A model of spontaneous flow driven by capillary pressure in nanoporous media

Anqi Shen, Yikun Liu, S. M. Farouq Ali

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The spontaneous capillary imbibition phenomenon is a fundamental mechanism in porous media with applications in many fields. In low permeability shale reservoirs, this flow driven by capillary pressure is extremely important due to the predominance of nano-scale pores, which enhance capillary pressure and weaken hydrodynamic viscous force. This paper presents the results of an analytical model for capillary rise in nano-channels by taking into consideration the effect of inherent surface roughness. Model predictions match better with available experiments results. Relevant experiments were carried out on silicon-based nano-channels with rectangular section, which height is between 5 and 50 nm using de-ionized water. Results proved that the capillary rise kinetics in nano-channels follows the modified Lucas-Washburn law. The surface roughness adds extra resistance during the process of capillary rise, which is calculated as an equivalent porous medium layer. The capillary model is extended to porous media using the capillary bundle concept. In this model, imbibition height versus time was defined. Using this equation, the weight of imbibed liquid by spontaneous imbibition can be obtained. The results from this study demonstrate that the spontaneous imbibition in nanoporous media could be scaled and predicted.

Cited as: Shen, A., Liu, Y., Farouq Ali, S.M. A model of spontaneous flow driven by capillary pressure in nanoporous media. Capillarity, 2020, 3(1): 1-7, doi:10.26804/capi.2020.01.01


Spontaneous imbibition; surface roughness; nano-scale; nanoporous media

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