Application of Fugacity Models to the Estimation of Chemical

9 Application of Fugacity Models to the Estimation of Chemical Distribution and Persistence in the Environment

Downloaded by EAST CAROLINA UNIV on March 8, 2017 | http://pubs.acs.org Publication Date: August 30, 1983 | doi: 10.1021/bk-1983-0225.ch009

DONALD MACKAY, SALLY PATERSON, and MICHAEL JOY University of Toronto, Department of Chemical Engineering and Applied Chemistry, Toronto, Ontario, Canada M5S 1A4 The r o l e s of mathematical models f o r p r e d i c t i n g the likely behavior of chemicals i n r e a l and e v a l u a t i v e environments are discussed, and it is suggested that more c o n s i d e r a t i o n should be given to d e f i n i n g acceptable l e v e l s of model complexity. The concepts underlying a s e r i e s of f u g a c i t y models are described and illustrated by applying the models to ( i ) an assessment of the behavior of a t r i c h l o r o biphenyl with four f u g a c i t y models of an e v a l u a t i v e lake environment as an illustration of various l e v e l s of complexity (ii) an assessment of the r e l a t i v e behavior of mono, di, tri and t e t r a chlorobiphenyls in the same environment as an illustration of the e f f e c t of changing chemical p r o p e r t i e s on behavior and(iii)a d e s c r i p t i o n of t r i c h l o r o b i p h e n y l behavior i n a lake s i m i l a r to Lake Michigan using the QWASI ( Q u a n t i t a t i v e Water A i r Sediment I n t e r a c t i o n ) f u g a c i t y model. I t i s concluded that e v a l u a t i v e models can generate behavior p r o f i l e information of value f o r hazard assessment purposes by i n t e g r a t i n g data on part i t i o n i n g , r e a c t i o n , advection, and inter-phase t r a n s p o r t . By a p p l y i n g the same concepts and equations to models of r e a l environments and validating them, the e v a l u a t i v e and r e a l modeling e f f o r t s become mutually supportive and the c r e d i bility of both is increased. In a s e r i e s of recent papers Q - 4), we have advocated the use of the f u g a c i t y concept as an a i d to compartmental modeling of chemicals which may be d e l i b e r a t e l y or i n a d v e r t a n t l y discharged i n t o the environment. The use of f u g a c i t y instead of concentrat i o n may f a c i l i t a t e the formulation and i n t e r p r e t a t i o n of environmental models; i t can s i m p l i f y the mathematics and permit processes which are quite d i f f e r e n t i n character to be compared 0097-6156/83/0225-0175$06.50/0 © 1983 American Chemical Society

Swann and Eschenroeder; Fate of Chemicals in the Environment ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

F A T E OF C H E M I C A L S I N T H E E N V I R O N M E N T


176

q u a n t i t a t i v e l y i n order that the dominant processes can be i d e n t i fied. F u g a c i t y i s e a s i l y conceived as an escaping tendency or pressure with u n i t s of pressure (eg. Pa). In t h i s paper, we review b r i e f l y the u n d e r l y i n g concepts of f u g a c i t y modeling, d i s c u s s i t s a p p l i c a t i o n to r e a l and e v a l u a t i v e environments, and demonstrate that the models may be a p p l i e d at v a r i o u s s e l e c t e d l e v e l s of complexity. We b e l i e v e that one key to s u c c e s s f u l environmental compartment modeling i s to i d e n t i f y f i r s t the r e q u i r e d or acceptable l e v e l of model complexity, then i n c l u d e the dominant processes i n the model followed by others i n order of decreasing importance u n t i l the d e s i r e d l e v e l of complexity i s achieved. Other, l e s s important processes are ignored. The modeler's defence to c r i t i cism that a process has been ignored i s then c l e a r - i n c l u s i o n would exceed acceptable complexity. The d i f f i c u l t and p o s s i b l y contentious step i s to rank processes i n order of importance. We suggest that t h i s ranking can r a r e l y be done a p r i o r i , i t i s u s u a l l y the r e s u l t of t r i a l and e r r o r . Indeed the a r t of e n v i r o n mental modeling l i e s i n the a b i l i t y of the modeler to concept u a l i z e the problem, i d e n t i f y a s u f f i c i e n t number of dominant processes and then w r i t e reasonable d e s c r i p t i v e equations f o r each process. Manipulating the equations to o b t a i n a s o l u t i o n i s u s u a l l y the l e a s t d i f f i c u l t task. Real environments are u s u a l l y c h a r a c t e r i z e d by inherent comp l e x i t y and a corresponding inadequacy of d e t a i l e d understanding of p r o p e r t i e s and process r a t e s . Chemical concentrations vary temporally and s p a t i a l l y . The bulk movement of a i r , water, suspended s o i l s and b i o t a i s i r r e g u l a r and d i f f i c u l t to d e s c r i b e n u m e r i c a l l y . Reactions are numerous, i n t e r a c t i v e and may vary d i u r n a l l y and s e a s o n a l l y . Faced with t h i s complexity, the modell e r ' s response i s to average p r o p e r t i e s and processes, assume homogeneity i n s t e a d of heterogeneity, and g e n e r a l l y s i m p l i f y the system u n t i l i t becomes t r a c t a b l e . Accomplishing t h i s task f o r a r e a l environment r e q u i r e s c o n s i d e r a b l e e f f o r t and i n s i g h t with the r e s u l t that the modeler may have l i t t l e i n t e l l e c t u a l energy (or funds) l e f t f o r i n t e r p r e t i n g the behavior of the chemical, as d i s t i n c t from the behavior of the environment. A very s i g n i f i c a n t advance was made by Baughman and L a s s i t e r (5) when they suggested using e v a l u a t i v e environments f o r e l u c i d a t i o n of the environmental behavior of chemicals. This l e d to the EXAMS model (6), the s t u d i e s of s e l e c t e d chemicals by Smith et a l (7, 8), the development of "Unit Worlds" by Neely and Mackay (9) and Mackay and Paterson (2), and the i n c o r p o r a t i o n of s i m i l a r Unit Worlds i n t o hazard assessment by Schmidt-Bleek et a l (10). The e v a l u a t i v e approach f r e e s the modeler from concerns about environmental i d e n t i f i c a t i o n and enables a l l a t t e n t i o n to be focused on the c h e m i c a l s behavior. An unfortunate consequence i s that d i r e c t v a l i d a t i o n i s not p o s s i b l e ; thus there may be r e l u c t a n c e to accept the c o n c l u s i o n s . Perhaps t h i s r e l u c t a n c e may best be a l l e v i a t e d by demonstrating that the e v a l u a t i v e model f


9.

