The dependence of electrical resistivity, saturation and saturation exponent on multi-phase flow instability

Multiphase flow channeling in oil reservoirs during water floods reduces oil recovery. Electrical methods may be used to monitor reservoirs and detect the onset of channeling, but the dependence of electrical resistivity on reservoir flow conditions is complex. The present study is directed toward understanding how the parameters of Archie's law, a commonly assumed relationship between electrical resistivity and water saturation in a porous medium, depends on multiphase flow instability leading to flow channeling. In this research a series of 34 flow experiments were conducted in a thin, two-dimensional tank (55cm x 55cm x 3.75cm) packed with 2mm glass beads where mineral oil was displaced by Nigrosine dyed water. The tank was designed to tilt to arbitrary angles, thereby allowing experiments to be conducted for different values of the generalized Bond number, which describes the overall balance between viscous, capillary, and gravity forces affecting flow instability, by varying the water application rate and orientation of the tank. The effective electrical resistivity of the tank was measured continuously during the flow experiments using a National Instruments digital multi-meter (NI PXI-4071 7 1/2 Digit Flex DMM). Concurrently, a light transmission method was used to monitor spatial variations of oil and water saturation in the tank using a digital camera. The saturation images were then used to derive the average tank saturation over time. The resistivity index derived from Archie's law generally decreases as the water saturation increases in the tank and sharp drops are observed when individual fingers of water span the entire tank to create a continuous electrically conductive pathway. The magnitude of this resistivity index drop decreases when the displacement pattern becomes more unstable and disappears under highly unstable flow conditions. Based on the resistivity and saturation data, the saturation exponent in Archie's law was estimated over the course of the experiment for each set of experimental conditions. The saturation exponent increases as the water displaces oil and reaches a constant value after water breakthrough occurs and a stable flow pattern is established. At equilibrium, the saturation exponent increases from 0.65 to 1.94 as the generalized Bond number is decreased to transition between stable and unstable flow conditions. The saturation exponent remains constant at 1.94 when the flow is unstable for generalized Bond numbers less than -0.106.