Dynamic partitioning of organic chemicals in regional environments: a

Environ. Sci. Technol. I990, 2 4 , 1549-1558

Dynamic Partitioning of Organic Chemicals in Regional Environments: A Multimedia Screening-Level Modeling Approach Yoram Cohen," Wangteng Tsal, Steven L. Chetty, and Glenn J. Mayer

Department of Chemical Engineering, University of California, Los Angeles, Los Angeles, California 90024-1 592 ~~~~

A screening-level spatial-multimedia-compartmental (SMCM) approach to modeling the fate and transport of volatile organic pollutants in regional environments is presented. The SMCM approach, which makes use of both uniform (i.e., well-mixed) and nonuniform (one-dimensional) compartments, incorporates a variety of transport phenomena associated with pollutant transport such as dry deposition, rain scavenging, runoff, infiltration, soil drying, and pollutant diffusion and convection in the vadose zone. The multimedia distributions of trichloroethylene, tetrachloroethylene, and l,l,l-trichloroethane in the Los Angeles area, and tetrachloroethylene in the San Diego area, were explored by using the SMCM model. The predicted concentrations were found to be in reasonable agreement with the available field data. The study suggests that the SMCM approach is useful and efficient for rapid screening-level analysis of the steady-state or dynamic multimedia distribution of chemical pollutants.

Introduction Pollutants released to the environment are distributed into various environmental compartments (e.g., water, soil, and biota) as a result of complex physical, chemical, and biological processes. The potential hazards of various pollutants released into the environment depend upon the degree of multimedia exposure of human and ecological receptors to these chemicals and the associated risks. Thus,multimedia modeling of pollutant partitioning in the environment is essential for appropriate exposure and risk assessment analyses. The existing multimedia models can be classified as spatial multimedia models and uniform compartmental models. Spatial multimedia models are designed to provide the spatial resolution of pollutant concentration-time profiles. However, most of the existing spatial multimedia models such as the UTM-TOX model (unified transport model for toxicant) (1,2),the ALWAS model (air, land, water analysis system) (3),and the TOX-SCREEN model ( 4 ) have been designed by using single-medium models that are linked in series. Hence, the model applications for the separate environments cannot be solved simultaneously, which makes the process of generating time series data with such models highly cumbersome to use, and require large amounts of data (5-7). Due to their structure of linked single-medium modules, existing spatial multimedia models often neglect feedback transport loops. Examples of compartmental models in which all compartments are assumed to be well mixed include sitegeneric equilibrium fugacity-type models (8-12), the ADL model (13),the kinetic-type model (14),and the GEOTOX model (15).These earlier models require user's input of intermedia transport parameters that are not calculated by these models. Moreover, the available compartmental multimedia models consider the multiphase soil matrix to be well mixed (5,6,8-11,13-17). This latter simplification is physically inappropriate, and as Cohen and Ryan noted (18),even the simplest multimedia model should treat the soil and sediment as nonuniform compartments in which pollutant transport is described by a diffusion-type 0013-936Xf90fO924-1549$02.50f0

equation with convection and chemical reactions (19-21). Despite the above shortcomings, compartmental models are attractive because of their simplicity and modest requirements for input data. With the above considerations, the spatial multimedia compartmental (SMCM) approach for modeling multimedia pollutant fate and transport has been developed to facilitate a rapid screening-level prediction of the multimedia partitioning of organic chemicals in the environment. In this hybrid approach, the environment is taken to consist of uniform (air, water, biota, and suspended solids) and nonuniform (soil and sediment) compartments (18). Although air and water compartments are treated as being uniform, nonideal mixing or corrected residence time is implemented in these compartments. The air and water compartments can also be subdivided in order to account for some degree of nonuniformity in these compartments. The hybrid approach provides a lower degree of spatial resolution compared to spatial multimedia models, but it yields greater resolution than the conventional uniform compartmental models. Yet, the SMCM approach results in models much less complex than the existing spatial models. The uniform and nonuniform compartments are linked through the appropriate boundary conditions. For example, interfacial mass transport, infiltration, and deposition of pollutant are taken into account at the top boundary of the soil compartment, whereas chemical transport to groundwater is considered at the bottom boundary of the soil compartment. In this paper, the SMCM modeling approach is presented with a focus on volatile organics. In the SMCM model, parameter estimation methods using theoretical equations and empirical correlations are incorporated such that the required input data are reduced to physicochemical parameters of the pollutant under consideration (e.g., solubility, molal volume, boiling temperature, molecular weight), compartmental configurations (dimensions), and a modest amount of meteorological data (wind speed, mixing height, average monthly temperature and precipitation). Examples of the application of the approach to determine the dynamic multimedia distribution of trichloroethylene, tetrachloroethylene, and l,l,l-trichloroethane in Los Angeles County, CA, and of tetrachloroethylene in San Diego, CA, are provided in the following sections.

SMCM Model Descriptions The spatial multimedia compartmental (SMCM) model of pollutant fate and transport makes use of both uniform (air, water, biota, suspended solids) and nonuniform compartments (soil and sediment). The configuration and features of the SMCM model are shown in Figure 1 and Table I. The model equations of both the uniform and nonuniform compartments, estimation methods of physicochemical parameters of pollutants, and source types for possible simulation scenarios are described below. Model Equations. 1. Uniform Compartments, The material balance equations for the uniform well-mixed

0 1990 American Chemical Society

Environ. Sci. Technol., Vol. 24, No. 10, 1990

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Table I. Features of the SMCM Model

1. is a user-friendly software package a. can be used to answer "what if" type questions b. allows for rapid scenario changes C. minimizes date input d. provides a graphical output display for quick scenario analysis e. provides specific online help for input data fields f. provides a menu system for user selection of data input, simulation execution, plotting, and printing a summary report of the calculated results g. allows the software to be run on an IBM-PC/XT/AT compatible computers h. allows an inexperienced user to run the SMCM software with virtually no background in transport phenomena

2. applies a new modeling approach a. makes use of both uniform (air, water, biota, suspended solid) and nonuniform Compartments (soil and sediment) b. allows for mass exchange of pollutant between the air compartment and its surrounding atmospheric environment. The water compartment is also treated in a similar way C. treats nonuniform compartments as a steady-state, one-dimensional diffusion-type equation with convection and chemical reaction d. incorporates the simulation of a chemical buried in the soil compartment e. considers a variety of source types and allows the user to select and input source data through the data input screens f. applies flux boundary conditions for nonuniform compartments. Although groundwater is not treated as a compartment in the SMCM model, flux condition at the bottom boundary of the soil compartment can be incorporated to account for the chemical transport to groundwater 3. accounts for the effects of rainfall and temperature on the environmental transport of pollutants a. the SMCM has a rain generation module that can generate rainfall in the form of a single event of specified intensity and duration or randomly distribute rainfall within specified levels of rainfall intensity, duration, and total rainfall b. the transport process associated with rainfall such as rain scavenging, infiltration, runoff, and soil drying are simulated by a water balance method that uses theoretically based correlations C. user-supplied average monthly temperatures are used to construct average daily temperatures 4. provides accurate and reliable parameter estimation methods

a. physicochemical parameters such as mass-transfer coefficient, diffusion coefficient, and partition coefficient are estimated by theoretical methods and empirical correlations. The user can input partition coefficients and diffusion coefficients if known. These will override any model-estimated values b. temperature variations of diffusivities, partition coefficients, mass-transfer coefficients, and reaction rate constants are included by either internal predictions or via user-input data C. moduction or degradation rates are treated as first-order reactions

L

_______-.........V

___..._._.........

j

GROUNDWATER

1

SEDIMENT

Sediment-Water Sediment-ScWs L__.________________~~.~.~-..~......

