A Novel Workflow to Model Permeability Impairment through Particle Movement and Deposition in Porous Media

This article presents a practical transfer function type solution to a complex problem in which variations in a number of parameters can be taken into account. A new mathematical model, which is based on mass balance transfer function of particles movement/retention in porous media, has been derived. It is used to predict permeability reduction as a function of time. The linear forms as well as the radial forms of the model are described. Although the differential equations derived are similar to the general form of diffusion–convection equations, the marked difference is the suitability of the model, for being applied for variation of parameters, such as particle concentration in the fluid, injection rate, density of solid particles, against the depth and time of invasion. This transfer function has been solved, and the results of the simulation run agree reasonably well with the experimental damage data obtained in laboratory. Owing to its simplicity, this model is more practical to describe permeability reduction for the flow of suspended particles in porous media.     

Rarefied Pure Gas Transport in Non-isothermal Porous Media: Validation and Tests of the Model

Viscous flow, effusion, and thermal transpiration are the main gas transport modalities for a rarefied gas in a macro-porous medium. They have been well quantified only in the case of simple geometries. This paper presents a numerical method based on the homogenization of kinetic equations producing effective transport properties (permeability, Knudsen diffusivity, thermal transpiration ratio) in any porous medium sample, as described, e.g. by a digitized 3D image. The homogenization procedure—neglecting the effect of gas density gradients on heat transfer through the solid—leads to closure problems in for the obtention of effective properties; they are then simplified using a Galerkin method based on a 21-element basis set. The kinetic equations are then discretized in space with a finite- volume scheme. The method is validated against experimental data in the case of a closed test tube. It shows to be coherent with past approaches of thermal transpiration. Then, it is applied to several 3D images of increasing complexity. Another validation is brought by comparison with other distinct numerical approaches for the evaluation of the Darcian permeability tensor and of the Knudsen diffusion tensor. Results show that thermal transpiration has to be described by an effective transport tensor which is distinct from the other tensors.     

Transport in Porous Media

Table of Contents

Transport in Porous Media     

Flow and Transport Properties of Deforming Porous Media. I. Permeability

Transport in Porous Media - Estimating flow and transport properties of porous media that undergo deformation as a result of applying an external pressure or force is important to a wide variety of...     

Transport in Porous Media

Table of Contents

Transport in Porous Media     

Transport in Porous Media

Volume Contents

Transport in Porous Media     

Rarefied Pure Gas Transport in Non-isothermal Porous Media: Effective Transport Properties from Homogenization of the Kinetic Equation

Viscous flow, effusion, and thermal transpiration are the main gas transport modalities for a rarefied gas in a macro-porous medium. They have been well quantified only in the case of simple geometries. This article develops a model based on the homogenization of kinetic equations producing effective transport properties (permeability, Knudsen diffusivity, thermal transpiration ratio) in any porous medium sample, as described e.g., by a digitized 3D image. The homogenization procedure—neglecting the effect of gas density gradients on heat transfer through the solid—leads to macroscopic transfer relations, and to closure problems in for the obtention of effective properties. Coherence of the approach with previous literature on the subject is discussed. The asymptotic limits of the model (rarefied and continuum regimes) are also studied. One of the main results is that the effect of the geometry on thermal transpiration has to be described by a tensor, which is distinct from the permeability and Knudsen diffusion tensors.     

Process-Dependent Solute Transport in Porous Media

Transport in Porous Media - Solute transport under single-phase flow conditions in porous micromodels was studied using high-resolution optical imaging. Experiments examined loading (injection of...     

Stochastic Estimation of the Slip Factor in Apparent Permeability Model of Gas Transport in Porous Media

Transport in Porous Media - In this paper, we introduce an estimation of the random Klinkenberg slip coefficient in the apparent permeability model using a chaos decomposition technique. The...     

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.     

Miscible Displacements of Reactive and Anisotropic Dispersive Flows in Porous Media

The viscous fingering instability of miscible reactive–dispersive flows in a homogeneous porous media is investigated through nonlinear numerical simulations. In particular, the role of velocity-dependent transverse and longitudinal dispersions as well as the type and rate of auto-catalytic chemical reactions is analyzed. It is found that for a third-order auto-catalytic reaction, the higher the reaction rate, the more complex the finger structures. Furthermore, major differences between the flow development of third-order and second-order autocatalytic reactions are reported. In addition, the anisotropy and velocity dependence of the dispersion tensor are found to have a more profound effect on the fingering instability in the case of reactive flows than in the non-reactive ones. The qualitative characterization of the finger structures is explained by examining the flow velocity field and further quantified through an analysis of the average concentration and relative contact area.     

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.

     

Transport in Porous Media Contents of Volume 45

Volume Contents

Transport in Porous Media Contents of Volume 45     

Transport in Porous Media Contents of Volume 44

Volume Contents

Transport in Porous Media Contents of Volume 44     

Transport in Porous Media Contents of Volume 43

Volume Contents

Transport in Porous Media Contents of Volume 43     

Transport in Porous Media Contents of Volume 46

Transport in Porous Media -     

Mechanisms of Particle Transport Acceleration in Porous Media

Experimental data show that the groundwater transport of radionuclides in porous media is frequently facilitated when accompanied with colloid particles. This is usually explained by the size exclusion mechanism which implies that the particles move through the largest pores where the flow velocity is higher. We call attention to three other mechanisms which influence the colloid particle motion, while determining both the probable transport facilitation and retardation. First of all, it is shown that the transport facilitation may be significantly reduced and even transformed into a retardation due to the growth of the effective suspension viscosity (a friction-limited facilitation). Secondly, we will show that the transport of particles through the largest pores can be retarded due to a reduced connectivity of the large-pore cluster (a percolation-breakup retardation). Thirdly, we highlight the Fermi mechanism of acceleration known in statistical physics which is based on the elastic collisions between particles. All three effects are analyzed in terms of the velocity enhancement factor, by using statistical models of porous media in the form of a capillary bundle and a 3D capillary network. Optimal and critical regimes of velocity enhancement are quantified. Estimations show that for realistic parameters, the maximal facilitation of colloid transport is close to the experimentally observed data.     

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.     

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.