Non-Fickian dispersion in a single fracture
Introduction
Solute transport in fractured rock is of great interest in groundwater pollution, CO2 sequestration, and oil recovery. One of the main research areas in hydrogeology is the selection of repository sites, either for nuclear waste or CO2 sequestration in geological formations. Integrity of reservoirs, which may present imperfections such as fractures and faults, is therefore a major issue, which makes flow characterization in fractures essential. Experiments on transparent replica of a real fracture have been wildly used to study two-phase flow (Persoff and Pruess, 1995), aperture fields (Detwiler et al., 1999, Isakov et al., 2001), and dispersion (Brown et al., 1998, Detwiler et al., 2000, Lee et al., 2003). Most of the later works focused on the outlet breakthrough curves, analyzing the dispersion from the overall fracture properties. The goal of this paper is the study of hydrodynamic dispersion due to aperture field heterogeneities through the interpretation of the breakthrough curves evolution along the flow direction. One-dimensional solutions were derived from three models: the advection-dispersion equation ADE, the continuous time random walk CTRW and the stratified model. Their ability to fit the breakthrough curves and the variation of their fitting parameters with the distance was studied. Although the experiment presented here is restrictive because of the uniqueness of the fracture, this work shows how model parameters may correlate with aperture field heterogeneity. The experiment was performed with non-reactive solute in a single-fracture with impermeable walls. The Peclet number was high enough to neglect molecular diffusion and to focus on the impact of the heterogeneities.
Section snippets
The advection-dispersion approach
The basic mass balance equation in one dimension is: where C is the average solute concentration and F is the mass flux per unit area. In a piston-like displacement without dispersion, the relationship between the flux and the concentration is simply F = UC, with U the average fluid velocity. In real tracer flow, the common approach for expressing the flux in accordance with the concentration is based on a Fickian law as follows (Bear, 1988, Dullien, 1992):This leads to the
Experimental setup and image processing
A transparent replica of a fracture was made from a split block of Vosges sandstone. A resin copy was made of each side, which, when placed together, reproduced the fracture. The length of the fracture, Lx, was 330 mm and the width, Ly, was 148 mm. In this notation, x stands for the flow direction and y stands for the transverse direction. The replica was placed in a transparent acrylic glass holder to allow for flow visualization. On one side, four ports allowed differential pressure
Interpretation of experiment
In order to characterize heterogeneities, the analytical solutions, given in Section 2, have been fitted to the one-dimensional concentration profiles versus time. These profiles, calculated from concentration map by averaging over the transverse direction y, represent the local concentration at each position x. We recall that the analytical solutions have been integrated from the inlet to a position x, assuming a step injection. Therefore, parameters contain information on the entire tracer
Conclusions
Tracer test experiments were conducted through a replica of a real fracture. The experiments were interpreted with different models in order to evaluate their ability to describe non-Fickian transport and to connect their parameters to the local heterogeneity of the fracture.
The results confirmed that the one-dimensional solution derived from the ADE does not give good results in modeling long-time tailing behavior. In comparison, the CTRW gave very good results, with three adjustable
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2022, Journal of HydrologyCitation Excerpt :Therefore, understanding solute transport process in fractures is of great importance to better understand biogeochemical cycles (Gu et al., 2020), and to determine the success of engineering applications, such as sequestration of CO2 (Deng et al., 2015; Wang and Cardenas, 2017; Wang and Cardenas, 2019) and contaminant remediation (Lee et al., 2017). The field tracer tests (Becker and Shapiro, 2000; Małoszewski and Zuber, 1985), laboratory experiments (Lee et al., 2015), and numerical simulations (Yoon and Kang, 2021) in fractured rocks all demonstrated that the non-Fickian transport regime prevails, where transport behavior deviates from the traditional Fickian theory described by the advection–dispersion equation (Bauget and Fourar, 2008). The non-Fickian transport is typically characterized by the power-law tailing process at the late time of breakthrough curves (Becker and Shapiro, 2000; Berkowitz, 2002; Li et al., 2020), which has been attributed to many driving mechanisms in fractured rocks, including flow channeling (Tsang and Neretnieks, 1998), fracture heterogeneity (Detwiler et al., 2000; Wang and Cardenas, 2014), solute diffusion into and out of matrix (Hoffmann et al., 2020; Houseworth et al., 2013; Hyman and Dentz, 2021; Zou et al., 2017), chemical reactions such as sorption and desorption (James et al., 2018), and trapping and release of solute in immobile zone such as recirculation zones (Wang et al., 2020; Zhou et al., 2019).
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