Water sorptivity of unsaturated fractured sandstone: Fractal modeling and neutron radiography experiment

Abstract

The spontaneous imbibition of water into the matrix and gas-filled fractures of unsaturated porous media is an important phenomenon in many geotechnical applications. Previous studies have focused on the imbibition behavior of water in the matrix, but few works have considered spontaneous imbibition along fractures. In this work, a new fractal model, considering the water losses from the fracture to the matrix, was established to predict the sorptivity of rough-walled fracture. A fractal model, considering the fractal dimension of tortuosity, was modified to estimate the sorptivity of the matrix. Both of the models have a time exponent α and can be simplified to the classical Lucas-Washburn (L-W) equation with α = 0.50. To verify the proposed models, quantitative data on the imbibition of water in both the matrix and the fracture of unsaturated sandstone were acquired by neutron radiography. The results show that the motion of the wetting front in both the matrix and the fracture does not obey the L-W equation. Both theory and experimental observations indicate that fracture can significantly increase spontaneous imbibition in unsaturated sandstone by

Forward prediction of early‐time spontaneous imbibition of water in unsaturated rock fractures

“…In reality, fracture surfaces are rough, not smooth, and their asperities likely influence the contact angle and rates of fluid uptake within the fracture. Roels et al (2003) and Zhao et al (2019) used equally sized Euclidean asperities to represent fracture surface roughness. However, it is difficult to obtain meaningful independent estimates of the shape, size, and spacing of such asperities for forward prediction with these models.…”

“…Formal extensions of the Lucas-Washburn approach to parallel plate geometry have been provided by Schwiebert and Leong (1996) and Xiao, Yang, and Pitchumani (2006) for early and late imbibition times, respectively (i.e., neglecting vs. including gravity). More recently, Zhao et al (2019) proposed and tested an analytical model for spontaneous imbibition in rough-walled fractures, with each face composed of a curved, smooth surface decorated with evenly spaced cylindrical posts. Their model applies to both early and late time uptake.…”

“…Figure 1 represents early‐time uptake in a low‐porosity rock core. At late times in higher porosity rocks, the wetting front also moves laterally from the fracture into the matrix (Cheng et al., 2015; Zhao et al., 2019).…”

“…(2003) and Zhao et al. (2019) used equally sized Euclidean asperities to represent fracture surface roughness. However, it is difficult to obtain meaningful independent estimates of the shape, size, and spacing of such asperities for forward prediction with these models.…”

An advanced discrete fracture model for variably saturated flow in fractured porous media

“…Understanding variably saturated flow (VSF) in fractured porous media has great significance to many environmental and geotechnical applications, such as groundwater recharge in karst aquifers, (Mudarra and Andreo, 2011;de Rooij et al, 2013de Rooij, 2019, epikarst (Chang et al 2019) and unconfined chalk aquifers (Ireson et al, 2009), geological disposal of nuclear waste such as at Yucca Mountain in the United States where the unsaturated zone is estimated as potential site for disposal of high-level nuclear waste (Hayden et al, 2012;Ye et al, 2007), contaminant transport and infiltration of landfill leachate (Brouyère, 2006;Ben Abdelghani et al, 2015), infiltration through unsaturated saprock in hillslopes with shallow fractured shale bedrock (Guo et al, 2019), unsaturated flow and contaminant transport in saprolite (Van der Hoven et al, 2003;Alazard et al, 2016), water flow in cracked soils and stability of soil slopes with cracks (Pouya et al, 2013;Wang at al., 2019;Yang and Liu, 2020), seepage through fissured dams (Jiang et al, 2014), tunnel excavation (Gokdemir et al, 2019) and protection of structure foundations in contact with water (Zhao et al 2019).…”