CHAPTER 20 MODELING OIL SPILLS ON RIVER SYSTEMS

20.1

CHAPTER 20MODELING OIL SPILLS ON RIVERSYSTEMS: EVALUATION OFAQUEOUS CONCENTRATIONS

John S. Gulliver and Vaughan R. VollerDepartment of Civil Engineering, University of Minnesota,Minneapolis, Minnesota

David E. HibbsBarr Engineering Company, Ann Arbor, Michigan

20.1 INTRODUCTION

Accidental releases of buoyant oils, fuels, and chemicals into water bodies can be cata-strophic events for the aquatic biota. Riverine spills can be particularly hazardous. Unlikespills onto oceans, in which the water column is subjected to almost an infinite dilution,rivers are shallow and confined by the river bed and banks. Consequently, aqueous concen-trations resulting from riverine spills can be several orders of magnitude higher than similarspills onto oceans.

Spills of any sparingly soluble buoyant compound initially form a slick on the watersurface. The slick spreads across the water surface and drifts downstream as the variouscompounds in the slick evaporate and dissolve into the water column. To predict the impactof spills on the river biota, the concentration of compounds dissolved in the water columnmust be assessed. There are many models that look at the hydrodynamics of the oil slick(Yapa and Shen, 1994). These models focus on the tracking, spreading, and containment ofthe oil slick and are applicable to wide rivers where the two-dimensionality of the slick isimportant. The focus of this chapter is not on the spread of the oil slick per se, but on theeffect that spread may have on the biota of the river. This requires a detailed tracking ofhow the aqueous concentrations develop as the slick moved downstream. Modeling the ev-olution of the aqueous concentrations requires an adequate accounting of the various trans-port coefficients that control the process. The contribution of this chapter is the identificationof these parameters, citations of appropriate literature sources, and, most importantly, a sen-sitivity analysis that identifies the coefficients that have the greatest impact on simulationresults. The model described was developed primarily for application to smaller, nonnavig-able rivers where the assumptions of a cross-sectional, well-mixed water body and slick areusually valid. When the cross-sectional uniform water body and oil slick assumptions arenot valid, a combination of a two-dimensional flow slick (Yapa et al., 1994; Shen et al.,

20.2 CHAPTER TWENTY

Slick # 3 Slick # 2 Slick # 1

River Bottom

C C C Cw,5 w,6 w,7 w,8

FIGURE 20.1 Numerical approximation of river cross-section with multiple surface slicks.

1995) and the aqueous transport and transfer processes described in this chapter would berequired.

A spill of JP-4 jet fuel is used to illustrate the operation of the model. The rate coefficientsused in this example spill are most applicable for smaller rivers, which exhibit a fair degreeof meandering and are often sheltered from wind by the riverbanks and vegetation. In keepingwith all environmental fate and transport modeling, the predicted aqueous concentrationshave an inherent level of uncertainty due to bias in the model input parameters. Since theuser-specified rate constants are seldom measured but are themselves often estimated frompredictive relationships, these input parameters can often be in significant error. Dependingon the particular parameter, the uncertainty associated with each input parameter can havean impact on the predicted aqueous concentrations ranging from drastic to insignificant.Within the context of a JP-4 jet fuel spill into a small river system, sensitivity analysis toidentify the model parameters and/or processes that are the most important in determiningaqueous concentrations of contaminants is a key component in the testing of the model.

20.2 THE DUAL-PHASE MODEL

The model is established on a mixture of Eulerian and Lagrangian coordinate systems. Theriver is approximated as a series of completely mixed cells (typically 10–1,000 m in length)fixed in position, as shown in Fig. 20.1. The slick is approximated as a series of completelymixed cells that move across the water surface in a Lagrangian coordinate system. Thistreatment of the slick as a series of moving cells allows for spatial variation in the concen-tration of the slick. The application of the model, per se, is to situations where both flowand slick can be described as one-dimensional. This occurs when the slick is spread com-pletely across the river, as with relatively narrow streams. The length of the river from thespill site before the one-dimensional assumption can be applied is approximately:

L Uw slickL � (20.1)dl /dt

where Uslick is the streamwise velocity of the centroid of the slick, Lw is the largest transverselength across the river from the location of the spill, and dl /dt is the spreading velocity ofthe slick. If the spill occurred on one bank of the river, Lw would be the river width.

All of the described processes for the evolution of aqueous concentration, however, wouldapply to both a one-dimensional and a two-dimensional spill model.

MODELING OIL SPILLS ON RIVER SYSTEMS 20.3

20.2.1 Movement of the Surface Slick

The movement of the slick on the water is largely a function of the velocity of the watersurface and the direction and magnitude of the wind:

U � � U � a U (20.2)slick vel drift wind

where U � the cross-sectional mean river velocityUwind � the streamwise component of the wind speed vector

�vel � the velocity profile correction factor (�vel � 1.1 [Addison, 1941])�drift � the wind drift coefficient (�drift � 0.03–0.04 [Wu, 1983])

For smaller rivers, which are often tortuous and sheltered, the wind drift term in Eq. (20.2)is dropped. The velocities of the leading and trailing edges of the slick are:

dlU � 1.1 U � � U � (20.3)leading drift wind dt

and

dlU � 1.1 U � � U � (20.4)trailing drift wind dt

where dl /dt is the spreading rate of the slick. While the oil is spilling onto the water surface,the leading edge of the slick is allowed to drift and spread downstream at a velocity deter-mined from Eq. (20.3) and the trailing edge of the slick is assumed to be fixed in position.The oil is added to the trailing end of the overall slick, i.e., into the upstream-most individualslick. This treatment of the spilling process reasonably simulates the behavior of a slickforming on a river. During the early stages of a riverine spill, dl /dt is on the order 0.1 m/s(Fay, 1971). Thus, the spreading velocity is less than typical water surface velocities, andthe slick is not likely to spread upstream from the point of spilling. Once the spilling stops,the trailing edge of the slick is released to drift and spread at a velocity determined fromEq. (20.4). The position of the leading and trailing edges of the overall slick are determinedfrom Eqs. (20.3) and (20.4) and the boundaries of the individual slicks are interpolated fromthe spreading rate of the leading edges based on their distance from the midpoint of theoverall slick.

