We visit several models of polymer flooding in reservoir simulation. A special common feature shared by the models, i.e., the thermo-dynamics is decoupled from the hydro-dynamics, leads to a scalar conservation law with discontinuous flux. We discuss solution of Riemann problems as the vanishing viscosity limit. In particular, we show by counter examples that there exists infinitely many vanishing viscosity solution as one varies the ratio of the two viscosity parameters. However, adding two monotonicity conditions, all double limits will converge to the same function.