FOR WASTE AND WASTEWATER

U.S. EPA Contract No. 68DlOll8

November 1994

prepared for the

U.S. Environmental Protection Agency

Office of Air Quality Planning and Standards

Research Triangle Park

North Carolina 27711
5.0 SURFACE IMPOUNDMENTS AND OPEN TANKS

This section discusses the approach used to estimate air

emissions from surface impoundments and open top tanks. The

emission models are described, model facilities are defined, andexample calculations are presented.

5.1 NARRATIVE DESCRIPTION OF EMISSIONS AND MODEL UNITS

Emissions from surface impoundments and open tanks originate

from the uncovered liquid surface that is exposed to the air. The

model used to estimate emissions from the liquid surface is based

on an overall mass transfer coefficient that incorporates two

resistances to mass transfer in series--the liquid-phase

resistance and the gas-phase resistance. Numerous correlations

are available to estimate the individual mass transfer coeffi

cients (or resistances), and they depend upon the compound’s

properties and the system’s parameters. The recommended

correlations and their applicability are described in subsequent

sections. The emission estimating procedure also incorporates a

flow model that describes the method of operation. For

flowthrough systems, the impoundment’s or tank’s contents may be

completely mixed, plug flow, or somewhere in between with varying

degrees of backmixing or axial dispersion. Biologically active

impoundments and aeration tanks can be designed for either

completely mixed or plug flow, and both types of flow models are

discussed for these types of systems. For disposal impoundments,

the contents are assumed to be well mixed, and the bulk

concentration is expressed as a function of time. An expression

for biodegradation is incorporated for those units specifically

5-1
p

, 

g

, and

removal with the effluent. Several different types of model units

are presented and include mass transfer to the air from quiescent,

mechanically aerated, diffused-air, and oil-film liquid surfaces.

The other major difference among the types of model units is the

type of flow model that is used. For flow-through systems, the

degree of mixing can range from complete mixing to plug flow (no

mixing), and both cases are presented. For disposal units with no

flow out, emissions are a function of time, and average emissions

are estimated for some specified time since disposal. The majordifference in the emission equations is the liquid-phase

concentration that is used for the driving force for mass transferto the air. The simplest case is represented by well-mixedsystems in which the driving force is represented by CL, theliquid-phase concentration in the bulk liquid, which is also equalto the effluent concentration. Relative removal rates can be com

pared for this well-mixed case from a simple material balance.

For plug flow, integration is required because the driving

force for mass transfer changes as the liquid flows through thesystem. This concentration is a function of location or time

(which are equivalent in plug flow) and is expressed as C(denoting a dependence on time) . The effluent from a plug flow

system is denoted as Ce• For disposal impoundments, the driving

force concentration changes with time and is also denoted as Ct;

however, there is no effluent from a disposal impoundment. The

integration required for plug flow is from t = 0, when the

material first enters the unit, to t = residence time, when thematerial leaves the unit. For disposal units, the integration is

from t = 0, when the material is first placed in the unit, to

5-2
p

g 

calculations are more straightforward, and the two types give

similar results. The only exception is a flowthrough impoundment

with an oil film surface, which uses the plug flow model because

the oil film inhibits mixing. Both models yield an estimate of

air emissions, biodegradation, and the quantity leaving with the

effluent. It is important to recognize that the quantity leaving

with the effluent may also eventually contribute to air emissions,

especially for treatment units in series or for discharges to

streams or publicly owned treatment works.

Equations are presented for estimating the various removal

rates, and example calculations for different types of

impoundments are also provided. Example calculations are not

presented separately for open tanks because the procedure is

analogous to that used for impoundments. In general, open tanks

will have different input parameters that will account fordifferences in emission rates compared to impoundments. For

example, the liquid surface area for open tanks will be less, and

the fetch-to-depth (F/ID) ratio will be much lower for tanks. Ifthe open tank has a wind barrier to reduce the wind velocity, the

reduced wind velocity can be used in the mass transfercorrelations. In addition, the modeling approach accounts for the

shorter retention times in tanks (on the order of hours) compared

to impoundments (on the order of days) . For open tanks, the mass

transfer correlation of Springer is recommended for windspeeds

less than 3.25 rn/s. and the correlation of MacKay and Yeun is

recommended for windspeeds greater than 3.25 rn/s. Both are

discussed in the following section.

