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Analytical approximation for nonlinear adsorbing solute transport and first-order degradation

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Abstract

Under some constraints, solutes undergoing nonlinear adsorption migrate according to a traveling wave. Analytical traveling wave solutions were used to obtain an approximation for the solute front shape,c(z, t), for the situation of equilibrium nonlinear adsorption and first-order degradation. This approximation describes numerically obtained fronts and breakthrough curves well. It is shown to describe fronts more accurately than a solution based on linearized adsorption. The latter solution accounts neither for the relatively steep downstream solute front nor for the deceleration in time of the nonlinear front.

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Abbreviations

A :

parameter

c :

concentration [mol/m3]

c *0 :

depth-dependent local maximum concentration [mol/m3]

δc; c 0;c i :

concentration difference, feed, and initial resident concentrations, respectively [mol/m3]

D :

pore scale diffusion/dispersion coefficient [m2/yr]

f :

adsorption isotherm

f′:

derivative off toc

f″:

second derivative off toc

G * :

parameter

K :

nonlinear adsorption coefficient [mol/m3)1−n]

l :

column length [m]

L d :

dispersivity [m]

m :

parameter

n :

Freundlich sorption parameter

P :

function ofc *0

δ q :

change inq [mol/m3]

q :

adsorbed amount (volumetric basis) [mol/m3]

q′:

derivative ofq toc

R :

nonlinear retardation factor

\(\tilde R\) :

retardation factor for concentrationc

R l :

linear retardation factor

〈R(z *)〉:

depth-dependent average retardation factor, for front at depthz *

s :

adsorbed amount (mass basis) [mol/kg]

t :

time [years]

u :

parameter

v :

flow velocity [m]

z * :

downstream front depth [m]

z :

depth [m]

η :

transformed coordinate [m]

η * :

reference point value ofη [m]

Μ :

first-order decay parameter [y−1]

ρ :

dry bulk density [kg/m3]

θ :

volumetric water fraction

ζ :

parameter

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Authors and Affiliations

  1. Department of Soil Science and Plant Nutrition, Agricultural University, PO Box 8005, 6700, EC Wageningen, The Netherlands

    Willem Jan P. Bosma & Sjoerd E. A. T. M. Van Der Zee

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  1. Willem Jan P. Bosma
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  2. Sjoerd E. A. T. M. Van Der Zee
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Bosma, W.J.P., Van Der Zee, S.E.A.T.M. Analytical approximation for nonlinear adsorbing solute transport and first-order degradation. Transp Porous Med 11, 33–43 (1993). https://doi.org/10.1007/BF00614633

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  • DOI: https://doi.org/10.1007/BF00614633

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