N

C(QjiCj- QijCi)+ Rj + Si

j=l

i = 1, ..., N

-J

i

# j

(1)

with the initial conditions

Ci = Ci(0) at t = 0 (2) where Vi is the volume of compartment i (m9, Ci is the concentration of the species of interest in compartment i (mol/m3),N is the total number of compartments, J is the total number of nonuniform compartments, Aij is the 1550 Environ. Sci. Technol., Vol. 24, No. 10, 1990

interfacial area between compartments i and j (m2),Koij is the ith side overall mass-transfer coefficient between compartments i and j (m/h), Cii* is the pollutant concentration in compartment i, which would be in equilibrium with compartment j , and it can be expressed as Cij* = C,Hij (refer to eq 19), Ri is the production or degradation rate of chemical (mol/h), Siis the source strength (mol/h), and Q j j and Qji are the volumetric flow rate (m3/h) from compartment I to compartment j , and compartment j to compartment i, respectively. The term on the left-hand side represents the rate of accumulation of chemical in compartment i. The first term on the right-hand side of eq 1represents the rate of the chemical mass entering or exiting compartment i by interfacial mass transfer. The second term CSlQij, accounts for additional intermedia transport processes between compartments i and j such as dry deposition of particle-bound organics and rain scavenging ( 1 4 2 2 ) . The third term accounts for the net convective flow of the chemical into compartment i. As proposed by Cohen and Ryan (18),the water flow rate (into and out from the water compartment) in a flowing water body such as a river is identified with the average river flow rate, while the water flow rate into a lake compartment can be estimated from the total volumetric flow rate into and out of the lake. The volumetric flow rate associated with the air compartment and its surrounding environment is evaluated on the basis of the concept of air recirculation, accounting for nonideal mixing (23). The fourth term represents the production/degradation by chemical reaction. Although this term is modeled in this work as a pseudo-first-order process, the inclusion of more complex kinetic expressions can be incorporated without a loss of generality. Finally, the last term is the net input into the compartment from source emissions. The loss of pollutant mass in the air compartment resulting from rain scavenging can be incorporated via the

second term of eq 1 (I&?), e.g. Qaw + Qas = -R*(A,,

+ A,)Xg*C,H,,

(3)

where the subscripts a, w, and s represent the air, water, and soil compartments, respectively;R* is the precipitation rate (e.g., mm/h); A, and A, are the &oil and &water interfacial areas, respectively; C, is the pollutant concentration in the air compartment; and H,, is the dimensionless chemical water-air partition coefficient (Le., Hw, = Cw/C,, at equilibrium). Xg* is a dimensionless gaseous rain scavenging ratio; it describes the efficiency by which raindrops can remove contaminants from the air and varies between 0 and 1for chemicals that are nonreactive in the aqueous phase (18). Contaminants entering to the water compartment due to rainfall are also incorporated by using the second term of eq 1, e.g. (4) Qwa + Qws = R*AawXg*CaHwa + fr$okflshXg*caHwa The terms on the right-hand side of eq 4 account for the amount of pollutant added to the water compartment by wet deposition and surface runoff, respectively. R, is the runoff rate (m/h), f , is the fraction of runoff that will reach surface waters, L,, is the length perpendicular (m) to the direction of runoff flow, and Hsh is the height of the sheet of runoff water (m) (24, 25). 2. Nonuniform Compartments. The soil and sediment are treated as nonuniform compartments in the SMCM model. The pollutant transport processes in these compartments are dominated by molecular diffusion under most conditions (e.g., nonrain case), which leads to significant concentration gradients in these compartments. I t is noted, however, that infiltration (or convective transport) may become a dominant transport process in the soil compartment under rain conditions. Convective solute transport due to water movement can also be significant for wet soils when moisture gradients exist (20). Although lateral contaminant movement in the soil is possible in the unsaturated soil zone, vertical migration of solute transport under most conditions will dominate. Thus, pollutant transport in the three-phase (air, water, and solids) soil matrix can be approximated, assuming the soil phases to be in local equilibrium (26,27), by a onedimensional diffusion equation with convection and chemical reaction.

With the initial condition C,, = Csm(O,z) at t = 0 and the flux boundary conditions

(6)

atz=L (8)

or

(%)=o

atz=L

where the depth from the soil-atmosphere surface is designated by z , C,, is the pollutant concentration in the soil matrix, and V,, is the effective water infiltration rate in the soil matrix (m/h) (27)as defined below.

in which Csp, C,,, and C, are the concentrations in the soil-solids, soil-water, and soil-air phases, respectively, t, and t,, are the volume fractions of the soil-air and soilwater, respectively, and V, is the interstitial velocity of water in the soil matrix (m/h), which can be determined by the empirical model of Smith (28). H,,,, and are the soil matrix/soil-air and the soil matrix/soil-water partition coefficients, respectively (defined in eqs 25 and 26). D,, is the effective diffusion coefficient (m2/h)that can be estimated as discussed later in the paper. k,,, is the air-side mass-transfer coefficient at the soil-atmois the water-side mass-transfer sphere interface, and,,k coefficient at the soil-groundwater interface. RE, is the rate of production or degradation per unit volume of soil ,, is the source strength of matrix (mol/h.m3), and S pollutant per unit volume of soil matrix (mol/h.m3). This source strength can in principle be a function of time and position. However, the above approach for the soil matrix with a buried chemical layer may be unreasonable. Therefore, for the case of buried chemical simulation, an alternative approach is applied as described in the following paragraph. Through the use of the boundary conditions (eqs 7-9), it is recognized that the uniform compartments and nonuniform compartments are not necessarily in dynamic equilibrium at the boundaries (181, and thus, more appropriate flux boundary conditions are applied at the top and bottom boundaries of the soil compartment (eqs 7-9). Specifically, the deposition of water-borne pollutant, the infiltration of rainwater, and the interfacial mass transfer constrained by equilibrium are incorporated to the top flux boundary condition (eq 7). Furthermore, two different flux boundary conditions are provided in the SMCM model for the bottom boundary. The first flux boundary condition accounts for the chemical transport to groundwater (eq 8); although groundwater is not treated as a compartment in the current work, a flux condition at the bottom boundary of the soil compartment is incorporated to account for chemical transport to groundwater. As a first approximation, the pollutant concentration in the bulk groundwater (i.e., C, in eq 8) is simply assumed to be zero, i.e., equivalent to assuming an initially uncontaminated groundwater. A modification of the above approach can be made by incorporating a simple groundwater model into the SMCM approach to account for the time variations of C,. The other flux condition (eq 9) allows the setting of the flux of the chemical through the bottom of the compartment to be zero. This is valid so long as the concentration front has not reached the bottom boundary at z = L , or if the bottom boundary is indeed impermeable to the solute. The alternate type of simulation of contaminant transport in the soil compartment supported by the SMCM model is the buried chemical simulation. In this simulation, a given mass of pure chemical is assumed to be buried at an assigned depth, and it is allowed to diffuse both downward and upward through the soil compartment. In this type of simulation, a (lower) soil compartment is introduced, and the chemical transport in this compartment is also described by a partial differential equation similar to the upper soil compartment (eq 5). In this simulation, the bottom boundary condition for the upper soil compartment and the top boundary condition for the lower soil compartment are written as upper compartment: [Csm,u]r=L = Cbur (12) lower compartment: [Csm,l]zt=O = Cbu (13) Environ. Sci. Technol., Vol. 24, No. 10, 1990

