Effect of Velocity and Diffusion Functionality on Nonlinear Mass Transfer Mechanisms in Solvent Oil Recovery

Abstract

Literature has indicated that, experimentally, solvent fronts in hybrid solvent recovery processes progress more rapidly than what can be predicted using current approximations and more rapidly than thermal processes alone. Research using finite differences to model the nonlinear advection, diffusion and dispersion (ADD) equation suggests that nonlinear mass transfer effects are important in predicting the rate of solvent advance. Nonlinearities can be ascribed to both diffusion and flow velocity functionality. Earlier work using linear concentration dependent diffusion and log-linear velocity behaviour confirmed the importance of nonlinear effects when compared to linear theory that uses constant diffusion, dispersion and velocity coefficients. The mathematical nature of the nonlinear ADD equation further suggests that the shape of concentration dependent diffusion and flow velocity will affect the shape of the solvent concentration profiles, and influence the rate of propagation of the solvent front. This research focuses on results obtained using finite differences to explore the effects of various diffusion and velocity functionalities that affect the solvent rate propagation using a nonlinear ADD equation. The results obtained from this analysis indicate that these functionalities determine the shape of the solvent concentration profile. The concentration dependent diffusion and velocity functions were chosen according to recent literature which proposes experimentally obtained functions to more accurately model solvent penetration in the media. Preliminary results from this study suggest that the velocity functionality has more influence on the process at both the lab and field scales for the parameters considered in this study. The shapes of the concentration profiles are affected by both diffusion functionality and velocity functionality.