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Journal Article

Advective–Dispersive Equation with Spatial Fractional Derivatives Evaluated with Tracer Transport Data All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

F. San José Martínez, Y. A. Pachepsky, W. J. Rawls
Published: 01 February 2009
Vadose Zone Journal (2009) 8 (1): 242–249.
DOI: https://doi.org/10.2136/vzj2008.0037
...F. San José Martínez; Y. A. Pachepsky; W. J. Rawls Abstract The classical model used to describe solute transport in soil is based on the advective–dispersive equation (ADE) in which an analog of Fick's law is used to model dispersion. The fractional ADE (FADE) has been proposed to address...
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View PDF for article title, <span class="search-highlight">Advective</span>–<span class="search-highlight">Dispersive</span> <span class="search-highlight">Equation</span> with Spatial <span class="search-highlight">Fractional</span> Derivatives Evaluated with Tracer Transport Data All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Ratio of RMSEs of the fractional advective–dispersive equation (FADE) and the advective–dispersive equation (ADE) applied to fit the same experimental breakthrough data as a function of the Lévy exponent α at which the FADE gave the best fit when the range of α values was scanned with a 0.05 increment. The experiment numbers correspond to Table 1.

Ratio of RMSEs of the fractional advective–dispersive equation (FADE) and t...

Published: 01 February 2009
F ig . 3. Ratio of RMSEs of the fractional advective–dispersive equation (FADE) and the advective–dispersive equation (ADE) applied to fit the same experimental breakthrough data as a function of the Lévy exponent α at which the FADE gave the best fit when the range of α values was scanned
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Examples of the effect of the Lévy parameter α on the fit of the fractional advective–dispersive equation to experimental breakthrough curves: (a) Exp. 3 in Table 1, □ measured, ○ simulated with α = 2 (classical advective–dispersive equation [ADE]), • simulated with α = 1.15; and (b) Exp. 36 in Table 1, □ measured, ○ simulated with α = 2 (classical ADE), • simulated with α = 1.7.

Examples of the effect of the Lévy parameter α on the fit of the fractiona...

Published: 01 February 2009
F ig . 2. Examples of the effect of the Lévy parameter α on the fit of the fractional advective–dispersive equation to experimental breakthrough curves: (a) Exp. 3 in Table 1 , □ measured, ○ simulated with α = 2 (classical advective–dispersive equation [ADE]), • simulated with α = 1.15; and (b
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Effect of the Lévy exponent α on the accuracy of the fit of the fractional advective–dispersive equation solution to breakthrough curves from selected miscible displacement experiments and on the fitted fractional dispersivity Df and pore water velocity v: (a) experiments of Biggar and Nielsen (1962) with transport of 3H+ and Cl− in Columbia loam, ○ Exp. 1, ∇ Exp. 2, □ Exp. 3, ⋄ Exp. 4 in Table 1; (b) experiments of Nielsen and Biggar (1961) with transport of Cl− in Yolo loam and Columbia silt loam, ○ Exp. 5, ∇ Exp. 6, □ Exp. 7, ⋄ Exp. 8 in Table 1; (c) experiments of Nielsen and Biggar (1961) with transport of Cl− in Oakley sand, ○ Exp. 9, ∇ Exp. 10, □ Exp. 11 in Table 1; and (d) experiments of Rao et al. (1976) with transport of 3H+ in Molokai silty clay loam and Wahiawa silty clay, ○ Exp. 36, ∇ Exp. 37 in Table 1.

Effect of the Lévy exponent α on the accuracy of the fit of the fractional...

Published: 01 February 2009
F ig . 1. Effect of the Lévy exponent α on the accuracy of the fit of the fractional advective–dispersive equation solution to breakthrough curves from selected miscible displacement experiments and on the fitted fractional dispersivity D f and pore water velocity v : (a) experiments
Journal Article

Stochastic Models of Solute Transport in Highly Heterogeneous Geologic Media All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

V. M. Goloviznin, I. A. Korotkin, K. Pruess, V. N. Semenov, O. S. Sorokovikova
Published: 01 November 2008
Vadose Zone Journal (2008) 7 (4): 1207–1217.
DOI: https://doi.org/10.2136/vzj2007.0150
..., the model reduces to the fractional-order advection–dispersion equation model. The model was extended to the multidimensional case with spatial anisotropy and compared with the results of field experiments. FADE, fractional-order advection–dispersion equation MADE, macrodispersion experiment D...
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View PDF for article title, Stochastic Models of Solute Transport in Highly Heterogeneous Geologic Media All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Journal Article

Influence of Shear Displacement on Fluid Flow and Solute Transport in a 3D Rough Fracture

Zhi Dou, Songxuan Tang, Xueyi Zhang, Richeng Liu, Chao Zhuang, Jinguo Wang, Zhifang Zhou
Journal: Lithosphere
Publisher: GSW
Published: 12 November 2021
Lithosphere (2021) 2021 (Special 4): 1569736.
DOI: https://doi.org/10.2113/2021/1569736
..., such as the long tail and the early arrival. Although the best-fitted results of the advection-dispersion equation (ADE) model and mobile-immobile model (MIM) were generally consistent with those of the BTCs, the MIM was more capable than the ADE model for characterizing the shear-induced anomalous behavior...
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Journal Article