20.2.2 Mass Balance for the Slick Phase

The mass of the slick decreases over time as the compounds dissolve into the water phaseand evaporate into the atmosphere. A mass balance for each compound in the slick is writtenas:

odm X P Mo isat� � �k W(X C � C ) � k W dx � r (20.5)� � ��dis o w w evapdt RTlength

of slick

where Cw � the aqueous concentration�satC w the aqueous saturation concentration

kdis � the dissolution rate coefficientkevap � the evaporation rate coefficient

m � the mass of the compound in the slickM � the compound’s molecular weight

20.4 CHAPTER TWENTY

r � the release rate (i.e., rate at which the compound is spilled)Po � the vapor pressure of the pure compoundR � the universal gas constantt � time

T � the absolute temperature of the interfacex � distance downstream

Xo � the mole fraction in the slickW � the width of the slick

This one-dimensional model formulation assumes the slick covers the water surface frombank to bank, therefore W is also the width of the river. The product XoP

o represents thevapor pressure of a compound at the slick–air interface based on Raoult’s law. The massflux rate is integrated over the length of the slick since W and Cw can vary as a function ofdistance. The concentration of each compound in the slick can then be expressed as a molefraction:

�1m(M)X � (20.6)o

�1m(M)�all compounds

20.2.3 Transport Equation for Aqueous Phase

The concentrations of compounds dissolved in the water change over time and distance asthe compounds dissolve from the slick into the water, volatilize from the water to the at-mosphere, and disperse in the river. The one-dimensional advection-diffusion equation foreach compound is written as:

�(AC ) �(QC ) � �Cw w w sat� � AD � �k W(X C � C ) � (1 � �) k WC� �L dis o w w vol w�t �x �x �x

(20.7)

where A � the cross-sectional area of riverDL � the longitudinal dispersion coefficientQ � discharge

kvol � the volatilization rate coefficient� � a phase marker (� � 1 if there is a slick at location x; � � 0 otherwise)

When the surface slick is present at location x, there is an exchange between the slick andthe water. When the surface slick is not present at location x, there is an exchange betweenthe water and the atmosphere.

The approximation of the river as a series of discrete well-mixed cells introduces addi-tional dispersion into the model. Even if a value of DL � 0 is input, some dispersion willstill be predicted by the model. Banks (1974) developed a mixed cell model which may beused to quantify this numerical dispersion:

D � 0.5 U �x (20.8)L�num

where �x is the length of the river control volume. Equation (20.8) is based on an infinitenumber of cells and is approximately valid as long as roughly 10 or more cells are used inthe model (Levenspiel, 1962). Since Eq. (20.7) is often approximated as a linear partialdifferential equation where superposition applies, the numerical dispersion and the user-specified dispersion are nearly additive. Thus, the value of longitudinal dispersion that should


be specified in the model to obtain the true dispersion, DL, can be estimated from the ex-pression:

D � D � D � D � 0.5 U �x (20.9)L�model L L�num L

where DL�model is the longitudinal dispersion coefficient that is supplied to the model in Eq.(20.8).

20.2.4 Solution Algorithm

Equations (20.3) through (20.7) form the basis of the model. A formulation of Eq. (20.7) isneeded for each compound that is to be modeled. A pair of Eqs. (20.5) and (20.6) are neededfor each compound and for each individual slick used in the simulation. No direct solutionfor the equation set is available, so the equations are solved numerically. At each time step,the extent and location of the oil slick is determined from Eqs. (20.3) and (20.4). The massof each compound in the oil phase is then determined by an explicit time integration of Eq.(20.5), i.e., the values of Cw and Xo are taken from the previous time step. The mole fractionof each compound in the slick is then determined from Eq. (20.6). Next, the aqueous con-centration of each compound at each location in the river is determined by a fully implicittime integration of Eq. (20.7), i.e., the current values of Cw and Xo are used in the calculation.

20.3 A SAMPLE APPLICATION

As an example of the capabilities of the model, consider a spill of 10,000 kg of JP-4 jetfuel released over a period of 10 minutes onto a river of the scale typical of a tributary toa navigable river. The approximate composition of the fuel, the physical properties of thecompounds, the river flow data, and the model parameters for the simulation are listed inTable 20.1. Most of the jet fuel is composed of several relatively insoluble long-chain ali-phatics (Burris and MacIntyre, 1987). For simplicity, these aliphatic compounds are groupedand modeled as a single compound with properties averaged from the individual aliphaticcompounds.

The results of the jet fuel spill simulation are shown in Figs. 20.2 through 20.5. Figure20.2 shows the aqueous concentrations of two compounds, ethylbenzene and 1-methyl-naphthalene, plotted versus distance downstream at times of 10, 20, 40, and 60 hours afterthe spill occurred. The concentration profiles are nearly Gaussian in shape, typical of pulseloadings in rivers. The profiles tend to broaden over time due to the streamwise mixing inthe river, approximated by the longitudinal dispersion term in Eq. (20.7). Notice that theconcentration profiles are slightly skewed to the downstream direction. Since the slick isdrifting downstream at a rate slightly higher than the mean river velocity, the compounds inthe slick are constantly dissolving into the river slightly downstream of the aqueous concen-tration peak, creating a skewed profile.

The peak aqueous concentrations of all eight compounds in the jet fuel are plotted versustime in Fig. 20.3. The peak aqueous concentrations of the more volatile compounds (e.g.,toluene and methylcyclohexane) reach maximums within the first 10 hours, then decrease asthese volatile compounds rapidly evaporate from the slick and are no longer available todissolve into the water. The aqueous concentration of each compound continues to rise untilthat compound has evaporated from the slick. Once a compound has been removed from theslick, the peak aqueous concentration of that compound decreases as its concentration isdiluted by longitudinal dispersion and as it volatilizes from the water to the atmosphere. Inthis example, the least soluble compounds also are least volatile and therefore tend to remainin the slick for a longer time and continue to dissolve into the water column, resulting in

20.6 CHAPTER TWENTY

TABLE 20.1 Input Parameters Used in Sample Application

Properties Toluene Ethylbenzene n-Butylbenzene Tetralin

X (�)a 0.04331 0.04785 0.03879 0.02922MW (g / mol) 92.1 106.2 134.2 132.2� (kg / m3)b 870 870 860 970

(mol / L)a,bsatC w 10�2.50 10�2.80 10�3.97 10�3.47

P o (atm)b,d 10�1.42 10�1.90 10�2.86 10�3.27

Dwater (ms / s)e 9.1 � 10�10 8.2 � 10�10 7.0 � 10�10 7.6 � 10�10

Doil (m2 / s)f 1.5 � 10�9 1.4 � 10�9 1.1 � 10�9 1.2 � 10�9

Dair (m2 / s)g 8.1 � 10�6 7.4 � 10�6 6.4 � 10�6 6.8 � 10�6

Properties 1-Methylnaphthalene 1,4-Dimethylnaphthalene Methylcyclohexane Aliphaticsh

X (�)a 0.02666 0.02613 .2123 .5759MW (g / mol) 142.2 156.2 98.2 145.7� (kg / m3)b 1,002 1,000 770 731

(mol / L)b,csatC w 10�3.67 10�4.22 10�3.77 10�6.52

P o (atm)b,d 10�4.07 10�4.60 10�1.23 10�2.77

Dwater (ms / s)e 7.4 � 10�10 6.8 � 10�10 8.2 � 10�10 6.2 � 10�10

Doil (m2 / s)f 1.2 � 10�9 1.1 � 10�9 1.4 � 10�9 1.0 � 10�9

Dair (m2 / s)g 6.6 � 10�6 6.2 � 10�6 7.7 � 10�6 5.8 � 10�6

River properties Rate constantsi

3Q � 3 (m / s)2A � 10 (m )

W � 10 (m)2D � 25 (m / s)L

U � 2 (m / s)wind�6k � 2.47 � 10 (m / s)L�oxygen

T � 20�C

�4k � 5.27 � 10 (m / s)evap�6k � 1.50 � 10 (m / s)dis�5k � 1.20 � 10 (m / s)vol

Model parameters

�t � 60 (sec)�x � 100 (m)

a Burris and MacIntyre, 1987.b Lide, 1993.c Schwarzenbach et al., 1993.d Lyman et al., 1990.e Approximated using Hayduk and Laudie, 1974.f Approximated using Wilke and Chang, 1995.g Approximated using Fuller et al., 1966.h Average properties of the 5 aliphatic compounds in JP-4 fuel, Burris and MacIntyre, 1987.i Approximate values. Actual values determined for each compound based on wind speed, reaeration rate, and

physical properties of individual compounds.

higher aqueous concentrations. Consequently, the highest aqueous concentrations resultingfrom this spill are not of the most soluble compounds, but rather of some of the least solubleand least volatile compounds (e.g., 1-methylnaphthalene and 1,4-dimethylnaphthalene).

