Learning objective and outline
Objectives:
• To understand what fate modelling is
• To understand the role of fate modelling in USEtox
• To understand how fate modelling is applied in USEtox
Chemical fate modelling
Overview of typical mass balance concepts and introduction
to transport and degradation rate calculations as well as
matrix solutions
Outline
1.What is chemical fate
2.Chemical fate processes
3.What is chemical fate modelling
4.How is chemical fate modelling applied in USEtox
5.Exercise
6.Presentation of solution to exercise
7.Questions
Assistant professor
Morten Birkved
[email protected]
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DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
2
What is chemical fate
A matter of (important) details?
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
What is chemical fate modelling
Do we need fate and exposure models in LCA?
Fate and exposure models serves
one purpose only in impact
assessment of chemical emissions:
Prediction of chemical behavior
in the environment
The prediction power of the
chemical fate and exposure models
facilitates the quantification of the
marginal toxicological impacts
occurring in LCIA caused by
chemical emissions.
3
DTU Management Engineering,
Technical University of Denmark
What is chemical fate
A matter of chance?
5
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
4
USEtox short course – chemical fate modelling
09/04/2010
USEtox short course – chemical fate modelling
09/04/2010
What is chemical fate
A matter of chance?
?
USEtox short course – chemical fate modelling
DTU Management Engineering,
Technical University of Denmark
09/04/2010
6
DTU Management Engineering,
Technical University of Denmark
What is chemical fate
Adressing chemical behaviour in the environment
in LCA
What is chemical fate
Severity of chemical emissions
a)What main fate properties determines the fate pattern of a
chemical emission - i.e. which overall properties controls the fate
of a chemical emission?
1. It’s mobility (transport potential)
2. Is ability to avoid degradation (persistence)
Assessment resolution:
”Single compound” assessment (CAS number resolution)
Impact potential
IP = Q × CF
b)What factors determines the severity/impact potential of a
chemical emission – i.e. which factors controls the impact
potential of a chemical emission?
1. It’s toxicity (affinity for a specific receptor)
2. It’s exposure pattern (availability to interact with a receptor)
3. It’s fate pattern (ability to reach (i.e. mobility) and have time (i.e.
persistence) to interact with a receptor)
Assessment of ecotoxicological impacts :
CF = EF × FF × XF
Assessment of human toxicological
impacts:
CF = EF × FF × XF = EF × IF
7
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
8
What is chemical fate
Role of fate models in LCA
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
What is chemical fate
Role of fate and exposure in LCIA
Emissions into compartment m
Inhalation
Plant
Air
Chemical
fate
Fraction transferred to n
Fate
factor
Time integrated concentration  in n
Soil
Degradation
+
Water
Concentration
- response
Effect
factor
Sediment
Direct source term
Inter-media
transfer factors
Environmental distribution of chemical – resulting human exposure
9
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
10
Chemical fate processes
Major grouping
Potentially affected
fraction of species
Risk of affected
persons
Human
exposure
Potency
(Dose response)
Severity
Effect
factor
Damage on
human health
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
Chemical fate processes
Multimedia partioning of chemicals
Abiotical processes
•Degradation
•Sorption
•Advection
•Convection
4
5
air
3
6
solid and
air
1
-1
log(Kaw)
Biological processes
•Biodegradation/biotransformation
•Biotransfer
Dose taken in
Time and space
integrated
damage on
ecosystems
Severity
Ingestion
Species
exposure - intake
Intake
fraction
iF
water and
air
-3
8
multimedia
-5
-7
-9
Solid
water
-11
water and
solid
-13
-15
-3
-1
1
3
5
7
9
Log(Kow)
11
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
12
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
Chemical fate modelling
Nested models
Chemical fate modelling
Modelling principles – model approaches
[A]i or j
Ki/j
Compartment i
Ki/j
Ki/j
Compartment j
Ki/j
[A]
Ki/j  i
[A]j
time
Huijbregts et al. 2010
13
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
14
Chemical fate modelling
Modelling principles – model approaches
[A]i
Steady state
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
Chemical fate modelling
Modelling principles – model approaches
d[A]i
0
dt
time
Mackay (2001)
15
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
16
OUT
TRANSFORMATION
– Degradation processes km,deg [hour-1]
• biodegr., hydrolysis, photolyis, etc.
dM/dt = In - Out
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Technical University of Denmark
09/04/2010
INPUTS
– Emission or Source, Sm [kg/hour]
– Intermedia transfer rate coefficient ki,m [hour-1]
• From other compartments
• From outside the system
OUTPUTS
– Intermedia transfer rate coefficient km,i [hour-1]
• To other compartments
• Burial processes into deep sediments
• Advection out of the system
Lavoisier principle of mass conservation:
« In all operations of nature, matter cannot be created/destroyed,
although it may be rearranged. This implies that for any chemical process
in a closed system, the mass of the reactants must equal the mass of the
products »
Air
USEtox short course – chemical fate modelling
Chemical fate modelling
Basic processes for environmental mass balance
modeling
Chemical fate modelling
Mass balance model
IN
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
18
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
Chemical fate modelling
Equilibrium and/or Steady state: IN = OUT
Chemical fate modelling
Rate Constant - Half-life Relationship
dM/dt = 0
dM/dt = In ‐ Out
Air
IN
OUT
OUT
Air
S
dM/dt = ‐k ∙ M
k∙M
k·M
Per definition: M(½ )/M(0)=0.5
Removal rate coefficient: k [day‐1]
Emission rate: S [kg/day]
(fraction of mass eliminated per day)
Mass in compartment: M [kg]
Half‐life: ½ [day]
S=
Removal rate coefficient: k [per day]
½ = ln(2)/k
(days to eliminate half of mass)
(fraction of mass eliminated per day)
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DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
20

