A Priori Error Estimates for a Discretized Multirate Undrained Split Poro-Elastic System

ABSTRACT: Recently, the coupling between reservoir flow and geomechanics received more importance and attention, as more unconventional resources are being extracted and utilized worldwide. To solve the underlying coupled problem, several sequential coupling schemes were proposed and analyzed. In such schemes, the flow and mechanics problems are solved separately (decoupled), and a coupling iteration is imposed between the two to ensure convergence in every time step. Due to the different time-scales of the two sequentially coupled problems, the flow problem can assume a finer time step compared to the mechanics problem resulting in what is known as the multirate scheme (Almani et al., 2016). In this work, we derive a priori error estimates for the multirate undrained split iterative coupling scheme. This scheme is a generalization of the well-known undrained split scheme (Kumar et al., 2016; Almani et al., 2020) in which the flow problem takes multiple fine time steps within one coarse mechanics time step. To the best of our knowledge, this is the first time in literature a priori error estimates are derived for the multirate undrained split iterative coupling scheme in poro-elastic media.