CHAPTER 24
FUGACITY MODELING TO PREDICT LONG-TERM ENVIRONMENTAL FATE OF CHEMICALS FROM HAZARDOUS SPILLS Rajesh Seth and Don Mackay Canadian Environmental Modelling Centre, Trent University, Peterborough, Ontario, Canada
24.1
INTRODUCTION As other sections of this Handbook indicate, there have been considerable efforts to model and predict the short-term fate of spilled hazardous materials over hours and days. These include estimates of spreading, evaporation, atmospheric dispersion, and flow in surface waters and groundwaters. A major incentive for such models is the protection of the public and remedial action personnel. Less attention is paid to the longer-term fate of the spilled material over months and years. In this section, we review the use of mass balance models to predict the long-term fate of spilled materials. Ultimately, the residual spilled material combines with the existing contaminant burden in the environment to raise general concentration levels and increase overall human exposure. The focus is thus on chronic exposure as distinct from short-term acute exposure, which is the primary initial concern of response agencies. An incentive for developing the capability of predicting the long-term fate of spilled materials is that such information can be used to guide and prioritize emergency response measures. Persistent chemicals should merit more vigorous cleanup measures. A potential groundwater contaminant may justify strenuous efforts to clean up a soil and prevent entry to an aquifer. A chemical that is known to hydrolyze rapidly in water can possibly be allowed to enter water after due consideration to reaction products. On the contrary, one that is nonreactive and bioaccumulative can cause contamination problems and contact with water should be avoided. It is suggested that multimedia mass balance models be used for this purpose. The specific class of models considered here are the fugacity models as described by Mackay (2001). Fugacity is used as a surrogate for concentration in these models because it simplifies the calculations. In the following sections we describe the fugacity concept and then introduce the approach of considering the environment as a set of connected well-mixed or homogeneous media or phases and the required input data of chemical properties. A series of pro24.1
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CHAPTER TWENTY-FOUR
gressively more complex models is then introduced, namely Level I, II, III, and IV calculations, it being suggested that the Level I–III models are adequate for general fate assessment of a chemical spill. For a more detailed site-specific evaluation, a Level IV or dynamic model is more appropriate, but implementation is more demanding. Such a model is detailed in a report by Mackay and Paterson (1985).
24.2
FUGACITY, Z-, AND D-VALUES Fugacity can be regarded as the ‘‘escaping tendency’’ of a chemical substance from a phase and has units of pressure, preferably Pa. It is identical to partial pressure in ideal gases and is logarithmically related to the equilibrium criterion of chemical potential. Fugacity is to mass diffusion as temperature is to heat diffusion. The concept of fugacity has been shown to be useful in identifying the static and dynamic behavior of toxic substances in the environment. Fugacity ( ƒ, Pa) is linearly related to concentration (C, mol / m3) at low environmental concentrations and can be related by the following expression: C⫽ƒ⫻Z
(24.1)
where Z is a proportionality constant, termed the ‘‘fugacity capacity’’ with units of mol / m3
䡠 Pa. This equation does not necessarily imply that C and ƒ are always linearly related. As
a rule of thumb, the linearity assumption may be considered to be valid for concentrations less than 10% of saturation. Nonlinearity at higher concentrations can be accommodated by allowing Z to vary as a function of C or ƒ. Z depends on temperature, pressure, the nature of the substance, and the medium in which it is present. It quantifies the capacity of a phase to dissolve or sorb a chemical. At a given concentration, if Z is low, then ƒ is high and the escaping tendency is high, whereas if Z is high, then f is low and the escaping tendency is low. Substances thus tend to accumulate in phases where Z is high, or high concentrations can be reached without creating high fugacities and a correspondingly high tendency to escape. The expressions for Z-values of pure air and water phases are shown in Table 24.1. The Z-values for any other medium can be calculated using these Z-values (air or water) and the dimensionless partition coefficient between that medium and air or water. For example, the Z-value for organic carbon (OC) can be calculated as follows: ZOC ⫽ ZW ⫻ KOC
(24.2)
where ZW is the Z-value for pure water phase and KOC is the dimensionless organic carbon/ water partition coefficient. Extension of ZOC to calculate the Z-value for bulk soil is shown in Table 24.1. The third group of parameters used in fugacity calculations is D-values, which are transport and transformation rate parameters with units of mol / Pa 䡠 h. When multiplied by a fugacity, they give rates of transport or transformation. Fast processes have large D-values. D-values can be added when multiplied by a common fugacity. Thus, it becomes obvious which D-value, and hence which process, is most important. Essentially, a D-value is a fugacity rate constant. For fate and transport of a chemical in the environment, various Dvalues defining loss of chemical by advection, reaction, or intermedia transport can be obtained for each environmental medium. An example of each is included in Table 24.1.
