| 1. |
- Liu, Longcheng, et al.
(författare)
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Solute transport along a single fracture in a porous rock : a simple analytical solution and its extension for modeling velocity dispersion
- 2017
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Ingår i: Hydrogeology Journal. - : Springer Berlin/Heidelberg. - 1431-2174 .- 1435-0157.
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Tidskriftsartikel (refereegranskat)abstract
- A simple and robust solution is developed for the problem of solute transport along a single fracture in a porous rock. The solution is referred to as the solution to the single-flow-path model and takes the form of a convolution of two functions. The first function is the probability density function of residence-time distribution of a conservative solute in the fracture-only system as if the rock matrix is impermeable. The second function is the response of the fracture-matrix system to the input source when Fickian-type dispersion is completely neglected; thus, the effects of Fickian-type dispersion and matrix diffusion have been decoupled. It is also found that the solution can be understood in a way in line with the concept of velocity dispersion in fractured rocks. The solution is therefore extended into more general cases to also account for velocity variation between the channels. This leads to a development of the multi-channel model followed by detailed statistical descriptions of channel properties and sensitivity analysis of the model upon changes in the model key parameters. The simulation results obtained by the multi-channel model in this study fairly well agree with what is often observed in field experiments—i.e. the unchanged Peclet number with distance, which cannot be predicted by the classical advection-dispersion equation. In light of the findings from the aforementioned analysis, it is suggested that forced-gradient experiments can result in considerably different estimates of dispersivity compared to what can be found in natural-gradient systems for typical channel widths.
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| 2. |
- Shahkarami, Pirouz, et al.
(författare)
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Analytical solution for N-member decay chain transport in fracture in rock
- 2013
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Ingår i: Rock Characterisation, Modelling and Engineering Design Methods - Proceedings of the 3rd ISRM SINOROCK 2013 Symposium. - : Taylor & Francis Group. ; , s. 323-328
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Konferensbidrag (refereegranskat)abstract
- A model is developed to describe the transport of an N-member radionuclide decay chain along a discrete fracture situated in a porous matrix. An analytical solution is presented and a series of simulations are performed to study the relative significance of diffusion process into rock matrix, stagnant water, chain decay and hydrodynamic dispersion. The results show that a simplified model that ignores the effect of stagnant water zone can lead to significant error in the estimated time of arrival and peak value of the nuclides. The results demonstrate that for a two-member decay chain, neglecting the parent and modeling its daughter as a single species can result in significant overestimation of peak value of the nuclide. Moreover, it is found that as the dispersion increases, the arrival time and peak time of daughter decrease, while the peak value increases.
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| 3. |
- Shahkarami, Pirouz, et al.
(författare)
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Channel network concept : an integrated approach to visualize solute transport in fractured rocks
- 2019
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Ingår i: Hydrogeology Journal. - : Springer. - 1431-2174 .- 1435-0157. ; 27:1, s. 101-119
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Tidskriftsartikel (refereegranskat)abstract
- The advection-dispersion equation, ADE, has commonly been used to describe solute transport in fractured rock. However, there is one key question that must be addressed before the mathematical form of the so-called Fickian dispersion that underlies the ADE takes on physical meaning in fractures. What is the required travel distance, or travel time, before the Fickian condition is met and the ADE becomes physically reasonable? A simple theory is presented to address this question in tapered channels. It is shown that spreading of solute under forced-gradient flow conditions is mostly dominated by advective mechanisms. Nevertheless, the ADE might be valid under natural flow conditions. Furthermore, several concerns are raised in this paper with regard to using the concept of a field-scale matrix diffusion coefficient in fractured rocks. The concerns are mainly directed toward uncertainties and potential bias involved in finding the continuum model parameters. It is illustrated that good curve fitting does not ensure the physical reasonability of the model parameters. It is suggested that it is feasible and adequate to describe flow and transport in fractured rocks as taking place in three-dimensional networks of channels, as embodied in the channel network concept. It is argued that this conceptualization provides a convenient framework to capture the impacts of spatial heterogeneities in fractured rocks and can accommodate the physical mechanisms underlying the behavior of solute transport in fractures. All these issues are discussed in relation to analyzing and predicting actual tracer tests in fractured crystalline rocks.
