Numerous applications of subsurface engineering involve injection and extraction of fluids. Examples include geothermal energy extraction, nuclear waste storage, carbon sequestration, petroleum engineering applications, and energy storage. These anthropogenic activities involve a complex set of processes involving flow, thermal, chemical reactions, and mechanical effects all possibly coupled to each other. These complex sets of processes interact with the complex geology that involves ubiquitous fractures and faults. The network of fractures form the primary conduit of flow and transport and furthermore, act as the most vulnerable regions for mechanical instability. The interaction of processes and the complex geometry of fractures brings computational and mathematical challenges in the simulation of these processes. The fractured medium is generally anisotropic, heterogeneous, and has substantially discontinuous material properties spanning several orders of magnitude.
Our objective is to study coupling of flow and geomechanics in a fractured porous medium setting. We present a mixed dimensional model for a fractured poro-elasic medium. The fracture is a lower dimensional surface embedded in a bulk poro-elastic matrix. The flow equation on the fracture is a Darcy type model that follows the cubic law for permeability. The bulk poro-elasticity is governed by fully dynamic Biot equations. The resulting model is a mixed dimensional type where the fracture flow on a surface is coupled to a bulk flow and geomechanics model.
There are two directions in which our work contributes to. The first is in extending Biot equations to include fracture flow model and complex friction and contact mechanics. The second is in considering different time schemes for the Multiphysics modelling. We consider finer time steps for the flow and coarser time steps for the mechanics. We provide a rigorous mathematical foundation in both directions.