Soulaine, C. and Davit, Y. and Quintard, M. (2012) A twopressure model for slightly compressible single phase flow in bistructured porous media. Chemical Engineering Science . (Submitted)

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Abstract
Problems involving flow in porous media are ubiquitous in many natural and engineered systems. Mathematical modeling of such systems often relies on homogenization of porescale equations and macroscale continuum descriptions. For single phase flow, Stokes equations at the porescale are generally approximated by Darcy’s law at a larger scale. In this work, we develop an alternative model to Darcy’s law that can be used to describe slightly compressible single phase flow within bistructured porous media. We use the method of volume averaging to upscale mass and momentum balance equations with the fluid phase split into two fictitious domains. The resulting macroscale model combines two coupled equations for average pressures with regional Darcy’s laws for velocities. In these equations, effective parameters are expressed via integrals of mapping variables that solve boundary value problems over a representative unit cell. Finally, we illustrate the behaviour of these equations in a twodimensional model porous medium and validate our approach by comparing solutions of the homogenized equations with computations of the exact microscale problem.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1565 
Deposited By:  Peter Hudston 
Deposited On:  20 Jul 2012 06:55 
Last Modified:  29 May 2015 19:15 
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