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Guy

Guy. SOULAS. KINETIC MODEL S. UMR Œnologie-Ampélologie Université Victor Segalen Bordeaux 2. 351 cours de la Libération, TALENCE Cedex. France. Where does first-order come from ? Reason 1: the experience

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Guy

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  1. Guy SOULAS KINETIC MODELS UMR Œnologie-Ampélologie Université Victor Segalen Bordeaux 2 351 cours de la Libération, TALENCE Cedex France

  2. 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)

  3. 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.

  4. 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).

  5. » S <<K S >>K S K 0 s 0 s 0 s - First - order Monod without growth Zero order dS - = kS dS kS dS - = - = dt k dt dt + K S S <<X s 0 0 m X 0 m = k = m k X 0 = m k X m 0 K m s Logistic growth Monod with growth Logarithmic dS - = + - kS ( S X S ) 0 0 dt m S dS dS m - = + - - = m + - ( S X S ) ( S X S ) S >>X 0 0 m m 0 0 0 0 dt dt m + K S = k s K s S : initial substrate concentration; X : 0 0 initial biomass concentration A phylogeny for the disappearance models The « Metabolism » case

  6. 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 …

  7. 100 80 k = 0.005 60 Concentration (% of initial) k = 0.020 40 k = 0.050 20 0 0 20 40 60 80 100 Time (days) Single first order kinetics (SFO)

  8. But First-order reaction kinetics may not be obeyed

  9. 100 90 80 70 alpha = 0.2 , beta = 5.00 60 alpha = 0.2 , beta = 1.00 Concentration 50 alpha = 0.2 , beta = 0.05 alpha = 1.0 , beta = 5.00 40 alpha = 2.0 , beta = 5.00 30 20 10 0 0 10 20 30 40 50 60 Time The bi-phasic Gustafson & Holden model (FOMC)

  10. 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

  11. 100 90 80 70 k1 = 0.05 , k2 = 0.01 , tb = 10 60 k1 = 0.07 , k2 = 0.01 , tb = 10 Concentration 50 k1 = 0.09 , k2 = 0.01 , tb = 10 k1 = 0.09 , k2 = 0.01 , tb = 15 40 k1 = 0.09 , k2 = 0.02 , tb = 15 30 20 10 0 0 10 20 30 40 50 60 Time The bi-phasic Hockey Stick model (HS)

  12. 100 90 80 70 k1 = 0.03 , k2 = 0.001 , M1 = 75 60 k1 = 0.06 , k2 = 0.001 , M1 = 75 Concentration 50 k1 = 0.09 , k2 = 0.001 , M1 = 75 k1 = 0.09 , k2 = 0.010 , M1 = 75 40 k1 = 0.09 , k2 = 0.010 , M1 = 90 30 20 10 0 0 10 20 30 40 50 60 Time The bi-phasic bi-exponential model (DFOP)

  13. 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

  14. A phylogeny for the disappearance models (1) Metabolism » S <<K S >>K S K 0 s 0 s 0 s - First - order Monod without growth Zero order dS - = kS dS kS dS - = - = dt k dt dt + K S S <<X s 0 0 m X 0 m = k = m k X 0 = m k X m 0 K m s Logistic growth Monod with growth Logarithmic dS - = + - kS ( S X S ) 0 0 dt m S dS dS m - = + - - = m + - ( S X S ) ( S X S ) S >>X 0 0 m m 0 0 0 0 dt dt m + K S = k s K s S : initial substrate concentration; X : 0 0 initial biomass concentration

  15. 100 80 a0 = 0.0001 , r = 0.2 a0 = 0.0001 , r = 0.4 60 a0 = 0.0001 , r = 0.8 Concentration a0 = 0.001 , r = 0.2 a0 = 0.08 , r = 0.2 40 20 0 100 0 20 40 60 80 Time True lag phase: The logistic model

  16. 100 80 60 Concentration 40 20 0 0 10 20 30 40 50 60 Time Lag phase: The Hockey stick model (HS)

  17. A phylogeny for the disappearance models (1) Metabolism » S <<K S >>K S K 0 s 0 s 0 s - First - order Monod without growth Zero order dS - = kS dS kS dS - = - = dt k dt dt + K S S <<X s 0 0 m X 0 m = k = m k X 0 = m k X m 0 K m s Logistic growth Monod with growth Logarithmic dS - = + - kS ( S X S ) 0 0 dt m S dS dS m - = + - - = m + - ( S X S ) ( S X S ) S >>X 0 0 m m 0 0 0 0 dt dt m + K S = k s K s S : initial substrate concentration; X : 0 0 initial biomass concentration

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