Characterizing the scaling coefficient ω between viscous and inertial permeability of fractures

Abstract

Abstract Quantitative analysis of flow in fractures is an important issue for hydrogeological and geological engineering. In this study, Forchheimer models involving viscous permeability (kv) and inertial permeability (ki) were developed for groundwater flow in different single fractures or fractured media. Based on experiments and numerical simulation, the relationship between viscous permeability and inertial permeability in a single fracture was disclosed and an important parameter ω (the scaling coefficient ω (ω\xa0=\xa0ki/kv3/2)) was characterized. The results showed: (1) the Forchheimer model fit the non-linear fluid flow in almost all types of artificial single fractures that investigated in this study; (2) inertial permeability could be predicted by viscous permeability based on the empirical quantitative model: k i = ω k v 3 / 2 \\* MERGEFORMAT(ω\xa0≈\xa0108 m−2); (3) the fluctuation range of ω was related to the number of medium types, more medium types would induce a larger fluctuation range; artificial single fractures produced a smaller ω than that in natural rock fractures; ω was inversely proportional to the magnitude of the inertial effect, roughness and average aperture; the roughness element shape that caused greater turbulence effects led to larger ω; and single fractures placed vertically produced larger ω than fractures placed horizontally. In addition, the ratio of viscous permeability to inertial permeability (kv/ki) in fractures could be used as the characteristic length of Forchheimer number (Fo). By characterizing scaling factor ω, the accuracy of the quantitative model could be improved, and basis for further quantification of non-Darcy flow was established.