Like electric resistances
Dynamic:
kout
Steady State:
ka,deg
i
Units = time
21
DTU Management Engineering,
Technical University of Denmark
1
 ½,tot

1
1


dM
dt
a
=
k
·

M
09/04/2010
1
Water
09/04/2010
22
How is chemical fate modelling applied in
USEtox
Exercise: Fate of TCE in a two-compart. Syst.
DTU Management Engineering,
Technical University of Denmark

+ S
Fate factor matrix
 0
M   k ‐1  S
Source
vector
(kg/h)
Rate coefficient
matrix (1/h)
Air
Air
 ½,1  ½,2  ½,3
USEtox short course – chemical fate modelling
M (t )
Mass
vector
(kg)
1 1 1 1
  
R R1 R 2 R 3
ka,i
k a,tot  k a,out   k a,i  k a,deg
USEtox short course – chemical fate modelling
How is chemical fate modelling applied in
USEtox
Matrix Algebra Solution Dynamic and steady
state solution
Chemical fate modelling
Removal rate coefficients k
Air
DTU Management Engineering,
Technical University of Denmark
  ka ,t
 Ma 

  1 
 Mw 
 kaw
Water
1
kwa   Sa 
  
 kw ,tot   Sw 
USEtox short course – chemical fate modelling
09/04/2010
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compart. syst.
Trichloroethylene (TCE) is a colourless, somewhat toxic, volatile liquid belonging to the family of organic halogen compounds. It is a chemical widely used in industry as a solvent in dry cleaning, in degreasing of metal objects, and in extraction processes, such as removal of caffeine from coffee or of fats and waxes from cotton and wool
Air volume = 2.5 · 1011 m3
kdeg,a =
Air outflow =
1.45 · 1012 m3/d air
kadv,a =
TCE emissions to water = 590 kg/d Water outflow = 2 · 107 m3/d water
Q1) Determine the total rate coefficients in air and water?
kadv,w =
kdeg,w =
Q2) Which is the dominant removal pathway in air and in water respectively?
Water volume = 3 · 109 m3
Air‐to‐water transfer factor, kaw = 5.57 · 10‐3 days‐1
Water‐to‐air transfer factor, kwa = 1.91 · 10‐1 days‐1
23
DTU Management Engineering,
Technical University of Denmark
Atmospheric degradation half‐life = 15 days
Aquatic degradation half life = 150 days USEtox short course – chemical fate modelling
09/04/2010
23
24
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compart. syst.
Solutions
Q3: Determine the Mass (or Concentration in air and water respectively)?
25
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
26
25
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compartment system - Q1
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
26
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compartment system - Q1
Compartment
Air
Calculation of rate costants for advective loss
Volume
Advective flow
Air
3
Vair=
Water
2,50E+11 m
3
Vwater= 3,00E+09 m
Fair=
Loss process
Rate constant for advective loss
3
1,45E+12 m /d
3
Fwater= 2,00E+07 m /d
Fair/Vair=
Fwater/Vwater=
5,80 days
‐1
0,0067 days
‐1
Water
Rate constant
Loss process
Rate constant
5,8000 days
‐1
Advection
0,0067 days
‐1
Degradation
0,0462 days
‐1
Degradation
0,0046 days
‐1
Inter‐media exchange (air→water)
0,0056 days
‐1
Inter‐media exchange (water→air)
0,1910 days
‐1
5,85 days
‐1
Total
0,20 days
‐1
Advection
Total
Conversions of half‐lives to rate coefficients
Rate constants for degradation
Half‐lives
15 days
kdegA=ln(2)/τ½ (degA)=
0,0462 days
‐1
150 days
kdegw=ln(2)/τ½ (degW)=
0,00462 days
‐1
Atmospheric degradation half‐life τ½ (degA)=
Aquatic degradation half‐life
27
τ½ (degW)=
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
28
27
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compartment system – Q2
Loss process
M   k ‐1  S
Rate constant
Advection
5,8000 days
‐1
Advection
0,0067 days
‐1
Degradation
0,0462 days
‐1
Degradation
0,0046 days
‐1
Inter‐media exchange (air→water)
0,0056 days
‐1
Inter‐media exchange (water→air)
0,1910 days
‐1
5,85 days
‐1
Total
0,20 days
‐1
Total
09/04/2010
28
Steady state mass
Water
Rate constant
USEtox short course – chemical fate modelling
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compartment system – Q3
Compartment
Air
Loss process
DTU Management Engineering,
Technical University of Denmark
Step 1:
Calculate fate matrix
(  k ‐1 )
1
  0.17  0.16 
 k  

