Atmospheric Aerosol - American Chemical Society

1

New Developments in Receptor Modeling Theory

Downloaded by KAOHSIUNG MEDICAL UNIV on June 10, 2018 | https://pubs.acs.org Publication Date: October 13, 1981 | doi: 10.1021/bk-1981-0167.ch001

S. K. FRIEDLANDER Department of Chemical, Nuclear, and Thermal Engineering, University of California—Los Angeles, Los Angeles, CA 90024

Receptor modeling has become an important tool for developing particulate air pollution control strategies. Current receptor models for ambient aerosol source resolution begin with the measured chemical properties of the aerosols at a given site and infer the mass contributions of various sources to the total measured mass. Rate processes are not involved in these models. In this paper, the theory is extended to the resolution of the v i s i b i l i t y degrading components of the aerosol and to chemically reactive families of chemical compounds. Conditions are discussed under which a linear relationship with constant coefficients exists between the aerosol light extinction coefficient and source mass contributions. Linear models for reactive chemical species are set-up and applied to polycyclic aromatic hydrocarbons using data from the literature. In both cases-light extinction and chemical r e a c t i v i t y - i t is useful to introduce rate process models in developing the theory. Emission inventories strategies

are often

used t o develop

control

f o r p a r t i c u l a t e p o l l u t i o n , butthere are d i f f i c u l t i e s

0097-6156/81/0167-0001 $ 0 5 . 0 0 / 0 © 1981 American Chemical Society

Macias and Hopke; Atmospheric Aerosol ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

2

ATMOSPHERIC AEROSOL

w i t h t h e i r use t r a n s p o r t and size.

i n c l u d i n g secondary a e r o s o l f o r m a t i o n ,

s u c h as s o i l

A different

dust

and

these d i f f i c u l t i e s .

the marine a e r o s o l .


the

i s a b l e t o d e a l w i t h some o f

A e r o s o l p r o p e r t i e s can be d e s c r i b e d by means

of d i s t r i b u t i o n f u n c t i o n s w i t h r e s p e c t and

composition.

The

to p a r t i c l e s i z e

and

d i s t r i b u t i o n f u n c t i o n s change w i t h

s p a c e as a r e s u l t o f v a r i o u s a t m o s p h e r i c p r o c e s s e s ,

and

d y n a m i c s o f t h e a e r o s o l can be d e s c r i b e d m a t h e m a t i c a l l y equations

which take

sedimentation wind f i e l d ,

O,

to

hard-to-characterize

approach which a l s o s t a r t s from

c h a r a c t e r i s t i c s of the emissions

chemical

range

p a r t i c l e d e p o s i t i o n from the atmosphere a c c o r d i n g

There a r e , i n a d d i t i o n , important

sources

long

time

the

by c e r t a i n

i n t o account p a r t i c l e growth, c o a g u l a t i o n

Chap. 1 0 ) .

These e q u a t i o n s

p a r t i c l e d e p o s i t i o n v e l o c i t y and

g a s - t o - p a r t i c l e conversion

can be rates

and

s o l v e d i f the

of

a r e known, t o p r e d i c t t h e p r o p e r t i e s o f

t h e a e r o s o l downwind f r o m e m i s s i o n

sources.

This approach i s

known as d i s p e r s i o n m o d e l i n g . W h i l e s u c h c a l c u l a t i o n s can be c a r r i e d out are

in principle,

i n f a c t r a r e l y p o s s i b l e i n t h e d e t a i l needed f o r

r e l i a b l e a i r q u a l i t y / e m i s s i o n source pollution.

relationships for particulate

D i s p e r s i o n m o d e l i n g however, i s n e c e s s a r y

t h e a i r q u a l i t y e f f e c t s o f a new

to p r e d i c t

s o u r c e w h i c h i s t o be

a r e g i o n where a i r q u a l i t y / e m i s s i o n s o u r c e poorly

they

developing

located i n

r e l a t i o n s h i p s are

understood.

A t h i r d method o f r e l a t i n g a i r q u a l i t y t o e m i s s i o n s f r o m the c h a r a c t e r i s t i c s o f t h e a e r o s o l a t a r e c e p t o r sites).

(A r e c e p t o r

site

i s a measurement p o i n t not

l o c a t e d i n t h e e f f l u e n t s t r e a m f r o m an e m i s s i o n

starts

site

(or

directly

source.)

The

m e a s u r e d p r o p e r t i e s o f t h e a e r o s o l i n c l u d i n g t o t a l mass,

light

e x t i n c t i o n or chemical

the

separate those

sources

composition

are then a l l o c a t e d to

c o n t r i b u t i n g t o t h e a e r o s o l by methods s u c h as

d e s c r i b e d below.

