Journal of Contaminant Hydrology 158 (2014) 14–22
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Predicting release and transport of pesticides from a granular formulation during unsaturated diffusion in porous media Marcos Paradelo a,b,⁎, Diego Soto-Gómez a, Paula Pérez-Rodríguez a, Eva Pose-Juan c, J. Eugenio López-Periago a a b c
Soil Science and Agricultural Chemistry Group, Department of Plant Biology and Soil Science, Faculty of Sciences, University of Vigo, E-32004 Ourense, Spain Department od Agroecology, Faculty of Science and Technology, Aarhus University, Blichers Allé 20, P.O. Box 50, DK-8830 Tjele, Denmark Institute of Natural Resources and Agrobiology of Salamanca (IRNASA-CSIC), 37008 Salamanca, Spain
a r t i c l e
i n f o
Article history: Received 5 February 2013 Received in revised form 20 July 2013 Accepted 28 October 2013 Available online 16 December 2013 Keywords: Soil pesticide transport Diffusion Controlled release Formulation Soil Agrochemicals
a b s t r a c t The release and transport of active ingredients (AIs) from controlled-release formulations (CRFs) have potential to reduce groundwater pesticide pollution. These formulations have a major effect on the release rate and subsequent transport to groundwater. Therefore the influence of CRFs should be included in modeling non-point source pollution by pesticides. We propose a simplified approach that uses a phase transition equation coupled to the diffusion equation that describes the release rate of AIs from commercial CRFs in porous media; the parameters are as follows: a release coefficient, the solubility of the AI, and diffusion transport with decay. The model gives acceptable predictions of the pesticides release from commercial CRFs in diffusion cells filled with quartz sand. This approach can be used to study the dynamics of the CRF-porous media interaction. It also could be implemented in fate of agricultural chemical models to include the effect of CRFs. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Controlled-release formulations (CRFs) are mixtures of one or more active ingredients (AIs) with a carrier. CRFs are designed to enhance the application of the pesticide to crops and the effectiveness of the pesticide (Collins et al., 1973). Granulates are a very common type of CRF used to regulate the release of AIs into the soil and to control soil-borne diseases within the natural variability of both the soil and rainfall. Therefore, studies examining the mechanisms that control the release of an AI and its transport in soil are of particular interest. The ability to model the coupled release and transport of AIs would facilitate the development of new CRFs, provide new methods to validate their effectiveness and improve existing methods for environmental risk assessments of pesticide usage. A variety of studies on the release of agricultural chemicals from CRFs have been published. These include field-scale studies that have shown that commercial starch-encapsulated ⁎ Corresponding author. E-mail address: [email protected] (M. Paradelo). 0169-7722/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jconhyd.2013.10.009
formulations of atrazine decrease pesticide losses in leachates and increase its persistence in soil (Gish et al., 1994). The behavior of different types of formulations has also been described. For example, commercial formulations of alachlor, atrazine and fenamiphos affect the potential of these pesticides to become water pollutants under severe rainfall conditions (Davis et al., 1996). A sepiolite-gel matrix CRF has been found to significantly decrease the leaching of metribuzin in soil column tests (Maqueda et al., 2008). Atrazine release from alginate-based CRFs in soil columns decreased regarding application of water suspension of herbicide (Malyszka and Jankowski, 2004). A decrease in the rate of the release of an alginate-based CRF of alachlor into the soil has been observed with a decrease in the soil water potential, suggesting a diffusion-controlled release rate (Nasser et al., 2008). The use of a pillared clay-controlled release formulation of alachlor can increase the persistence of alachlor in the soil (Gerstl et al., 1998). More recently, the use of modified montmorillonites as carriers has been shown to decrease the potential losses of simazine (Cornejo et al., 2008), fluometuron (Gámiz et al., 2010) and other anionic herbicides (Undabeytia et al., 2003).
M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
The influence of CRFs on pesticide losses by leaching has been studied using field-deployed lysimeters together with rainfall simulations (Potter et al., 2010); these authors reported that the use of a CRF with a clay-alginate polymer can decrease metolachlor leaching. Organo-clay formulations influence the bioavailability of AIs via their adsorption of AIs (Sánchez-Verdejo et al., 2008; Trigo et al., 2009). Ligninbased CRFs can decrease the leaching losses of isoproturon, imidacloprid and cyromazine (Garrido-Herrera et al., 2009). A physically based model to describe release of AIs from membrane coated CRFs in free water was reported (Shaviv et al., 2003a; Shaviv et al., 2003b). The classical description of controlled release process is the Higuchi's model (Higuchi, 1961) which defines three stages: i) a lag period during which water penetrates and dissolve the AI, ii) a linear release when water penetration and AI release occur together and, iii) a decaying release due to the depletion of the AI into the granule. Since a complete implementation of the Higuchi's model can be cumbersome for practical purposes, simplifications to model controlled release of agrochemicals are often used in several fields. A simplification assuming that release can be as a pseudo-first order kinetics was used to test experimental CRFs of carbofuran in soil (Choudhary et al., 2006). Another approach assumes that release is controlled by a solubilizationlimited process and decay of the AI (Collins et al., 1973). This is only valid if transport is negligible regarding the flux rate; such in the case of granules submerged in water, but may not be valid for unsaturated soil. Empirical release models and closed forms of physically based release equations have been developed (Ritger and Peppas, 1987), but these cannot reproduce the influence of varying soil moisture conditions in the field. In addition, changes in the pore water velocity have influence on the time course of the release rate of AI from CRFs (Paradelo et al., 2012). A full mathematical description of the release process should reproduce all the environmental effects described above, but this approach is very demanding in terms of computation. Therefore, it is desirable to provide an efficient approach to model the pesticide release from CRF in varying moisture conditions. The objective of this paper is to propose a simpler approach as a tool to simulate the controlled release of pesticides buried in soil. This paper focuses on modeling the release of pesticides from uncoated granulated CRFs in porous media. The model was compared with diffusion experiments of carbofuran and fenamiphos CRFs embedded in sand diffusion cells under unsaturated moisture conditions.
15
where k1 is the specific rate, and SI is the saturation index of the pesticide, A V−1 is the relationship between the area of surface contact (A) and the volume (V) of the solid per unit of mass. The values of m0 and m are the initial and actual (at time t) mass of the solid phase of the AI in the granules, respectively, and b is a shape factor of the granule. 2.2. Transport model If the pesticides react with the porous matrix, the expression for diffusion with linear adsorption model and first order decay in the liquid phase takes the form: ρ K ∂c ∂ ∂c ∂c 1þ b D ¼ D þ s θ ∂t ∂t ∂x ∂x
ð2Þ
where ρb is the bulk density of the porous matrix, θ is the water content on a volume basis; KD is the linear coefficient partition, c is the resident concentration in the liquid phase; t is time; x is the distance; D is the effective diffusion coefficient in the pores porous matrix, given by D = θ τ D0, where D0 is the molecular diffusion coefficient for infinite volume dissolution and τ is the tortuosity factor calculated by the Millington and Quirk formula (Millington and Quirk, 1961), that is valid for an isotropic porous medium granular matrix (Radcliffe, 2010): 7=3
τ¼
θ θ2s
ð3Þ
where θs is the saturated water content. For our diffusion cells τ = 0.17 (Table 2). If the pesticide is linearly adsorbed the solid/liquid equilibrium partition coefficient KD can be used to calculate the linear retardation term in the left hand of Eq. (2) 1 þ ρb θK D . The ∂cs/∂t is the sink rate to account the removal rate of the pesticide from pore water by degradation, the subscript s indicates the concentration depleted in the liquid phase. Using the appropriate initial and boundary conditions that meet the conditions imposed in the diffusion experiments, numerical solutions of Eq. (2) can be obtained. Modeling of the redistribution of unreactive Br− is better done by using analytical solutions of the non-reactive diffusion (Crank, 1975): δc δ2 c ¼D 2: δt δx
ð4Þ
If the domain is defined by the impermeable boundaries at x = 0 and x = L, being L the length of the cell, Eq. (4) can be solved for diffusion cells with the initial conditions:
2. Materials and methods 2.1. Release kinetics model
cð0 ≤ x b L=2; t ¼ 0Þ ¼ c0 The solubilization kinetics was modeled by a phase transition kinetics equation that was proposed by other authors to model the solubilization kinetics of minerals (Parkhurst and Appelo, 1999). The rate of the phase transition during the solubilization takes the form:
dm A m ¼ −k1 dt V m0
b
SI
1−10
and cðL ≥ x ≥ L=2; t ¼ 0Þ ¼ 0: If diffusion does not reach the ends of the cell the boundary conditions are
ð1Þ
cðx ¼ 0; t N 0Þ ¼ c0
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in Tomlin (2009). Granules between 1 and 2 mm in diameter of each formulation were used in the release experiments. Their composition was carbofuran (about 5%) and a mixture of violet crystal used as a tint in matrix of calcium carbonate and carboxy methyl cellullose as aglomerant (95% in weight). Fenamiphos takes the form of white–gray granules containing 10% of active ingredient. Visual inspection indicated that CRF granules are equant and angular in shape, and non coated. Granules are very cohesive after a month immersed in deionized water. The AI content in all CRFs was determined in triplicate in separate samples by the method described by Fernández-Pérez et al. (2005). The concentration of the AI in granules was measured in quintuplicate (5 samples each containing 50 mg of granules). Technical-grade carbofuran and fenamifos with purity higher than 90% were supplied by Riedel-de Haën (Seelze-Hannover, Germany). It was used for quantification standards and in testing the diffusion of carbofuran without the influence of CRF.
