Macroscopic Conductivity of Vugular Porous Media

A systematic numerical study of the macroscopic electrical conductivity of vugular porous media has been conducted by solving the Laplace equation. The structure of these bimodal media is characterized by the micro and macroporosities and by the micro and macro correlation lengths. The overall correlation function is analyzed. It is shown that mainly depends on the total porosity, and very little on the other parameters. Moreover, similar results are obtained when the microporous medium is considered as a continuum. Finally, these predictions are compared to experimental data for the formation factor and the thermal conductivity of limestones; the agreement is good in the first case, and excellent in the second.     

Surface Permeability of Particulate Porous Media

The dispersion process in particulate porous media at low saturation levels takes place over the surface elements of constituent particles and, as we have found previously by comparison with experiments, can be accurately described by superfast nonlinear diffusion partial differential equations. To enhance the predictive power of the mathematical model in practical applications, one requires the knowledge of the effective surface permeability of the particle-in-contact ensemble, which can be directly related with the macroscopic permeability of the particulate media. We have shown previously that permeability of a single particulate element can be accurately determined through the solution of the Laplace–Beltrami Dirichlet boundary value problem. Here, we demonstrate how that methodology can be applied to study permeability of a randomly packed ensemble of interconnected particles. Using surface finite element techniques, we examine numerical solutions to the Laplace–Beltrami problem set in the multiply-connected domains of interconnected particles. We are able to directly estimate tortuosity effects of the surface flows in the particle ensemble setting.

     

Macroscopic Flow Potentials in Swelling Porous Media

In swelling porous media, the potential for flow is much more than pressure, and derivations for flow equations have yielded a variety of equations. In this article, we show that the macroscopic flow potentials are the electro-chemical potentials of the components of the fluid and that other forms of flow equations, such as those derived through mixture theory or homogenization, are a result of particular forms of the chemical potentials of the species. It is also shown that depending upon whether one is considering the pressure of a liquid in a reservoir in electro-chemical equilibrium with the swelling porous media, or the pressure of the vicinal liquid within the swelling porous media, a critical pressure gradient threshold exists or does not.     

Permeability of Porous Media from Simulated NMR Response

Nuclear Magnetic Resonance (NMR) is an increasingly popular well-logging tool in petroleum industry because it is the only tool that attempts to estimate formation permeability. In this paper, spatially correlated porous media are generated. Permeabilities of these media are computed by the lattice Boltzmann method. NMR relaxation responses are simulated by a random walk technique and formation factors are computed by solving a Laplacian equation. The testing of commonly used NMR permeability correlations shows that three conditions should be met for the validity of these correlations. The surface relaxivity should not vary significantly. The formation factor should depend only on porosity. And the characteristic pore body radius should be proportional to the characteristic throat radius. The correlations are improved by including surface relaxivity and formation factor.     

Permeability of the Fluid-Filled Inclusions in Porous Media

In this article, we propose an approach to obtain the equivalent permeability of the fluid-filled inclusions embedded into a porous host in which a fluid flow obeys Darcy’s law. The approach consists in the comparison of the solutions for one-particle problem describing the flow inside the inclusion, firstly, by the Stokes equations and then by using Darcy’s law. The results obtained for spheres (3D) and circles (2D) demonstrate that the inclusion equivalent permeability is a function of its radius and, additionally, depends on the host permeability. Based on this definition of inclusion permeability and using effective medium method, we have calculated the effective permeability of the double-porosity medium composed of the permeable matrix (with small scale pores) and large scale secondary spherical pores.     

Macroscopic Behavior of Swelling Porous Media Derived from Micromechanical Analysis

A new macroscopic model for swelling porous media is derived based on a rigorous upscaling of the microstructure. Considering that at the microscale the medium is composed of a charged solid phase (e.g. clay platelets, bio-macromolecules, colloidal or polymeric particles) saturated by a binary monovalent aqueous electrolyte solution composed of cations + and anions – of an entirely dissociated salt, the homogenization procedure is applied to scale up the pore-scale model. The microscopic system of governing equations consists of the local electro-hydrodynamics governing the movement of the electrolyte solution (Poisson–Boltzmann coupled with a modified Stokes problem including an additional body force of Coulombic interaction) together with modified convection–diffusion equations governing cations and anions transport. This system is coupled with the elasticity problem which describes the deformation of the solid phase. Novel forms of Terzaghi's effective principle and Darcy's law are derived including the effects of swelling pressure and osmotically induced flows, respectively. Micromechanical representations are provided for the macroscopic physico-chemical quantities.     