This approach-starting

from

the

measurement s i t e and w o r k i n g b a c k t o t h e s o u r c e s - i s known as r e c e p t o r m o d e l i n g . The reviewed

by Gordon

Aside

r e c e p t o r m o d e l a p p r o a c h has

r e c e n t l y been

(2).

from a p p l i c a t i o n s to s p e c i f i c r e g i o n s

or

l o c a t i o n s , new

d e v e l o p m e n t s i n r e c e p t o r m o d e l i n g have t e n d e d t o t a k e p l a c e i n of t h r e e broad c a t e g o r i e s : e x p e r i m e n t a l

one

m e t h o d s , d a t a a n a l y s i s and


1.

FRIEDLANDER

Receptor

physical theory.

Modeling

Theory

3

The d e v e l o p m e n t o f n o v e l e x p e r i m e n t a l t e c h n i q u e s

has been s t i m u l a t e d by t h e need f o r c l o s i n g mass b a l a n c e s on t h e c o l l e c t e d a e r o s o l o r o f measuring substances.

c o n c e n t r a t i o n s o f key t r a c e

C a r b o n and i t s compounds have b e e n a p a r t i c u l a r l y

d i f f i c u l t component o f t h e a e r o s o l on w h i c h t o c l o s e mass b a l a n c e s b e c a u s e o f measurement

difficulties.

A c o n s i d e r a b l e e f f o r t has statistical

gone i n t o t h e a p p l i c a t i o n o f

techniques t o the a n a l y s i s o f a e r o s o l data f o r t h e


e x t r a c t i o n of source c o n t r i b u t i o n s .

The use o f n o v e l

methods has been s t i m u l a t e d by u n c e r t a i n t i e s

statistical

i n the data

collected

i n f i e l d measurements and i n s o u r c e c h a r a c t e r i z a t i o n ; i n some c a s e s n o t a l l o f t h e s o u r c e s a r e known. The

b a s i c t h e o r e t i c a l e q u a t i o n (3.) r e l a t i n g

source

c o n t r i b u t i o n s and c h e m i c a l c o m p o s i t i o n i s a mass b a l a n c e r e q u i r e s no c o n s i d e r a t i o n o f r a t e p r o c e s s e s . theory i s extended

which

I n t h i s paper, t h e

t o the r e s o l u t i o n o f the v i s i b i l i t y

degrading

components o f t h e a e r o s o l and t o c h e m i c a l l y r e a c t i v e f a m i l i e s o f c h e m i c a l compounds. analyses which and

These e x t e n s i o n s r e q u i r e new t h e o r e t i c a l

take i n t o account

the dynamics o f a e r o s o l growth

chemical k i n e t i c s , r e s p e c t i v e l y .

processes are the s u b j e c t o f t h i s

The e x t e n s i o n t o t h e s e

We s t a r t f r o m t h e c h e m i c a l e l e m e n t b a l a n c e s o u r c e r e s o l u t i o n as a r e f e r e n c e a p p r o a c h necessary t o a l l o f the d i s c u s s i o n which

c o n c e n t r a t i o n o f element

measured a t a r e c e p t o r s i t e

i

(CEB) method (3.) o f

a l t h o u g h i t i s not follows.

C h e m i c a l E l e m e n t B a l a n c e s : Maximum L i k e l i h o o d The

rate

paper.

Method

(mass p e r u n i t volume o f a i r )

i s r e l a t e d t o the source

contributions

by

p.

-

Z

c. .

i = 1,

m

2

(1)

n

where c . . = mass f r a c t i o n o f s p e c i e s from source

j

a t the r e c e p t o r

i

m. = mass o f m a t e r i a l f r o m s o u r c e at

1

the r e c e p t o r The

i n the p a r t i c u l a t e

matter

site. j

p e r u n i t volume o f a i r

site.

source c o n c e n t r a t i o n m a t r i x

c.. should correspond


t o the

ATMOSPHERIC

4 p o i n t o f measurement.

AEROSOL

I f t h e r e i s no f r a c t i o n a t i o n between t h e

s o u r c e and r e c e p t o r s i t e ,

c..

i s equal to i t s v a l u e at the

s o u r c e ; t h i s i s t h e assumption* u s u a l l y made. The g o a l o f t h e a n a l y s i s i s t o d e t e r m i n e contributions equations m.


a least

the source

U s u a l l y t h e r e a r e more

t h a n unknowns, t h a t i s , more m e a s u r e d e l e m e n t a l p.

concentrations of

by i n v e r t i n g E q . ( 1 ) .

m.

t h a n s o u r c e c o n t r i b u t i o n s m. . The v a l u e s

f o r t h i s over-determined s q u a r e s method i n w h i c h

system

estimated

can be

the f o l l o w i n g assumptions

using are

made: 1.