Analytical Advection–Dispersion Model for Transport and Plant Uptake of Contaminants in the Root Zone All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

T. H. Skaggs, N. J. Jarvis, E. M. Pontedeiro, M. Th. van Genuchten, R. M. Cotta
Published: 01 November 2007
Vadose Zone Journal (2007) 6 (4): 890–898.
DOI: https://doi.org/10.2136/vzj2007.0124
... system model to remain at manageable levels, it is desirable that subcomponent models be relatively simple and require few input parameters. In this work, we develop an advective–dispersive solute transport equation that includes plant uptake of water and solute and present an analytical solution...
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View PDF for article title, Analytical <span class="search-highlight">Advection</span>–<span class="search-highlight">Dispersion</span> Model for Transport and Plant Uptake of Contaminants in the Root Zone All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Journal Article

Influence of Grain Size Transition on Flow and Solute Transport through 3D Layered Porous Media

Zhi Dou, Xueyi Zhang, Jinguo Wang, Zhou Chen, Yunbo Wei, Zhifang Zhou
Journal: Lithosphere
Publisher: GSW
Published: 26 October 2021
Lithosphere (2021) 2021 (Special 5): 7064502.
DOI: https://doi.org/10.2113/2021/7064502
... Random Walk (CTRW) framework [ 44 ], the Tempered Time Fractional Advection-Dispersion Equation (tt-fADE) model [ 45 ], and the nonequilibrium mobile and immobile (MIM) model [ 46 ]. The nonequilibrium mobile and immobile (MIM) model has been commonly used to describe solute transport through layered...
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Journal Article

Fractal and Multifractal Models Applied to Porous Media All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

E. Perfect, Y. Pachepsky, M. A. Martín
Published: 01 February 2009
Vadose Zone Journal (2009) 8 (1): 174–176.
DOI: https://doi.org/10.2136/vzj2008.0127
... curve data from previously published column studies to evaluate a numerical form of the fractional advection–dispersion equation (relative to the performance of the standard advection–dispersion equation). Although the fractional advection–dispersion equation is more general than the standard advection...
View PDF for article title, Fractal and Multifractal Models Applied to Porous Media All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Journal Article

Determination of Water Saturation in Relatively Dry Porous Media Using Gas-Phase Tracer Tests All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

M. Oostrom, G. D. Tartakovsky, T. W. Wietsma, M. J. Truex, J. H. Dane
Published: 01 May 2011
Vadose Zone Journal (2011) 10 (2): 634–641.
DOI: https://doi.org/10.2136/vzj2010.0101
... to organic matter and to mineral surfaces, primarily associated with the clay and silt fractions. The direct air to solid-phase sorption is not included in the typical derivation of retardation factors from advection–dispersion equations such as shown in Eq. [1] . Alternative equations for tracer...
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View PDF for article title, Determination of Water Saturation in Relatively Dry Porous Media Using Gas-Phase Tracer Tests All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Journal Article

Assessment of Root Zone Nitrogen Leaching as Affected by Irrigation and Nutrient Management Practices

K. Nakamura, T. Harter, Y. Hirono, H. Horino, T. Mitsuno
Published: 01 November 2004
Vadose Zone Journal (2004) 3 (4): 1353–1366.
DOI: https://doi.org/10.2113/3.4.1353
... columns under single (lumped) and split NH 4 –N applications. The column experiments were successfully simulated using Richards' equation and an advection–dispersion model with equilibrium nonlinear sorption conditions and first-order transformation for N speciation. Using the model for the two soils...
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View PDF for article title, Assessment of Root Zone Nitrogen Leaching as Affected by Irrigation and Nutrient Management Practices
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One-Dimensional Modeling of Transport in Soils with Depth-Dependent Dispersion, Sorption and Decay

Jan Vanderborght, Harry Vereecken
Published: 01 February 2007
Vadose Zone Journal (2007) 6 (1): 140–148.
DOI: https://doi.org/10.2136/vzj2006.0103
... . 29 : 4019 – 4030 . Benson , D.A. , S.W. Wheatcraft , and M.M. Meerschaert . 2000 . Application of a fractional advection–dispersion equation . Water Resour. Res . 36 : 1403 – 1412 . Beven , K.J. , D.E. Henderson , and A.D. Reeves . 1993 . Dispersion...
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View PDF for article title, One-Dimensional Modeling of Transport in Soils with Depth-Dependent <span class="search-highlight">Dispersion</span>, Sorption and Decay
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Unsaturated-Zone Modeling: Progress, Challenges, and Applications All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

