Convergence and Error Analysis of Fully Discrete Iterative Coupling Schemes for Coupling Flow with Geomechanics

摘要

The modeling of fluid flow coupled with mechanical deformations is needed for reliable production forecasts, especially in stress sensitive, and structurally weak reservoirs. It also plays a critical role in accurately predicting surface subsidence, well stability. C02 sequestration, and sand production. Traditionally, changes in mechanical deformations are visible to fluid flow through a pore compressibility factor, which is insufficient for purposes described above. In fact, it is only through the coupling between flow and mechanics that reliable reservoir models can be obtained In this work, we consider the multirate fixed-stress split iterative coupling scheme for the Biot system modeling coupled flow with geomechanics in a poro-elastic medium. Due to its physical nature, the geomechanics problem can cope with a coarser time step compared to the flow problem. This makes the multirate coupling scheme, in which several flow finer time steps are solved within one coarser mechanics time step, a natural candidate in this setting.