scholarly journals Experimental Research on the Thresholds of Scale-Dependent Dispersivity of Solute Transport

Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 3) ◽  
Author(s):  
Ruigang Zhang ◽  
Mingxi Chu ◽  
Yong Liu ◽  
Dun Wu ◽  
Wenyong Zhang
Keyword(s):  
Porous Media ◽  
Solute Transport ◽  
Threshold Value ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Travel Distance ◽  
Asymptotic Model ◽  
Linear Scale ◽  
Advection Dispersion ◽  
Early Arrival

Abstract The conventional advection-dispersion equation (ADE) has been widely used to describe the solute transport in porous media. However, it cannot interpret the phenomena of the early arrival and long tailing in breakthrough curves (BTCs). In this study, we aim to experimentally investigate the behaviors of the solute transport in both homogeneous and heterogeneous porous media. The linear-asymptotic model (LAF solution) with scale-dependent dispersivity was used to fit the BTCs, which was compared with the results of the ADE model and the conventional truncated power-law (TPL) model. Results indicate that (1) the LAF model with linear scale-dependent dispersivity could better capture the evolution of BTCs than the ADE model; (2) dispersivity initially increases linearly with the travel distance and is stable at some limited value over a large distance, and a threshold value of the travel distance is provided to reflect the constant dispersivity; and (3) compared with the TPL model, both the LAF and ADE models can capture the behavior of solute transport as a whole. For fitting the early arrival, the LAF model is less than the TPL; however, the LAF model is more concise in mathematics and its application will be studied in the future.

Experimental Study and Models Comparison for Solute Transport through Riparian Zones

2014 ◽  
Vol 1073-1076 ◽  
pp. 1604-1608
Author(s):  
Zhou Chen ◽  
Jin Guo Wang ◽  
Wen Zhang Zhang ◽  
Jia Hui Shi
Keyword(s):  
Solute Transport ◽  
Riparian Zone ◽  
Tracer Tests ◽  
Breakthrough Curves ◽  
Advection Dispersion ◽  
Early Arrival ◽  
Models Comparison ◽  
Silt Layer ◽  
Better Than ◽  
Peak Value

Solute transport through riparian zone was studied experimentally and numerically with the consideration of silt layer. The silt layer had markable change on flow field and lead to a significant variation of the breakthrough curves (BTCs). BTCs of solute tracer tests show non-Fickian features as early arrival of peak value and long tailings. BTCs were fitted by advection dispersion equation (ADE), mobile and immobile model (MIM) and the continuous time random walk (CTRW) models. MIM and CTRW can fit BTCs better than ADE and MIM fit better on the capture of the peak value and CTRW fit better in description of the long tailing.

Analytical Solution for Solute Transport in Semi-Infinite Heterogeneous Porous Media

2011 ◽  
Vol 312-315 ◽  
pp. 495-499
Author(s):  
B.Q. Deng ◽  
Y.F. Qiu ◽  
C.N. Kim
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Solute Transport ◽  
Integral Transform ◽  
Integral Transforms ◽  
Heterogeneous Porous Media ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Integral Transform Technique ◽  
Linear Decay

Solute transport in porous media concerns advection, dispersion, sorption, and reaction. Since porous media is commonly heterogeneous, the properties of porous media are spatially and temporally variable. In this paper, one dimensional unsteady solute transport in semi-infinite heterogeneous porous media is investigated. Both linear and nonlinear decay is considered. Analytical solution is obtained for linear decay with spatially and temporally diffusion coefficient and velocity by using generalized integral transform technique. The inverse integral transforms are developed for the problems in semi-infinite space based on some weighted functions. Some examples are given to show the application of the method and analytical solutions.

scholarly journals Modelling solute transport in homogeneous and heterogeneous porous media using spatial fractional advection-dispersion equation

2018 ◽  
Vol 13 (No. 1) ◽  
pp. 18-28 ◽  
Author(s):  
G. Moradi ◽  
B. Mehdinejadiani
Keyword(s):  
Sensitivity Analysis ◽  
Solute Transport ◽  
Dispersion Equation ◽  
Dispersion Coefficient ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Average Pore ◽  
Advection Dispersion ◽  
Estimated Parameters ◽  
Heterogeneous Soil

