Effects Of Anisotropic Permeability Research Articles

A numerical approach for CFD-DEM coupling method with pore network model considering the effect of anisotropic permeability in soil-rock mixtures

A new fluid–solid coupled numerical approach is developed by combining the CFD (Computational Fluid Dynamics) − DEM (discrete element method) with the pore network model (PNM) to simulate the erosion of the soil-rock mixture. The pore network with pore and pore pipes is constructed based on the particles and updated regularly. A relationship equation is derived between the permeability scalar for micro-scaled pore pipe and the anisotropic permeability tensor for macro-scaled fluid element. By the Delaunay-PorePy-PFC3D program framework, the erosion process of the soil-rock mixture with different fine contents (FCs) is simulated. The results show that the PNM-CFD-DEM model can meet the computational accuracy for simulating the rule-arranged uniform particles. The duration of the erosion stage is different for specimens with different FCs. The PNM-CFD-DEM model can reproduce the particle erosion paths in different specimens, as well as the adjustment of the pore network between their coarse particles. The preferential drag forces in the discrete portion take into account the pore network formed by the state of the particle buildup within each fluid element.

Effects of anisotropic permeability on EMHD nanofluid flow and heat transfer in porous microchannel with wavy rough walls

This theoretical study thoroughly examines the complexities of fluid flow and heat transfer within microfluidic devices by employing anisotropic porous media with wavy walls. The effect of anisotropic permeability and electromagnetohydrodynamics (EMHD) on nanofluid transport is examined in a wavy microchannel under a constant pressure gradient. The nonlinear coupled governing equations for electric double-layer potential, velocity, temperature, and nanoparticle volume fraction are solved numerically using shooting techniques with the Runge–Kutta method. The numerical results are validated with the asymptotic analytical solutions. We explore the impact of parameters like the Hartmann number, Darcy number, and joule heating on nanofluidic flow. The interplay between anisotropic permeability ratio and angle significantly influences flow, temperature profiles, and nanoparticle volume fraction. Reduction in nanoparticle concentration is attributed to constrained entry into the porous medium due to elevated anisotropic permeability. Frictional heating, influenced by the Forchheimer inertial effect, enhances temperature and induces slug flow at low Darcy numbers. The Nusselt number peaks at low Darcy numbers with an anisotropic angle of φ=π/2, experiencing a minimum when φ=0. These findings deepen our understanding of the role of anisotropic permeability in shaping fluid flow and heat transfer in microfluidic systems influenced by EMHD effects.

The Effect of Anisotropic Permeability on the Temperature Profiles Obtained In a River Discharge Scenario to a Deep Aquifer

The Effect of Anisotropic Permeability on the Temperature Profiles Obtained In a River Discharge Scenario to a Deep Aquifer

Three-Dimensional Wave-Induced Dynamic Response in Anisotropic Poroelastic Seabed

This paper presents a novel analytical solution, which is developed for investigating three-dimensional wave-induced seabed responses for anisotropic permeability. The analytical solution is based on the assumption of the poroelastic and the u − p dynamic form, which considers the inertia force of the soil skeleton. In this paper, the problem is regarded as an eigenvalue problem through a first-order ordinary differential equation in matrix form. The problematic eigenvector involved in the solution is dealt with using numerical computation, and a process is proposed to implement the present solution for the desired dynamic response. A verification, which is compared with two existing solutions, demonstrates an agreement with the present solution. The results show that the amplitude profile of seabed response for a shorter wave period varies significantly. A comparison between the anisotropic and transverse isotropic, as well as isotropic permeabilities reveals that the error of vertical effective stress on the seabed bottom can reach 74 . 8 % for the isotropic case. For anisotropic permeability, when the wave direction is parallel to the higher horizontal permeability direction, the amplitude profiles of pore pressure and vertical effective stress exhibit the greatest dissipation and increment, respectively. For transverse isotropic permeability, the vertical effective stress is independent of the wave direction, which results in the two horizontal effective stresses on the seabed bottom being identical to each other and independent of the wave direction. Our comprehensive analysis provides insight into the effect of anisotropic permeability on different wave periods and wave directions.

Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-newtonian Fluid

In this paper, an analytical study is reported on double-diffusive natural convection in a shallow porous cavity saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. A Cartesian coordinate system is chosen with the x- and y- axes at the geometrical center of the cavity and the y’-axis vertically upward. The top and bottom horizontal boundaries are subject to constant heat (q) and mass (j) fluxes. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. The permeabilities along the two principal axes of the porous matrix are denoted by K1 and K2. The anisotropy of the porous layer is characterized by the permeability ratio K*=K₁/K₂ and the orientation angle φ, defined as the angle between the horizontal direction and the principal axis with the permeability K2. The viscous dissipations are negligible. Based on parallel flow approximation theory, the problem is solved analytically, in the limit of a thin layer and documented the effects of the physical parameters describing this investigation. Solutions for the flow fields, Nusselt and Sherwood numbers are obtained explicitly in terms of the governing parameters of the problem.

Borehole stability analysis: A new model considering the effects of anisotropic permeability in bedding formation based on poroelastic theory

The mechanical properties of bedding planes in laminated shale rocks have attracted great attention especially when assessing borehole stability. However, the anisotropic permeability effects, though proved significant in bedding rocks by many experiments, are seldom indicated for the borehole-stability problem in the literature. In this paper, a new borehole-stability model was developed to thoroughly analyze the anisotropic permeability effects: the equivalent permeability coefficient of bedding formation is first defined according to the permeability tensor theory in anisotropic medium; the poroelastic solutions of the stress state around inclined boreholes are then obtained incorporating the anisotropic permeability effects; the failures of both rock matrix and bedding planes are considered to evaluate borehole stability. The results show that the permeabilities around deviated boreholes are quite different in bedding formation, which will lead to the change of stress state, failure area around the borehole and the change of collapse pressure and fracture pressure. The pore pressure around the borehole calculated under anisotropic permeability condition (APC) is usually lager than that calculated under isotropic permeability condition (IPC), while for other effective stresses the opposite holds true. The failure depth around borehole is quite different for APC and IPC under the Mohr-Coulomb and Mogi-Coulomb criteria. In general, the collapse failure of rock matrix can be initiated at some distance away from the borehole while the collapse failure of weak planes is usually initiated at the borehole wall. It is more crucial to consider the anisotropic permeability effects to calculate collapse pressure than fracture pressure when assessing borehole stability. Besides, the time growth may lead to collapse or fracture failures near the borehole. The developed analytical model can provide a theoretical basis for drilling design in laminated shale formation.

Numerical Simulation Study on Fracture Parameter Optimization in Developing Low-Permeability Anisotropic Reservoirs

The diamond-shape inverted nine-spot well pattern is widely used in developing low-permeability reservoirs with fractures. However, production wells with equal fracture lengths will lead to nonuniform displacement, especially in anisotropic reservoir. Previous researches mainly focused on equal-length fractures, while studies on the unequal-length fractures which can dramatically improve the development efficiency were little. In this paper, a corresponding numerical model with unequal length of fracture designed in the edge and the corner wells was built in a low-permeability anisotropic reservoir. The main objective was to examine and evaluate the effects of anisotropic permeability and fracture parameter on the waterflooding in the diamond-shape inverted nine-spot well pattern. The results indicate that different fractures penetration ratio and anisotropic permeability both result in different development efficiency. Fracture of the edge well are more easily to be water breakthrough, while the increase of penetration ratio of injection well effectively enhance oil recovery. Moreover, the most optimal penetration ratios of production well fractures under different kx : ky are determined. With the increase of kx : ky, the optimized penetration ratio of corner wells fracture decrease, while that of the edge wells increase. Setting unequal length fractures in low-permeability anisotropic reservoirs can effectively improve the oil displacement efficiency in the waterflooding process.