24.3
ENVIRONMENT AS COMPARTMENTS Mass balance models are based on Lavoisier’s fundamental axiomatic law of the conservation of mass. The environment is very complex and changes in time and space. Since it is too
FUGACITY MODELING
24.3
TABLE 24.1 Expression and Estimates for some Z and D-values at 25⬚C Calculated and Used
by the Models Value Parameter Z-values Air (all levels) Water (all levels) Other, e.g., Soil Level I and II Level III D-values Advection (Level II and III) e.g., in air Reaction (Level II and III) e.g., in soil (Level III) Intermedia transport (Level III) e.g., water to air
Expression
Styrene
Dinitrotoluene
1 / RT 1/H
4.03 ⫻ 10⫺4 3.6 ⫻ 10⫺3
4.03 ⫻ 10⫺4 11.15
vOC ZOC vA ZA ⫹ vW ZW ⫹ vOC ZOC
7.95 ⫻ 10⫺2 4.09 ⫻ 10⫺2
22.45 14.57
GAZA
4.03 ⫻ 108
4.03 ⫻ 108
kSVSZS
9.28 ⫻ 105
1.07 ⫻ 108
Kv AZW
1.65 ⫻ 106
2.01 ⫻ 107
R ⫽ gas constant (Pa 䡠 m3 䡠 mol⫺1 䡠 K⫺1) T ⫽ temperature (K) H ⫽ Henry’s law constant (Pa 䡠 m3 䡠 mol⫺1 䡠 K⫺1) v ⫽ volume fraction G ⫽ flow rate (m3 䡠 h⫺1) A ⫽ surface area (m2) Kv ⫽ overall water mass transfer coefficient (m 䡠 h⫺1) k ⫽ reaction rate constant (h⫺1) Subscripts: A ⫽ air; W ⫽ water; S ⫽ soil; OC ⫽ organic carbon
complex to describe in accurate detail, the art of modeling lies in selecting only the key media and processes. The fugacity models described here attempt to describe chemical fate in the entire relevant environment consisting of the atmosphere, terrestrial soils, water bodies, and bottom sediments. It proves useful to assemble evaluative environments that can later be used in calculations. It is convenient to define two evaluative environments and undertake calculations of chemical entry, transport, and transformations in these environments. The simplest approach is to define a four-compartment (or medium) system of air, water, soil, and sediment. Second is a more complex eight-compartment system (including aerosols, suspended sediment, and terrestrial and aquatic biota), which is more representative of real environments and is correspondingly more data-intensive. For a detailed discussion on these environments or ‘‘unit worlds,’’ the reader can consult Neely and Mackay (1982). The values and properties assigned to various environmental compartments or media can be modified if chemical fate in a specific region is required.