Analytical Solutions to Gas Flow Problems in Low Permeability Porous Media

In most of conventional porous media the flow of gas is basically controlled by the permeability and the contribution of gas flow due to gas diffusion is ignored. The diffusion effect may have significant impact on gas flow behavior, especially in low permeability porous media. In this study, a dual mechanism based on Darcy flow as well as diffusion is presented for the gas flow in homogeneous porous media. Then, a novel form of pseudo pressure function was defined. This study presents a set of novel analytical solutions developed for analyzing steady-state and transient gas flow through porous media including effective diffusion. The analytical solutions are obtained using the real gas pseudo pressure function that incorporates the effective diffusion. Furthermore, the conventional assumption was used for linearizing the gas flow equation. As application examples, the new analytical solutions have been used to design new laboratory and field testing method to determine the porous media parameters. The proposed laboratory analysis method is also used to analyze data from steady-state flow tests of three core plugs. Then, permeability (k) and effective diffusion coefficient (D _e) was determined; however, the new method allows one to analyze data from both transient and steady-state tests in various flow geometries.     

Sensitivity of Intrinsic Permeability to Electrokinetic Coupling in Shaly and Clayey Porous Media

Classical Darcy’s law assumes that the intrinsic permeability of porous media is only dependent on the micro-geometrical and structural properties of the inner geometry of the medium. There are, however, numerous experimental evidences that intrinsic permeability of shaly and clayey porous material is a function of the fluid phase used in the experiments. Several pore-scale processes have been proposed to explain the observed behavior. In this study, we conduct a detailed investigation of one such mechanism, namely the electrokinetic coupling. We have developed a numerical model to simulate this process at the pore-scale, incorporating a refined model of the electrical double layer. The model is used to conduct a detailed sensitivity analysis to elucidate the relative importance of several chemical–physical parameters on the intensity of the electrokinetic coupling. We found that permeability reduction due to this mechanism is likely to occur only if the effective pore-radius is smaller than 10⁻⁶ m. We also observed that electrokinetic coupling is strongly sensitive to electrophoretic mobility, which is normally reduced in clays compared to free-water conditions. Based on these findings, we set up a suite of stochastic pore-network simulations to quantify the extent of permeability reduction. We found that only if the effective pore-radius is ranging from 5 × 10⁻⁷ m to 5 × 10⁻⁸, electrokinetic coupling can be responsible for a 5–20% reduction of the intrinsic permeability, and, therefore, this mechanism has a minor impact on situations of practical environmental or mining interest.     

Predicting Resistivity and Permeability of Porous Media Using Minkowski Functionals

Transport in Porous Media - Permeability and formation factor are important properties of a porous medium that only depend on pore space geometry, and it has been proposed that these transport...     

The Effective Permeability of Cracks and Interfaces in Porous Media

The presence of interfaces in fluid/solid biphasic media is known to strongly influence their behavior both in terms of solid deformation and fluids flow. Mathematical models have traditionally represented these interfaces as lines of no-thickness and whose behavior is given in terms of effective permeabilities whose physical meaning is often disconnected to the microscopic nature of the interface. This article aims to reconcile macroscopic and microscopic interface representations by investigating how the nature of microscopic flows and pressures in the interface can be used to explain its macroscopic behavior. By invoking a proper thickness average operation, we derive an closed form expression that relates the effective interfaces permeabilities to its microscopic properties. In particular, we find that the effective interface permeabilities are strongly influenced by three factors: the ratio of bulk and interface permeabilities, the fluid viscosity, and the physical thickness of the interface.

     

Effective Correlation of Apparent Gas Permeability in Tight Porous Media

Gaseous flow regimes through tight porous media are described by rigorous application of a unified Hagen–Poiseuille-type equation. Proper implementation is accomplished based on the realization of the preferential flow paths in porous media as a bundle of tortuous capillary tubes. Improved formulations and methodology presented here are shown to provide accurate and meaningful correlations of data considering the effect of the characteristic parameters of porous media including intrinsic permeability, porosity, and tortuosity on the apparent gas permeability, rarefaction coefficient, and Klinkenberg gas slippage factor.     

