Modeling capillary pressure using capillary bundles with arbitrary cross-sections obtained from photomicrographs

We describe a model for the distribution of two liquid phases in the void space of porous rock at capillary equilibrium. The model consists of a bundle of capillary tubes of arbitrary cross-sections, which are taken directly from photomicrographs of thin sections. In spite of its simplicity compared to a full 3D model, the proposed model retains some important features of realistic pore space geometry, in particular, curvature and roughness of the pore walls, which play an important role in the mechanism of wettability change.Equilibrium configurations at primary drainage are simulated by the inscribed ball algorithm. An expression for drainage entry pressure is based on the balance of thermodynamic and mechanical energy. For a capillary tube of arbitrary cross-section, the equation reflecting this balance is solved numerically in contrast to analytical solutions published previously for the idealized polygonal shapes.The model is used to compute drainage capillary pressure for a number of chalk sample images, and the results are compared to the experimentally measured mercury injection data. The observed discrepancies are believed to be caused mainly by the unrealistic accessibility of all the capillaries in the capillary bundle model, the resolution limit of the image, and the reduction of the real 3D geometry to 2D. The overestimated interconnectivity of the pores gives the main contribution to the observed discrepancy between the computed and the experimentally measured drainage capillary pressure.A correction is proposed for the modeled capillary pressure curves based on the combined use of the information from the micro-images and the mercury injection data. Theoretically, the connectivity correction is justified by the representation of the porosity space and the invaded space as fractals. The simulated and measured data agree well provided the proposed corrections are accounted for.