M A C K A Y ET A L .

Fugacity Model Application

111


process can be a p p l i e d s u c c e s s f u l l y to microcosms, to w e l l cont r o l l e d outdoor environments such as small ponds or a g r i c u l t u r a l p l o t s , or to r i v e r s or lakes. Modeling of e v a l u a t i v e and r e a l environments should be viewed as complementary. E v a l u a t i v e models are p a r t i c u l a r l y s u i t a b l e f o r assessment of new chemicals, f o r comparing chemicals, and f o r o b t a i n i n g general chemical behavior p r o f i l e s . Real models are obviously best used f o r e l u c i d a t i n g the a c t u a l or p o t e n t i a l nature of contamination s i t u a t i o n s and remedial a c t i o n s . The use of s i m i l a r or i d e n t i c a l c a l c u l a t i o n techniques i n both i s very d e s i r a b l e since success i n the r e a l case may lead to greater c r e d i b i l i t y i n the e v a l u a t i v e case. Fugacity

Models

An a t t r a c t i v e feature of the f u g a c i t y models i s that they can be a p p l i e d at various l e v e l s of complexity, depending on the perceived modelling need and the a v a i l a b i l i t y of data. The determinants of complexity are b e l i e v e d to be as f o l l o w s . 1. Number of compartments considered. 2. I f phase e q u i l i b r i u m i s assume^ between some or a l l compartments. 3. I f degradation r e a c t i o n s are included. 4. I f advection processes are included. 5. I f steady s t a t e i s assumed or time dependence of concentration and emissions i s included. A f u g a c i t y l e v e l I c a l c u l a t i o n may be 6 compartment e q u i l i brium, no r e a c t i o n , no advection, steady s t a t e ; a l e v e l I I may be e q u i l i b r i u m , with r e a c t i o n and advection, steady s t a t e ; l e v e l I I I may be non e q u i l i b r i u m , with r e a c t i o n and advection, steady state,and l e v e l IV and EXAMS are non e q u i l i b i u m , with r e a c t i o n and advection, unsteady s t a t e . With models being formulated by many independent groups, i t i s i n e v i t a b l e that comparisons w i l l be made i n the hope of i d e n t i f y i n g the b e t t e r or more u s e f u l models. Comparison between models of d i f f e r e n t c l a s s e s i s u s u a l l y not meaningful. Equilibrium. E q u i l i b r i u m between compartments can be expressed e i t h e r as p a r t i t i o n c o e f f i c i e n t s K.. ( i . e . concentration r a t i o at e q u i l i b r i u m ) or i n the f u g a c i t y models as f u g a c i t y c a p a c i t i e s and Z. such that K.. i s Z./Z., the r e l a t i o n s h i p s being depicted i n F i g u r e 1. Z i s d e i i n e d as tne r a t i o of concentration C (mol/m ) to f u g a c i t y f (Pa), d e f i n i t i o n s being given i n Table I. An advantage of the f u g a c i t y c a p a c i t y approach i s that f o r N compartments N values of Z are defined while there may be N(N-l)/2 p a r t i t i o n c o e f f i c i e n t s . Using Z values the p a r t i t i o n i n g propert i e s between two phases are a t t r i b u t e d independently to each phase. I t i s p o s s i b l e to a s s i g n ( a c c i d e n t a l l y ) three i n c o n s i s t e n t p a r t i t i o n c o e f f i c i e n t s between a i r , s o i l and water but the three Z values are i n h e r e n t l y c o n s i s t e n t . 3


178

FATE OF CHEMICALS IN THE ENVIRONMENT

VAPOR PRESSURE PVRT (

C

°

A

Z =I/RT

^

I Z =K 0

O W

/H

Zp=l/P"v

Z =K yO VH B


PURE

A

\OCTANOLi

B

X

B

Z =K /> /H S

B \ =C /P BIOTA / BI0OTN^ENTRAT10N| FACTOR S

P

S

/

S

SORBED J

x

ow OCTANOL WATER PARTITION COEFE

AQUEOUS SOLUBILITY HENRY'S LAW CONSTANT S

S

H/RTor P /RTC — F i g u r e 1. R e l a t i o n s h i p s between f u g a c i t y c a p a c i t i e s and partition coefficients. See T a b l e 1 f o r symbol d e f i n i t i o n s .

Table I.

D e f i n i t i o n of Fugacity

Capacities 3

D e f i n i t i o n of Z (mol/m Pa)

Compartment

3

Air

1/RT R=8.314 Pa m /mol K T=Temp. (K)

Water

1/H or C / P

S

S

C

S

P

S

= aqueous s o l u b i l i t y (mol/m ) 3

= vapor pressure (Pa) = Henry's law constant (Pa m /mol)

H

3

S o l i d Sorbent (e.g. s o i l sediment, p a r t i c l e s )

K p /H p

K

p

P Biota

K p /H B

B

K 15

p Pure

Solute

g

S

l/P v

fi

= p a r t i t i o n coeff. (L/kg) = density (kg/L) = bioconcentration f a c t o r (L/kg) = density (kg/L)

v = Solute molar volume (m /mol) 3


9.

MACKAY ET A L .


179

Reactions. Reactions are expressed by f i r ^ t order equations in chemical c o n c e n t r a t i o n (rate constant k.h ) such that the rates of processes such as h y d r o l y s i s , o x i d a t i o n , p h o t o l y s i s , or b i o l y s i s can be combined by adding the k terms to y i e l d a t o t a l r a t e constant k^. 3

rate = k ^ + k C + k C etc = 2

= C k mol/m h

3

T

This r a t e can a l s o be expressed i n terms of f u g a c i t y f f o r a compartment of volume Vm as 3


Rate (mol/h) = VCk

= VZkf = D f

1

I

K

The D term or group (VZk ) has u n i t s of mol/hPa and can be viewed as a r a t e of l o s s of chemical from the compartment (by r e a c t i o n ) per u n i t of f u g a c i t y . R

T

Advection. Advection to and from a compartment of volume V at flow r a t e G m /h by, f o r example, a i r or water flow can be expressed as a pseudo f i r s t order r a t e process with a r a t e constant k^ equal to G/V. The r a t e i s a l s o given by 3

Rate (mol/h) = GC = VCk

A

= V Z k f = GZf = D^f A

The D term or group (GZ) again has u n i t s of mol/hPa and i s a r a t e of Toss or gain of chemical from the compartment (by adv e c t i o n ) per u n i t of f u g a c i t y . Interphase D i f f u s i o n . When interphase transport rates are c h a r a c t e r i z e d i t can be shown that the d i f f u s i o n r a t e between two compartments i and j can be expressed as (3) Rate (mol/h) = D „ (f

i

- f j

Where D.. can be c a l c u l a t e d from mass t r a n s f e r c o e f f i c i e n t s or an u p t a k e n a l f - t i m e . For example, f o r air-water exchange D AW i s given by 1

D

A W

=A/(1/K Z A

A +

l/K^) 2

where A i s the surface area (m ) and K and and water phase mass t r a n s f e r c o e f f i c i e n t s Tm/h). f i s h ( s u b s c r i p t F) a h a l f - t i m e 1* (h) can be used. D

FW = ° -

6 9 V

F

Z F

are the a i r For uptake by

A

Inter-phase d i f f u s i o n processes can be viewed as the net r e s u l t of two counter-processes with rates of D..f. and D..f..


180

F A T E OF CHEMICALS I N T H E

ENVIRONMENT

Interphase M a t e r i a l T r a n s f e r . In some cases there i s unid i r e c t i o n a l bulk t r a n s f e r of m a t e r i a l and a s s o c i a t e d chemical between compartments (e.g. sediment d e p o s i t i o n or atmospheric p a r t i c l e f a l l o u t ) i n which case the r a t e i s given by an express i o n s i m i l a r to that f o r advection i n which Gg (m /h) i s the r a t e of t r a n s f e r of the m a t e r i a l namely 3

Rate (mol/h) = G^C = G Zf = D f


again D i s a l o s s or gain c o e f f i c i e n t and has u n i t s of mol/hPa. Time Dependence. The i m p l i c a t i o n s of i n t r o d u c i n g time dependence are obvious. Steady s t a t e models u s u a l l y y i e l d a l g e b r a i c equations which are amenable to simple s o l u t i o n . Unsteady s t a t e models y i e l d d i f f e r e n t i a l equations i n time (or o c c a s i o n a l l y i n p o s i t i o n as i n the case of r i v e r s ) which are s o l u b l e only i n a few simple cases, the r i v e r oxygen r e a e r a t i o n equation being the c l a s s i c example. Although numerical s o l u t i o n i s s t r a i g h t f o r w a r d , i t i s l e s s s a t i s f y i n g because the s e n s i t i v i t y of the r e s u l t s to the assumed parameter values i s not immediately apparent, there being no general s o l u t i o n . The amount of data generated by numerical s o l u t i o n i s o f t e n overwhelming and the e s s e n t i a l f e a tures of the chemical's behavior may be d i s g u i s e d i n the mass of d e t a i l e d data output. Some economies are p o s s i b l e i f e q u i l i b r i u m i s assumed between s e l e c t e d compartments, an equal f u g a c i t y being a s s i g n a b l e . This i s p o s s i b l e i f the time f o r e q u i l i b r a t i o n i s short compared to the time constant f o r the dominant processes of r e a c t i o n or advection. For example, the r a t e of chemical uptake by f i s h from water can o f t e n be ignored (and thus need not be measured or known w i t h i n l i m i t s ) i f the chemical has a l i f e time of hundreds of days s i n c e the uptake time i s u s u a l l y only a few days. This i s equivalent to the f r e q u e n t l y used "steady s t a t e " assumption i n chemical k i n e t i c s i n which the d i f f e r e n t i a l equation f o r a short l i v e d intermediate species i s s e t to zero, thus reducing the equation to a l g e b r a i c form. When the compartment contains a small amount of chemical or adjusts q u i c k l y to i t s environment, i t can be t r e a t e d a l g e b r a i cally. Summary. In summary, when modeling with the f u g a c i t y concept, a l l e q u i l i b r i a can be t r e a t e d by Z values (one f o r each compartment) and a l l r e a c t i o n , advection and t r a n s p o r t processes can be t r e a t e d by D values. The only other q u a n t i t i e s r e q u i r i n g d e f i n i t i o n are compartment volumes and emission r a t e s or i n i t i a l concentrations. A major advantage i s that since a l l D q u a n t i t i e s are i n equivalent u n i t s they can be compared d i r e c t l y and the dominant processes i d e n t i f i e d . By converting d i v e r s e processes such as v o l a t i l i z a t i o n , sediment d e p o s i t i o n , f i s h uptake and stream flow i n t o i d e n t i c a l u n i t s , t h e i r r e l a t i v e importance can be e s t a b l i s h e d d i r e c t l y and e a s i l y . Further, a l g e b r a i c manipulation


9.

MACKAY ET A L .


181

i s f a c i l i t a t e d because many of the D q u a n t i t i e s can be grouped and e r r o r i s l e s s l i k e l y s i n c e there i s no need to manipulate a large number of symbols i n d i v e r s e u n i t s .


Illustrative Application We i l l u s t r a t e these concepts by a p p l y i n g v a r i o u s f u g a c i t y models to PCB behavior i n e v a l u a t i v e and r e a l lake environments. The e v a l u a t i v e models are s i m i l a r to those presented e a r l i e r (3, 4). The r e a l model has been developed r e c e n t l y to provide a r e l a t i v e l y simple f u g a c i t y model f o r r e a l s i t u a t i o n s such as an already contaminated lake or r i v e r , or i n a s s e s s i n g the l i k e l y impact of new or changed i n d u s t r i a l emissions i n t o aquatic e n v i ronments. T h i s model i s c a l l e d the Q u a n t i t a t i v e Water A i r S e d i ment I n t e r a c t i v e (or QWASI) f u g a c i t y model. Mathematical d e t a i l s are given elsewhere (15). The e v a l u a t i v e f u g a c i t y model equations and l e v e l s have been presented e a r l i e r (1, 2, 3). The l e v e l I model gives d i s t r i b u t i o n at e q u i l i b r i u m of a f i x e d amount of chemical. L e v e l I I gives the e q u i l i b r i u m d i s t r i b u t i o n of a steady emission balanced by an equal r e a c t i o n (and/or advection) r a t e and the average residence time or p e r s i s t e n c e . L e v e l I I I gives the n o n - e q u i l i b r i u m steady s t a t e d i s t r i b u t i o n i n which emissions are i n t o s p e c i f i e d compartments and t r a n s f e r r a t e s between compartments may be r e s t r i c t e d . L e v e l IV i s e s s e n t i a l l y the same as l e v e l I I I except that emissions vary with time and a set of simultaneous d i f f e r e n t i a l equations must be solved n u m e r i c a l l y (instead of a l g e b r a i c a l l y ) . The QWASI f u g a c i t y model contains expressions f o r the 15 processes d e t a i l e d i n F i g u r e 2. For each process, a D term i s c a l c u l a t e d as the r a t e d i v i d e d by the p r e v a i l i n g f u g a c i t y such that the r a t e becomes Df as described e a r l i e r . The D terms are then grouped and mass balance equations d e r i v e d . The f o l l o w i n g assumptions apply. The a i r f u g a c i t y i s d e f i n e d and i s not a f f e c t e d by the water or sediment processes. Common f u g a c i t i e s apply to ( i ) the a i r , a i r p a r t i c l e s and r a i n ( f . ) , ( i i ) to water,suspended sediment i n the lake and f l o w i n g from i t ( f ^ ) , and to the i n f l o w water and suspended sediment f j ) . I f f i s h concentrations are to be i n c l u d e d , they can be c a l c u l a t e d as f^Zg, but the amount i n f i s h i s considered n e g l i g i b l e . In the most general case two d i f f e r e n t i a l equations are d e r i v e d , one f o r the water i n f and one f o r the sediment i n f g . I f steady s t a t e i s assumed the two equations become a l g e b r a i c and d i r e c t a n a l y t i c a l s o l u t i o n i s p o s s i b l e . An intermediate s i t u a t i o n can e x i s t i f the amount i n the water i s small compared to the amount i n the sediment, a steady s t a t e water s i t u a t i o n can be assumed. The water d i f f e r e n t i a l equation then becomes a l g e b r a i c and can be s u b s t i t u t e d i n t o the sediment equation. D e t a i l s of these equations and t h e i r s o l u t i o n s are given by Mackay et a l (15) Table I I gives estimated p r o p e r t i e s of a s e r i e s of c h l o r o biphenyls and are average values f o r each c h l o r i n e number group of



1500

7xlO

Z r

>

\

\

a

DRY)

AIR/WATER ABSORPTION

SEDIMENT BURIAL

\

4x10

3*

2.5 x l O

EXCHANGE

4 x 10

J

x

l

° — >

TRANSFORMATION

SEDIMENT

WATER TRANSFORMATION

SUSPENDED SEDIMENT OUTFLOW

OUTFLOW

WATER

showing D v a l u e s f o r a

2

Lx 1

VOLATILIZATION

SEDIMENT/WATER DIFFUSION

V; SEDIMENT.

) SEDIMENT DEPOSITION

FISH a S U S P E N D E D S E D I M E N T IN EQUILIBRIUM" WITH W A T E R

(WET

SEDIMENT RESUSPENSION

WATER

2 x 10

*J

\f

4 J : 10

b

PARTICLE

DEPOSITION

AIR

F i g u r e 2A. D i a g r a m o f p r o c e s s e s i n c l u d e d i n t h e QWASI f u g a c i t y model t r i c h l o r o b i p h e n y l i n a l a k e s i m i l a r t o Lake M i c h i g a n .

SUSPENDED SEDIMENT INFLOW

WATER INFLOW

AIR

AIR RAIN-OUT

( B O T H RAIN & AIR P A R T I C L E S IN E Q U I L I B R I U M W I T H A I R )



T

r002

r

07 ]

^

6

10 mol/h f = l . O x l O " Pa

u

\1

2.500

a DRY)

0.200

SEDIMENT BURIAL

4.000

4.663

f

s

EXCHANGE

6

Pa

7.46

I

t

= l.00x10 (.048 ug/g)

Pa

.746 .400 0.800

.373

VOLATILIZATION

SEDIMENT/WATER DIFFUSION

(6.2 ng/L)

= 1.865 x l O

[SEDIMENT-'

-^SEDIMENT ^DEPOSITION

3

Pa (5.1 ng/m )

AIR/WATER

8

ABSORPTION

FISH a S U S P E N D E D S E D I M E N T IN EQUILIBRIUM' W I T H W A T E R

(WET

SEDIMENT RESUSPENSION

WATER

0.200

t

1f

.002

PARTICLE

DEPOSITION

AIR

f =5 x l O

.003

.131.