and cðx ¼ L; t ≥ 0Þ ¼ 0: And the analytical solution is c ¼ 0:5 erfc c0
x pffiffiffiffiffiffi 2 Dt
ð5Þ
where c0 is the concentration in the half-cell charged with solute before the diffusion starts. For larger diffusion times, the concentration change reaches the impermeable ends of the cell, the concentration gradient becomes zero and the boundary conditions are ∂c= ∂xðx ¼ 0; t ≥ 0Þ ¼ 0; ∂c= ∂xðx ¼ L; t ≥ 0Þ ¼ 0 and the solution is (Crank, 1975): " c ¼ c0
∞ nπ n π x 1 2X 1 2 2 2 þ sen exp −Dn π t=L cos 2 π n¼1 n 2 L
2.4. Water release experiments
#
The rate of the solubilization of the AI in a CRF can be limiting in the release in porous media. Kinetic release experiments were performed with the stirred water tank method as reported by Fernández-Pérez et al. (2000). Briefly, granules from the commercial formulas containing 25 mg of the active ingredient were added to 100 mL of deionized water in a 250 mL stoppered Erlenmeyer flask. The samples were orbitally shaken at 24 rpm in a thermostatic chamber at 25 ± 1 °C. Aliquots of 1 mL were collected at different time intervals and analyzed using high performance liquid chromatography (HPLC) (Paradelo et al., 2012). These data were used to model the carbofuran release kinetics with a phase transfer equation that uses the saturation index (SI) of dissolved carbofuran and the interface area of the undissolved pesticide into the granule.
ð6Þ Eqs. (5) and (6) can be used to obtain the non-reactive transport parameters for Br− and technical grade pesticide by fitting to experimental data by the Levenberg–Marquardt optimization algorithm (Marquardt, 1963) using the package LM-OPT supplied by Clausnitzer and Hopmans (see Supporting Information S1). The model of release Eq. (1) was used to describe the release of pesticide from the granules, and was included in the numerical solution of the diffusion model Eq. (2) to simulate the concentration of carbofuran in the center of the diffusion cell. Coupling Eqs. (1) and (2) can be used to model the pesticide release and diffusional transport from the CRF granules embedded in the diffusion cells.
2.5. Diffusion experiments 2.3. Characterization of the CRFs The coupled model for the release and transport of carbofuran and fenamiphos was compared with experimental profiles from the diffusion experiments. The study of pesticide release under the no-advection conditions has been performed using the half-cell diffusion method. This consists in determining the concentration profile of a solute in a diffusion cell after an appropriate diffusion time (Flury and Gimmi, 2002). Quartz sand was chosen as a model of unreactive porous media to minimize adsorption and decay. Unsaturated moisture condition was established to mimic the field conditions between rain episodes. The properties of diffusion cells used in all experiments are shown in Table 2.
We used two pesticide formulations based on carbofuran and fenamiphos (Table 1) as CRF models, which were widely used in the control of insects and nematodes as CRF granules that usually are buried in soil at adequate depth. Carbofuran (N-methylcarbamate 0,0-dimethyl 2,3-dihydro-7 benzofuranyl) is a systemic insecticide moderately persistent in soil, with a half-life of 30 to 120 days, and it has a variable degree of mobility depending on the soil characteristics. Fenamiphos (N-ethyl isopropilfosforoamidate and O-(3-methyl 4-methylthiophenyl)) is absorbed well by plant roots in a systemic manner. The main physico-chemical properties of both pesticides are available Table 1 Principal characteristics of active ingredients used in the tests. Name
CAS number
Chemical formula
Molecular weight (g mol−1)
Melting point °C
Water solubility @20 ºC (mg L−1)
a
D0 (cm2 d−1)
Log KOW:
Carbofuran Fenamiphos
1563-66-2 22224-92-6
C12H15NO3 C13H22NO3PS
221.3 303.4
151 46
320 329
0.545 0.424
2.32 3.23
a
Obtained from quantitative relationships between molecular structure and the activity (QSAR) using SPARC program.
M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
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Table 2 Properties of the half-cells used in diffusion experiments. The coefficient of variation is minor than 2.6% in all properties. Length (cm)
Internal diameter (cm)
Mass of quartz sand (g)
Porosity (cm3 cm−3)
Water content (cm3 cm−3)
Bulk density (g cm−3)
Degree of saturation (cm3 cm−3)
a Tortuosity coefficient (τ)
10
1.04
13
0.39
0.21
1.61
0.53
0.17
a
Using the Millington and Quirk equation.
Two sets of diffusion experiments were done. Diffusion experiments of Br− as a nonreactive tracer together with technical grade AIs were done to test the experimental procedure against the theoretical diffusion parameters in the cells and in the absence of other substances (adjuvants) present in the CRFs. Each diffusion cell consisted of two half-cells: one charged with a solution of the technical grade pesticide and KBr (50 mg L−1 pesticide and 0.83 mmol L−1 KBr), the other half-cell contained only 0.83 mmol L−1 KNO3 to minimize the osmotic-driven flow by differences in electrolyte concentrations between cells and charge balance. The water content in the cells was set to 20%. The cells were joined and sealed with electrical tape to prevent evaporation. Immediately, the cells were incubated horizontally in a chamber at 25 °C. Concentration profiles were measured at 15, 30 and 60 days of incubation. Diffusion cells were prepared in triplicate (n = 3). The second set of diffusion experiments was conducted using CRF granules of carbofuran or fenamiphos to examine the simultaneous effect of the release from the granule and the diffusion through the sand. The procedure used in the experiments performed with CRF carbofuran granules is almost identical to that used in the technical grade AIs. The sole difference is that, instead of adding the technical grade AI to one half-cell, the CRF granules were inserted between the contacting faces of a pair of half-cells. The number and weight of the granules calculated to add 50 mg of AI per cell was 5 granules per cell. The granules were uniformly distributed on the contact plane. The concentration profiles were also measured at 15, 30 and 60 days of incubation. Diffusion cells were also prepared in triplicate (n = 3). The coefficient of the diffusion of Br− in water reported in the literature; D0 = 1.797 cm2 d− 1 at 25 ºC (Flury and Gimmi, 2002), and the self-diffusion coefficient D0 of carbofuran (0.545 cm2 d− 1) and fenamiphos (0.424 cm2 d− 1) were estimated from quantitative structure activity relationships
A
(QSAR) using the SPARC chemical computational software (Hilal et al., 2003). 2.6. Chemical determinations The concentration profiles in the diffusion cells were determined by dividing each half-cell into sections of 1 cm in length. Each section was analyzed to measure the concentrations of Br− and pesticides. The bromide concentrations in the aqueous extracts were determined by colorimetry (van Staden et al., 2003) using a segmented flow autoanalyzer (Bran + Luebbe AutoAnalyzer 3, United Kingdom). Carbofuran and fenamiphos concentrations were measured by UV–visible HPLC. HPLC analyses were performed on a Dionex liquid chromatography system (Dionex Corp. Sunnyvale, USA) equipped with a P680 quaternary pump, an ASI-100 autosampler, a TCC-100 thermostated column compartment and a UVD170U detector linked to a PC running Chromeleon version 6.8 (Dionex corp., Sunnyvale, USA). Separations were performed with a Luna C18 (150 mm × 4.6 mm i.d., 5.0 μm particle size) analytical column obtained from Phenomenex (Madrid, Spain) and a guard column (4.0 mm × 3.0 mm i.d., 5.0 μm particle size) containing the same packing material. The mobile phases were ammonium acetate 0.1 M (A) and methanol (B). Isocratic elution 45% A and 55% B was performed at room temperature. The injection volume was set to 50 μL at a flow rate of 1.5 mL min−1. 3. Results and discussion 3.1. Solubilization of the active ingredients in the CRFs Measured richness of AIs in the CRF samples was 4% carbofuran and 10% fenamiphos, the variation coefficient was less than 1.7%. Kinetics of the solubilization of the CRFs in
B
Fig. 1. Cumulative release of carbofuran (A) and fenamiphos (B) from their respective controlled release formulations in water. Symbols represent the concentration of pesticide in water and lines are the prediction obtained using transition phase and degradation equations (Eq. 1), r2 N 0.996.