Examples of successful numerical modelling of complex geotechnical problems

Over the last decades, numerical methods have gained increasing importance in practical geotechnical engineering and numerical methods have become a standard tool in geotechnical design, widely accepted by the geotechnical profession. The advantages of numerical analyses for solving practical problems have been recognised, and developments in software and hardware allow their application in practice with reasonable effort. However, there is still a gap between practice and research and, often unnecessary, simplifications are made in practice and therefore the full power of numerical analyses is not always utilised. One reason for this discrepancy is a lack of transfer of knowledge from research into practice but also a lack of theoretical background of numerical methods, constitutive modelling and modern soil mechanics in practice. In this paper, the application of advanced numerical models for solving practical geotechnical problems is shown, whereas the examples have been chosen in such a way that different aspects are highlighted in each case. Results from fibre-optic measurements for a pull-out test of a ground anchor in soft soil could be reproduced by employing advanced constitutive models, in particular for the grout, in the bonded length of the anchor. For this test, a class-A prediction has been made and numerical results have then been compared with in situ measurements. The back-analysis of a slow-moving landslide is presented next, where the rate of deformation is influenced by water level changes in a reservoir for a pumping power plant, creep of lacustrine sediments and environmental effects such as rainfall infiltration. Finally, some results of modelling cone penetration testing in silts are presented highlighting the effects of anisotropic permeability.

Numerical analysis of wave-induced poro-elastic seabed response around a hexagonal gravity-based offshore foundation

In order to prevent the future risk of soil and structural failures for the offshore foundations, it is essential to evaluate the seabed soil behaviors in the vicinity of the foundation under dynamic wave loadings. The objective of this paper is to investigate the wave-induced soil response and liquefaction risk around a hexagonal gravity-based offshore foundation. Three-dimensional (3D) numerical analysis is performed by applying an integrated multiphysics model developed in the finite volume method (FVM) based OpenFOAM framework. The integrated model incorporates solvers of the nonlinear waves, the linear elastic structure and the anisotropic poro-elastic seabed soil. The free surface model and soil model are verified by grid convergence studies. The wave-induced soil response model is validated by reproducing a laboratory experiment and a good agreement is obtained.Distributions of wave-induced shear stress, pore pressure, vertical displacement and seepage flow structure in the seabed are investigated. It is found that the presence of the foundation significantly amplifies the wave-induced shearing effect and vertical displacement in the underlying seabed soil. Seabed consolidation state in the presence of the structure is evaluated. Since the foundation is embedded in the seabed at a depth, the vertices of the hexagonal foundation cause the stress concentration in the nearby soil during the consolidation process. Therefore, the momentary liquefaction at the vertices is not as significant as that at the edges due to the high initial effective stress. A parametric study with different wave heights is conducted to examine the changes of soil response and momentary liquefaction depth around the hexagonal foundation. Effects of isotropic and anisotropic soil permeability on the pore pressure distribution are investigated. It shows that the effect of anisotropic permeability should be considered for the medium sand that is modelled in the present study.

Consolidation of an Anisotropic Soil Stratum on a Smooth-Rigid Base Due to Surface Loads

The solution of fully coupled system of equations governing the axisymmetric quasi-static deformation of a poroelastic medium with anisotropic permeability is employed to obtain the expressions for pore pressure, stresses and displacements in a soil stratum overlying a smooth-rigid pervious or impervious base. Both fluid as well as solid constituents are taken to be compressible. We use the stiffness formulation. The solution is obtained in the Laplace–Hankel transform domain. The problem of a normal circular loading is discussed in detail. The vertical settlement of the soil stratum and diffusion of pore-pressure in the stratum has been computed numerically in the space–time domain. The effect of anisotropic permeability and compressibilities of the fluid as well as solid constituents on the consolidation process is studied.

Effect of anisotropic permeability on convective flow through a porous tube with viscous dissipation effect

Fully developed convective flow in a tube filled with an anisotropic porous material with viscous dissipation due to an internal heat source is considered. An analytical solution is obtained subject to constant heat flux at the wall of the tube. The effect of the anisotropy parameters (anisotropic permeability ratio $$\lambda $$ and inclination angle of principal axes $$\varphi $$ ) of the porous medium on the hydrodynamic and convective heat transfer inside the tube is shown. The singular behavior of the Nusselt number is discussed. Asymptotic analysis for high and low Darcy numbers is shown to support the validity of the present study. Detailed analysis showing the effect of anisotropy on the convective heat transfer is performed.

