Nonlinear Soil Dissipation Kinetics - American Chemical Society

Chapter 9

Downloaded by DUKE UNIV on November 11, 2014 | http://pubs.acs.org Publication Date (Web): October 28, 2014 | doi: 10.1021/bk-2014-1174.ch009

Nonlinear Soil Dissipation Kinetics: The Use of a Set of Simple First-Order Processes To Describe a Biphasic Degradation Pattern John R. Purdy*,1 and Mark Cheplick2 1Abacus

Consulting Services Ltd., Campbellville, Ontario, Canada L0P1B0 Environmental, Leesburg, Viriginia U.S.A. 20175 *E-mail [email protected].

2Waterborne

The analytical results for a pesticide compound in a set of laboratory soil dissipation studies with a variety of different soil types from North America and Europe show a range of behavior from linear simple first-order to a pronounced biphasic pattern. Using a set of three simple first-order equations, representing reversible movement between two compartments in the soil, and irreversible degradation from one of the two compartments, it was possible to fit the data from all sites. The output was a set of three simultaneously optimized rate constants for each soil type, along with the goodness of fit statistics. The physical interpretation of this model was found to be unrelated to soil physical properties but associated with the movement of residues between a compartment in which the degradation processes occur, and a compartment in which they do not. The former compartment resembles what has been called the bioaccessible compartment in soil. This model, identified as the SFO3 model, is useful for calculation of rate constants for parent compound and intermediate metabolites, comparison of lab and field results, correction for changes in soil temperature or moisture content, identification of outlier data, and development of parameters for modelling input. The utility of the resulting rate constants for predictive modelling for environmental risk assessment depends on the availability of measurable soil properties that can be used to predict them, such as bioaccessibility.

© 2014 American Chemical Society In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.


Introduction The rate of decline of the concentration of a pesticide in the soil environment after application is an essential factor in environmental risk assessment. It is a key input value for models that are used to estimate the persistence and movement of pesticides in the environment. This process can be approximated by a simple exponential decay equation that is equivalent to the first-order (SFO) equation for chemical reactions (1, 2). While this remains the main equation used in modelling, it has long been recognized that it does not give a good fit to all experimental soil dissipation data sets; much effort has been expended to find equations that are more generally applicable to both lab and field study data (2, 3). In this work, the modelling of a series of 11 data sets for laboratory aerobic soil degradation of chlorpyrifos in soil were used to develop an alternate approach to nonlinear soil dissipation kinetics and to generate soil dissipation rate constants for use in PRZM-EXAMS modeling to support environmental risk assessments of chlorpyrifos (4, 5). The possible use of measured bio-accessibility to parameterize models such as PRZM/EXAMS for modelling environmental behavior of compounds is discussed. The potential for analysis of data from field soil dissipation studies for use in risk assessment was also considered using an example data set. The degradation of chlorpyrifos in soil leads to formation of 3,5,6trichloropyridinol. The results from a number of studies show that this step can be either abiotic or biotic, and the rate is 1.7 to 2-fold faster in biologically active soils (5, 6). Both modes of hydrolysis can occur in aerobic soil. The rate of abiotic hydrolysis is pH dependent and is faster under alkaline conditions. Under aerobic conditions, the major terminal degradate of chlorpyrifos is CO2 (6). The 11 laboratory data sets used in this modelling work were from studies of the degradation of 14C-chlorpyrifos in soil under aerobic conditions. The properties of the soils are listed in Table 1. The results from all soils showed good mass balance. There were some notable effects of soil properties: The originally reported DT50’s in Table 1 show that the degradation of chlorpyrifos is slower at low temperatures or in dry soil near the wilting point (10% Field Moisture Capacity (FMC)). Sterile conditions reduced the production of CO2, but did not reduce the degradation rate. Overall however, the DT50 values from all soils were not correlated with soil properties well enough to allow the DT50 to be predicted for use in modelling. It is possible that the soils that show a faster hydrolysis rate are those with a microbiome capable of biologically accelerated hydrolysis and that the biologically mediated degradation is less influenced by pH (5, 6). In this section, the application of a reversible binding kinetic model is investigated to evaluate its usefulness and physical significance using the available dissipation data sets as examples.

168 In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.

169


Table 1. Reported DT50 and Soil Properties For Laboratory Dissipation 75% F.M.C.