24.4
MODELS OF INCREASING COMPLEXITY To develop a full understanding of how chemical and environmental properties affect the fate and transport of a chemical in the environment, a series of models of increasing complexity has been developed designated Levels I, II, and III. Salient features of Level I, II, and III models described by Mackay (1991) are presented below. These models are available for free download from the website of the Canadian Environmental Modelling Centre at
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CHAPTER TWENTY-FOUR
Trent University (http: / / www.trentu.ca / envmodel). Extension of Level III model to simulate unsteady-state conditions (Level IV model) is also discussed. Three types of chemicals are treated in these models, viz. chemicals that partition into all media (type 1), involatile chemicals (type II), and chemicals with zero or near-zero water solubility (type III). The models cannot treat ionizing or speciating chemicals. Chemicals that can potentially be discharged as spills are predominantly of type I, and illustrative application of Levels I–III models to two such industrial chemicals, styrene and dinitrotoluene, using EQC-standard environment (Mackay et al., 1996b) is presented. The models are also capable of treating type 2 and 3 chemicals, which differ slightly in terms of data requirement (Mackay et al., 1996b), and are not discussed here. These models are totally transparent, easy to use and understand, and can be modified by the user to suit individual needs. Relevant physical-chemical properties of styrene and 2,4-dinitrotoluene (henceforth referred to as dinitrotoluene) are shown in Table 24.2. The data are from Mackay et al. (1992, vols. 3, 4). The area selected for the evaluative environment of these models is 100,000 km2, which is about the size of Ohio or England. Terrestrial land (or soil) is assumed to cover 90% of the area, the remaining 10% being water. This region is similar to that used in the EQC models described by Mackay et al. (1996a, b, c). The volumes and depths of the four primary media are included in Table 24.2. The calculated air, water and soil Z-values for styrene and dinitrotoluene are presented in Table 24.1. Values for one each of advection, reaction, and intermedia transport D-values are also included in Table 24.1 for the two chemicals. 24.4.1
Level I
Level I models describe the equilibrium distribution of a fixed quantity of conserved (nonreacting) chemical between different media. There is no input, output, degradation, or intermedia transport. The environmental medium in which the chemical is discharged is not important because the chemical is assumed to become instantaneously distributed to an equilibrium condition. This is useful for gaining an initial impression of a chemical’s partitioning tendencies. Level I also gives an order-of-magnitude relative concentrations in different environmental media. TABLE 24.2 Selected Properties for Styrene and Dinitrotoluene
Property
Styrene
Molecular mass (g / mol) Water solubility (g / m3) Vapor pressure (Pa) Log KOW Melting point (⬚C) Assumed reaction half-lives (h) Environmental Volumes (m3) Air (depth ⫽ 1,000 m) Water (depth ⫽ 20 m) Soil solidsa (depth ⫽ 0.1 m) Sediment solidsa (depth ⫽ 0.01 m) a
Same as bulk volume in Level I and II models
104.1 300 800 3.05 ⫺30.6 5 170 550 1700
Air Water Soil Sediment 1 2 9 1
⫻ ⫻ ⫻ ⫻
1014 1011 109 108
Dinitrotoluene 182.1 270 0.133 2.01 70 17 55 1700 5500
FUGACITY MODELING
24.5
Mathematically, if there are four environmental media of volume Vi (i ⫽ 1 to 4), with respective Z-values Zi, and the total amount of chemical present is M mol, then: M⫽
冘 (V C ) ⫽ ƒ 冘 (V Z ) i
i
i
i
(24.3)
where Ci is concentration and ƒ is the common fugacity, which can be readily calculated as M/ 兺(Vi Zi). Each concentration Ci can then be calculated as ƒ Zi and the amounts in each medium Mi as Vi Zi ƒ or ViCi. Obviously 兺Mi will equal M. In Level I calculations, soil and sediment are considered as solid phases, i.e., their porosity and the presence of interstitial air or water are ignored. Interstitial air and water are, however, included in Level III calculations. Apart from the four primary media, three other media, aerosols in air and suspended matter in water and fish, are included for interest. The volume of these media is small, but they often have the highest concentrations. In addition, the mass of chemical partitioning to aerosols can be quite significant. Mass balance diagrams for l00,000 kg of styrene and dinitrotoluene in an evaluative environment are shown in Fig. 24.1. Some similarities and differences in the behavior of two chemicals due to differences in their properties immediately becomes obvious. Since neither of the chemicals is hydrophobic (low KOW), only small amounts partition to phases containing organic matter (soil, suspended, and bottom sediment). Due to its relatively high vapor pressure, styrene tends to migrate to the air phase with more than 90% partitioning there at equilibrium. However, due to its low vapor pressure and moderate solubility in water, more than 90% of dinitrotoluene tends to be in the water phase. These simple calculations readily show where the chemical is likely to partition and where concentrations are likely to be highest. This information can be useful in guiding remediation and monitoring efforts.
