Published January, 1996
Phosphorus Transport during Transient, Unsaturated Water Flow in an Acid Sandy Soil J. S. Chen,* R. S. Mansell, P. Nkedi-Kizza, and B. A. Burgoa ABSTRACT
A number of different transport models incorporating various types of time-dependent sorption reactions are reported in the literature for describing P transport in soils. A two-site model with an instantaneous reaction in Type I sites and a kinetic reaction in Type II sites was developed by Selim et al. (1976) and used by others (Cameron and Klute, 1977; De Camargo et al., 1979; Mansell et al., 1993). A model with adsorption and diffusion precipitation processes was used by Van der Zee et al. (1989) to describe the reaction of P with soil. A model with simultaneous reactions of P with different minerals was developed by Lin et al. (1983). Notodarmojo et al. (1991) presented a transport model with two consecutive reactions given in an earlier sorption model by Barrow and Shaw (1979). Among these models, rate coefficients were often assumed to be constant with time. Gerritse (1989) developed a P transport model in which the sorption rate was assumed to be time dependent. Differences between model-simulated and observed P breakthrough curves are commonly reported for miscible displacement experiments with soil columns. Such differences have been attributed to experimental inaccuracies (or inconsistencies) in different experiments performed for parameter assessment (Selim, 1987; Van der Zee et al., 1989), and failure of models to adequately describe transport-sorption processes. Most P sorption studies in soils have been conducted in aqueous soil suspensions using batch reactor or stirred slurry techniques. Unfortunately, soil/solution ratios (7?s/w = mass of soil per volume of water) for aqueous batch suspensions are much smaller than commonly observed for soils under field conditions (Selim et al., 1975; Barrow and Shaw, 1979). In actual soil profiles, /?s/w is equivalent to the ratio p/0, where p is bulk density and 9 is volumetric water content. Thus values of /?s/w for soils under conditions of water saturation tend to be smaller than when unsaturated. Little information has been reported for P sorption in unsaturated soils, especially for P sorption in relatively dry soils when a rainfall event begins. Helyar and Munns (1975) investigated P sorption at a soil water pressure of 33 kPa and reported great variability. Selim et al. (1975) reported that greater P retardation occurred during steady, unsaturated flow in sandy soil than during steady, saturated flow. A transport model for P under transient, unsaturated water flow was reported by Shah et al. (1975) and Tim and Mostaghimi (1989) but due to nonavailability of experimental data it was not validated. Hence, the objectives of this research were to experimentally determine P sorption rate coefficients in unsaturated soils (with different soil-solution ratios) using a parallel twosite kinetics model, to determine the impacts of applied flux and P concentration of aqueous influent on P sorption during constant-flux infiltration into columns of air-dry
Sorbent-sorbate interactions heavily retard the movement of P during water flow in most soils. The effect of soil/solution ratio on sorption kinetics and movement of P during unsteady unsaturated water flow were investigated. A series of batch experiments with soil/ solution ratios ranging from 0.1 to 6.4 Mg m~ 3 were conducted to obtain sorption rate coefficients. Aqueous P solutions (100-800 g m~ 3 ) were applied at two constant fluxes (1.4 x 10~* and 6.9 X 10"' m s"1) to columns of an air-dry spodic soil. The experimental data were simulated with a parallel two-site nonlinear, nonequilibrium transport model during unsteady, unsaturated water flow. Phosphorous sorption followed Freundlich-type reversible kinetics with a very fast reaction occurring in Type I sites and a slow reaction occurring in Type II sites. The sorption reaction of P in batch experiments was satisfactorily described by the model but the rate coefficients varied with the soil/ solution ratio. Experimentally determined rate coefficients described P movement in column experiments at an influx rate of 6.9 x 10"' m s" 1 , but not for the slower influx rate of 1.4 x 10"6 m s"1, hence calibration of rate coefficients was necessary for describing P movement during the slower water influx. We developed a technique for determining rate coefficients under water saturated-unsaturated conditions that provides a way to validate P transport models during transient, unsaturated water flow.
