Physics-informed neural network (PINNs) for convection equations in polymer flooding reservoirs

This paper realizes the application of the physics-informed neural network (PINN) in the polymer flooding reservoir model, achieving high-precision calculations of the water saturation and polymer concentration distributions in a one-dimensional polymer flooding channel. The paper investigates the impacts of different PINN network structures, the forms of the governing equations used, and the strength of the artificial viscosity added to the governing equations on the computational performance of PINN, especially the computational accuracy. Three numerical examples are implemented in this paper, with the high-fidelity numerical solution serving as the benchmark. The results show that, when the total number of grid parameters is similar, PINN-1, which estimates both the water saturation and the polymer concentration using a single network, exhibits significantly better computational performance than PINN-2, which estimates the water saturation and the polymer concentration using two separate networks. The simplification of the governing equation for the polymer concentration can improve the training accuracy of PINN. The addition of artificial viscosity can enhance the computational accuracy of PINN, and the improvement effect first increases and then decreases as the artificial viscosity coefficient increases. The research of this paper provides a reference for the subsequent development of high-accuracy PINN proxy models for reservoir engineering.