Environ. Sci. Technol. 1985, 19, 412-417
Multimedia Modeling of Environmental Transport: Trichloroethylene Test Case Yorarn Cohen” and Patrlck A. Ryan Department of Chemical Engineering and National Center for Intermedia Transport Research, University of California, Los Angeles, California 90024
W
A simple approach to multimedia compartmental
modeling of environmental fate and transport of chemical pollutants in the environment is presented. A six-compartment system is used to explore the transport behavior of trichloroethylene (TCE) in a multimedia environment. The predicted concentrations of TCE are in reasonable agreement with the available field measurements. The study suggests that gaseous mass transfer of TCE from the air compartment into the soil and water compartments is the major dispersion route of TCE in the environment. Introduction Environmental management is becoming increasingly concerned with predicting the fate and transport of potential chemical pollutants in a multimedia environment. Multimedia understanding of pollutant behavior in the environment is of particular concern for chemicals that are toxic and persistent and are subject to accumulation in environmental compartments where biota and human exposure is significant. For example, the design of environmental monitoring requires knowledge of the pathways and estimates of concentration levels of pollutants in order to optimize the design of sampling and detection strategies. The evaluation of exposure-dose-response relationships requires more accurate knowledge of concentration levels, since toxicity and response are sensitive functions of concentation levels and time histories. A quantification of the interactions of different environmental media will most likely contribute to the planning of optimal strategies of pollution abatement. In principle, detailed single-medium models can be coupled to yield a multimedia description of environmental transport. Such an approach, however, would require a large number of model parameters that are often unavailable. Moreover, since complex models are difficult to apply and interpret, their regulatory role may be limited. Therefore, at the present state of the art of multimedia transport research, the most practical approach is to formulate models that make use of compartmental systems to describe the events occurring in various parts of the environment. These compartments may correspond to actual environmental media or to abstract mathematical constructs designed for convenience. The direct results from such multimedia-compartmental models (MCM models) are in the form of concentration time profiles for each of the environmental compartments under consideration. Although the spatial description of some of the compartments may be sacrificed, quantitative estimates can be obtained regarding the macrobehavior of the system. This information can be utilized in determining pollutant pathways, fluxes, accumulation, and environmental “hot spots” and to assess the level of human exposure. The concept of compartmental modeling is not new in environmental research (1). Compartmental models have been used in modeling the transport of carbon dioxide (2, 3) and trace pollutants in the oceans and across the airocean interface (4-6), in the design and interpretation of 412
Environ. Sci. Technol., Vol. 19, No. 5, 1985
multimedia monitoring data (7-14), and in pollutant mass balance studies in the environment (7-25). In recent years there has also been a growing awareness that multimedia-compartmental models may also aid in the design of comprehensive pollution control strategies (7,12,13, 15, 16, 18, 23, 25). Many of the early compartmental models were restricted to the determination of steady-state mass budgets or concentrations. The steady-state approach has proven useful in identifying the presence of potential sinks and sources in specific regions (20, 21). Steady-state compartmental models have also been used to estimate human uptake of specific pollutants (8-12). The steady-state approach, however, does not yield information regarding the transient behavior of the compartmental system. Important information regarding, for example, temporal exposure variations due to variable source strength and climatic conditions cannot be