A single-phase diffusion model for gas injection in tight oil reservoirs

This paper presents a mechanistic simulation study of one-dimensional multicomponent diffusion when the miscible injectant diffuses into a tight porous medium through the fracture/matrix interface with constant pore volume and temperature. The numerical implementation of diffusion based on the dusty gas model uses the fugacity gradient for each component in the mixture as the driving force to the diffusive flux. The Peng-Robinson equation of state is used to model the non-ideal interactions among components in the miscible diffusive process. Phase stability analysis by minimization of the Helmholtz free energy is performed for each grid block at every time step to ensure that mixtures are single-phase fluids throughout the simulation. The main novelty of this paper lies in the diffusion model and its theoretical analysis, in which the fluid non-ideality affects the multicomponent diffusion through two pathways: the fugacity coefficients and the volume change on mixing that causes local pressures to change under ultra-low permeability in tight porous media. Previous studies based on the Maxwell-Stefan model did not consider the latter pathway, while others based on Fick's law are even more simplistic by not considering the non-ideal chemical potential. Analysis in this research showed that the Maxwell-Stefan model was inconsistent with its own assumption of no pressure gradient when non-ideal mixing was considered for tight reservoirs. The dusty gas model does not have this issue because it allows for pressure gradients to drive mass transfer by Knudsen diffusion. The non-ideal interaction of components should be properly characterized and utilized to enhance the early-time flux through the fracture/matrix interface in miscible gas injection into a tight reservoir. Case studies show that the volume change on mixing may substantially increase local pressures and the rate of mass transfer in tight reservoirs. Also, the fugacity coefficients of oil components at infinite dilution in the solvent had a major influence on the rate of diffusion. These two factors highlight the importance of properly characterizing reservoir fluids through an equation of state.