Pore-Scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. I. Cusp Formation and Collapse

We present a pore-scale network model of twoand three-phase flow in disordered porous media. The model reads three-dimensional pore networks representing the pore space in different porous materials. It simulates wide range of twoand three-phase pore-scale displacements in porous media with mixed-wet wettability. The networks are composed of pores and throats with circular and angular cross sections. The model allows the presence of multiple phases in each angular pore. It uses Helmholtz free energy balance and Mayer–Stowe–Princen (MSP) method to compute threshold capillary pressures for twoand three-phase displacements (fluid configuration changes) based on pore wettability, pore geometry, interfacial tension, and initial pore fluid occupancy. In particular, it generates thermodynamically consistent threshold capillary pressures for wetting and spreading fluid layers resulting from different displacement events. Threshold capillary pressure equations are presented for various possible fluid configuration changes. By solving the equations for the most favorable displacements, we show how threshold capillary pressures and final fluid configurations may vary with wettability, shape factor, and the maximum capillary pressure reached during preceding displacement processes. A new cusp pore fluid configuration is introduced to handle the connectivity of the intermediate wetting phase at low saturations and to improvemodel’s predictive capabilities. Based on energy balance and geometric equations, we show that, for instance, a gas-to-oil piston-like displacement in an angular pore can result in a pore fluid configuration with no oil, with oil layers, or with oil cusps. Oil layers can then collapse to form cusps. Cusps can shrink and disappear leaving no oil behind. Different displacement mechanisms for layer and cusp formation and collapse based on the MSP analysis are implemented in the model. We introduce four different layer collapse rules. A selected collapse rule may generate different corner configuration depending on fluid occupancies of the neighboring elements and capillary pressures. A new methodology based on the MSP method is introduced to handle newly created gas/water interfaces that eliminates inconsistencies in relation between capillary pressures and pore fluid occupancies.Minimization of Helmholtz free energy for each relevant displacement enables the model to accurately B Arsalan Zolfaghari [email protected]; [email protected] 1 Dept. 3295, 1000 E. University Avenue, Laramie, WY 82071, USA