Figure 20.4 shows the mass of each compound in the slick as a function of time. Figure20.5 shows the mole fraction of each compound in the slick plotted versus time. For sim-plicity, this simulation was run using only one slick. The composition of the slick changesdrastically with time. Notice that the evaporation and dissolution flux rates of compoundsfrom the slick, as inferred from the slopes of the lines in Figs. 20.4 and 20.5, increase as acompound’s mole fraction in the slick increases. This behavior exemplifies the fact that thedissolution and evaporation rates are governed not only by environmental parameters butalso by slick composition. Since the slick composition is constantly changing over time, theconcentration of compounds in the slick must be modeled in conjunction with the aqueousconcentrations.


0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70 80distance (km)

aqu

eou

s co

nce

ntr

atio

n (

pp

m)

ethylbenzene

1-methylnaphthalene

t =10 hr

t = 20

t = 60 hrs

location of slick

t = 40 hrs

FIGURE 20.2 Results of jet fuel spill simulation: aqueous concentration profiles for ethylbenzeneand 1-methylnaphthalene.

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70 80 90time (hrs)

pea

k aq

ueo

us

con

cen

trat

ion

(p

pm

)

toluene

ethylbenzene

n-butylbenzene

tetralin

1-methylnaphthtalene

1,4-dimethylnaphthalene

methylcyclohexane

aliphatics

FIGURE 20.3 Results of jet fuel spill simulation: peak aqueous concentrations of compounds.

20.8 CHAPTER TWENTY

1

10

100

1000

10000

0 10 20 30 40 50 60 70 80 90time (hrs)

mas

s in

slic

k (k

g)

toluene

ethylbenzene

n-butylbenzene

tetralin

1-methylnaphthalene


methylcyclohexane

aliphatics

FIGURE 20.4 Results of jet fuel spill simulation: mass of compounds in slick.

0.001

0.01

0.1

1

0 10 20 30 40 50 60 70 80 90

time (hrs)

mo

le f

ract

ion

(--

)

toluene

ethylbenzene

n-butylbenzene

tetralin

1-methylnaphthalene


methylcyclohexane

aliphatics

FIGURE 20.5 Results of jet fuel spill simulation: mole fraction of compounds in slick.

As shown in Fig. 20.5, the composition of the slick, and therefore the nature of the slick,can change drastically over the duration of the spill as the more volatile, more soluable, andlower molecular weight compounds evaporate and dissolve from the slick. Most notably, thespecific gravity of the slick increases over time. At 30 hours, the specific gravity of the slickreaches 1.0 and the slick should break up into globules dispersed in the water column or


TABLE 20.2 Summary of Sensitivity Analysis. Confidence Interval ofInput Parameters and Resulting Range of Maximum AqueousConcentrations are Relative to the Original Values

User-suppliedparameter

Approximate uncertaintyof input parameter

Resulting range of maximumaqueous concentration

DL � Factor of 4 �30%kevap � Factor of 4 �50%kvol � Factor of 3 �5%kdis � Factor of 20 �2000%

satC w � Factor of 2 �200%dl /dt � Factor of 2 �10%

sink to the bottom. Even if the slick breaks up, however, the aqueous concentration of thecompounds remaining in the oil phase will continue to rise, though perhaps not precisely asshown in Fig. 20.3. If the slick degrades to small globules suspended in the water column,the aqueous concentrations of the compounds in the oil phase will increase more rapidlythan predicted in Fig. 20.3 due to the increased surface area of the globules compared tothe surface slick. If the globules sink, they will not be drifting downstream suspended in thewater column, and therefore the peak concentrations will likely be lower than those predictedby Fig. 20.3 which assumes that the slick is drifting at roughly the same velocity as the riversurface. The viscosity of the slick also increases over time, leading to an increase in resis-tance to transfer in the oil phase. Additionally, the surface tension and the activity coefficientsof the compounds in the slick will change over time, altering the spreading rate and theslick–water and slick–air equilibrium partitioning of the compounds. Thus, the slick com-position can affect the physical characteristics of the slick and, consequently, the aqueousconcentrations resulting from the spill.

20.4 SENSITIVITY ANALYSIS

Using the hypothetical spill of 10,000 kg of a JP-4 jet fuel, the uncertainty associated witheach model parameter is estimated and the sensitivity of the predicted aqueous concentrationsto variations in the input parameters over the estimated range of uncertainty is presented.As a summary of the main findings, estimates of the uncertainties in the user-supplied pa-rameters and the resulting variations in the highest aqueous concentrations are given in Table20.2.

20.4.1 Longitudinal Dispersion

Longitudinal dispersion accounts for the dilution of the cross-sectional average concentrationof compounds dissolved in the water due to mixing in the streamwise direction. The lon-gitudinal dispersion coefficient, DL, can be estimated as (Fischer et al., 1979):

2 20.011 U WD � (20.10)L

h �g h S

where h � the average depth of riverg � acceleration due to gravityS � the slope of the water surface

20.10 CHAPTER TWENTY

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

0 100 200 300 400 500

% of original value

hig

hes

t aq

ueo

us

con

cen

trat

ion

(p

pm

)

toluene

ethylbenzene

1-methylnaphthalene


FIGURE 20.6 Sensitivity analysis: effect of longitudinal dispersion on maximum aqueous con-centration.

Fischer et al. (1979) list numerous predictive equations for longitudinal dispersion, andperhaps not inconsequentially, estimates of DL from stream parameters are notoriously in-accurate. Fischer et al. state that the recommended relationship, i.e., Eq. (20.10), will gen-erally predict DL only within a factor of 4.

Figure 20.6 shows the highest aqueous concentrations of four compounds that occurduring the duration of the JP-4 jet fuel spill simulation, using the same parameters listed inTable 20.1. The highest aqueous concentrations are plotted as a function of DL over the rangeof uncertainty of the predicted value (i.e., from approximately 25 to 400% of the originalvalue of DL � 25 m2 /s). Higher values of DL tend to dilute the dissolved compounds in thestreamwise direction, yielding lower maximum aqueous concentrations. Lower values of DL

correspond to less dilution, and therefore higher aqueous concentrations. The maximumaqueous concentration of both the soluble /volatile compounds (toluene and ethylbenzene)and the relatively insoluble /nonvolatile compounds (1-methylnaphthalene and 1,4-dimethyl-naphthalene) vary by approximately 30% from the high end value of DL to the low end.Therefore, longitudinal dispersion is a fairly significant process, and whenever possible, thevalue of DL should be measured by performing a dye study on a river reach (Fischer et al.,1979). Dye study measurements can also be used to precisely determine the spatial meanvalue of U (Kilpatrick and Wilson, 1989).

