thermodynamic modeling of atmospheric inorganic …€¦ · thermodynamic modeling of atmospheric...

Andrey Martynenko, University of Houston, [email protected] Annual CMAS Conference, Chapel Hill, North Carolina, October 1, 2007

Thermodynamic Modeling of AtmosphericInorganic Aerosols.

F.-Y. Cheng†, J. W. He†, A. V. Martynenko † and J. H. Seinfeld⋆

† University of Houston, Houston, TX⋆California Institute of Technology, Pasadena, CA

http://aero.math.uh.edu

Modeling Inorganic Aerosols – p.1/18


Thermodynamic Models• The inorganic constituents of atmospheric particles typically consist of electrolytes of

ammonium, sodium, calcium, sulfate, nitrate, chloride, carbonate, etc. The phase state of such a

mixture at a given temperature and relative humidity will tend to thermodynamic equilibrium

with the gas phase.

• A series of thermodynamic models such asSEQUILIB, SCAPE2, EQUISOLVII, and

ISORROPIA have been developed that attempt to predict the proper ties of inorganic aerosols.

• One of the most challenging parts for the available models isthe prediction of the partitioning

of the inorganic aerosol components between aqueous and solid phases.

• CMAQ uses ISORROPIA model to predict gas-liquid-solid equilibrium in inorganic aerosol.

• UHAERO–Inorganic Module: a new thermodynamic equilibriummodel for multicomponent

inorganic aerosols.



Differences of the Models1. Difference in activity coefficient models:

• ISORROPIA uses Bromley’s model (1973) and the Kusik and Meissner model (1978) for

calculation of activity coefficients.

• UHAERO incorporatesPSC (Clegg et al., 1998) and theExtended UNIQUAC (ExUNIQUAC)

(Thomsen, Rasmussen, 1999) mole fraction based activity coefficients models.

2. Difference in prediction of the aerosol water content:

• ISORROPIA relies on the standard ZSR equation to estimate the aerosol water content.

• UHAERO. The aerosol water content is directly calculated during the computational

process from the activity coefficient model.

3. Difference in prediction of solid phase:

• ISORROPIA relies ona priori knowledge of the presence of phases at a certain relative

humidity and overall composition.

• UHAERO detects crystallization in computational process.

4. Difference in solution method:

• ISORROPIA uses reaction oriented approach to describe the chemical equilibrium.

• UHAERO is based oncanonical formulation of the electrolyte solution system.



Modeling Thermodynamic Equilibrium. UHAERO

• Optimality conditions:

µg + ATg λ = 0,

µl + ATl

λ = 0,

ns ≥ 0, µs + ATs λ ≥ 0, n

Ts (µs + A

Ts λ) = 0,

Agng + Alnl + Asns = b.

• ng , nl, ns: concentration vectors in gas, liquid, and solid phases,

• Ag , Al, As: component-based formula matrices,

• b is the component-based feed vector,

• chemical potential vectors:

µg = µ0g + RT ln ag,

µl = µ0l + RT ln al,

µs = µ0s,

• A primal-dual active set/Newton algorithm is used for the efficient and accurate solution of

thermodynamic equilibrium problems related to modeling ofatmospheric inorganic aerosols.



Ammonium/Sulfate/Nitrate Phase Diagram at 298.15 K

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

Ammonium Fraction − X

Sul

fate

Fra

ctio

n −

Y

T = 298.15K

30 75

70

65

60

55

5045

4035 60

D EF

55

50

60

55

ABC25

20

15

30

G

25

30

35

(NH 2) SO4H SO2 4

3 NH4 NO3

4

HNO

• Ammonium fraction

X =[NH+

4]

[NH+4

] + [H+]

• Sulfate fraction

Y =[SO2−

4]

[SO2−4

] + [NO−

3]

• Seven possible solid phases exist in

this system, labeled as

A = (NH4)2SO4

B = (NH4)3H(SO4)2

C = NH4HSO4

D = NH4NO3

E = 2NH4NO3 · (NH4)2SO4

F = 3NH4NO3 · (NH4)2SO4

G = NH4NO3 · NH4HSO4

• Regions outlined by heavy black lines showthe first solid that reaches saturation with

decreasing RH.

• The thin labeled solid lines arewater activity contours at saturation.

