RADIAN
'3RPQRA71QN
84-222-078-17-07
PROTOCOLS FOR CALCULATING VOC EMISSIONS
FROM LAND APPLICATIONS
USING EMISSION MODELS
TECHNICAL NOTE
EPA Contract No. 68-02-3850
Work Assignment 17
Prepared for:
Mr. Clyde E. Riley
Task Manager
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
Prepared by:
G. B. DeWolf
R. G. Wetherold
Radian Corporation
P.O. Box 9948
Austin, Texas 78766
17 December 1984
8501 Mo-Pac Blvd./P.O. Box 9948 / Austin, Texas 78766 / (512)45^7C>7
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CORPOMTIOfl
SECTION 1
INTRODUCTION
A number of emission models have been proposed for estimating volatile
organics emissions from landfills and landfarming sites. This technical
note discusses these models in detail and presents a protocol for their use.
Equations for the models are presented, required input variables defined,
sources of information for these variables suggested, and approximate preci-
sion levels for the variables presented. Physical property inputs are
discussed and methods for their estimation are provided, as are selected
values for some materials. Models are presented for covered landfills and
for landtreatment (landfarming). For landfills, the recommended model is
that of Farmer, as modified by Shen and Hwang, and for landtreatment, the
Thibodeaux-Hwang model is recommended (1).
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SECTION 2
LANDTREATMENT EMISSIONS
Two models which have been proposed for predicting emissions of vola-
tile compounds from landtreatment operations are the Hartley and the
Thibodeaux-Hwang models. These two models were presented and briefly dis-
cussed in an earlier report(l). Since the Hartley model is inadequate for
describing evaporation of volatile waste material which has permeated below
the soil surface, it is not recommended for consideration in the kinds of
applications addressed by this protocol. Therefore, the Thibodeaux-Hwang
model must be used.
This model is presented in Table 2-1. In the development of this
model, the emission rate of a volatile chemical compound was assumed to be a
funct ion of:
• the evaporation rate of the compound from the inter-
stitial soil surfaces, and
• the diffusion rate of the chemical compound through the
air-filled pore spaces of the soil.
The emission rate is assumed to be controlled by the diffusion rate in the
air pore pace when the oil loading and soil particles are both small.
At soil loadings substantially greater than typical1waste loadings, the
mathematical description of the emission process is extremely complex.
Thibodeaux and Hwang made a significant number of simplifying assumptions to
develop a usable mathematical expression. The resulting model is a highly
idealized and simplified description of a very complex process.
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TABLE 2-1. THIBODEAUX-HWANG MODEL FOR VOLATILE ORGANIC EMISSIONS FROM
LANDTREATMENT OPERATIONS
Basis:
Emission rate is controlled by diffusion rate of vapor
through the air-filled pores of the landtreated soil.
Form:
E. =
i
D C
ei ig
"a
'2 D t A (h -h )C
ei p s ig
M
10
1/2
H C.
c io
ig
1 +
H D . Z
c ei o
D . A f(y)
wi s
and
Symbo1
f(y) = (hp + ys - 2hs)/6
Symbol/Parameter Definition
Typical Source of
Precision Input Parameter
surface area over which waste is applied, _+ 2%
cm'
measured
interfacial area per unit volume of soil
interracial area per unit v
for the oily waste, cm^/cm
calculated
effective wet zone pore space concentration
of component i, g/cm
Cio
Dg^ ^effective diffusivity of component i in the +_ 25%
air-filled soil pore spaces, cm^ls
calculated
concentration of component i in oil, g/cm +_ 25% calculated
published
data; esti-
mat ion
soil clump diameter, cm
average cal-
culated from
measurement s
or estimated
(Continued)
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TABLE 2-1. THIBODEAUX-HWANG MODEL FOR VOLATILE ORGANIC EMISSINS FROM
LANDTREATMENT OPERATIONS (Continued)
Dwi
effective diffusivity of compound i in the
oil, cm^/s
+
52
published
data; esti-
mat ion
Ei
flux of component i from the soil surface,
g/cm^-sec
-
calculated
f (y)
(h^ + hphg-2hg)/6 accounts for the
lengthing dry zone
-
calculated
Hc
Henry's Law constant in concentration form,
cm^ oil/cm air
+
15%
publ ished
data or
measurement
hP
depth of soil contaminated or wetted with
landtreated waste, cm
+
10%
measured
Mio
initial mass of component i incorporated
into the zone (h -h ), g
r b
+
5%
measured
t
time after application, sec
measured
y
height of wetted soil remaining after
partial drying, cm
-
measured
wf
weight fraction oil in film form in soil
-
calculated
Zo
oil layer diffusion length, cm
calculated
or esti-
mated
f
fraction of oil in film form
-
estimated
PP
soil clump density, g/cm
+
10%
measured or
estimated
j?aste-oil density, g/cm
+
10%
measured or
estimated
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Much of the material that is typically landtreated consists of oily
sludges. These sludges are usually mixtures of solids, water, and a complex
solution of a very large number of organic compounds. The sludges may
consist of two- or three-phase solutions or even emulsions. They are
applied to the landtreatment area at high soil loadings. At this time, the
Thibodeaux-Hwang model has not been validated and/or calibrated under ex-
perimental and field conditions in the range of typical landtreatment opera-
ting conditions. Without such validation, no estimate of the accuracy of
the model predicted emission rates can be determined.
