Prediction of initial-time spontaneous imbibition of water coupled with fractal tortuosity and water loss in unsaturated low-permeability sandstone fractures

Abstract

Investigating the spontaneous imbibition behavior of water in unsaturated low-permeability sandstone fractures is crucial for elucidating the mechanisms of fluid migration in porous media. Previous studies on water imbibition in fractures have rarely considered both the fractal tortuosity and the transfer of water from the fractures to the matrix in a systematic manner. A dynamic model is developed based on fractal theory to account for the fractal tortuosity and water loss. To validate the reliability of the new model, experimental data obtained via neutron radiography are utilized to evaluate the spontaneous imbibition process in an unsaturated fractured sandstone. Finally, we analyzed the effects of the experimentally measured tortuosity fractal dimension D_Tf and water loss on the imbibition height. The results show that the wetting front migration in a single rough-walled fracture deviates from classical imbibition behavior, with the imbibition height exhibiting a power-law relationship with time. Compared with the prediction results of existing models, the imbibition height varying with time predicted by the new model is consistently closer to the observed values. Moreover, the imbibition height of water in rough fractures decreases as the fractal dimension of fracture tortuosity increases. The new model demonstrates a deviation of less than 1% in predicting the imbibition height within rough-walled fractures in low-permeability sandstone when compared to the scenario without considering water loss. This suggests that the transfer of water from fractures into the surrounding matrix exerts a relatively limited influence on the imbibition height within low-permeability sandstone formations.