Molecular diffusion is a proven oil recovery mechanism in fractured reservoirs. Neglecting diffusion during the simulation of gas injections can lead to underestimated oil recoveries. This is particularly important in fractured reservoirs with low permeabilities. This paper presents the implementation of a diffusion model in a reservoir simulator. The implementation is verified with discrete fracture and dual-porosity model cases. The adopted diffusion model is based on irreversible thermodynamics. It uses full matrices of diffusion coefficients and chemical potential gradients as the driving force. To evaluate how much diffusion is dominant during fluid flow in fractured reservoirs, a form of the Péclet number is proposed as the ratio of characteristic times of diffusion to gravity drainage for a given reservoir and fluid properties. The incremental oil recovery from gas injection simulation results confirms the flow regime predicted by the Péclet number. This paper also examines the performance of simulations that involve diffusion by using various solution schemes, including explicit, fully implicit, and partially implicit methods. Optimal performance is achieved with the partially implicit method in which diffusion coefficients are updated at each timestep, while driving forces are updated inside Newton iterations. The simulation results also show that constant diffusivities might not provide a good representative for diffusion coefficients during gasflooding. They can cause oil recovery overestimation or underestimation. The authors demonstrate a technique to forgo diffusion calculations in the regions with convection-dominated flow regimes to help reduce computational time of the simulations involving diffusion. The speedup obtained for gas injection cases with a wide range of Péclet numbers is also examined.

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