Advances and benefits of fractal models to predict streaming potentials in partially saturated porous media

Abstract

Understanding streaming potential generation in porous media is of high interest for hydrologicaland reservoir studies as it allows to relate water fluxes to measurable electrical potentialdistributions in subsurface geological settings. The evolution of streaming potential stems fromelectrokinetic coupling between water and electrical fluxes due to the presence of an electricaldouble layer at the interface between the mineral and the pore water. Two different approachescan be used to model and interpret the generation of the streaming potential in porous media: theclassical coupling coefficient approach based on the Helmholtz-Smoluchowski equation, and theeffective excess charge density. Recent studies based on both approaches use a mathematical upscalingprocedure that employs the so-called fractal theory. In these studies, the porous medium isrepresented by a bundle of tortuous capillaries characterized by a fractal capillary-size distributionlaw. The electrokinetic coupling between the fluid flow and electric current is obtained byaveraging the processes that take place in a single capillary. In most cases, closed-formexpressions for the electrokinetic parameters are obtained in terms of macroscopic hydraulicvariables like permeability, saturation and porosity. In this presentation we propose a review ofthe existing fractal distribution models that predict the streaming potential in porous media anddiscuss their benefits compared against other published models.