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M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
Table 3 Kinetic parameters for the transition phase model (Eq. (1)) calculated for the solubilization of active ingredient from CRF. Active ingredient Carbofuran Fenamiphos
k1 A V−1 −7
b −7
1.4 10 ± 0.1 10 9.7 10−8 ± 0.1 10−8
1.7 ± 0.02 1.9 ± 0.02
ks −3
−3
9.0 10 ± 0.02 10 1.0 10−7 ± 0.01 10−7
ME
EF
RMSE
CRM
r2
2.79 2.84
0.995 0.964
0.0097 0.0309
0.010 0.091
0.996 0.997
k1 A V−1 phase transition kinetic constant (mol L−1 s−1); b shape factor (dimensionless); ks kinetic constant for sink, second order for carbofuran (L mol−1 s−1), first order for fenamiphos (s−1) ME maximum error (mg L−1); EF model efficiency; RMSE root mean square error; CRM coefficient of residual mass; Pearson's r square.
stirring water (Fig. 1) show a rapid rise in carbofuran concentration, with a maximum achieved after 10 h, with a subsequent decrease with time. For fenamiphos, the release rate was slower than that of carbofuran and the decay of fenamiphos was small. The granules have co-adjuvants that do not dissolve, and the variation in the specific surface area during the release is unknown. To model the release kinetics with Eq. (1) the parameter search procedure involved the simultaneous optimization of two parameters, namely, the quantity given by the expression k1 A V−1 (mol L−1 s−1) and the exponent b in Eq. (1) was solved by numerical integration using the Runge–Kutta method included in PHREEQC chemical computation software (see Supporting Information S2). Only decay of carbofuran in water was incorporated to the model. Good predictions were obtained with a second order model. In the diffusion experiments with technical grade carbofuran the decay rate was much slower than in the CRF. A more detailed analysis of the decay kinetics of the carbofuran in the CRF in water exceeds the scope of this work. Nonetheless, identical results were obtained for the replicates, and the model predictions with the second order
model were in very good agreement with the experimental results. The best-fit parameters of the model of the release of carbofuran and fenamiphos are listed in Table 3, and the predictions obtained with the model with the best fitting set of parameters are plotted in Fig. 1. 3.2. Tests of experimental conditions for diffusion cells Determinations of the moisture profiles resulted in coefficients of variation (CV) that were less than 2.6% (n = 10 segments per half-cell), this error is acceptable and was accounted to the overall experimental error in the mass balance of solutes in the diffusion calculations. The recoveries of Br− and technical grade pesticides, applied in aqueous solutions mixed with sand, were greater than 98% in all cases. This recovery rate is high enough to neglect any retardation in transport. Solute concentration gradients in the half-cells before the diffusion experiments were measured and demonstrated a uniform distribution profile (i.e., no trend along the length of the cell) and CV was less than 4%. The Br− profiles obtained at different incubation times (Fig. 2) show the redistribution of Br− . Experimental profiles were compared with the model of the transport by diffusion (Eq. (4)), by using the analytical expressions Eqs. (5) or (6) as the best for different diffusion times. The computed profiles are shown as lines in Fig. 2. Inverse modeling of the diffusive transport of Br− or pesticide allowed us to obtain their respective effective diffusion coefficients (D) from profile concentrations. The estimated effective diffusion coefficients D for Br− at 15, 30 and 60 d (Table 4) increased with time. However, there were no significant differences between the estimated D for the three time studies. For t = 30 d fitted D = 0.537 ± 0.270 cm2 d−1, and therefore the estimated self-diffusion is D/τ θ = D0 = 1.927 ± 0.15 cm2 d−1. That is the closest value to the selfdiffusion coefficient D0 = 1.797 cm2 d−1. 3.3. Diffusion of technical grade pesticide Fig. 3 shows the concentration profiles of carbofuran and fenamiphos in the pore water after 5, 15 and 30 days of
Table 4 Parameters of the diffusion from tests of KBr for different profiles. D* (cm2 d−1) using the self diffusion for Br− in water at 25 ºC in infinite dilution as D0 = 1.797 cm2 d−1, τ = 0.17 and θ = 0.21.
Fig. 2. Concentration profiles of Br− in pore water (mg L−1) in the diffusion cells after 15, 30, and 60 days in contact. Observed data (symbols) and predicted by the Eq. (4) (lines).
Time (d)
D* (cm2 d−1)
D0* (cm2 d−1)
D*/D0
15 30 60
0.302 ± 0.103 0.537 ± 0.270 0.948 ± 0.305
1.084 ± 0.06 1.927 ± 0.15 3.403 ± 0.17
0.60 ± 0.27 1.07 ± 0.71 1.89 ± 0.81
M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
A
19
B
Fig. 3. Concentration profile (mg L−1 in the pore water) of technical grade carbofuran (A), and fenamiphos (B) after 15, 30, and 60 days in contact. Observed data (symbols) and predicted by the Eq. (4) (lines).
incubation. The fitting of the parameters of the diffusion model to the experimental profiles (Table 5) indicates that the diffusion of carbofuran increased compared to what was expected from the pure diffusion process. The best fitting diffusion coefficient is D = 0.34 ± 0.076 cm2 d−1, which yields a good prediction of the profile (r2 = 0.949), using the value of D0 = 0.545 cm2 d−1 from the QSAR calculations. A better prediction was obtained with Eq. (2) after incorporating a first-order sink term that resulted in a half-life of 112 d; this result is in good agreement with literature data (Tomlin, 2009). Both the reaction mechanisms of transport retardation and decay for carbofuran are in accordance with the conditions of the low reactivity of the quartz sand and the abiotic conditions of the experiments performed in darkness. The model fitting for the diffusion of fenamiphos (Table 5) resulted in a diffusion coefficient (D = 0.983 ± 0.0496 cm2 d−1) that provides a good prediction of the concentration profile (r2 = 0.908). This value is about twice the value estimated from QSAR (D0 = 0.424 cm2 d−1). The surface tension of fenamiphos (47.2 mN m−1) (FOOTPRINT, 2012) can generate a gradient in air liquid interface along the diffusion cell and promotes the
water movement (Karkare and Fort, 1993) that speeds up the transport of fenamiphos. On the other hand, the degradation rate of fenamiphos (half-life of 471 d) was smaller than that of carbofuran. 3.4. Release of the active ingredients from the granular formulation The concentration profiles of carbofuran and fenamiphos released from the CRF at different times are shown in Fig. 4. Profile shapes show the transport of the AIs from the granules placed in the center of the diffusion cell toward the ends of the cells. The shape of the carbofuran profile is two symmetrical hyperbolas that show a large concentration gradient near the source (the location of granules) that is related with its smaller D and the sink rate regarding the fenamiphos. This shape suggests that release of carbofuran is limited by diffusion rate and decay. The shape of the fenamiphos profile at 15 d incubation is more sigmoidal (i.e., small concentration gradients near the granules), indicating a faster diffusion and negligible decay.
Table 5 Fitted parameters of diffusion model for technical grade active ingredient in insaturated quartz sand cells. Active ingredient Carbofuran Fenamifos
D 0.340 ± 0.076 0.983 ± 0.0496
KD
ks −9
b10 b10−9
−3
−3
6.0 10 ± 1.1 10 1.5 10−3 ± 0.3 10−3
ME
EF
RMSE
CRM
r2
11.6 15.0
0.871 0.856
0.029 0.034
−0.07 0.114
0.940 0.913
D diffusion coefficient; KD partition constant, ks kinetic degradation coefficient; ME maximum error (mg L−1); EF model efficiency; RMSE root mean square error; CRM coefficient of residual mass; Pearson's r square.
