Velocity Enhancement Models for Polymer Flooding in Reservoir Simulation

Polymer flooding is a well-known technique used in EOR. In order to accurately predict oil recovery, a velocity enhancement effect for the polymer molecules, also known as hydrodynamic acceleration, has to be included in the governing equations. The traditional model of a constant velocity enhancement factor, widely used in commercial simulators, leads to an ill-posed problem. As a consequence, simulations may produce unphysical solutions, showing an unlimited accumulation of polymer at the propagation front. Therefore, alternative models have been derived in order to formulate a well-posed problem. In this paper, these models are re-examined. Using mathematical theory of hyperbolic laws, an analytical solution is computed for the velocity enhancement model proposed by Bartelds et al. (G.A. Bartelds, J. Bruining, and J. Molenaar. The modeling of velocity enhancement in polymer flooding. Transport in Porous Media, 26(1):75–88, 1997). A property of this solution is that the polymer concentration decreases as polymer flows through the porous medium and no accumulation effect occurs. The polymer front travels faster than the case where no enhancement model is used, but a constraint on a parameter, needed to ensure well-posedness of the problem, limits the magnitude of the polymer acceleration. Hence, Hilden et al. (S.T. Hilden, H.M. Nilsen, and X. Raynaud. Study of the well-posedness of models for the inaccessible pore volume in polymer flooding. Transport in Porous Media, 114(1):65–86, 2016) proposed an extended model in order to overcome this constraint. However, it is shown in this paper that the model of Hilden results in a loss of hyperbolicity of the system of equations and may lead again to an unphysical accumulation of polymer at the propagation front. As many simulators still employ the ill-posed traditional model because of the uncertainty of the outcomes of alternative approaches, this analysis will hopefully help to understand the consequences of velocity enhancement modeling on the analytical and numerical solutions of polymer flooding.