Hybrid Integral Transform Solution of a Nonlinear Core-Flooding Model with Capillary Pressure and End Effects
Abstract Oil-water displacement in coreflooding experiments is governed by a nonlinear convection-diffusion equation derived from the extended Buckley-Leverett formulation that accounts for capillary pressure effects. When realistic constitutive relations are combined with nonlinear capillary end-effect boundary conditions, such as those proposed by Chang and Yortsos, the problem becomes significantly more challenging due to the strong coupling between saturation and capillary pressure gradients at the inlet and outlet boundaries. In this work, a hybrid numerical-analytical solution based on the Generalized Integral Transform Technique (GITT) is developed for the one-dimensional immiscible displacement problem, incorporating the nonlinear Chang-Yortsos boundary conditions into the mathematical formulation. The governing partial differential equation is integral transformed with just a simple filter to make the boundary conditions homogeneous and reduced to a coupled system of nonlinear ordinary differential equations in modal space via eigenfunction expansion. Nonlinear diffusion and boundary flux contributions are preserved explicitly through the application of Green´s second identity, thereby maintaining the physical structure of capillary end effects. Validation against a literature benchmark core-flood case demonstrates excellent agreement and rapid spectral convergence. The resulting reduced-order framework provides an accurate and computationally efficient tool for forward simulation of unsteady-state coreflooding experiments.