oa Experimental Evidence for the Dependence of Archie’s Law on Multiphase Flow Dynamics

Archie’s law is a powerful tool for relating electrical measurements to fluid saturations in applications ranging from oil production to the migration of organic contaminants. However, the formation of channels or fingers during unstable multiphase flow is an issue that leads to preferential flow within the subsurface that is not typically considered in the analysis of electrical data. This study is directed toward understanding how the parameters of Archie’s law depend on multiphase flow instability. Flow experiments were conducted in a thin, two-dimensional tank (55cm x 55cm x 3.75cm) packed with 2 mm glass beads where mineral oil was displaced by Nigrosine dyed water. the light transmission method was used to provide time-lapse images of oil and water saturations in the tank over the course of the experiment while measurements of the bulk electrical resistivity of the tank are simultaneously completed. Different experiments were performed by varying the water application rate and orientation of the tank to control the generalized Bond number, which describes the balance between viscous, capillary, and gravity forces that affect flow instability. the experimental results show that overall the resistivity index gradually decreases as water saturation increases in the tank, but drops sharply as individual capillary fingering fronts reach the outlet to create a high-conductivity pathway that bridges the tank. the magnitude of this drop decreases as the displacement becomes increasingly unstable and disappears for highly unstable flow leading to the generation of many small fingers. At flow equilibrium, the saturation exponent in Archie’s law increases from 0.65 to 1.94 and is linearly dependent on the generalized Bond number. As the flow becomes increasingly unstable, the saturation exponent reaches a constant value of 1.94 for values of the generalized Bond number less than -0.106. these results document a dependence of Archie’s law on multiphase flow dynamics.