Efficient fully coupled 3D poroelastic modeling of geomechanical deformation during depletion and reinjection: An asymptotic transformation of Biot's poroelasticity from a dynamic to a quasistatic response

We develop an approach for efficient 3D simulation of the quasistatic fully coupled poroelastic response of a reservoir during depletion and subsequent reinjection. The approach uses a scaling of the solid and fluid densities in Biot's po-roelastic equations. This scaling impacts the critical fre-quency fc of Biot's slow wave that defines diffusive flow (f < fc) and wave propagation (f > fc). We find the cri-terion for the density scaling range over which the poroelas-tic response is accurately modeled and benchmark the approach against Terzaghi's 1D and Rudnicki's 3D analytic solutions. The density scaling approach is presently limited to single-phase fluid flow. To illustrate the utility of this ap-proach, we simulate microseismic depletion delineation (MDD) in a fractured unconventional reservoir. The reser-voir, which is subjected to an anisotropic stress field, is first produced for 1000 days, and then a reinjection (below the in situ pressure) is performed for 100 days. We find that stress reorientation during production produces favorable condi-tions for the generation of Mohr-Coulomb slip-related mi-croseismicity. The locations of these microseismic events are found to be consistent with depleted portions of the frac -ture system, in accordance with the MDD concept.