A multi-timestep Dirichlet-Neumann domain decomposition method applied to the polymer injection in porous media

The study of polymer flooding is of utmost relevance due to the diversity of applications. This paper proposes an innovative mathematical and computational model for polymer flooding that efficiently couples the process in the near-well region and the reservoir. For the mathematical model, in addition to the single-phase flow and transport equations, we postulate closure relationships for the adsorption isotherms, mechanical retention kinetics, and non-Newtonian pseudoplastic behavior. For the computational model, we propose a space-time domain decomposition method based on a predictor-corrector strategy. The resulting system of equations is discretized by the finite element method and linearized by the Newton-Raphson method. Moreover, we apply a consistent flux method to obtain the flow at the boundaries and quantify the injectivity ratio. Then, we validate the accuracy of the proposed method by comparing the discrete solutions with analytical and high-fidelity solutions. We also discuss the loss of injectivity due to the non-Newtonian behavior, mechanical retention, and formation damage at 2D and 3D domains that replicate a five-spot injection pattern. The numerical simulations show that the proposed computational model accurately captures the solutions with low computational costs in several scenarios for polymer injection in porous media.