EVALUATION OF A NON-INTERACTIVE BUNDLE-OF-TUBES MODEL FOR CALCULATION OF UNSTEADY-STATE RELATIVE PERMEABILITIES WITH LABORATORY MEASUREMENTS

Several interactive and non-interactive bundle-of-tubes models have been proposed to analyze immiscible displacements in porous media. However, evaluations of these models on whether they can quantitatively predict multiphase flows are lacking. The purpose of this work is to present development and evaluation of a constant-rate non-interactive bundle-of-tubes model. Tubes were constructed using pore size distribution data from mercury injection, and tortuosities of the tubes were varied to match the permeabilities of tested neutrally wet sandstone core samples. Evaluation of the model shows that tortuosity affected rates or pressures of a displacement through its control over the permeability. Tortuosity, however, does not appear to affect relative permeability. Changing pressures in constant-pressure flows and changing rates in constant-rate flows led to largely identical unsteady-state relative permeability curves, despite some small differences that were observed between constant-pressure and constant-rate flows. As we compare unsteady-state relative permeabilities from our model to those from experiments, an excellent match was found for oil's relative permeabilities. The match for water's relative permeabilities, however, was poor. This study shows that improvement in the relative permeability of the injected fluid is needed.