A Relaxation Method for the Simulation of Possibly Non-hyperbolic Polymer Flooding Models with Inaccessible Pore Volume Effect

Polymer flooding models used in the simulation of enhanced oil recovery of reservoirs commonly involve a system of conservation laws that may be ill-posed, especially when an inaccessible pore volume (IPV) empirical law is considered. Depending on the IPV law, the flow model is either weakly hyperbolic with resonance or non-hyperbolic with complex eigenvalues. In this paper, we propose a Suliciu-type relaxation, which unconditionally ensures hyperbolicity for any IPV law. This approximation gives rise to a new numerical scheme, which is compared with the classical upwind scheme and the exact solution whenever possible.