  0.01  5.01 
Step 2:
Dominant removal process
for air
29
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Technical University of Denmark
Calculate product of and source vectors
Dominant removal process
for water
USEtox short course – chemical fate modelling
09/04/2010
29
30
DTU Management Engineering,
Technical University of Denmark
(k ‐1  S)
USEtox short course – chemical fate modelling
09/04/2010
30
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compartment system –
Q3 step 1
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compartment system –
Q3 step 1
Inversion of matrix
Compartment
Air
Water
Loss process
Rate constant
Loss process
Rate constant
Advection
5,8000 days
‐1
Advection
0,0067 days
‐1
Degradation
0,0462 days
‐1
Degradation
0,0046 days
‐1
Inter‐media exchange (air→water)
0,0056 days
‐1
Inter‐media exchange (water→air)
0,1910 days
‐1
5,85 days
‐1
Total
0,20 days
‐1
Total
 kair _ tot
k  
 kair _ water
 5 . 85
k  
 0 . 01
31
kwater _ air
kwater _ tot



0 . 19 

0 . 20 
Source: mathworld.wolfram.com
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
31
32
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compartment system –
Q3 step 1
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
32
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compartment system – Q3
Steady state mass
 5 .85  0 .19 

k  
0 .2 
  0 .01
1
 0 .20
1  5 .85  0 .19 
1


k  
0 .2  5 .85  0 .2  0 .19  0 .01  0 .01
k   0 .01
1

k
1
k
33
1  0 .20

1 .17  0 .01
0 .19 

5 .85 
 0 .17
  1  
 0 .01
M   k ‐1  S
0 .16    0 .17

5 .01    0 .01
09/04/2010
33
 0 

S  
 590 
Original scenario
Comparative scenario
Air
Water
Air
0.171 0.163
Water 0.009 5.008
Additive scenario
Air
Water
Air
0.171 0.163
Water 0.009 5.008
35
DTU Management Engineering,
Technical University of Denmark
1
  0.17  0.16 

 k  
  0.01  5.01 
Source matrix
[kg/day]
Air
Water
Air
0.171 0.163
Water 0.009 5.008
Air
x
Mass matrix
[kg]
Water
Air
0
0
=
0
590
Air
x
Water
0 96.0
0 2954.8
590
0
Water
Air
Water
0
101.0 96.0
=
590
5.1 2954.8
0
0
Water
Air
Water
590
0.0 197.0
=
590
0.0 2959.8
Air
x
1
  0.17  0.16 

 k  
  0.01  5.01 
Step 2:
(k ‐1  S)
 0 .16 

 5 .01 
USEtox short course – chemical fate modelling
Fate matrix
[days]
(  k ‐1 )
Calculate product of and source vectors
How is chemical fate modelling applied in
USEtox
Fate of TCE in a two-compartment system –
Q3 step
M   k ‐1  S
Calculate fate matrix
Fate factor matrix
DTU Management Engineering,
Technical University of Denmark
Source matrix [kg/day]
Step 1:
0 .19 

5 .85 
USEtox short course – chemical fate modelling
09/04/2010
35
34
DTU Management Engineering,
Technical University of Denmark
USEtox short course – chemical fate modelling
09/04/2010
34