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We develop a theory for the problem of high pressure air injection into deep reservoirs containing light oil. Under these conditions, the injected fluid (oxygen + inert components) is completely miscible with the oil in the reservoir. Moreover, exothermic reactions between dissolved oxygen and oil are possible. We use Kovals model to account for the miscibility of the components, such that the fractional-flow functions resemble the ones from Buckley-Leverett flow. This allows to decompose the solution of this problem into a series of waves. We then proceed to obtain full analytical solutions in each wave. Of particular interest {is the case where} the combustion wave presents a singularity in its internal wave profile. Evaluation of the variables of the problem at the singular point determines the macroscopic parameters of the wave, i.e., combustion temperature, wave speed and downstream oil fraction. The waves structure was observed previously for reactive immiscible displacement and we describe it here for the first time for reactive miscible displacement of oil. We validate the developed theory using numerical simulations.
Immiscible fluid displacement in porous media is fundamental for many environmental processes, including infiltration of water in soils, groundwater remediation, enhanced recovery of hydrocarbons and carbon geosequestration. Microstructural heterogen
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some interfaces.
We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. In this model, the materia
Fully discrete Galerkin finite element methods are studied for the equations of miscible displacement in porous media with the commonly-used Bear--Scheidegger diffusion-dispersion tensor: $$ D({bf u}) = gamma d_m I + |{bf u}|bigg( alpha_T I + (alpha_
Transport of viscous fluid through porous media is a direct consequence of the pore structure. Here we investigate transport through a specific class of two-dimensional porous geometries, namely those formed by fluid-mechanical erosion. We investigat