Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system
Andro Mikelić, Mary Fanett Wheeler · Journal of Mathematical Physics · 2012
We undertake establishing well-posedness of the dynamic Biot-Allard equations. It is obtained using the precise properties of the dynamic permeability matrix following the homogenization derivation of the model. By taking the singular limit of the contrast coefficient, the quasi-static Biot system can be obtained from the dynamic Biot equations. These results can be used to formulate an efficient computational algorithm for solving dynamic Biot-Allard equations for subsurface flows with the characteristic reservoir time scales larger than the intrinsical characteristic time. This result appears to be completely new in the literature on Biot's theory. We conclude by showing that in the case of periodic deformable porous media the dynamic permeability has the required properties.