There is very little available data which can be used to validate this
model under any conditions. Thibodeaux and Hwang (2) used two sets of data
to compare measured emission rates with rates predicted by the model. The
initial results of a joint API/EPA study were used as one data set. Partial
agreement of the data with predicted results was obtained. However, the
conditions during the short period (<30 minutes after sludge application) of
time in which data were reported deviated substantially from those described
by the model. Much of the applied sludge was still in the process of
soaking into the soil, and substantial amounts were still present as liquid
pools on the soil surface.
Thibodeaux and Hwang also used experimentally determined emission rates
of Spencer and Cliath (3) and Farmer and Letey (4) to compare with emission
rates predicted with the model. There appears to be good agreement between
the predicted and measured emission rates of the pesticide dieldrin. How-
ever, the dieldrin soil loadings were two orders of magnitude lower than
those typically encountered in landtreatment operations. Dieldrin is also a
solid iri*the normal ambient temperature range.Therefore, the experimental
conditions are very different from those encountered during typical land-
treatment operations, and this comparison is not a verification of the model
under typical landtreatment conditions.
The computational procedure for using the Thibodeaux-Hwang model is:
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1. Calculate ZQ.
If oil is in film form ZQ = dpPpf/6Pw
if oil is in lump form ZQ = dp/2
2. Calculate As, the interfacial area per unit volume of soil,
If oil is in film form A = 6/d
s p
If oil is in lump form Ag = 2.70/dp
3. Calculate f(y) = (hp+hphs~2hg)/6.
4. Calculate wet zone pore space concentration.
H C.
c io
C- =
L8 / H D .Z
/ c ei o
1 +
D„iAsf(y> )
5. Calculate emission rate for component i,
Ei =
D C
ei lg
2D t A (h -h )C \ 1/2
2 I ei p s lg
n _ + '
3 ^ Mio
6. Calculate total emission rate of all components,
N
Et = E Ei
i=l
In practice, it is often not practical to calculate individual compo-
nent emissions in order to estimate total emissions. In such cases, an
estimate of total emissions may be made by summing the emissions estimated
for several classes of compounds using a representative individual component
for each class.
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The selection of a representative individual component is somewhat -
arbitrary. Some compounds are more likely to be encountered than others,
and compounds in the mid-molecular weight ranges (4-8 carbons) are likely to
dominate in frequency of occurrence. Therefore, at this time, the following
classes and compounds have been selected as representative for making emis-
sions estimates:
Clas s
Compound
Paraffins
Olef ins
Aromatics
Halogenated hydrocarbons
Oxygenated hydrocarbons
Toluene
Acetone
Hexane
Butene
Methylene chloride
Key properties of some compounds are found in Table 5-1 of Section 5.