20.4.2 Evaporation Rate

Evaporation is generally described by a resistance in series model, commonly used to de-scribe mass-transfer between phases. The overall transfer coefficient depends on the ratetransfer coefficients on either side of the interface:

o1 P M 1i� � (20.11)k k R T � kevap oa o G

where koa is the oil-film transfer coefficient at the oil-air interface, kG is the gas-film transfer


coefficient, and �o is the density of the oil. For thick oil layers, the oil-film transport coef-ficient controls the evaporation of hydrocarbons due to the relatively high vapor pressures(Thibodeaux and Carver, 1997). However, in most riverine spills, the oil layer is so thin(�1 mm) that the resistance to transfer in the oil film is small, even if transport is assumedto be only by molecular diffusion, and kevap can be approximated by kG (Mackay and Yeun,1983).

The gas-side mass transfer coefficient for compound i can be estimated from the windfunction coefficient by Ryan et al. (1974), which relates evaporative heat flux to a vaporpressure difference:

�0.67Scik � ƒ(w ) (20.12)� �o z Scwater

where kG is the gas-side mass transfer coefficient for compound i (m/s), f (wz) is the windfunction (m/s). The coefficient, f (wz), is a weak function of temperature but is nearly con-stant for the range of temperatures typically seen in rivers. Scwater is the Schmidt number ofwater in air (Scwater � � /D, where � is kinematic viscosity of air and D is diffusivity ofwater in air), and Sci is the Schmidt number of compound i in air. The ratio of Schmidtnumbers in Eq. (20.12) converts the gas-side mass transfer coefficient for water vapor to anequivalent coefficient for compound i.

The �0.67 power on the ratio of diffusivities has been used by several investigators,including Mackay and Yeun (1983), Mackay and Matsugu (1973), and Goodwin et al. (1976),and is generally associated with a ‘‘dirty’’ or fixed surface. The function f (wz) is used todescribe the influence of natural convection, wind, and waves on evaporation. The two knownsets of field experiments to characterize the wind function in a sheltered stream resulted inthe relationships of Gulliver and Stefan (1986) and Jobson and Keefer (1979). Gulliver andStefan’s relation is used herein:

1 / 3 �4f (w ) � [8.57 U � 14.7 (��) ] � 10 (20.13)z 9

where U9 is the wind speed at a height of 9 m (m/s), and �� is the virtual temperaturedifference (Ryan et al., 1974) between the water surface and the air at a height of 2 m (�C).

Many existing spill models use a relationship for kG developed by Mackay and Matsugu(1973) from pan evaporation and wind tunnel experiments. Values of kG used in this analysisare based on measurements taken in sheltered streams and are typically two to five timeslower than those for spills in open areas determined by Mackay and Matsugu. Regardlessof the relationship used to predict the value of kG, there is likely a large uncertainty due toits dependence on the local air turbulence level. Under similar wind velocities at a height of10 m, the wind velocity profile over open water may be significantly different than thevelocity profile over a river due to the topography and the vegetation on the river banks.Even on open lakes, the measured evaporation transfer coefficient can vary as much as�100% for a given wind speed (Adams et al., 1990). Thus, evaporation is a complicatedand site-specific process. The confidence interval of the predicted evaporation-rate constantfor rivers is estimated to be plus or minus a factor of 4. The confidence interval for thevalue of kG is likely smaller for wide rivers in areas without significant vegetation or changesin topography.

Figure 20.7 shows the highest aqueous concentrations of four compounds resulting froma series of JP-4 jet fuel spill simulations over the anticipated range of uncertainty in kG. Themaximum aqueous concentrations range from 130 to 60% of the original value as the valueof kG is varied from 50 to 400% of the original value. The value of kG indirectly affects theaqueous concentrations by forcing changes in the composition of the slick. At low values ofkG, the compounds evaporate more slowly and remain in the slick for a longer time. In theslick, compounds continue to dissolve, increasing the aqueous concentration. At high valuesof kG, the compounds evaporate more quickly and are available to dissolve for less time,creating lower aqueous concentrations.


sensitivity analysis effect of kevap

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

1.40E+00

0 100 200 300 400 500

% of original value

hig

hes

t aq

ueo

us

con

cen

trat

ion

(p

pm

)

toluene

ethylbenzene

1-methylnaphthalene


FIGURE 20.7 Sensitivity analysis: effect of variations in evaporation rate on maximum aqueousconcentration.

20.4.3 Volatilization Rate

Volatilization from the water column (rather than from the slick) is also generally describedby a two-resistance model:

1 1 R T� � (20.14)

k k H kvol L G

where kL is the liquid-side mass transfer coefficient for compound i and kG is determinedfrom Eq. (20.12). Values of kL used in the model are adapted from the stream reaerationcoefficient of Cadwallader and McDonnell (1969):

�3 0.5k � 2.15 � 10 (SU ) (20.15)L oxygen

where kL oxygen � the liquid mass transfer coefficient for oxygen at 20�C (m/s)S � the average slope of riverU � the average streamwise velocity (m/s)

Several empirical relationships for reaeration coefficients were recently reviewed and testedby Moog and Jirka (1995), who found that the form of the relationship given in Eq. (20.15)best characterized stream reaeration rates. A liquid mass transfer coefficient for each com-pound, kL i, can then be determined from a ratio of the Schmidt numbers (Mackay and Yven,1983):

�0.5Scik � k (20.16)� �Li L oxygen Scoxygen

where Scoxygen � �20 /Doxygen, Sci� � /Di, � is the kinematic viscosity of water at the modeledtemperature, �20 is the kinematic viscosity of water at 20�C, Doxygen is the diffusivity ofoxygen in water, and Di is the diffusivity of component i in water.


sensitivity analysis effect of kvol

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

9.00E-01

0 100 200 300 400 500

% of original value

hig

hes

t aq

ueo

us

con

cen

trat

ion

(p

pm

)

toluene

ethylbenzene

1-methylnaphthalene


FIGURE 20.8 Sensitivity analysis: effect of variations in volatilization rate on maximum aque-ous concentration.

Estimates of volatilization rates from stream parameters are also notoriously inaccurate.Moog and Jirka (1995) found that even the best empirical relationships have a 95% confi-dence interval of greater than a factor of 3. Values of kvol for a given river reach can bemeasured by conducting a gas tracer study when greater accuracy is desired (Kilpatrick etal., 1989; Hibbs et al., 1998).

