Fickian Diffusion in Discrete-Fractured Media from Chemical Potential Gradients and Comparison to Experiment

Fickian diffusion can be an important oil recovery mechanism from fractured reservoirs by gas injection, especially when gravitational drainage is inefficient. Without diffusion, injected gas will flow predominantly through the fractures, resulting in early breakthrough and low oil recovery, but compositional gradients between the fractures and the matrix can drive considerable cross-flow. Additionally, this species exchange can lead to favorable phase behavior, such as swelling and viscosity reduction of oil in the matrix. The modeling of Fickian diffusion in fractured reservoirs has been hampered by two deficiencies in existing simulators. The first is the use of the generalized classical Fick's law for multicomponent mixtures, which violates molar balance. The second is the computation of diffusive fluxes across grid edges aligned with phase boundaries. Traditionally, diffusive fluxes are derived from gradients in compositions, computed by finite differencing of compositions in neighboring grid cells. This approach fails when one grid cell contains only gas and the neighboring cell only oil, because the compositional gradients are only defined within a single phase. This problem often occurs in fractured domains when the fractures fill with injected gas while the matrix blocks remain in single-phase oil. We implement an alternative approach, in which gradients in chemical potential are the driving force for Fickian diffusion. Unlike phase compositions, chemical potentials do not require phase identification and the gradient can be computed self-consistently across phase boundaries. Away from phase boundaries the two approaches are equivalent. We demonstrate the strengths of our implementation by simulating experiments in which CO2 is injected in a tall vertical core surrounded by fractures. After injecting CO2 for 22 days, 65% of the oil in place is recovered. However, modeling with a commercial simulator results in only 12% recovery, despite adjusting parameters. We present additional examples at larger scales that further confirm the promising prospects of CO2 injection for enhanced oil recovery in fractured reservoirs and show the equivalence of the composition- and chemical-potential-based formulations in the absence of sharp phase boundaries.