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M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
Fig. 4. Concentration profiles of carbofuran (A) and fenamiphos (B) released from CRF after 15, 30 and 60 days in the diffusion cells filled with quartz sand at 0.2 v/v water content. Lines represent predictions using the numerical solution of one-dimension diffusion equation coupled to the phase transfer equation. r2 N 0.962 in all cases.
The results were analyzed by modeling using the onedimensional diffusion model by solving coupled Eqs. (1) and (2). This solution was determined with an explicit finite difference scheme centered in space; the model was implemented in the PHREEQC computer program (Parkhurst and Appelo, 1999) (see Supporting Information S2). The initial conditions were stated as follows: the AI is initially in the granules, which occupies a segment of 1 mm in length at the center of the cell (equals to the average diameter of granules), and the concentration in the pore water is zero throughout the domain. The boundary conditions are zero flux at both ends, and the concentration in the center is controlled by the solubilization rate of the CRF in the central segment, using the phase transition equation (Eq. (1)). The kinetics of the degradation of the AI in the aqueous phase was applied to the entire cell, including the interstitial water inside the granules, for t N 0. The parameters used to feed the model were those obtained in independent experiments (Tables 2, 3 and 5), except the kinetic decay parameter ks for carbofuran. The performance indicators of the predictions made by the model are shown in Table 6. In general, the predictions were good, especially the model efficiency indicator. The fitted values of ks decreased over time for the water release experiments (i.e. from 9.0 10−3 L mol−1 s−1 in water to 0.6 10−3 at 15 d diffusion, and to 0.2 10−3 at 60 d diffusion). This behavior agrees with the literature data, which indicate a greater persistence of pesticides in soil than in water (Arias-Estévez
et al., 2008). The predicted profiles of commercial fenamiphos reproduced the sigmoidal shaped profile at t = 15 d. The sensitivity analysis of the concentration profile of carbofuran release to D, k1 and ks is depicted in Fig. 5. Pesticide saturation with respect to the pure phase (10SI) is shown to illustrate the magnitude of the difference between the concentration in solution and the concentration of carbofuran at saturation (SI = 0). The shapes of the profiles demonstrate that diffusion can be a limiting step in the release of carbofuran. The influence of k1 indicates that a value of k1 A V−1 near 10−5 mol L−1 s−1 transport becomes limited by diffusion. These conditions provide a more uniform distribution of carbofuran. Lowering k1 A V−1 from 10−6 to 10−7 mol L−1 s−1 increased the mass of carbofuran near the granule due to the decreased decay rate at lower concentrations; this relationship occurs because the decay kinetics outside of the granule mimic second order. The optimal rate of release is given by k1 A V−1 = 1.4 10−5 mol L−1 s−1, which results in the maximum mass of carbofuran into the pore water of the diffusion cell. Table 6 Overall performance tests of the predictions made by the release model for AI released from CRF within diffusion cells using the parameters in Tables 2, 3 and 5. The parameter fitted was ks for the carbofuran only. Active ingredient
ks
ME
EF
RMSE
CRM
r2
Carbofuran Fenamifos
4.0 10−4 1.0 10−7
11.6 15.0
0.87 0.856
0.0295 0.0336
−0.079 0.114
0.929 0.912
M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
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Appendix A. Supplementary data Supporting Information available: Fitting routine and PHREEQC code used in this work. Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j. jconhyd.2013.10.009.
References
Fig. 5. Sensitivity of the release model with regards to the diffusion coefficient in the porous media (D), and the kinetic parameters k1 and ks. Other parameters were set to the optimum values to carbofuran (Table 5).
4. Conclusions The proposed model coupling release and diffusion processes provided acceptable predictions of the release and redistribution of the active ingredient from the granule to the unsaturated porous matrix. Using a phase transition equation saves large computer calculations required to compute the moving solubilization boundary of the AI inside the granule. Therefore, diffusion-limited or solubilization limited release can be assessed by a rather simple approach. Using an almost inert porous media such as quartz sand improves the reproducibility and reduces the time consuming experiment, but further studies with real soil should be desirable for a better approach to the field conditions. However, the model already incorporates decay and sorption processes and can be suitable using soil matrices. The experimental system and the model presented here can be used to efficiently evaluate the performance of controlled-release formulations. This approach can be used in modeling risk assessment of nonpoint water pollution incorporating the effects controlled release formulations. Acknowledgments This work was funded by the INCITE program (INCITE 08PXIB383190PR, Xunta de Galicia). M. Paradelo and P. Pérez-Rodríguez wish to acknowledge the funding of their work by the Predoctoral Fellowship Program (FPU) of Spain's Ministry of Education, and E. Pose-Juan by Juan de la Cierva contract (JCI-2011-10150) of Spain's Ministry of Science and Innovation, respectively. We also thank Natalia Outeiriño for helping us in the laboratory.
Arias-Estévez, M., López-Periago, E., Martínez-Carballo, E., Simal-Gándara, J., Mejuto, J.C., García-Río, L., 2008. The mobility and degradation of pesticides in soils and the pollution of groundwater resources. Agric. Ecosyst. Environ. 123, 247–260. Choudhary, G., Kumar, J., Walia, S., Parsad, R., Parmar, B.S., 2006. Development of controlled release formulations of carbofuran and evaluation of their efficacy against Meloidogyne incognita. J. Agric. Food Chem. 54, 4727–4733. Collins, R.L., Doglia, S., Mazak, R.A., Samulski, E.T., 1973. Control release of herbicides: theory. Weed Sci. 21, 1–5. Cornejo, L., Celis, R., Domínguez, C., Hermosín, M.C., Cornejo, J., 2008. Use of modified montmorillonites to reduce herbicide leaching in sports turf surfaces: laboratory and field experiments. Appl. Clay Sci. 42, 284–291. Crank, J., 1975. The Mathematics of Diffusion. Oxford University Press, London. Davis, R.F., Wauchope, R.D., Johnson, A.W., Burgoa, B., Pepperman, A.B., 1996. Release of fenamiphos, atrazine, and alachlor into flowing water from granules and spray deposits of conventional and controlled-release formulations. J. Agric. Food Chem. 44, 2900–2907. Fernández-Pérez, M., Villafranca-Sánchez, M., González-Pradas, E., MartinezLópez, F., Flores-Céspedes, F., 2000. Controlled release of carbofuran from an alginate-bentonite formulation: water release kinetics and soil mobility. J. Agric. Food Chem. 48, 938–943. Fernández-Pérez, M., Villafranca-Sánchez, M., Flores-Céspedes, F., GarridoHerrera, F.J., Pérez-García, S., 2005. Use of bentonite and activated carbon in controlled release formulations of carbofuran. J. Agric. Food Chem. 53, 6697–6703. Flury, M., Gimmi, T.F., 2002. Solute diffusion. In: Dane, J.H., Topp, C.G. (Eds.), Methods of Soli Analysis Part 4. Physical Methods. SSSA Book Series, no. 5. SSSA, Madison. Gámiz, B., Celis, R., Hermosín, M.C., Cornejo, J., 2010. Organoclays as soil amendments to increase the efficacy and reduce the environmental impact of the herbicide fluometuron in agricultural soils. J. Agric. Food Chem. 58, 7893–7901. Garrido-Herrera, F.J., Daza-Fernández, I., González-Pradas, E., FernándezPérez, M., 2009. Lignin-based formulations to prevent pesticides pollution. J. Hazard. Mater. 168, 220–225. Gerstl, Z., Nasser, A., Mingelgrin, U., 1998. Controlled release of pesticides into water from clay–polymer formulations. J. Agric. Food Chem. 46, 3803–3809. Gish, T.G., Shirmohammadi, A., Wienhold, B.J., 1994. Field-scale mobility and persistence of commercial and starch-encapsulated atrazine and alachlor. J. Environ. Qual. 23, 355–359. Higuchi, T., 1961. Rate of release of medicaments from ointment bases containing drugs in suspension. J. Pharm. Sci. 50, 874–875. Hilal, S.H., Karickhoff, S.W., Carreira, L.A., 2003. Prediction of Chemical Reactivity Parameters and Physical Properties of Organic Compounds from Molecular Structure Using SPARC. Karkare, M.V., Fort, T., 1993. Water movement in ‘unsaturated’ porous media due to pore size and surface tension induced capillary pressure gradients. Langmuir 9, 2398–2403. Malyszka, T., Jankowski, T., 2004. Controlled release formulations of atrazine produced by tumbling agglomeration. J. Plant Prot. Res. 44, 221–230. Maqueda, C., Villaverde, J., Sopeña, F., Undabeytia, T., Morillo, E., 2008. Novel system for reducing leaching of the herbicide metribuzin using clay-gelbased formulations. J. Agric. Food Chem. 56, 11941–11946. Marquardt, D.W., 1963. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11, 431–441. Millington, R.J., Quirk, J.P., 1961. Permeability of porous solids. Trans. Faraday Soc. 57, 1200–1207. Nasser, A., Mingelgrin, U., Gerstl, Z., 2008. Effect of soil moisture on the release of alachlor from alginate-based controlled-release formulations. J. Agric. Food Chem. 56, 1322–1327. Paradelo, M., Pérez-Rodríguez, P., Arias-Estévez, M., López-Periago, J.E., 2012. Influence of pore water velocity on the release of carbofuran and fenamiphos from commercial granulates embedded in a porous matrix. J. Contam. Hydrol. 142–143, 75–81.