Figure 20.8 shows the highest aqueous concentrations resulting from a series of JP-4 jetfuel spill simulations over the anticipated range of uncertainty in the value of kvol. The highestaqueous concentrations of all the compounds are essentially unaffected by variations in thevalue of kvol from 50 to 300% of its original value. The insensitivity of the aqueous concen-trations to variations in kvol can be explained by examining the mass balance of the com-pounds dissolved in the water. From Eq. (20.7), the aqueous concentration of a compoundis a function of both the dissolution flux rate and the volatilization flux rate. Even thoughthe value of kvol is typically of the same order as kdis or larger, the concentration differencedriving the mass transfer is usually much greater for dissolution than it is for volatilization.Due to the extremely low concentrations of most compounds dissolved in the water after aspill, the volatilization flux is typically very small, and the aqueous concentrations are fairlyinsensitive to variations in the volatilization rate.

20.4.4 Dissolution Rate

Like evaporation and volatilization, dissolution is also commonly described by a two-resistance model:

sat1 1 C Mw o� � (20.17)k k k �dis w o o

where kw is the water film transfer coefficient, ko is the oil (slick) film transfer coefficient,


�o is the density of the slick, and Mo is the average molecular weight of the slick. In mostinstances, the resistance to transfer in the oil film can be ignored due to the small value of

for most hydrocarbons, such that kdis kw. Values of ko and kw can be estimated fromsatC w

reaeration rates. Cohen et al. (1980, 1978) measured dissolution rates of phenol from asurface slick and volatilization rates of benzene from the water to the atmosphere in a windtunnel at wind speeds of 0 to 9 m/s. The measured water-film volatilization rate coefficientsof benzene, kL benzene, were found to be roughly 8 times the water-film dissolution rate co-efficients for phenol, kw phenol, at all but the highest wind speeds when it was thought thatthe oil slick had a significant dampening effect on the turbulence at the oil-water interface:

k � 8 k (20.18)L benzene w phenol

Since the molecular diffusivities of phenol and benzene in water are similar, the rate coef-ficients for phenol and benzene are nearly interchangeable:

k � 8 k (20.19)L benzene w benzene

Values of kw can then be estimated from values of kL oxygen by accounting for the differencesin molecular diffusivities between benzene and oxygen using Eq. (20.16):

�0.5k ScL oxygen benzenek � (20.20)� �w benzene 8 Scoxygen

More generally, the water-film dissolution rate coefficient for any compound, i, can be es-timated from the reaeration rate coefficient, again by correcting for the differences in mo-lecular diffusivities:

�0.5k ScL oxygen ik � (20.21)� �wi 8 Scoxygen

Cohen et al. (1980, 1978) also found the measured water-film volatilization rate coefficientsof benzene to be roughly 20 times the measured water-film dissolution rate coefficients forphenol. Similarly, the oil-film dissolution rate coefficient for any compound, i, can be esti-mated as:

�0.5k ScL oxygen ik � (20.22)� �oi 20 Scoxygen

Values of kL oxygen can be obtained indirectly from stream parameters using Eq. (20.13), ormore directly from volatilization measurements by conducting a gas tracer study (Kilpatricket al., 1989; Hibbs et al., 1998).

Hibbs and Gulliver (1999) recently found that when the turbulence responsible for masstransfer at the water surface is generated from the bottom, such as in a stream or in a stirredreactor, the near-surface turbulence that dominates the mass transfer process on the waterside of the interface is essentially unaffected by the presence and/or the properties of an oilslick. Thus, the water-film dissolution rate coefficient can be estimated directly from the air–water liquid–film coefficient, corrected by a ratio of Schmidt number to the �1⁄2 power.

�0.5SciK � K (20.23)� �wi L oxygen Scoxygen

Equation (20.23) was also verified with the stirred beaker data of Southworth et al. (1983).The laboratory results of Southworth et al. (1983) and Hibbs and Gulliver (1999), without

wind, are much different than the wind-influenced results of Cohen et al. (1978), and thus


0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

3.00E+00

0 100 200 300 400 500

% of original value

hig

hes

t aq

ueo

us

con

cen

trat

ion

(p

pm

)

toluene

ethylbenzene

1-methylnaphthalene


FIGURE 20.9 Sensitivity analysis: effect of variations in dissolution rate on maximum aqueousconcentration.

there is no definitive relationship to use in the estimation of kdis. Additionally, there are noknown field studies from which to estimate the uncertainty in the value of kdis on rivers.Many existing oil spill models assume constant values for the film coefficients, even thoughLamont and Scott (1970) have shown that the values of the individual film coefficientsdepend on the level of turbulence on either side of the oil–water interface. Shen and Yapa(1988) used kdis � 1.0 cm/hr for all applications in their riverine oil spill model. Herbes andYeh (1985) used values of ko � 0.5 cm/hr and kw � 2.0 cm/hr for navigable rivers, whichfor most compounds gives kdis � 2.0 cm/hr. The relationships used in this analysis are basedon laboratory experiments relating kdis to kvol, but the dependence of kdis on kvol varies bymore than a factor of 8, depending on the importance of the wind. As previously mentioned,predictive relationships for reaeration coefficients are usually only accurate to within a factorof 3. Therefore, the overall uncertainty in the estimation of kdis is a factor of 3 times a factorof 8, or roughly a whopping factor of 20 to 30. When wind is not a factor in the reaerationcoefficient, the overall uncertainty of plus or minus a factor of 3 is more appropriate.

Figure 20.9 shows the highest aqueous concentration resulting from a series of JP-4 jetfuel spill simulations with the value of kdis varied from 50 to 300% of its original value. Theslopes of the lines in Fig. 20.9 are nearly 1:1. Thus, over the estimated range of uncertaintyin the value of kdis, the maximum aqueous concentrations can be expected to range fromroughly 5 to 2000% of their original values, or over several orders of magnitude. Thispresents a serious problem for spill modelers.

20.4.5 Saturation Concentration

Measured values of the aqueous solubility of pure compounds are available in the literaturefor most hydrocarbons of interest in the environment (Schwarzenbach et al., 1993). However,solubilities of compounds not available in the literature must be estimated. Depending onthe compound, empirical relationships based on molecular structure can predict the aqueous


0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

0 100 200 300 400

% of original value

hig

hes

t aq

ueo

us

con

cen

trat

ion

(p

pm

)

toluene

ethylbenzene

1-methylnaphthalene


FIGURE 20.10 Sensitivity analysis: effect of variations in saturation concentration on maximumaqueous concentration.

solubility within �25% to �300% (Lymann et al., 1990). Additionally, for mixtures ofstructurally dissimilar compounds, Burris and MacIntyre (1987) have shown that the aqueoussolubilities can be 1.5 to 2.5 times higher due to increased activities in the hydrocarbonphase. In this analysis, the uncertainty in is assumed to be plus or minus a factor of 2.satC w

Figure 20.10 shows the highest aqueous concentrations resulting from a series of JP-4 jetfuel spill simulations over the anticipated range of uncertainty in the values of ThesatC .w

slopes of the lines in Fig. 20.10 are nearly 1:1. As the values of are varied from 50 tosatC w

200% of the original values, the resulting maximum aqueous concentrations range fromroughly 50 to 200% of their original values. Thus, the aqueous concentrations of all com-pounds are extremely sensitive to variations in the saturation concentration.

