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 optimize production and minimize costs. However, traditional numerical reservoir simulations are computationally expensive, while innovative data-driven models may not adhere to physical laws. A physics-informed machine learning approach that combines deep neural networks with governing fluid flow equations is proposed to overcome these limitations. This approach is augmented with reinforcement learning to estimate model's parameters that define the variation of relative permeability with water saturation in an inverse problem. Using the estimated parameters and solving a forward problem, the model predicts water saturation and estimate capillary pressure in a core sample during unsteady state water flooding. The proposed model accurately approximates water saturations over time and estimates the trend of capillary pressure. Additionally, a sensitivity analysis is conducted to understand the impact of the estimated parameters on the model predictions.