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Parkhurst, D.L., Appelo, C.A.J., 1999. User's Guide to PHREEQC (Version 2)—A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations (99–4259:312). Potter, T.L., Gerstl, Z., White, P.W., Cutts, G.S., Webster, T.M., Truman, C.C., Strickland, T.C., Bosch, D.D., 2010. Fate and efficacy of metolachlor granular and emulsifiable concentrate formulations in a conservation tillage system. J. Agric. Food Chem. 58, 10590–10596. Radcliffe, D., 2010. Soil Physics with HYDRUS: Modeling and Applications. CRC Press, Taylor & Francis Group. Ritger, P.L., Peppas, N.A., 1987. A simple equation for desciption of solute release I. Fickian and non-Fickian release from non-swellable devices in the form of slabs, spheres, cylinders or discs. J. Control. Release 5, 23–36. Sánchez-Verdejo, T., Undabeytia, T., Nir, S., Maqueda, C., Morillo, E., 2008. Environmentally friendly slow release formulations of alachlor based on clay-phosphatidylcholine. Environ. Sci. Technol. 42, 5779–5784. Shaviv, A., Raban, S., Zaidel, E., 2003a. Modeling controlled nutrient release from a population of polymer coated fertilizers: statistically based model for diffusion release. Environ. Sci. Technol. 37, 2257–2261.
Shaviv, A., Raban, S., Zaidel, E., 2003b. Modeling controlled nutrient release from polymer coated fertilizers: diffusion release from single granules. Environ. Sci. Technol. 37, 2251–2256. The FOOTPRINT Pesticide Properties DataBase (PPDB), 2012. Footprint. University of Hertfordshire (http://sitem.herts.ac.uk/aeru/footprint/ index2.htm). Tomlin, C.D.S., 2009. The Pesticide Manual. British Crop Protection Council Publication, Surrey, U.K. Trigo, C., Celis, R., Hermosín, M.C., Cornejo, J., 2009. Organoclay-based formulations to reduce the environmental impact of the herbicide diuron in olive groves. Soil Sci. Soc. Am. J. 73, 1652–1657. Undabeytia, T., Mishael, Y.G., Nir, S., Papahadjopoulos-Sternberg, B., Rubin, B., Morillo, E., Maqueda, C., 2003. A novel system for reducing leaching from formulations of anionic herbicides: clay-liposomes. Environ. Sci. Technol. 37, 4475–4480. van Staden, J.F., Mulaudzi, L.V., Stefan, R.I., 2003. On-line speciation of bromine and bromide using sequential injection analysis with spectrophotometric detection. Anal. Bioanal. Chem. 375, 1074–1082.
Contents lists available at ScienceDirect
Journal of Contaminant Hydrology journal homepage: www.elsevier.com/locate/jconhyd
Predicting release and transport of pesticides from a granular formulation during unsaturated diffusion in porous media Marcos Paradelo a,b,⁎, Diego Soto-Gómez a, Paula Pérez-Rodríguez a, Eva Pose-Juan c, J. Eugenio López-Periago a a b c
Soil Science and Agricultural Chemistry Group, Department of Plant Biology and Soil Science, Faculty of Sciences, University of Vigo, E-32004 Ourense, Spain Department od Agroecology, Faculty of Science and Technology, Aarhus University, Blichers Allé 20, P.O. Box 50, DK-8830 Tjele, Denmark Institute of Natural Resources and Agrobiology of Salamanca (IRNASA-CSIC), 37008 Salamanca, Spain
a r t i c l e
i n f o
Article history: Received 5 February 2013 Received in revised form 20 July 2013 Accepted 28 October 2013 Available online 16 December 2013 Keywords: Soil pesticide transport Diffusion Controlled release Formulation Soil Agrochemicals
a b s t r a c t The release and transport of active ingredients (AIs) from controlled-release formulations (CRFs) have potential to reduce groundwater pesticide pollution. These formulations have a major effect on the release rate and subsequent transport to groundwater. Therefore the influence of CRFs should be included in modeling non-point source pollution by pesticides. We propose a simplified approach that uses a phase transition equation coupled to the diffusion equation that describes the release rate of AIs from commercial CRFs in porous media; the parameters are as follows: a release coefficient, the solubility of the AI, and diffusion transport with decay. The model gives acceptable predictions of the pesticides release from commercial CRFs in diffusion cells filled with quartz sand. This approach can be used to study the dynamics of the CRF-porous media interaction. It also could be implemented in fate of agricultural chemical models to include the effect of CRFs. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Controlled-release formulations (CRFs) are mixtures of one or more active ingredients (AIs) with a carrier. CRFs are designed to enhance the application of the pesticide to crops and the effectiveness of the pesticide (Collins et al., 1973). Granulates are a very common type of CRF used to regulate the release of AIs into the soil and to control soil-borne diseases within the natural variability of both the soil and rainfall. Therefore, studies examining the mechanisms that control the release of an AI and its transport in soil are of particular interest. The ability to model the coupled release and transport of AIs would facilitate the development of new CRFs, provide new methods to validate their effectiveness and improve existing methods for environmental risk assessments of pesticide usage. A variety of studies on the release of agricultural chemicals from CRFs have been published. These include field-scale studies that have shown that commercial starch-encapsulated ⁎ Corresponding author. E-mail address: [email protected] (M. Paradelo). 0169-7722/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jconhyd.2013.10.009
formulations of atrazine decrease pesticide losses in leachates and increase its persistence in soil (Gish et al., 1994). The behavior of different types of formulations has also been described. For example, commercial formulations of alachlor, atrazine and fenamiphos affect the potential of these pesticides to become water pollutants under severe rainfall conditions (Davis et al., 1996). A sepiolite-gel matrix CRF has been found to significantly decrease the leaching of metribuzin in soil column tests (Maqueda et al., 2008). Atrazine release from alginate-based CRFs in soil columns decreased regarding application of water suspension of herbicide (Malyszka and Jankowski, 2004). A decrease in the rate of the release of an alginate-based CRF of alachlor into the soil has been observed with a decrease in the soil water potential, suggesting a diffusion-controlled release rate (Nasser et al., 2008). The use of a pillared clay-controlled release formulation of alachlor can increase the persistence of alachlor in the soil (Gerstl et al., 1998). More recently, the use of modified montmorillonites as carriers has been shown to decrease the potential losses of simazine (Cornejo et al., 2008), fluometuron (Gámiz et al., 2010) and other anionic herbicides (Undabeytia et al., 2003).
