Findina u fuaacitv ua feasible ~
The fugacity approach can be used to gain insights into the likely behavior of toxic compounds. Widely used in describing chemical engineering operations, fugacity is a new and perhaps better way to quantify toxics transport and bioaccumulation in the air, water, and sediment
Donald Mackay University of Toronto Toronto, Ontario, Canada Considerable effort is currently being devoted to elucidating the mechanisms and rates by which toxic substances are transported and transformed in the environment. It is generally accepted that before a new chemical compound is released into the market (and thus into the environment) it should undergo some assessment of its likely environmental behavior and effects. It is hoped that such assessments will bring prior warning of potential impacts of toxic substances. This “prevention rather than cure” policy is preferable to waiting until the substance is widely distributed and irrecoverable. Perhaps the future PCBs, mirex, and DDTs can be detected earlier and environmental damage held to an acceptable level. In accomplishing this objective, one approach is to insert the characteristics of the substance into an environmental model which will predict: transport rates of transformation regions of accumulation concentrations Since actual location-specific environments are necessarily highly complex, one attractive approach is to use a general or “evaluative” model of a hypothetical but typical environment as described first by Baughman and Lassiter and developed further by SRI. These models contain both kinetic and equilibrium data for the substance, for 1218
EnvironmentalScience & Technology
example, photolysis rate (kinetic) and aqueous solubility (equilibrium). It is believed that the concept of fugacity can be potentially very useful in identifying the static and dynamic behavior of toxic substances in the environment. Phenomena such as bioaccumulation become readily understandable and predictable. The approach suggested here is capable of implementation at various levels of complexity and could form the basis for a procedure to assess the likely environmental behavior of new chemical substances that have the potential for displaying adverse environmental effects. The approach is also valuable in assisting the elucidation of the dominant processes responsible for a substance’s degradation or removal from the environment and in identifying the significant transfer processes. Viewing environmental processes in terms of fugacity brings a certain degree of order into a very complex subject. Anything which simplifies environmental science would be of immense value scientifically and pedagogically as well as for regulatory purposes. The fugacity approach has this potential.
Thermodynamics The environment comprises several compartments, as illustrated. These compartments could be the atmosphere, a lake, sediment, soil, or biota; some are in contact (for example, lake-atmosphere) and others are not (for example, atmosphere-aquatic sediment). I f it is assumed that each compartment is well mixed, that is, homogeneous, and sufficient time has
elapsed so that all compartments are in equilibrium, then thermodynamics provides information about the nature of the partition. It is recognized that these assumptions are generally invalid because of in- and outflows of a physical, chemical, or biological nature, but interestingly they tend to be most valid for persistant substances that are often of greatest toxicological concern. When compartments are not in equilibrium, only thermodynamics can tell which direction the substance tends to diffuse to reach equilibrium. Within a phase or compartment, mass diffuses because of concentration differences, the rate usually being expressed by Fick’s law. Between phases, equilibrium usually is achieved at considerably different concentrations. For example, oxygen in equilibrium between air and water has a concentration of about 0.3 mol/m3 (10 mg/L) in the water and 8.0 mol/m3 in the air. Gibbs showed that such partitioning (which corresponds to maximization of the entropy of the system) can be expressed by equating the chemical potential of the substance in each phase. Unfortunately chemical potential is a difficult concept to grasp and use, as is attested by generations of physical chemistry students. Lewis introduced the much simpler concept of fugacity, which has become deservedly more popular in recent years in chemical engineering texts.