24.4.2
Level II
Level II includes the effects of advection and degradation reactions (represented as halflives) in various media on the fate of chemicals. It describes a situation in which a chemical is discharged into the environment at a constant rate and achieves steady state (input equals output). The Level II model also assumes intermedia equilibrium, and thus rates of intermedia transport are again not considered. The environmental medium of discharge is therefore not important and the relative distribution of chemical among the various media is similar to Level I. Mathematically, if the emission rate is E mol / h, then at steady state this must equal the total loss rate of ƒ兺Di where ƒ is the common fugacity and each D-value represents a loss, either by degradation or advection. Concentrations and amounts can be calculated as for Level I. The ratio of the calculated total amount M in the system to E (or ƒ兺Di) is the overall average residence time of the chemical. When M is divided by the degradation rate, the result is a residence time (longer than the overall residence time) attributable to degradation only, which is useful in assessing the chemical’s persistence in the global environment. Level II provides a measure of the relative rates of chemical loss by advection and reaction and a first estimate of overall chemical residence time or persistence, which is an important chemical property governing environmental exposures. The potential for global persistence is indicated by reaction persistence (controlled by reaction half-lives), whereas local persistence is indicated by overall persistence. The magnitude of chemical loss by advection in air gives an impression of the chemical’s potential for long-range transport. Level II diagrams for discharge of 1,000 kg / h of styrene and dinitrotoluene into an evaluative environment are shown in Fig. 24.2. Again there are similarities and differences in the behavior of the two chemicals due to differences in their properties. Although more styrene than dinitrotoluene is removed by advection in air, only less than 10% is lost by this process. Hence neither of the two chemicals is a candidate for long-range transport. The fate
24.6
CHAPTER TWENTY-FOUR
FIGURE 24.1 Level I diagram for partitioning of 100,000 kg of styrene and dinitrotoluene.
of both chemicals in the evaluative environment is primarily controlled by reaction (or degradation). However, reaction in air for styrene and reaction in water for dinitrotoluene are the dominant removal mechanisms and control their overall persistence in the environment. It is therefore important that accurate estimates of these half-lives, rate constants, and rates should be sought. Large uncertainties in values would translate into corresponding uncertainties in the estimated persistence. Due to differences in reaction rates, dinitrotoluene is about 10 times more persistent than styrene and their total masses in the environment at
FUGACITY MODELING
FIGURE 24.2 Level II diagrams for discharge of 1,000 kg / h of styrene and dinitrotoluene.
24.7
24.8
CHAPTER TWENTY-FOUR
steady state differ by this ratio. Figure 24.2 shows that the environmental persistences of styrene and dinitrotoluene in the evaluative environment are low at 7.5 and 76 hours respectively. Since this persistence is dominated by reaction, the two chemicals are not very persistent in the global context. Although spill situations are inherently dynamic in nature with continuously changing concentrations and it is usually desired to estimate recovery times, the Level II results provide indirect insights into these times. The persistence or residence time under steady-state conditions (calculated as mass in the system divided by total rate of input or output) is closely related to the recovery time. Indeed the dynamic half-life can be shown to be 69% of the steady-state residence time. The relative importance of various loss processes also becomes apparent.
24.4.3
Level III and IV
The Level III model includes all the important fate and transport processes in a real environment and is one step more complex than Level II. As in the Level II model, the chemical is discharged at a constant rate into the environment to reach a steady state (at which input equals output). Unlike Level II, equilibrium between different media is not assumed and rates of chemical transfer by intermedia transport processes are defined. The individual discharges to all environmental media must be specified because the distribution of the chemical between media now depends on how the chemical enters the system. Depending on the properties of a chemical, the mode of entry can also significantly alter chemical persistence or residence time in the environment to values that are quite different from Level II results. A series of 12 transport velocities control chemical transfer between the four primary environmental media (air, water, soil, and sediment). Equilibrium is assumed, however, within each medium. For example, suspended matter and fish are assumed to be at the same fugacity as water. Mathematically, a steady-state mass balance equation is set up for each of the four compartments. These take the form for compartment i as follows Ei ⫹
冘 (ƒ D ) ⫺ 冘 (ƒ D ) ⫽ ƒ 冘 D j
ji
i
ij
i
(24.4)
i
where Ei is emission into i, the second term is the sum of all intermedia transport process rates into i from other j compartments, the third term is the sum of all intermedia transport process rates from i to other j compartments, and the fourth term is the sum of all loss processes from compartment i by transport and transformation. There are thus four equations and four unknown fugacities thus a solution is possible. All concentrations and amounts can be calculated as before, leading to a mass balance diagram as illustrated in Figs. 24.3 and 24.4. The important new information is the intermedia fluxes. The extension to a Level IV or unsteady-state model is obvious, the mass balance equations taking the form of differential equations, i.e.: d (ViZi ƒi) ⫽ Ei ⫹ dt
冘 (ƒ D ) ⫺ 冘 (ƒ D ) ⫺ ƒ 冘 D j
ji
i
ij
i
i
(24.5)
These can be solved numerically or in some simple cases analytically by defining an initial condition and the time course of emission. This is essentially the approach described by Mackay and Paterson (1985). Chemical fate and exposure following a spill is dynamic in nature, and thus a Level IV simulation is the preferred option. Much of the information that results from such a calculation can, however, be gleaned from inspection of Level III results. A Level III model is easier to use without site- and spill-specific input data and can provide important information for directing a spill response. It can identify dominant fate and exposure processes and the
FUGACITY MODELING
FIGURE 24.3 Level III diagrams for discharge of 1,000 kg / h of styrene into water and soil.
