Relative permeability and capillary pressure estimation via physics-informed machine learning and reinforcement learning

Accurately predicting multiphase fluid flow in oil and gas reservoirs is crucial to optimizing production and minimizing costs. However, traditional numerical reservoir simulations are computationally expensive, while innovative data-driven models may not adhere to physical laws. Building on established physics-informed machine learning (PIML) formulations, we present an integrated PIML–reinforcement learning (RL) workflow that embeds the governing fluid-flow equations and uses RL to solve the inverse problem of estimating relative-permeability model parameters from average water-saturation measurements. Using the inferred parameters, the forward physics-consistent model predicts saturation dynamics and enables inference of capillary-pressure trends during unsteady-state waterflooding. The proposed model accurately predicts the average water saturation over time and estimates trends in capillary pressure across three laboratory experiments. Additionally, a sensitivity analysis is performed to understand the impact of the estimated parameters on the model predictions.