Advancing Relative Permeability and Capillary Pressure Estimation in Porous Media through Physics-Informed Machine Learning and Reinforcement Learning Techniques

Recent advances in machine learning have opened new possibilities for accurately solving and understanding complex physical phenomena by combining governing equations with data-driven models. Considering these advancements, this study aims to leverage the potential of a physics-informed machine learning, complemented by reinforcement learning, to estimate relative permeability and capillary pressure functions from unsteady-state core-flooding (waterflooding) data. The study covers the solution of an inverse problem using reinforcement learning, aiming to estimate LET model parameters governing the evolution of relative permeability to achieve the best fit with experimental data through a forward problem solution. In the forward problem, the estimated parameters are utilized to determine the water saturation and the trend of capillary pressure. The estimated curves portray the relationship between relative permeability values and saturation, demonstrating their asymptotic progression towards residual and maximum saturation points. Additionally, the estimated capillary pressure trend aligns with the existing literature, validating the accuracy of our approach. The study shows that the proposed approach offers a promising method for estimating petrophysical properties and provides valuable insights into fluid flow behaviour within a porous media.