摘要
We provide the capillary pressure curves p_(c)(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 p_(c)(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.
基金
by the Program for Professor of Special Appointment(Eastern Scholar,No.TP2020009)at Shanghai Institutions of Higher Learning。
