Electrokinetic coupling in single phase flow in periodically changed capillary with a very small throat size

A new capillary model is proposed to simulate fluid flow through tight formations considering electrokinetic coupling effects at the pore scale. The capillary is constructed by using trigonometric functions to mimic pore and throat structures of porous media. The coupled Navier–Stokes equation, Poisson equation and Planck–Nernst equation are solved simultaneously using finite element method to obtain the velocity profile, the distribution of electric potential and the concentration of ions in the model. The numerical results are then compared with that of the model which does not consider the electrokinetic coupling effects. The results show that the electric charges on the capillary wall can strongly affect the distribution of pressure, especially at the locations of throats, and we also give our explanation to account for this new observation. Besides, the coupling of electrical potential field and flow field can increase the resistance of fluid flow through the capillary and therefore decrease the total flow rate. Finally, we investigate the relationship between flow rate and pressure gradient under different conditions considering the electrokinetic coupling effects, and the result shows that this relationship remains linear. Therefore, our simulation result suggests that the nonlinear relationship between flow rate and pressure gradient observed in tight formations cannot be explained by electrokinetic coupling effect.