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  • 1.
    Liu, Longcheng
    et al.
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering.
    Neretnieks, Ivars
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering.
    Shahkarami, Pirouz
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering.
    Meng, Shuo
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering.
    Moreno, Luis
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering.
    Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion2017In: Hydrogeology Journal, ISSN 1431-2174, E-ISSN 1435-0157Article in journal (Refereed)
    Abstract [en]

    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.

  • 2.
    Meng, Shuo
    et al.
    KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Chemical Engineering.
    Liu, Longcheng
    KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Chemical Engineering.
    Mahmoudzadeh, Batoul
    KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Chemical Engineering.
    Neretnieks, Ivars
    KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Chemical Engineering.
    Moreno, Luis
    KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Chemical Engineering.
    Solute transport along a single fracture with a finite extent of matrix: A new simple solution and temporal moment analysis2018In: Journal of Hydrology, ISSN 0022-1694, E-ISSN 1879-2707, Vol. 562, p. 290-304Article in journal (Refereed)
    Abstract [en]

    A new simple and robust solution, based on uniform steady-state flow velocity, is developed for the problem of solute transport in a fracture-matrix system with a finite penetration depth of a radioactive contaminant into the rock matrix. The solution is an extension of Liu et al. (2017) to finite penetration depth and an alternative solution strategy to the problem solved by Sudicky et al. (1982). The solution takes the form of a convolution of two functions. The first function describes the probability density function of the residence time distribution of a conservative solute resulting merely from advection and Fickian dispersion. The second function is actually the impulse response of the fracture-matrix system in the case of a plug flow without any hydrodynamic dispersion. As a result, the effects of Fickian dispersion and matrix diffusion on solute transport are decoupled, and thus the resulting breakthrough curve can be analyzed in terms of those two functions. In addition to this, the derived Péclet numbers of those two functions, based on temporal moments, are also found to be associated with the derived Péclet number of the resulting breakthrough curve. By comparing the Péclet numbers of those two functions, the contribution of Fickian dispersion and matrix diffusion to solute spreading is determined in a straightforward way. This can aid to find out the dominating mechanism on solute transport, and therefore the performance of breakthrough curve.

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