P.

The e r r o r s a f f e c t i n g t h e measurement o f

are

n o r m a l l y d i s t r i b u t e d and u n c o r r e l a t e d . 2.

The m e a s u r e d v a l u e s o f t h e s o u r c e c o n c e n t r a t i o n s a r e exact.

3.

s e t (maximum l i k e l i h o o d If

p.

The s e t o f measurements o f

the f i r s t

i s t h e most

probable

principle).

two c o n d i t i o n s a r e met, t h e p r o b a b i l i t y ,

o b s e r v i n g a s e t o f m e a s u r e d c o n c e n t r a t i o n s between p.

p +dp

, . . . p + dp

where

c^.m.

1 1

n

n

is

l

(A) :

P.

represents the exact v a l u e of

1

the a b s e n c e ^ ' ' e r r o r

i n the measurements;

a

P , of

, . . . P n

and

obtained i n

i s the standard P.

d e v i a t i o n i n t h e measurement o f By t h e t h i r d a s s u m p t i o n p.

P

i n Eq.

.

1

above, the measured s e t o f v a l u e s o f

r e p r e s e n t s t h e most p r o b a b l e

maximizing

p.

s e t , which

i s equivalent to

(2).


1.

FRIEDLANDER

Receptor

The v a l u e o f P 1f

m. s m^

Modeling

i s m a x i m i z e d by c h o o s i n g t h e v a l u e s o f t h e

w h i c h m i n i m i z e tt h e argument o f t h e

function

5

Theory

exponential

i n Eq. ( 2 ) :

fp . - E c. .m.\ X

=

; Z

r

i = i

-

3

1

^

J

J

n

/

'

(3)


1 = 1

S e t t i n g the d e r i v a t i v e o f X

with

r e s p e c t t o each

z e r o r e s u l t s i n an e x p r e s s i o n w h i c h c a n be s o l v e d i n d i v i d u a l source c o n t r i b u t i o n s

equal t o

m. .

o f t h e CAB method have b e e n r e v i e w e d by

Previous applications the

m.

for*'the

NAS ( 5 ) . The method has been a p p l i e d

by M i z o h a t a and Mamuro

(6.) t o s e p a r a t e s i z e r a n g e s o f t h e Osaka ( J a p a n ) a e r o s o l with

a cascade impactor.

t o c a s e s where t h e r e a r e u n c e r t a i n t i e s source concentrations

V i s u a l Range-Emission Source The v i s u a l r a n g e by

the

o f known v a l u e i n t h e

a s w e l l as i n P . .

c.

( b a s e d on F r i e d l a n d e r ,

collected

Watson (7_) h a s e x t e n d e d t h e CEB method

Relationships

Chap. 11 (1_) a n d O u i m e t t e ( 8 ) ) s

i s r e l a t e d t o the e x t i n c t i o n c o e f f i c i e n t

expression: s* =

1412

(4)

The e x t i n c t i o n c o e f f i c i e n t f o r an a e r o s o l particles

i s given by: r°° , 2 TTd j£K

e x t

composed o f s p h e r i c a l

(x,m) n ( d ) d ( d ) p

p

(5)

where K

i s the p a r t i c l e e x t i n c t i o n c r o s s - s e c t i o n , x = TTd / X , ext . . p m = r e f r a c t i v e i n d e x and X i s the wavelength o f the i n c i d e n t light.

I t i s necessary t o c l a r i f y

cross-section.

the nature o f the e x t i n c t i o n

I f a l l the p a r t i c l e s i n the aerosol

are s p h e r i c a l


6

and

ATMOSPHERIC AEROSOL

composed o f t h e same m a t e r i a l , t h e r e i s no a m b i g u i t y , and

e x t i n c t i o n c r o s s - s e c t i o n can be o b t a i n e d f r o m Mie homogeneous s p h e r e

of a g i v e n r e f r a c t i v e

o r i g i n a t e from d i f f e r e n t

sources

and

index.

the

theory for a I f the

consequently

particles

are of

different

c h e m i c a l c o m p o s i t i o n (and r e f r a c t i v e i n d e x ) , a s t r o n g c o a g u l a t i o n p r o c e s s w o u l d be n e c e s s a r y particle level.

The

to achieve uniform composition at

the

time t o a c h i e v e t h i s d e g r e e o f c o a g u l a t i o n i s

u s u a l l y t o o g r e a t compared w i t h a t m o s p h e r i c

residence times.