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to 3.25 m/s. Although Springer examined only the mass transfer of

ethyl ether, his results are extrapolated to other compounds bythe ratio of the compound’s and ether’s diffusivities in water tothe 2/3 power. The windspeed in Springer’s correlation is defined

as the windspeed 10 m above the liquid surface. For practicalapplication of his correlation, typically reported values of

windspeed are used. Springer’s model does not include the case inwhich the F/ID ratio is less than 14 and the windspeed is greater

than 3.25 m/s. For this specific case, kL was estimated from

MacKay and Yeun’s correlation shown in Table 5l7,8 MacKay andYeun 9 did not address the effect of depth; however, their

correlation is based on data from 11 organic compounds in a wellmixed system, the compounds represent a broad range of Henry’s lawconstants, and their general correlation is applicable for the

case described above that is not covered by Springer’s

correlation.

The gas-phase coefficient (kG) was estimated from the

correlation of MacKay and Matasugu as shown in Table 5l.10 Thiscorrelation was developed from experiments on the evaporation ofisopropyl benzene, gasoline, and water into air. These

researchers verified that previous work, which assumed that the

wind velocity profile follows a power law, could be used to

quantify the rate of evaporation from a smooth liquid surface.

The result was a correlation that expressed kG as a function ofwindspeed and the fetch or effective diameter of the liquid

surface.

The individual mass transfer coefficients estimated from the

correlations in Table 5-1 are used in Equation (5-2) to estimate

5-6
D 

kL = 2.78 x D W (0 < U10 < 3.25 ether (All F/D ratios)

D 2/3

kL = [2.605 x (F/D) + 1.277 x l0] D ether

(U10 >3.25) (m/s) (14 < F/D <51.2)

-7 2 D 2/3 (U10>3.25) (m/s)

kL = 2.611 x 10 U10 Dth (F/D>51.2)

where,

U10 = windspeed at 10 m above the liquid surface, m/s;

= diffusivity of constituent in water, cm2/s;

D = diffusivity of ether in water, cm2/s; and ether

F/ID = fetch-to-depth ratio (fetch is the linear distance

across the impoundment)

Gas phase

MacKay and Matasugu (in Hwang 5):

4.82 x U° 78Sc067 d0 (m/s)

where,

U windspeed, m/s;

G

ScG Schmidt number on gas side DGa

= viscosity of air, g/cm•s;

(continued)

5-7
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for mass transfer. For an impoundment that is instantly filled

with waste, the driving force (CL) is the initial concentration

in the waste. However, this concentration will decrease with

time as the constituent is lost to the air, which suggests that

emissions may also decrease with time (assuming constant K and

A) . For flowthrough systems, the concentration may be cyclical

if the loading of the process is cyclical. Continuous

flowthrough systems may attain some equilibrium concentration.

The flow model assumed for quiescent impoundments and tanks

with no biodegradation is that the contents of the system arewell mixed and that the bulk concentration (driving force) in the

system is equal to the effluent concentration, CL. A material

balance around this system yields:

or

QC KACL + QCL

CL = QC./(KA+Q) (5-6)

where,

Q = volumetric flow rate, m3/s;

initial concentration in the waste, g/m3;

C equilibrium or blk concentration in the L impoundment, g/m

overall mass transfer coefficient, m/s; and

liquid surface area, m2.

The well-mixed assumption is made for the sake of simplicity

and assumes that bulk convection and wind-induced eddies combine

to mix the basin contents. Axial dispersion in the flow

5-9
p

g 

the plug-flow assumption yielded estimates that were higher by

11 percent for acetaldehyde, 5 percent for acetone, and 0 percent

11 for phenol.

The approach described to estimate emissions from quiescent

impoundments with no biodegradation includes the following steps:

1. Estimate the individual mass transfer coefficients from

Table 5-1.