多孔介质渗透率的一种新分形模型

多孔介质的渗流特性是油气藏工程、地下水资源利用、高放废物深地质处置等实际工程领域的热门研究问题．基于分形理论及多孔介质由一束面积大小不等的椭圆形毛细管组成的假设,本文建立了流体在分形多孔介质中渗流时的绝对渗透率及相对渗透率的分形渗透率模型．结果表明,绝对渗透率是最大和最小孔隙面积、分形维数、形状因子ε的函数,且当ε =1时,本文模型可以简化成Yu与Cheng模型;而非饱和多孔介质的相对渗透率与饱和度和多孔介质微结构参数有关．将本文提出的渗透率分形模型预测与实验测量数据及其他模型结果进行对比,显示它们整体吻合很好．     

Low Pressure Gas Percolation Characteristic in Ultra-low Permeability Porous Media

Low pressure gas percolation characteristic in ultra-low permeability porous media is investigated in this article through core flow experiments. The results show that the wall-slip layer covers more than 10% of the average porous channel radius on account of minimum pore size when the permeability is below 0.1 × 10^?3μ m ² order, and seepage behavior is contrasted to that in mid-high permeability pore media. When the gas pressure is not high enough, the flow regime turns into transitional flow instead of slip flow, and nonlinear relationship between the measured gas permeability and the reciprocal of average pressure exists. The gas measuring permeability experiment would be influenced by the non-linear relationship. If Klinkenberg-corrected method is applied to speculate the equivalent liquid permeability, the extrapolated value will become less or minus. Simultaneously, actual gas flow velocity at the outlet is beyond the calculated value with Klinkenberg formula. A new gas seepage model based on the general slip boundary condition is derived from the homogenization technique in this article. At last the flow model is examined to be suitable for representing the gas flow behavior in ultra-low permeability media and estimating the absolute permeability from single-point, steady-states measurements.     

3D Morphology and Permeability of Highly Porous Cellulosic Fibrous Material

Fibrous materials are structures whose complexity depends on the size and geometry of the fibres and on their arrangement induced by the manufacturing process. We interest here in the permeability for air of wood-based fibrous materials with high porosity on which experimental measurements are difficult to be implemented without structural modifications. In this study, we show the usefulness of 3D X-ray tomography imaging in both experimental and numerical permeability measurements. Image analysis tools derived from mathematical morphology are used to access quantitative structural parameters of the interconnected pores (porosities, pore size distributions and correlation lengths), as well as needed information on the experimental samples (cross-section area and length). A specific experimental setup and methodology is proposed to assess the permeability derived from Darcy’s law. Results are then compared to direct numerical simulation of Stokes flow carried out on 3D representative volumes of the fibrous materials.     

Non-isothermal Permeability Impairment by Fines Migration and Deposition in Porous Media including Dispersive Transport

Particle migration and deposition, and resulting permeability impairment occurring in porous media are described by a practical phenomenological model considering temperature variation and particle transport by advection and dispersion. Variation of the filter coefficient and permeability of porous matrix by temperature and particle deposition, and other essential factors are considered by means of the special correlations of the relevant variables and dimensionless numbers. Comparison of the numerical results, obtained using a finite-difference numerical scheme with and without considering the dispersion mechanism and temperature variation, reveals the significance of such effects on fines migration and deposition, and consequent permeability impairment in porous media. Improved model presented in this article can be instrumental for scientifically guided experimentation, analysis, and optimal design of processes involving in transport of colloidal and fine particles through geological subsurface formations.     

Use of a Downscaling Procedure for Macroscopic Heat Source Modeling in Porous Media

Many porous media such as rocks have mesoscale inhomogeneities. The characteristic sizes of such inhomogeneities are much larger than the pore size but much less than the characteristic scale of the problem, such as the length of the sample on which measurements are taken. In this paper, we have solved the one-particle problem for depolarization of an ellipsoidal particle located in a porous medium with electrokinetic effect. To calculate the effective physical properties of a porous medium with many ellipsoidal inclusions, we have applied the effective field method. The application of this method allows us to take into account the texture of an inhomogeneous medium. The analysis performed has shown that three effective properties of inhomogeneous media (permeability, electroosmotic coupling coefficient and electrical conductivity) are not completely independent variables. General theory is illustrated by calculations of the effective properties of media containing spherical and spheroidal inclusions.     

Beyond Kozeny–Carman: Predicting the Permeability in Porous Media

Transport in Porous Media - Various processes such as heterogeneous reactions or biofilm growth alter a porous medium’s underlying geometric structure. This significantly affects its...     

Macroscopic Two-phase Flow in Porous Media Assuming the Diffuse-interface Model at Pore Level

The paper presents a model for two-phase flow, where liquid and gas are treated as one fluid with variable density. A one-component fluid and the diffuse-interface model for two-phase flow are assumed at pore level. The wetting properties of the fluid are described by the Cahn theory. Macroscopic equations are deduced in the framework of the Marle formalism. It is shown that two-phase flow in porous media can be described by the Cahn–Hilliard equation for the mass density. The concept of relative permeability is not needed. For non-neutral wetting, it is shown that a capillary pressure exists but that it is not a function of state. Two numerical illustrations are presented, one of them showing that the model is, at least in a simple steady-state situation, compatible with the generalized two-continuum model.