Dimensional reduction of a fractured medium for a polymer EOR model

Abstract

Dimensional reduction strategy is an effective approach to derive reliable conceptual models to describe flow in fractured porous media. The fracture aperture is several orders of magnitude smaller than the characteristic size (e.g., the length of the fracture) of the physical problem. We identify the aperture to length ratio as the small parameter 𝜖� with the fracture permeability scaled as an exponent of 𝜖�. We consider a non-Newtonian fluid described by the Carreau model type where the viscosity is dependent on the fluid velocity. Using formal asymptotic approach, we derive a catalogue of reduced models at the vanishing limit of 𝜖�. Our derivation provides new models in a hybrid-dimensional setting as well as models which exhibit two-scale behaviour. Several numerical examples confirm the theoretical derivations of the upscaled models. Moreover, we have also studied the sensitivity of the upscaled models when a particular upscaled model is used beyond its range of validity to provide additional insight.