Inverse coefficient problem for mass transfer in two-zone cylindrical porous medium

In the paper posed and solved numerically the inverse problem of mass transfer in a medium consisting of macroporous and microporous cylindrical zones. By solving the direct problem on the basis of the diffusion approach developed “initial data,” and inverse problem was solved using the identification method to determine the mass transfer coefficient in the kinetic equation. Also solved the direct problem on the basis of the kinetic approach, using the obtained the solution of the inverse problem, and it is shown that the diffusion and kinetic approaches yield similar results

Single-Phase Flow of Non-Newtonian Fluids in Porous Media

The study of flow of non-Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield-stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non-Newtonian fluids are generally classified into three main categories: time-independent whose strain rate solely depends on the instantaneous stress, time-dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article the key aspects of these fluids are reviewed with particular emphasis on single-phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling.Comment: 94 pages, 12 figures, 1 tabl

Anomalous Solute Transport in a Cylindrical Two-Zone Medium with Fractal Structure

In this paper, a problem of anomalous solute transport in a coaxial cylindrical two-zone porous medium with fractal structure is posed and numerically solved. The porous medium is studied in the form of cylinder with two parts: macropore—with high permeability characteristics in the central part and micropore—with low permeability around it. Anomalous solute transport is modeled by differential equations with a fractional derivative. The solute concentration and pressure fields are determined. Based on numerical results, the influence of the fractional derivatives order on the solute transport process is analysed. It was shown that with a decrease in the order of the derivatives in the diffusion term of the transport equation in the macropore leads to a “fast diffusion” in both zones. Characteristics of the solute transport in both zones mainly depend on the concentration distribution and other hydrodynamic parameters in the macropore

Ecoulement transitoire d'un fluide viscoélastique linéaire en milieu poreux

National audienceLe but de cette étude est de déterminer une loi de filtration pour décrire l'écoulement transitoire d'un fluide viscoélastique linéaire en milieu poreux. Pour cela on utilise une méthode d'homogénéisation : le comportement macroscopique est déterminé à partir de la description à l'échelle des pores. On montre que, dans l'espace de Fourier, la loi de filtration macroscopique ainsi obtenue est une loi de Darcy généralisée avec un tenseur de perméabilité dynamique

Derivation of Macroscopic Filtration Law for Transient Linear Viscoelastic Fluid Flow

International audienceThis work is concerned with deriving a macroscopic filtration law for describing transient linear viscoelastic fluid flow in porous media. This is performed using a homogenisation technique, i.e. by upscaling the heterogeneity scale description. The macroscopic filtration law is expressed in Fourier space as a generalised Darcy's law with a dynamic permeability tensor. This model is valid at low Reynolds and Deborah numbers. Analytical results are determined in the particular case of the flow of an Oldroyd fluid in a bundle of capillary tubes and are compared to those obtained by a corresponding phenomenological model

Macroscopic modelling of solute transport in porous media saturated by two immiscible liquids

International audienc

Ecoulement transitoire d'un fluide viscoélastique linéaire en milieu poreux

National audienceLe but de cette étude est de déterminer une loi de filtration pour décrire l'écoulement transitoire d'un fluide viscoélastique linéaire en milieu poreux. Pour cela on utilise une méthode d'homogénéisation : le comportement macroscopique est déterminé à partir de la description à l'échelle des pores. On montre que, dans l'espace de Fourier, la loi de filtration macroscopique ainsi obtenue est une loi de Darcy généralisée avec un tenseur de perméabilité dynamique

An Axi-Symmetric Problem of Suspensions Filtering with the Formation of a Cake Layer

In this paper, we consider a vertically positioned cylindrical filtering element. Filtering occurs in the radial direction, therefore, the direction of the velocities of the liquid and suspended particles coincide with this radial direction. The flow can be considered to be one-dimensional and radially axisymmetric. To describe such a filtering process, the axisymmetric Stefan problem will be formulated. The radial mass balance formalism and Darcy’s law are utilized to obtain a basic equation for cake filtration. The boundary condition at the moving surface is derived and the cake filtration is formulated in a Stefan problem. Equations are derived that describe the dynamics of cake growth in the cake filtration, and they are numerically solved. The influence of different model parameters on the compression and fluid pressure across the cake and the growth of its thickness are studied

Numerical study of suspension filtration model in porous medium with modified deposition kinetics

Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone