Streaming potential during drainage and imbibition

Abstract

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 (Qs) 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 Qs (or other transport properties such as relative permeability and electrical conductivity) at partial saturation (Sw) because Sw within the sample is not uniform. An interpretation method is required to determine the saturation dependence of C and Qs 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 Sw = 1. Moreover, Qs increases with decreasing Sw but is not given by 1/Sw as is often assumed. The variation in Qs with Sw 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.

An analytical effective excess charge density model to predict the streaming potential generated by unsaturated flow

“…Recently, Zhang et al [2017] proposed a power law function to model the relative effective excess charge densityQ rel v as a function of effective saturation for two sandstone core samples during drainage and imbibition experiments. This empirical model depends on three parameters p, q and r which are determined by curve fitting to the mean values ofQ rel v (S e ) at each value of water saturation for a given sample and displacement.…”

“…In this section, we compare the proposed model with the effective excess charge models proposed by , Jougnot et al [2012] and Zhang et al [2017] described previously.…”

“…Comparison between the relative effective excess charge density model(Eq. (32)) and the empirical model proposed byZhang et al [2017] for two sandstones: a) Stainton and b) St. Bees, during drainage and imbibition experiments5 Comparison with experimental dataIn the present section, we test the proposed model against available experimental data from the research literature.…”

Transpiration‐ and precipitation‐induced subsurface water flow observed using the self‐potential method

“…where R [m] is the capillary size, f D [−] is the equivalent pore-size distribution function inferred from hydrodynamic parameters (i.e., van Genuchten parameters and permeability k), and v R [m/s] is the mean pore-water velocity for a given capillary radius. This approach is more complex than Equation (10) but better describes SP amplitudes in natural media over a large range of saturations in which b Q v can increase multiple orders of magnitude as saturation decreases (Jougnot et al, 2012(Jougnot et al, , 2015Soldi, Jougnot, & Guarracino, 2019;Zhang, Vinogradov, Leinov, & Jackson, 2017). Given the large variation in saturation observed during the period of data collection in this work, we use Once b Q v S w ð Þ is defined, the streaming-current term of water movement in variable saturated conditions can be written:…”

“…The soil‐specific effective excess charge is then calculated by integrating the effective excess charge of saturated capillaries for given pore‐size distribution: where R [m] is the capillary size, f D [−] is the equivalent pore‐size distribution function inferred from hydrodynamic parameters (i.e., van Genuchten parameters and permeability k ), and v R [m/s] is the mean pore‐water velocity for a given capillary radius. This approach is more complex than Equation but better describes SP amplitudes in natural media over a large range of saturations in which can increase multiple orders of magnitude as saturation decreases (Jougnot et al, , ; Soldi, Jougnot, & Guarracino, ; Zhang, Vinogradov, Leinov, & Jackson, ). Given the large variation in saturation observed during the period of data collection in this work, we use the Jougnot et al () relative permeability flux‐averaging approach in this work (Figure ).…”