Dependence of Dynamic Electrokinetic-Coupling-Coefficient on the Electric Double Layer Thickness of fluid-filled porous formations

Abstract

Electrokinetic coupling between pore-fluid flow and electric field arising from the electrical double layer (EDL) has many applications in geoscience. In this study, we extended the formulas for the dynamic electrokinetic coupling coefficient (ECC) to arbitrary scaled capillaries. These two ECC formulas for the cylindrical and slit apertures, respectively, were derived without the thin or thick EDL assumption used in previous studies, relating to the normalized radius (the ratio of capillary radius to Debye length). By the identical ECC formulas for streaming current and electroosmosis effects, it is confirmed that Onsager's reciprocity is generally satisfied for arbitrary scaled and shaped apertures. This ECC tends to the results using the thick and the thin EDL assumptions respectively with the decrease and increase of the normalized radius. It is shown that the relative error is less than 10.0% if the normalized radius is less than 0.8 and is larger than 20, respectively. Otherwise, the thick and the thin EDL assumptions are inapplicable. The high-frequency limit phase of this ECC increases from 45° to 90° with the decrease of the normalized radius, rather than that remains at 45° under the thin EDL assumption. The linear approximation for solving the Poisson-Boltzmann equation influences the electric potential in the EDL and the ECC, which increases with the decrease of the normalized radius. If the normalized radius is larger than 7, the error is within 5.0% even though the linear approximation has been mathematically invalid when the salinity is 0.001 mol/L and zeta potential is -150 mV.

Predicting Electrokinetic Coupling and Electrical Conductivity in Fractured Media Using a Fractal Distribution of Tortuous Capillary Fractures

“…However, this extra complexity does not really make the model any more representative of real porous media or affect the key results of the model, e.g., [46]. For a laminar flow, the velocity profile and average velocity (see Figure 2) inside the fracture are, respectively, given by, e.g., [57,80]…”

“…where a is the half aperture and y is the coordinate along the aperture as shown in Figure 2, v(y) (m/s) is the velocity profile given by Equation ( 9) andQ v (y) (C/m 3 ) is the charge distribution in a fracture. Under Debye-Hückel approximation and the fluid of a binary symmetric 1:1 electrolyte, e.g., [51,91],Q v (y) is given by, e.g., [57,92]…”

“…However, microstructure of porous media is normally very complex with tortuous and non-circular pores. Recently, Shi et al (2018) have theoretically studied the dependence of dynamic electrokinetic coupling coefficient on the electrical double layer thickness for a single cylindrical capillary and a single capillary fracture [57]. Then, they directly extended the obtained electrokinetic coupling coefficient from a single capillary to porous media without applying the upscaling technique.…”

Predicting Electrokinetic Coupling and Electrical Conductivity in Fractured Media Using a Bundle of Tortuous Capillary Fractures

“…For a laminar flow, the velocity profile and average velocity (see Fig. 2) inside the fracture are, respectively, given by [e.g., 57,81]…”

“…(9) andQ v (y) (C/m 3 ) is the charge distribution in a fracture. Under Debye-Hückel approximation and the fluid of a binary symmetric 1:1 electrolyte [e.g.,51,92],Q v (y) is given by [e.g.,57,93]…”