Streaming potential during drainage and imbibition

The rock pore space in many subsurface settings is saturated with water and one or more immiscible fluid phases. Examples include nonaqueous phase liquids (NAPLs) in contaminated aquifers, supercritical CO₂ during sequestration in deep saline aquifers, the vadose zone, and hydrocarbon reservoirs. Self-potential (SP) and seismoelectric (SE) methods have been proposed to monitor multiphase flow in such settings. However, to properly interpret and model these data requires an understanding of the saturation dependence of the streaming potential. This paper presents a methodology to determine the saturation dependence of the streaming potential coupling coefficient (C) and streaming current charge density (Q_s) in unsteady state drainage and imbibition experiments and applies the method to published experimental data. Unsteady state experiments do not yield representative values of C and Q_s (or other transport properties such as relative permeability and electrical conductivity) at partial saturation (S_w) because S_w within the sample is not uniform. An interpretation method is required to determine the saturation dependence of C and Q_s within a representative elementary volume with uniform saturation. The proposed method makes no assumptions about the pore space geometry. Application of the method to published experimental data from two natural sandstone samples shows that C exhibits hysteresis between drainage and imbibition, can exhibit significant nonmonotonic variations with saturation, is nonzero at the irreducible water saturation, and can exceed the value observed at S_w = 1. Moreover, Q_s increases with decreasing S_w but is not given by 1/S_w as is often assumed. The variation in Q_s with S_w is very similar for a given sample and a given drainage or imbibition process, and the difference between samples is less than the difference between drainage and imbibition. The results presented here can be used to help interpret SP and SE measurements obtained in partially saturated subsurface settings.