M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
The influence of CRFs on pesticide losses by leaching has been studied using field-deployed lysimeters together with rainfall simulations (Potter et al., 2010); these authors reported that the use of a CRF with a clay-alginate polymer can decrease metolachlor leaching. Organo-clay formulations influence the bioavailability of AIs via their adsorption of AIs (Sánchez-Verdejo et al., 2008; Trigo et al., 2009). Ligninbased CRFs can decrease the leaching losses of isoproturon, imidacloprid and cyromazine (Garrido-Herrera et al., 2009). A physically based model to describe release of AIs from membrane coated CRFs in free water was reported (Shaviv et al., 2003a; Shaviv et al., 2003b). The classical description of controlled release process is the Higuchi's model (Higuchi, 1961) which defines three stages: i) a lag period during which water penetrates and dissolve the AI, ii) a linear release when water penetration and AI release occur together and, iii) a decaying release due to the depletion of the AI into the granule. Since a complete implementation of the Higuchi's model can be cumbersome for practical purposes, simplifications to model controlled release of agrochemicals are often used in several fields. A simplification assuming that release can be as a pseudo-first order kinetics was used to test experimental CRFs of carbofuran in soil (Choudhary et al., 2006). Another approach assumes that release is controlled by a solubilizationlimited process and decay of the AI (Collins et al., 1973). This is only valid if transport is negligible regarding the flux rate; such in the case of granules submerged in water, but may not be valid for unsaturated soil. Empirical release models and closed forms of physically based release equations have been developed (Ritger and Peppas, 1987), but these cannot reproduce the influence of varying soil moisture conditions in the field. In addition, changes in the pore water velocity have influence on the time course of the release rate of AI from CRFs (Paradelo et al., 2012). A full mathematical description of the release process should reproduce all the environmental effects described above, but this approach is very demanding in terms of computation. Therefore, it is desirable to provide an efficient approach to model the pesticide release from CRF in varying moisture conditions. The objective of this paper is to propose a simpler approach as a tool to simulate the controlled release of pesticides buried in soil. This paper focuses on modeling the release of pesticides from uncoated granulated CRFs in porous media. The model was compared with diffusion experiments of carbofuran and fenamiphos CRFs embedded in sand diffusion cells under unsaturated moisture conditions.
15
where k1 is the specific rate, and SI is the saturation index of the pesticide, A V−1 is the relationship between the area of surface contact (A) and the volume (V) of the solid per unit of mass. The values of m0 and m are the initial and actual (at time t) mass of the solid phase of the AI in the granules, respectively, and b is a shape factor of the granule. 2.2. Transport model If the pesticides react with the porous matrix, the expression for diffusion with linear adsorption model and first order decay in the liquid phase takes the form: ρ K ∂c ∂ ∂c ∂c 1þ b D ¼ D þ s θ ∂t ∂t ∂x ∂x
ð2Þ
where ρb is the bulk density of the porous matrix, θ is the water content on a volume basis; KD is the linear coefficient partition, c is the resident concentration in the liquid phase; t is time; x is the distance; D is the effective diffusion coefficient in the pores porous matrix, given by D = θ τ D0, where D0 is the molecular diffusion coefficient for infinite volume dissolution and τ is the tortuosity factor calculated by the Millington and Quirk formula (Millington and Quirk, 1961), that is valid for an isotropic porous medium granular matrix (Radcliffe, 2010): 7=3
τ¼
θ θ2s
ð3Þ
where θs is the saturated water content. For our diffusion cells τ = 0.17 (Table 2). If the pesticide is linearly adsorbed the solid/liquid equilibrium partition coefficient KD can be used to calculate the linear retardation term in the left hand of Eq. (2) 1 þ ρb θK D . The ∂cs/∂t is the sink rate to account the removal rate of the pesticide from pore water by degradation, the subscript s indicates the concentration depleted in the liquid phase. Using the appropriate initial and boundary conditions that meet the conditions imposed in the diffusion experiments, numerical solutions of Eq. (2) can be obtained. Modeling of the redistribution of unreactive Br− is better done by using analytical solutions of the non-reactive diffusion (Crank, 1975): δc δ2 c ¼D 2: δt δx
ð4Þ
If the domain is defined by the impermeable boundaries at x = 0 and x = L, being L the length of the cell, Eq. (4) can be solved for diffusion cells with the initial conditions:
2. Materials and methods 2.1. Release kinetics model
cð0 ≤ x b L=2; t ¼ 0Þ ¼ c0 The solubilization kinetics was modeled by a phase transition kinetics equation that was proposed by other authors to model the solubilization kinetics of minerals (Parkhurst and Appelo, 1999). The rate of the phase transition during the solubilization takes the form:
dm A m ¼ −k1 dt V m0
b
SI
1−10
and cðL ≥ x ≥ L=2; t ¼ 0Þ ¼ 0: If diffusion does not reach the ends of the cell the boundary conditions are
ð1Þ
cðx ¼ 0; t N 0Þ ¼ c0
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M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
in Tomlin (2009). Granules between 1 and 2 mm in diameter of each formulation were used in the release experiments. Their composition was carbofuran (about 5%) and a mixture of violet crystal used as a tint in matrix of calcium carbonate and carboxy methyl cellullose as aglomerant (95% in weight). Fenamiphos takes the form of white–gray granules containing 10% of active ingredient. Visual inspection indicated that CRF granules are equant and angular in shape, and non coated. Granules are very cohesive after a month immersed in deionized water. The AI content in all CRFs was determined in triplicate in separate samples by the method described by Fernández-Pérez et al. (2005). The concentration of the AI in granules was measured in quintuplicate (5 samples each containing 50 mg of granules). Technical-grade carbofuran and fenamifos with purity higher than 90% were supplied by Riedel-de Haën (Seelze-Hannover, Germany). It was used for quantification standards and in testing the diffusion of carbofuran without the influence of CRF.
and cðx ¼ L; t ≥ 0Þ ¼ 0: And the analytical solution is c ¼ 0:5 erfc c0
x pffiffiffiffiffiffi 2 Dt
ð5Þ
where c0 is the concentration in the half-cell charged with solute before the diffusion starts. For larger diffusion times, the concentration change reaches the impermeable ends of the cell, the concentration gradient becomes zero and the boundary conditions are ∂c= ∂xðx ¼ 0; t ≥ 0Þ ¼ 0; ∂c= ∂xðx ¼ L; t ≥ 0Þ ¼ 0 and the solution is (Crank, 1975): " c ¼ c0
∞ nπ n π x 1 2X 1 2 2 2 þ sen exp −Dn π t=L cos 2 π n¼1 n 2 L
2.4. Water release experiments
#
The rate of the solubilization of the AI in a CRF can be limiting in the release in porous media. Kinetic release experiments were performed with the stirred water tank method as reported by Fernández-Pérez et al. (2000). Briefly, granules from the commercial formulas containing 25 mg of the active ingredient were added to 100 mL of deionized water in a 250 mL stoppered Erlenmeyer flask. The samples were orbitally shaken at 24 rpm in a thermostatic chamber at 25 ± 1 °C. Aliquots of 1 mL were collected at different time intervals and analyzed using high performance liquid chromatography (HPLC) (Paradelo et al., 2012). These data were used to model the carbofuran release kinetics with a phase transfer equation that uses the saturation index (SI) of dissolved carbofuran and the interface area of the undissolved pesticide into the granule.
ð6Þ Eqs. (5) and (6) can be used to obtain the non-reactive transport parameters for Br− and technical grade pesticide by fitting to experimental data by the Levenberg–Marquardt optimization algorithm (Marquardt, 1963) using the package LM-OPT supplied by Clausnitzer and Hopmans (see Supporting Information S1). The model of release Eq. (1) was used to describe the release of pesticide from the granules, and was included in the numerical solution of the diffusion model Eq. (2) to simulate the concentration of carbofuran in the center of the diffusion cell. Coupling Eqs. (1) and (2) can be used to model the pesticide release and diffusional transport from the CRF granules embedded in the diffusion cells.
2.5. Diffusion experiments 2.3. Characterization of the CRFs The coupled model for the release and transport of carbofuran and fenamiphos was compared with experimental profiles from the diffusion experiments. The study of pesticide release under the no-advection conditions has been performed using the half-cell diffusion method. This consists in determining the concentration profile of a solute in a diffusion cell after an appropriate diffusion time (Flury and Gimmi, 2002). Quartz sand was chosen as a model of unreactive porous media to minimize adsorption and decay. Unsaturated moisture condition was established to mimic the field conditions between rain episodes. The properties of diffusion cells used in all experiments are shown in Table 2.
We used two pesticide formulations based on carbofuran and fenamiphos (Table 1) as CRF models, which were widely used in the control of insects and nematodes as CRF granules that usually are buried in soil at adequate depth. Carbofuran (N-methylcarbamate 0,0-dimethyl 2,3-dihydro-7 benzofuranyl) is a systemic insecticide moderately persistent in soil, with a half-life of 30 to 120 days, and it has a variable degree of mobility depending on the soil characteristics. Fenamiphos (N-ethyl isopropilfosforoamidate and O-(3-methyl 4-methylthiophenyl)) is absorbed well by plant roots in a systemic manner. The main physico-chemical properties of both pesticides are available Table 1 Principal characteristics of active ingredients used in the tests. Name
CAS number
Chemical formula
Molecular weight (g mol−1)
Melting point °C
Water solubility @20 ºC (mg L−1)
a
D0 (cm2 d−1)
Log KOW:
Carbofuran Fenamiphos
1563-66-2 22224-92-6
C12H15NO3 C13H22NO3PS
221.3 303.4
151 46
320 329
0.545 0.424
2.32 3.23
a
Obtained from quantitative relationships between molecular structure and the activity (QSAR) using SPARC program.
