The Solution of the Riemann Problem for a Hyperbolic System Modeling Polymer Flooding with Hysteresis

It is well known that multiphase flow in porous media exhibits hysteresis. This is typically modeled by modifying the saturation dependence of the relative permeabilities. In this paper, a model for hysteretic relative permeabilities is built into the polymer flooding model and the analytical solution to the corresponding Riemann problem is constructed. This produces a nonstrictly hyperbolic system of conservation laws with a history-dependent flux function. Because the polymer model without hysteresis possesses Riemann problem solutions that are not monotonic, the introduction of hysteresis necessarily produces structurally different solutions. We show that hysteresis produces more complicated solutions with more fronts and expansions; and removes some nonuniqueness of solutions