International Journal of Science, Engineering and TechnologyAuthors: Bitla Saritha, Assistant Professor
Abstract: This paper presents a rigorous mathematical analysis of three-phase (oil-water-gas) flow in deformable porous media. Using a novel synthetic dataset generated from high-resolution pore network reconstructions, we derive and validate a set of governing equations that respect conservation laws, interfacial jump conditions, and thermodynamic equilibrium. The proposed analytical framework eliminates the need for empirical closure approximations by introducing a hysteresis-free capillary pressure model and a relative permeability tensor that accounts for flow direction anisotropy. Numerical simulations based on the finite volume method show that our approach reduces phase misplacement error by 18% compared to existing models. The dataset, which includes porosity fields (0.12–0.38), permeability tensors (10–800 mD), and fluid properties (viscosity ratios up to 1:100), is made available for benchmarking. Our findings demonstrate that mathematical consistency between the hyperbolic saturation transport equation and elliptic pressure equation ensures stability even for adverse mobility ratios. This work provides a foundation for developing next-generation reservoir simulators with verified accuracy.
DOI: http://doi.org/10.5281/zenodo.20584343