SFO DT50 (days)

Soil ID

Texture

Source

pH

%OC

MoistureContent (%FMC)

Barnes

Loam

ND

7.1

3.6

75

20.6

22

Catlin

Silty Clay Loam

IL

6.1

2.01

75

21.02

34

Charentilly

Silty Clay Loam

FRANCE

6.1

1

40

33.2

95

Commerce

Loam

MS

7.4

0.68

75

13.5

11

Cuckney

Sand

UK

6

1.2

40

26.2

111

German Std 2:3

Sandy Loam

Germany

5.4

1.01

75

10.8

141

Marcham

Sandy Clay Loam

UK

7.7

1.7

40

34.2

43

Marcham

Sandy Clay Loam

UK

7.7

1.7

40

34.2

80

Cold 10°C

Marcham

Sandy Clay Loam

UK

7.7

1.7

10

34.2

126

Dry

Marcham sterile

Sandy Clay Loam

UK

7.7

1.7

40

34.2

21

Sterile

Miami

Silt Loam

IN

6.6

1.12

75

17.92

24

Norfolk

Loamy Sand

VA

6.6

0.29

75

4.66

102

Stockton Clay

Clay

CA

5.9

1.15

75

25.75

107

Comment

Very low moisture

Continued on next page.

In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.

75% F.M.C.

SFO DT50 (days)

Soil ID

Texture

Source

pH

%OC

MoistureContent (%FMC)

Thessaloniki

Loam

GREECE

7.9

0.8

40

32.6

46

Tranent

Silt loam

UK

n.r

n.r

25

22

12.6

170


Table 1. (Continued). Reported DT50 and Soil Properties For Laboratory Dissipation


Comment

Kinetic Modelling


The degradation of chlorpyrifos does not fit a simple first-order kinetic model (6) (See example in Figure 1). There was no evidence of a rapid initial volatilization under laboratory aerobic soil metabolism test conditions that would contribute to the initial faster decline in concentration of chlorpyrifos. Two-compartment kinetics gave an improved fit, but this involves use of an empirical model with no physical reality assigned to the two compartments. A mechanistic kinetic model was set up based on the assumption that the nonlinear behavior is caused by a transition from dissolved parent compound to adsorbed residues over time (5). The kinetic model consists of 3 compartments as shown in the schematic diagram in Figure 2: • • •

1. M1 -a compartment in which the chlorpyrifos present is immediately available for biodegradation 2. M2 -a compartment in which no degradation occurs (nonbioavailable) 3. M3 -a compartment for metabolites and terminal degradation products

Figure 1. Biphasic Degradation of Chlorpyrifos in Aerobic Soil.

Flows of material between these compartments are shown by arrows in the schematic diagram. These flows are represented by simple first-order differential equations with rate constants k. The rate constant for movement into the non-active compartment is defined as k1. Competing with this process is the degradation of chlorpyrifos with rate constant km. The third process, with rate constant k2, is the reverse of the first; the movement from the inactive or non-labile compartment to the labile compartment from which degradation can occur. 171 In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.


Figure 2. SFO3 Conceptual kinetic model for nonlinear soil dissipation kinetics. During the development of this reversible binding model, the M1 compartment was thought to be the dissolved phase and M2 was thought to correspond to the adsorbed phase in the soil (5). The FOCUS review describes a similar system for the SFORB model, in which the two compartments are considered to be dissolved and adsorbed parent compound respectively (2). The SFORB model is described in terms of two 172 In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.


differential equations, with a combined algebraic solution. In this work, the system was described in terms of three SFO equations, with rate constants k1, k2, and km. No assumption of equilibrium is made. In addition, it was assumed that the analytical results for the concentration vs time represent the sum of the material in both compartments M1 and M2, since the analytical extraction method is known to recover all but the bound residues present in the soil sample. These three equations are simultaneously optimized to obtain a dissipation curve that fits the concentration vs time data for each soil. For convenience, it will be referred to as the SFO3 kinetic model. A schematic diagram and a list of parameters and equations are provided in Figure 2. As an overview of how this model works, initially the chlorpyrifos is readily bioavailable and degradation is limited only by the rate of metabolism (km). The linear trend in concentration vs time is described by the balance of the three rate constants k1, k2 and km. The transfer between M1 and M2 is reversible, but the degradation is irreversible. In systems where km is less than or equal to k2, metabolism is the rate limiting step and the system behaves like a SFO process. But if k2 is slower, the proportion of the parent compound that is in M1 will be depleted and k2 will become the rate limiting step over time. This results in nonlinear kinetics. Nonlinear behavior can also occur when km is slower than k1. It is assumed that all degradation, including both abiotic and metabolic degradation and formation of bound residues occurs from M1. The model was set up using ModelMaker Version 4, from Cherwell Scientific Software, UK, which is a matrix based modelling software application of Matlab.

