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DIVISION S-1 - SOIL PHYSICS

Numerical Analysis of Transport of Trifluralin From a Subsurface Dripper

^a Department of Environmental Physics and Irrigation, Institute of Soils, Water and Environmental Sciences Agricultural Research Organization The Volcani Center, Bet Dagan 50250, Israel
^b Department of Environmental Physics and Irrigation, AGRA Earth & Environmental Ltd., 160 Traders Blvd. East, Suite 110, Mississauga, ON, L4Z 3K7 Canada
^c Department of Soil Physical & Environmental Chemistry, Institute of Soils, Water and Environmental Sciences Agricultural Research Organization, The Volcani Center, Bet Dagan 50250, Israel

* Corresponding author (vwrosd{at}volcani.agri.gov.il)

	ABSTRACT

TOP ABSTRACT INTRODUCTION THEORY RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
The transport of a pulse of trifluralin (2,6-dinitro-N,N-dipropyl-4-[trifluoromethyl] benzenamime) applied via a subsurfacedripper was analyzed numerically. Results of the analyses suggest that the movement and spread of trifluralin in the soil is considerably retarded by its strong adsorption to the solid phase of the soil. This is particularly so in soils which contain aconsiderable fraction of organic C and in fine-textured (clayey) soils with low hydraulic conductivity and high water retentivity. Water uptake by plant roots and the resultant rapid decrease of water velocity with increasing distance from the dripper restricts further the downward movement of trifluralin and its potential to pollute the groundwater. The presence of dissolved organic matter (DOM) in the irrigation water may enhance both the movement and the spread of trifluralin in the soil, particularly in coarse-textured soils with a relatively small fraction of organic C. Because of the strong adsorption of trifluralin to the soil, its concentration in the aqueous phase of the soil is very low and it decreases further with increasing time because of degradation and nonequilibrium sorption. This is particularly so in coarse-textured soils with a relatively large fraction of organic C. Nevertheless, results of the analyses suggest that for soils of quite widely differing textures and organic C contents, a trifluralin concentration of c_t = 10^-6 kg m^-3 may persist in the vicinity of the dripper for a relatively long period of time (90 d) even with relatively small applied mass (3 x 10^-5 kg).

Abbreviations: 3-D, three-dimensional • CDE, convection dispersion equation • DOM, dissolved organic matter • HOC, hydrophobic organic compounds • PPCG, polynomial preconditioned conjugate gradient

	INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORY RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
TRIFLURALIN which is a potentially hazardous chemical, is a soil-active preemergence herbicide that has been extensively used to control annual weeds. Its primary mode of action is by affecting the physiological growth processes associated with root growth and elongation. Most of the studies conducted to determine the effect of trifluralin on root growth used relatively high trifluralin concentrations (Talbert, 1965; Hackskaylo and Amato, 1968; Mallory and Bayer, 1972). Thus, no minimum concentration has been reported below which plant roots grow and divide normally. In a recent study (Ganmore-Neumann and Gerstl, 1996), it was found that concentrations as low as a few 10^-6 kg m^-3 could inhibit corn (Zea mays L.) root growth and elongation.

In recent years trifluralin has been used with much success to prevent clogging of subsurface drip emitters by plant roots. In initial studies, commercially available trifluralin was applied via the irrigation water and was found to remain in the immediate vicinity of the emitter. However, degradation of the chemical and ensuing irrigations that leached the material from the emitter zone reduced its effectiveness. Quantitative descriptions of the fate and transport of trifluarlin in the soil, therefore, are essential for the management of this potentially hazardous chemical in the ecosystem with the aims of maximizing its efficiency to prevent clogging of subsurface drip emitters and minimizing the potential of drainage water to pollute underlying groundwater supplies. To the best of our knowledge, there has been no attempt to quantify the fate and transport of trifluarlin in the soil.

The general objective of our study is to investigate the fate and transport of trifluralin applied to the soil via a subsurface dripper. The specific objectives of this study, were: (i) to investigate the effects of the soil hydraulic properties, the fraction of organic C in the soil and the concentration of DOM in the irrigation water on the fate and transport of trifluralin for a given applied mass of trifluralin and a given dripper discharge, and (ii) to assess the effect of the aforementioned characteristics of the soil and the irrigation water on the persistence of trifluralin in the vicinity of the subsurface dripper, and on its potential to pollute underlying groundwater supplies.

