Streaming potential in heterogeneous networks

Author:
  • YBYves Bernabé
    Yves Bernabé
Publisher website
Google Scholar
Abstract
It is well‐known that when in contact with an electrolyte, the surfaces of minerals like quartz become charged. In porous rocks, this causes coupling of fluid flow and electrical conduction. In this paper, the theory of electrokinetic coupling in a single capillary is first reviewed. The rest of the paper is concerned with the upscaling of the microscopic (i.e., pore scale) equations and parameters into their macroscopic counterparts. Upscaling was explicitly performed here in a large number of arbitrarily heterogeneous, two‐dimensional networks. As a result, the macroscopic equations were established in a new form using C, the macroscopic coupling coefficient, and δk, a dimensionless correction to permeability. In particular, it was shown that Onsager's [1931] reciprocity holds at macroscopic scales and that the scale invariant Helmholtz‐Smoluchowski formula is not always valid. Accordingly, the macroscopic coupling coefficient C may not always be independent of permeability. In the networks considered here, the coupling coefficient appeared to be controlled by Johnson and Schwartz's [1989] weighted average length scale Λ. Another goal of this paper was to examine the spatial and statistical distributions of electrical currents and potential gradients in networks with varying heterogeneity levels. Similar to local fluid fluxes and pressure gradients, local electrical currents and potential gradients become localized in highly heterogeneous networks. The current field can equivalently be described in terms of current loops, and their spatial distribution can be analyzed. It was found that the current loop field becomes increasingly structured as the level of heterogeneity augments. One important consequence of the spatial distribution of currents and current loops is that at high levels of heterogeneity, the possibility exists to generate a magnetic field of significant intensity over wide areas of the networks. It was also observed that the magnitude of the local electric field appears normally distributed at low variance of the pore radii distribution and becomes increasingly non‐Gaussian as the heterogeneity is increased. Owing to the fact that the total current is zero, the local currents have an unusual distribution, i.e., uniform with a high‐end, −1 power, tail.

This publication has 45 references indexed in Scilit: