Integral Transforms Solution of Immiscible Two-Phase Flow in Porous Media with Capillary Pressure Effects

Waterflooding is a key secondary recovery method in oil production, enhancing reservoir pressure and increasing extraction efficiency. Laboratory models, such as coreflood ex-periments, provide essential data on multiphase flow dynamics and reservoir properties, crucial for optimizing recovery techniques. Traditional analytical solutions for two-phase flow in porous media often neglect capillary pressure, limiting their accuracy in representing realistic scenarios. This study employs the Generalized Integral Transform Technique (GITT) to address nonlinear two-phase flow problems in heterogeneous porous media.The proposed solution considers the classical boundary condition, where maximum water saturation is assumed at the injection boundary. The Kirchhoff transformation is utilized to rewrite the governing equations, enabling a computationally more efficient GITT implementation. Results include the convergence analysis of the transformed and reconstructed solutions, verification against a numerical approximate solution, and an evaluation of low-order approximations, highlighting the method’s accuracy, computational efficiency, and potential applicability in inverse modeling scenarios.