To pursue these objectives, we used the Richards equation to describe the flow, and the convection–dispersion equation (CDE) with a bicontinuum sorption model to describe the transport, modifying an efficient numerical method to solve the pertinent partial differential equations (Russo et al., 1998). The present study is a numerical experiment that provides detailed information on the consequences of characteristics of the soil and the irrigation water for the transport of trifluralin under realistic conditions. At the price of reduced generality, this approach circumvents most of the stringent assumptions of theoretical studies and facilitates analysis of simplified yet realistic situations, at a fraction of the cost of physical experiments.

	THEORY

TOP ABSTRACT INTRODUCTION THEORY RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
The Physical Domain and the Simulated Scenario
We considered the movement of trifluralin from a subsurface dripper in a flow domain in the shape of a parallelepiped consisting of a rigid, homogeneous, and isotropic soil with a prescribed initial pressure head, _i. A scheme of the flow domain is depicted in Fig. 1 . Water is infiltrated into the soil from a subsurface dripper by an imposed time-dependent discharge, [F = Q, t^'_j < t < t^''_j, F = 0, elsewhere], where Q is the dripper discharge, t^I = t^''_j - t^'_j is the duration of an irrigation event, tⁱ = t^'_j - t^''_j-1 is the time interval between successive events, j = 1 to NI, NI is the number of events, and t^I + tⁱ is the duration of an irrigation cycle.

View larger version (20K): [in this window] [in a new window]   Fig. 1. Scheme showing the simulation domain.

A single trifluralin pulse of duration t₀, with concentration C₀, invades the soil via the subsurface dripper source. The application of the trifluralin pulse is followed by successive daily irrigations with solute-free water. There is no solute transport across the upper-horizontal face of the flow domain, nor across the vertical faces of the flow domain for which the normal derivatives of the trifluralin concentration vanish. In addition, zero-gradient boundary is specified for the trifluralin concentration at the lower horizontal face of the flow domain.

It should be emphasized that for homogeneous and isotropic soil and root effectiveness function, the flow and transport problem can be formulated as an axisymmetric model described by the cylindrical coordinates, x₁ and r = . The model that we developed in the past (Russo et al., 1994; 1998) was modified for the present study, however, and is formulated as a 3-D model involving the three Cartesian coordinates x₁, x₂, x₃. The latter is much more versatile than the axisymmetric model. Although there is increased computer time, it can deal with the general case in which the soil and the root effectiveness function are nonhomogeneous and anisotropic. Furthermore, it can deal with other shapes of sources (e.g., line source), and with multiple sources and sinks.

Governing Partial Differential Equations
Water flow is described by the Richards equation, the physical parameters of which are the soil hydraulic properties. Transport is described by the CDE with a bicontinuum sorption model. The reactive solute may exchange with both the solid and the gaseous phases of the soil and may undergo degradation (chemical or biological) in both the aqueous and the solid phases. The dissolved and the gaseous phases are assumed to be in equilibrium in accordance with a modified Henry's law. The exchange between the liquid and the solid phases is a nonequilibrium sorption process described by a bicontinuum sorption model. This model assumes that the sorption occurs in two types of domains, an instantaneous equilibrium type and a reversible, rate-limited type; they are characterized by a solid–liquid partition coefficient, and a first-order rate coefficient, respectively.

In a Cartesian coordinate system, assuming isotropy, the mixed form of the Richards equation, governing saturated–unsaturated flow in the presence of water uptake by plant roots, is

[1]

where = (m³ water m^-3 soil) is the volumetric water content; = (m water) is the pressure head; K = K is the hydraulic conductivity (scalar); x = (m) is the spatial coordinate vector (x₁ is directed vertically downwards); t is time (d); and S_w = S_w is a sink term representing water uptake by plant roots (d^-1).

Similarly, assuming that the transport volume comprises the entire aqueous phase of the soil, , the two-region CDE governing the transport of the reactive solute is:

[2a]

[2b]

where c (kg m^-3) is the resident concentration of solute in the aqueous phase; s (dimensionless) is the instantaneous mass fraction of solute sorbed according to first-order kinetics; f is the mass fraction of the solid phase that is in instantaneous sorption equilibrium with the solute in the aqueous phase; K_d (m³ kg^-1) is the liquid–solid partitioning coefficient; _b (kg m^-3) is the bulk density; µ (d^-1) is the first-order degradation rate coefficient; k (d^-1) is the first-order mass transfer rate coefficient; K_h (dimensionless) is a dimensionless form of Henry's constant; u_i (i = 1,2,3) (m d^-1) are components of the pore water velocity vector; and D_ij (i,j = 1,2,3) (m² d^-1) are components of the pore-scale dispersion tensor, given (Bear, 1972) as:

[3a]

where _L and _T (m) are the longitudinal and the transverse pore-scale dispersivities; _ij is the Kronecker delta; |u| = ; and D (m² d^-1) is the effective molecular diffusion coefficient, given (Jury et al., 1983) as

[3b]

where D_lw (m² d^-1) and D_ga (m² d^-1) are the liquid diffusion coefficient in water and the gaseous diffusion coefficient in air, respectively, and _s (m³ water m^-3 soil) is the saturated volumetric water content.

