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GuySOULAS UMR Œnologie-Ampélologie Université Victor Segalen Bordeaux cours de la Libération, TALENCE CedexFrance KINETIC MODELS

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Where does first-order come from ? Reason 1: the experience Experience shows that many biotic and abiotic processes in environmental compartments such as soil effectively follow single first order kinetics (exponential decay)

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Reason 2: pragmatism The equation is simple and has only two parameters It is easy to fit the equation to experimental data DT50 and DT90 values are easy to calculate Parameters are theoretically independent of concentration and time … and appropriate for use as input for pesticide leaching models.

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Reason 3: scientific justifications abiotic hydrolytic processes often follow first- order reaction kinetics biotic degradation processes may be approximated by first-order reaction : ex. when responsible microbial agents (or enzymes) are in excess compared to the chemical (pseudo first order reaction kinetics).

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A phylogeny for the disappearance models The « Metabolism » case

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Reason 1: heterogeneity The Gustafsson and Holden assumption: The soil can be divided into a large number of independent compartments whith distributed first order rate constants. If pdf = Gamma distribution …

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Single first order kinetics (SFO)

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But First-order reaction kinetics may not be obeyed

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The bi-phasic Gustafson & Holden model (FOMC) alpha = 0.2, beta = 5.00 alpha = 0.2, beta = 1.00 alpha = 0.2, beta = 0.05 alpha = 1.0, beta = 5.00 alpha = 2.0, beta = 5.00 Time Concentration

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Reason 2: limited availability. In the soil, pesticides are distributed between a solid phase and a liquid phase where they are available for degradation. This partition induces a bi-phasic pattern of degradation

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Time Concentration k1 = 0.05, k2 = 0.01, tb = 10 k1 = 0.07, k2 = 0.01, tb = 10 k1 = 0.09, k2 = 0.01, tb = 10 k1 = 0.09, k2 = 0.01, tb = 15 k1 = 0.09, k2 = 0.02, tb = 15 The bi-phasic Hockey Stick model (HS)

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k1 = 0.03, k2 = 0.001, M1 = 75 k1 = 0.06, k2 = 0.001, M1 = 75 k1 = 0.09, k2 = 0.001, M1 = 75 k1 = 0.09, k2 = 0.010, M1 = 75 k1 = 0.09, k2 = 0.010, M1 = Time Concentration The bi-phasic bi-exponential model (DFOP)

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Reason 3: microbial behaviour Different environmental factors affect the activity of the microbial degraders. Respective substrate concentration and cell density may induce very different degradation patterns

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S 0 <

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True lag phase: The logistic model a0 = , r = 0.2 a0 = , r = 0.4 a0 = , r = 0.8 a0 = 0.001, r = 0.2 a0 = 0.08, r = Time Concentration

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Time Concentration Lag phase: The Hockey stick model (HS)

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A phylogeny for the disappearance models (1) Metabolism S 0 <

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