Calculation of electroosmotic inflow to hydraulic fractures

A plane flow through a porous medium in the neighborhood of a hydraulic fracture under the action of a potential difference applied between a well (sink) and an external electrode is considered. The problem of calculating the electric field and the induced flow through the porous medium is solved with allowance for the finite electric and hydraulic resistance of the fracture. The problem reduces to a system of singular integral equations for the distribution of the densities of hydraulic and electric sinks along the fracture. This is solved numerically, after which all the parameters of interest can readily be reconstructed. Calculation results illustrating the effect of the fracture resistance on the magnitude and distribution of the electroosmotic flow are given.