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where Cam,,and Cam,,are the pollutant concentrations in the upper soil and lower soil compartments, respectively. C h is the saturation concentration of the buried chemical (mol/m3) at the specified soil temperature with the assumption that the buried chemical is in its pure form. The saturation concentration of the buried chemical, Cbur,is estimated from (14) in which Ham,,,is the soil matrix/soil-air partition coefficient (defined in eq 25), and the chemical concentration in the soil-air phase, C,,, is estimated from C,, = Pat/RT,, where PBBt is the saturated vapor pressure (Pa) of the buried chemical at the specified soil temperature (T,,, in K), and R is the gas constant (8.314 Pa.m3/mol.K). One should note that since the buried chemical diffuses away from the buried zone, the mass of chemical remaining in the buried layer decreases with time. The material balance of pollutant transport in the sediment compartment is also treated by a one-dimensional diffusion equation similar to eq 5. In the current screening approach, convection due to water infiltration into the sediment compartment is neglected, and the sediment matrix is assumed to be a two-phase system (water and solids). The flux boundary conditions for the sediment compartment are

(%)=o

atz=L

where Csdmis the pollutant concentration in the sediment matrix as defined by in which CdP and Cadware the pollutant concentrations in the sediment-solids and sediment-water phases, respectively. The volume fraction of water in the sediment is denoted by tsdw, and kw,,dm is the water-side mass-transfer coefficient at the water-sediment interface. D s d m is the effective diffusion coefficient in the sediment, and it can be estimated as discussed later in the paper. Finally, HhPy is the sediment matrixlsediment-water partition coef icient as defined in eq 24. Parameter Estimation Methods. In the SMCM model, various theoretical and empirical parameter estimation methods are used (as shown in Table 11) such that the required input data are substantially reduced, and the temperature variations of diffusivities, partition coefficients, and mass-transfer coefficients are taken into account. Also, the temperature dependence of the reaction rate constants can be incorporated via user input for parameters for the Arrhenius-type equation for the rate constants. The estimations of major model parameters such as partition coefficients, mass-transfer coefficients, diffusion coefficients, transport parameters associated with rainfall, and meteorological parameters are briefly described below. 1. Partition Coefficients, The partition coefficients, Hii, which appear in the model equations are defined by using the fugacity approach (9) i.e. (19) Hij = Ci/Cj = Zi/Z; where Ziis the fugacity capacity (mol/m3.Pa) of com1552


Table 11. Parameter Estimation Equations Utilized in the SMCM Model

parameter

estimation method

1. Partition Coefficients a. fugacity capacities for the Mackay et al. (9) air and water (&, 2), b. fugacity of the sorbed Mackay et al. (9) phase (ZSJ c. correlation of the Chiou et al. (31) octanol-water partition coefficient (Kow)with aqueous solubility (S) d. correlation of the organic Karickhoff (30) carbon partition coefficient (K,)with KO, e. correlation of Mackay (36) bioconcentration factor (BCF) with KO,

2. Mass-Transfer Coefficients a. overall mass-transfer Lewis et al. (39) coefficients (Koij) b. gas-side mass-transfer Fernandez de la Mora et al. (40) coefficient at the atmosphere-soil interface (ka,sm)

c. overall volumetric water-biota mass-transfer coefficients d. water-side mass transfer at the water-suspended solid interface e. sediment-water mass-transfer coefficient (water side) f. air-water mass-transfer coefficient (air side) g . liquid-side mass-transfer coefficient at the water-air interface

Cohen and Ryan (18) Rowe et al. (44) Thibodeaux and Becker (45) Brutsaert (42) Cohen and Ryan (46)

3. Diffusion Coefficients a. air-phase diffusion Chapman-Enskoa- method (48) coefficient (D,) b. water-phase diffusion Wilke-Chang correlation (48) coefficient (D,) c. effective diffusivity in the Jury et al. (27) soil matrix (Dsm) d. air- and water-phase Sallam et al. (47) tortuosities (laand 7,) e. effective diffusivity in the apply eqs 30-32 for a watersaturated soil sediment (Dsdm) 4. Transport Parameters Associated with Rainfall a. infiltration rate (V,) Smith (28) b. runoff rate (R,) Smith and Cherry (24) c. Soil drying rate Van Bavel (50)

5. Meteorological Parameters Jamison (51)

a. daily temperature b. rainfall

this work

partment i. Thus, using the fugacity approach, one needs only to calculate the fugacity capacity for each compartment, and all the partition coefficients are defined. The fugacity capacities for the air and water are given by (9) air: Z, = 1/RT (20) water:

Z, = 1 / H

(21)

where H is the Henry’s law constant for the solute (Pa. m3/mol). The partitioning between soil-air, sedimentwater, and suspended solids-water partition coefficients can be correlated with the organic carbon content of the solid phase, and the solute octanol/water partition coefficient (29-32). For example, the fugacity capacity of the sorbed phase Z,, can be evaluated as (9)

where pap is the density of the solid particles (g/cm3), and K pis the sorption coefficient (m3of water/l@ g of sorbent) given by (30) Kp = K J , (23) in which K , is the organic carbon-water partition coefficient which has units of milliliters of solution per gram of organic carbon, and X, is the mass fraction of organic carbon contained in the solid phase (dry weight basis). Various correlations of K , with the odanol-water partition coefficient (KO,)have been proposed in the literature (30, 33),and K , has been experimentally determined for many substances (29,34). These values are well established and should be used whenever possible. If the KO,values are not available for the solutes of interest, the correlations of Chiou et al. (31) for the octanol-water partition coefficient with aqueous solubility for 12 types of homologous series are utilized in the SMCM model. An alternative approach that may be of greater versatility is the empirical correlation proposed by Mailhot and Peters (3.9, which is based on multiple regression analyses to relate KO,to 9 different physicochemical properties by using data for 301 organic compounds from 10 chemical families. The fugacity capacities of sorbed phases can be calculated given eqs 22 and 23 and the densities and the organic carbon contents of the solid particles in the sediment, soil, and suspended solids compartments. Subsequently, the dimensionless sediment matrix/sediment-water partition is estimated from a mass balance over coefficient (Hsdmdw) the water and solid phases contained in the sediment. Hsdm,sdw

=

Csdm/Csdw

= (l - %dw)Hadp,sdw + esdw

(24)

where esdw is the volume fraction of water in the sediment, and H d p r d w is the sediment solid particle/sediment-water partition coefficient evaluated by taking the ratio of Zap for sediment to 2,. Similarly, the soil matrix/soil-air partition coefficient (Ha,,sa) and soil matrix/soil-water partition coefficients (Hmm) can be estimated from a mass balance over the soil-air, soil-solids and soil-water phases. The resulting expressions for and H8,,s, are given by H s m r = C,m/Cm = ( 1 - esw - esa)Hsp,sa + eswHsw,sa + em (25) tea

