Two-phase displacement between cement slurry and drilling fluid in wellbore systems is inherently nonlinear, interface-dominated, and strongly affected by geometric confinement, posing substantial challenges to efficient and stable numerical simulation. Conventional CFD approaches rely on mesh discretization and explicit interface tracking, which become computationally demanding and sensitive to grid quality in complex geometries and convection-dominated regimes. To address these limitations, this study develops a unified physics-informed neural network (PINN) framework for directly solving the coupled incompressible Navier–Stokes and Volume of Fluid (VOF) equations governing pressure-driven displacement. The framework is first validated against canonical transient flows and then applied to two-phase displacement in parallel-plate channels, semicircular bends, and a casing–annulus geometry representative of well cementing operations. The predicted velocity, pressure, and volume fraction fields exhibit strong agreement with ANSYS Fluent (2024R1) results, with relative errors generally around 5%, thereby demonstrating physical consistency and numerical stability without mesh generation or pressure–velocity splitting, while also showing favorable computational efficiency for the cases considered. Sensitivity analyses demonstrate that a smoother casing-shoe geometry significantly enhances PINN convergence, while higher Péclet numbers deteriorate training stability by increasing convection-dominated stiffness and optimization difficulty. The results demonstrate that the proposed PINN framework, with its mesh-free and geometrically flexible characteristics, is a promising approach for modeling multiphase displacement in cementing applications.
Wen et al. (Sat,) studied this question.