Note that at the small k limit, k 0, there is no mass transfer to the region in which solute is sorbed according to first-order kinetics, i.e., s = 0. On the other hand, at the large k limit, k , equilibrium is reached between the region in which the solute is sorbed according to instantaneous equilibrium type and the region in which solute is sorbed according to first-order kinetics, i.e., s = cK_d. Consequently, for these two limits, Eq. [2] reduces to the classical one-region CDE with s = 0 and s = cK_d, respectively.

Boundary and Initial Conditions
For the water flow, the boundary and initial conditions are:

[4a]

[4b]

[4c]

[4d]

[4e]

[4f]

where G is the volume given by G = ₁₂₃, and ₁ = ₁₂ - ₁₁, ₂ = ₂₂ - ₂₁, and ₃ = ₃₂ - ₃₁ are the dripper dimensions along the x₁, x₂, and x₃ axes, respectively.

For the transport, the boundary and initial conditions for the resident concentration, c are

[5a]

[5b]

[5c]

[5d]

[5e]

The corresponding boundary and initial conditions for s are given by:

[6a]

[6b]

[6c]

[6d]

Binding to Dissolved Organic Matter
Dissolved organic matter may interact with hydrophobic organic compounds (HOC) through hydrophobic binding, forming humic solute complexes in the aqueous phase. This phenomenon has been shown (e.g., McCarthy and Zachara, 1989) to increase the apparent solubility of the organic solute. Assuming linear relationships between bound and free solute, the DOM–HOC binding coefficient, k_b can be defined (Rav-Acha and Rebhun, 1992) as:

[7]

where c_b is the concentration of the bound solute, c_fr is the concentration of the free solute and c_dom is the concentration of the DOM.

Following Rav-Acha and Rebhun (1992), an expression for the liquid/solid partitioning coefficient, K_d, which takes sorption of both the free and the bound organic solute into consideration is:

[8]

where K^*_d is the overall liquid/solid partitioning coefficient, and K^fr_d is the liquid/solid partitioning coefficient of the free organic solute.

The Sink Term in Equation [1]
It is assumed here that locally, the rate of water uptake by roots is proportional to the unsaturated conductivity and to the difference between the total pressure head at the root–soil interface, _r, and the reduced water pressure head of the soil, + , where is the osmotic pressure head of the soil solution. According to this approach (i.e., Nimah and Hanks, 1973a; Feddes et al., 1974, Bresler, 1987), the sink term S_w in [1] is:

[9]

where R_e, the root effectiveness function, is proportional to the specific area of the soil–root interface and inversely proportional to the impedance of the soil–root interface; it can be estimated from root distribution data (e.g., Nimah and Hanks, 1973a,b).

Characterization of the Flow and Transport Parameters
The properties of the soil and the chemical that for a given set of boundary and initial conditions, are hypothesized to control the solute spread are the soil hydraulic properties, characterized by the K() and the () relationships; the partitioning coefficient, K_d; the first-order mass transfer rate coefficient, k; the first-order degradation rate coefficient, µ; the dimensionless Henry's constant, K_h; the pore-scale dispersivities, _L and _T; the bulk density of the soil, _b; the liquid diffusion coefficient in water, D_lw; the gaseous diffusion coefficient in air, D_ga; and in the case of DOM, the DOM–HOC binding coefficient, k_b. Regarding the soil hydraulic properties, it is assumed here that the K() and () relationships are described by the van Genuchten (1980) parametric expressions. Ignoring hysteresis and local anisotropy, and considering the pressure head, as the dependent variable, they read:

[10a]

[10b]

where = , is the effective water saturation; _s and _r are the saturated and residual water contents, respectively; K_s is the saturated conductivity; and m are parameters which are related to the soil pore-size distribution; and n = .

Parameters of Eq. [10] for the two different soils used in this study, as well as the other relevant parameters are summarized in Table 1. In addition, values of _L = 2 x 10^-3 m and _T = 1 x 10^-4 m (Perkins and Johnston, 1963), D_lw = 4.3 x 10^-5 m² d^-1, D_ga = 0.43 m² d^-1 (Jury et al., 1983), and f = 0.5 were adopted for both soils.

View this table: [in this window] [in a new window]   Table 1. Properties of the soil Ks, , n, s, r, b and trifluralin Kd, k, Kh, kb and µ.

For each time step, t the CDE (Eq. [2]) governing solute transport in a 3-D flow domain was approximated by an operator-splitting approach (e.g., Konikow and Bredehoeft, 1978; Wheeler and Dawson, 1987). According to this approach, during the first stage of computation, only the advective part of the equation is solved over the time interval, t. During the second stage, the solution obtained in the first stage, becomes the initial condition for solving a pure dispersion equation over the same t. Numerical solution of the advection equation was obtained by a second-order accurate, explicit finite difference scheme proposed by Zaidel and Levi (1980), while dispersive fluxes were approximated by a standard central difference scheme. For more details see the appendix in Russo et al. (1994). Note that the numerical scheme for the one-region CDE model was modified to account for the two-region CDE model (Eq. [2] subject to Eq. [5] and [6]).

The capability of the aforementioned scheme to solve the two-region CDE for mesh Peclet number, Pe, varying from two to infinity, mesh Courant number, Cr, varying from 0.1 to 1, and Damkohler number, Da, varying from 0.01 to 100, was tested using the analytical solution of Eq. [2] for a narrow-pulse input of solute under one-dimensional, steady-state water flow (Sposito et al., 1986). Results of these tests show that the solutions obtained using this procedure are in a very good agreement with the exact solutions for the aforementioned range of Cr, Da, and Pe < 50. Furthermore, there was no apparent oscillations in the solutions, even for Pe , and numerical dispersion seems to be visible only for extremely large Peclet numbers.

A time-invariant root effectiveness function pertinent to a citrus orchard with a complete cover of the soil surface (Mantell and Goell, 1972, p. 16), was considered here. Water uptake by plants was implemented by a maximization iterative approach (Neuman et al., 1975). In this approach, the rate of transpiration per unit area of the soil surface at time, t, given by T_r = S_wdx, is maximized subject to two requirements: (i) the actual rate of transpiration is not allowed to exceed the potential rate of transpiration, T_p and (ii) the total pressure head at the root-soil interface, _r, is not allowed to fall below a critical value, _c, equivalent to the so-called wilting point of the soil–plant system (e.g., _c = -150 m). To simplify the problem, the osmotic pressure head of the soil solution, , was not taken into account in the sink term Eq. [9]. Furthermore, soil evaporation was set to zero, i.e., ET_p = T_p. The potential daily transpiration was taken as time invariant, T_p = 3.6 mm d^-1.

The flow domain which measures L₁ = 0.85 m in the vertical direction and L₂ = L₃ = 0.65 m in the horizonal directions, was discretized into a grid of 51 by 41 by 41 cells, whose size gradually increases from 0.01 m (in the vicinity of the source) to 0.02 m. The movement of a pulse of t₀ of trifluralin, applied via the subsurface dripper was simulated for a single dripper discharge, Q = 0.002 m³ h^-1 , a single trifluralin inlet concentration, C₀ = 0.075 kg m^-3 , and two concentrations of DOM . The dripper was represented by a single cell, the center of which located at (0.255 m, 0.325 m, 0.325 m) with ₁₁ = 0.25 m, ₁₂ = 0.26 m, ₂₁ = ₃₁ = 0.32 m, and ₂₂ = ₃₂ = 0.33 m and ₁ = ₂ = ₃ = 0.01 m.

For both soils, the uniform initial pressure head, _i, was selected as the pressure head, , corresponding to relative conductivity, K_r = = 10^-4. A trifluralin pulse of 12-min duration was applied after 17 min of irrigation with solute-free water, i.e., t₀ = t₂ - t₁ = 0.02014 d - 0.01181 d = 0.00833 d. The trifluralin pulse was followed by irrigation with solute-free water for an additional 0.01736 d (25 min). The total mass of trifluralin entering the flow domain via the dripper was M₀ = 30 mg. The flow and transport simulations proceeded for 90 d, considering daily irrigations (4 mm d^-1) with solute-free water.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION THEORY RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
The movement and spread of trifluralin in the soil are determined by sorption, dispersion, degradation and volatilization processes, and by the velocity field, which itself is controlled by inherent properties of the soil (e.g., saturated hydraulic conductivity, and parameters that relate the unsaturated conductivity, K, to the water saturation, [Eq. 10]), by flow-controlled attributes (e.g., pressure head, []), by the boundary conditions imposed on the flow domain, and by water uptake by plant roots.