Hsm,sw

= Cem/Csw = (1 - tsw - esa)Hsp,sw + esw + Hswra

(26) where e, is the volumetric soil water content, em is the volumetric soil air content, HSp,- is the soil solid particle/soil-air partition coefficient, and Hspgw is the soil solid particle/soil-water partition coefficient. Finally, the partitioning between biota and water is estimated by the use of a bioconcentration factor (BCF). BCF = Cb/C, (27) where Cbis the pollutant concentration in biota. If BCF data are not available, then an appropriate correlation of BCF with KO, should be utilized (36-38). 2. Mass-Transfer Coefficients. The overall masstransfer coefficients, Koij from compartment i to compartment j can be estimated by using the two-film resistance theory (39) l/Koij = l / k i + H i j / k j (28) where ki and kj are the ith and j t h side individual mass-

transfer coefficients. The estimation of each individual mass-transfer coefficient is briefly described below. The gas-side mass-transfer coefficient at the atmosphere-soil interface can be determined from the deposition velocity to a fully rough surface for a reference chemical. Accordingly ka,sml

= ka,smdDal/D~J~’~

(29)

where Da is the molecular diffusivity of the pollutant in air, subscript 1 denotes the pollutant species under study and subscript 2 defines a reference species. It should be noted that eq 29 is based on the observation that the gas-side mass-transfer coefficient at the atmosphere-soil interface is correlated with the Schmidt number SC2I3 (40). Experimental data on the gas-side mass-transfer coefficient for a variety of chemicals have been reported by Sehmel (41),and these data can be applied for the reference species in eq 29. In addition, the correlation of Brutaaert (42)can also be used to evaluate the air-side mass-transfer coefficient a t the atmosphere-soil interface. The volumetric mass-transfer coefficient for watel-biota exchange can be estimated from either experimental data (43)or an appropriate empirical kinetic model such as the recent model proposed by Barber et al. (38) for a variety of fish species. For the biota compartment, it is often more convenient to use a volumetric water-biota mass-transfer coefficient, which is preferred since it is difficult to quantify the surface area for water-biota interfacial mass transfer. In the SMCM model, the sediment-water mass-transfer coefficient (water side) is determined by using the correlation of Thibodeaux and Becker (45),which expresses the mass-transfer coefficient as a function of wind speed and the depth and fetch of the lake. The watemuspended soil mass-transfer coefficient (water side) is estimated from the correlation of Rowe et al. (44). The air-side masa-transfer coefficient is evaluated from the set of correlations of Brutsaert (42), which is recommended for the gas-side mass-transfer coefficient to a smooth or rough water-air interface. Finally, the liquid-side mass-transfer coefficient at the water-air interface is determined from the correlation developed by Cohen and Ryan (46), which is a predictive momentum-mass-transfer analogy for the liquid-side mass-transfer coefficient. 3. Diffusion Coefficients. The effective diffusivity of the chemical of interest, D,,, in the soil matrix is calculated by using the method proposed by Jury et al. (27), which assumes local chemical equilibrium between the soil phases

where em is the volumetric soil air content, e, is the volumetric soil water content, HBWris the water-air partition coefficient, HSp,,, is the soil-sorbed phase/ soil-water partition coefficient, and Da and D, are the air and water molecular diffusivities, respectively. The air- and waterphase tortuosities, 7a and 7,, respectively, can be approximated by using the following empirical correlations (47):

The air-phase and water-phase diffusion coefficients are calculated by using the Chapman-Enskog method and the Wilke-Chang correlation (48),respectively. Finally, the effective diffusivity in the sediment is determined from an equation similar to eq 30 with Dsmreplaced by D h , Environ. Sci. Technol.. Vol. 24, No. 10, 1990

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and the subscript s in eqs 30-32 replaced by sd. 4. Transport Parameters Associated with Rainfall. The transport processes associated with rainfall include infiltration, runoff, and evapotranspiration. These processes are intimately related and are considered integral parts of the hydrologic cycle. The water deposited during a rain event generally has three pathways to follow after leaving the atmosphere. First is the process of infiltration in which the water can percolate through the soil column, increasing the soil water content along the vertical axis of the column. The second water pathway is overland runoff of water that cannot find its way into the soil column via infiltration. The third pathway involves the evaporation of surface water and the plant transpiration of subsurface water; these two subprocesses are lumped together and referred to as evapotranspiration. The empirical model of Smith (a), which was developed for different soil types and requires minimum input data, is utilized in the SMCM model to calculate the interstitial velocity or infiltration rate of rainwater in the soil matrix ( Vw).As presented in eq 4, the runoff rate (R,) predicted in the SMCM model is adapted from the simple screening-level surface runoff model developed by Smith et al. (24),which is based on a simple balance of water mass at the soil surface; e.g., the rainfall in excess of the infiltration capacity will be runoff. Finally, soil drying by evapotranspiration can be estimated by the energy balance approach proposed by Penman (49). Accordingly, the calculations in the SMCM model are based on modifications to the Penman approach made by Van Bavel (50). The calculations of evapotranspiration are made by using daily temperature, wind speed, humidity, and radiant energy for the climate of the region. 5. Meteorological Parameters. Temporal variations in weather conditions such as changes in temperature and changes in precipitation are incorporated in the SMCM model. For example, the daily ambient temperature in the region under consideration is approximated from the average monthly ambient temperatures by the method of Jamison (51). The required input data are thus reduced to 12 monthly values for each year of simulation. The SMCM model has a rain generation module that utilizes a simple approach to mimic the typical rainfall distributions within a given region. A typical year can be simulated by using monthly averages of rainfall and the average number of rain events of a given intensity (Le., mm/h) within a given month. Subsequently, in the SMCM simulation, monthly rain events of the specified intensities are randomly distributed within a given month while preserving the monthly mass balance of rain. Thus, one can select various rain distributions while maintaining the general features of the rainfall distribution in the region of interest. The required input data for rainfall simulations are therefore reduced to the average amount of total rainfall (mm) for each month and the number of events of a given intensity for each month. Source Types for Possible Simulation Scenarios. In order to provide for a variety of scenario simulations, four types of uniformly distributed (UD) sources (nonrepetitious constant, nonrepetitious sinusoidal, constant repetitious, and sinusoidal repetitious) were considered for the air and water compartments, whereas only a nonrepetitious constant UD source was applied for the soil and sediment compartments. The nonrepetitious constant source is applicable for scenarios where the pollutant is released with a constant source strength, and it allows the source strength to be turned on at any given time and turned off at any time before the end of simulation. The 1554


