Mathematical modelling of flow through consolidated isotropic porous media |
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| Authors: | J Prieur Du Plessis Jacob H Masliyah |
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| Affiliation: | (1) Dept. of Mechanical Engineering, University of Pretoria, Pretoria, South Africa;(2) Dept. of Chemical Engineering, University of Alberta, T6G 2G6 Edmonton, Alberta, Canada |
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| Abstract: | A new mathematical model is proposed for time-independent laminar flow through a rigid isotropic and consolidated porous medium of spatially varying porosity. The model is based upon volumetric averaging concepts. Explicit assumptions regarding the mean geometric properties of the porous microstructure lead to a relationship between tortuosity and porosity. Microscopic inertial effects are introduced through consideration of flow development within the pores. A momentum transport equation is derived in terms of the fluid properties, the porous medium porosity and a characteristic length of the microstructure. In the limiting cases of porosity unity and zero, the model yields the required Navier-Stokes equation for free flow and no flow in a solid, respectively. |
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| Keywords: | Porous medium REV averaging inertial effects tortuosity isotropic square duct |
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