20.4.6 Slick Spreading Velocity

Oils spread across a water surface due to differences in density and surface tension betweenthe slick and the water. Spreading is resisted by inertial and viscous forces. Except duringthe initial minutes following an extremely large spill, the extent of the slick due to spreadingcan be determined by the larger of an expression equating the surface tension and viscousforces (Fay, 1971):

0.252 3 tl � k (20.24)� �1t 2� �

or an expression equating the gravitational and viscous forces (Fay, 1971):

0.252 1.5� g V tl � k (20.25)� �1� 0.5�


where l � the length of slick resulting from spreading in one directionk1t � the spreading law coefficient for surface tension spreading (k1t � 1.33 [Garrett

and Barger, 1970])kl� � the spreading law coefficient for viscous spreading (k1� � 1.5 [Fay, 1971]) � the net surface tension ( � air–oil � oil–water � air–water)� � the density of water, � is the kinematic viscosity of water� � the ratio of density difference between water and oil to density of waterg � gravity, t is timeV � the volume of slick per unit length normal to the direction of spreading (per unit

width of the river)

Equations (20.24) and (20.25) were developed for spills of constant volume, constantsurface tension, and low viscosity on calm water. The effects of wind and currents on spread-ing rates are not well studied and are difficult to estimate. Therefore, the quantifiable un-certainty in the spreading rate lies in the estimation of the parameters used in Eqs. (20.24)and (20.25). The transition from a viscous spread, i.e., Eq. (20.25) to a surface tension spread,i.e., Eq. (20.23) occurs rapidly for most spills, and the spreading rate is described by Eq.(20.24). Since the density and viscosity of water can be estimated fairly confidently, mostof the uncertainty in the spreading rate lies in the estimation of the net surface tension,specifically in the estimation of the air–oil surface tension and the oil–water surface tension.There is also an uncertainty in the applications of the slick-spreading model to a cross-sectional nonuniform velocity profile, where the nonuniformities would add to the spreading.In this case, the slick would experience a longitudinal dispersion in addition to the water.This phenomenon is not a component of the sensitivity analysis.

There are two sources of uncertainty in estimating an interfacial surface tension for anoil slick. First, there can be a substantial error in estimating the initial value of the surfacetension. For most organic compounds, the air–oil surface tension can be predicted within�20% and the oil–water surface tension can be predicted within �50% (Lyman et al., 1990).Second, the surface tension of a slick changes over time as the volatile and more solublecompounds selectively evaporate and dissolve from the slick. However, the range of surfacetensions for most organic compounds is fairly narrow. Values for the air–oil surface tensionfor most organics range from approximately 0.02 to 0.04 N/m, and for oil–water surfacetension from approximately 0.020 to 0.035 N/m (Lyman et al., 1990). This indicates thatthe uncertainty in the interfacial surface tension, and also in the overall spreading rate, isroughly a factor of 2.

Figure 20.11 shows the highest aqueous concentrations resulting from a series of JP-4 jetfuel spill simulations over the anticipated range of uncertainty in the values of the spreadingrate. Over the range of spreading rates simulated, the highest aqueous concentrations of allcompounds are fairly insensitive to the spreading rates. Variations in the spreading rateranging from 50 to 200% of its original value produce changes in the maximum aqueousconcentration ranging from 90 to 110% of their original values. Higher spreading rates createa larger slick and more surface area for both dissolution and evaporation. A large rate ofevaporation would tend to produce lower aqueous concentrations since the slick would beon the water surface for a shorter time. However, a larger dissolution rate would tend toproduce higher aqueous concentrations. It is believed that effect of slick size on dissolutionand evaporation counteract each other, producing little net change in the highest aqueousconcentration due to variations in the spreading rate.

20.5 SPATIAL VARIATIONS IN SLICK COMPOSITION

The preceding application was modeled using only one slick, and thus it was assumed thatthe concentration of compounds within the slick was uniform over the entire length of the


0.00E+00

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4.00E-01

6.00E-01

8.00E-01

1.00E+00

0 50 100 150 200 250

% of original value

high

est a

queo

us c

once

ntra

tion

(ppm

)

tolueneethylbenzene1-methylnaphthalene1,4-dimethylnaphthalene

FIGURE 20.11 Sensitivity analysis: effect of variations in spreading rate on maximum aqueousconcentration.

slick. However, for slicks that are several kilometers in length or that are being fed slowlyby a point source such as a leaky pipe, the concentration of compounds within the slick mayin fact vary with distance downstream. Since the aqueous concentration is controlled largelyby the concentration within the overlying slick, the assumption of a uniform concentrationover the entire length of the surface slick may introduce significant errors in the predictionof the aqueous concentration.

Assuming that the evaporation rate coefficient, kevap, is constant over the entire length ofthe slick, a streamwise variation in the concentrations of compounds within the slick can becaused in only two ways. First, a variation in slick composition could be caused by spillinga mixture of compounds into one end of a slick while compounds rapidly and selectivelyevaporate and dissolve from the slick. In such a case, the composition of the slick near thespilling point would resemble the composition of the spilled product, while the portions ofthe slick farther downstream from the spilling point could contain less of the more volatilecompounds. Second, a variation in slick composition may be caused by variations in theaqueous concentration of a compound beneath the slick. If the aqueous concentration beneaththe slick varies significantly from one end of the slick to the other, the dissolution rate, whichis driven by the difference between the actual water concentration and the equilibrium con-centration in the water, would also vary from one end of the slick to the other. Over time,the variation in dissolution rate could create a variation in slick composition.

To investigate the conditions under which the composition could vary from one end ofthe slick to the other due to rapid evaporation, consider the following analysis of a binaryspill. Let compound 1 be volatile and semisoluble, and let compound 2 be perfectly non-volatile and insoluble. The mass balance for compound 1 in the farthest downstream end ofthe slick can be simplified from Eqs. (20.5) and (20.6) by assuming that the evaporative fluxis much greater than the dissolution flux, and by setting M1 � M2:

odm m p M1 1 1 1� �k (20.26)evapdt m � m R T1 2

where t is the time since the product was spilled onto the water surface. Integrating Eq.


0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

# slicks

max

imum

aqu

eous

con

cent

ratio

n (p

pm) toluene

ethylbenzene1,4-dimethylnapthalene1-methylnaphthalene

FIGURE 20.12 Multiple-slick model: effect of the number of slicks on the maximum aque-ous concentration for a release of 10,000 kg of jet fuel over 10 min.

(20.26) from t � 0 to ts and from m1 � to m1, the time to achieve a specified reductionom1

in the initial, or the spilled, concentration of compound 1 in the slick can be estimated as:

R T m1ot � (m � m ) � m ln (20.27)� �s 1 1 2o oP M k m1 1 evap 1

Thus, larger variations in the concentration of a compound within a slick (as indicated bym1 / ) will occur when the duration of the spilling period is long, i.e., ts is large, when oneom1

of the compounds evaporates quickly, i.e., � kG is large, or when the slick is thin, i.e.,oP1

m1 and m2 are small. Inserting values of � 100 g/m2 and m2 � 900 g/m2, i.e., slickom1

thickness approx. � 1 mm, kevap � 5 � 10�4 m/s, � 10�1 atm, and M1 � 100 g/moloP1

into Eq. (20.27), the time to achieve a 10% reduction in the concentration of compound 1in the downstream end of the slick is on the order of ts � 10 min.