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| 4. |
- Shahkarami, Pirouz, 1986-, et al.
(författare)
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Channel Network Concept — an Integrated Approach to Visualize Solute Transport in Fractured Rocks
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The advection-dispersion equation, ADE, has commonly been used to visualize solute transport in fractured rock. However, there is one key question that has to be addressed before the mathematical form of the so-called Fickian dispersion that underlies the ADE takes on physical meaning in fractures. What is the travel distance, or travel time, required before the Fickian condition is met and the ADE becomes physically reasonable? A simple theory is presented in this study to address this question in tapered channels. It is shown that spreading of solute under forced-gradient flow conditions is mostly dominated by advective mechanisms, though the ADE might be valid in the channels under natural flow conditions. This implies that the use of the ADE and macro dispersion coefficient might be misleading when applied to interpret field tracer experiment results. Furthermore, several concerns are raised in this paper with regard to utilizing the concept of field-scale matrix diffusion coefficient in fractured rocks. The concerns are mainly directed toward the uncertainties and potential bias involved in finding the continuum model parameters.In light of the findings of this study and empirical evidences, it is suggested that it is feasible and more realistic to describe flow and solute transport in fractured rocks as taking place in three-dimensional networks of channels, as embodied in the channel network concept, CN-concept. It is argued that this conceptualization provides a convenient framework to capture the impacts of spatial heterogeneities in fractured rocks and can accommodate the physical mechanisms underlying the behavior of solute transport in such porous media. All these issues are discussed in this paper in relation to analyzing and predicting actual tracer tests in fractured crystalline rocks.
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| 5. |
- Shahkarami, Pirouz, 1986-, et al.
(författare)
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Radionuclide migration through fractured rock for arbitrary-length decay chain: Analytical solution and global sensitivity analysis : new
- 2015
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Ingår i: Journal of Hydrology. - : Elsevier. - 0022-1694 .- 1879-2707. ; 520, s. 448-460
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Tidskriftsartikel (refereegranskat)abstract
- This study presents an analytical approach to simulate nuclide migration through a channel in a fracture accounting for an arbitrary-length decay chain. The nuclides are retarded as they diffuse in the porous rock matrix and stagnant zones in the fracture. The Laplace transform and similarity transform techniques are applied to solve the model. The analytical solution to the nuclide concentrations at the fracture outlet is governed by nine parameters representing different mechanisms acting on nuclide transport through a fracture, including diffusion into the rock matrices, diffusion into the stagnant water zone, chain decay and hydrodynamic dispersion. Furthermore, to assess how sensitive the results are to parameter uncertainties, the Sobol method is applied in variance-based global sensitivity analyses of the model output. The Sobol indices show how uncertainty in the model output is apportioned to the uncertainty in the model input. This method takes into account both direct effects and interaction effects between input parameters. The simulation results suggest that in the case of pulse injections, ignoring the effect of a stagnant water zone can lead to significant errors in the time of first arrival and the peak value of the nuclides. Likewise, neglecting the parent and modeling its daughter as a single stable species can result in a significant overestimation of the peak value of the daughter nuclide. It is also found that as the dispersion increases, the early arrival time and the peak time of the daughter decrease while the peak value increases. More importantly, the global sensitivity analysis reveals that for time periods greater than a few thousand years, the uncertainty of the model output is more sensitive to the values of the individual parameters than to the interaction between them. Moreover, if one tries to evaluate the true values of the input parameters at the same cost and effort, the determination of priorities should follow a certain sequence.