M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
17
Table 2 Properties of the half-cells used in diffusion experiments. The coefficient of variation is minor than 2.6% in all properties. Length (cm)
Internal diameter (cm)
Mass of quartz sand (g)
Porosity (cm3 cm−3)
Water content (cm3 cm−3)
Bulk density (g cm−3)
Degree of saturation (cm3 cm−3)
a Tortuosity coefficient (τ)
10
1.04
13
0.39
0.21
1.61
0.53
0.17
a
Using the Millington and Quirk equation.
Two sets of diffusion experiments were done. Diffusion experiments of Br− as a nonreactive tracer together with technical grade AIs were done to test the experimental procedure against the theoretical diffusion parameters in the cells and in the absence of other substances (adjuvants) present in the CRFs. Each diffusion cell consisted of two half-cells: one charged with a solution of the technical grade pesticide and KBr (50 mg L−1 pesticide and 0.83 mmol L−1 KBr), the other half-cell contained only 0.83 mmol L−1 KNO3 to minimize the osmotic-driven flow by differences in electrolyte concentrations between cells and charge balance. The water content in the cells was set to 20%. The cells were joined and sealed with electrical tape to prevent evaporation. Immediately, the cells were incubated horizontally in a chamber at 25 °C. Concentration profiles were measured at 15, 30 and 60 days of incubation. Diffusion cells were prepared in triplicate (n = 3). The second set of diffusion experiments was conducted using CRF granules of carbofuran or fenamiphos to examine the simultaneous effect of the release from the granule and the diffusion through the sand. The procedure used in the experiments performed with CRF carbofuran granules is almost identical to that used in the technical grade AIs. The sole difference is that, instead of adding the technical grade AI to one half-cell, the CRF granules were inserted between the contacting faces of a pair of half-cells. The number and weight of the granules calculated to add 50 mg of AI per cell was 5 granules per cell. The granules were uniformly distributed on the contact plane. The concentration profiles were also measured at 15, 30 and 60 days of incubation. Diffusion cells were also prepared in triplicate (n = 3). The coefficient of the diffusion of Br− in water reported in the literature; D0 = 1.797 cm2 d− 1 at 25 ºC (Flury and Gimmi, 2002), and the self-diffusion coefficient D0 of carbofuran (0.545 cm2 d− 1) and fenamiphos (0.424 cm2 d− 1) were estimated from quantitative structure activity relationships
A
(QSAR) using the SPARC chemical computational software (Hilal et al., 2003). 2.6. Chemical determinations The concentration profiles in the diffusion cells were determined by dividing each half-cell into sections of 1 cm in length. Each section was analyzed to measure the concentrations of Br− and pesticides. The bromide concentrations in the aqueous extracts were determined by colorimetry (van Staden et al., 2003) using a segmented flow autoanalyzer (Bran + Luebbe AutoAnalyzer 3, United Kingdom). Carbofuran and fenamiphos concentrations were measured by UV–visible HPLC. HPLC analyses were performed on a Dionex liquid chromatography system (Dionex Corp. Sunnyvale, USA) equipped with a P680 quaternary pump, an ASI-100 autosampler, a TCC-100 thermostated column compartment and a UVD170U detector linked to a PC running Chromeleon version 6.8 (Dionex corp., Sunnyvale, USA). Separations were performed with a Luna C18 (150 mm × 4.6 mm i.d., 5.0 μm particle size) analytical column obtained from Phenomenex (Madrid, Spain) and a guard column (4.0 mm × 3.0 mm i.d., 5.0 μm particle size) containing the same packing material. The mobile phases were ammonium acetate 0.1 M (A) and methanol (B). Isocratic elution 45% A and 55% B was performed at room temperature. The injection volume was set to 50 μL at a flow rate of 1.5 mL min−1. 3. Results and discussion 3.1. Solubilization of the active ingredients in the CRFs Measured richness of AIs in the CRF samples was 4% carbofuran and 10% fenamiphos, the variation coefficient was less than 1.7%. Kinetics of the solubilization of the CRFs in
B
Fig. 1. Cumulative release of carbofuran (A) and fenamiphos (B) from their respective controlled release formulations in water. Symbols represent the concentration of pesticide in water and lines are the prediction obtained using transition phase and degradation equations (Eq. 1), r2 N 0.996.
18
M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
Table 3 Kinetic parameters for the transition phase model (Eq. (1)) calculated for the solubilization of active ingredient from CRF. Active ingredient Carbofuran Fenamiphos
k1 A V−1 −7
b −7
1.4 10 ± 0.1 10 9.7 10−8 ± 0.1 10−8
1.7 ± 0.02 1.9 ± 0.02
ks −3
−3
9.0 10 ± 0.02 10 1.0 10−7 ± 0.01 10−7
ME
EF
RMSE
CRM
r2
2.79 2.84
0.995 0.964
0.0097 0.0309
0.010 0.091
0.996 0.997
k1 A V−1 phase transition kinetic constant (mol L−1 s−1); b shape factor (dimensionless); ks kinetic constant for sink, second order for carbofuran (L mol−1 s−1), first order for fenamiphos (s−1) ME maximum error (mg L−1); EF model efficiency; RMSE root mean square error; CRM coefficient of residual mass; Pearson's r square.
stirring water (Fig. 1) show a rapid rise in carbofuran concentration, with a maximum achieved after 10 h, with a subsequent decrease with time. For fenamiphos, the release rate was slower than that of carbofuran and the decay of fenamiphos was small. The granules have co-adjuvants that do not dissolve, and the variation in the specific surface area during the release is unknown. To model the release kinetics with Eq. (1) the parameter search procedure involved the simultaneous optimization of two parameters, namely, the quantity given by the expression k1 A V−1 (mol L−1 s−1) and the exponent b in Eq. (1) was solved by numerical integration using the Runge–Kutta method included in PHREEQC chemical computation software (see Supporting Information S2). Only decay of carbofuran in water was incorporated to the model. Good predictions were obtained with a second order model. In the diffusion experiments with technical grade carbofuran the decay rate was much slower than in the CRF. A more detailed analysis of the decay kinetics of the carbofuran in the CRF in water exceeds the scope of this work. Nonetheless, identical results were obtained for the replicates, and the model predictions with the second order
model were in very good agreement with the experimental results. The best-fit parameters of the model of the release of carbofuran and fenamiphos are listed in Table 3, and the predictions obtained with the model with the best fitting set of parameters are plotted in Fig. 1. 3.2. Tests of experimental conditions for diffusion cells Determinations of the moisture profiles resulted in coefficients of variation (CV) that were less than 2.6% (n = 10 segments per half-cell), this error is acceptable and was accounted to the overall experimental error in the mass balance of solutes in the diffusion calculations. The recoveries of Br− and technical grade pesticides, applied in aqueous solutions mixed with sand, were greater than 98% in all cases. This recovery rate is high enough to neglect any retardation in transport. Solute concentration gradients in the half-cells before the diffusion experiments were measured and demonstrated a uniform distribution profile (i.e., no trend along the length of the cell) and CV was less than 4%. The Br− profiles obtained at different incubation times (Fig. 2) show the redistribution of Br− . Experimental profiles were compared with the model of the transport by diffusion (Eq. (4)), by using the analytical expressions Eqs. (5) or (6) as the best for different diffusion times. The computed profiles are shown as lines in Fig. 2. Inverse modeling of the diffusive transport of Br− or pesticide allowed us to obtain their respective effective diffusion coefficients (D) from profile concentrations. The estimated effective diffusion coefficients D for Br− at 15, 30 and 60 d (Table 4) increased with time. However, there were no significant differences between the estimated D for the three time studies. For t = 30 d fitted D = 0.537 ± 0.270 cm2 d−1, and therefore the estimated self-diffusion is D/τ θ = D0 = 1.927 ± 0.15 cm2 d−1. That is the closest value to the selfdiffusion coefficient D0 = 1.797 cm2 d−1. 3.3. Diffusion of technical grade pesticide Fig. 3 shows the concentration profiles of carbofuran and fenamiphos in the pore water after 5, 15 and 30 days of
Table 4 Parameters of the diffusion from tests of KBr for different profiles. D* (cm2 d−1) using the self diffusion for Br− in water at 25 ºC in infinite dilution as D0 = 1.797 cm2 d−1, τ = 0.17 and θ = 0.21.