The second possible cause of streamwise variations in concentrations of compounds inthe slick could be the variation in dissolution rates due to streamwise gradients in the aqueousconcentration beneath the slick. Hibbs et al. (1999a), however, have shown that significantstreamwise concentration gradients within the slick are not likely to be caused by concen-tration-driven variations in dissolution fluxes. Thus, spatial variations in slick compositionare likely due to the rapid evaporation of volatile compounds from the slick.

20.5.1 Simulation of Short-Duration Spill

The results of a series of simulations of the jet fuel spill using the multiple slicks areconsistent with the above analysis. The concentrations of the more volatile compounds inthe downstream end of the slick decrease only slightly during the 10 minutes that the jetfuel is being spilled onto the water. Figure 20.12 shows the maximum aqueous concentrationof four compounds resulting from a 10-minute spill plotted as a function of the number of


0

0.2

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0.6

0.8

1

0 10 20 30 40 50 60 70 80time (hrs)

peak

aqu

eous

con

cent

ratio

n (p

pm)

ethylbenzene1-methylnaphthalene

1 slick

1 slick

10 slicks

10 slicks

FIGURE 20.13 Multiple-slick model: peak aqueous concentrations resulting from a releaseof 10,000 kg of jet fuel over 10 min.

slicks used in the model. As more slicks are used in the model, larger concentration gradientsdevelop in the slick and the maximum aqueous concentration decreases.

The variations in the slick concentration that occur while the slick is being formed affectnot only the maximum highest aqueous concentrations resulting from the spill, but also thelocation and time at which the maximum aqueous concentration occurs after a spill. Figure20.13 shows the model simulation results for a spill of 10,000 kg of jet fuel over a periodof 10 minutes. The peak aqueous concentrations of ethylbenzene and 1-methylnaphthaleneare plotted against time for simulations using the single-slick model and a 10-slick model.Similar to what was shown in Fig. 20.12, the peak concentrations of both compounds areroughly 25% lower when 10 slicks were used than when only 1 slick was used in thesimulation. Also, the highest aqueous concentration occurs roughly 25% earlier when 10slicks are used in the simulation than when only 1 slick is used. The decrease in the max-imum aqueous concentration and the shift in the time of occurrence of the maximum aqueousconcentration can be attributed to the selective evaporation of the more volatile compoundsover the length of the slick, during the period that the fuel is being spilled onto the watersurface. We were surprised that the results of the single-slick model and the multi-slickmodel differed for a spill of such short duration. We thus investigated the mechanisms insome detail.

Using the 10-slick model for this 10-minute spill, each individual slick has fuel added toit for 60 seconds. The slick then drifts downstream while the more volatile compoundsrapidly evaporate, creating a concentration gradient in the overall slick. The effective lengthof the overall slick for dissolution of the volatile compounds becomes shorter as the morevolatile compounds evaporate from the downstream end of the slick. At roughly six hours,the effective length of the slick has become so small that the dispersion in the river dilutesany further dissolution from the slick, and the peak aqueous concentration of ethylbenzenebegins to decline. In the single-slick model, as the concentration of ethylbenzene is uniformthroughout the slick, it has a long effective length for dissolution. The peak aqueous con-centration is able to increase until roughly eight hours, after which the dispersion in the riveroverpowers the declining dissolution flux.


0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16 18 20

# slicks

max

imum

aqu

eous

con

cent

ratio

n (p

pm)

tolueneethylbenzene1,4-dimethylnapthalene1-methylnaphthalene

FIGURE 20.14 Multiple-slick model: effect of the number of slicks on the maximum aque-ous concentration for a release of 10,000 kg of jet fuel over 10 h.

While the effective length of the slick for the volatile compounds is decreasing, theeffective length for dissolution of the nonvolatile compounds is increasing. The peak aqueousconcentration of 1-methylnaphthalene in the 10-slick model shown in Fig. 20.13 rises slightlyfaster than the peak aqueous concentration of the single-slick model. The 1-methyl-naphthalene dissolves and volatilizes faster from the effectively longer 10-slick model thanfrom the single-slick model. The 1-methylnaphthalene is thus completely gone from the slickfaster in the 10-slick model than in the single slick model, resulting in a lower maximumaqueous concentration.

20.5.2 Simulation of Long-duration Spill

The same selective evaporation phenomena illustrated in Figs. 20.12 and 20.13 can be seenin a similar plot of peak aqueous concentrations resulting from a 10-hour release of 10,000kg of jet fuel, shown in Figs. 20.14 and 20.15. Figure 20.14 shows the maximum aqueousconcentration of four compounds plotted as a function of the number of slicks used in themodel. As in the 10-minute spill simulation, the highest aqueous concentration of all com-pounds decreases as the number of slicks in the model increases.

Figure 20.15 shows peak aqueous concentrations of ethylbenzene and 1-methyl-naphthalene plotted against time for simulations using the single-slick model and a 10-slickmodel. In the 10-minute release shown in Fig. 20.13, each slick in the 10-slick model wasfilled with jet fuel for 1 minute before being released. In the 10-hour spill simulation shownin Fig. 20.15, each slick is also filled with jet fuel for 1 hour before being released. Duringthat 1-hour time period, a significant portion of the more volatile compounds evaporatesfrom the slick. By the time the slick is released to drift downstream, most of the volatilecompounds have already evaporated from the slick. Any remaining dissolution of the morevolatile compounds is diluted by dispersion. Consequently, the maximum aqueous concen-tration of ethylbenzene occurs very early after the spill. With the single-slick model, newjet fuel is uniformly distributed over the entire slick during the 10-hour spilling period.


0

0.1

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0.3

0.4

0.5

0 10 20 30 40 50 60 70 80time (hrs)

peak

aqu

eous

con

cent

ratio

n (p

pm)

ethylbenzene1-methylnaphthalene

1 slick

1 slick

10 slicks

10 slicks

FIGURE 20.15 Multiple-slick model: peak aqueous concentrations resulting from a releaseof 10,000 kg of jet fuel over 10 h.

Consequently, the peak aqueous concentration of ethylbenzene continues to rise for 10 hours,after which the peak concentration is diluted by dispersion in the river.

The maximum aqueous concentrations shown in Figs. 20.12 and 20.14 appear to decreaselogarithmically as a function of the number of slicks used in the model, suggesting that thereis a diminishing rate of return on the quality of the model prediction with the increasingnumber of slicks used in the model. The decrease of the maximum aqueous concentrationfor each compound can be described by the empirical equation:

dCmax � (C � C ) (20.28)max �dn

where Cmax � the maximum aqueous for a given number of slicksn � the number of slicks used in the simulation, is a fitted constant

C� � a fitted constant that represents the maximum aqueous concentration for aninfinite number of slicks

Table 20.3 shows values of and C� for four compounds determined from regressions ofEq. (20.28) against the data shown in Figs. 20.12 and 20.14. Table 20.3 also shows themaximum aqueous concentrations plotted in Figs. 20.12 and 20.14 as a percentage of C�.For the 10-minute release simulation, the concentrations of all four compounds were within50% of C� using only 1 slick, within 10% of C� using 10 slicks, and within 1% of C� whenusing 20 slicks. For the 10-hour release simulation, the maximum aqueous concentrations ofthe volatile compounds varied from nearly four times the value of C� using only 1 slick towithin 5% using 20 slicks, while the range of variation of the maximum aqueous concen-trations of the nonvolatile compounds was similar to that of the 10-minute release simulation.Thus, the number of slicks used in the simulation can have a significant impact on thepredicted aqueous concentrations, especially in models of slow, continuous spills containinghighly volatile compounds.