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| 6. |
- Shahkarami, Pirouz, 1986-
(författare)
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Solute Transport in Fractured Rocks : The Effect of Stagnant Water Zones and Velocity Dispersion
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The focus of this thesis is on the development of new models to improve our understanding of radionuclide transport in the repository “far-field” in fractured rocks. The proposed models contribute to the channel network concept and describe the recently developed models with stagnant water zones (STWZs) and channels with variable aperture allowing to consider their possible impacts on the overall transport of radionuclides in fractured rocks. New conceptual models are also proposed to better understand hydrodynamic dispersion in fractured rocks by taking into account velocity distribution within tapered channels, i.e., Fickian-type dispersion, and between different flow paths, i.e., velocity dispersion, as embodied in the proposed multi-channel model.The results of both deterministic and probabilistic analyses reveal that over the long times of interest for safety assessment of high-level radioactive waste repositories, STWZs can substantially enhance the retardation of both short- and long-lived nuclides, with the exception of the non-sorbing species, i.e., 36Cl and 129I. Nevertheless, over the short time-scales the impact of STWZs is not very strong and is not expected to affect the results of short-term field experiments. It is also shown that the proposed multi-channel model can explain the apparent scale dependency of the dispersion coefficient that is often observed in tracer experiments. It is further discussed that the interpreted results of short-range tracer experiments cannot necessarily give information on what would take place over longer distances because the spreading mechanisms are expected to be entirely different. Usefulness of the continuum model to interpret tracer experiments is, thereafter, discussed and arguments are presented to support the premise that it is more physically meaningful to describe flow and transport as taking place in a three-dimensional network of channels.
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| 7. |
- Shahkarami, Pirouz, 1986-, et al.
(författare)
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The effect of stagnant water zones on retarding radionuclide transport in fractured rocks : An extension to the Channel Network Model
- 2016
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Ingår i: Journal of Hydrology. - : Elsevier. - 0022-1694 .- 1879-2707. ; 540, s. 1122-1135
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Tidskriftsartikel (refereegranskat)abstract
- An essential task of performance assessment of radioactive waste repositories is to predict radionuclide release into the environment. For such a quantitative assessment, the Channel Network Model and the corresponding computer program, CHAN3D, have been used to simulate radionuclide transport in crystalline bedrocks. Recent studies suggest, however, that the model may tend to underestimate the rock retarding capability, because it ignores the presence of stagnant water zones, STWZs, situated in the fracture plane. Once considered, the STWZ can provide additional surface area over which radionuclides diffuse into the rock matrix and thereby contribute to their retardation.The main objective of this paper is to extend the Channel Network Model and its computer implementation to account for diffusion into STWZs and their adjacent rock matrices.In the first part of the paper, the overall impact of STWZs in retarding radionuclide transport is investigated through a deterministic calculation of far-field releases at Forsmark, Sweden. Over the time-scale of the repository safety assessments, radionuclide breakthrough curves are calculated for increasing STWZ width. It is shown that the presence of STWZs enhances the retardation of most long-lived radionuclides except for 36Cl and 129I.The rest of the paper is devoted to the probabilistic calculation of radionuclide transport in fractured rocks. The model that is developed for transport through a single channel is embedded into the Channel Network Model and new computer codes are provided for the CHAN3D. The program is used to (I) simulate the tracer test experiment performed at Äspö HRL, STT-1 and (II) investigate the short- and long-term effect of diffusion into STWZs. The required data for the model are obtained from detailed hydraulic tests in boreholes intersecting the rock mass where the tracer tests were made.The simulation results fairly well predict the release of the sorbing tracer 137Cs. It is found that over the short time-scale of the tracer experiment, the effect of diffusion into STWZs is not as pronounced as that of matrix diffusion directly from the flow channel, and the latter remains the main retarding mechanism. Predictions for longer time-scale, tens of years and more, show that the effect of STWZs becomes strong and tends to increase with transport time. It is shown that over the long times of interest for safety assessment of radioactive waste repositories, STWZs can substantially contribute to radionuclide retardation, though for the short time-scales the impact is not very strong and is not expected to affect the results of short-term field experiments.
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