nonrepetitious sinusoidal source can be applied for scenarios where chemical emission follows the pattern of sinusoidal variation, such as chemicals emitted from industrial plumes. In such a case, the SMCM application would only be appropriate if multiple plumes exist over an area of sufficient size to treat the point sources as distributed sources. The constant repetitious source allows the source strength to be turned on and turned off sequentially. Finally, the Sinusoidal repetitious source provides for modeling of seasonal or diurnal variation such as nonstationary automobile emissions of pollutants. In this latter example, the average source strength may represent the average daily pollutant emission rate from traffic, whereas the source amplitude represents the maximum (or minimum) variation from the average source strength. The SMCM model can also simulate scenarios without source emissions by setting the source strength to zero. Such scenarios may be of interest in modeling the distribution of pollutants in areas that are initially polluted. For such scenarios, sufficiently high initial concentrations (above background) are required as input for the appropriate SMCM compartments. Numerical Method. With appropriate initial conditions and boundary conditions, the SMCM model equations (partial and ordinary differential equations) are solved simultaneously by the finite difference method and the operator splitting technique (52, 53). The operator splitting technique is used to separate the generation part (or reaction part) and the transport part of the model equation of nonuniform compartment (52). The transport parts of the model equations for the nonuniform compartments, which are PDEs, are integrated by using an explicit finite difference method (53). The model equations of uniform compartments and the generation parts of the model equations of nonuniform compartments, which are ODEs, are integrated by using the predictor and corrector method. For stiff ODEs, the asymptotic integration technique was applied (52). I t is worth noting that the pollutant transport and transformation processes are highly nonlinear and stiff, and thus the solution procedure often requires a very small integration time step (54,55). However, in order to speed computational time, the operator splitting technique is applied in the SMCM model. The operator splitting technique allows the transport parts of the model equations to be integrated by use of a much larger time step than that required for integrating the generation parts of the model equations. Thus, the above approach results in substantial reduction of computing time. Therefore, the numerical technique utilized in the SMCM model enables its execution on the IBM PC/XT/AT type computers. Case Studies: Trichloroethylene, Tetrachloroethylene, and 1,1,1 -Trichloroethane in a Multimedia Environment As a demonstration of the SMCM approach, simulations are provided for the multimedia partitioning of trichloroethylene (TCE), tetrachloroethylene or perchloroethylene (PERC), and l,l,l-trichloroethane (TCA) in Los Angeles County, CA, and of tetrachloroethylene in San Diego, CA. Limited field data for the average concentrations of TCE, PERC, and TCA in air and drinking water are available for Los Angeles County from the Total Exposure Assessment Methodology (TEAM) study, which was a 5-year EPA study of personal exposures of urban populations to a number of organic chemicals in air and drinking water in several US. cities (56). Also, field

measurements of PERC concentrations in air and water have been reported for the La Jolla region (California) (57). These data were used to illustrate the application of the SMCM model. TCE, TCA, and PERC in Los Angeles County. 1.

Region Description and Model Parameter Values. Prior to applying the SMCM model to assess the multimedia partitioning of chemicals in a specific environment, one must first gather the required data for the simulation such as compartmental data, meteorological conditions, and physicochemical properties of pollutants. The required data for the simulation of TCE, PERC, and TCA concentrations in Los Angeles are described below. The land and water surface areas of Los Angeles County were determined to be approximately 1.04 X 1O'O m2 for land surface area (or air-soil interfacial area) and 5.27 X lo7 m2 for total water surface areas, which consisted primarily of the natural water resources (4.9 X lo7 m2) such as reservoirs, lakes, and rivers (58). The average depth of water bodies was estimated to be 4.9 m by using the average depths of both natural water bodies and man-made water bodies. The average diameter of the suspended solids was set to 10 pm, which is an upper estimate on the diameter based on the diameter of nonsettling particles in natural water bodies (18). Suspended solids were assumed to occupy 5 X lo4% of the water compartment on a volume basis (18). The off-shore region was taken to be outside of the simulation region, but with the allowed exchange of air mass between the two regions. In general, there are local variations in soil types throughout the region. However, for screening purposes, moderately permeable fine sandy soil is assumed for Los Angeles. This type of soil corresponds to average conditions in the soil of 34% air content, 8% water content, and the remainder, 58%, occupied by soil solids. The depths of the soil and sediment compartments were assumed to be 8 and 1 m, respectively. The interfacial water-sediment area was assumed to be the same as the surface areas of the water compartment. A biota compartment for the Los Angeles area may be of interest; however, the biota volume occupied is not easily quantified. Therefore, the biota compartment was assumed to occupy 5 X lo"% of the water compartment on a volume basis (18). The height of the air compartment was taken to be 400 m, which represents the average mixing height over the coastal plain of the South Coast Air Basin of California (59). The monthly average temperature data for Los Angeles (60) were used in the model to calculate the daily temperature for the region. Moreover, the monthly precipitation data for Los Angeles (60)including the total amount of rainfall (mm) and the total number of events of each intensity were used for the rainfall simulation. Finally, the annual wind speed for the region was estimated to be -2.7 m/s (61). TCE is a major industrial solvent, and it is introduced mainly by fugitive emissions into the air. The emission rate of TCE in the Los Angeles atmosphere has not been explicitly reported. However, for screening purposes, it can be estimated by (total emissions of TCE in Los Angeles) = (total emissions of solvents in Los Angeles) (total emissions of TCE in California) / (total emissions of solvents in California) (33) Then, by use of the approach to eq 33 and the reported data of total emissions of solvents in Los Angeles, total emissions of TCE in California, and total emissions of solvents in California (62),the emission rate of TCE in the Los Angeles atmosphere was determined to be 92 mol/h. Similarly, with the above approach, the emission rates of

PERC and TCA in the atmosphere of the study region were estimated to be 1238 and 4537 mol/h, respectively. Average ambient concentrations of 80 and 981 ng/m3 were used as background concentrations for TCE and TCA in Los Angeles (631,respectively. The initial concentrations of these two chemicals were assumed to be the same as their background concentrations. Moreover, a value of 1 pg/m3, the median air concentration of tetrachloroethylene in rural areas (64),was applied as background and initial concentrations for PERC in Los Angeles. The first-order degradation rate constants of TCE, PERC, and TCA in the atmosphere were estimated to be 4.6 X and 6.7 X lo4 h-l, respectively, based 1.0 X on the data reported by Yung et al. (65) at a hydroxyl radical concentration of 2.5 X mol/m3 and an average air compartment temperature of 13 "C, which is applicable for the month of February for which the field data were reported (56). The water-phase degradation rate constants of TCE, PERC, and TCA were reported by Dilling et al. 1.1 X lo4, and 1.7 X h-l, re(66) to be 1.2 X spectively. The soil-phase biodegradation rate constant of TCA in clay loam and sandy soils was reported by Rai et al. (67) to be 6.5 X lo4 h-l, whereas biodegradation under aerobic conditions for TCE and PERC was not detected in the study by Bouwer et al. (68). Partition, mass-transfer, and diffusion coefficients for TCE, PERC, and TCA were calculated internally in the SMCM model by the parameter estimation methods discussed in the previous section. 2. Simulation Results. With the above compartmental data, physicochemical properties of TCE, PERC, and TCA, as well as other information necessary for the simulation such as molecular weight, solubility, Henry's law constant, normal boiling temperature, and molal volume, simulations of the dynamic distribution of TCE, PERC, and TCA in Los Angeles County under no-rainfall condition and of PERC with rainfall were performed. Furthermore, for demonstration purposes, a simple simulation of buried PERC in a reduced Los Angeles like region is presented. The results of those simulations are described below. The steady-state results for TCE, PERC, and TCA from the SMCM model and results of the TEAM study in Los Angeles County are shown in Table 111. The concentrations reported for the soil and sediment are the average calculated concentrations for the top 10 cm of both compartments, whereas the amounts of the chemical (kg) reported for these two compartments are calculated on the basis of the entire volume of both compartments. It should be noted that the chemical distribution in the soil compartment is not uniform, as is illustrated by the example of Figure 2 for the concentration profiles of PERC in the soil and sediment compartments. The temporal variations of predicted concentrations of PERC in the different compartments of study area under rainfall condition are presented in Figure 3. From Table 111, it is seen that the air-phase and water-phase concentrations predicted by the SMCM model for PERC and TCA are in reasonable agreement with the monitored values except for the predicted water concentration of TCE in the Los Angeles area. A similar outcome was reported by Cohen and Ryan (18) for TCE distribution in the Liverpool area (England). As in the Liverpool area analysis, it is likely that there is a direct discharge of TCE into the Los Angeles water compartment. As an illustration, a TCE discharge into the water compartment equal to 2.5% of the emission rate of TCE into the air phase would account for the measured concentration in the water compartment (see Table 111). Environ. Sci. Technot., Vol. 24, No. 10, 1990