Environmental applications There are two general areas in which the fugacity-concentra tion approach can contribute to a better un-
0013-936X/79/0913-1218$01.00/0 @ 1979 American Chemical Society
derstanding of the fate of toxic substances. First, if concentration data are available for a pollutant in several phases, presumably as a result of a monitoring program, these concentration data can be converted to fugacities and the fugacity levels compared. Consider, for example, a simple airwater system; if the fugacity in air is lower than the fugacity in water the compound will volatilize. Often the direction of transfer is not obvious, for example, between sediment and water. Where the fugacity in fish is lower than the fugacity in water this indicates either that the uptake is kinetically controlled or that some pollutant removal mechanism is operational in the fish. In any such analysis it is critically important to discriminate between solute in true solution and in sorbed state. Only if the “speciation” between solution and sorbed state is also available are the data useful. For example, a total PCB concentration of 10 mg/L in water provides no useful fugacity information. This also applies to the atmosphere and is a particularly difficult problem for very hydrophobic solutes which sorb appreciably. Examination of fugacity levels in various environmental compartments thus provides an insight into sources, transportation routes and directions, and to regions in which transformation or other removal processes occur. An interesting observation is that when control of concentration of a persistant compound is kinetic (as occurs with PCB uptake by fish) the older members of the community tend to be closest to the high equilibrium value. Long-lived species should therefore be particularly concerned and cautious about this problem! The second application is to the prediction of the likely environmental fate of a compound which is being marketed for the first time. Eventually, complex all-encompassing environmental models may be developed into which such compounds can be inserted and their environmental fate predicted and exposures of humans and biota assessed. In the near future, however, toxic substance legislators will probably be forced to use simpler models in support of their actions and decisions. The fugacity approach can be used to obtain insights into the likely behavior of toxic compounds. In illustrating this approach we examine the application of these concepts through a series of levels of increasing complexity. This facilitates understanding and illustrates that various levels of complexity and detail can be
The fugacity approach; how it works in the environmenta
’ accessible volume of m3 1010
i
1
1/
Soil (B) 1000 rn x 100m x 14 cm loFca$ssible volume
Water (C) 1000 m x 300m x 3.3m accessible volume of 106
m3
Aquatic biota & suspended solids (E) in l o 6 m3 water Sediment (D) lOOOrn x 300m x 3.3 crn accessible volume of IO4 rn3
“Each compartment has an accessible volume (m3)
Volume 13, Number 10, October 1979
1219
used with perhaps the most thorough scrutiny and greatest effort being devoted to the most potentially hazardous compounds. To apply the approach we first construct an environment in which to observe the distribution. Consider a square kilometer of typical land area with atmosphere above, soil, some water, sediment, and biota. T h e quantities can he varied as desired. Each compartment has an accessible volume V (m3). W e ignore deep soils or deep ocean water, which are not accessible in a period of (say) one year. Justification for the volumes used is given in the figure.
Level 1: approximate distribution Equilibrium distribution of a fixed amount of toxicant without transformation is the simplest application. This requires Z values for the toxicant in each compartment, which implies knowing the physical chemical parameters and sorption characteristics defined earlier. An estimate is made of the total amount of solute ( M moles) likely to be present in the entire environment at any given time. This could be one years’ manufacture on a mol/ km2 basis. If each compartment is assigned a subscript i ( I , 2,3, etc.) then a t equilibrium: fl
=f 2 =
f3
’
Table2 T&l
ma80 ___...-...... Air Water
Sediment
BlodopradeUon
PhO101ys16
”.
AdrWon
K
200 510
...
20
100
0 1W
10
50 200
0
0
0
0
0
130
1W 0.1
Hy*lrolysls Oxidallon ...... . .... ...”
01
= .. .f;
but
Thus
f; = M/C(ViZi) and Mj = 5 ViZj where Mi is the number of moles in each compartment, X M j = M . Table 1 illustratesthis simple calculation for six compartments and a hydrophobic solute with properties similar to that of a halogenated hydrocarbon. Most (90%) of the solute is associated with soil, 9% with sediments, 0.35% is in the atmosphere, and only small quantities are present in the water column either dissolved, sorbed, or biosorbed. However, the concentrations on a p g / g of substrate basis show a different picture. The “negligible” amounts present in the biota represent a concentration of 0.2 pg/g, which is within a factor IO of levels considered unsafe for consumption in many cases. T h e sediment. which has 1000 times as 1220
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much material, could obviously act as a source of biotic contamination for a prolonged period. T h e conclusion is that the compartments of greatest concern (usually biota) may contain negligible amounts of toxicant compared to other compartments. Although the toxicant sorbs strongly, its sorbed concentration in the water column is only IO% of the dissolved concentration. This simple analysis is quite hypothetical since it ignores inputs, outputs, and transformations and it assumes that intercompartment transfer is fast. It cannot, therefore, be used to predict concentrations. It merely presents a picture of the ultimate distribution of a persistent substance in the environment in terms of both relative con-
centrations and relative masses. This information in itself is useful in throwing some light on the likely compartments of conce’rn.
