An efficient reduced order model for nonlinear transient porous media flow with time-varying injection rates

An intrusive Reduced Order Model (ROM) is developed for nonlinear porous media flow problems with transient and time-discontinuous fluid injection rates. The proposed ROM is significantly more computationally efficient than the Full Order Model (FOM). The training regime is generated using the FOM with constant injection rates during the offline stage. The trained ROM exhibits high accuracy for complex pumping schedules (rate vs time) simulated online. The proposed ROM uses the combination of Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method (POD-DEIM), which is compared with the classical POD-Galerkin. The use of an approximated column-reduced Jacobian is shown to be vital to achieving a substantial speedup of ROM vs FOM run-times. An analysis of the trade-off between accuracy and run-time is conducted for ROMs of different sizes and hyper-parameters. The impact of the training regime on the performance of the presented ROM is assessed. The performance of the ROM is studied in the context of a two-dimensional analysis of time-varying injection into a two-well system in a layered porous media reservoir. The accuracy and efficiency of POD-DEIM motivate its potential use as a surrogate model in the real-time control and monitoring of fluid injection processes.