Numerical homogenization of mesoscopic loss in poroelastic media

• We develop a numerical homogenization approach for poroelastic media.
• We substitute the heterogeneous poroelastic by a homogeneous viscoelastic medium.
• Small scale pressure diffusion is interpreted as viscous contribution on large scale.
• SVE size must be chosen large enough to contain the relevant diffusion processes.
• Pressure boundary conditions strongly influence the predicted transition frequency.

This contribution deals with the numerical homogenization of mesoscopic flow phenomena in fluid-saturated poroelastic media. Under compression, mesoscopic heterogeneities induce pore pressure gradients and consequently pressure diffusion of the pore fluid. Since this process takes place on a scale much smaller than the observable level, the dissipation mechanism is considered as a local phenomenon. The heterogeneous poroelastic medium is substituted by an overall homogeneous Cauchy medium accounting for viscoelastic properties. Applying volume averaging techniques we derive a consistent upscaling procedure based on an appropriate extension of the Hill-Mandel lemma. We introduce various sets of boundary conditions for the poroelastic problem and discuss the relation between size of the SVEm (Statistical Volume Element) and maximum diffusion length. Numerical examples for two- and three-dimensional problems are given.