SEDIMENT TRANSFORMATION

WATER TRANSFORMATION

SUSPENDED SEDIMENT OUTFLOW

WATER OUTFLOW

Figure 2B. Steady state mass balance f o r the lake g i v i n g mass flows (mol/h), each flow being a product of D (from Figure 2A) and the appropriate f u g a c i t y .

SUSPENDED SEDIMENT INFLOW

WATER INFLOW

AIR

b

AIR RAIN-OUT

( B O T H RAIN a AIR P A R T I C L E S IN E Q U I L I B R I U M W I T H A I R )


184

FATE

OF CHEMICALS

IN T H E ENVIRONMENT

Table I I P h y s i c a l Chemical

P r o p e r t i e s of the C h l o r i n a t e d Biphenyls (CBP)


Subscripts are:- A a i r , W water, S sediment, P suspended sediment, B biota. Property Mono CBP

Di CBP

T r i CBP

Mol. wt.

189

223

257

292

60

60

77

76

H

4.66 757

K P

T e t r a CBP

Units

g/mol 3

Pa m /mol

6.35 5.76 5.19 Partition Coefficients 37100 2560 9530

L/kg

7570

25600

95300

371000

L/kg

2290

7740

28800

112000

L/kg

P

*B

Fugacity C a p a c i t i e s Z

z

A w

s

z

z

0.0004

0.0004

0.0004

0.0004

0.017

0.016

0.013

0.013

19.0 190

3

mol/m Pa it it

63

186

730

630

1860

7300

ii

130

375

1500

ii

p Z

B

38.0

Transport Parameters D

Aw

D ws D wp D

wB

81.2

80.6

64.1

64.6

16.4

16.4

13.0

13.1

397

394

7.60

Reaction Rate k

w

k

4.0xl0

-3

0.01

6.24

6.24

II

II

315

313

7.72

mol/Pah

II

Constants

2.0xl0~

4

I.OXIO'

5.1xl0"

4

3.5x10

5

5

5.0xl0"

1.13x10

7

5

s


h"

1

h"

1


9.

MACKAY ET A L .

185


congeners (13). The corresponding Z values are c a l c u l a t e d as shown i n Table I I and f o l l o w i n g the general approach described e a r l i e r f o r e v a l u a t i v e environment c a l c u l a t i o n s (2). These quant i t i e s should be taken as estimates r a t h e r than p r e c i s e determinations since the o b j e c t i v e here i s to describe the approach and method rather than prepare a d e t a i l e d e v a l u a t i o n or s i m u l a t i o n model. The e v a l u a t i v e lake environment i s s i m i l a r to the " u n i t world" described by Mackay and Paterson (2), c o n s i s t i n g of a 1 km square area with an atmosphere 6000 m high, a water column 80 m deep (the approximate depth of Lake Michigan) c o n t a i n i n g suspended s o l i d s (5 parts per m i l l i o n by volume) and b i o t a (considered to be f i s h ) of 1 ppm by volume, and u n d e r l a i n by a s e d i ment 3 cm deep. The bottom sediment contains 4% organic carbon and the value f o r suspended sediment was a r b i t r a r i l y s e l e c t e d as ten times these bottom sediment values r e f l e c t i n g the enhanced s o r p t i o n discussed by 0 Connor and Connally (14). Chemicals were supplied to the e v a l u a t i v e lake by two routes; by emissions of 0.001 mol/h d i r e c t l y i n t o the water, and by ^ advection i n t o the aj.j c o n s i s t i n g of an a i r flow of 6.0 x 10 m /h c o n t a i n i n g 5.0 x 10 mol/m (approximately 1.3 ng/m ) r e s u l t i n g i n a net i n f l o w of 0.0003 mol/h. T o t a l emissions are thus 0.0013 mol/h. This advection r a t e corresponds to an a i r residence time (volume/flowrate) of 100 hours. Reaction r a t e constants are postulated as shown i n Table I I f o r degradation i n water ( b i o l y s i s and p h o t o l y s i s ) , i n bottom sediments (probably b i o l y s i s ) , and f o r permanent b u r i a l of s e d i ment. The values were s e l e c t e d from a p e r u s a l of the l i t e r a t u r e and must be regarded as s p e c u l a t i v e . A f a c t o r of 20 r e d u c t i o n i n r e a c t i o n r a t e constant i s assumed f o r a d d i t i o n of each c h l o r i n e . T r a n s f e r r a t e constants are postulated as shown i n Table I I , f o l l o w i n g the approach described by Mackay and Paterson (4). The air-water value s e l e c t e d was lower than i s g e n e r a l l y used since i t appears that a low value i s necessary to r e c o n c i l e observed a i r and water concentration, and mass balances as discussed i n a recent review of PCB behavior i n the Great Lakes (Mackay et a l . (13)). The f i r s t set of c a l c u l a t i o n s i l l u s t r a t e s various l e v e l s of complexity f o r one chemical (a t r i c h l o r o b i p h e n y l ) . Figure 3, 4, 5 and 6 show L e v e l I, I I , I I I and IV c a l c u l a t i o n s , the L e v e l IV c a l c u l a t i o n s being f o r emissions of 0.001 mol/h f o r 25 years followed by response to an emission r e d u c t i o n by a f a c t o r of ten to 0.0001 mol/h. The L e v e l I c a l c u l a t i o n ( F i g . 3) suggests that the dominant compartment i s sediment which contains 57% of the chemical, followed by a i r (25%), water (10%) and suspended sediment (7%). The f i s h concentration i s 30000 times that of the water. The absolute concentrations have no s i g n i f i c a n c e since they depend on the assumed amount and volumes. T

3

3

3


Swann and Eschenroeder; Fate of Chemicals in the Environment ACS Symposium Series; American Chemical Society: Washington, DC, 1983. 6

9

186

1860

1.0/9.79xl0

6

=

1.9x10

1.9x10

5

1.02 x10

7

0.31 0.0031

56.9

100

0.569

1.000

7.58

10.6 0.106

0.076

24.6

%

0.246

m=CV mol

distribution

Pa

(0.003 yg/g)

(0.033 ug/g)

Figure 3. Level I c a l c u l a t i o n f o r a t r i c h l o r o b i p h e n y 1 i l l u s t r a t i n g e q u i l i b r i u m with no r e a c t i o n of 1 mol of chemical.