predicted. This deficiency has been recognized in the literature as well as the need for dynamic multimedia-compartmental models (9,15-18, 23-25). It is emphasized that a properly formulated MCM model should be a true predictive model based on transport parameters derived from a fundamental description of the governing intermedia transport processes. Many of the existing MCM models have failed to recognize this point and have simply employed transport coefficientsthat are essentially long time averages of approximate flux/ concentration ratios or estimates based on first-order kinetics without thermodynamic constraints. In this paper a treatment of multimedia-compartmental modeling is presented for a compartmental system consisting of both uniform and nonuniform compartments. The present analysis is restricted to nonaerosol pollutants. The results of the model for the distribution of trichloroethylene (TCE) in a six-compartment system are presented and compared with available field data. Multimedia-Compartmental Model The global scheme for the multimedia-compartmental model (MCM model) requires the input of media properties, physicochemical and thermodynamic properties of the pollutant under consideration, partition and transport coefficients, sources, climatic conditions, and initial background concentrations. The output from the model is in the form of concentration vs. time profiles for each of the environmental compartments. The transport of a given pollutant in a compartmental system can be described by a set of unsteady mass balance equations. The model equations for compartments (or subcompartments) in which the distribution of chemical species is assumed to be uniform are
N
CQiiCi+ si
i = 1, ... N,i
# j (1)
j=l
The initial concentrations are set to Ci(0)at t = 0, and the source strength (mol/h) is designated by si. Ci is the
0013-936X/85/0919-0412$01.50/0
0 1985 American Chemical Society
concentration (mol/cm3) of the species of interest in compartment i. Kkl values are the overall mass-transfer coefficients in units of meters per hour (26,27),based on compartment i, for the exchange of mass between compartments i and j , aL,is the corresponding interfacial area (m2),and V, is the compartmental volume (m3). It is noted that C,* - C, is the concentration driving force for interfacial mass transport constrained by equilibrium (26,27). The variable C,* is defined as the concentration of the pollutant in compartment i in equilibrium with compartment j . The equilibrium relationship is assumed to have the following linear form: 'k]*
=
(2)
cH]L]
in which H,c is the dimensionless i to j partition coefficient. For simplicity it is assumed that the pollutant undergoes a first-order transformation reaction (chemical or biochemical). If more complex rate expressions are applicable, they can be included without a loss of generality. The reaction rate constant is k,, and the corresponding coefficient f , equals -1 for a degradation reaction and +1 for a production reaction. The terms Q C and Q,C, represent the pollutant mass flow rates (moi')i) from compartment j to compartment i and from compartment i to compartment j , respectively, where QIIand Q, are the corresponding flow rates (m3/h) or convection terms. For example, in a flowing water body such as a river, the water flow rate into and out from the water compartment is readily identified with the average river flow rate. The convection term for the atmospheric compartment, however, must account for the extensive degree of air recirculation. Atmospheric recirculation in the air compartment increases the convective residence time of the pollutant in the air compartment. Consequently, the convection terms associated with the air compartment and the atmospheric region outside the study area can be defined by (28) =
Qra
Qar
=
va/da
= 4U ( 1 + g )
(4)
where u is the wind velocity, L is the compartment length in the windward direction, and D is the horizontal eddy diffusivity. Precipitation scavenging of gaseous pollutants can also be quantified by the convection terms with an appropriate definition of the flow rate variable Qij. For example, the concentration, Cd, of a given pollutant in rain falling through a polluted atmosphere of concentration Ca is given by (5,29, 30) Cd
=
