Application of Triple Porosity Nonequilibrium Model to Simulate Fate of Solute through Heterogeneous Soil Column
Publication: Journal of Hazardous, Toxic, and Radioactive Waste
Volume 26, Issue 1
Abstract
This study presents the application of a triple-porosity nonequilibrium model (TPNE) trifurcating the liquid phase within representative elementary volume (REV) in a saturated porous medium. The model accounts for both physical and chemical nonequilibrium conditions to capture the fate of solute through a porous medium. The governing equation is numerically solved using the finite volume method and validated with semi-analytical solution of dual advection dispersion equation (DADE). Temporal moment analysis is carried out to demonstrate the model's response for a range of Peclet and Damkohler numbers. The sensitivity of number of input parameters is highlighted using global sensitivity analysis. A sensitivity-based model calibration using parameter estimation package (PEST) is employed to describe observed BTC through a heterogeneous soil column. The TPNE model captured the skewed BTC with enhanced accuracy compared with mobile immobile (MIM) model. It is concluded that TPNE model is capable of capturing the detailed signature of the various processes of a skewed breakthrough curve (BTC) having multiple inflection points.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request (extracted graphical data, numerical code, optimization algorithm).
Acknowledgments
We sincerely acknowledge the funding support from MOES project number MoES/PAMC/H&C/81/2016-PC-II.
Notation
The following symbols are used in this paper:
- Cf
- concentration of solute in macropore region;
- Ci
- normal concentration;
- mean of normal concentrations;
- Cim
- concentration of solute in micropore region;
- Cs
- concentration of solute in mesopore region;
- Csk
- coefficient of skewness;
- d
- mean arrival time;
- d2
- variance;
- dispersion coefficient in macropore region;
- Dm
- Damkohler's number;
- dispersion coefficient in mesopore region;
- Ff
- instantaneous sorption fraction in macropore region;
- ff
- fraction of sorption site available for macropore region;
- Fim
- instantaneous sorption fraction in micropore region;
- fim
- fraction of sorption site available for micropore region;
- Fs
- instantaneous sorption fraction in mesopore region;
- fs
- fraction of sorption site available for mesopore region;
- Kf
- equilibrium sorption coefficient in the macropore region;
- Kim
- equilibrium sorption coefficient in the micropore region;
- Ks
- equilibrium sorption coefficient in the mesopore region;
- L
- length of the medium;
- Mn
- nth temporal moment of the origin;
- N
- sample size;
- p
- number of parameters in the model plus 1;
- Pe
- Peclet number;
- q
- Darcy flux of mobile region for MIM model;
- R2
- determination coefficient;
- Rim
- retardation factor of micropore region;
- Rs
- retardation factor of mesopore region;
- Sf2
- rate limited sorbed solute conc. for macropore region fluid;
- Sim2
- rate limited sorbed solute conc. for micropore region fluid;
- Ss2
- rate limited sorbed solute conc. for mesopore region fluid;
- α
- longitudinal dispersivity;
- θf
- porosity of the macropore region (fast region);
- θim
- porosity of the micropore region (immobile region);
- θm
- porosity of mobile region for MIM model;
- θs
- porosity of the mesopore region (slow region);
- μn
- normalized nth temporal moment with zeroth temporal moment;
- ρb
- bulk density of porous media;
- σ2
- residual sum of squares per sample size;
- ω
- mass transfer coefficient between mobile and immobile region for MIM model;
- ωim
- solute mass transfer rate b/w mesopore and micropore region; and
- ωsf
- solute mass transfer rate b/w mesopore and macropore region.
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Journal of Hazardous, Toxic, and Radioactive Waste
Volume 26 • Issue 1 • January 2022
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© 2021 American Society of Civil Engineers.
History
Received: Mar 12, 2021
Accepted: Jun 13, 2021
Published online: Sep 20, 2021
Published in print: Jan 1, 2022
Discussion open until: Feb 20, 2022
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