6 Fugacity Models Level 1 : Equilibrium Level 2 : Equilibrium between compartments & Steady-state over entire environmentLevel 3 : Steady-State between compartmentsLevel 4 : No steady-state or equilibrium / time dependent
7 fugacity of chemical in medium 1 = fugacity of chemical in medium 2 = Level 2 :Steady-state over the entire environment & Equilibrium between compartmentFlux in = Flux outfugacity of chemical in medium 1 =fugacity of chemical in medium 2 =fugacity of chemical in medium 3 =…..
8 Level II fugacity Model: Steady-state over the ENTIRE environmentFlux in = Flux outE + GA.CBA + GW.CBW = GA.CA + GW.CWAll Inputs = GA.CA + GW.CWAll Inputs = GA.fA .ZA + GW.fW .ZWAssume equilibrium between media : fA= fWAll Inputs = (GA.ZA + GW.ZW) .ff = All Inputs / (GA.ZA + GW.ZW)f = All Inputs / Sum (all D values)
10 Fugacity Models Level 1 : Equilibrium Level 2 : Equilibrium between compartments & Steady-state over entire environmentLevel 3 : Steady-State between compartmentsLevel 4 : No steady-state or equilibrium / time dependent
11 Level III fugacity Model: Steady-state in each compartment of the environmentFlux in = Flux outEi + Sum(Gi.CBi) + Sum(Dji.fj)= Sum(DRi + DAi + Dij.)fiFor each compartment, there is one equation & one unknown.This set of equations can be solved by substitution and elimination, but this is quite a chore.Use Computer
23 Recipe for developing mass balance equations 1. Identify # of compartments2. Identify relevant transport and transformation processes3. It helps to make a conceptual diagram with arrows representing the relevant transport and transformation processes4. Set up the differential equation for each compartment5. Solve the differential equation(s) by assuming steady-state, i.e. Net flux is 0, dC/dt or df/dt is 0.6. If steady-state does not apply, solve by numerical simulation
26 Application of the Models To assess concentrations in the environment(if selecting appropriate environmental conditions)To assess chemical persistence in the environmentTo determine an environmental distribution profileTo assess changes in concentrations over time.
27 What is the difference between Equilibrium & Steady-State?