Hence s u c h a e r o s o l s , i n t e r n a l m i x t u r e s , a r e u s u a l l y n o t good r e p r e s e n t a t i o n f o r a p o l l u t e d atmosphere c o n t a i n i n g p a r t i c l e s many d i f f e r e n t

sources.

I n t h e g e n e r a l c a s e , i n d i v i d u a l p a r t i c l e s have compositions in detail

from

and r e f r a c t i v e

i n d i c e s and

differing

to take t h i s

into

i s not p o s s i b l e from a p r a c t i c a l p o i n t of view.

a l l o w f o r a v a r i a t i o n of r e f r a c t i v e

account To

i n d e x , a convenient model i s

t h a t of a m i x t u r e of a e r o s o l s from the s e v e r a l s o u r c e s , each w i t h its

own

extinction cross-section.

The

particles

a r e assumed n o t

t o c o a g u l a t e so t h a t t h e a e r o s o l i s n o t m i x e d on t h e particle basis.

individual

Such an a e r o s o l i s known as an e x t e r n a l m i x t u r e .

T h i s m o d e l w o u l d a l s o be a p p l i c a b l e , a p p r o x i m a t e l y , t o an a e r o s o l m i x t u r e whose p a r t i c l e s

are growing

i n s i z e by

gas-to-particle

conversion. Equation aerosol.

(5)

can t h e n be a p p l i e d t o e a c h component o f

F o r component

r e w r i t t e n as

i

the

o f t h e m i x t u r e , t h i s e x p r e s s i o n can

follows:

r

0

0

b. = — m. \ - — r l 2 l I p ,d ) i 1

p K

i

.m. l

dM. —^ — d log d

d log d P

P

(6)

where dM. = p. , n . ( d ) d ( d ) i s t h e mass o f m a t e r i a l f r o m l i o i p p source I i n the p a r t i c l e s i z e range between d and d + d ( d ) , P P p. i s the d e n s i t y of the m a t e r i a l from source i and m. i s t n e t o t a l mass o f m a t e r i a l f r o m s o u r c e The

extinction coefficient b =

£ b. = i 1

E i

i .

f o r the m i x t u r e

i s t h e n g i v e n by

Y.m. 1

1


(7)

be

1.

FRIEDLANDER

where

y.

component

Receptor

Modeling

7

Theory

t h e e x t i n c t i o n c o e f f i c i e n t p e r u n i t mass f o r e a c h i s g i v e n by t h e e x p r e s s i o n : dM. 1


p.m. d l o g d l i p

(8)

d log d p

T h e r e a r e a t l e a s t two ways t o e v a l u a t e t h e c o e f f i c i e n t s

y. : l

They c a n be c a l c u l a t e d f r o m t h e o r y i f t h e e x t i n c t i o n c r o s s - s e c t i o n and mass d i s t r i b u t i o n s a r e known.

C a l c u l a t i o n s o f t h i s t y p e have

r e c e n t l y been made by O u i m e t t e ( 8 ) . The c o e f f i c i e n t s measuring

y.

c a n a l s o be o b t a i n e d e m p i r i c a l l y b y

b , t h e m.'s and t h e n c a r r y i n g o u t a r e g r e s s i o n

a n a l y s i s t o determine

the best set o f values f o r

C o n d i t i o n s f o r Constant Values

o f y.

Y^ ( 9 ) .

y^

v a r y f o r d i f f e r e n t a e r o s o l components, t h e

l a r g e v a l u e s c o r r e s p o n d i n g t o t h e components w i t h t h e h i g h e s t e x t i n c t i o n c o e f f i c i e n t s p e r u n i t mass o f a e r o s o l m a t e r i a l . y.

i s constant, the e x t i n c t i o n c o e f f i c i e n t

through

the c o e f f i c i e n t s

y.

i s linearly

t o t h e mass c o n t r i b u t i o n s o f t h e

various sources; t h i s considerably s i m p l i f i e s analyses visibility

degradation t o source

E q u a t i o n (8) shows t h a t

When

related

y.

relating

contributions. depends p r i m a r i l y on two f a c t o r s ,

the e x t i n c t i o n c r o s s - s e c t i o n K

a n d t h e n o r m a l i z e d mass ext

d i s t r i b u t i o n o f the a e r o s o l .

F o r y.

t o be c o n s t a n t a t a g i v e n

l o c a t i o n , t h e n o r m a l i z e d mass d i s t r i b u t i o n must be i n d e p e n d e n t o f time.

Similarly

f o r y. t o be i n d e p e n d e n t

of location, the

n o r m a l i z e d mass d i s t r i b u t i o n must n o t v a r y f r o m p l a c e t o p l a c e . R e c e n t measurements by O u i m e t t e (

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