Search results for "Porous medium"

The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media

2012

A novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium. The computational domain is descretized using triangular meshes and the governing PDEs are discretized using a lumped in the edge centres numerical technique. The dependent unknown variable of the problem is the piezometric head. A fractional time step methodology is applied for the solution of the original system, solving consecutively a prediction and a correction problem. A scalar potential of the flow field exists and in the prediction step a MArching in Space and Time (MAST) formulation is applied for the sequential solution of the Ordinary Differential Equation of…

Calculation of heat and moisture distribution in the porous media layer

2007

In this paper we study the problem of the diffusion of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. The transfer of moisture and the heat are described by the model. The system of two partial differential equations (PDEs) is derived, one equation expresses the rate of change of concentration of water vapour in the air spaces and the other the rate of change of temperature. The obtained initial‐boundary value problem is approximated by using the finite volume method. This procedure allows us to reduce the 2D transfer problem described by a system of PDEs to initial value problem…

Finite speed of propagation in porous media by mass transportation methods

2004

Abstract In this Note we make use of mass transportation techniques to give a simple proof of the finite speed of propagation of the solution to the one-dimensional porous medium equation. The result follows by showing that the difference of support of any two solutions corresponding to different compactly supported initial data is a bounded in time function of a suitable Monge–Kantorovich related metric. To cite this article: J.A. Carrillo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).

The Effect of Tomography Imaging Artefacts on Structural Analysis and Numerical Permeability Simulations

2011

Fluid flow phenomena in porous materials can be found in many important processes in nature and in society. In particular, fluid flow through a porous medium contribute to several technological problems, e.g. extraction of oil or gas from porous rocks, spreading of contaminants in fluid-saturated soils and certain separation processes, such as filtration (Torquato, 2001). In paper and wood industry single and multi phase fluid flow properties in porous media play important roles related to manufacturing process and product development. The general laws describing creeping fluid flows are well known. However, a detailed study of fluid flow in porous heterogeneous media is complicated. This i…

Permeability and conductivity for reconstruction models of porous media

2001

The purpose of this paper is to examine representative examples of realistic three-dimensional models for porous media by comparing their geometrical and transport properties with those of the original experimental specimen. The comparison is based on numerically exact evaluations of permeability, formation factor, porosity, specific internal surface, mean curvature, Euler number, local porosity distributions, and local percolation probabilities. The experimental specimen is a three-dimensional computer tomographic image of Fontainebleau sandstone. The three models are examples of physical and stochastic reconstructions for which many of the geometrical characteristics coincide with those o…

Quantitative prediction of effective material properties of heterogeneous media

1999

Effective electrical conductivity and electrical permittivity of water-saturated natural sandstones are evaluated on the basis of local porosity theory (LPT). In contrast to earlier methods, which characterize the underlying microstructure only through the volume fraction, LPT incorporates geometric information about the stochastic microstructure in terms of local porosity distribution and local percolation probabilities. We compare the prediction of LPT and of traditional effective medium theory with the exact results. The exact results for the conductivity and permittivity are obtained by solving the microscopic mixed boundary value problem for the Maxwell equations in the quasistatic app…

Photoluminescent and paramagnetic centers in gamma irradiated porous silica

2005

Abstract The photoluminescence and electron spin resonance properties of gamma irradiated (up to 500 kGy) porous silica are reported. By exciting at 5.6 eV a photoluminescence contribution can be detected before irradiation, peaked at about 4.1 eV. Gamma irradiation causes the generation of the E′ centers (about 1 × 1014 defects cm−3) of paramagnetic hole centers and modifies the photoluminescence properties of the sample: the emission amplitude decreases and three contributions can be singled out at about 3.3, 3.8 and 4.4 eV.

Corrigendum: Generalized Buckley–Leverett theory for two-phase flow in porous media

2012

Generalized Buckley–Leverett theory for two-phase flow in porous media

2011

Hysteresis and fluid entrapment pose unresolved problems for the theory of flow in porous media. A generalized macroscopic mixture theory for immiscible two-phase displacement in porous media (Hilfer 2006b Phys. Rev. E 73 016307) has introduced percolating and nonpercolating phases. It is studied here in an analytically tractable hyperbolic limit. In this limit a fractional flow formulation exists, that resembles the traditional theory. The Riemann problem is solved analytically in one dimension by the method of characteristics. Initial and boundary value problems exhibit shocks and rarefaction waves similar to the traditional Buckley-Leverett theory. However, contrary to the traditional th…

A comparison between simulation and experiment for hysteretic phenomena during two-phase immiscible displacement

2014

[1] The paper compares a theory for immiscible displacement based on distinguishing percolating and nonpercolating fluid parts with experimental observations from multistep outflow experiments. The theory was published in 2006 in Physica A, volume 371, pages 209–225; the experiments were published in 1991 in Water Resources Research, volume 27, pages 2113. The present paper focuses on hysteretic phenomena resulting from repeated cycling between drainage and imbibition processes in multistep pressure experiments. Taking into account, the hydraulic differences between percolating and nonpercolating fluid parts provides a physical basis to predict quantitatively the hysteretic phenomena observ…