Volume Averaged Equations for Mass Transport and Reaction for In-Situ Combustion

In-situ combustion (ISC) is an oil recovery technique where many phenomena can take place simultaneously such as: chemical reactions, phase change, heat transfer, mass transport, thermodynamic equilibrium, and so on. Each one of these phenomena may have important contributions over the ISC behavior at any scale of interest as lab-scale, inter-wells or reservoir-scale. In this work, a mass transport study is presented. Firstly, the appropriate phase and interface governing equations at pore-scale are set up. Later, the volume averaged equations valid at macroscale are rigorously derived using the volume averaging method (VAM). The theoretical analysis is general and applies for typical oil-water-gas-rock systems found in petroleum reservoirs, and for any number of chemical species distributed in the phases. The model also allows the existence of several heterogeneous and homogeneous chemical reactions. From this general point of view, the volume averaged equations governing species and phase mass transport at macroscale, along its closure scheme to predict the effective transport parameters, are presented. We have clearly identified the length scale constraints and assumptions that support our derivations. In future works, we shall expand the range of applicability of the model by relaxing some of these assumptions. To demonstrate the applicability of the average models, we numerically predicted the longitudinal mass dispersion of oxygen for passive and reactive mass transport problems at lab-scale. The general trends of theoretical results are in concordance with previous works.