24.9
24.10
CHAPTER TWENTY-FOUR
FIGURE 24.4 Level III diagrams for discharge of 1,000 kg / h of dinitrotoluene into water and soil.
FUGACITY MODELING
24.11
associated environmental media, which can then be targeted for monitoring and / or remedial action. For example, it can show how fast a chemical will evaporate from soil or water into the atmosphere. Hence, a detailed site- and spill-specific dynamic simulation (Level IV model) is not always necessary. A well-tested version of a Level IV model is not yet available. Level III diagrams for the discharge of 1000 kg / h of styrene in water and soil respectively are shown in Fig. 24.3 and those for dinitrotoluene are shown in Fig. 24.4. Since spill situations are of interest here, only discharges to soil and water are illustrated. It may be desired to estimate how long it will take spilled chemical to evaporate from soil. A Level III calculation gives a steady-state rate of evaporation, not a time. In Fig. 24.3 with a constant discharge of 1000 kg / h styrene in soil, the mass of styrene in soil at steady-state is 423,000 kg and the evaporation rate is 458 kg / h. The rate constant for evaporation is thus 458 / 423,000 or 1.08 ⫻ 10⫺3 h⫺1 and the corresponding half-life is 640 hours or about four weeks. We thus expect that half the initial styrene will evaporate every four weeks, assuming there is no degradation. After 20 weeks or five half-lives, only 1 / 25 or 3% will remain. The Level III model used here and available for download (http: / / www.trentu.ca / envmodel) does not include a separate groundwater compartment. However, concern for groundwater contamination can still be evaluated using this model as follows. Soil water leachate to groundwater can be considered equivalent in characteristics to soil water runoff included in the model, which is assumed to be in equilibrium (i.e., equifugacity) with soil pore water and in turn with soil. The soil runoff rate in the model can therefore be modified to include both leaching and runoff. For the illustrative examples presented here, the leaching rate was considered equal to that of runoff, and the default runoff rate of 0.00005 m / h (or m3 / m2 䡠 h) in Level III model was modified to 0.0001 m / h to include both soil water leaching to groundwater and runoff. A groundwater depth of 1 m is considered. Figure 24.3 shows that although styrene tends to evaporate, it is constrained to stay in the medium of discharge if emitted to soil or water. Slower degradation rates in these media increase the overall persistence of styrene in the environment to five days or more, which is more than an order of magnitude higher than that for the equilibrium situation in Level II. Overall, Fig. 24.3 shows that although discharge of styrene into water or soil tends to increase its persistence in the environment, it is still removed quite rapidly from the environment. If discharged as a spill, therefore, styrene is not likely to be of concern for long-term exposure. Calculations including the groundwater reveal that only about 1% or less of styrene is likely to be transferred to groundwater if discharged on soil and it may be of little concern as a potential groundwater contaminant. The key emergency response procedures for a styrene spill are to limit short-term exposure. The Level III model can be useful in directing such a response. Figure 24.4 shows that, if discharged to water, dinitrotoluene would stay in water, with reaction in water being the dominant removal mechanism. The Level III diagram for discharge of dinitrotoluene to water is very similar to the Level II diagram (which assumes equilibrium between different media), which is expected due to the chemical’s preference for the water phase at equilibrium. The overall persistence in the environment is expected to be a relatively short 74 hours, which is controlled by its reaction