Streaming Potential Dependence on Water Saturation during Drainage and Imbibition

Friday, 19 December 2014
Jiazuo Zhang1, Jan Vinogradov2 and Matthew Jackson1, (1)Imperial College London, London, United Kingdom, (2)Imperial College London, London, SW7, United Kingdom
Vinogradov and Jackson [2011] reported measurements of the streaming potential during drainage and imbibition in two sandstone plugs and reported effective values of the streaming potential coupling coefficient (C) across plugs with non-uniform saturation (Sw). The aim of this study is to determine the true value of C as a function of Sw.

We determine the relative permeability (kr), resistivity index (I) and relative coupling coefficient (Cr = C(Sw)/C(Sw=1)) using numerical simulation and optimization to minimize the difference between observed and simulated values. The relative streaming charge transported by the flow of water

Qrw(Sw)=Qw(Sw)/Qw(Sw=1)=Cr(Sw)/I(Sw)Kr(Sw) (1)

is constrained to vary monotonically during drainage and imbibition.

We obtain 160 and 320 solutions for the saturation dependence of Cr during drainage and imbibition respectively, which yield a similar quality of match. We find that Cr (i) exhibits hysteresis between drainage and imbibition, (ii) can vary non-monotonically with saturation, (iii) can be non-zero at the irreducible water saturation, (iv) can exceed the value observed at Sw=1, and (v) varies over a wide range. However, the corresponding variation in Qrw is relatively narrow. A reasonable model for Qrw is Qrw(Sw)=a[(Sw-Swr)/(1-Snwr-Swr)]^b+c (2)

where a, b and c are determined from experimental data (a+c=1) and Swr, Snwr are the residual phase saturations after drainage and imbibition. Values for a, b and c obtained here are similar for both rock samples for a given displacement, but differ significantly between drainage and imbibition. The saturation dependence of Qrw is not given by 1/Sw as suggested in previous studies and Cr can exhibit complex, non-monotonic behaviour, depending upon the physically meaningful (monotonic) saturation dependence of the other parameters in (1). The saturation dependence of the streaming potential is best determined by fitting models for krw, I  and Qrw to experimental data.

Vinogradov, J. and Jackson, M.D. (2011), Geophys. Res. Lett. 38, L01301, doi:10.1029/2010GL045726