Effect of anisotropic permeability on fluid flow through composite porous channel

This paper presents a theoretical model for a fully developed flow through a composite porous channel. The channel consists of a fluid layer sandwiched between two porous layers. A generalized Brinkman-extended Darcy model for the porous layers and Navier–Stokes equations for the fluid layer are used to investigate the flow in detail. The continuity of stress and velocity are used at the interface and no slip at the impermeable walls. We assume that the porous layers are anisotropic. Accordingly, \(\varphi \) is taken as the angle between the horizontal direction and the principal axes with permeability \(K_{2}\) or \(K_{4}\) for the lower or upper porous layers considering the anisotropic nature of the porous medium. It is shown that the anisotropic permeability and orientation angle \(\varphi \) have a strong effect on the fluid flow and skin friction. We present some important findings based on the response to variations in the anisotropy.

A numerical study on miscible viscous fingering instability in anisotropic porous media

In this paper, the viscous fingering of miscible flow displacements in an anisotropic porous media is investigated for the first time. The effect of anisotropic permeability and dispersion tensor on the generation, form and growth rate of finger-like patterns, is studied using both linear stability analysis and computational fluid dynamics (CFD). The linear stability analysis is performed using the quasi-steady state approximation and six order shooting method to predict the growth rate of the disturbance in the flow. It is found that the flow is more stabilized when the ratio of the longitudinal to transverse anisotropic permeability is increased and longitudinal to transverse anisotropic dispersion is decreased. In CFD simulation, Hartley transformation (as a spectral method) and fourth-order Adams-Bashforth technique is used to solve the governing equations. It is shown that anisotropic permeability and dispersion have significant effects on the development of the fingers and also on the mechanisms of interactions between neighboring fingers. The development of the finger structures is discussed using concentration contours and diagrams of transversely average concentration, mixing length, and sweep efficiency for different anisotropic scenarios.

Effect of anisotropic permeability on convective heat transfer through a porous river bed underlying a fluid layer

A study is made of convective heat transfer through packed porous beds which consist of a horizontal fluid layer (river bed) and a porous zone with anisotropic permeability and underlaid by a surface heated to a constant temperature \(T_1\). The free surface of the fluid layer overlying the horizontal porous layer is heated isothermally at temperature \(T_2\) (\(>T_1\)). Using the Navier–Stokes model for the fluid layer and the generalized Brinkman-extended Darcy model for the porous zone, an exact solution is found for a fully developed system of forced convective flow through the superposed layers. The Beavers–Joseph condition is applied at the interface between the two layers. The influence of hydrodynamic anisotropy on the convective phenomenon is investigated analytically. It is shown that the anisotropic permeability ratio \(K^*\), the inclination angle of the principal axes \(\varphi \) of the porous medium, and the thickness of the porous lining \(\epsilon \) have a strong influence on the convective flow and the heat transfer rate. This analysis helps to predict environmental aquatic behavior.

Micropolar fluid squeeze film lubrication between rough anisotropic poroelastic rectangular plates: special reference to synovial joint lubrication

The effect of anisotropic permeability on micropolar squeeze film lubrication between poroelastic rectangular plates is studied. The non-Newtonian synovial fluid is modelled by Eringen’s micropolar fluid, and the poroelastic nature of cartilage is taken in to account. The stochastic modified Reynolds equation, which incorporates the elastic as well as randomised surface roughness structure of cartilage with micropolar fluid as lubricant, is derived. Modified equations for the mean fluid film pressure, mean load carrying capacity and squeeze film time are obtained using the Christensen’s stochastic theory for the study of roughness effects. The effects of surface roughness, micropolar fluid and anisotropic permeability on the squeeze film characteristics of synovial joint are discussed. It is found that the surface roughness effects are more pronounced for micropolar fluids as compared to the Newtonian fluids, and the anisotropic nature of permeability of cartilage off-squares the plate size for optimum performance.

