A semi-empirical modified geometry model for long-term co-current spontaneous imbibition of porous media based on convoluted, nonuniform and topological pore network

Abstract

Hydraulic diffusivity or imbibition is a well-known unsaturated hydrodynamics phenomenon in water resources and geosciences study. Currently, there have been numerous analytical or numerical models describing the spontanneous imbibition of porous rock and soil. However, the most existing models do not consider hydrostatic pressure and elaborate pore geometry characteristics. Assuming that the penetration direction is one-dimensional and infinitely continuous, a long-term co-current spontaneous imbibition (SI) model is proposed by average and fractal geometries, respectively accordingly obtaining the general expression of dimensionless comprehensive parameter. The practicability and accuracy of the model are verified by experimental data and compared with other models. The influence mechanisms of tortuosity, pore-throat, fractal, shape and topological characteristics on initial and equilibrium SI behaviors are comprehensively revealed. The new models are applied to inversely predict the dimensionless comprehensive parameters, variations of which with porosity are analyzed along with their influence on long-term SI characteristics. The results are shown as follows. Compared with the existing classical models, the prediction accuracy of the new model consistent with experiment is greatly improved, generalizing the existing models. The dimensionless comprehensive parameters based on average and fractal geometries show the decreasing trend in power-law and increasing trend in linear with the increase of porosity, respectively. The equilibrium height or mass is only related to topology factor, fractal dimension and shape factor, whereas the equilibrium time is also correlated to pore-throat ratio and tortuosity. The sensitivities of fractal dimension, topological factor and shape factor to equilibrium time are stronger than that of equilibrium mass or height. The sensitivities of topological characteristics, pore-throat structure, tortuosity, pore geometry and fractal characteristics to SI reduce successively for porous media. The influences of dimensionless comprehensive parameter on evolution of SI mass with time go through four stages, i. e., no influence at initial stage, increasing influence at initial later stage, weakening influence at later stage and increasing influence at end, whereas on evolution of SI velocity versus time and recovery rate go through two stages, that is, significant influence at initial stage and no influence at later stage.