Direct pore-level examination of hydraulic-electric analogy in unconsolidated porous media

Taking advantage of the analogy between hydraulic and electrical flows to facilitate the prediction of porous media characteristics is a longstanding practice in engineering and science applications. The relationships between hydraulic and electrical properties are widely used in the characterization of transport phenomena relying on the strong correlation between electric and hydraulic flow conductance. However, due to the lack of small-scale investigations the similarity among their pathways/tortuosities is still unclear. Here a series of direct finite element numerical simulations are conducted within pore-level microstructures to extract and compare the streamlines of both electric and fluid flow currents and examine the accuracy of the hydraulic-electric analogy by predicting the petrophysical characteristics of the case studies. The fluid flow and electric transports are simulated through low-porosity digital unconsolidated packings of polydispersed grains representing the Athabasca oil sands deposit as the second largest oil reserve in the world. The formation factor, porosity, and absolute permeability of the media under consideration are predicted, and consequently, the streamlines of both electric and hydraulic currents are extracted and compared in terms of length, shape, and pathways. According to the results, the fluid flow streamlines are longer and pose differently than the homogeneous electric current streamlines. The average ratio between the hydraulic and electric tortuosities is 1.15 and a local extremum occurs at the porosity of eighteen percent. Pedotransfer functions for tortuosities, dimensionless permeability, and formation factor are proposed underpinning the rigorous relationships between transport processes in porous media.