It is well-known that fluid flow in porous media is well-described at the microscale by Navier-Stokes' equations for fluids in the pores but at the macroscale the behavior instead obeys Darcy's equation. Rigorous methods for establishing the form of such equations for macroscale behavior include multiscale homogenization methods and also the volume averaging method. In particular, it has been shown that Biot's equations of single-porosity poroelasticity follow in a scale-up of the microscale equations of elasticity coupled to Navier-Stokes (Burridge and Keller, 1981).
We have found that the equations of single-porosity poroelasticity are not the correct equations at the macroscale when there is significant heterogeneity in fluid permeability. However, the double-porosity dual-permeability approach appears to permit consistent modeling of such reservoirs and also shows that no further up-scaling is required beyond the double-porosity stage in many circumstances. Recent extensions of these ideas by Pride and Berryman (2003a,b) and Pride et al. (2003) confirm these conclusions.