Simulation of upscaling effects due to wave-induced fluid flow in Biot media using the finite-element method

An important upscaling effect in heterogeneous poroelastic Biot media is the dissipation mechanism due to wave-induced fluid flow caused by mesoscopic scale heterogeneities. A typical mesoscopic heterogeneity has a size of tens of centimeters and can be due to local variations in lithological properties or to patches of immiscible fluids. For example, a fast compressional wave traveling across a porous rock saturated with water and patches of gas induces a greater fluid pressure in the gas patches than in the water saturated parts of the material. This in turn generates fluid flow and slow Biot waves which diffuse away from the gas–water interfaces generating significant losses in the seismic range. In this work an iterative domain-decomposition finite-element procedure is presented and employed to simulate this type of upscaling effects in alternating layers of poroelastic rock saturated with either gas or water. The domain-decomposition procedure is naturally parallelizable, which is a necessity in this type of simulations due to the large number of degrees of freedom needed to accurately represent these attenuation effects. The numerical simulations were designed to show the effects of the wave-induced fluid flow on the traveling waves. Our results are the first numerical evidence of the mesoscopic loss mechanism in the seismic range of frequencies for this type of porous heterogeneous media.