This paper compared the abilities of advection-dispersion equation (ADE) and spatial fractional advection-dispersion equation (sFADE) to describe the migration of a non-reactive contaminant in homogeneous and heterogeneous soils. To this end, laboratory tests were conducted in a sandbox sizing 2.5 × 0.1 × 0.6 m (length × width × height). After performing a parametric sensitivity analysis, parameters of sFADE and ADE were individually estimated using the inverse problem method at each distance. The dependency of estimated parameters on distance was examined. The estimated parameters at 30 cm were used to predict breakthrough curves (BTCs) at subsequent distances. The results of sensitivity analysis indicated that average pore-water velocity and dispersion coefficient were, respectively, the most and least sensitive parameters in both mathematical models. The values of fractional differentiation orders (α) for sFADE were smaller than 2 in both soils. The scale-dependency of the dispersion coefficients of ADE and sFADE was observed in both soils. However, the application of sFADE to describe solute transport reduced the scale effect on the dispersion coefficient, especially in the heterogeneous soil. For the homogeneous soil, the predicting results of ADE and sFADE were nearly similar, while for the heterogeneous soil, the predicting results of sFADE were more satisfactory in comparison with those of ADE, especially when the transport distance increased. Compared to ADE, the sFADE simulated somewhat better the tailing parts of BTCs and showed the earlier arrival of tracer. Overall, the solute transport, especially in the heterogeneous soil, was non-Fickian and the sFADE somewhat better described non-Fickian transport.

scholarly journals Numerical and experimental study on solute transport through physical aquifer model

2021 ◽  
Author(s):  
Muskan Mayank ◽  
Pramod Kumar Sharma
Keyword(s):  
Porous Media ◽  
Numerical Model ◽  
Solute Transport ◽  
Breakthrough Curves ◽  
Time Dependent ◽  
Environmental Concerns ◽  
Transport Parameters ◽  
Spatial Moments ◽  
Advection Dispersion ◽  
Simplifying Assumptions

Abstract Environmental concerns have drawn much research interest in solute transport through porous media. Thus, contaminants of groundwater permeate through pores in the ground, and adsorption attenuates the pollution concentration as the pollutants adhere to the solid surface. Mathematical models based on certain simplifying assumptions have been used to predict solute transport. The transport of solutes in porous media is governed by a partial differential equation known as the advection-dispersion equation. In this study, a two-dimensional numerical model has been developed for solute transport through porous media. Results of spatial moments have been predicted and analysed in the presence of both constant and time-dependent dispersion coefficients. Afterward, a numerical model is used to simulate experimentally observed breakthrough curves for both conservative and non-conservative solutes. Thus, transport parameters are estimated through numerical simulation of observed breakthrough curves. Finally, this model gives the best simulation of observed breakthrough curves, and it can also be used in the field scale.

Pore-scale Mixing and the Evolution from Anomalous to Normal Hydrodynamic Dispersion

2021 ◽  
Author(s):  
Marco Dentz ◽  
Alexandre Puyguiraud ◽  
Philippe Gouze
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Pore Space ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Hydrodynamic Dispersion ◽  
Pore Scale ◽  
Sandstone Sample ◽  
Flow Variability

<p>Transport of dissolved substances through porous media is determined by the complexity of the pore space and diffusive mass transfer within and between pores. The interplay of diffusive pore-scale mixing and spatial flow variability are key for the understanding of transport and reaction phenomena in porous media. We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion: (i) The smoothing of intra-pore velocity contrasts, (ii) the increase of the tortuosity of particle paths, and (iii) the setting of a maximum time for particle transitions. Based on these mechanisms, we derive an upscaled approach that predicts anomalous and normal hydrodynamic dispersion based on the characteristic pore length, Eulerian velocity distribution and Péclet number. The theoretical developments are supported and validated by direct numerical flow and transport simulations in a three-dimensional digitized Berea sandstone sample obtained using X-Ray microtomography. Solute breakthrough curves, are characterized by an intermediate power-law behavior and exponential cut-off, which reflect pore-scale velocity variability and intra-pore solute mixing. Similarly, dispersion evolves from molecular diffusion at early times to asymptotic hydrodynamics dispersion via an intermediate superdiffusive regime. The theory captures the full evolution form anomalous to normal transport behavior at different Péclet numbers as well as the Péclet-dependence of asymptotic dispersion. It sheds light on hydrodynamic dispersion behaviors as a consequence of the interaction between pore-scale mixing and Eulerian flow variability. </p>

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