caA/Hwa
(5)
in which Hwais the air to water partition coefficient (defined as in eq 2) and A is a dimensionless scavenging ratio which varies from zero to unity. For most sparingly soluble organics that do not transform chemically in rain water, A is practically unity at distances greater than about 100 m below the cloud base (5,29,30). With the use of eq 5, the mass flow rates of the scavenged pollutant into the water and soil compartments become Qawca
= (RawaA/Hwa)Ca
= (RasaA/Hwa)Ca
(7)
and the mass flow rate of the scavenged pollutant out from the air compartment is (Qaw
+ Qa,&Ca= [R(aaw + aa,)A/HwalCa
(8)
in which R is the rate of rainfall (dimensions of m/h). Note that if the volumes of the water and soil compartments are fixed then there must be outflow terms (Qij) equivalent to the volume of rainfall input into the soil and water compartments. Therefore, during the duration of a rain event, the mass outflow of the pollutant from the water and soil compartments into the surrounding environment, designated by an arbitrary compartment k , is given by
QwkCw = RaawCw
(9)
and in which Cwis the water compartment concentration and Cwsis the concentration of the chemical in the soil-water assumed to be in equilibrium with the soil-air and soilsolids. This concentration can be related to the overall soil matrix concentration, C,, through a mass balance over the three soil phases. Accordingly, CwBis expressed by Cws = Cs/[esHw.,p
+ EaHwa + (1- E , - ea)]
(11)
in which e, and ea are the volume fractions of the solid and are the air phases in the soil, respectively. Hwa,and Hw.sp dimensionless air/ water and soil-solid/water partition coefficients, respectively, as defined by eq 2. The soil matrix is a complex three-phase system (air, water, and solids) dominated by slow diffusive transport processes that lead to significant concentration gradients in the soil matrix. The description of gaseous transport in the soil can be approximated by a simple one-dimensional diffusion equation (31)
(3)
in which da is the convective residence time in the air compartment, which can be estimated from the various atmospheric dispersion models. If the wind blows primarily in one direction, then the prediction for 0, from the one-dimensional dispersion model (28) is oa
Qasca
(6)
in which C,, is the concentration matrix and D, is the effective diffusivity in the soil matrix (30). The initial condition Csm(O,x)may be determined from available background concentrations. The boundary condition at the soil/atmosphere interface Csm(t,O)may be set equal to the atmospheric concentration for dry soil or to the interfacial equilibrium concentration calculated from eq 2 and 11, for wet soil conditions. We note that diffusion of dissolved pollutants in the sediment can also be treated by a model analogous to eq 12. The solution of the model equations (eq 1-12) may be simplified if it is assumed that the model parameters do not vary appreciably with concentration, for the range of environmental concentrations that are normally encountered. Equations 1-12 can be solved numerically, and the details of the solution procedure are described elsewhere (30). Trichloroethylene (TCE) in a Multimedia Environment In this paper the distribution of trichloroethylene (TCE) in the San Diego basin (California) is studied by using the MCM model. TCE has a high vapor pressure (Table I) which accounts for its rapid introduction into the atmosphere from various local sites (18). It is estimated that about 60% of the total TCE produced in the United States is lost to the atmosphere (6, 19, 32, 33) with negligible Environ. Sci. Technol., Vol. 19, No. 5, 1985
413
Table I. Physicochemical Properties of TCE (20 "C)
Table 111. Partition Coefficients For TCE (20 "C) Ci/C,
ref molecular weight aqueous solubility vapor pressure K , (octanol partition coefficient) degradation constant air water
131.4 11OOmg/L 60 mmHg 214.6
54 55 39
0.01 h-l 0.000124 h-'
52 6,56
Table 11. Compartmental volumes and densities"
compartment air soil water
volume, m3 2.8
X lo1' 1.2 X lo6 2.8 X lo8
compartment
volume, m3
biota suspended solids sediment
1.4 X lo2 1.4 X lo3 2.8 X
lo6
a Densities of sediment-solids, soil-solids, and suspended solids are all 1.5 g/cm3. Densities of water and biota are taken to be 1 g/cm3.
