Impact of model error on the measurement of flow properties needed to describe flow through porous media

Indirect methods are commonly employed to determine the fundamental flow properties needed to describe flow through porous media. Consequently, if one or more of the postulates underlying the mathematical description of such indirect methods is invalid, significant model error can be introduced into the measured value of the flow property. In particular, this study shows that effective mobility curves that include the effect of viscous coupling between fluid phases differ significantly from those that exclude such coupling. Moreover, it is shown that the conventional effective mobilities that pertain to steady-state, cocurrent flow, steady-state, countercurrent flow and pure countercurrent imbibition differ significantly. Thus, it appears that traditional effective mobilities are not true parameters: rather, they are infinitely nonunique. In addition, it is shown that. while neglect of hydrodynamic forces introduces a small amount of model error into the pressure difference curve for cocurrent flow in unconsolidated porous media, such neglect introduces a large amount of model error into the pressure difference curve for countercurrent flow in such porous media. Moreover, such neglect makes it difficult to explain why the pressure gradients that pertain to steady-state, countercurrent flow are opposite in sign. It is shown also that improper handling of the inlet boundary condition can introduce significant model error into the analysis. This is because, if a short core is used with one of the unsteady-state methods for determining effective mobility, it may take many pore volumes of injection before the inlet saturation rises to its maximal value, which is in contradiction with the usual assumption that the inlet saturation rises immediately to its maximal value. Finally, it is pointed out that, because of differences in flow regime and scale, the effective mobilities measured in the laboratory may not be appropriate for inclusion in the data base for a reservoir-scale simulation.