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• W2899896632 abstract "Trinchero et al. 2018 (TRI18 from now on) raise some interesting issues concerning our paper Antonellini et al. (2017, ANT17 from now on) that we would like to answer and clarify in the following. We thank the authors for their interest in our work and we think that this discussion is useful to clarify the framework in which analytical solutions may be helpful in tackling real field situations. The first issue raised by TRI18 is that of the DO concentration in the water infiltrating the fractures. TRI18 claims that the water infiltrating the fractures should have a DO concentration in equilibrium with that of the atmosphere (0.3 mol/m3), which is what is expected for meteoric water. ANT17, however, uses a concentration that is 10% of that (0.03 mol/m3). The reason we used a lower DO concentration is that meteoric water does not enter directly the fractures but needs first percolating through a 20-cm-thick layer of fine-grained, low-hydraulic-conductivity soil. This soil (see section 2.2 in ANT17), which developed in a humid climate and is often saturated, is rich in organic matter and CO2 production. These soil characteristics result in a lower DO concentration reported in the literature for similar situations and measured in percolating waters of the area (Chong et al., 2003; Estop-Aragonés et al., 2012; Werner et al., 2011). The lower bound DO concentration used by Sidborn and Neretnieks (2007) in their modeling was also useful for our case. We do not say in our paper that Sidborn and Neretnieks (2007) claim meteoric water DO concentration is 0.03 mol/m3. The value of W in Table 2 was left behind (we apologize for that) but as TRI18 correctly figured out it is 1 m, which is coherent with the outcrop observations. For the reasons explained above, we do not think that there is a bias toward higher values in our timing estimate as claimed by TRI18. The second issue raised by TRI18 is that a constant input of oxygen in the fracture would form the alteration halos but would not cause the precipitation of the hydroxide material within the fracture. We agree on this point and we think that TRI18 also answer this issue. The use of steady state models in a real field case is a first order approximation as we have stated also in our paper (section 2.2). We know that DO concentration in the infiltrating water is low and that it may have varied trough time under controls of rainfall recharge and soil saturation conditions as also is clearly shown by the width of the redox front in Figure 4b (ANT17), which suggests some oscillations in time. In addition, fracture flow might have been periodic because of a variable hydraulic head. In our field situation, however, we have to account for two important features: the alteration halos and the hydroxide filling in some of the fractures (Figure 5 in ANT17). These features suggest two different processes were at work implying that during some periods, there was not a constant input of oxygen into the fractures and/or there was no vertical flow in the fractures. This is also what TRI18 say. The two processes are, therefore, distinct and do not happen simultaneously. The assumptions and hypothesis used for these two models can be different. The use of different assumptions might not have been clear enough in ANT17 and we clarify it further in the following. Our simple steady-state model based on Fick's law for back-diffusion of Fe2+ toward the fracture is valid for the time in which relatively oxygenated water fills the fractures in static conditions and the availability of Fe2+ is the limiting species (probable high concentration of Fe2+ in pore water within a reducing aquifer). We computed a mass flux into an existing fracture opening and, based on the volume of the opening and fracture fillings observed in the field, we attempted to give an estimate of the time scale of the process. We also would like to stress that it is more difficult to evaluate fracture partial or complete fillings (order of microns) in comparison with the width of reactive fronts (order of centimeters) by direct field or optical observations. The uncertainties associated with our second method, therefore, are larger than the first one as also shown in Figure 11 of ANT17. One further thing that we would like to clarify is that it is not true that Figure 11 in ANT17 shows that the time of fracture filling depends on fracture aperture as stated in TRI18. Figure 11 in ANT17 reports the time required for filling different joint openings with hydroxide mineral under the mass flux computed with our steady-state model. The volume of mineral mass carried into the fractures fills an existing void not necessarily as a homogeneous layer starting from the fracture wall. We agree that ANT17's explanation of Figure 11 (ANT17) is not clear when compares the timing estimate for filling with those obtained for the formation of the alteration halos. The two processes, in fact, are different and were active in different times. It is interesting, however, that the time scales for the two processes are similar; this was the meaning of our observation in ANT17. The important question however is “For how long did the fractures actively carry oxygen (flowing conditions) and for how long they did not (static conditions)?” If we had an answer to this, the application of coupled models with time-dependent boundary conditions would be a better approach to pursue. As we do not have an answer, we need to accept the limitations of the analytical solutions approach, because in our opinion they still provide an acceptable time scale for the process. The model for the timing of fracture filling presented by TRI18 is interesting and coherent with the time scale of our calculations. Our concern, however, is that it is difficult to determine based on field and optical observations alone the relative filling (b/b0; see Figure 3 in TRI18) of fractures especially when they have small apertures, so that TRI18 model would be difficult to validate. Hydroxide fillings, furthermore, do not always grow homogeneously from the fracture wall. Anyway, this is worth exploring in future work by focusing on partial fracture fillings and wall rock morphology. In conclusion, ANT17's main objective was to explore the possibility that analytical model predictions might be of use in explaining the space and time scale of reactive front development. It is clear that there are uncertainties in the estimate of some parameters and the time boundary conditions of the processes involved. In the perspective of Earth scientists with field expertise, as the three of us are, an uncertainty of a factor of two in the estimate of the time scale of a process occurred about 10,000 years is not a bad estimate. As we stated in ANT17, we observe that the age of the rock dates back to about 70–75 Ma ago (Late Campanian-Maastrichtian) and deformation resulting in the structures observed in outcrop started 56 Ma ago (Late Paleocene) (Cibin et al., 2001). Fluid flow might have happened at any time in the last 56 Ma. Our analysis, however, constrains the timing to the last 10,000 ± 4,000 years, which we consider a good approximation in a geologic perspective. For this reason, we still think that the analytical models presented are useful for a first order approximation of the spatial and time scale of reactive transport processes in fractures where applied to real field data." @default.
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• W2899896632 date "2018-11-01" @default.
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• W2899896632 title "Reply to Comment by Trinchero et al. on “Application of Analytical Diffusion Models to Outcrop Observations: Implications for Mass Transport by Fluid Flow Through Fractures”" @default.
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• W2899896632 doi "https://doi.org/10.1029/2018wr023312" @default.
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