Flow‐dependence of matrix diffusion in highly heterogeneous rock fractures

Abstract

[1] Diffusive mass transfer in rock fractures is strongly affected by fluid flow in addition to material properties. The flow-dependence of matrix diffusion is quantified by a random variable (''transport resistance'') denoted as b [T/L] and computed from the flow field by following advection trajectories. The numerical methodology for simulating fluid flow is mesh-free, using Fup basis functions. A generic statistical model is used for the transmissivity field, featuring three correlation structures: (i) highly connected non-multiGaussian; (ii) poorly connected (or disconnected) non-multi-Gaussian ; and (iii) multiGaussian. The moments of b are shown to be linear with distance, irrespective of the structure, after approximately 10 integral scales of ln T. Percentiles of b are found to be linear with the mean b when considering all three structures. Taking advantage of this property, a potentially useful relationship is presented between b percentiles and the fracture mean water residence time that integrates all structures with high variability; it can be used in discrete fracture network simulations where T statistical data on individual fractures are not available.Citation: Cvetkovic, V., and H. Gotovac (2013), Flow-dependence of matrix diffusion in highly heterogeneous rock fractures, Water Resour. Res., 49,[7587][7588][7589][7590][7591][7592][7593][7594][7595][7596][7597]

Statistical Formulation of Generalized Tracer Retention in Fractured Rock

“…On the block scale used for a discrete fracture network (DFN) or stochastic continuum conceptualization, we will typically require the flow porosity n f , but also an active specific surface area ω [1/ L ] (Figure b). A m is defined in the usual way for porous media (in this case the rock matrix), whereas ω is pertinent to fractures and depends on the flow; this fact is emphasized by the attribute “active.” For further discussion on the physical meaning of ω , see e.g., Cvetkovic et al (), Cheng et al (), Cvetkovic and Gotovac ().…”

“…Statistics of β with have been studied in 2‐D fractures (Cheng et al, ), in 2‐D DFNs (Frampton & Cvetkovic, ), and in 3‐D DFNs (Cvetkovic & Frampton, ; Makedonska et al, ), as well as analytically (Cvetkovic et al, ). A common simplification is to assume that is perfectly correlated to τ which writes for the non‐Fickian case as where is an effective specific surface area (Cvetkovic & Gotovac, ). The classical Fickian case is obtained with .…”

Power law breakthrough curve tailing in a fracture: The role of advection

“…There is unfortunately little field evidence of velocity distribution in bedrock fractures (Cvetkovic and Gotovac, 2013). Shapiro and Hsieh (1998) performed injection tests over short intervals in a crystalline granite/gneiss in central New Hampshire, USA, and found up to 5 orders of magnitude variation in transmissivity.…”

On the upscaling of chemical transport in fractured rock

“…Investigations of single fractures as well as fracture networks have shown that a random variable referred to as ''transport resistance'' (b [T/L]) is required for inferring the SSA of rock fractures [e.g., Cvetkovic et al, 1999;Cvetkovic and Gotovac, 2013]. Theoretical and simulation studies over the past two decades have shed some light on the dependence of the transport resistance on fracture heterogeneity [Cvetkovic, 1991;Moreno and Neretnieks, 1993;Cvetkovic et al, 1999;Cheng et al, 2003;Frampton and Cvetkovic, 2007;Cvetkovic and Frampton, 2012;Larsson et al, 2012].…”

“…The flow heterogeneity controls advective transport (Fickian or non-Fickian), but even more significantly controls the SSA. A recent simulation study by Cvetkovic and Gotovac [2013] focuses on residence time and transport resistance in single rock fractures for Gaussian and non-Gaussian transmissivity fields; using these results for a single fracture, we propose here a simple time domain random walk (TDRW) methodology for upscaling of SSA to a network of fractures. The results are compared to discrete fracture network (DFN) simulation results that are based on the most comprehensive field data set currently available [Frampton and Cvetkovic, 2011;Cvetkovic and Frampton, 2012]; even more importantly, the results are compared to the only broad range of SSA estimates from tracer tests reported in the literature Cvetkovic and Frampton, 2010].…”