A fractal model for effective excess charge density in variably saturated fractured rocks

Estimating hydraulic properties and monitoring water flow in fractured rocks using self-potential observations essentially relies on our ability to model streaming potential. One of the most promising approaches for modeling electrokinetic couplings is based macroscopic quantification excess charge which effectively transported by pore flow. In this study, we derive a fractal predict effective density fully partially saturated media. Fractures are conceptualized as parallel plates with pattern described Sierpinski carpet. From calculation single fracture flux averaging upscaling procedure, obtain closed-form expressions density. This new analytical explicitly depends ionic concentration, interface properties, saturation, porosity permeability. Model predictions under conditions compared published data measured laboratory during fracturing. The development also shows independence from shapes: when expressed terms hydrological parameters, one can find an expression identical recently models sedimentary porous media capillary tubes. These results extend validity existing highlight importance parameters accurate couplings.