To understand the effect of the soil hydraulic properties on the trifluralin transport in the soil properly, the flow regimes associated with the two different soils are illustrated in Fig. 2 . This figure displays contour lines of the simulated pressure head distribution, (x), in the vertical cross section of the soil (located at x = 0.32 m), just after an irrigation event. The pressure head distributions depicted in Fig. 2 were obtained from the solution of Eq. [1] subject to Eq. [4] for Q = 2 l h^-1. Figure 2 clearly demonstrates that for a given dripper discharge, Q, the pattern of the pressure head distribution associated with the sandy soil is quite different from that associated with the clayey soil. In the case of the sandy soil, the capillary forces are relatively small, gravity has a stronger effect and the flow is more concentrated along the vertical axis. As will be shown below, the different flow patterns associated with the different soils manifest themselves in the transport. The trifluralin spreading patterns associated with the two different soils are illustrated in Fig. 3 and 4 . These figures display contour lines of the simulated solute resident concentrations, c, in the vertical cross section of the soil (located at x₃ = 0.32 m) 30 d after the injection of the trifluralin into the soil. They were obtained from the solution of Eq. [2] subject to Eq. [5] and [6], for Q = 2 l h^-1, C₀ = 0.075 kg m^-3 , for two different organic C fractions , and two different concentrations of DOM, c_dom = 0 and c_dom = 0.1 kg m^-3. The exterior contours in Fig. 3 and 4 correspond to c = 10^-7 and the successive contours represent increases by an order of magnitude (i.e., c = 10^-7, 10^-6, 10^-5, and 10^-4 kg m^-3). Figure 3 and 4 clearly demonstrate that for a given dripper discharge, Q, and inlet concentration, C₀, the pattern of the plumes of the trifluralin concentrations is affected by both the hydraulic properties and the organic C content of the soil and by the concentration of the DOM. When the soil is relatively coarse textured and its organic C content is relatively small, the plume of the trifluralin concentration may exhibit considerable spreading and dilution, particularly in the vertical longitudinal direction. The greater solute spreading in the vertical direction associated with the sandy soil than with the clayey soil, stems from the gravity-dominated flow (Fig. 2) and the smaller water content associated with the sandy soil. Consequently, for a given cumulative amount of water applied, the leaching and the accompanying dilution of trifluralin are more significant in the sandy soil than in the clayey soil. This is particularly so in the presence of DOM in the irrigation water.

View larger version (64K): [in this window] [in a new window]   Fig. 2. Contours of the simulated pressure head, , in a vertical cross-section of the soil (parallel to the x1–x2 plane at x3 = 0.32 m) at the end of an irrigation event. Results are depicted for both the sandy (a) and the clayey (b) soils for Q = 2 l/h. The exterior contour corresponds to = -1 and -9.3 m of water for (a) and (b), respectively, and the corresponding contour increments are 0.02 and 0.5 m of water, respectively.

View larger version (38K): [in this window] [in a new window]   Fig. 3. Contours of the simulated aqueous concentration, c, of trifluralin in a vertical cross-section of the soil (parallel to the x1–x2 plane at x3 = 0.32 m). Results are depicted for cdom = 0, t = 30 d and M0 = 30 mg, for the clayey soil (top) and the sandy soil (bottom) for two different values of the fraction of organic carbon in the soil, foc = 0.002 (left) and foc = 0.025 (right). The exterior contour corresponds to c = 10-7 kg m-3 and successive contours differ by a factor of 10.

View larger version (44K): [in this window] [in a new window]   Fig. 4. Contours of the simulated aqueous concentration, c, of trifluralin in a vertical cross-section of the soil (parallel to the x–x2 plane at x3 = 0.32 m). Results are depicted for cdom = 0.1 kg m-3, t = 30 d and M0 = 30 mg, for the clayey soil (top) and the sandy soil (bottom) for two different values of the fraction of organic C in the soil, foc = 0.002 (left) and foc = 0.025 (right). The exterior contour corresponds to c = 10-7 kg m-3 and successive contours differ by a factor of 10.

View larger version (12K): [in this window] [in a new window]   Fig. 5. Normalized degraded mass of trifluralin, Md/M0 as function of elapsed time, t. Note that Md/M0(t) is independent of soil type, fractin of organic C (foc), and cdom.

