Journal of Food, Agriculture and Environment

Vol 9, Issue 1,2011
Online ISSN: 1459-0263
Print ISSN: 1459-0255

Using the fractal geometry method for modeling scale factor on dispersivity of adsorbent elements in soil


Hadi Moazed 1, Yaser Hoseini 1*, Abde Ali Naseri 1*, Fariborz Abbasi 2*, Hosain Mohammad Vali Samani 1, Hojat Allah Seddighnejad 3

Recieved Date: 2010-09-08, Accepted Date: 2011-01-12


Better understanding of transport of dissolved chemicals in soils and aquifers is important to evaluate and remediate contaminated soils and aquifers. Solute dispersivity defined from the classical advective–dispersive equation (ADE) was found to increase as the length of a soil column or the soil depth increased. The heterogeneity of soil is a physical reason for this scale dependence. Such transport can be described assuming that the random movement of solute particles belongs to the family of so-called Lévy motions. Recently a differential solute transport equation was derived for Lévy motions using fractional derivatives to describe advective dispersion. Our objective was to test the applicability of the fractional ADE, or FADE, to solute transport in soils and to compare results of FADE and ADE applications. The one-dimensional FADE with symmetrical dispersion included two parameters: the fractional dispersion coefficient and the order of fractional differentiation a, b. The objectives of this paper were to look into the transportation of P from soil columns and determining the function of dispersivity relationship with the column lengths. Dispersivity of different depths from the first experiment has the exponential relationship with length of column. This relation equation is λ = 0.236 × L0.81, in this equation L is the length of column (cm) and λ is dispersivity (cm). In the second experiment we derived λ = 0.341 × L0.66 relationship between the length of column and dispersivity, regression coefficient of the first equation is 86% and for the second one 66%. This showed that in the first experiment we obtained better relationship between dispersivity derived computer program and column experiment. We derived λ = 0.284 × L0.74 equation for all dispersivity and column lengths with 76% regression coefficient.


Fractal, dispersivity, phosphorus, column

Journal: Journal of Food, Agriculture and Environment
Year: 2011
Volume: 9
Issue: 1
Category: Environment
Pages: 762-770

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