equivalent permeability with an interval of rotation angle of [Formula: see text]. Fluid flow through fractures in both horizontal and vertical directions is simulated. The results show that when the side length of DFN models are larger than 40[Formula: see text]m, the equivalent permeability of both [Formula: see text] and [Formula: see text] become stable, indicating that a DFN model size of 40[Formula: see text]m can be approximated as a representative elementary volume (REV) for those studied rocks. Penetration ellipses are fitted using the least square method on the basis of the calculated equivalent permeability tensor and the main seepage directions of this fractured rock were determined as 63–67[Formula: see text]. Fractal characteristics of DFN models are analyzed with box-counting method by changing the fracture trace length and fracture density, and the results show that equivalent permeability exhibits a logarithmic increasing trend with the increment of fractal dimension.

The principal permeability tensor of inclined coalbeds during pore pressure depletion under uniaxial strain conditions: Developing a mathematical model, evaluating the influences of featured parameters, and upscaling for CBM recovery

In situ coalbeds are commonly inclined to one or multiple directions. The principal permeability tensor of an inclined coalbed may thus be non-coaxial to the uniaxial strain conditions, which are composed of two underlying assumptions: invariant vertical stress and confined horizontal boundaries. This paper developed a mathematical model to represent the principal permeability tensor of inclined coalbeds during pore pressure depletion under uniaxial strain conditions. This model adopted two geological properties to correlate the orientations of principal permeabilities and uniaxial strain conditions. One is the dip angle of inclined coalbeds, and the other is the pitch angle of cleats. The developed model was verified by field permeability data of the coalbeds in the San Juan Basin. Dip angle and pitch angle are the featured parameters of the developed model. This paper thus evaluated how the two angles influenced the magnitudes and evolution behaviors of principal permeabilities during pore pressure depletion under uniaxial strain conditions. The influences of dip angle and pitch angle on principal permeabilities can be attributed to their influences on the effective stresses normal to principal permeabilities. In order to upscale the principal permeability tensor for CBM recovery, this paper formulated a tensor-based index system for coal permeability evaluation. The tensor-based index system is composed of three indexes: the principal permeability tensor, the equivalent permeability tensors coaxial to engineering issues, and the geometric mean (GM) permeability of the three principal permeabilities. The principal permeability tensor can be used to optimize the pattern of vertical CBM wells, to determine the optimal directions of lateral wells, and to predict the propagating orientation of hydraulic fractures. The equivalent permeability tensors coaxial to engineering issues can be implemented into numerical simulators to improve the precision when evaluating and predicting the production performance of CBM wells. The GM permeability represents the ensemble transport capacity of coalbeds and can be used as an indicator to represent the productivity of coalbed reservoirs. This paper also preliminarily discussed how to use the tensor-based index system in CBM recovery.

Tensor Analysis of the Relative Permeability in Naturally Fractured Reservoirs

Summary Fluid evidence shows that prediction of water breakthrough and oil recovery from fractured reservoirs cannot be performed accurately without upscaled relative permeability functions. Relative permeability is commonly assumed to be a scalar quantity, although the justification of that—specifically for naturally fractured reservoirs (NFRs)—is rarely attempted. In this study, we investigate the validity of this scalar-quantity assumption and how it affects fracture/matrix equivalent relative permeabilities, kri(Sw), achieved by a numerical simulation of unsteady-state waterflooding of discrete-fracture/matrix models (DFMs). Numerical determination of relative permeability requires a realistic model, a spatially adaptive simulation approach, and a sophisticated analysis procedure. To fulfil these requirements, we apply the discrete-fracture/matrix modeling to well-characterized outcrop analogs at the hectometer to kilometer scale. These models are parameterized with aperture and capillary entry pressure data, taking into account variations from fracture segment to segment, trying to emulate in-situ conditions. The finite-element-centered finite-volume method is used to simulate two-phase flow in the fractured rock, while also considering a range of wettability conditions from water-wet to oil-wet. Our results indicate that the fracture/matrix equivalent relative permeability is a weakly anisotropic property. The tensors are not necessarily symmetric, and the absolute-permeability tensor is the most influential factor, determining the level of anisotropy of kri. The anisotropy ratio (AR) changes with saturation, is influenced by the fracture/matrix-interface wetted area (Awf), and differs for each phase. In addition, the diagonal terms of the equivalent relative permeability tensor (krii), determined using our novel approach, can be different from those obtained using the assumption that kri is scalar. The magnitude of the difference is controlled by the absolute permeability, wettability, flow rate, and orientation of the fractures in the model. It is worth mentioning that the type and direction of imbibition can be determined by off-diagonal terms of the kri tensor. Furthermore, krii largely depends on the direction of the waterflood along the i-axis.

Estimation of equivalent permeability tensor for fractured porous rock masses using a coupled RPIM-FEM method

PurposeUnderstanding the fluid flow through rock masses, which commonly consist of rock matrix and fractures, is a fundamental issue in many application areas of rock engineering. As the equivalent porous medium approach is the dominant approach for engineering applications, it is of great significance to estimate the equivalent permeability tensor of rock masses. This study aims to develop a novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses.Design/methodology/approachThe radial point interpolation method (RPIM) and finite element method (FEM) are coupled to simulate the seepage flow in fractured porous rock masses. The rock matrix is modeled by the RPIM, and the fractures are modeled explicitly by the FEM. A procedure for numerical experiments is then designed to determinate the equivalent permeability tensor directly on the basis of Darcy’s law.FindingsThe coupled RPIM-FEM method is a reliable numerical method to analyze the seepage flow in fractured porous rock masses, which can consider simultaneously the influences of fractures and rock matrix. As the meshes of rock matrix and fracture network are generated separately without considering the topology relationship between them, the mesh generation process can be greatly facilitated. Using the proposed procedure for numerical experiments, which is designed directly on the basis of Darcy’s law, the representative elementary volume and equivalent permeability tensor of fractured porous rock masses can be identified conveniently.Originality/valueA novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses is proposed. In the approach, the RPIM and FEM are coupled to simulate the seepage flow in fractured porous rock masses, and then a numerical experiment procedure directly based on Darcy’s law is introduced to estimate the equivalent permeability tensor.