[11a]

[11b]

[11c]

where M is the total dissolved mass of the solute, R = is the coordinate of the centroid of the solute plume, and S^'_ij (i, j = 1, 2, 3) are second spatial moments, proportional to the moments of inertia of the solute plume. Note that Eq. [11a], [11b], and [11c], respectively, provide measures of the mass, location and spread of the solute plume.

The coordinate of the centroid of the solute plume, R(t) is used to define the effective solute velocity vector, V as the time rate of change of the displacement of the center of mass

[12]

Under the assumption that V is constant, S_ij(t) (i, j = 1, 2, 3) are used to define a generalized effective dispersion coefficient tensor as follows (Aris, 1956)

[13]

The change with elapsed time, t, in the normalized dissolved mass of trifluralin, M_r = , is depicted in Fig. 6 . As expected, because of degradation, the rate of decrease of M/M₀ with increasing t, decreases with increasing t. Note the time fluctuations in M/M₀, originating from the irrigation cycles, are smoothed out as time elapses and the solute plume becomes sufficiently large as compared with the volume of the source. Note also that M/M₀ depends on the soil type and on f_oc and c_dom. When the organic C fraction in the soil is relatively small, the partition coefficient, K_d = K_ocf_oc is relatively small and the mass transfer coefficient, k is relatively large. Consequently, the kinetics of the mass exchange between the aqueous and the solid phases of the soil is rapid, and equilibrium between the aqueous and the solid phases is reached in a relatively short time. In this case, M decreases rapidly, immediately after the application of trifluralin to the soil, and then decreases (because of degradation) at a much slower rate as more time further elapses. On the other hand, when the organic C fraction is relatively large, K_d is relatively large and k is relatively small. Consequently, the total amount of the sorbed trifluralin is larger, and the exchange between the aqueous and the solid phases of the soil is controlled by a nonequilibrium sorption process. In this case, both the initial decrease and the continuing rate of decrease of the dissolved mass of trifluralin with increasing time are larger than in the case of a relatively small fraction of organic C.

View larger version (30K): [in this window] [in a new window]   Fig. 6. Normalized dissolved mass of trifluralin, M/M0 (in %) as functions of elapsed time for the clayey and the sandy soils, for various values of fraction of organic C (foc) and cdom.

The dependence upon t, of the longitudinal vertical component, R₁, of the coordinate of the centroid of the solute plume, R is depicted in Fig. 7 . Note that because the soil is considered here as uniform and isotropic, the transverse components of R, R₂, and R₃ (not shown here) are essentially zero, independently of time. The center of mass of trifluralin is displaced vertically as t increases, in a manner which depends on the soil type and the fraction of organic C in the soil. Generally, R₁ increases with decreasing f_oc and as the soil texture becomes more coarser. Note, however, that even in the case of relatively low f_oc in the sandy soil, after 90 d, the center of mass of trifluralin is displaced vertically by only about 9 cm only. As expected, for given soil type and f_oc, the presence of DOM is shown to enhance the vertical displacement of the trifluralin center of mass, particularly in coarse-textured soils with relatively low organic C content. For example, for the sandy soil, f_oc = 0.002 and t = 90 d, R₁ = 9.2 cm and 12.3 cm, for c_dom = 0 and 0.1 kg m^-3, respectively. In other words, in this case, the presence of DOM increased the vertical displacement of the trifluralin center of mass by 34%.

View larger version (26K): [in this window] [in a new window]   Fig. 7. Longitudinal (R1) component of the coordinate location of the trifluralin center of mass, relative to the position of the dripper (x1 = 25 cm) as functions of elapsed time for the clayey and the sandy soils and for various values of fraction of organic C (foc) and cdom.

View larger version (30K): [in this window] [in a new window]   Fig. 8. Longitudinal (S11) and transverse (S22 and S33) components of the spatial covariance tensor of the trifluralin concentration as functions of elapsed time for the clayey and the sandy soils and for various values of fraction of organic C (foc) and cdom = 0.

View larger version (31K): [in this window] [in a new window]   Fig. 9. Longitudinal (S11) and transverse (S22 and S33) components of the spatial covariance tensor of the trifluralin concentration as functions of elapsed time for the clayey and the sandy soils and for various values of fraction of organic C (foc) and cdom = 0.1 kg m-3.

Note that because the rates of change with time of S₁₁ and R₁ are similar, the longitudinal component, ₁₁ of the effective dispersivity tensor, _ij = , is essentially time-invariant, independent of f_oc and c_dom; ₁₁ 50 and 30 cm, for the clayey and the sandy soils, respectively. The larger effective dispersivity associated with the clayey soil demonstrates the larger capability of fine-textured soils to disperse the solute plume relative to the rate of the displacement of the plume.