• The dotted lines are the so-calledliquidus linesintroduced by Potukuchi and Wexler (1995).



Phase diagram at T = 283.15K, RH = 50%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1PSC Relative Water Content

0.6

0.6

0.6

11

1

1

1.51.5

1.5

22

2(NH

4)2SO

4

NH4NO

3HNO

3

H2SO

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Sul

fate

Fra

ctio

n −

Y

ISORROPIA Relative Water Content

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.8

0.8

0.8

1

1

1.21.4

H2SO

4

HNO3

NH4NO

3

(NH4)2SO

4

• Isolines of relative water content for two models.

• Metastable equilibrium (no solid phase), open system (reverse ISORROPIA mode).




0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Sul

fate

Fra

ctio

n −

Y

PSC , NH3 (g) , ppb

0.00010.0001

0.0001

0.001

0.001

0.001

0.01

0.01

0.01

0.05

0.05

0.05

0.50.5

0.5

1

1

1

55

5

10

10

(NH4)2SO

4

NH4NO

3HNO

3

H2SO

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Sul

fate

Fra

ctio

n −

Y

ISORROPIA , NH3 (g) , ppb

0.00

01

0.00

1 0.01

0.05

0.05

0.01

0.001

0.00

1

10

0.5

10

0.01

H2SO

4

HNO3

NH4NO

3

(NH4)2SO

4

• Isolines of concentration ofNH3 in gas phase for two models.





0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Sul

fate

Fra

ctio

n −

Y

PSC , HNO3 (g) , ppm

0.01

0.01

0.1

0.10.1

1

1

1

10

10

10

1010

50

50

50

50

100

100

100

100

200

200

200

200

300

300

300

400

400

400

500

500

500

600

600

700

700

800

800

9001000

H2SO

4

HNO3

NH4NO

3

(NH4)2SO

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Sul

fate

Fra

ctio

n −

Y

ISORROPIA , HNO3 (g) , ppm

1

10

0.1

50

100

500

1000

2500

5000

10000

1050

100

250500

1000

2500

5000

1000

0

H2SO

4

HNO3

NH4NO

3

(NH4)2SO

4

• Isolines of concentration ofHNO3 in gas phase for two models.




Phase diagrams in presence of solid phase

Seven possible salts may exist in the system:

A = (NH4)2SO4 (AS),

B = (NH4)3H(SO4)2 (LET),

C = NH4HSO4 (AHS),

D = NH4NO3 (AN),

E = 2NH4NO3 · (NH4)2SO4 (2AN·AS),

F = 3NH4NO3 · (NH4)2SO4 (3AN·AS),

G = NH4NO3 · NH4HSO4 (AN·AHS).




0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

ABE

BEF

L+BD

L+B

PSC Relative Water Content


Sul

fate

Fra

ctio

n −

Y

BDFL+D

L

HNO3

H2SO

4(NH

4)2SO

4

NH4NO

3

2.2 1.8 1.4

1

0.6

0.20.6

0.20.1

0.1

2.2

1.8 1.4

1 0.2

Ammonium Fraction − XS

ulfa

te F

ract

ion

− Y

L+B

AD


ABL

1.2

1.4

1

0.8

0.6

0.4

0.2

0.6

0.8

0.4

0.2

HNO3

H2SO

4(NH

4)2SO

4

NH4NO

3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

• Isolines of water content for two models.

• Heavy black lines outline the regions where indicated saltsexist in solid phase.

• Red colored salts indicate a dry particle, blue colored – liquid particle.

• Open system (reverse ISORROPIA mode).




0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

ABE

BEF

L+BD

L+B

PSC, NH3 (g) , ppb


Sul

fate

Fra

ctio

n −

Y

BDFL+D

L

HNO3

H2SO

4(NH

4)2SO

4

NH4NO

3

5e−05

0.0001

0.0001

5e−05 0.0005

0.0005

0.0005

0.00

5

0.005

0.01


ulfa

te F

ract

ion

− Y

L+B

AD

ISORROPIA, NH3 (g) , ppb

ABL

0.02

0.01

0.00

50.

