On the upscaling of chemical transport in fractured rock

Abstract

The impact of flow heterogeneity on chemical transport from single to multiple fractures is investigated. The emphasis is on the dynamic nature of the specific surface area (SSA) due to heterogeneity of the flow, relative to a purely geometrical definition. The flow-dependent SSA is interpreted probabilistically, following inert tracer particles along individual fractures. Upscaling to a fracture network is proposed as a time domain random walk based on the statistics of SSA for single fractures. Statistics of SSA are investigated for three correlation structures of transmissivity: multi-Gaussian and two non-multi-Gaussian. The mean of SSA stabilizes after $20 fractures at different values depending on whether the cubic or quadratic hydraulic law is assumed. The results are tested against comprehensive DFN simulations based on sitespecific data but also against direct estimates from a wider range of tracer tests. The proposed time domain random walk methodology sets bounds for SSA in a 75% confidence interval as $1800 1/m and 27,000 1/m, with a median of 14,000 1/m; these values capture reasonably well both the DFN simulation and tracer test SSA data. Presented results may be particularly relevant when quantifying uncertainty of reactive transport modeling in fractured rock.

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 .…”

Simulation of chemical reaction localization using a multi-porosity reactive transport approach

“…Other studies have focused on more complex chemical systems Steefel and Lichtner, 1998). Research has been carried out on specific surface area heterogeneity (Cvetkovic and Gotovac, 2014) and on network fracture heterogeneities Frampton and Cvetkovic, 2007;Painter et al, 2008). The effect of chemical heterogeneity was addressed by Dentz et al (2011b), but on an abstract system that did not allow acknowledging explicitly that porous media consist of multiple mineral phases, which create their own local conditions and precipitation/dissolution reactions.…”

Groundwater Flow Modeling in Karst Aquifers: Coupling 3D Matrix and 1D Conduit Flow via Control Volume Isogeometric Analysis—Experimental Verification with a 3D Physical Model

“…Until recently, Fup basis functions were used mostly in the collocation framework in a manner conceptually similar to the finite difference method. Applications of the adaptive Fup collocation method (AFCM) to groundwater flow and transport problems are presented in, e.g., Gotovac et al [48], Cvetkovic and Gotovac [49], Fiori et al [50]. However, the main drawback was the lack of local and global mass balance due to the collocation nature of the algorithm.…”