=

6

6

9.79x10°

5.58 x l O

0.74xl0

(0.01 ug/g)

3.9x10

6

4

3

(10.5 ng/m )

0.03 x l O

1

375

1

(0.34ng/L)

4.1x10

1.3x10

6

3

6

2.4 x l O

C=fZ mol/m

1.04 x l O

4

VZ

0.013

4.0 x l O "

3

mo I /m Pa

f = M/SVZ

30000

BOTTOM SEDIMENT

TOTAL

400

80

80xl0

6.0xl0

SUSPENDED SEDIMENT

FISH

WATER

AIR

3

VOLUME m


H

w

o

g

w

w

O

O

H W

>

00


B

0.0030 mmol/h

0.00056 mmol/h

3

0.0074 mmol/h

SEDIMENT BURIAL

TOTAL

BOTTOM 'SEDIMENT 5

B

E + GC ZVZK+GZ.AIR

5

4

(0.0017 yg/g)

(0.017 yg/g)

0,52 = 0.0013

400 h

Pa

100

0.52

5.37 x l O

56.9

0.29

7.58

0.31

0.0016 0.040

10.6

24.6

%

0.056

0.13

m = CV mol

5

7

0.000011

1.04xl0"

0

0

5.6xlO~

0

RATE = VCk mol/h

i l l u s t r a t i n g e q u i l i b r i u m with r e a c t i o n

B

0.0010 4- 0.0003 205.7 + 24000

1.0 x l O "

l.Oxlo"

= M/(E + G C ) =

205.7

195.3

0

3

(0.005 yg/g)

2.0xl0"

0

U

5

7.0x10

RESIDENCE TIME

f =

3.5 x l 0 ~

0

0

3

(5.5 ng/m )

3

i (0.18 ng/m" )

1 1

C=fZ mol/m

-in

2.15 x l O "

10.4

0

0 l.Oxlo"

VZk

k

5

RATE CONSTANT

Figure 4. Level II c a l c u l a t i o n f o r a t r i c h l o r o b i p h e n y 1 and advection.

SEDIMENT REACTION

3

SUSPENDED "SEDIMENT

= 1.29 mmol/h

WATER REACTION

1.0 mmol/h

s 0.3 mmol/h

7

C = 2.l xlO"" mol/m

3

ADVECTION OUT

C = 5.0xlO-' mol/m

2

3

G= 6.0xl0 m /h

7

G= 6.0xl0 m /h

ADVECTION IN


Swann and Eschenroeder; Fate of Chemicals in the Environment ACS Symposium Series; American Chemical Society: Washington, DC, 1983. 2

5

0

0

0

BURIAL

i

0.040

Figure 5.

r

o

1

o.ioT"**

REACTION

(2.2 years)

m

—

0.121

H

10

10

10

u -

10

-10

-9

-8

7

-6

_^

1.1 yg/g

3.7 yg/g

•10

10

10

3

-12

-10

-8

.10 6

4.4 ng/m

39 ng/L

•10 •4 0.022 yg/g

r 1.0

CONCENTRATION C mol/m

Air

Water

Bottom Sediment—*

Suspended. Sediment Fish

trichlorobiphenyl.

FUGACITY f Pa

Air

Bottom Sediment

REACTION

1.038

ADVECTION

Level III calculation for a

AMOUNT IN SYSTEM RESIDENCE TIME 19300 h

0,300

ADVECTION

Water Fish . Suspended Sediment 10~"

10


MACKAY ET A L .



9.

YEARS Figure 6. Level IV c a l c u l a t i o n f o r a t r i c h l o r o b i p h e n y l showing response to emission changes.