0005

0.00

01

HNO3

H2SO

4(NH

4)2SO

4

NH4NO

3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1








0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

ABE

BEF

L+BD

L+B

PSC, HNO3 (g) , ppm


Sul

fate

Fra

ctio

n −

Y

BDFL+D

L

HNO3

H2SO

4(NH

4)2SO

4

NH4NO

3

500

300

100

600

600

800

1000

500

400

400 200

200

100

50 50

50

10

10 10


ulfa

te F

ract

ion

− Y

L+B

AD

ISORROPIA, HNO3 (g) , ppm

ABL

50

10 1

10

50

100300

500

750

1000

2500

300

500

5000

HNO3

H2SO

4(NH

4)2SO

4

NH4NO

3

200

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

• Isolines of concentration ofHNO3 in gas phase for two models.






Ammonium/Sulfate Phase Diagram at T = 298.15K

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

L+A

ABL+B

BCL+C

L


RH

PSC Relative Water Content

0.20.6

1

1.4

1.8

2.2

2.6

3

3.43.8

4

0.2

0.6

1.2

1.6

2

2.4

3

4 4

2.8

1.6 0.8

(NH4)2SO

4H

2SO

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

(NH4)2SO

4


RH

H2SO

4

L+A

AB

L+C BC

L+BCL+B

L


0.2

0.61

1.4

0.8

0.4

1.2

1.8

2.2

2.6

3.23.64

0.20.

6

1

1.4

2.4

3.24

2

2.8

4







Ammonium/Sulfate Phase Diagram at T = 298.15K

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

L+A

ABL+B

BCL+C

L

Ammonium Fraction − XH

2SO

4(NH

4)2SO

4H

2SO

4

RH

PSC, NH3 (g) , ppb

0.0001

0.001

0.001

0.0001

0.005

0.00

5

0.005

0.1

0.1

0.5

1

1

1020

0.5

0.5

0.5

0.5

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

(NH4)2SO

4


RH

H2SO

4

L+A

AB

L+C BC

L+BCL+B

L

ISORROPIA, NH3 (g) , ppb

0.02

0.001

0.001

0.005

0.02

0.02

0.1

0.1

0.5

1

10

0.5

0.05

0.05

0.25







http://aero.math.uh.edu

– p.15/18


UHAERO-Inorganic Module

YES

YES

NO

NO

Initializations of concentrations and dual variables

Define the set of active constraints Is

Construction of the Newton systemprojected on the set of active constraints

Computation of the Newton direction

Add new saturated solidsto the active set Is

Check if the algorithm converges

When convergence is achieved,check if solid concentrationsare negative (ns < 0)

If yes, delete solidfrom the active set Is

Optimum is reached

• UHAERO-Inorganic Module can be run in two modes:

(1) the water content in the system is specified; (2) the

system is equilibrated to a fixed relative humidity

(RH).

• In case (2),the aerosol water content is directly

computed from the minimization process, i.e., without

using an empirical relationship such as the ZSR

equation.

• The water activity is predicted using either PSC or

ExUNIQUAC.

• The equilibration of trace gases between the vapor and

condensed phases can be enabled or disabled as re-

quired, as can the formation of solids, whichallows

the properties of liquid aerosols supersaturated with re-

spect to solid phases to be investigated.

UHAERO-Inorganic Module – p.16/18


Phase diagram at T = 298.15K, RH = 75.78%

2.25

2.25

2.5

2.5

2.5

2.5

2.5

3

3

3

3.53.5

3.5

44

44.5


Sul

fate

Fra

ctio

n −

Y

Relative water contentRH = 75.78 % T = 298.15 K

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

0.5

1

1

1

1.5

1.51.5

1.5

2

2

2

2

2

2.5

2.5

2.5

2.5

2.5

3

3

3.54


Sul

fate

Fra

ctio

n −

Y


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

PSC model ISORROPIA model



PSC & ISORROPIA Water Content – p.17/18


Phase diagram at T = 298.15K, RH = 75.78%

2.25

2.25

2.5

2.5

2.5

2.5

2.5

3

3

3

3.53.5

3.5

44

44.5


Sul

fate

Fra

ctio

n −

Y


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

2.5

3

3

3

3.5

3.5

3.5

44

4

4.5

4.5


Sul

fate

Fra

ctio

n −

Y


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PSC model ExUNIQUAC model


• Metastable equilibrium (no solid phase), open system.

PSC & ExUNIQUAC Water Content – p.18/18

thermodynamic modeling of atmospheric inorganic …€¦ · thermodynamic modeling of atmospheric...

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