Numerical simulation of flow in porous media is an important tool in recent applications relevant to sustainable energy transition such as carbon capture and storage (CCS), geothermal energy or subsurface hydrogen extraction .
These simulations of complex physics deal with large geological domains and time scales. Their use is therefore often limited by the computational time required. These limits are essentially due to the injection and production of fluids through the various wells in the domain which undermines the stability of the system and requires very small integration time steps to preserve numerical stability and accuracy. These events however are quite similar from one simulation to another. The objective of this research is then to use deep learning models incorporating the relevant physical equations (« physics informed deep learning ») in order to predict the solution of the partial differential equations characterizing fluid flow in porous media due to well injection and production.
This research results from a collaboration between the Jacques-Louis Lions laboratory at Sorbonne University and the Applied Mathematics Department at IFP Energies nouvelles in Rueil-Malmaison. The PhD candidate will spend an equal amount of time in both laboratories.