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SECTION 3
LANDFILL EMISSIONS
The most generally accepted model for the prediction of emission rates
from covered landfills is the mathematical expression proposed by Farmer,
et. al. (5). In this model, shown in Table 3-1, the emission rate from a
covered landfill is assumed to be controlled by the diffusion rate of pollu-
tant gases through the soil cover. Two forms of the model were developed; a
rigorous form and a simplified form. The model in its rigorous form was
validated by Farmer using laboratory simulation data for hexachlorobenzene.
The model was simplified by Farmer for use in the predictive mode, and
modified slightly by Shen (6). A multiplicative factor of 6.0 was added to
account for convective effects due to gases generated by the codisposal of
biologically degradable wastes (7).
The limited validation performed by Farmer supports the basic technical
integrity of the rigorous model. It should not be considered as verifica-
tion of the simplified model with the added codisposal factor. Furthermore,
the validity of the model for predicting emissions from complex, multicom-
ponent waste mixtures has not been tested.
The computational procedure for the Farmer model is as follows:
1. From field measurements or a given value, calculate A, the land-
fill surface area.
2. Calculate the saturation vapor concentration.
cs = P1m/rt
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TABLE 3-1. FARMER MODEL FOR VOLATILE ORGANIC EMISSIONS FROM
COVERED LANDFILLS
Bas is:
Emission rate is assumed to be mass transfer controlled by
diffusion of gases through the air-filled soil pores.
Form:
E. = K D. C A
i D i s
(P )
a
10/3
(ptr
1 \/Wi
2 \ L A W
P M
i i
RT
P = 1
C P,
P, = P„
a c
Symbol/Parameter Definition
Symbol
A Surface area of the landfill (cn^)
Precision Input Parameter
+0.1% File data or
direct measure-
ment
Soil bulk density (g/cnio)
Cg Saturation vapor concentration (g/m^)
_+8% Varies from 1 to
2 g/cc. Need
direct measure-
ment for accuracy.
.05% Calculated from
gas law and
species vapor
pressure.
(Continued)
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TABLE 3-1. FARMER MODEL FOR VOLATILE ORGANIC EMISSIONS FROM
COVERED LANDFILLS (Continued)
D- Diffusion coefficient of the species of +5%
i.air . 2/ \ ~
interest in air (cm /sec)
Mi
Mass emission rate (g/sec)
Codisposal factor. Use 1.0 for isolated +_10%
toxic waste disposal and 6.0 for toxic -21
waste codisposed with biologically de-
gradable wastes.
Depth of soil cover (cm) _^17%
Molecular weight of the species (g/mole)
Air-filled porosity (dimensionless) +30%
Vapor pressure of the species in interest 5%
(mm Hg)
Soil particle density (g/cm )
Soil porosity (dimensionless)
Density of water (g/cm )
+ 8%
+ 13%
+ 2%
Calculated value
from literature
or ratio to a
compound with a
known D by
molecular weight.
Literature
Gas constant 62,300
mm Hg - cm'
°K - mole
File data or
measurement
Literature
Calculated
Literature or
direct measure-
ment .
Recommends 2.65
g/cm3 for most
mineral material.
Can be estimated
based on soil bulk
density and soil
particle density.
L iterature
Given
(Cont inued)
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TABLE 3-1. FARMER MODEL FOR VOLATILE ORGANIC EMISSIONS FROM
COVERED LANDFILLS (Continued)
WL/y Weight fraction of the species of +20% Direct measure-
interest in the disposed waste (gig) ment.
W ,/W Weight fraction of water in the soil cover +5% Direct measure-
w ~~
ment.
T Temperature (°K) +_1°K Direct measure-
ment .
9 Volume fraction of water in the soil +_17% Direct measure-
cover (g/g) ment.
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3. Calculate soil porosity.
Pt = 1 - B/Ps
4. Calculate volume fraction water in soil.
e = (ww/w)(b/pw)
5. Calculate mass emission rate of component i,
(Pa)10/3 / 1 \ / W-
E- = Kn D C„ A —1-
1 ° s (Pt)2 \LA«.
6. Calculate total emissions.
N
Et = Z Ei
i=l
In practice, it is often not practical to calculate individual compo-
nent emissions in order to estimate total emissions. In such cases, an
estimate of total emissions may be made by summing the emissions estimated
for several classes of compounds using a representative individual component
for each class.
