Diffusion and Matrix-fracture Interactions during Gas Injection in Fractured Reservoirs

Molecular diffusion can play a significant role in oil recovery during gas injection in fractured reservoirs. Diffusion of gas components from a fracture into the matrix extracts oil components from matrix and delays, to some extent, the gas breakthrough. This in turn increases both sweep and displacement efficiencies. In current simulation models, molecular diffusion is commonly modeled using a classical Fick’s law approach with constant diffusion coefficients. In the classical Fick’s law approach, the dragging effects (off-diagonal diffusion coefficients) are neglected. In addition, the gas-oil diffusion at the fracture-matrix interface is normally modeled by assuming an average composition at the interface which does not have a sound physical basis. In this paper, we present a dual-porosity model in which the generalized Fick’s law is used for molecular diffusion to account for the dragging effects; and gas-oil diffusion at the fracture-matrix interface is modeled based on film theory in which the gas in fracture and oil in the matrix are assumed to be at equilibrium. A novel shape factor is also introduced for gas-oil diffusion based on film theory. Diffusion coefficients are calculated using the Maxwell-Stefan model and are pressure, temperature and composition dependent. A time-dependent transfer function is used for matrix-fracture exchange in which the shape factor is adjusted using a boost factor to differentiate between the transfer rate at early and late times. Field-scale examples are used to demonstrate that the dragging effects (off-diagonal diffusion coefficients) can significantly impact the oil recovery during gas injection in fractured reservoirs. It is also shown that using proper physical models for matrix-fracture interactions (film theory for gas-oil diffusion and transfer function with boost factor) can considerably affect the simulation results as compared to conventional models. We also show that miscibility is not developed in the matrix blocks even at pressures above minimum miscibility pressure (MMP) when molecular diffusion is the main recovery mechanism during gas injection in fractured reservoirs. The work presented in this paper is directly applicable to the study and design of gas injection processes in fractured reservoirs through an improved understanding of the effect of diffusion and matrix-fracture interactions on these processes.