Impact of Concentration-Dependence of Diffusion Coefficient on VAPEX Drainage Rates

Abstract

Abstract The VAPEX analytical model is extended to cover situations when diffusion coefficients are dependent on concentration due to the extreme viscosity reduction with solvent dissolution into bitumen. The new analytical model covers such situations along with the cases in which the diffusion coefficient and viscosity relate to each other under the Stokes-Einstein law. In the process, a new concept of the 'average flow fraction of bitumen' in the flowing mixtures is introduced. The modelled result on overall functionality of the drainage rate of bitumen has confirmed the square-root relationships to most of the key reservoir parameters as the previous theories indicate. However, its dependence to the inverse of kinematic viscosity at the interface is closer to linear rather than square-root correlation with the concentration-dependent diffusion coefficient. The theoretical relationships are confirmed by the correlations of the unified bitumen rates to kinematic viscosity at the interface using the existing VAPEX and SAGD experimental data in the literature. This finding indicates that VAPEX process in heavy oils with lower native viscosity can be more effective than originally recognized. Introduction Dunn et al.(1) developed the theoretical model of the gravity drainage process for bitumen recovery known as VAPEX based on the model of the steam-assisted gravity drainage (SAGD) process by Butler et al.(2) This model assumed that the diffusion coefficients of solvent-bitumen systems are constant similar to the case of thermal diffusivity. Thus, the steady-state profiles of solvent concentration ahead of the solvent-bitumen interface is the smooth exponential decay towards an infinite distance. In reality, the diffusion coefficients of both solvent and bitumen are strongly dependent upon compositions due to the extreme viscosity contrasts between the solutes and solvents. As a result, the observed concentration profiles in diffusion experiments exhibit the abrupt front-end profiles(3). The theoretical endeavour here is to understand the impact of the non-exponential concentration profiles on the VAPEX drainage and bitumen rates. Governing Mechanisms The most fundamental mechanism of the process is the gravity drainage caused by the density difference between the liquid-bitumen phase and the injected vapour phase. The drainage flow of the bitumen phase occurs only from viscosity reduction due to the impact of the injected solvent (or heat in the case of SAGD) of the otherwise semi-solid bitumen. Therefore, how the injected solvent penetrates into the bitumen phase in the reservoir is of primary importance to the process. According to Fick's law, a material balance across a differential distance, dx, in this situation can be expressed as a continuity equation for the change of concentration (volume fraction is chosen), C, with time, t, by using the diffusion coefficient, D: Equations (available in full paper)