Kinetic Models Considered Jeremy Dyson Basel, Switzerland

1. Kinetic Models ConsideredJeremy DysonBasel, Switzerland

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

5. Single First Order (SFO)

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

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. Gustafson & Holden (FOMC)

9. Bi-Exponential (DFOP or FOTC)

10. Hockey Stick (HS)

11. Lag Phase Models Lag Phase

12. Modified Hockey Stick

13. Logistic

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. Alternatives & Links to Leaching Models

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