E
XCESSIVE APPLICATIONS of P fertilizers, animal wastes, or treated municipal wastewater to acid, sandy soils with low sorption capacities and high permeabilities create a conducive environment for P leaching during periods of heavy rainfall (Mansell et al., 1991). Downward seepage of P-laden water through unsaturated soil to groundwater, subsequent lateral saturated subsurface flow to streams, and runoff during periods of shallow water tables are the major routes of P entry in the lakes (Mansell et al., 1995), which might deteriorate water quality through eutrophication (Collins and Young, 1987). Sorption of P by soils is a dynamic process and might retard the transport of P during the flow of P-laden water through soils. Phosphorus-soil interactions exhibit kinetic, reversible, nonlinear sorption often with some degree of irreversibility (Selim et al., 1975; Mansell et al., 1993). This process is characterized by a very fast initial transfer of P molecules from solution to sorbed phase, followed by a slow transfer (Barrow, 1983). Quantities of P sorbed during miscible displacement of P-laden solutions in soil columns tend to decrease with increasing water flow velocity (i.e., decreasing contact time) (Selim et al., 1975; De Camargo et al., 1979; Overman and McMahon, 1980). J.S. Chen, Dynamac Corp., 3601 Oakridge Blvd., Ada, OK 74820; R.S. Mansell and P. Nkedi-Kizza, Soil and Water Science Dep., Univ. of Florida, Gainesville, FL 32611; and B.A. Burgoa, Univ. of Tennessee, Knoxville, TN. Florida Agric. Exp. Stn. Journal Series no. R-04647. Received 28 July 1994. ""Corresponding author (
[email protected]. okstate.edu) Published in Soil Sci. Soc. Am. J. 60:42-48 (1996).
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43
CHEN ET AL.: PHOSPHORUS TRANSPORT DURING UNSATURATED WATER FLOW
Transient, Unsaturated Water Flow
where kt and fe are forward and backward rate coefficients (s"1), respectively, for Type I sites, fc3 and ki, are the forward and backward rate coefficients (s"1), respectively, for Type II sites, and n is the Freundlich exponent. Under very long contact or exposure times, the sorbed-phase concentration, S, can be expressed as a Freundlich equilibrium sorption isotherm
The pressure-head-based continuity equation governing onedimensional vertical, transient, unsaturated water flow can be expressed as
5= [10] where KA is the overall sorption distribution coefficient (m3 Mg~' when n = 1) given by
Spodosol soils, and to evaluate a convective-dispersive
transport model to address P-transport behavior in soils. MATHEMATICAL MODEL
dh =
6
[H]
dt
dz dz where h is pressure head (m), t is time (s), z is depth below the soil surface (m), r\(h) is specific water storage capacity (m), and K(h) is hydraulic conductivity (m s"1). Water flux (m s~'), q, through the soil is given by
q=-K(h) --1 .
where K\ and K\\ are sorption distribution coefficients for Type I and II sites, respectively, and 6
[12a]
~ *' — pfc
[2]
[12b] Solute Transport in Soil during Transient, Unsaturated Flow
For unsteady, unsaturated water flow, the initial and boundary conditions are:
The convective-dispersive transport of P during transient, unsaturated water flow can be expressed by
dt
+
ear
=
0dz
0 D
dz 3
_
o
dz
3
where 9 is soil water content (m m" ), p is soil bulk density (Mg m~ 3 ), C is the concentration of P in soil solution (g m"3), 5 is the amount of overall P in the sorbed phase (g Mg"'1), D is the hydrodynamic dispersion coefficient (m2 s"1), and o = q/Q is the pore velocity (m s"1)- The parameters 9(z,r), D(z,t), and u(z,0 are variables in space and time. A parallel two-site sorption-desorption kinetics model by Selim et al. (1976) assumed that a fraction (/) of adsorption sites interact rapidly with the solute molecules in solution (Type I sites) and the remaining fraction (1 - /) of sites interacts more slowly with the solute in solution (Type II sites). The total P concentration in the sorbed phase, S, is given as the sum of P sorbed by these two types of sites: f* S = OSi +i Su
r A ~i
Si=fS
[5]
[4]
and 5n = (l-/)5 [6] where Si and Stt are the amounts of P absorbed at Type I and II sites, respectively. The overall rate of sorption is expressed as the sum of sorption rates for the sites having fast and slow reactions: 9S _ dSi
dSn
[7]
dt ~ dt dt Freundlich-type kinetics were used to provide expressions for Types I and II sorption rates, respectively,
[8] dS
0
_„
—-u = -k3C" dt p
[9]
/
0 = 61 C=Ci 5 = Si
forz > OaU = 0 [13a] f o r z > 0 a t r = 0 [13b] for z > 0 at t = 0 [13c]
q = qo
atz = 0 f o r f > 0
qoC0 = qC- DdC/dz
[13d]
at z = 0 for * > 0
[13e]
: 0 [13f]
' * 0 [13g] where the subscript i denotes an initial value for that variable,
