Streaming Potential Dependence on Water Saturation during Drainage and Imbibition

Abstract:

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 (S_w). The aim of this study is to determine the true value of C as a function of S_w.

We determine the relative permeability (k_r), resistivity index (I) and relative coupling coefficient (C_r = C(S_w)/C(S_w=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

Q_rw(S_w)=Q_w(S_w)/Q_w(S_w=1)=C_r(S_w)/I(S_w)K_r(_Sw) (1)

is constrained to vary monotonically during drainage and imbibition.

We obtain 160 and 320 solutions for the saturation dependence of C_r during drainage and imbibition respectively, which yield a similar quality of match. We find that C_r (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 S_w=1, and (v) varies over a wide range. However, the corresponding variation in Q_rw is relatively narrow. A reasonable model for Q_rw is Q_rw(S_w)=a[(S_w-S_wr)/(1-S_nwr-S_wr)]^b+c (2)

where a, b and c are determined from experimental data (a+c=1) and S_wr, S_nwr 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 Q_rw is not given by 1/S_w as suggested in previous studies and C_r 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 k_rw, I  and Q_rw to experimental data.

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