When regions of three-phase flow arise in an oil reservoir, each of the flow parameters, i. e. capillary pressures and relative permeabilities, are generally functions of two phase saturations and depend on the wettability state. The idea of this work is to generate consistent pore-scale based three-phase capillary pressures and relative permeabilities. These are then used as input to a 1-D continuum core- or reservoir-scale simulator. The pore-scale model comprises a bundle of cylindrical capillary tubes, which has a distribution of radii and a prescribed wettability state. Contrary to a full pore-network model, the bundle model allows us to obtain the flow functions for the saturations produced at the continuum-scale iteratively. Hence, the complex dependencies of relative permeability and capillary pressure on saturation are directly taken care of. Simulations of gas injection are performed for different initial water and oil saturations, with and without capillary pressures, to demonstrate how the wettability state, incorporated in the pore-scale based flow functions, affects the continuum-scale displacement patterns and saturation profiles. In general, wettability has a major impact on the displacements, even when capillary pressure is suppressed. Moreover, displacement paths produced at the pore-scale and at the continuum-scale models are similar, but they never completely coincide.

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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.@en