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 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.

ONE-DIMENSIONAL TEMPORALLY DEPENDENT ADVECTION-DISPERSION EQUATION IN POROUS MEDIA: ANALYTICAL SOLUTION

2010 ◽  
Vol 23 (4) ◽  
pp. 521-539 ◽  
Author(s):  
R. R. YADAV ◽  
DILIP KUMAR JAISWAL ◽  
HAREESH KUMAR YADAV ◽  
GUL RANA
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Dispersion Equation ◽  
One Dimensional ◽  
Advection Dispersion
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