Simulation of coupled flow and geomechanics is of rising importance as unconventional subsurface exploration pushes the operational envelope of geological media. However, coupled simulations remain challenging since the different physics and the different mathematical structure of the corresponding equations favor different discretization techniques. Therefore common and established software packages are tailored to either flow or geo-mechanical simulations, while the fluid-mechanical problem is addressed through various coupling schemes.
Coupling schemes are commonly assigned to three categories (e.g. (Settari & Walters, 2001)): Decoupled, iteratively coupled and fully coupled schemes. Stability and accuracy as well as implementation effort increase from decoupled to fully coupled schemes. Despite disadvantages, decoupled and iteratively coupled schemes are preferred in practice because they allow for using established software packages (see e.g. (Pettersen, 2012)).
Here, we focus on iterative coupling and propose a new coupling scheme: Full pressure coupling. In contrast to established iterative schemes we solve the geo-mechanics fully coupled to a single-phase flow problem using global pressure, and iteratively couple the resulting deformation to a multi-phase multi-component flow solver. As most geo-mechanic simulators include fully coupled single-phase flow solvers, this does not require any new software development. The splitting scheme requires solving the pressure field twice. However, since solving the deformation equations and the non-linear flow equations represent the majority of the computational cost, we expect the overhead per iteration step to be small, and justified if the number of iterations can be reduced.
To illustrate the full pressure coupling scheme we present a finite volume Implicit Pressure and Deformation Explicit Masses (ImPDEM) scheme that builds on a finite volume discretization for geo-mechanics and single-phase flow (Jan Martin Nordbotten, 2014b) and a robust finite volume Implicit Pressure Explicit Masses (ImPEM) method for multi-phase multi-component flow (Doster, Keilegavlen, & Nordbotten, 2013). For this time-stepping scheme the coupling is exact and the iterative scheme converges in one iteration, even for nonlinear flow and nonlinear geo-mechanics. The finite volume discretization of stress and strain further enables a seamless integration of geo-mechanical phenomena into existing ImPEM solvers. Advanced transport and thermodynamic solvers hence can be applied without additional modifications. We illustrate our new coupling scheme through numerical examples for test problems related to geological carbon storage.