Level 2 transformations, etc. This level shows significant transformations and persistence. Equilihrium distribution with transformation is the second and more difficult application. Assume again that all compartments are in equilibrium, but allow steady-state input of the solute, I moles/year, and transformation by photolysis, hydrolysis, oxidation, hiodegradation, and advection of the solute out of the region of interest. All these processes a r e expressed in firstorder form as a function of concentration (regardless of whether first-
order kinetics prevail). There is thus a series of rate constants k l , k2, k3, etc., to k j (years-’) reflecting the degradative process where: rate [mol/(m3 year)] = kjC For advection the rate constant k, is A/V, where A is the outflow of the fluid (m3/year) and Vis the volume of the compartment. If the inflow is as contaminated as the outflow, advection can be ignored and, of course, intermediate situations a r e possible. Fortunately, for many compartments (such as soil) advection is negligible, and most of the kj terms are effectively zero. The reason for insisting on a first-order format is that the rate constants a r e additive. Thus, the total removal rate from compartment i is: V i C i C k j = ViCiKi (mol/year)
where: Ki = C j k i (for compartment i)
But the total input rate f must equal the total removal rate; thus:
where Mi is the number of moles in compartment i. But since M = E M i , the overall environmental rate constant for removal is f / M (years-I) or the average residence time is M / f (years). This provides a method of calculating an environmental “persistence,” which takes into account different volumes, concentrations, and rate constants in the various compartments. Essentially it is a weighed mean rate constant defined as K M ,where: Clearly the most significant contributors to K M are fast processes in large compartments with high concentrations (or high Z values). Tables 2 and 3 give a hypothetical example of this approach to calculating the overall persistence of a substance distributed between three phases in which the annual input rate is 1000 mol. It illustrates the utility of the approach in providing a format for combining the various equilibrium and kinetic terms in a manner such that the dominant processes are exposed. In this case the primary degradative process is atmospheric photolysis, despite the facts that most of the solute is in the sediment and the fastest degradative rates occur in water. In relVolume 13, Number 10, October 1979
1221
FIGURE 1
Intercompartment transfer and concentrations. Values from Table 3 for equilibrium (level 2) are shown in parenthesis ( ).
566 (928)
Level 3: nonequilibrium distribution This level includes steady-state input, transformation, and intercompartment transfers, and permits the solute to be introduced into one or more compartments at a rate of f; mol/year, and establishes a transfer rate between compartments in terms of an exchange rate constant that is driven by the fugacity difference. If we have two compartments, 1 and 2, with volumes V I and Vz (m3), concentrations C1 and Cr, the fugacities will be f l = C;/Z; and fr = C2/Z2. We postulate a steady-state transfer rate N (mol/year) as:
N = Dl2cfl
1000
395
rnoliyear
(60)
ative importance the degradative processes are: atmospheric 93%, water 6%, and sediment 1%. The overall persistence corresponds to a rate constant of 8.26 years-I or a residence time of 0.121 year (44 days). This is considerably slower than many of the individual rate constants. For example, the aquatic degradative processes give a time rate constant of 510 years-' (corresponding to a
half-life less than one day), but only 0.1% of the solute is exposed to these conditions. It is thus easy to be misled by individual compartment degradation rates. The overall rates are controlled by volume, concentration, and rate constant, but their relative magnitudes are not immediately clear. Only by calculating along the lines indicated does a truer degradative picture emerge.
-f2)
D has units of mol/(year.atm) and depends on factors such as common transfer area between the compartments and the rate of diffusion. For example, for volatilization it can be shown that D is KocalRT, where Koc is the overall gas mass transfer coefficient (m/year) and a is the interfacial area (m2). Presumably other expressions can be devised for soilatmosphere, sediment-water transfer, and even for uptake of solutes by biota. Again, many terms will be zero or negligible and only the important transfer mechanisms need be quantified. At steady state for compartment i:
I, = V;C;K;+ CjDijV; - A ) The summation is over all compartments except i. This can be rearranged to give:
fi
=fi(
+ 2,D;j)
V,K;Z;
- C;(D;&) I f there are n compartments, this reduces to n simultaneous linear equations with n unknowns V;.), which can be readily solved by conventional methods. From thef; values, C; can be calculated as can the various transformation and transfer rates. Figure 1 illustrates this calculation for the same system as level 2, except that the solute is now introduced into only the water phase and allowed to transfer into the other two at rates controlled by postulated values of D;,. These results are obtained by solving the three simultaneous equations: i = 10 = 88 X 1012fl - 8 X
lO'*f2
i = 21 000 = 14.1 X 10'2fl
-
10'2f3
i = 30 = 2 X 1012f3- 101*,f2 The values offthat result are given in Figure 1 with calculated concentrations. 1222
Environmental Science & Technology
Of the 1000 mol introduced into the water, 395 mol is degraded in the water compared to 60 in Table 3. The reason for this increase is the slow water to air transfer, which results in a nearly sevenfold increase in the water concentration. The air phase concentration drops by nearly a factor of two, as does the air degradation rate. Because of the higher water concentration, the sediment concentration increases. If biota had been included, they would have exhibited concentrations of about 1.5 pg/g. The conclusion is that water body concentrations may be significantly controlled by either degradation rates in other phases (for example, air) or by transfer rates to these phases. This approach elucidates such interdependencies and identifies the dominant processes that control exposure to toxicants. Level 4: unsteady-state distribution The ultimate level can be expressed mathematically as a set of differential equations in which input rates, concentration, and fugacity can vary with time ( t ) : fj(t)
=f,( VjKjZ; + CjDjj) - CjDj/r; + V;Z;(df,/dt)
By inserting an initial condition and appropriate input rates, the time change in concentration in various compartments can be calculated. This is essentially the approach developed by Baughman and Lassiter and implemented by S R I in their study of the environmental dynamics of several toxic substances. Such an approach is essential for determining the persistence of a substance after emissions have ceased, or in identifying how long it may take for concentrations to build up to certain levels. Its utility in environmental management of toxic substances is obvious.
