A Hybrid Model of Reactive Immiscible Displacement

Abstract:

Subsurface processes can be modeled at multiple scales with varying degrees of fidelity. For example, many pore-scale key features of reactive transport might not be properly resolved in Darcy-scale models. Their pore-scale counterparts might be “closer to reality", but are computationally unfeasible when deployed on, e.g., field scale. Hybrid algorithms aim to combine the physical rigor of a pore-scale model with the computational efficiency of its continuum-scale representation. We present a hybrid model of immiscible displacement of one fluid by another, with a chemical reaction occurring in the region of contact between the two. Away from the reactive front, fluid flow in a fracture is described by one-dimensional Darcy’s law. In the vicinity of the reaction front, two-dimensional Stokes equations are used to model fluid flow and solute transport is described with advection-diffusion-reaction equations. The hybrid algorithm couples these two scales by introducing a small overlapping region, in which both models are solved. An iterative procedure is used to ensure the continuity of state variables and their fluxes across the interface between the two models. Results demonstrate significant improvement upon standard continuum-scale formulations.