6.2.estimating phase distribution of contaminants in model worlds ep environmental processes
TRANSCRIPT
6.2. Estimating phase distribution of contaminants in model worlds
EP
Environmental Processes
2
Aims and Outcomes
Aims:
i. to provide overview of main transport mechanisms in all environmental compartments
ii. to give information about methods of estimation of distribution of pollutants in the environment
Outcomes:
iii. students will be able to estimate main transport mechanisms of real pollutants on the base of their physical-chemical properties
iv. students will be able to estimate the distribution of pollutants in the environment on the base of environmental models
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Lecture Content
β’ Description of basic transport mechanisms of pollutants in environmental compartments (diffusion, dispersion, advection)
β’ Definition of fugacityβ’ Multi-media fugacity models (level I, II, III)
Content of the practical work:
1. Transport in porous media.
2. Transport through boundaries (bottleneck/wall and diffusive boundaries)
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Compartment system
β’ The whole environment is highly structuredβ’ Simplification for modeling: compartment system
β Compartmentβ’ Homogeneously mixedβ’ Has defined geometry, volume, density, mass, β¦
β’ Closed and open systems
Compartment 1
Compartment 2 Compartment 3
Closedsystem
Compartment 1
Compartment 2
Compartment 3
Opensystem
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Transport Mechanisms in the Environment
β’ Diffusion β movement of molecules or particles along a concentration
gradient, or from regions of higher to regions of lower concentration.
β does not involve chemical energy (i.e. spontaneous movement)
Fickβs First Law of Diffusion:
xC
DAAJN diffdiff
Ndiff β¦ net substance flux [kg.s-1]Jdiff β¦ net substance flux through the unit
area [kg s-1 m-2]A β¦ cross-sectional area (perpendicular to
diffusion) [m2]D β¦ diffusion coefficient [m2 s-1]οΏ½C/x β¦ concentration gradient [kg m-3 m-1]
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Transport Mechanisms in the Environment
β’ Diffusion (contd.) β Fickβs First Law of Diffusion is valid when:
β’ The medium is isotropic (the medium and diffusion coefficient is identical in all directions)
β’ the flux by diffusion is perpendicular to the cross section areaβ’ the concentration gradient is constant
β Usual values of D:β’ Gases: D 10-5 - 10-4 m2 s-1
β’ Liquids: D 10-9 m2 s-1
β’ Solids: D 10-14 m2 s-1
Barrow, G.M. (1977): Physikalische Chemie Band III. Bohmann, Wien, Austria, 3rd ed.
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Transport Mechanisms in the Environment
β’ Diffusion coefficient (or diffusivity)β Proportional to the temperatureβ Inversely proportional to the molecule volume (which is related
to the molar mass)β Relation between diffusion coefficients of two substances:
Tinsley, I. (1979): Chemical Concepts in Pollutant Behaviour. John Wiley & Sons, New York.
i
j
j
i
M
M
DD
Di, Dj β¦ diffusion coefficients of compounds i and j [m2 s-1]Mi, Mj β¦ molar masses of compounds i and j [g mol-1]
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Transport Mechanisms in the Environment
β’ Diffusion conductance (g), diffusion resistance (r)
xD
rg
1
g β¦ diffusion conductance [m s-1]r β¦ diffusion resistance [s m-1]D β¦ diffusion coefficient [m2 s-1]x β¦ diffusion length [m]
More than 1 resistance in system calculation of total resistance using Kirchhoff laws
Resistances in series: π πππππ=ππ+ππ+β¦+ππ
Resistances in parallel: ππππππ=ππ+ππ+β¦+ππ
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Transport Mechanisms in the Environment
β’ Fick Second Law of Diffusion:
ππΆππ‘
=π·π2πΆππ₯2
For three dimensions:
ππΆππ‘
=π·π₯π2πΆππ₯2 +π· π¦
π2πΆππ¦2 +π·π§
π2πΆππ§2
Dx, Dy, Dz β¦ diffusion coefficients in x, y and z direction
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Transport Mechanisms in the Environment
β’ Dispersion:β Random movement of surrounding medium in one direction (or
in all directions) causing the transport of compound β Mathematical description similar to diffusion
xC
DAAJN dispdispdisp
Ndisp β¦ net substance flux [kg.s-1]Jdisp β¦ net substance flux through the unit
area [kg s-1 m-2]A β¦ cross-sectional area (perpendicular to
