1. Kinetic Models Considered Jeremy Dyson Basel, Switzerland

2. 2 Introduction Selected core models for parent compounds & metabolites in soil and water-sediment studies Models can be applied to other studies, e.g. hydrolysis Models chosen as simple & sensible approaches to representing behaviour from pseudo-mechanistic to more pragmatic perspectives Models displayed in terms of: Integrated equations based on initial conditions Differential of above for solving new problems Differential equations without initial conditions Endpoint calculation (DT50/DT90) from parameters

3. 3 Outline The Core Models Single First Order Biphasic Models – Gustafson & Holden – Bi-Exponential – Hockey Stick Lag Phase Models – Modified Hockey Stick – Logistic Alternatives & Links to Leaching Models Conclusion

4. 4 Single First Order (SFO) Fixed Shape DT90 = 3.32 x DT50 Assumes microbes not limiting Degradation % Remaining

5. 5 Single First Order (SFO)

6. 6 Biphasic Models DT50 DT90 Generally: DT50s Shorter DT90s Longer

7. 7 Biphasic Models Some Causes of Biphasic Behaviour Aged sorption Non-linear sorption Declining microbial activity Spatial variations in field Seasonal changes in weather

8. 8 Gustafson & Holden (FOMC)

9. 9 Bi-Exponential (DFOP or FOTC)

10. 10 Hockey Stick (HS)

11. 11 Lag Phase Models Lag Phase

12. 12 Modified Hockey Stick

13. 13 Logistic

14. 14 Alternatives & Links to Leaching Models Alternatives models can be used, but: Needs to be justified, e.g. Michaelis-Menten kinetics Need to avoid, where possible: – Time-dependent endpoints – Concentration-dependent endpoints – Large number of parameters – Microbial population dynamics Avoid Timme et al. as already noted in Guideance Identify biphasic kinetics for use in leaching models Not possible, but can link to DFOP for estimation

15. 15 Alternatives & Links to Leaching Models

16. 16 Conclusion Core models able to handle most kinetics problems Hence focus on solving problems using these models