1555

Table 111. Comparison of Steady-State Results from the S M C M Model and Results of the Team Study in Los Angeles County, C A

mol/m3 x

compartment air water soil sediment biota suspended solids

predicted concn in other units

% chemical in compartment”

io8

1. Trichloroethylenec 0.2 (0.2) pg/m3 5 X lo-‘ (0.07) pg/L 0.7 (0.7) ng/kg 0.3 (40.1) ng/kg 4.7 (728.0) ng/kg 1.7 (259.0) ng/kg

0.2‘ (0.2)f 0.3 (54.0) 0.8 (0.8) 0.3 (45.8) 3.6 (554.0) 1.9 (295.0)

monitored concnb

0.1 pg/m3 0.07 pg/L

97.8 (96.1) 1.2 X (1.8) 2.1 (2.1) 1.5 X lo-’ (2.2 X

6.2 X 10” (9.3 X lo4) 3.3 X 10-1 (5.0 X 10”)

2. Tetrachloroethylenec

2.0 pg/m3 0.04 pg/L

air water soil sediment biota suspended solids

3.6 10.1 37.1 13.3 192.0 101.0

6.0 pg/m3 0.02 pg/L 41.0 ng/kg 14.7 ng/kg 318.0 ng/kg 112.0 ng/kg

97.6 1.7 X 2.3 2.5 X lo-‘ 1.6 X 10-1 8.4 X 10-7


3.6 10.4 40.6 13.8 200.0 105.0

3. Tetrachloroethylened 6.0 rg/m3 0.02 pg/L 44.8 ng/kg 15.2 ng/kg 332.0 ng/kg 116.0 ng/kg

97.4 1.7 X 2.6 2.6 X lo-’ 1.7 X 10-1 8.7 x 10-7


25.68 (25.6)h 35.6 (35.6) 81.3 (86.0) 27.6 (27.7) 362.0 (362.0) 193.0 (193.0)

4. l,l,l-Trichloroethane‘ 34.2 (34.2) pg/m3 0.05 (0.05) pg/L 72.3 (76.5) ng/kg 24.6 (24.6) ng/kg 483.0 (483.0) ng/kg 172.0 (172.0) ng/kg

98.6 (98.3) 8.5 x 10-3 (8.4 x 1.4 (1.7) 8.8 X (8.8 X 4.3 x 10-8 (4.3 x 2.3 X 10-1 (2.3 X

34.0 pg/m3 0.15 pg/L

10-3) 10“) 10”) 10-I)

a Predicted total amounts of trichloroethylene, tetrachloroethylene and l,l,l-trichloroethane (mol) in the multimedia system (at simulation time 1000 h) are 7.5 X IO3, 1.6 X 1@and 1.1 X lo6, respectively; all simulations started from February 1, 1984. *The reported environmental concentrations are average values (56). Without rainfall. With randomly distributed rainfall. e Neglecting discharge to the water compartment. f2.5% of the emission rate of TCE in the air phase is assumed to be discharged to the water compartment. #With soil-ohase degradation rate constant 6.5 X lo-‘ h-l (67). hNeglectine degradation in the soil.

1E-5

_____------

NORhlALIZED AVERAGE SEDIMENT CONCENTRATION

1E-8

i

02

,BIOTA

I I -

n^

7

1i

NORMALIZED AVERAGE SOIL CONCENTRATION

t

E

=

ii

,O 1E-7

z

P4

E 1E-8

8

0 08-

1E-9

...-. ... SOIL

__

SEDIMENT 1E-10

+)i

1.00.0

0.1

0.2

0.8

1

09

c I c (2.0)

Flgure 2. Concentration proflles of PERC in the soil and sediment compartments at t = 1000 h. C(z=O) is the concentration at the soil or sediment surface and L Is the depth of the soil or sediment compartment.

Table I11 also indicates that the masses of TCE, PERC, and TCA in the air compartment are orders of magnitude greater than those in any of the other compartments due to the large size of the air compartment. Another fact to note from Table I11 is that rain scavenging of PERC, in the Los Angeles area, has little effect on the time-averaged concentration of PERC in the soil matrix after lo00 h. Nonetheless, the inclusion of rainfall in the simulation reveals the temporal fluctuations of PERC concentration

-

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Envlron. Scl. Technol., Voi. 24. No. 10, 1990

I

0

200

400

600

800

1000

TIME (hours)

Figure 3. Distribution of tetrachloroethylenein Los Angeles County: random rainfall.

in the soil matrix (Figure 3). It is also interesting to note (Figure 3) that, with the exception of the sediment compartment, the remaining compartments have reached their respective steady-state values within -500 h, with the air and water reaching steady-state values faster than the biota and suspended soils. The sediment is slower in reaching steady state as a result of the slow solute diffusion that dominates chemical transport within the sediment compartment. Finally, the results for the hypothetical test case of buried PERC in a reduced Los Angeles like region for 10and 100-h simulations are shown in Table IV. It should

~

Table IV. PERC Distribution Resulting from Pure PERC Buried at 1 Meter after 10 and 100 Hours of Chemical Movement' compartment air water soil (upper layer)( soil (lower layer)( sedimentc biota

predicted concn mol/m3 in other units 8.7 X 3.0 X 1.1 X 8.9 3.0 X 1.9 X

(A) 10 Hours lo* 1.4 kg/m3 lo4 4.9 X lo-' pg/L lou8 1.2 ng/kg 9.8 X lo8 ng/kg lo4 0.3 ng/kg 3.2 ng/kg

Table V. Comparison of the Tetrachloroethylene Concentrations from the SMCM Model and Multimedia Measurements in the La Jolla Region (California)

% chemical in compartmentb

5.4 x io-' 2.5 X 7.3 X 11.6 2.5 X 2.6 X 10"

90.0 pg/m3 0.04 pg/L 8.0 X lo6 ng/kg 1.3 X lo9 ng/kg 28.1 ng/kg 426.0 ng/kg

predicted concn mol/m3 x % chemical in lo8 in other units compartment'

monitored concnb

2.4 X 5.3 X 93.4 6.6 3.1 x 1.7 x

10" 10"O

5.7 x 1.7 X 91.5 8.5 1.0 x 8.7 x

10-4 10"

'Predicted total amount of tetrachloroethylene in the multimedia system is 2.1 X lo4 mol. *The reported environmental concentrations are average values (57).

