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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.

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Presentation on theme: "Fugacity Models Level 1: Equilibrium Level 2: Equilibrium between compartments & Steady-state over entire environment Level 3: Steady-State between compartments."— Presentation transcript:

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2 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

3 Level 1: Equilibrium “Chemical properties control” fugacity of chemical in medium 1 = fugacity of chemical in medium 2 = fugacity of chemical in medium 3 = …..

4 Mass Balance Total Mass = Sum (C i.V i ) Total Mass = Sum (f i.Z i.V i ) At Equilibrium : f i are equal Total Mass = M = f.Sum(Z i.V i ) f = M/Sum (Z i.V i )

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6 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

7 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 = …..

8 Level II fugacity Model: Steady-state over the ENTIRE environment Flux in = Flux out E + G A.C BA + G W.C BW = G A.C A + G W.C W All Inputs = G A.C A + G W.C W All Inputs = G A.f A.Z A + G W.f W.Z W Assume equilibrium between media : f A = f W All Inputs = (G A.Z A + G W.Z W ).f f = All Inputs / (G A.Z A + G W.Z W ) f = All Inputs / Sum (all D values)

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10 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

11 Level III fugacity Model: Steady-state in each compartment of the environment Flux in = Flux out E i + Sum(G i.C Bi ) + Sum(D ji.f j )= Sum(D Ri + D Ai + D ij.)f i 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

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13 Time Dependent Fate Models / Level IV

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22 Evaluative Models vs. Real Models

23 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 If steady-state does not apply, solve by numerical simulation

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26 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.

27 What is the difference between Equilibrium & Steady-State?

28 Time Dependent Fate Models / Level IV

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