2. Estimate the equilibrium constant from Equation (5-3)

3. Estimate the overall mass transfer coefficient from

Equation (5-2)

4. Estimate the liquid-phase concentration from Equation

(5-6)

5. Estimate emissions from Equation (5-1)

The major assumptions associated with this procedure are:

• The two-resistance model and the correlations for the

individual mass transfer coefficients are applicable to

the system of interest.

• The impoundment’s contents are well mixed.• There is no significant removal by biodegradation,

seepage, adsorption, or other forms of degradation.

• The waste material of interest is aqueous waste with no

separate organic phase.

• The estimate of Henry’s law constant (equilibrium

partitioning between the vapor and liquid) is

reasonably accurate.

The recommended procedure for quiescent impoundments is to

assume that the liquid is well mixed. This assumption is used in

5-10
y p

y

g

g

system. There is no uniform liquid concentration within the

plug-flow unit as there was in the well-mixed system, and the

lowest concentration occurs in the effluent (i.e., there is no

backmixing of the effluent with the influent) . FOr plug flow,

the rate of disappearance of a compound by air emissions is given

by:

ô(C V) -

=KAC (5-7)

ót

where,

= concentration after the plug has traveled t seconds;

t = time, S;

3 V = volume, m

and with the other symbols as previously defined.

Rearranging Equation (5-7) yields:

o(c) KA 

= -———ôt (5-8)

Ct V

Integrating Equation (5-8) from C1 at t = 0 to C =CL at

t = v/Q (one residence time) gives:

(.S)=EXF(i)

3 where CL = effluent concentration, g/m ,and with the other

symbols as previously defined.

5-11
The ratio CL/Ci represents the fraction removed with the

effluent; therefore, 1 -CL/Cl represents the fraction that isemitted air from the plug-flow system:

fair

= ( 1 - = 1 -EXP ( - (5-11)

The average emission rate is calculated from:

E fair Q C1 (5-12)

where,

E emissions, g/s;

f = fraction emitted from Equation (5-11); air

Q flow rate, m3/s; and

C. influent concentration, g/m3.

5.2.2 Model Plant Parameters for Quiescent Impoundments

A model facility was developed for quiescent impoundments to

illustratethe emission estimating procedure. A 1981 survey

compiled by Westat 12 showed that the median surface area for

storage impoundments was approximately 1,500 m2 and that the

median depth was 1.8 m. Detention times ranged from 1 to 550

days, with over half of the values at 46 days or less. For this

example, a detention time of 20 days was chosen. The area anddepth yield a total volume of 2,700 m3, and the detention time of

20 days yields a flow rate of 1.6 L/s (0.0016 m3/s)

Meteorological conditions are also needed as input

parameters for the emission models. For this emission estimate,

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5.3 BIODEGPADATION

This section identifies some of the major design features of

biological treatment processes, such as activated sludge units

and impoundments designed for biodegradation. Mathematical

models for biodegradation are also presented and incorporated

into predictive fate models.5.3.1 Description of Biological Active Systems

The activated sludge process is an aerobic biological

treatment in which the pollutants are degraded by microorganisms

suspended uniformly in the reaction tank. Oxygen is introduced

by mechanical means, and the microorganisms are maintained by

recycling the activated sludge that is formed. In most units,the sludge is removed by settling in a separate unit, a portionof the sludge is recycled, and a small portion is wasted (removed

from the system) on a continuous basis. Oxidation or stabiliza

tion impoundments and aerated impoundments are used to treat

entire plant wastes as well as to polish the effluent from othertreatment processes. Solids usually settle out in the

impoundment or are removed in a separate vessel. Generally, the

solids are not recycled; however, if the solids are returned, the

process is the same as a modified activated sludge process. 13

Typical design parameters for an activated sludge process

are given in Table 5-3. Two of the most commonly used parameters

are the food-to-microorganism (F/M) ratio and residence time.

The F/M ratio describes the organic loading on the biological

system and is calculated as the weight of BOD 5 (biochemical

5-17