We investigate the relationship between apparent electrical resistivity and water saturation during unstable multiphase flow. We conducted experiments in a thin, two-dimensional tank packed with glass beads, where Nigrosine dyed water was injected uniformly along one edge to displace mineral oil. The resulting patterns of fluid saturation in the tank were captured on video using the light transmission method, while the apparent resistivity of the tank was continuously measured. 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. We observed the resistivity index to gradually decrease as water saturation increases in the tank, but sharp drops occurred as individual fingers bridged the tank. The magnitude of this effect decreased as the displacement became increasingly unstable until a smooth transition occurred for highly unstable flows. By analyzing the dynamic data using Archie’s law, we found that the apparent saturation exponent increases linearly between approximately 1 and 2 as a function of generalized Bond number, after which it remained constant for unstable flows with a generalized Bond number less than ？0.106. 1. Introduction Multiphase fluid flow in porous media is an important problem for applications including petroleum production [1–3], migration of nonaqueous phase liquids (NAPLs) in soils and aquifers [4–6], and CO2 sequestration [7]. Viscous, capillary and gravity forces interact in immiscible two phase flow systems to produce stable or unstable flow regimes [8–11]. In a stable flow regime the displacement of one fluid for another will occur along a stable front. In unstable flow regimes, fingering can occur along the displacement front. As a result, the invading fluid phase can bypass significant amounts of the original fluid phase, leaving it in place in the medium. Electrical resistivity measurements are commonly used to investigate fluid saturations in multiphase flow systems [12–16]. The resistivity index provides an expression of resistivity for multiphase flow systems that is directly related to the degree of water saturation of the medium, , through Archie’s law [17]. When mineral surface conductivity is insignificant, the resistivity index is equal to the ratio of the resistivity of the sample ( ) measured at saturation to the resistivity of the sample measured at 100% water saturation ( ) (Equation (1)). The saturation exponent, , is
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