.... «
The selection of a representative individual component is somewhat
arbitrary. Some compounds are more likely to be encountered than others,
and compounds in the mid-molecular weight ranges (4-8 carbons) are likely to
dominate in frequency of occurrence. Therefore, at this time, the following
classes find compounds have been selected as representative for making emis-
sions estimates:
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cogpoajmow
Class Compound
Paraffins Hexane
Olefins Butene
Aromatics Toluene
Halogenated hydrocarbons Methylene chloride
Oxygenated hydrocarbons Acetone
Key properties of some compounds are found in Table 5-1 of Section 5.
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SECTION 4
SOURCES OF PHYSICAL PROPERTY DATA
Physical property data for air, water, and some chemical species are
available in various literature sources. Where data are not available, it
is possible to use methods to estimate the properties. Properties required
for the models discussed in this report are listed in Table 4-1.
4.1 GASEOUS DIFFUSION COEFFICIENTS
A recommended equation for estimating the diffusivity of a nonpolar
specie"i" in air is the method of Fuller, Schettler, and Giddings (8):
-3 1-75 r, w ,1/2
10 T »V"ai.r»MiMai.r'
"i.air " P[(Ev)l'3 «¦ (Zv)1'3] 2
air
where, P = pressure, (atm)
T = temperature, (°K)
= molecular weight of "i"
Ma^r = molecular weight of air
v = diffusion volume increments for components of species "i1
molecular structure tabulated in Table 4-2.
20-1
Errors are in the range of 5 to 10%.
For a polar specie, the method of Brokaw is recommended (6):
-3 3/2 l("irtlair'/MiMairl1/2
D. . = 1.858x10 T o
i.air P a: . fL
i,air D
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TABLE 4-1. PHYSICAL PROPERTIES REQUIRED FOR EMISSIONS ESTIMATE MODELS
a£r Diffusivity of compound i in air (cm /sec)
2,
D- Diffusivity of compound i in water (cm /sec)
1 • W
y Viscosity of air (cp)
O
1^ Viscosity of water (cp)
Pg Density of air (g/cm )
pw Density of water (g/cm )
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TABLE 4-2. ATOMIC DIFFUSION VOLUMES FOR NON-POLAR DIFFUSIVITY
ESTIMATES
Structural Increment Diffusion Volume Increment, v
C 16.5
H 1.98
0 5.48
N 5.69
CI 19.5
S 17.0
Aromatic ring -20.2
Heterocyclic ring -20.2
Source: Adapted from Reference 8,
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RADflAN
where, P = pressure (atm)
T = temperature (°K)
0- • = characteristic length (A°)
1 I a ir
^ = dimensionless collision integral
and ^ are calculated from additional equations as follows:
D =
+
c
+
T* expDT* expFT* expHT*
where, T* = kT/ i>air
k = Boltzman's constant
T = temperature, °K
,1/2
+
(0.19)6 .
i ,air
T*
= (£ • E • )
'i,air v i' air'
+
6- = 1.94 x 103 Vi ,-/VKl-T
= 1.18k (1 + 1.36?)Tbi
l rpi' bi bi
Vi • = dipole moment, debyes
P >1
n
Vbi = liquid molar volume at boiling point, cm /g-mol
Tbi = normal boiling point, °K
1.585V . \ 1/3
a, = I b>1
1+1.36^
l.air
A
*
B
C
D
(0i °air>
1.06036
0.15610
0.19300
0.47635
1/2
E
F
G
H
1.03587
1.52996
1.76474
3.89411
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A discussion of these equations and terms and sources of values for
various terms for some compounds are given in Reference 8.
4.2 LIQUID DIFFUSION COEFFICIENTS
The diffusion coeffient in water at infinite dilution can be estimated
from the Wilke-Chang method (8) which when expressed specifically for a specie
O —g Q £
D. = 50.6xl0~ TU\i V * )
iw w i
where, D = diffusion coefficient of i in water at infinite dilution,
L'w ( 2/ ^
(cm /sec)
= viscosity of water at temperature of interest, (cp)
V. = mol^l volume of solute at its normal boiling point,
(cm /g-mole)
T = temperature (°K)
Diffusion in multicomponent mixtures can be approximated by taking the
molal average value of the diffusion coefficient of i in each of the
possible binary combinations in the system (9). The molal volume of a solute
can be estimated from the following equation (8): V^ = 0.285 Vc ^'04-8
where = the critical volume of specie "i" (cm /g-mol). Values of
Vc are available in various literature sources.