Fig. 2. Concentration profiles of Br− in pore water (mg L−1) in the diffusion cells after 15, 30, and 60 days in contact. Observed data (symbols) and predicted by the Eq. (4) (lines).
Time (d)
D* (cm2 d−1)
D0* (cm2 d−1)
D*/D0
15 30 60
0.302 ± 0.103 0.537 ± 0.270 0.948 ± 0.305
1.084 ± 0.06 1.927 ± 0.15 3.403 ± 0.17
0.60 ± 0.27 1.07 ± 0.71 1.89 ± 0.81
M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
A
19
B
Fig. 3. Concentration profile (mg L−1 in the pore water) of technical grade carbofuran (A), and fenamiphos (B) after 15, 30, and 60 days in contact. Observed data (symbols) and predicted by the Eq. (4) (lines).
incubation. The fitting of the parameters of the diffusion model to the experimental profiles (Table 5) indicates that the diffusion of carbofuran increased compared to what was expected from the pure diffusion process. The best fitting diffusion coefficient is D = 0.34 ± 0.076 cm2 d−1, which yields a good prediction of the profile (r2 = 0.949), using the value of D0 = 0.545 cm2 d−1 from the QSAR calculations. A better prediction was obtained with Eq. (2) after incorporating a first-order sink term that resulted in a half-life of 112 d; this result is in good agreement with literature data (Tomlin, 2009). Both the reaction mechanisms of transport retardation and decay for carbofuran are in accordance with the conditions of the low reactivity of the quartz sand and the abiotic conditions of the experiments performed in darkness. The model fitting for the diffusion of fenamiphos (Table 5) resulted in a diffusion coefficient (D = 0.983 ± 0.0496 cm2 d−1) that provides a good prediction of the concentration profile (r2 = 0.908). This value is about twice the value estimated from QSAR (D0 = 0.424 cm2 d−1). The surface tension of fenamiphos (47.2 mN m−1) (FOOTPRINT, 2012) can generate a gradient in air liquid interface along the diffusion cell and promotes the
water movement (Karkare and Fort, 1993) that speeds up the transport of fenamiphos. On the other hand, the degradation rate of fenamiphos (half-life of 471 d) was smaller than that of carbofuran. 3.4. Release of the active ingredients from the granular formulation The concentration profiles of carbofuran and fenamiphos released from the CRF at different times are shown in Fig. 4. Profile shapes show the transport of the AIs from the granules placed in the center of the diffusion cell toward the ends of the cells. The shape of the carbofuran profile is two symmetrical hyperbolas that show a large concentration gradient near the source (the location of granules) that is related with its smaller D and the sink rate regarding the fenamiphos. This shape suggests that release of carbofuran is limited by diffusion rate and decay. The shape of the fenamiphos profile at 15 d incubation is more sigmoidal (i.e., small concentration gradients near the granules), indicating a faster diffusion and negligible decay.
Table 5 Fitted parameters of diffusion model for technical grade active ingredient in insaturated quartz sand cells. Active ingredient Carbofuran Fenamifos
D 0.340 ± 0.076 0.983 ± 0.0496
KD
ks −9
b10 b10−9
−3
−3
6.0 10 ± 1.1 10 1.5 10−3 ± 0.3 10−3
ME
EF
RMSE
CRM
r2
11.6 15.0
0.871 0.856
0.029 0.034
−0.07 0.114
0.940 0.913
D diffusion coefficient; KD partition constant, ks kinetic degradation coefficient; ME maximum error (mg L−1); EF model efficiency; RMSE root mean square error; CRM coefficient of residual mass; Pearson's r square.
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M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
Fig. 4. Concentration profiles of carbofuran (A) and fenamiphos (B) released from CRF after 15, 30 and 60 days in the diffusion cells filled with quartz sand at 0.2 v/v water content. Lines represent predictions using the numerical solution of one-dimension diffusion equation coupled to the phase transfer equation. r2 N 0.962 in all cases.
The results were analyzed by modeling using the onedimensional diffusion model by solving coupled Eqs. (1) and (2). This solution was determined with an explicit finite difference scheme centered in space; the model was implemented in the PHREEQC computer program (Parkhurst and Appelo, 1999) (see Supporting Information S2). The initial conditions were stated as follows: the AI is initially in the granules, which occupies a segment of 1 mm in length at the center of the cell (equals to the average diameter of granules), and the concentration in the pore water is zero throughout the domain. The boundary conditions are zero flux at both ends, and the concentration in the center is controlled by the solubilization rate of the CRF in the central segment, using the phase transition equation (Eq. (1)). The kinetics of the degradation of the AI in the aqueous phase was applied to the entire cell, including the interstitial water inside the granules, for t N 0. The parameters used to feed the model were those obtained in independent experiments (Tables 2, 3 and 5), except the kinetic decay parameter ks for carbofuran. The performance indicators of the predictions made by the model are shown in Table 6. In general, the predictions were good, especially the model efficiency indicator. The fitted values of ks decreased over time for the water release experiments (i.e. from 9.0 10−3 L mol−1 s−1 in water to 0.6 10−3 at 15 d diffusion, and to 0.2 10−3 at 60 d diffusion). This behavior agrees with the literature data, which indicate a greater persistence of pesticides in soil than in water (Arias-Estévez
et al., 2008). The predicted profiles of commercial fenamiphos reproduced the sigmoidal shaped profile at t = 15 d. The sensitivity analysis of the concentration profile of carbofuran release to D, k1 and ks is depicted in Fig. 5. Pesticide saturation with respect to the pure phase (10SI) is shown to illustrate the magnitude of the difference between the concentration in solution and the concentration of carbofuran at saturation (SI = 0). The shapes of the profiles demonstrate that diffusion can be a limiting step in the release of carbofuran. The influence of k1 indicates that a value of k1 A V−1 near 10−5 mol L−1 s−1 transport becomes limited by diffusion. These conditions provide a more uniform distribution of carbofuran. Lowering k1 A V−1 from 10−6 to 10−7 mol L−1 s−1 increased the mass of carbofuran near the granule due to the decreased decay rate at lower concentrations; this relationship occurs because the decay kinetics outside of the granule mimic second order. The optimal rate of release is given by k1 A V−1 = 1.4 10−5 mol L−1 s−1, which results in the maximum mass of carbofuran into the pore water of the diffusion cell. Table 6 Overall performance tests of the predictions made by the release model for AI released from CRF within diffusion cells using the parameters in Tables 2, 3 and 5. The parameter fitted was ks for the carbofuran only. Active ingredient
ks
ME
EF
RMSE
CRM
r2
Carbofuran Fenamifos
4.0 10−4 1.0 10−7
11.6 15.0
0.87 0.856
0.0295 0.0336
−0.079 0.114
0.929 0.912
M. Paradelo et al. / Journal of Contaminant Hydrology 158 (2014) 14–22
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Appendix A. Supplementary data Supporting Information available: Fitting routine and PHREEQC code used in this work. Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j. jconhyd.2013.10.009.
References
Fig. 5. Sensitivity of the release model with regards to the diffusion coefficient in the porous media (D), and the kinetic parameters k1 and ks. Other parameters were set to the optimum values to carbofuran (Table 5).
4. Conclusions The proposed model coupling release and diffusion processes provided acceptable predictions of the release and redistribution of the active ingredient from the granule to the unsaturated porous matrix. Using a phase transition equation saves large computer calculations required to compute the moving solubilization boundary of the AI inside the granule. Therefore, diffusion-limited or solubilization limited release can be assessed by a rather simple approach. Using an almost inert porous media such as quartz sand improves the reproducibility and reduces the time consuming experiment, but further studies with real soil should be desirable for a better approach to the field conditions. However, the model already incorporates decay and sorption processes and can be suitable using soil matrices. The experimental system and the model presented here can be used to efficiently evaluate the performance of controlled-release formulations. This approach can be used in modeling risk assessment of nonpoint water pollution incorporating the effects controlled release formulations. Acknowledgments This work was funded by the INCITE program (INCITE 08PXIB383190PR, Xunta de Galicia). M. Paradelo and P. Pérez-Rodríguez wish to acknowledge the funding of their work by the Predoctoral Fellowship Program (FPU) of Spain's Ministry of Education, and E. Pose-Juan by Juan de la Cierva contract (JCI-2011-10150) of Spain's Ministry of Science and Innovation, respectively. We also thank Natalia Outeiriño for helping us in the laboratory.
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