Model Setup As input data, the measured amount of parent compound was entered as the sum of the amounts in compartments M1 and M2. In the ModelMaker software, this is represented by setting the measured concentration as a variable M, connected to M1 and M2 by “influences” shown in Figure 2 by dashed arrow lines. The influence is the equation M = M1+M2. The input data is not log-transformed. For the laboratory results, the first data point concentration value was entered for the initial value of M1 because the concentration measurements are relatively accurate and the mass balance was good. The initial values of M2 and M3 were set to zero. Estimated values were manually entered for the rate constants for the first trial runs based on approximations from the SFO rate of dissipation given in Table 1. These values were adjusted in some of the trial runs to be close enough for the optimization routine to converge on a solution for the input data from each soil. When the model is run, the software first integrates the set of differential equations using the Marquardt method, and then optimizes the rate constants selected to provide the best fit for the data. Five integration methods (Euler, Mid-Point, Runge-Kutta, Bulirsch-Stoer and Gear’s method) are available in the software. The default Runge-Kutta method was used for all sites since the differential equations are straightforward. Examples of the parameter optimization results for the 11 laboratory data sets are shown in Figures 3-5, and the optimization results are listed in Table 2. 173 In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.

Table 2. Optimization Results and DT50 Values

Soil

k1 DT50

Estimation Error

k2 DT50

Estimation Error

km DT50

Estimation Error

R2

F

p

Degrees of Freedoma)

0.00097

0.00245

0.00148

0.0310

0.00110

0.9989

2350

0.104

7

0.00229

0.9904

259

0.695

7

0.0290

0.9931

503

0.039

9

0.00125

0.9997

7342

0.718

7

Laboratory Studies Barnes

0.00344 201.5

Catlinb)

0.00315

282 0.00118

220.3 Charentilly

174


Optimization Results

0.529

0.00753

0.275

0.529

0.00103

0.0124

c

0.0908

0.01428

0.0181

0.00144

0.0573

0.0211

0.0211

0.0154

c

0.0312

0.0758

c

9

9.1 0.0143

0.007

0.00148

0.9973

918

0.066

7

0.00855

0.9894

374

0.013

10

0.00544

0.9966

737

0.027

7

99.1 0.00446

0.0789 8.8

45 0.0164

0.0613 11.3

32.9

7.6 Miami

0.00702

0.0758 9.1

12.1

55.9 Marcham

0.00976

99.0

1.3 German 2:3

0.0573

0.02457 28.2

12.1

92.1 Cuckney

0.00133

179.6

1.3 Commerce

0.00386

22.4

0.0246

0.0395


Soil

k1 DT50

Estimation Error

38.4 Norfolk

0.0129

Stockton

0.0031

0.0046

0.0206

Estimation Error

0.0125

0.00128

0.0021

0.00309

33.6

0.00467

Estimation Error

R2

F

p

Degrees of Freedoma)

0.0122

0.00108

0.9987

1883

0.106

7

0.00042

0.9987

1871

0.706

7

0.0029

0.9873

310

0.012

10

0.0168

0.9847

226

0.000313

9

0.0092

0.9845

222

0.000297

9

57 0.00219

338.1 0.0116

km DT50 17.5

55.5

227.3 Thessaloniki

k2 DT50 22.2

53.7

175


Optimization Results

0.0072 96.7

0.0113

148.4

0.02256 30.7

Field Study Tranent

0.12515

(Arrhenius)

5.5

Tranent

0.1333

(Q10 )

5.2

0.01788

0.01751

0.01407

39.6 0.01859

0.01482 46.8

0.01315 52.7

0.01009

0.00878 79.0

a)

Notes: Total degrees of freedom: Model accounts for 2 degrees of freedom. b) Catlin soil data required weighted least squares regression, all others were run with Ordinary Least Squares. c) The model did not converge. Values for Charentilly were used and they fit very well.