189


190

FATE OF CHEMICALS

IN THE ENVIRONMENT

The L e v e l I I c a l c u l a t i o n ( F i g . 4) has the same d i s t r i b u t i o n as F i g . 3. The i n f l o w of 1.30 m mol/h i s l a r g e l y removed by advection (1.284 m mol/h) with c o n t r i b u t i o n s by sediment b u r i a l (.0074 m mol/h)> by sediment r e a c t i o n (.0030 m mol/h) and by water r e a c t i o n (.0006 m mol/h). This assumes that water to a i r t r a n s f e r i s r a p i d thus p r o v i d i n g a r e s i s t a n c e to t h i s t r a n s f e r , as i n l e v e l I I I w i l l a l t e r the f a t e c o n s i d e r a b l y . Atmospheric d i s t r i b u t i o n of PCBs i s l i k e l y to be important. The residence time of 400 h i s l a r g e l y c o n t r o l l e d by a i r advection. The l e v e l I I I c a l c u l a t i o n ( F i g . 5) shows that the air-water v o l a t i l i z a t i o n r a t e c o n s t r a i n t reduces a i r advective loss to 1.038 m mol/h and other r e a c t i o n processes assume greater importance. The residence time i s now 2.2 years, i n f a i r agreement with observations. The concentrations i n a i r , water, sediment and f i s h are w i t h i n an order of magnitude of values observed i n contaminated lakes such as Lake Michigan. The L e v e l IV c a l c u l a t i o n ( F i g . 6) shows the buildup i n concentrations and f u g a c i t y to the steady state ( l e v e l I I I values) then the subsequent decay. C l e a r l y , sediments are slower to respond to buildup and decay, i . e . they have a longer "time constant." A t e n f o l d drop i n sediment c o n c e n t r a t i o n would r e q u i r e 15 years. I t can be concluded that these models y i e l d a s a t i s f a c t o r y p i c t u r e of the behavior and p e r s i s t e n c e of t h i s PCB. The dominant processes are apparent. A new chemical of s i m i l a r p r o p e r t i e s i s u n l i k e l y to r e c e i v e environmental r e g u l a t o r y approval, thus the model i s apparently capable of i d e n t i f y i n g such chemicals p r i o r to t h e i r d i s p e r s a l i n t o the environment. The L e v e l I I I c a l c u l a t i o n s are p a r t i c u l a r l y e n l i g h t e n i n g and i t i s b e l i e v e d that they w i l l u l t i m a t e l y be used f o r r e g u l a t o r y purposes. This i s i l l u s t r a t e d by Figures 7, 8, 5 and 9 which are f o r mono, d i , t r i and t e t r a c h l o r o b i p h e n y l s . The e f f e c t of i n c r e a s i n g c h l o r i n e number i s s t r i k i n g . The lower congeners are f a i r l y s h o r t - l i v e d , p a r t i t i o n l e s s i n t o sediments and b i o t a and most r e a c t i o n tends to occur i n the water column, advection with a i r and b u r i a l i n sediment being r e l a t i v e l y unimportant. As c h l o r i n e number i n c r e a s e s , the amounts and p e r s i s t e n c e i n c r e a s e , more chemical p a r t i t i o n s i n t o the sediments and b i o t a , while water column degradation becomes l e s s important compared to s e d i ment degradation and advection. U l t i m a t e l y , sediment b u r i a l and advection dominate the chemical's f a t e . I t i s c l e a r that congeners w i l l s u f f e r q u i t e d i f f e r e n t environmental f a t e s and equal emissions of each w i l l r e s u l t i n very d i f f e r e n t concentrations and thus exposures. These d i f f e r e n c e s should be r e f l e c t e d i n changes i n congener d i s t r i b u t i o n of commercial PCB mixtures. From the hazard assessment viewpoint, i t i s apparent that the lower c h l o r i n e content congeners are of l e s s concern than the l o n g e r - l i v e d higher c h l o r i n e content congeners. This p o i n t has been made p r e v i o u s l y by Neely (11, 12).


9.


MACKAY ET A L .

00

00

00 3-

00 p.

191

00

co co I

I

I

o o

o CO

0)

M •H

P4



8.8xl0

BURIAL

0.0449

0.223

- 4

Figure 8.

-7 10

0.044

REACTION -9

Level I I I calculation

4

7.9x10

1 2

2.0 ng/m

-10

10 ng/L

3

4

-2

yg/g

yg/g

0.26 yg/g

-6 4.4 x 1 0

_

L10"

10

-10

-10

-10

10


Air

Water

Bottom^ Sediment

Fish-

Suspended Sediment

1.0

f o r a dichlorobiphenyl.

10r l O FUGACITY f Pa L

10

REACTION Bottom^ ^ Sediment Air-8 0.733 10

AMOUNT IN SYSTEM 4530 mmol RESIDENCE TIME 3490 h (145 days)

1.000

E mmol/h

""15.300

ADVECTION

Suspended Sediment ADVECTION Water-* -6 Fish -10 0.523

-5 .10

10


>

H

w

w w < o

H

w o o X w

H


t

(6 years)

mmol

.'0.018

REACTION

0.0068

REACTION

10"

-10

10

1 0

-7 -10

FUGACITY f Pa

Air

JL0

-6

10

-10

10

10

2

5.5 ng/m

-12

3

9 x 10

50 ng/L

-10

-8

10

-4


Air

Water

Bottom Sediment*

y

5.5 yg/g

Fish10 -2

18.4 yg/g

-1.0

Suspended Sediment j.

Level I I I Calculation f o r a tetrachlorobiphenyl.

51700 h

67300

Figure 9.

RESIDENCE TIME

0.143

•, •; •:

T BURIAL

0.161

0.832

AMOUNT IN SYSTEM

1.000

E mmol/h

~~0.300

ADVECTION

ADVECTION Bottom "Sediment 1.132

-10"

