In previous research regarding the numerical simulation of a single phase miscible displacement, a numerical procedure which does not exhibit serious grid effects and is highly compatible with nine point finite difference models has been developed. To determine if this procedure could successfully deal with grid effects in general reservoir simulators, this numerical procedure has been implemented in a simplified thermal recovery model. In the initial implementation of this procedure in a complex setting, multiple phase mass transfer between the computational molecules associated with the discretization procedure utilized the well known concepts of fractional flow and total Darcy velocity. The resulting numerical model exhibits unrealistic phenomena, which is unexpected in light of the realistic simulations earlier obtained for the model problem. By changing the model of multiple phase mass transfer, these physically unrealistic effects are eliminated. The new model uses the total molar flux instead of the total Darcy velocity. The fractional flows are defined in a fashion compatible with the total molar flux.