Effects of anisotropic permeability and electrical conductivity of gas diffusion layers on the performance of proton exchange membrane fuel cells

A 3-dimensional model for an in-house proton exchange membrane (PEM) fuel cell with serpentine channels has been developed in order to investigate the sensitivity of the fuel cell performance to the anisotropic gas permeability and electrical conductivity of gas diffusion layers (GDLs). For a realistic range of transport properties being investigated, the fuel cell performance was found to be very sensitive to the electrical conductivity but almost insensitive to the gas permeability of the GDL. For the given operating conditions, the current density was found to be a maximum in the vicinity of the edge between the flow channel and the rib of the current collector. Since the most common GDL materials present a rather significant anisotropy in the in-plane directions, the effects of such anisotropy has been evaluated. Given that the through-plane conductivity is maintained constant for all the cases investigated, for a realistic range of the in-plane electrical conductivity, the fuel cell performance was found to be almost insensitive to this parameter. Therefore such anisotropy can be practically ignored. Finally, for single phase operating conditions, the U-bend in the serpentine channel has no effect on the overall performance of the fuel cell. Hence, only a straight channel of the fuel cell may be modelled and used as a quick performance indicator.

On some integral equations arising in the pressure analysis of inclined wells in anisotropic formations

In this note we look at the effects of anisotropic permeability on the distribution of pressure around an uncased or cased wellbore. We suggest a useful approximation for the form of the density of point sources distributed around the wellbore in order to simulate its influence on the pressure field. We consider both steady state and transient pressure distributions and perform full numerical calculation of some examples to check the accuracy of the approximation.

Penetrative convection in anisotropic porous media with variable permeability

The onset of penetrative convection in an anisotropic porous medium, for fluids with quadratic density law, is studied. In particular, the effects of anisotropic permeability and thermal diffusivity have been taken into account.

Effects of anisotropic permeability of fractured rock masses on underground oil storage caverns

An isotropic assumption is often applied to analyze permeability tests of in situ fractured rock mass, and the homogeneous hydraulic conductivities are then used directly in the seepage analysis. However, the hydraulic conductivities are normally anisotropic in fractured rock masses and the effects of the anisotropic permeability should be taken into account in rock engineering analysis, especially for seepage analysis of underground oil storage caverns. In this study, an underground oil storage cavern project is analyzed and the Oda’s method is used to determine the anisotropy in permeability, where the anisotropy in permeability is determined using the fracture orientation and the in situ stress information from the field survey. The horizontal hydraulic conductivities are obtained based on the geometric average hydraulic conductivities from the injection tests of six boreholes. A typical cavern unit is numerical modeled using code FLAC. The effects of anisotropic permeability on water pressure, water quantities and critical gas pressure are studied carefully. The results indicate that most calculated results based on in situ hydraulic tests with isotropic permeability assumption can be used safely in the underground oil storage cavern project.

Effects of anisotropic permeability on stabilization and pore water pressure distribution of poorly cemented stratified rock slopes

Slopes composed of stratified and poorly cemented rocks that fail during heavy rainfalls are typical in the outer zone of Taiwan's Western Foothills. This study investigates how hydraulic conductivity anisotropy influences pore water pressure (PWP) distributed in stratified, poorly cemented rock slopes and related slope stability through numerical simulation. The notion of representing thin alternating beds of stratified, poorly cemented rocks as an equivalent anisotropic medium for ground-water flow analysis in finite slopes was validated. PWP was then derived in a modelled slope comprising an anisotropic medium with suitable boundary conditions. Simulation results indicate the significance of the principal directions of hydraulic conductivity tensor and the anisotropic ratio on PWP estimation for anisotropic finite slopes. For a stratified, poorly cemented rock slope, estimating PWP utilizing a phreatic surface with isotropic and hydrostatic assumptions will yield incorrect results. Stability analysis results demonstrate that hydraulic conductivity anisotropy affects the slope safety factor and slip surface pattern. Consequently, steady-state groundwater flow analysis is essential for stratified, poorly cemented rock slopes when evaluating PWP distribution and slope stability. This study highlights the importance of hydraulic conductivity anisotropy on the stability of a stratified, poorly cemented rock slope. Copyright © 2006 John Wiley & Sons, Ltd.