discharge into water bodies. Despite the fast degradation rate of TCE in the atmosphere (Table I), it has been detected in air, water, sediment, and rainwater around the globe (6). Field measurements of TCE concentrations have been reported for both the La Jolla (California) and Liverpool (England) areas (32,33). These data will be used for comparison with the predictions of the MCM model. Model Environment. The model environment selected for the TCE study consists of the following six compartments: air, water, soil, sediment, suspended solids (in water), and biota (in water). The sediment, suspended solids, and biota interact only with the water compartment, while the water compartment interacts with the atmosphere. The atmosphere in turn interacts with both the water and soil compartments, and the soil compartment is assumed to interact only with the atmosphere. The above simple compartmental system which was suggested by several previous investigators (12,18,22-25) is adequate for organic pollutants that are not present in the atmospheric aerosol phase. The above model environment was scaled by setting the compartmental volume/ interfacial area ratios for the soil and water in contact with the air to 0.1 and 10 m3/m2. The corresponding scaling ratios for the air in contact with the water and soil and for the sediment in contact with water were set to 700 and 0.1 m3/m2,respectively. The scaling ratio for the suspended solids in the water compartment is 0.167 X m3/m2. The volumes of the suspended solids and biota were set of the total water volume reand 5 X at 5 X spectively. The air compartment was assumed to be in contact with the water and soil compartments, with the ratio of the air/soil to the air/water interfacial area set at 3:7. In the 400-km2San Diego Study region (34)with an atmospheric height of 700 m [the effective mixing height in the San Diego region ( 3 5 ) ] ,the depth of the water compartment in the coastal region was set to 10 m. The compartmental volumes and the estimated densities of the different compartments are given in Table 11. Partition Coefficients. The partition coefficients for TCE at 20 "C are given in Table 111. The water/air partition coefficient, Haw,was determined based on the data reported by Leighton and Calo (36). The suspended solid/water partition coefficient, H,,, was calculated from the correlation proposed by Karickhoff et al. ( 3 3 ,assuming an organic content of 2.7% (38) and using the correlation of Mackay et al. (39) for the octanol-water partition coefficient. The water/sediment partition coefficient, 414
Environ. Sci. Technol., Vol. 19, No. 5, 1985
air/ water air/soil
0.313
water/sediment water/suspended solids water/ biota
0.136b 0.301 0.186 0.052
0.158"
" Composition: 50% solids, 25% air, 25% water. bComposition: 50% solids. 50% water. Table IV. Mass Transfer and Diffusion Coefficients For TCE (20 "C)
air/soil: air-side air/water: overall water phase water/biota: overall biota phase water/suspended solids: overall water phase water/sediment: water-side diffusion coefficient in sediment diffusion coefficient in soil
0.072 m/h 0.04 m/h
0.091 h-' 0.7 m/h 0.011 m/h 1.14 X lo4 cm2/sb 3.32 X 10~3~cm2/sa 4.12 X 10" cm2/sb
" See footnote a in Table 111. See footnote b in Table 111. Hw.sed, was estimated from a mass balance over the water and solid phase contained in the sediment Hw.sed = (1 - Ew)Hw.sp + t w
(13)
in which eWis the volume fraction of water in the sediment (assumed to be 0.4) and Hw.sed is the water/sediment solid was also estimated from the partition coefficient. Hw.sed correlation of Karickhoff et al. (37) with the organic content of the sediment solids assumed to be about 2.7% (40). The biota/water partition coefficient was estimated from the correlation of Veith et al. (41)for the biconcentration factor. Finally, the air/soil matrix partition coefficient was expressed through a mass balance over the soil-air, solidsolid, and soil-water phases
Cam
Ha.,, = - = ~sH*sp+ Ca
+ (1-
€8
- tw)
(14)
in which C,, is the overall soil matrix concentration and tw and E , are the volume fractions of the soil-water and soil-solids, respectively. Hasp is the soil particle/soil-air partition coefficient determined similar to the previous estimates of H,, and HWwd with an estimated soil organic content of 2% (38). The composition of the soil matrix was set to 50% solids, 25% air, and 25% water by volume (38). Under the conditions of rainfall the soil matrix was assumed to consist of 50% solids and 50% water by volume. Transport Coefficients. The mass transport coefficients (Table IV) were estimated for an average temperature of 20 "C and the estimated wind velocity of 4 m/s. The corresponding convective residence time (eq 6) in the air compartment was determined to be 100 h on the basis of the estimated horizontal eddy diffusivity of 3 X lo1' cm2/s (42). The above conditions are believed to be reasonable averages for the San Diego study region (35). Although a temporal description of both temperature and wind conditions is possible, the above average values will suffice to demonstrate the utility of the MCM approach. The air-side air/soil transport coefficient was estimated on the basis of the gaseous deposition velocities reported by Sehmel (43),assuming that the transport coefficient is related to the mass diffusivity, D as D2I3 (44). The effective diffusivity, D,,, in the soil matrix was calculated
10-5
I -----BIOTA \
10-6
10-6
