Consistent Capillary Pressure and Relative Permeability for Mixed-wet Systems in Macroscopic Three-phase Flow Simulation

WAG flooding of an oil reservoir can give rise to large regions of three-phase flow, where the flow parameters, i.e. capillary pressure and relative permeability, are history dependent. This means that three-phase capillary pressure and relative permeability data have to be updated during the flow to account accurately for hysteresis. The idea of this work is to connect a pore-scale model that calculates capillary pressure and relative permeability for given saturations to a three-phase reservoir simulator. This will allow us to calculate the actual saturation paths based on pore-scale physics. The pore-scale model comprises a bundle of cylindrical capillary tubes of different radii and wettability, which are randomly distributed according to the given density functions. Within the bundle the capillary pressure controls the displacement sequence, and for given capillary pressures it is therefore possible to find the corresponding phase saturations in the bundle. However, for using the pore-scale model in the reservoir simulator it is required to obtain capillary pressure and relative permeability from saturation data, rather than the other way around. We hence invert the capillary bundle model iteratively to find the capillary pressures for given saturations. Depending on the required accuracy, these calculations can be time consuming, especially when the behaviour changes between two-phase and three-phase. A capillary bundle is completely accessible, so there will not be any trapped or residual saturations. In principle a more complex network model including residual saturations could be used. Incorporation of the bundle model into the simulator demonstrates the effects of consistent pore-scale based three-phase capillary pressure and relative permeability for different wettability on the continuum, i.e. reservoir scale. This also shows under which conditions pore-scale displacement paths can be reproduced by the macro-scale model.