Vertically integrated models for coupled two phase flow and geomechanics in porous media
Models of reduced dimensionality have been found to be particularly attractive in simulating the fate of injected CO2 in supercritical state in the context of carbon capture and storage. This is motivated by the confluence of three aspects: the strong buoyant segregation of the lighter CO2 phase above water, the relatively long time scales associated with storage, and finally the large aspect ratios that characterize the geometry of typical storage aquifers. However, to date, these models have been confined to considering only the flow problem, as the coupling between reduced dimensionality models for flow and models for geomechanical response has previously not been developed. Herein, we develop a fully coupled, reduced dimension, model for multiphase flow and geomechanics. It is characterized by the aquifer(s) being of lower dimension(s) while the surrounding overburden and underburden being of full dimension. The model allows for general constitutive functions for fluid flow (relative permeability and capillary pressure) and uses the standard Biot coupling between the flow and mechanical equations. The coupled model retains all the simplicities of reduced dimensional models for flow, including less stiff nonlinear systems of equations (since the upscaled constitutive functions are closer to linear) longer time steps (since the high grid resolution in the vertical direction can be avoided) and less degrees of freedom. We illustrate the applicability of the new coupled model through both a validation study and a practical computational example.