Values of aqueous phase diffusion coefficients for various compounds
are given in Section 5.
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4.3 VISCOSITY
Viscosities of air and water are readily available from handbooks (10).
In Section 5, Table 5-2 presents the viscosity of air and Table 5-4 the
viscosity of water as functions of temperature.
4.4 DENSITY
Densities of air and water are readily available from handbooks (10).
In Section 5, Table 5-3 presents the density of air and Table 5-5 the
density of water as functions of temperature.
4.5 HENRY'S LAW CONSTANT
Henry's law constant is central to expressing the vapor-liquid
equilibrium relationship between the liquid and gaseous phases. This
relationship is:
Pi = Hi Ci
wherej = partial pressure of specie "i" in the air
C^ = concentration of specie "i" in the water
= Henry's law constant
Compilations of Henry's law constant for various materials are avail-
able in literature sources. Values for selected compounds are given in
Table 5-1 of Section 5 along with other properties. In the absence of
experimentally determined values, methods exist for estimating Henry's law
constants by calculation (9).
The calculational method is based on the foregoing equation written as:
H (m^-atm/g-mole) = 18x10"^ Y Pv
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where, Y = the liquid phase activity coefficient, and is the pure
component vapor pressure.
Y can be estimated as a function of molecular properties as discussed
in Reference 9. Another method of estimating is :
"i ' Pi/Si,sat
whe
re Si sat = max solubility in water at system temperature.
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SECTION 5
TABULATIONS OF DATA FOR USE IN EMISSION'S MODEL CALCULATIONS
This section presents constants, conversion factors, and property data
to be used in the emission models. The following tables are included:
• Table 5-1 Property Data for Use in Emissions Estimates of
Selected Organic Compounds
• Table 5-2 Viscosity of Air at Various Temperatures
• Table 5-3 Density of Air at Various Temperatures
• Table 5-4 Viscosity of Water at Various Temperatures
• Table 5-5 Density of Water at Various Temperatures
• Table 5-6 Units Conversion Factors
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TABLE 5-1.
PROPERTY DATA FOR USE LN EMISSIONS ESTIMATES OF SELECTED ORGANIC COMPOUNDS3
Compound
Solub i1j t y
Molecular Normal Vapor Henry1* Law in IUO
CAS Weight Boiling Pt . Pressure @ 25*C Conalant 0 @ 25"C
Number (HW^ (Tfa i)f *C (P^, D>m II g
Liquid
Ho 1 a 1 Volume
a t No rma1 B.P.
Diffuaivity Diffuaivity
in Air
0 2 5 *C
in WaIe r
0 25*C
- , - -- - , -
-------
TAliM:) 5-l • (Continued)
Compound
Mo 1 ecu 1 a r
Norma I
Vapor
SolubiI it y
llenry'a Law in ll70
CAS
Humbe r
Weight Boiling PL. Prefigure (? 25*C Constant $ 25#C 0 2?C
(HW-) (T^ •), *C Hlin •tm-m /do 1 (mg/t)
Oiffuaivity Diffueivity
(V
Llqu id
Ho 1 a I Vo 1 time
at No rma 1 B . P .
