Physics informed neural networks simulation of fingering instabilities arising during immiscible and miscible multiphase flow in oil recovery processes.

Numerical simulation and experimental techniques are the primary methods for solving fluid dynamics problems. However, while numerical simulation approaches are sensitive when meshing a complex structure, experimental methods have difficulty simulating the physical challenges. Therefore, building an affordable model to solve the fluid dynamics problem is very important. Deep learning (DL) approaches have great abilities to handle strong nonlinearity and high dimensionality that attract much attention for solving fluid dynamics problems. In this paper, we used a deep learning-based framework, physics-informed neural networks (PINNs). The main idea of PINN approaches is to encode the underlying physical law (i.e., the partial differential equation) into the neural network as prior information. In the oil recovery process involving the injection of fluids and multiphase flow in porous media, fingering instability is observed if a fluid with low viscosity displaces a high viscosity fluid. This paper provides a deep learning framework to simulate the instability (fingering) phenomenon during secondary and enhanced oil recovery methods. We have considered two models, namely, the first model on immiscible multiphase flow from the secondary oil recovery method, which is analyzed both with and without deliberating mass flow rate. In the second model, instability arising during the enhanced oil recovery method involving miscible displacement of multiphase is examined, focusing on oil recovery using carbonated water injection. We solve the governing nonlinear partial differential equation using PINNs. Furthermore, we have compared results from PINNs with the semi-analytical solution from the literature. The results show that PINNs are very effective in fluid flow problems and deserve further research.