The most significant mechanism that controls the fate of the trifluralin in the soil is sorption. Note that in this study it was assumed that the sorption of trifluralin occurs in two types of domain, an instantaneous equilibrium type (fast) and a reversible, rate-limited type (slow). The fraction of equilibrium-controlled adsorbed trifluralin, _eq, and the fraction of kinetically controlled adsorbed trifluralin _neq = 1 - _eq depend on the elapsed time, t, the fraction of organic C in the soil and the soil type. The fraction of equilibrium-controlled adsorbed trifluralin is initially large and decreases with increasing time, while the opposite is true for _neq (Fig. 10) . The rates of change of _eq and _neq with increasing time depend on f_oc, and to a lesser extent on soil type. When f_oc is relatively small both _eq and _neq change rapidly with time and approach constant, asymptotic values. On the other hand, for relatively large f_oc, both _eq and _neq change slowly as time increases, at a rate that decreases with increasing time and as the soil texture becomes coarser. The latter results are to be expected inasmuch as the rapid sorption is controlled by the partition coefficient, _bf_ocK_oc, while the slow sorption is controlled by the first-order mass transfer rate coefficient, k, that in turn, is negatively correlated with f_ocK_oc. The presence of DOM in the irrigation water is shown to increase the rates of change of _eq and _neq with increasing time and to accelerate the approaches of _eq and _neq to their constant, asymptotic values. These results are to be expected because, in the presence of DOM, the partition coefficient diminishes while the mass transfer coefficient increases.

View larger version (25K): [in this window] [in a new window]   Fig. 10. The fraction of the kinetically controlled adsorbed trifluralin neq, as functions of the elapsed time for the clayey and the sandy soils and for various values of fraction of organic C (foc) and cdom.

View larger version (37K): [in this window] [in a new window]   Fig. 11. Positions of given trifluralin concentrations as functions of time relative to the position of the dripper (25, 32, and 32 cm) in the vertical plane (x1x2; x3 = 32 cm) parallel to the x1 axis, above (a and b) and below (c and d) the dripper, and in the horizontal plane (x2x3; x1 = 25 cm) parallel to the x2 axis (e and f), for two different values of fraction of organic C (0.002 and 0.025), M0 = 30 mg and cdom = 0.

View larger version (37K): [in this window] [in a new window]   Fig. 12. Positions of given trifluralin concentrations as functions of time relative to the position of the dripper (25, 32, and 32 cm) in the vertical plane (x1x2; x3 = 32 cm) parallel to the x1 axis, above (a and b) and below (c and d) the dripper, and in the horizontal plane (x2x3; x1 = 25 cm) parallel to the x2 axis (e and f), for two different values of fraction of organic C (0.002 and 0.025), M0 = 30 mg and cdom = 10-7 kg m-3.

The effect of the fraction of organic C in the soil on the distance from the dripper of a given c_t is clearly demonstrated in Fig. 11 and 12. As f_oc increases, the exchange of mass between the aqueous and the solid phases of the soil is more controlled by a nonequilibrium sorption process. Consequently, the rate of decrease of trifluralin concentration in the aqueous phase increases with time, and both the movement and spreading of trifluralin are retarded. Consequently, for a given soil type, the distance from the dripper of a given ct decreases with increasing f_oc. For given soil type and f_oc, the presence of DOM is shown to increase the distance from the dripper of a given c_t. For example, for f_oc = 0.002, c_dom = 0.1 kg m^-3 and t = 90 d in the clayey soil, the horizontal distance from the dripper of c_t = 10^-6 kg m^-3 is 26.3 cm, while the vertical distances from the dripper of c_t = 10^-6 kg m^-3 are 23.7 and 27.3 cm, above and below the dripper, respectively; for the sandy soil the corresponding distances are 23.1, 19.5, and 44.5 cm. This is to be expected, since the partition coefficient diminishes and the mass transfer coefficient increases in the presence of DOM. In other words, as c_dom increases, the adsorbed fraction of trifluralin decreases and the exchange of mass between the aqueous and the solid phases of the soil is less controlled by a nonequilibrium sorption process. Consequently, both the movement and spreading of trifluralin are accelerated and the distance from the dripper of a given c_t increases with increasing c_dom.