b,i>' cm it-
in Air
g 25'C
(D
J I
in Uaier
£ 25*C
l,alr> -tDi}w)
'/eec 10 cm/se
NJ
UJ
Epichlorohydrin 106-89-8 92.5 116.5
Ethy1 benzene 100-41-4 106.2 136,2
Methyl acetate 79-20-9 74.08 57
Methyl chloride 74-87-3 50 -24,2
(Chlo rome th ane)
Naphthalene 91-20-3 81 218
n-Propyl benzene 103-65-1 120 159.2
Propylene oxide 75-56-9 58.08 34.3
Styreiiu 100-42-5 104. 16 145.2
1,1,2,2-Tetrachloroethane 79-34-5 168 146.2
Tet rach loroethy 1 ene 1 27-18 — 4 166 12]
Toluene 108-88-3 92 110.6
1,1,1-Trichloroethane 71-55-6 133 74.1
Trichloroethylene 79-01-6 131 87
Vinyl chloride 75-01-4 62.5 -13.4
Vinylidene chloride 75-35-4 97 37
(1,1-Dichloroethylene)
o-Xylene 95-47-6 J06 137-140
ta-Xylene 108-38-3 106 139
£-Xylene 106-42-3 106 138
18.8
1 .27
5(20)
6.7(30)
3.8 x 10
4.2
26.8
1 17**
71.6
344(20*)
630. 1
2.77
3.20
3.15
4.8 x 10
2.8 X 10
-2
6.64 i 10
4.92 x 10**
5.92 x 10"
-3
1.5 x 10
5.27 x 10
2.55 x 10
2.51 x 10
60,000
4,000
30
3,000
100
515
9 50
1 ,100
1 75
141.6
84.3
50. 6
156.0
166.0
68. 1
108. 5
118.7
95.2
61.6
89.0
J 39. 7
142.4
143.6
0.086
0.075
0. 1 26
0.0622
0.079
0.0794
0.0875
0.090
0.0628
0.98
0.76
0.65
0.893
0.60
0.79
0.877
0.88
0 .9 '< 5
1.04
Blanka indicate that data were not found In readily available sourcoa.
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TABLE 5-2. VISCOSITY OF AIR AT VARIOUS TEMPERATURES AT PRESSURE = 1 ATM
Temperature, °C
Viscosity, cp
38
0.0185
27
0.0181
16
0.0178
4
0.0170
Source: Reference 10.
TABLE 5-3. DENSITY OF AIR AT VARIOUS
TEMPERATURES AT PRESSURE - 1 ATM
Temperature, °C
Density3 g/L
40
1.1034
30
1.1507
20
1.1981
10
1.2454
0
1.2928
aFarm Reference 10 at 0°C. Other values calculated from ideal gas law
absolute temperature ratio dependence.
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TABLE 5-4. VISCOSITY OF WATER AT VARIOUS TEMPERATURES AT
PRESSURE = 1 ATM
Temperature, °C Viscosity, cp
38
0.73
32
0.82
27
0.90
21
1.02
16
1.13
10
1.27
4
1.40
Source: Reference 10
TABLE 5-5. DENSITY OF WATER AT VARIOUS TEMPERATURES AT
PRESSURE - 1 ATM
O
Temperature, °C Density g/cm
40
0.9922
35
0.9941
30
0.9957
25
0.9971
20
0.9982
15
0.9991
10
0.9997
Source: Reference 10
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TABLE 5-6. UNITS CONVERSION FACTORS
To Convert From:
To:
Multiply By:
liter (L)
meter (m )
grams (g)
pounds (lb)
foot (ft)
meter (m)
foot (ft)
centimeter (
cm)
foot3 (ft3)
centimeter (
cm)
lb/ft3
g/cm3
Btu/hour
horsepower*
f t-lb/sec
horsepower*
Ergs/sec
horsepower*
Kilowatts
horsepower*
watts
horsepower*
lb/ft-sec
cent ipo ises
(cp)
g/cm-sec (poise)
centipoises
(cp)
lb/ft2-hr
g/cm^-s
mm Hg
atmospheres
(atm)
1 x 10"3
2.2046 x 10
-1
-3
3.048 x
30.48
2.832 x
10
10
1.6017 x 10
-2
3.933
1.818
1.341
1.341
1.341
1.488
1 x 10
1.3566
1.3158
10"
10
10
-3
-10
x 10
-3
10-
10
10
-4
-3
Temperature Conversion
°C = 5/9 (°F - 32)
°K = 273.15 + °C
Constants
acceleration of gravity (g)
32.17 ft/sec^
9.807 x 10^ cm/sec^
*Mechanical horsepower, equal to 550 ft-lb/sec
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SECTION 6
REFERENCES
1. Wetherold, R.G. and D.A. DuBose. A Review of Selected Theoretical
Models for Estimating and Describing Atmospheric Emissions from Waste
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