10-10 10-14

with the reported in situ measurement (Table V).

10-l2 10-l6

(B)100 Hours air water soil (upper layer)( soil (lower layer)( sediment biota

compartment

'The source strength of PERC in the air phase for this simulation is derived by reducing the source strength of PERC in the Los Angeles atmosphere by a factor of 1 X 10'. bPredicted total amounts of PERC in the multimedia system at simulation times of 10 and 100 h are 1.5 X lo7 and 3.8 X lo7 mol, respectively; amounts of chemical remaining in the buried layer at simulation times of 10 and 100 h are 1.8 X lo6 and 9.8 X lo6 kg, respectively. Saturation concentrations of the buried PERC is 14.5 mol/m3. The predicted concentrations for the soil (upper layer), soil (lower layer), and sediment are the average concentrations in the top 10 cm of these three compartments, whereas the percentage of chemical in each compartment is calculated on the basis of the entire volume of each compartment.

be noted that in this simulation, for demonstration purposes, a region similar in characteristics to the Los Angeles region but of smaller size by a factor of 1 X lo4was used, resulting in a soil-air interfacial area of 1 km2. A mass of 2 X lo6 kg of tetrachloroethylene, which would provide a sufficient amount of PERC for a 100-h simulation, was buried at a depth of 1 m in pure liquid form. Table IV reveals the rapidity with which a chemical such as PERC could be transported to the air and surrounding media. Although the above modeling approach is approximate, the relative magnitudes of the concentrations in Table IV can serve as an indication of the extent of multimedia contaminant migration that can arise, for example, as a result of improper disposal of toxic pollutants. Tetrachloroethylene in San Diego. The compartmental data and meteorological conditions for this simulation as given by Cohen and Ryan (18) were used. The simulation area for the San Diego study area was taken to be 400 km2 with a mixing height of 700 m. The water compartment's depth was set at 10 m and the water-atmosphere interfacial area was 280 km2. In the present work, however, the depths of soil and sediment compartments were taken to be 8 and 1m, respectively, in order to avoid potential violations of no flux bottom boundary condition (eq 9) during the simulation. The suspended solids and biota compartments were assumed to occupy 5 X lo4% and 5 X respectively, of the water compartment on a volume basis (18). In addition, the emission rate of PERC in the San Diego atmosphere was estimated to be 276 mol/h by using the approach to eq 33 for San Diego. The calculated tetrachloroethylene concentrations from the SMCM model and multimedia measurements in the La Jolla region (California) by Su and Goldberg (57) are given in Table V. It is worth noting that in the San Diego simulation, the off-shore region was incorporated into the model environment in order to allow comparison with reported field data. Again, it is seen that the screeninglevel concentration predictions are in reasonable agreement


7.4 20.9 77.6 29.1 398.0 211.0

12.3 pg/m3 0.03 rg/L 85.8 ng/kg 32.2 ng/kg 660.0 ng/kg 233.0 ng/kg

96.8 2.7 0.4 2.2 X 2.6 X 1.4 X lo-'

4.1 pg/m3 0.01 rg/L

Summary and Conclusion The spatial multimedia compartmental (SMCM) model of pollutant fate and transport has been developed to provide a convenient and comprehensive simulation tool for exploring the dynamic (or steady-state) partitioning of volatile organic chemicals in the environment. Results of case studies in this work illustrated that the SMCM model predictions agreed with the available field data within a factor of 2-4, which is better that the accuracy recommended by EPA for screening-level models. The SMCM model improves on the existing compartmental models by providing a more accurate treatment of nonuniform compartments, parameter estimation, and dynamic simulations that accounts for a variety of processes including rain scavenging, infiltration, and runoff. The SMCM model is computationally efficient and it requires a modest data input relative to existing spatial multimedia models. Thus, the SMCM is well suited for rapid screening analyses. Finally, the extension of the SMCM model to include particle-bound organics will be reported in a future publication. Readers who are interested in obtaining copies of the SMCM software for IBM PC/XT/AT compatible computers and accompanying documentation should contact Professor Yoram Cohen. Literature Cited (1) Patterson, M. R.; et al. A User's Manual for UTM-TOX A Unified Transport Model; ORNL-6064; Oak Ridge National Laboratory: Oak Ridge, T N , 1984. (2) Browman, M. G.; Patterson, M. R.; Sworski, T. J. Formu-

lation of the Physicochemical Processes in the ORNL Unified Transport Model for Toxicants (UTM-TOX)Interim Report; ORNL/TM-8013; Oak Ridge National Laboratory, Oak Ridge, T N , 1982. (3) Tucker, W. A.; Eschenroeder, A. G.; Magil, G. C. Air, Land, Water Analysis System (ALWAS): A Multimedia Model for Assessing the Effect of Airborne Toxic Substances on Surface Quality. First draft report, prepared by Arthur D. Little for Environmental Research Laboratory, EPA: Athens, GA, 1982. (4) Hetrick, D. M.; McDowell-Boyer, L. M. A User's Manual for TOX-SCREEN: A Multimedia Screening-Level Program for Assessing the Potential Fate of Chemicals released t o the Environment; ORNL-6041; Oak Ridge National Laboratory, Oak Ridge, T N , and U.S.EPA, Office of Toxic Substances: Washington, DC, EPA-560/5-85-024; 1984. (5) Cohen, Y. In Geochemical and Hydrologic Processes and Their Protection: The Agenda for Long-Term Research and Development; Draggan, S., Cohrssen, J. J., Morrison, R. E., Eds.; Praeger Publishing Co.: New York, 1987. Environ. Sci. Technol., Vol. 24, No. 10, 1990

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(6) Cohen, Y. Enuiron. Sci. Technol. 1986, 20, 538-544. (7) Onishi, Y.; Shuyler, L.; Cohen, Y. Presented at the In-

ternational Symposium on Water Quality Modeling of Agricultural Non-Point Sources, June 1988; Utah State University: Logan, UT, 1988. (8) Neely, W. B. Chemicals in the Environment; Marcel Dekker: New York, 1980. (9) Mackay, D.; Paterson, S. Environ. Sci. Technol. 1981, 15, 1006-1014. (10) Mackay, D.; Paterson, S. Environ. Sci. Technol. 1982, 16, 654-660. (11) Mackay, D., Paterson, S. In Pollutants in a Multimedia Environment; Cohen, Y., Ed.; Plenum: New York, 1986; pp 117-131. (12) Hedden, K. F. J. Toxicol. Clin. Toxicol. 1984,21, 65-69. (13) Lyman, W. J. Prediction of Chemical Partitioning in the

