Numerical Modeling of Diffusion in Fractured Media for Gas-Injection and -Recycling Schemes

Diffusion in fractured reservoirs, unlike in unfractured reservoirs, can affect significantly the efficiency of gas injection in oil reservoirs and recycling in gas/condensate reservoirs. The physical diffusion, similar to gravity, results in the change of the path of the injected gas species from the fractures to the matrix, giving rise to late breakthrough. In this work, we present, for the first time, a consistent model to incorporate physical diffusion of multicomponent mixtures for gas-injection schemes in fractured reservoirs. The multicomponent diffusion flux is related to multicomponent diffusion coefficients, which are dependent on temperature, pressure, and composition. These coefficients are calculated from a model based on irreversible thermodynamics. Current simulation models of fractured reservoirs that include diffusion are based on inconsistent models of gas-to-liquid diffusion at the fracture/matrix interface. We avoid this deficiency by assuming that the gas and liquid phases are in equilibrium at the interface. The concept of crossflow equilibrium (i.e., vertical equilibrium) is invoked in our model to avoid the use of transfer functions. In this work, we use the combined discontinuous Galerkin and mixed methods on 2D structured grids to calculate fluxes accurately and to have low numerical dispersion to study physical diffusion. Four examples are presented. In one of the examples, a field-scale study is performed to investigate gas injection in a fractured reservoir away from miscibility pressure and close to miscibility pressure. Results show a significant effect of diffusion on recovery performance away from miscibility pressure. In another example, recycling in a fractured gas/condensate reservoir is presented to demonstrate that diffusion has a significant effect on condensate recovery.