A study of flow‐wetted surface area in a single fracture as a function of its hydraulic conductivity distribution

Abstract

[1] The contact area between flowing water and rock-the flow-wetted surface (FWS)-is a main factor controlling the rock-matrix diffusion and sorption of flowing solute in a rock fracture. Flow channeling, therefore, has a strong effect on the retardation of mass transport due to the resulting lower contact area. This work presents a systematic study of the dependency between fracture aperture statistics and FWS in strongly heterogeneous fractures. Particle tracking is used to determine the transversal width of the particle flow lines, FWS, and factor, where is a variable that has been proposed as controlling tracer retention. The conductivity distribution over the fracture is assumed to be lognormal with standard deviation ( ln K ) ranging from 0.23 to 4.61, with correlation lengths from 2% to 18% of the width of the flow domain. Results show a clear dependency between the specific flow-wetted surface (sFWS), defined as FWS divided by the total fracture area, and the standard deviation of the logarithm of fracture conductivity. The behavior is independent of the correlation length for the range of correlation lengths tested. The results are presented in the form of type curves and an empirical equation that provide a simple way to determine the sFWS as a function of ln K . This information can then be used to adjust the results of large-scale fracture network simulations by taking into account the effect of single fracture heterogeneity, an effect that is in practice infeasible to directly take into account in largescale fracture network simulations.

A new approach to account for fracture aperture variability when modeling solute transport in fracture networks

“…Fracture aperture heterogeneity causes the water flow in a single fracture to be channelized through channels with relatively large local flow rate compared to the surrounding areas [Neretnieks, 1983;Tsang and Tsang, 1989;Tsang and Neretnieks, 1998]. The channeling effect is significant ; for example, in some cases only 25% of the fracture can carry 90% of the flow as shown in a numerical study by Larsson et al [2012], and it has significant impact on solute transport retardation, as it decreases the interaction surface area where the retarding processes of matrix diffusion and sorption can occur. Advective flow dominates in fast flowing channels, giving rise to early arrival for part of the contaminant and also an early concentration peak, while the retarding processes slow down the later part of the transport so that the tracer breakthrough curve displays a long tail at late time [see, e.g., Carrera et al, 1998;Moreno and Neretnieks, 1993;Shapiro, 2001;Od en et al, 2008].…”

“…If, however, the area of the retarding surface is overestimated by assuming the entire fracture plane to contribute to the retarding processes, the time delay on the breakthrough curve may be overestimated. In this work (section 3) we present an approach to include the effect of the FWS in a variable aperture fracture into a fracture network model, making use of the empirical formula by Larsson et al [2012]. The solute transport is then analyzed by simulating the travel time of advective nonsorbing particles at block scale.…”

“…Thus, in many cases such as when investigating for a nuclear waste repository, the FWS is an important factor [Neretnieks, 1980;Elert, 1997]. Larsson et al [2012] examined the influence of single fracture aperture heterogeneities on flow and transport channeling and subsequently on the FWS. In this article an empirical relationship showing the FWS as a function of the variance of the underlying hydraulic conductivity field is presented.…”

“…[7] Prior to applying the results of Larsson et al [2012] into a fracture network analysis, we shall elaborate (section 2) the development of their relationship, alongside with a more general form of the equation, to enable users to find a more accurate relationship, if needed, for their particular applications.…”

“…Our approach is based on the concept of specific flow-wetted surface (sFWS), which is the fraction of the contact area over the total fracture surface area. Larsson et al (2012) studied the relationship between sFWS and the standard deviation ln K of the conductivity distribution over the fracture plane. Here an approach is presented to incorporate this into a fracture network model.…”