dispersion direction) [m2]Ddisp β¦ dispersion coefficient [m2 s-1]οΏ½C/x β¦ concentration gradient [kg m-3 m-1]
ππΆππ‘
=π·πππ ππ2πΆππ₯2
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Transport Mechanisms in the Environment
β’ Advection (convection):β the directed movement of chemical by virtue of its presence in a
medium that happens to be flowing
CuAAJN advadv Nadv β¦ net substance flux [kg.s-1]Jadv β¦ net substance flux through the unit
area [kg.s-1.m-2]A β¦ cross-sectional area (perpendicular to
u) [m2]uοΏ½ β¦ flow velocity of medium [m.s-1]
ππΆππ‘
=π΄ππ’ βπΆ
ππΆππ‘
=βπ’ βππΆππ₯
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Chemical reaction
β Process which changes compoundβs chemical nature (i.e. CAS number of the compound(s) are different)
Zero order reaction β’ reaction rate is independent on the concentration of parent compounds
ππΆππ‘
=βπ0
πΆπ‘=πΆ0βπ0 β π‘
k0 β¦ zero order reaction rate constant [mol.s-1]
C0 β¦ initial concentration of compound [mol.L-1]
Ct β¦ concentration of compound at time t [mol.L-1]
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Chemical reaction
First order reaction:β’ Reaction rate depends linearly on the concentration of one parent compound
ππΆππ‘
=βπ1 βπΆ
πΆπ‘=πΆ0πβπ1 βπ‘
k1 β¦ first order reaction rate constant [s-1]C0 β¦ initial concentration of compound
[mol.L-1]Ct β¦ concentration of compound at time t
[mol.L-1]
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Chemical reaction
Second order reaction:β’ Reaction rate depends on the product of concentrations of two parent compounds
ππΆπ΄
ππ‘=βπ2 βπΆπ΄βπΆπ΅
k2 β¦ second order reaction rate constant of compound A [molΛ1.s-1]
CA, CB β¦ initial concentration of compounds A and B [mol.L-1]
Pseudo-first order reaction:Reaction of the second order could be expressed as pseudo-first order by multiplying the second order rate constant of compound A with the concentration of compound B:
π1 ,π΄=π2 βπΆπ΅k2 β¦ pseudo-first order reaction rate constant
of compound A [s-1]
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Chemical reaction
Michaelis-Menten kinetics:β’ Takes place at enzymatic reactions β’ Reaction rate v [mol.L-1] depends on
β’ enzyme concentrationβ’ substrate concentration Cβ’ affinity of enzyme to substrate Km
(Michaelis-Menten constant)β’ maximal velocity vmax
π=ππππ βπͺπ²π+πͺ
When C << Km approx. first order reaction (transformation velocity equal to C)When C >> Km approx. zero order reaction (transformation velocity independent on C)
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Fugacity
β’ Fugacity β symbol f - proposed by G.N. Lewis in 1901β From Latin word βfugereβ, describing escaping tendency of
chemicalβ In ideal gases identical to partial pressureβ It is logarithmically related to chemical potentialβ It is (nearly) linearly related to concentration
β’ Fugacity ratio F: β Ratio of the solid vapor pressure to supercooled liquid vapor
pressureβ Estimation: π₯π¨π π=βπ .ππ (π»π΄βπππ ) TM β¦ melting point [K]
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Fugacity
β’ Fugacity capacity Z
Gas phase: π π¨=πͺ π¨
π
ZA β¦ fugacity capacity of air [mol.m-3.Pa-1]CA β¦ air concentration [mol.l-1]f β¦ fugacity [Pa]
Water phase: ππΎ=ππ―
ZW β¦ fugacity capacity of water [mol.mΛ3.Pa-1]
H β¦ Henryβs law constant [Pa.m3.mol-1]
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Multimedia Environmental Models
Reason for the using of environmental models:β’ Possibility of describing the potential distribution and environmental
fate of new chemicals by using only the base set of physico-chemical substance properties
β’ Their use recommended e.g. by EU Technical Guidance Documentsβ multi-media model consisting of four compartments
recommended for estimating regional exposure levels in air, water, soil and sediment.β’ Technical Guidance Documents in Support of The Commission Directive
93/67/EEC on Risk Assessment For New Notified Substances and the Commission Regulation (EC) 1488/94 on Risk Assessment For Existing Substances
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Multimedia Environmental Models
Classification of environmental models:β’ Level 1: Equilibrium, closed system, no reactionsβ’ Level 2: Equilibrium, open system, steady state, reactionsβ’ Level 3: Non-equilibrium, open system, steady-stateβ’ Level 4: Non-equilibrium, open system, non-steady state.
