Physics-inspired pseudo-transient method and its application in modelling focused fluid flow with geological complexity

Abstract

SUMMARY Two-phase flow equations that couple solid deformation and fluid migration have opened new research trends in geodynamic simulations and modelling of subsurface engineering. Physical non-linearity of fluid-rock systems and strong coupling between flow and deformation in such equations lead to interesting predictions such as spontaneous formation of focused fluid flow in ductile/plastic rocks. However, numerical implementation of two-phase flow equations and their application to realistic geological environments with complex geometries and multiple stratigraphic layers is challenging. This study documents an efficient pseudo-transient solver for two-phase flow equations and describes the numerical theory and physical rationale. We provide a simple explanation for all steps involved in the development of a pseudo-transient numerical scheme for various types of equations. Two different constitutive models are used in our formulations: a bilinear viscous model with decompaction weakening and a viscoplastic model that allows decompaction weakening at positive effective pressures. The resulting numerical models are used to study fluid leakage from high porosity reservoirs into less porous overlying rocks. The interplay between time-dependent rock deformation and the buoyancy of ascending fluids leads to the formation of localized channels. The role of material parameters, reservoir topology, geological heterogeneity and porosity is investigated. Our results show that material parameters control the propagation speed of channels while the geometry of the reservoir controls their locations. Geological layers present in the overburden do not stop the propagation of the localized channels but rather modify their width, permeability, and growth speed.