The basic goal of scale up procedures is to simulate on coarse grids, with modified equations, multiphase reservoir flow and transport problems defined on fine grids. Scaling up is in general difficult. Difficulties arise both from the highly nonlinear fluid-fluid interactions in the flow of multiphase fluid mixtures and from the complex interactions between heterogeneities and nonlinearities. Our recent results show that several different flow regimes occur, depending on the relative strengths of flow nonlinearity and medium heterogeneity, as well as on the spatial structure of such heterogeneity. In the present study such results are used to investigate the applicability of a simplifying assumption made in several studies in the development of theories for the scale up problem for immiscible (water-oil) displacement. Our results indicate that such assumption is not appropriate to describe a typical mixing regime encountered in petroleum reservoirs, namely, the nonlinear unstable regime, in which nonlinearities in the governing equations dominate the fluid mixing process.