Characterization of pore shapes for pore network models

Simulation of multi-phase flow processes for enhanced oil recovery requires accurate descriptions of the capillary pressures and relative permeabilities as functions of the phase saturations Pore-scale network modelling is useful tool to estimate these flow parameters. Some of the main network model characteristics are the pore and throat conductances and capillary entry pressures. Both parameters strongly depend on the pore and throat geometries. Because the shapes of the real pore cross-sections are generally highly irregular, it is important to use idealized shapes that lead to accurate approximations of the above parameters. The most common approach has been to choose a circle/ (irregular) triangle / square (C-T-S) pore geometry with a shape factor that matches that of the real pore shape. For these shapes, simple correlations between the flow parameters and the shape factor are available. However, it is well known that the parameters for these very regular convex shapes are often inaccurate compared to the real pore shapes. Here, we propose to represent the shapes by the regular, but generally non-convex, n-cornered star shapes. A new n-corner star shape characterization technique has been developed, which takes shape factor and dimensionless hydraulic radius as input parameters. A novel numerical technique has been used to derive the real pore entry pressures, whereas analytical expressions are used for the star shape. A set of 70 individual pores has been extracted from high-resolution 2D images of a Bentheim rock sample. The real shapes have been approximated by C-T-S, as well as by n-corner star shapes. The comparison results between predicted and real shape parameters for the entire set of pores show that the accuracy of the entry radius prediction for both approaches is approximately the same and quite good. The single phase conductance estimation is much better for n-corner star approximation than for C-T-S. Finally, a capillary bundle model has been constructed from the 70 pores to test the predictive capabilities of the characterization approaches in terms of relative permeabilies and capillary pressures. It has been shown that the n-corner star provides a better approximation of the "real shape" capillary pressure curve than C-T-S. The real shape relative permeabilities are in a good agreement with curves predicted by both shape approximations.