-4 Water ,J-0 Fish Suspended Sediment



194

FATE OF CHEMICALS IN

THE

ENVIRONMENT

No claim i s made that PCBs behave exactly i n the r e a l e n v i ronment as i s suggested here, but the same p r i n c i p l e s are b e l i e v e d to apply. The QWASI f u g a c i t y model was then run f o r a t r i c h l o r o b i p h e n y l i n a lake the s i z e of Lake Michigan, being approximately 60,000 times the s i z e of the e v a l u a t i v e environment. A d e t a i l e d j u s t i f i c a t i o n f o r the s e l e c t i o n of D values i s beyond our scope here but i n s e l e c t i n g values, we have r e l i e d on recent reports by Neely (11), Rogers (15), Armstrong and Swackhamer (16), Thomann (17), and Andren (18). To i l l u s t r a t e the model a steady s t a t e s o l u t i o n i s given which would apply to the lake a f t e r prolonged steady exposure to water emission of 10 mol/h and atmospheric input from a i r of 5.3 ng/m . The s o l u t i o n i s given i n Figure 2B i n the form of f u g a c i t i e s , concentrations and transport and transformation process r a t e s . The dominant processes are apparently sediment d e p o s i t i o n , sediment b u r i a l , v o l a t i l i z a t i o n , a n d d e p o s i t i o n with a i r p a r t i c l e s ( i . e . dry d u s t f a l l and scavenging by r a i n ) . I t i s b e l i e v e d that the concentrations and process rates may be broadly c o n s i s t e n t with average conditions i n Lake Michigan i n the e a r l y 1970s. No claim i s made that the model simulates Lake Michigan p r e c i s e l y since the Lake has complex heterogeneous water movement and s e d i mentation. But the general behavior i s b e l i e v e d to be c o r r e c t and, with adjustment of the parameters, a b e t t e r f i t could be obtained. If emissions were reduced by a f a c t o r of 10 to 1 mol/h and the a i r concentration i s reduced by a f a c t o r of 5, a new steady s t a t e would emerge with a h a l f time f o r change of approximately 4 years, the behavior being s i m i l a r to that of the L e v e l IV evalua t i v e model shown e a r l i e r . An a t t r a c t i v e feature of the QWASI model i s that the rates of the 15 processes (corresponding to 15 D values ) can be compared d i r e c t l y and the i m p l i c a t i o n s of changing the assigned values can be r e a d i l y explored. In some cases, the assigned values are q u i t e s p e c u l a t i v e , p a r t l y because of u n c e r t a i n t y about transport rates (eg. d e p o s i t i o n rates or v o l a t i l i z a t i o n mass t r a n s f e r c o e f f i c i e n t s ) and p a r t l y because of u n c e r t a i n t y about the associated e q u i l i b r i a (eg. Z values f o r d e p o s i t i n g p a r t i c l e s i n a i r and water). I t i s p o s s i b l e to reach s i m i l a r concentrations by a d j u s t i n g sets of parameters, f o r example, i n c r e a s i n g emissions and simultaneously i n c r e a s i n g r e a c t i o n r a t e constants. Examina t i o n of the a l g e b r a i c s t r u c t u r e of the steady s t a t e s o l u t i o n shows which D values act together i n groups; f o r example, s e d i ment b u r i a l and transformation rates can be v a r i e d i n d i v i d u a l l y provided that t h e i r t o t a l remains constant. Assembling a model of a complex system such as Lake Michigan thus becomes a process of parameter s e l e c t i o n and m o d i f i c a t i o n , using a v a i l a b l e process r a t e and e q u i l i b r i u m data, and r e s o r t i n g to i n t u i t i o n where necessary. I t i s b e l i e v e d , however, that t h i s 3


9.

MACKAY ET A L .


195


f u g a c i t y model has the a b i l i t y to reproduce the r e a l i t y yet remain reasonably simple. By using expressions which have a s i m i l a r p h y s i c a l and chemical b a s i s as those i n e v a l u a t i v e models, the two modeling e f f o r t s can be mutually supportive and increase c r e d i b i l i t y and usage. Progress can best be made by applying these models to new and e x i s t i n g chemicals at a l l s c a l e s , i . e . to r e a l environments such as Lake Michigan, to r i v e r s or small ponds, to microcosms and u l t i m a t e l y to l a b o r a t o r y f l a s k s i n which one process i s i s o l a t e d f o r study. The f u g a c i t y models described here w i l l , i t i s hoped, c o n t r i b u t e to the i n t e g r a t i o n of such d i s p a r a t e data i n t o more accurate p r o f i l e s of chemical behavior i n the environment. Literature Cited 1. 2. 3.

4. 5.

6. 7. 8.

9.

10. 11.

12. 13.

Mackay, D., E n v i r o n . S c i . & Technol. 1979, 13, 1218. Mackay, D.; Paterson, S. Environ. S c i . & Technol., 1981, 15, 1006. Mackay, D.; Paterson, S. "Fugacity Models f o r P r e d i c t i n g the Environmental Behavior of Chemicals", report prepared f o r Environment Canada 1982. Mackay, D.; Paterson, S. Environ. S c i . & Technol., 1980, 16, 654A. Baughman, G.; L a s s i t e r , R. " P r e d i c t i o n of Environmental P o l l u t a n t C o n c e n t r a t i o n s , " ASTM STP 657, p 35, P h i l a d e l p h i a , Pa., 1978. Prospectus on "Research and Development on an Exposure A n a l y s i s M o d e l l i n g System (EXAMS) USEPA Athens, Ga., 1979. Smith, J . H. "Environmental Pathways of Selected Chemicals i n Freshwater Systems" Part I . EPA Report 600/7-77-113,1977. Smith, J . H. "Environmental Pathways of Selected Chemicals i n Freshwater Systems, Part I I : Laboratory Studies", EPA600/7-78-074, 1978. Neely, W. B.; Mackay, D. "An E v a l u a t i v e Model f o r E s t i m a t i n g Environmental Concentrations", in "Modelling the Fate of Chemicals i n the Aquatic Environment", e d i t o r s , Dickson, K.L. Maki, A. W. and C a i r n s , J . , Jr., Ann Arbor Science, Ann Arbor 1982, 127-143. Schmidt-Bleek, F.; Haberland, W.; K l e i n , A. W.; C a r o l i , S. Chemosphere, 1982, 11, 383. Neely, W. B. " R e a c t i v i t y and Environmental P e r s i s t e n c e of PCB Isomers", i n " P h y s i c a l Behavior of PCBs in the Great Lakes", Mackay, D.; Paterson, S.; E i s e n r e i c h , S. J . ; Simmons, M. S. (Eds.). Ann Arbor Science, 1982. Neely, W. B. Chemtech, 1981, 11, 249. Mackay, D.; Shiu, W. Y.; B i l l i n g t o n , J . ; Huang, G. L.; " P h y s i c a l Chemical P r o p e r t i e s of P o l y c h l o r i n a t e d B i p h e n y l s " i n P h y s i c a l Behavior of PCBs in the Great Lakes", Mackay, D.; Paterson, S.; E i s e n r e i c h , S. J . ; Simmons, M. S. (Eds.). Ann Arbor Science, 1982 ( i n p r e s s ) .


F A T E OF CHEMICALS I N T H E E N V I R O N M E N T

196 14. 15.

O'Connor, D. J . and Connolly, J . P. Water Res. 1980, 14, 1517. Mackay, D.; Joy, M.; Paterson, S. "AQuantitative Water Air Sediment I n t e r a c t i o n (QWASI) Fugacity Model f o r D e s c r i b i n g Chemical Fate i n Lakes and R i v e r s " submitted to Chemosphere, 1983.


R E C E I V E D April 15, 1983.


Application of Fugacity Models to the Estimation of Chemical

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