Hydraulic and electrical tortuosity: numerical experiments based on X-ray CT slices of real rocks

As one of the important parameters affecting seepage, accurate measurement of hydraulic tortuosity is crucial. Due to the similarity between the fluid transport path and the electrical conduction path in the media, electrical tortuosity is often used as hydraulic tortuosity. However, the difference in values between hydraulic and electrical tortuosity has been fuzzy in real porous media. Here we reconstruct sandstone’s three-dimensional (3D) digital rocks using its X-ray Computed Tomography (CT) slices first, then perform the simulations of hydraulic and electrical transport by finite element method to extract the path of fluid and current and compute the hydraulic and electrical tortuosity. The simulation results show that the electrical tortuosity is smaller than the hydraulic tortuosity, and the average ratio between hydraulic and electrical tortuosity is about 1.09. A visual discussion of the path confirms that the reason for the difference in the two values is that their choices of the main transport channels are different. Moreover, new functions between tortuosity and porosity are proposed for the hydraulic and electrical tortuosity based on the simulation results, respectively. Compared with the previous model, it is found that the new model has better applicability in the sandstone. Finally, the calculated tortuosity is substituted into the permeability prediction formula, and the perfect fit between the predicted and the simulated permeability indicates that the tortuosity of real rocks obtained by the simulation is reliable. These conclusions provide a reference for the study of the hydraulic and electrical tortuosity of real rocks and rocks with different lithologies.