IJPAM: Volume 49, No. 3 (2008)

A STOKES-LIKE PROBLEM APPLICATION TO COMPUTE
EFFECTIVE PERMEABILITY COEFFICIENTS
IN POROUS MEDIA

Ciro Flores$^1$, Francisco J. Valdés-Parada$^2$
$^1$Departamento de Matematicas
Instituto Tecnológico y de Estudios Superiores de Monterrey en Hidalgo
Blvd. Felipe Ángeles 2003, Pachuca, Hgo, C.P. 42080, MEXICO
e-mail: ciro.flores@itesm.mx
$^2$Departamento de Ingeniería de Procesos e Hidráulica
Universidad Autónoma Metropolitana Iztapalapa
Mexico D.F., C.P. 09340, MEXICO


Abstract.An important area of research to identify proper models describing transport phenomena in porous media is the formulation of macroscopic equations. Such equations are expressed in terms of effective coefficients which, in turn, depend upon punctual characteristics of the multiphasic system. Among the methods to formulate macroscopic equations, the method of volume averaging plays an important role, since it allows the adequate boundary value problems (BVP) to be determined, from which effective coefficients can be computed. Momentum transfer processes involve an effective permeability coefficient which needs to be computed. In this report we present several BVP comparing different boundary conditions which have not been reported in specialized literature, in order to compute effective coefficients. This leads to a Stokes-like problem formulation. The numerical method (finite element) used to solve this problem is based on an Uzawa's method. Furthermore, an ad hoc mesher was built for the particular domain to control conditions for several porous media characteristics. The results confirm the empirical Carman-Kozeny model, as well as the predictions reported in the literature.

Received: August 14, 2008

AMS Subject Classification: 65N30, 76S05

Key Words and Phrases: volume averaging, permeability coefficient, Stokes-like problem, mesher

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 3