The Physics Inspired Machine Learning (PIML) is emerging as a viable numerical method to solve partial differential equations (PDEs). Recently, the method has been successfully tested and validated to find solutions to both linear and non-linear PDEs. To our knowledge, no prior studies have examined the PIML method in terms of their reliability and capability to handle reservoir engineering boundary conditions, fractures, source and sink terms. Here we explored the potential of PIML for modelling 2D single phase, incompressible, and steady state fluid flow in porous media.
The main idea of PIML approaches is to encode the underlying physical law (governing equations, boundary, source and sink constraints) into the deep neural network as prior information.
The capability of the PIML method in handling reservoir engineering boundary including no-flow, constant pressure, and mixed reservoir boundary conditions is investigated. The results show that the PIML performs well, giving good results comparable to analytical solution. Further, we examined the potential of PIML approach in handling fluxes (sink and source terms). Our results demonstrate that the PIML fail to provide acceptable prediction for no-flow boundary conditions. However, it provides acceptable predictions for constant pressure boundary conditions.
We also assessed the capability of the PIML method in handling fractures. The results indicate that the PIML can provide accurate predictions for parallel fractures subjected to no-flow boundary. However, in complex fractures scenario its accuracy is limited to constant pressure boundary conditions. We also found that mixed and adaptive activation functions improve the performance of PIML for modeling complex fractures and fluxes.