The capillary pressure curves from upscaling interfacial and unsaturated flows in porous layers with vertical heterogeneity

Abstract

We provide the capillary pressure curves pc(s¯) as a function of the effective saturation s¯ based on the theoretical framework of upscaling unsaturated flows in vertically heterogeneous porous layers proposed recently (Z. Zheng, Journal of Fluid Mechanics, 950, A17, 2022). Based on the assumption of vertical gravitational-capillary equilibrium, the saturation distribution and profile shape of the invading fluid can be obtained by solving a nonlinear integral-differential equation. The capillary pressure curves pc(s¯) can then be constructed by systematically varying the injection rate. Together with the relative permeability curves k¯rn(s¯) that are already obtained. One can now provide quick estimates on the overall behaviours of interfacial and unsaturated flows in vertically-heterogeneous porous layers.

Keywords

• Flow upscaling
• Interfacial and unsaturated flow
• Wetting and capillary effects
• Porous layer
• Heterogeneity