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Multimedia Environmental Models
Environmental Models Level 1: Closed system, equilibrium, no reactions
Com
part
men
t 1
Com
part
men
t 2
Com
part
men
t 3
Total mass in system: m [kg]Volumes of compartments Vn [m3]Unknown concentrations Cn
π=πͺπ βπ½π+πͺπ βπ½π+β¦+πͺπ βπ½ π
In equilibrium:
πΆπ
πΆ1
=πΎ π ,1 i = 1, β¦, n
πͺπ=π
π½ π+π²π ,π βπ½π+β¦+π²π ,π βπ½ π
πͺπ=π² π ,π βπͺπ
ππ=π½ π βπͺ π
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Multimedia Environmental Models
Environmental Models Level 2: Equilibrium with source and sink, steady-state, no reactions
Com
part
men
t 1
Com
part
men
t 2
Com
part
men
t 3
INPUT
OUTPUT
Steady-state:
π ππ π
=π
Input = Output
Advection into the system [mol.s-1] : I = Q . C Q β¦ flow [m3.s-1]C β¦ concentration [mol.m-3]
Advection out of the system:
π=βπ
(π π βπΆπβ π ) I β¦ elimination rate (first order rate), flux per volume
π=ππ
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Multimedia Environmental Models
Environmental Models Level 2: Equilibrium with source and sink, unsteady state, no reactions
π ππ π
=πππππβππππππ
ππππ‘
=βπ
πΌ πββπ
(π π βπΆπ βπ )
In equilibrium:πΆπ
πΆ1
=πΎ π ,1 i = 1, β¦, n
ππππ‘
=π 1
ππΆ1
ππ‘+π 2
ππΆ2
ππ‘+β¦+π π
ππΆπ
ππ‘
ππππ‘
=π 1
ππΆ1
ππ‘+πΎ 2,1 βπ 2
ππΆ1
ππ‘+β¦+πΎ π , 1βππ
ππΆ1
ππ‘
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Multimedia Environmental Models
Environmental Models Level 2: Equilibrium with source and sink, non-steady state, no reactions (cont.)
ππΆ1
ππ‘=βπ
πΌ πβπΆ1βπ
(π π βπΎ π , 1 βπ )
π 1+πΎ 2,1βπ 2+β¦+πΎπ ,1 βπ π
orππΆ1
ππ‘=βπ βπΆ1+π
π=βπ
(π π βπΎ π ,1 βπ )
π 1+πΎ 2,1βπ 2+β¦+πΎπ , 1 βπ π
π=βπ
πΌπ
π 1+πΎ 2,1 βπ 2+β¦+πΎ π ,1 βπ π
Solution for C1(t): πͺπ (π )=πβππ+ππ
(πβπβππ )
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Multimedia Environmental Models
Environmental Models Level 3: β’ No equilibrium, sources and sinks, steady state, degradation. β’ For every single compartment input and/or output may occur. β’ The exchange between compartments is controlled by transfer
resistance.
Com
part
men
t 1
Com
part
-m
ent 2
Com
part
-m
ent 3
INPUT 1
OUTPUT 2
INPUT 2
OUTPUT 1
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Multimedia Environmental Models
Environmental Models Level 3 (contd.):
π ππ
π π=π½
π
π πͺ π
π π=π° π+π΅ π+β
π(π΅ ππ )βπͺπ βπ½ π βπ=π
Change of substance mass in compartment (i) = Input Ii + advective transport Ni + diffusive transport Nij β output = 0 (steady state)
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Multimedia Environmental Models
Environmental Models Level 4: β’ No equilibrium, sources and sinks, unsteady state, degradation. β’ For every single compartment input and/or output may occur. β’ The exchange between compartments is controlled by transfer
resistance.
π ππ
π π=π½
π
π πͺ π
π π=π° π+π΅ π+β
π(π΅ ππ )βπͺπ βπ½ π βπβ π
Change of substance mass in compartment (i) = Input Ii + advective transport Ni + diffusive transport Nij β output 0 (unsteady state)
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Further reading
β’ D. Mackay: Multimedia environmental models: the fugacity approach. Lewis Publishers, 2001, ISBN 978-1-56-670542-4
β’ S. Trapp, M. Matthies: Chemodynamics and environmental modeling: an introduction. Springer, 1998, ISBN 978-3-54-063096-8
β’ L. J. Thibodeaux: Environmental Chemodynamics: Movement of Chemicals in Air, Water, and Soil. J. Wiley & Sons, 1996, ISBN 978-0-47-161295-7
β’ M.M. Clark: Transport Modeling for Environmental Engineers and Scientists. J. Wiley & Sons, 2009, ISBN 978-0-470-26072-2
β’ C. Smaranda and M. Gavrilescu: Migration and fate of persistent organic pollutants in the atmosphere - a modelling approach. Environmental Engineering and Management Journal, 7/6 (2008), 743-761
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