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Fugacity Models Level 1 : Equilibrium

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Fugacity Models Level 1 : Equilibrium Level 2 : Equilibrium between compartments & Steady-state over entire environment Level 3 : Steady-State between compartments Level 4 : No steady-state or equilibrium / time dependent. Level 1 : Equilibrium “Chemical properties control”

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slide2

Fugacity Models

Level 1 : Equilibrium

Level 2 : Equilibrium between compartments & Steady-state over entire environment

Level 3 : Steady-State between compartments

Level 4 : No steady-state or equilibrium / time dependent

slide3

Level 1 : Equilibrium

“Chemical properties control”

fugacity of chemical in medium 1 =

fugacity of chemical in medium 2 =

fugacity of chemical in medium 3 =

…..

slide4

Mass Balance

Total Mass = Sum (Ci.Vi)

Total Mass = Sum (fi.Zi.Vi)

At Equilibrium : fi are equal

Total Mass = M = f.Sum(Zi.Vi)

f = M/Sum (Zi.Vi)

slide6

Fugacity Models

Level 1 : Equilibrium

Level 2 : Equilibrium between compartments & Steady-state over entire environment

Level 3 : Steady-State between compartments

Level 4 : No steady-state or equilibrium / time dependent

slide7

Level 2 :

Steady-state over the entire environment & Equilibrium between compartment

Flux in = Flux out

fugacity of chemical in medium 1 =

fugacity of chemical in medium 2 =

fugacity of chemical in medium 3 =

…..

slide8

Level II fugacity Model:

Steady-state over the ENTIRE environment

Flux in = Flux out

E + GA.CBA + GW.CBW = GA.CA + GW.CW

All Inputs = GA.CA + GW.CW

All Inputs = GA.fA .ZA + GW.fW .ZW

Assume equilibrium between media : fA= fW

All Inputs = (GA.ZA + GW.ZW).f

f = All Inputs / (GA.ZA + GW.ZW)

f = All Inputs / Sum (all D values)

slide10

Fugacity Models

Level 1 : Equilibrium

Level 2 : Equilibrium between compartments & Steady-state over entire environment

Level 3 : Steady-State between compartments

Level 4 : No steady-state or equilibrium / time dependent

slide11

Level III fugacity Model:

Steady-state in each compartment of the environment

Flux in = Flux out

Ei + Sum(Gi.CBi) + Sum(Dji.fj)= Sum(DRi + DAi + Dij.)fi

For 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

slide23

Recipe for developing mass balance equations

1. Identify # of compartments

2. Identify relevant transport and transformation processes

3. It helps to make a conceptual diagram with arrows representing the relevant transport and transformation processes

4. Set up the differential equation for each compartment

5. 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

slide26

Application of the Models

  • To assess concentrations in the environment
  • (if selecting appropriate environmental conditions)
  • To assess chemical persistence in the environment
  • To determine an environmental distribution profile
  • To assess changes in concentrations over time.
slide27

What is the difference between

Equilibrium & Steady-State?

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