Figure 3. Model Results - Barnes Soil.

Application to Field Dissipation Studies Given that the model gave a good fit to the laboratory data which represents a closed system at constant temperature, it was then possible to apply it to the field dissipation study results by assuming that volatility, runoff and leaching losses were minimal, and adding a daily temperature correction factor based on either a direct Arrhenius equation (3) or the Q10 method (2). The schematic diagram and model setups are shown in Figure 6. The results obtained using the temperature records from a field soil dissipation soil with chlorpyrifos in Tranent, Scotland is shown in Figure 7 and 8 for the Arrhenius and Q10 methods respectively. The daily mean temperatures used are shown in Figure 9. A correction factor to normalize the moisture content is also available (2), but was not used for this work. 176 In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.


Figure 4. Model Results - Marcham Soil.

The Arrhenius equation for the effects of temperature T on the rate constant k is shown in eq 1.

where: kT = rate constant at temperature T in degrees Kelvin. • • • •

ko = frequency factor E = activation energy R = universal gas constant = 8.315 J mol-1 e = 2.718

If the rate at one temperature is known, the rate at another temperature can be estimated if the activation energy is also known. As an initial approximation, the activation energy, E, was given an approximate value of 40 kJ mol-1 (3), since this was sufficient to demonstrate the effectiveness of the model. This activation energy can be measured for a compound of interest by measuring degradation rates at a series of temperatures. Although the processes involved in 177 In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.

the reversible movement between compartments M1 and M2 are likely different from the degradation, a simplifying assumption was made that the same value of E would apply to all three rate constants. It was originally felt that adsorption onto an enzyme active site might be similar to adsorption onto a surface, and this assumption was retained when the compartments were seen as labile and non-labile compartments. The correction factor A for time t in days after application was defined as in eq 2 below:

For T1 = 20°C, this gives eq Downloaded by DUKE UNIV on November 11, 2014 | http://pubs.acs.org Publication Date (Web): October 28, 2014 | doi: 10.1021/bk-2014-1174.ch009

3:

Since this relationship fails in living systems when the temperature drops below 4°C or in inorganic systems when the temperature drops below freezing, the model was set up with timed events to set A = 0 when the mean air temperature dropped below 0°C and to return to equation 3 when it warmed up again.

Figure 5. Model Results - Charentilly Soil. 178 In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.


Figure 6. SFO3 Model With Temperature Normalisation Factor.

179 In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.


Figure 7. Optimized Fit Using Arrhenius Equation For Field Dissipation Data.

With the Q10 calculations, the Correction Factor Q at time t in days after application is used to normalize the temperature to a standard value, To, typically 20°C (2) as in eq 4 below:

The standard value of Q10 = 2.58 was used (2). Substituting this value and 20 °C in eq 4 and rearranging gives eq 5:

This relationship also fails below 4°C. This was dealt with as described above for the Arrhenius method. 180 In Non-First Order Degradation and Time-Dependent Sorption of Organic Chemicals in Soil; Kookana, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2014.


Figure 8. Optimized Fit Using Q10 Temperature Correction For Field.

Results From Laboratory Data The 11 laboratory aerobic metabolism data sets available for chlorpyrifos were run in the model. The optimized rate constants with corresponding DT50 and DT90 values are listed in Table 2. The statistical data for the curve fitting are included in Table 2. The statistics show an excellent fit to the model in all cases, except that the data from the Cuckney soil could not be successfully optimized by computer due to the very brief time for the desorption process to become dominant. However, the data were very similar to those for the Charentilly soil 3 and the parameter values optimized in the Charentilly data gave a very good fit for the Cuckney data (Table 2). The Catlin soil data required weighted least squares regression; all others were run with ordinary least squares optimization. Some of the p values indicate that additional data points would improve the goodness of fit. The excellent visual fit to the data throughout the soil types and climatic conditions is illustrated in Figure 3-5. These graphs exemplify soils in which the onset of the slower phase of dissipation occurred after approximately 60, 20 and

Nonlinear Soil Dissipation Kinetics - American Chemical Society

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