TABLE 20.3 Extrapolation of Cmax to an Infinite Number of Slicks. Cmax is Determined from SpillSimulations. C� and are Determined from a Curve Fit of Cmax Versus the Number of Slicks UsingEq. (20.28).

C�

(ppm)

Cmax as a percentage of C� (i.e., Cmax /C� � 100)

1 slick 2 slicks 5 slicks 10 slicks 20 slicks

10-minute releaseToluene 0.103 �0.193 142 133 120 108 101Ethylbenzene 0.081 �0.195 140 130 119 107 1011-Methylnaphthalene 0.585 �0.194 138 128 118 108 1001,4-Dimethylnaphthalene 0.603 �0.213 136 127 116 107 100

10-hour releaseToluene 0.012 �0.214 386 325 224 141 105Ethylbenzene 0.015 �0.253 337 283 181 135 961-Methylnaphthalene 0.297 �0.889 134 113 105 100 971,4-Dimethylnaphthalene 0.314 �0.312 114 108 105 101 99

20.6 CONCLUSIONS

Oil spill modeling needs to be performed before a spill occurs as part of a planning processfor emergency response. This avoids the ‘‘chicken-with-its-head-cut-off’’ look that is oftenapparent in spill response teams. There will not be sufficient time following a spill to collectappropriate data and bring a model up to speed. Oil spill models are also valuable in aforensic investigation following an oil spill event.

In rivers and streams, the largest impact of an oil spill is often the aqueous concentrationsthat result from dissolution of the slick. The water cannot leave the slick through mixingwith a surrounding water body, and aqueous concentrations of toxic compounds in the slickcontinue to rise. The modeling team must understand the importance of accurate interfacialchemical transfer rates between the slick and the water.

This chapter discussed the best physical characterizations of chemical transfer rates andperformed a sensitivity analysis on the more significant parameters. Table 20.2 indicates thataqueous concentrations resulting from spills of hydrocarbons into rivers were most sensitiveto the following, listed in descending order of significance:

Dissolution rate coefficientsAqueous concentration in equilibrium with the oil slickEvaporation rate coefficient of the oil slick to the atmosphereLongitudinal dispersion coefficientSpreading rate of the slickVolatilization rate between the water and the atmosphere

For spills that are longer in duration and cannot be simulated by a pulse, streamwisegradients caused by the rapid evaporation of the more volatile components can have a sig-nificant impact on aqueous concentrations. A multiple-slick model can account for thesestreamwise gradients in the slick.

For any planning of an oil spill into rivers or streams, a field investigation needs to beundertaken. This investigation involves determining the travel time of the reach, the longi-tudinal dispersion coefficient of the reach, and the gas transfer coefficient of the reach. An


aqueous concentration model with acceptable results can then be formulated from the rela-tionships and references provided in this chapter.

20.7 ACKNOWLEDGMENTS

This model was developed with support from a Section 104 grant distributed by the Uni-versity of Minnesota Water Resources Center, a doctoral dissertation fellowship from theUniversity of Minnesota Graduate School, and the National Science Foundation under grantNo. BES-9522171.

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Addison, H. 1941. Hydraulic Measurements, John Wiley & Sons, New York, pp. 155–156.Banks, R. B. 1974. ‘‘A Mixing Cell Model for Longitudinal Dispersion in Open Channels,’’ Water

Resources Research, vol. 10, pp. 357–358.Burris, D. R., and W. G. MacIntyre. 1987. ‘‘Water Solubility Behavior of Hydrocarbon Mixtures Impli-cations for Petroleum Dissolution,’’ in Oil in Freshwater, ed. J. H. Vandermeulen and S. E. Hrudey,Pergamon Press, New York, pp. 85–94.

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Cohen, Y., W. Cocchio, and D. Mackay. 1978. ‘‘Laboratory Study of Liquid-Phase Controlled Volatili-zation Rates in the Presence of Wind Waves,’’ Environmental Science and Technology, vol. 12, 553–558.

Cohen, Y., D. Mackay, and W. Y. Shiu. 1980. ‘‘Mass Transfer Rates between Oil Slicks and Water,’’Canadian Journal of Chemical Engineering, vol. 58, pp. 569–575.

Fay, J. A. 1971. ‘‘Physical Processes in the Spread of Oil on a Water Surface,’’ in Prevention and Controlof Oil Spills, American Petroleum Institute, Washington, DC, pp. 463–467.

Fischer, H. B., E. J. List, R. C. Y. Koh, J. Imberger, and N. H. Brooks. 1979. Mixing in Inland andCoastal Waters, Academic Press, New York, pp. 136–138.

Fuller, E. N., P. D. Schettler, and J. C. Giddings. 1966. ‘‘A New Method for Prediction of Binary Gas-phase Diffusion Coefficients,’’ Industrial and Engineering Chemistry, vol. 58, 19–27.

Garrett, W. D., and W. R. Barger. 1970. ‘‘Factors Affecting the Use of Monomolecular Surface Filmsto Control Oil Pollution on Water,’’ Environmental Science and Technology, vol. 4, pp. 123–127.

Goodwin, S. R., D. Mackay, and W. Y. Shiu. 1976. ‘‘Characterization of the Evaporation Rates ofComplex Hydrocarbon Mixtures under Environmental Conditions,’’ Canadian Journal of ChemicalEngineering, vol. 54, pp. 290–294.

Gulliver, J. S., and H. G. Stefan. 1986. ‘‘Wind Function for a Sheltered Stream,’’ Journal of Environ-mental Engineering, vol. 112, pp. 387–399.

Hayduk, W., and H. Laudie. 1974. ‘‘Prediction of Diffusion Coefficients for Non-electrolysis in DiluteAqueous Solution,’’ AiChE Journal, vol. 20, pp. 611–615.

Herbes, S. E., and G. Yeh. 1985. ‘‘A Transport Model for Water-soluble Constituents of Synthetic OilSpills in Rivers,’’ Environmental Toxicology and Chemistry, vol. 4, pp. 241–254.

Hibbs, D. E., and J. S. Gulliver. 1999. ‘‘Dissolved Rate Coefficients for Surface Slicks on Rivers,’’ WaterResearch, vol. 33, pp. 1811–1816.

Hibbs, D. E., K. L Parkhill, and J. S. Gulliver. 1998. ‘‘Sulfur Hexafluoride Gas Tracer Studies inStreams,’’ Journal of Environmental Engineering, vol. 124, pp. 752–760.

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CHAPTER 20 MODELING OIL SPILLS ON RIVER SYSTEMS