A fractal irregular bundle-of-tubes model estimating the relationship between the capillary coefficient and sorptivity coefficient in porous sandstones

Natural rock as a typical type of porous medium, quantifying the dynamic migration of internal wetting fronts is a scientific issue prevailing in rock mechanics and engineering. The process of water migration inside rocks is represented by a black box, and it is difficult to observe this phenomenon in conventional experiments. Therefore, it is extremely necessary to establish a quantitative relationship between the moisture content and the dynamic evolution of the wetting front. Porous medium been simplified into tortuous capillary bundles, a mathematical model including pore-throat and without pore-throat is constructed to describe the quantitative relationship between the capillary coefficient and sorptivity coefficient by applying fractal geometry and fluid mechanics. Meanwhile, advanced neutron imaging experiments are used to monitor the dynamic evolution of wetting front over time for 5 different types of sandstones, thereby verifying the models. These research results are concluded as follows: 1) Compared with the existing model, the prediction accuracy of this fractal geometric model has been improved to a certain extent, and the average relative error of its prediction is 41.5% for five various sandstones; 2) For these porous media such as sandstones and limestones, the square of the ratio of capillary coefficient to sorptivity coefficient shows a increasing trend with increasing porosity as its power function, and these values predicted by this model are closer to the empirical fitting that; 3) When the porosity of sandstone-based porous media is less than 17%, the square of the ratio indicates increasing trend as a power function with the increase of porosity, and when their porosities are greater than 17%, it decreases with the increasing porosity; 4) When the permeability of sandstones is less than 141 mD, the square of the ratio increases with the increase of their permeability as a power function, and it decreases with increasing permeability for sandstones having permeability greater than 141 mD. These results predicted by the non-pore-throat model which does not show the influence of pore geometry are either higher or lower compared to experiments for certain rocks. However, the pore-throat ratio and the longitudinal length ratio in pore-throat model affect the ratio of capillary coefficient to sorptivity coefficient, which to a certain extent can reveal the reasons for the deviation of non-pore-throat model from the experiments.