Robert M. Holt
Published: 01 February 2008
Vadose Zone Journal (2008) 7 (1): 392–393.
DOI: https://doi.org/10.2136/vzj2006.0162br
...' discussion of four approaches for modeling transport: the convection–dispersion equation, the stochastic–convective model, the fractional advection–dispersion equation, and the continuous-time random walk. In Chapter 2, van Genuchten and Šimůnek (“Integrated Modeling of Vadose-Zone Flow and Transport...
View PDF for article title, Unsaturated-Zone Modeling: Progress, Challenges, and Applications All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Journal Article

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

Ruigang Zhang, Mingxi Chu, Yong Liu, Dun Wu, Wenyong Zhang
Journal: Lithosphere
Publisher: GSW
Published: 12 October 2021
Lithosphere (2021) 2021 (Special 3): 7998907.
DOI: https://doi.org/10.2113/2021/7998907
... coefficient ( D f ) in the space fractional advection-dispersion equation (s-FADE) with the dispersion coefficient ( D ) in the advection-dispersion equation (ADE) by six solute transport experiments at three flow rates, and they concluded that the s-FADE model could efficiently explain...
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View PDF for article title, Experimental Research on the Thresholds of Scale-Dependent <span class="search-highlight">Dispersivity</span> of Solute Transport
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Journal Article

Using Groundwater Numerical Simulation To Improve the Accuracy of Electromagnetic Interpretation

Xuelan Li, Diquan Li, Yanhui Dong
Published: 29 May 2018
Journal of Environmental and Engineering Geophysics (2018) 23 (2): 171–181.
DOI: https://doi.org/10.2113/JEEG23.2.171
... groundwater flow of a confined aquifer can be described as ( Panday et al., 2013 ): where K is hydraulic conductivity, h is the pressure head, S s is storage coefficient, t is time, and W is a source term. Then, the one-dimensional fractional advection-dispersion equation for describing non...
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Implications of kinetically controlled mineral-fluid exchange on the geometry of stable-isotope fronts

Rainer ABART, Diego POZZORINI
Published: 01 November 2000
European Journal of Mineralogy (2000) 12 (6): 1069–1082.
DOI: https://doi.org/10.1127/0935-1221/2000/0012-1069
... as predicted from equation (10) is shown in Fig. 1. An initially sharp front at x = 0 is displaced by fluid advection and distended by diffusion/dispersion in the pore fluid. The displacement of the front with respect to its original position is a measure of the time-integrated fluid flux. The distension...
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Nonclassical Transport Processes in Geologic Media: Review of Field and Laboratory Observations and Basic Physical Concepts All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

Leonid Bolshov, Peter Kondratenko, Karsten Pruess, Vladimir Semenov
Published: 01 November 2008
Vadose Zone Journal (2008) 7 (4): 1181–1190.
DOI: https://doi.org/10.2136/vzj2007.0153
... western Norway . J. Struct. Geol . 19 : 563 – 571 . Pachepsky , Ya. D. Benson , and W. Rawls . 2000 . Simulating scale-dependent solute transport in soils with the fractional advective–dispersive equation . Soil Sci. Soc. Am. J . 64 : 1234 – 1243 . Patashinskii , A.Z...
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View PDF for article title, Nonclassical Transport Processes in Geologic Media: Review of Field and Laboratory Observations and Basic Physical Concepts All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Efficient Schemes for Reducing Numerical Dispersion in Modeling Multiphase Transport through Heterogeneous Geological Media All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

Yu-Shu Wu, P. A. Forsyth
Published: 01 February 2008
Vadose Zone Journal (2008) 7 (1): 340–349.
DOI: https://doi.org/10.2136/vzj2006.0076
... strict limitation in time-step size. Among these schemes, the fully implicit method has proven itself to be most effective in handling numerical problems associated with solving highly nonlinear multiphase flow equations. In particular, the theoretical analysis of advective–dispersive transport through...
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View PDF for article title, Efficient Schemes for Reducing Numerical <span class="search-highlight">Dispersion</span> in Modeling Multiphase Transport through Heterogeneous Geological Media All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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Coupled Vadose Zone and Atmospheric Surface-Layer Transport of Carbon Dioxide from Geologic Carbon Sequestration Sites

Curtis M. Oldenburg, André J. A. Unger
Published: 01 August 2004
Vadose Zone Journal (2004) 3 (3): 848–857.
DOI: https://doi.org/10.2113/3.3.848
... ; Stull, 1988 ; Arya, 1999 ). The mean turbulent transport of CO 2 as a passive gas in the surface layer can be described by the advective–dispersive transport equation with variable eddy diffusivities ( K x , K y , K z ) ( Arya, 1999 , p. 137). For the three-dimensional ( x , y , z...
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Approaches to modelling saline intrusion for assessment of small island water resources

A. W. Herbert, J. W. Lloyd
Published: 01 February 2000
Quarterly Journal of Engineering Geology and Hydrogeology (2000) 33 (1): 77–86.
DOI: https://doi.org/10.1144/qjegh.33.1.77
... based on a sharp interface approximation are inappropriate. The current modelling approach is based on the advection–dispersion equation. However, key parameters in this equation are scale, density and problem specific, making the approach difficult to use predictively. The density dependence...
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