Caveats Two obvious criticisms can be levelled a t this approach. First, it fails to allow for heterogeneity within a phase, for example, an epilimnion and hypolimnion or various trophic levels of biota. However, such situations can be accommodated readily by dividing a compartment into subcompartments. But this introduces a greater degree of complexity. Second, it assumes first-order processes throughout. Although it is possible to allow for non-first-order behavior (with respect to the solute) or nonlinear sorption isotherms, the introduction of such subtleties levies a high cost in terms of complexity. A preferable approach is believed to be
to force pseudo-first-order behavior in the concentration range of environmental interest. Clearly, by proceeding from level to level, a “profile” of the environmental behavior of the solute emerges that becomes increasingly close to the actual environmental behavior. Obviously, if many hundreds of new compounds are introduced annually, it will be impossible to gather all the necessary physical, chemical, and biological data to permit comprehensive modeling to be undertaken. It is worth noting that complexity brings not only the need for more input data and the greater possibility of error or mistakes, but it also strains the modelers ability to remain “in tune” with the model such that the results remain intuitively reasonable. When this feeling of “reasonableness of output” is lost, the risk of error or mistake increases enormously and the results become less comprehensible. Perhaps the aim should be to proceed slowly in the direction of increasing complexity with the most suspect substances being subjected to the most detailed modeling with the all-attendant experimental determination. It is generally accepted that models should be validated by comparison with real environmental data. Models of the type described here are “evaluative” and d o not purport to describe any particular real environment; thus, they cannot be validated except by general comparison of observed environmental concentrations with the predicted values. Environmental samples are notoriously variable with concentration ranges often over a factor of IO. I f the model predicts concentrations within the range of observed values, it can be considered successful. It should be noted that validation really requires measurement of fugacity, not merely concentration. It is essential to discriminate between total sorbed and dissolved concentrations in all phases, but this is unfortunately often a difficult analytical task.
Research needs An interesting aspect of this analysis is that it highlights the need for the development of specific predictive capabilities and it provides a degree of organization to environmental science. Research needs can be categorized as follows: 2 values: These are obviously obtained from physical chemical measurements such as solubility, volatility, octanol-water (or lipid-water) partition coefficients, and sorption coefficients. The recent work of Kar-
ickhoff et al. relating sorption to octanol-water partition coefficient is potentially very valuable in facilitating these calculations for hydrophobic organics. The many biosorption or bioaccumulation studies likewise bring the potential for considerable economy in effort. K values: There is a need for development of rapid and reliable methods of predicting or measuring these constants in environmental conditions. It seems likely that standard laboratory tests could be devised to give data that can be translated into environmental rates. D values: There is a need to quantify the physical transfer processes between phases. A considerable literature exists for volatilization and wet and dry deposition, but more information is required on sedimentwater transfer or volatilization from depths m soils. Such a categorization may also be valuable for pedagogical purposes in bringing some systems into the often overwhelmingly complexities of the environmental dynamics of toxic substances.
Additional reading Baughman, G., Lassiter, R., “Prediction of Environmental Pollutant Concentration,’’ ASTM S T P 657, p 35, Philadelphia, Pa., 1978. S R I International, “Environmental Pathways of Selected Chemicals in Freshwater Systems,” Parts I and 11, EPA Reports 60017-77- 1 13 and 60017-70-074. Prausnitz, J . M., “Molecular Thermodynamics of Fluid Phase Equilibrium,” Prentice-Hall, Englewood Cliffs, N.J., 1973. Paris, D. F., Steen, W. C., Baughman, C. L., Chemosphere, 4, 319 (1978). Clayton, J . R., Pavlou, S. P., Breitner, N . F., Enciron. Sci. Technol., 11, 676 (1977). Karickhoff, S. W., Brown, D. S., Scott, T. A , , Water Res., 13,241 (1979).
Donald Mackay is a professor in the Department of Chemical Engineering and Applied Chemistry and in the Institute for Enoironniental Studies of the Unioersity of Toronto. His research interests are the behavior of toxic organic chemicals in the enoironment, particularly oolatilization and the physical behaoior of oil spills. Volume 13, Number 10, October 1979
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