Two-phase flow mechanisms in cylindrical heterogeneous-wet capillaries

Pore-scale displacement mechanisms govern the flow patterns in heterogeneous-wet porous media. Existing theoretical models built on the polygonal capillaries fail to capture fluid transport across the entire range of wettability parameters due to the limitations in fluid and wettability distributions, posing challenges for accurate prediction of macroscale flow processes. To address this knowledge gap, a novel model of two-phase flow for cylindrical capillaries featuring heterogeneous-wet state is proposed based on the Mayer-Stowe-Princen theory, taking into account the geometric evolution of displacement interfaces. According to the present model, the piston-like displacements driven by main terminal meniscus with dual curvatures, stepwise and mixed displacements controlled alternately by the main terminal and arc menisci are identified. Sensitivity analyses show that a diminished difference in contact angle facilitates the occurrence of piston-like flow, and reduces the influence of oil-wet proportion on capillary entry pressure. Moreover, stepwise displacements are primarily governed by the main terminal meniscus with a single curvature structure, whereas the upward sweep range of arc meniscus is wider during mixed flow involving both drainage and imbibition mechanisms. For stepwise displacement, as oil-wet proportion increases, the sweep range of the main terminal meniscus in oil-wet region expands, and that of the arc meniscus first increases and then decreases, reaching a maximum at an oil-wet proportion of 50 %. Furthermore, nonlinear flow occurs when arc meniscus is close to the capillary surfaces with strong wettability. Compared with the stepwise displacement, the piston-like flow exhibits stronger drainage resistance and imbibition dynamics due to the combined impacts of two wettabilities on the main terminal meniscus. This theoretical model effectively simulates two-phase flow across the full range of wettability parameters, laying the foundation for precise prediction of macroscale flow patterns.