Environment: An Assessment of Two Screening Models. Prepared under Contract 68-01-5949; EPA: Washington, DC, 1981. (14) Wiersma, G. B. Kinetics and Exposure Commitment Analyses of Lead Behavior in a Biosphere Reserve. Technical Report, Monitoring and Assessment Research Center, Chelsea College, University of London: London, 1979. (15) McKone, T. E. The Use of Environmental Health-Risk Analysis for Managing Toxic Substances; UCRL-92329; Lawrence Livermore National Laboratory: Livermore, CA, 1985. (16) Swann, R. L.; Eschenroeder, A., Eds. ACS Symp. Ser. 1983, No. 225. (17) McKone, T. E.; Layton, D. W. Regul. Toxicol. Pharmacol. 1986,6, 359-380. (18) Cohen, Y.; Ryan, P. A. Environ. Sci. Technol. 1985, 19, 412-417. (19) Cohen, Y.; Taghavi, H.; Ryan, P. A. J. Environ. Qual. 1988, 17, 198-204. (20) Cohen, Y.; Ryan, P. A. J. Hazard. Mater. 1989,22,283-304. (21) Thibodeaux, L. J. In Geochemical and Hydrologic Pro-

cesses and Their Protection: The Agenda for Long-Term Research and Development; Draggan, S., Cohrssen, J. J., Morrison, R. E., Eds.; Praeger, Publishing Co.: New York, 1987. (22) Ryan, P. A.; Cohen, Y. Chemosphere 1986,15, 21-47. (23) Levelspiel, 0.;Bischoff, K. B. Adv. Chem. Eng. 1963, 4 , 95-198. (24) Smith, R. E.; Cherry, D. L. J. Hydraul. Diu., Am. SOC.Civ. Eng. 1973, 1139-1350, (HY9). (25) Dunne, T.; Leopold, L. Water in Environmental Planning; W. H. Freeman and Co.: San Francisco, CA, 1978. (26) Dullien, F. A. L. Fluid Transport and Pore Structure; Academic Press: New York, 1979. (27) Jury, W. A.; Spencer, W. F.; Farmer, W. J. J. Environ. Qual. 1983, 12, 558. (28) Smith, R. E. J. Hydrol. 1972, 17, 1-21. (29) Karickhoff, S.; Brown, D.; Scott, D. Water Res. 1979, 13, 241-248. (30) Karickhoff, S. Chemosphere 1981, 10, 833-846. (31) Chiou, C. T.; Schmedding, D. W. Environ. Sci. Technol. 1982, 16, 4-10. (32) Minglegrin, V.; Gerstl, E. J. Enuiron. Qual. 1983, 12, 195-197. (33) Kenaga, E.; Goring, C. Aquat. Toxicol. 1980, 78-115,

(41) Sehmel, G. A. Atmos. Environ. 1980, 14, 984-1011. (42) Brutaaert, W. Water Resour. Res. 1975,11, 543-550. (43) Neely, W. B.; Branson, D. R.; Blau, G. E. Environ. Sci. Technol. 1974,8, 1113. (44) Rowe, P. N.; Claxton, K. T.; Lewis, J. B. Trans.Znst. Chem. Eng. 1965, 43, 714. (45) Thibodeaux, L.; Becker, B. Enuiron. Prog. 1982, 1, 4. (46) Cohen, Y.; Ryan, P. A. Int. Commun. Heat Mass Transfer 1985, 12, 139. (47) Sallam, A.; Jury, W. A.; Letey, J. Soil Sci. SOC.Am. J. 1984, 48, 3. (48) Reid, R., Prausnitz, J.; Sherwood, T. The Properties of Gases and Liquids, 3rd ed.; MacGraw Hill: New York, 1979. (49) Penman, H. L. Proc. R. SOC.London A 1948,193,120-146. (50) Van Bavel, C. H. M. Water Resour. Res. 1966,2,455-467. (51) Jamison, S. On the Derivation of Mean Daily and Weekly

Values from Monthly Climatological Values; Climate Analysis Center, U.S. Department of Commerce: Washington, DC, 1982. (52) Easter, R. C.; Hales, J. M. PLUVZUS: A Generalized One-Dimensional Model of Reactive Pollutant Behavior, Including Dry Deposition, Precipitation Formation, and Wet Removal; Report PNL-4046 ED2; Batelle Pacific Northwest Laboratories: Richland, WA, 1984. (53) Roache, P. J. Computational Fluid Dynamics; Hermosa Publications: Albuquerque, NM, 1985. (54) Tremblay, A.; Leighton, H. Atmos. Environ. 1984, 18, 1885-1894.

(55) Hegg, D. A.; Rutledge, S. A.; Hobbs, P. V. J. Geophys. Res., D 1984,89, 7133-7147. (56) Wallace, L.; Pellizzari, E.; Sheldon, L.; Hartwell, T. In Pollutants in a Multimedia Environment; Cohen, Y., Ed.; Plenum: New York, 1986; pp 289-315. (57) Su, C.; Goldberg, E. D. In Strategies for Marine Pollution Monitoring; Goldberg, E. D., Ed.; Wiley: New York, 1976; pp 353-374. (58) California Almanac, 1988 Edition; Fay, J. S., Lipow, A. G., Fay, S. W., Eds.; Presidio Press and Pacific Data Resources: Novato, CA, 1988. (59) Williamson, S. J. Fundamentals of Air Pollution; Addison-Wesley: Reading, MA, 1973. (60) National Climatic Data Center, Climatological Data (California), 1984. (61) California Almanac, 1984185 Edition; Fay, J. S., Lipow, A. G., Fay, S. W., Eds.; Presidio Press and Pacific Data Resources: Novato, CA, 1984. (62) Rogozen, M. B.; Rapoport, R. D.; Shochet, A. Development and Improvement of Organic Compound Emission Inventories for California. Prepared under Contract AO-101-32; State of California Air Resources Board: Sacramento, CA, 1985. (63) Singh, H. B.; Sala, L. S.; Stiles, R. E. Environ. Sci. Technol. 1982,16, 872-880. (64) Frank, H.; Franck, W. Environ. Sci. Technol. 1989, 23, 365-367. (65) Yung, Y. L.; McElroy, M. B.; Wofsy, S. C. Geophys. Res. Lett. 1975, 2, 397-399. (66) Dilling, W. L.; Tefertiller, N. B.; Kallos, G. J. Enuiron. Sci. Technol. 1975,9, 833-838. (67) Rai, G. S.; Hammer, C. L. Weeds 1953, 2, 271. (68) Bouwer, E. J.; Rittman, B. E.; McCarty, P. L. Environ. Sci. Technol. 1981, 15, 596.

(ASTM STP707). (34) Hansch, C.; Leo, A.; Elkins, D. Chem. Rev. 1971, 71,525. (35) Mailhot, H.; Peters, R. H. Environ. Sci. Technol. 1988,22, 1479-1488. (36) Mackay, D. Enuiron. Sci. Technol. 1982, 16, 274-278. (37) Chiou, C. T. Environ. Sci. Technol. 1985, 19, 57-62. (38) Barber, M. C.; Suarez, L. A.; Lassiter, R. R. Environ. Toxicol. Chem. 1988, 7, 545-758. (39) Lewis, W. K.; Whitman, W. G. Znd. Eng. Chem. 1924,16, 1215. (40) Fernandez de la Mora, J.; Friedlander, S. K. Znt. J . Heat Mass Transfer 1982, 25, 1725-1735.

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Received for review November 1, 1989. Revised manuscript received May 18,1990. Accepted June 11,1990. Although the information in this document has been funded in part by the United States Environmental Protection Agency under Assistance Agreement CR-812271-03 to the National Center for Intermedia Transport Research at UCLA, it does not necessarily reflect the views of the Agency and no official endorsement should be inferred. This work was also partially funded by the University of California Toxic Substances Research and Teaching Program.

Dynamic partitioning of organic chemicals in regional environments: a

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