Abstract
Summary The present study adopts a two-phase formulation for oil and water in porous media, augmented with terms that capture the physics of emulsion transport and retention. Following the framework proposed by ( Ding et al., 2022 ), the flow is governed by mass conservation and Darcy’s law with a permeability reduction factor linked to trapped droplets. In the current work, these governing equations are embedded into a physics-informed neural network (PINN) framework, allowing direct enforcement of conservation laws and permeability reduction effects within the training loss function. This strategy enables mesh-free simulation of emulsion flooding, making it possible to analyze pressure buildup and saturation profiles without relying on conventional grid-based solvers. The PINN framework is constructed to approximate the coupled system of pressure, saturation, and emulsion transport by directly embedding the governing equations into the loss function. The PINN reproduces expected emulsion effects: (i) mobility control via permeability reduction yields a slower, more diffuse S_w -front vs. waterflood; (ii) pressure build-up near the injector increases due to pore plugging; (iii) sweep improvement at breakthrough (1D surrogate: delayed water arrival). Errors vs. a fine-grid FD baseline are small in pressure (≤1%) and acceptable in saturation except in a narrow zone around the front.