Modeling diffusion and gas–oil mass transfer in fractured reservoirs

Abstract

Diffusion may play a key role in a number of oil recovery processes such as heavy oil and naturally fractured reservoirs. In fractured media, several laboratory experiments and numerical studies demonstrated that CO2 injection can improve recovery. Molecular diffusion, gravity drainage, and oil swelling are the main contributing mechanisms. Proper modeling of diffusion at the reservoir PVT and geological conditions is not a trivial task. The challenge is in computing the diffusion coefficients for the non-ideal multicomponent mixtures in the oil and gas phases, and in physically accurate representation of the diffusion driving forces. One common approach in most numerical models is to use the classical Fick's law which simplifies the multicomponent diffusion fluxes by only considering the main-diffusion (diagonal) terms and neglecting the cross-diffusion (off-diagonal) terms in the diffusion matrix. The diffusion fluxes are assumed independent and the diffusion driving force of each component is proportional to the component self concentration gradient. In this work, we demonstrate analytically and numerically that this simplified approach may not honor the total flux balance and, in some applications, fails to capture the right direction of the diffusion flux. We propose an alternative model based on the generalized Fick's law. The proposed model can be seen equivalent to the Maxwell–Stefan model. The diffusion fluxes take into account the species interactions and the diffusion coefficients are dependent on temperature, pressure, and composition. We also tackle another problem related to cross-phase mass transfer of components in the gas and oil phases. This mechanism may occur in fractured media when fractures saturated with gas get in contact with under-saturated oil in the surrounding matrix. Intra-phase gas (gas-in-gas) and oil (oil-in-oil) diffusions cannot be initiated due to phase discontinuities between the fracture and the rock matrix. Some approaches in the literature that allow for direct gas-to-oil diffusion may not have a sound basis. We propose an accurate and numerically efficient model to describe the gas–oil transfer mechanism. The proposed model, based on irreversible thermodynamics, uses the chemical potential gradient as the driving force. The gas–oil transfer coefficients are functions of the gas and oil diffusion coefficients. In this model, the component fluxes are assumed continuous across the gas–oil contact and the interface fluid is in thermodynamic equilibrium. Several numerical and experimental cases are provided to validate the proposed model.