Imbibition in multiple continuum representations of fractured porous media: Early and late time behaviour

Abstract:

Fractured porous media are notoriously challenging to model but of significant importance for many subsurface applications. In the common modelling approach A fractured geological formation is represented through distinct flow domains, the mobile fractures and the immobile matrix that provides additional storage for the fracture. The rate at which fluids exchange between the domains is represented by a transfer function. For imbibition during two-phase incompressible immiscible flow a simple first-order rate law can be formulated based on the saturation difference between the domains. While this is mathematically convenient it fails to capture the onset of imbibition at early times that is observed in simulations and experiments. Here we present an improved approach that captures the early time behaviour accurately by using semi-analytical self-similarity solutions for capillary driven flow. We also use this concept to predict the transitions from early to late-time-behaviour and construct a new hybrid transfer function. High resolution numerical simulations as well as experimental data are used to validate the results for different wetting and non-wetting phases viscosities and rock types that span a wide range of capillary diffusion coefficient for applications ranging from CO2 storage to oil recovery and beyond.