	SUMMARY AND CONCLUSIONS

TOP ABSTRACT INTRODUCTION THEORY RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES

 
The main purpose of the present study was to analyze the transport of a pulse of trifluralin applied via a subsurface dripper. The Richards equation and the CDE with a bicontinuum sorption model were used for description of the flow and the transport, respectively. Water uptake by plant roots and the absence or presence of DOM in the irrigation water were considered. The analyses were performed by means of 3-D simulations of the flow and the transport, employing soil hydraulic properties pertinent to clayey and sandy soils, and partition and binding coefficients and first-order degradation and mass transfer rate coefficients pertinent to the chemical. The main results of the present investigation may be summarized as follows:

1. The fate of trifluralin in the soil is mainly controlled by two processes: degradation and sorption. Almost two-thirds of the applied mass of trifluralin is degraded after 90 d, while most of the mass remaining in the soil (98.5 and 99.6% for the clayey and the sandy soils, respectively) is adsorbed to the solid phase of the soil, even when the fraction of organic C in the soil is rather small (f_oc = 0.002). On the other hand, the effect of volatilization on the fate of trifluralin in the soil is negligibly small.
   
2. The change with time of the mass of trifluralin in the aqueous phase of the soil is considerably affected by the fraction of organic C in the soil, which in turn determines the type of the controlling sorption process (nonequilibrium or equilibrium). When f_oc is relatively large, the exchange of mass between the aqueous and the solid phases of the soil is controlled by a nonequilibrium sorption process. In this case, the decrease in the dissolved mass of the trifluralin persists much longer than in the case of relatively low f_oc in which the partition of mass between the aqueous and the solid phases of the soil is essentially controlled by an equilibrium sorption process.
   
3. The movement and spread of trifluralin in the soil are considerably retarded by its strong adsorption to the soil. This is particularly so in soils which contain a considerable fraction of organic C and in fine-textured soils with low hydraulic conductivity and high water retentivity.
   
4. The movement and spread of trifluralin in the soil are enhanced with increasing concentration of DOM in the irrigation water. However, even with a relatively high concentration of DOM (c_dom = 0.1 kg m^-3), which, for example, is much larger than the concentration of DOM in treated sewage water, the effect of DOM on the movement and spread of trifluralin in the soil may be rather limited, particularly in fine-textured soils with relatively high organic C content.
   
5. Because of the strong adsorption of trifluralin to the solid phase of the soil, the concentration of trifluarin in the aqueous phase of the soil is very low; it decreases further with increasing time because of degradation, nonequilibrium sorption, and to a much lesser extent because of leaching in the vicinity of the dripper. This is particularly so in coarse-textured soils with relatively large f_oc. Nevertheless, results of the analyses suggest that for soils of distinctly differing textures and organic C contents, and even with a relatively small applied mass (30 mg), which, for example, is much smaller than the amount of trifluralin applied in practice (125 mg), a trifluralin concentration of c_t = 10^-6 kg m^-3 may be maintained in the vicinity of the dripper for relatively long period of time.
   
6. For soils of distinctly differing textures and organic C contents, the potential of trifluarlin to pollute underlying groundwater supplies is rather small. The downward movement of trifluralin below the subsurface dripper is considerably restricted by the strong adsorption of trifluralin to the solid phase of the soil, and by the rapid decrease of the water velocity with increasing distance from the dripper due to water uptake by plant roots.
   

We would like to stress that the numerical experiments conducted in the present study provide detailed information on the consequences of soil and irrigation water characteristics for the transport of trifluralin under quite realistic conditions; information that, in general, cannot be obtained in practice from field investigations. We would like to emphasize, however, that the conclusions drawn from the present study should be considered with caution, in as much as the presented numerical results are based on several simplifying assumptions.

The assumptions regarding the soil (rigid, homogeneous, and isotropic), the constitutive relationships for unsaturated flow (van Genuchten model), and the transport (the degradation model with a constant, first-order rate coefficient, independent of water content, the bicontinuum sorption model with inverse relationships between the solid-liquid partition coefficient and the first-order rate coefficient, and the model of binding to DOM with linear relationships between bound and free solute) might limit the applicability of the results of the present study. A rigorous analysis of these assumptions, however, would be beyond the limited scope of this study.

	ACKNOWLEDGMENTS

 
This is contribution 625/00 from the Institute of Soils, Water, and Environmental Sciences, ARO, the Volcani Center, Bet Dagan, Israel. Research was supported in part by a grant from the Chief Scientist, Ministry of Agriculture, Israel, and by a grant from Netafim, Drip and Irrigation Products Ltd., Hatzerim, Israel.

Received for publication October 27, 2000.

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