persistence in water. If discharged to soil, dinitrotoluene would tend to build up, increasing its overall environmental persistence to over two months. Inclusion of groundwater compartment in Level III calculations suggests that, if discharged to soil, dinitrotoluene could contaminate groundwater with persistence similar to that in soil. It must be noted that the estimated reaction half-lives of dinitrotoluene in soil (672 to 4,320 hours) and in groundwater (48 to 8,640 hours), and therefore its persistence, are quite uncertain and will be a function of local conditions such as temperature. Overall Level III calculations suggest that the mode of entry of a dinitrotoluene spill can lead to very different environmental impacts. If spilled in surface water, it is expected to degrade quite rapidly. However, if spilled onto soil, dinitrotoluene is expected to persist in soil and contaminate groundwater for a period of several months unless preventive measures
24.12
CHAPTER TWENTY-FOUR
are taken. Hence, in such an event, the contamination of these compartments and the resulting potential exposure would have to be monitored for a period well beyond the initial emergency response. A useful response measure suggested by Level III results is to prevent soil leachate from contaminating the groundwater by, for example, directing it in a controlled manner to a surface water body where it will degrade rapidly.
24.5
SUMMARY In summary, it has been shown that mass balance models can be used for assessing the longterm behavior of spilled materials and can guide and prioritize emergency response measures. Fugacity-based Level I, II, and III models are transparent, easy to use and understand, and can be used for general fate assessment of a chemical spill. There is a compelling incentive to use standard, well-tested, widely available models for such evaluations. One such source of Level I, II, and III models on the World Wide Web is the Canadian Environmental Modelling Centre (http: / / www.trentu.ca / envmodel). The models have been widely used and can be easily adapted to suit specific needs.
24.6
ACKNOWLEDGEMENTS The authors are grateful to the Natural Science and Engineering Research Council of Canada (NSERC) and the consortium of chemical companies that support the Canadian Environmental Modelling Centre at Trent University.
24.7
REFERENCES Mackay, D. 2001. Multimedia Environmental Fate Models: The Fugacity Approach, 2nd ed., Publ. / CRC Press, Boca Raton, FL. Mackay, D., and S. Paterson. 1985. A Model of the Long-Term Fate of Chemical Spills, Report EE-64, Environment Canada, Ottawa. Mackay, D., A. Di Guardo, S. Paterson, G. Kicsi, and C. E. Cowan. 1996a. ‘‘Assessing the Fate of New and Existing Chemicals: A Five-Stage Process,’’ Environmental Toxicology and Chemistry, vol. 15, no. 9, pp. 1618–1626. Mackay, D., A. Di Guardo, S. Paterson, and C. E. Cowan. 1996b. ‘‘Evaluating the Fate of a Variety of Types of Chemicals Using the EQC Model,’’ Environmental Toxicology and Chemistry, vol. 15, no. 9, pp. 1627–1637. Mackay, D., A. Di Guardo, S. Paterson, G. Kicsi, C. E. Cowan, and D. Kane. 1996c. ‘‘Assessment of Chemical Fate in the Environment Using Evaluative, Regional and Local-Scale Models: Illustrative Application to Chlorobenzene and Linear Alkylbenzene Sulfonates,’’ Environmental Toxicology and Chemistry, vol. 15, no. 9, pp. 1638–1648. Mackay, D., W. Y. Shiu, and K. C. Ma. 1992–1997. Illustrated Handbook of Physical–Chemical Properties and Environmental Fate for Organic Chemicals, CRC Press, Boca Raton, FL, 5 volumes also available as a CD ROM, Chapman and Hall / CRCnetBASE 2000. Neely, W. B., and D. Mackay. 1992. ‘‘Evaluative Model for Estimating Environmental Fate,’’ in Modeling the Fate of Chemicals in the Aquatic Environment, ed. K. L. Dickson, A. W. Maki, and J. Cairns, Jr., Ann Arbor Science, Ann Arbor, MI, pp. 127–143.
