Derivation of Macroscopic Filtration Law for Transient Linear Viscoelastic Fluid Flow
Résumé
This 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.
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