Streaming potential coupling coefficient of quartz glass bead packs: Dependence on grain diameter, pore size, and pore throat radius

Abstract

The Helmholtz-Smoluchowski (HS) equation is commonly used to relate the streaming potential coupling coefficient of rocks to their zeta potential, pore fluid dielectric permittivity, conductivity, and viscosity despite it being known for almost [Formula: see text] that it does not work well for porous media. One of the problems is that the HS equation contains no implicit dependence on grain size, pore size, or pore throat size. Another has been the lack of high-quality data relating the streaming potential coupling coefficient to rock microstructural parameters. In this, predominantly experimental work, we have measured the streaming potential coupling coefficient for 12 sizes of quartz glass beads and two fluid salinities. A comparison of the new data and the existing data with the conventional HS equation and Revil’s grain size-dependent HS model shows the grain size-dependent model to be far superior in describing the data. Recognizing their utility in reservoir characterization, we have developed new equations that describe how the streaming potential coupling coefficient varies with pore diameter and pore throat diameter. We have compared experimental determinations as a function of pore throat diameter with these new relationships and found them to work very well if the ratio of the mean pore diameter to the pore throat diameter is 1.662, which is valid for random arrangement of monodisperse spheres. The zeta potential has also been calculated from the grain size-dependent HS equations and are found to be approximately constant and in agreement with the theoretically predicted values. The equations presented in this paper allow the streaming potential coupling coefficient of a reservoir rock to be calculated as a function of grain size, pore size, and pore throat size.