Derivation of macroscopic filtration law for transient linear viscoelasticfluid flow in porous media

This work is concerned with deriving a macroscopic filtration law for descr ibing transient linear viscoelastic fluid flow in porous media. This is per formed using a homogenisation technique, i.e. by upscaling the heterogeneit y scale description. The macroscopic filtration law is expressed in Fourier space as a generalised Darcy's law with a dynamic permeability tensor. Thi s model is valid at low Reynolds and Deborah numbers, Analytical results ar e determined in the particular case of the flow of an Oldroyd fluid in a bu ndle of capillary tubes and are compared to those obtained by a correspondi ng phenomenological model. (C) 2000 Elsevier Science Ltd, All rights reserv ed.