&EPA
United States
Environmental Protection
Agency
Office of Air Quality
Planning and Standards
Research Triangle Park NC 27711
EPA-450/3-84-020
December 198
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EPA-450/3-84-020
Evaluation and Selection of Models for
Estimating Air Emissions from Hazardous
Waste Treatment, Storage, and Disposal
Facilities
Prepared by
GCA/Technologv Division of GCA Corporation
Under EPA Contract No. 68-02-31 63
U.S. Environmental Protection Agency
Region V,
230 So.:;;
Chic^o. \-::
Prepared for
U.S ENVIRONMENTAL PROTECTION AGENCY
Office of Air Quality Planning and Standards
Emission Standards and Engineering Division
Research Triangle Park, North Carolina 27711
December 1984
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US. Environmental Pretsetion Agency
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ABSTRACT
Mathematical models describing the release rate of volatile air emissions
from hazardous waste treatment, storage and disposal facilities were compiled
and reviewed. Mathematical modeling techniques which predict volatile air
emissions release rates from landfills, landfarms, surface impoundments,
storage tanks, wastewater treatment processes, and drum handling and storage
facilities were assessed. Existing field test validation efforts were also
reviewed .
Tne purpose of tr.is report is to provide a source of current information
available on tiis subject area. A guidance manual of practice_will ultimately
be prepared to assist regulatory engineers and others in applying the
recommendec models. Since many new papers in this area are continually being
-^olisnea, tnis selection of modeling techniques may be considered present
state-of-the-art as of spring 1983. Field validation scheduled to be
condactec in 1933 and l^o-i unaer EPA and private directives should provide
additional information regarding model precision.
111
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SPECIAL NOTE
A Draft Final Report (October 1932) and a Revised Draft Final Report
(May 1983) previously developed for this project were prepared and furnished
to U.S. Environmental Protection Agency, Office of Solid Waste and Eraergencv
Response (OSWER), Land Disposal Branch under Contract No. 68-02-3168
•Technical Service Area 3, Assignment No. 77). Ms. Alice C. Gagnon served a?
L?A Project Officer and Dr. Seong T. Hwang of EPA/OS'^ER served as Task Office;
for tnese efforts. On December 23, 1933, hazardous waste treatment, storage,
ana disposal facility (T5DF) area source emissions regulatory development was
:r? isrerrec from "S.s'^R to tne ">ffice of Air Quality Planning and Standards
,OAO?S). T-iis Final HeDor: was prepared under the direction of E?A/OAQ?£ Tas-
orricer Ken: 2. riustvedt in partial fulfillment of Contract No. 68-01-5871,
Assisn^en- No. 37.
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CONTENTS
Ill
Abstract vii
Tables I'.'.'.".'.".!! V1xi
Acknowledgment
1
1. Introduction 1
Background and Purpose
Project Scope and Technical Approach ^
Tecnnical Introduction
2. Summary and Conclusions
Introduction ...
Availability and Selection of Mass Transfer
Coefficients >'k-Values) • ^"
Selection of Most Appropriate AERR Models ^
Waste Treatment Processes .,7
Open Tank with Mixing . . • • J
Waste Piles (Particulate Emissions) ^
3. AERR Model Validation Efforts Reported in the Literature ... ^
Introduction , ^
AERR Model Comparison with Field Data ^
Additional Data Available w^
u. Review of Surface Impoundment AERR Models "^
Introduction ",,
Nonaerated Surface Impoundments 7"
o -*
Aerated Impoundments
5. Review of Landfill AERR Models . . . • _~
Introduction '.^
Fanner, et al. (1978) for Covered Landfills -
Shen's (1980) Modification of Farmer's Equation = <•
Thibodeaux's (1980, 1981) Landfill Equations ^
Shen's (1980) Open Dump Equation *7
6. Review of Land Treatment AERR Models
Introduction
Thibodeaux-Hwang: Modeling Air Emissions from
Landfarming of Petroleum Wastes (1982) ^
Hartley Model •
7. Storage Tank Air Emission Estimation Techniques ^
Introduction '
Fixed Roof Tanks "
External and Internal Floating Roof Tanks
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.-. D o e ". z i c e s
Rererer.ces
"~l~ *'-a.~~0r' o: Currie '•'•-- -Oli Correlation for Effective
- 11 f j s i v i c v
CONTENTS (continued)
Other Storage Tank Models 105
Special Considerations
8. Air Emission Estimation Techniques for Wastewater Treatment
Processes ..-
Introduction ! ! ! " 113
Open Tank System-No Mixing [
Open Tank-Mixing: Biological Treatment Systems
9. Air Emissions from Drum Storage and Handling Facilities .... 140
Introduction ,/Q
Description of Drum Storage and Handling Facilities ... 140
Source of Volatile Air Emissions 141
Literature Survev ,/T
••••»•••»•»»•., i. -» 1
Otner Considerations j,^
lu. Particulate Emissions Estimation Techniques for Waste Piles . . 143
Introduction - -
AP-42 Emission Factor Equation for Storage Piles 145
MR! Emission Factor Equations for Storase Piles 145
VI
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5 KL correlations versus wind speed for benzene at 25 C .
6 Comparison of Hartley and Thibodeaux-Hwang Landfarming AERR
models with measured air emissions data
FIGURES
Number
1 Non-turbulent two-layer model of mass transfer 4
2 Controlling layer for diffusion losses from different TSDFs . . 5
3 Interface problems investigated by respective researchers for
treatment and disposal AERR models 7
4 Dependence of coefficient of diffusion on porosity log (D/Dg)
versus log • ^
7 Typical fixed roof storage tank ................ 9^
8 Typical external floating roof storage tank .... ...... 100
9 Noncontact internal floating roof storage tank ......... 102
10 Contact internal floating roof storage tank .......... 102
11 Model of activated sludge system ... * ........... 121
12 Map of Thornthwaite1 s Precipitation-Evaporation Index values
for state climatic divisions ................. l^7
vii
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TABLES
Number
Page
1 Mass Transfer Coefficients (k's) Available in the Literature
Applicable to Modeling TSDF Air Emission Rates 12
2 Liquid-Phase Mass Transfer Coefficient Correlations for Wind
and Flow Turbulence
*****••••••••«• 18
3 Gas Phase Mass Transfer Coefficient Correlations 24
4 AZRR Models for Surface Impoundments 29
5 AERR Models for Landfills 7,
5 Waste Treatment Processes
1 AERR Model Validation Efforts 41
8 Input Parameters Required for Each Surface Impoundment Model . 47
9 Mackay and Leinonen Unsteady-State Predictive Model for
Nonaerated Surface Impoundments 53
10 Thibodeaux, Parker and Heck Steady-State Prediccive Model
for Nonaerated Surface Impoundment 55
11 Summary of Empirical Relationships to Determine the
Individual Liquid and Gas Phase Mass Transfer Coefficients
for a Nonaerated Impoundment 56
12 Hwang's (1932) Simplification of the Empirical Liquid and Gas
Phase Mass Transfer Coefficients for a Nonaerated Impoundment 59
13 Summary of Techniques Developed by Smith, Bomberger and
Haynes to Estimate the Volatilization Rate Constant (fcc)
for High, Low and Intermediate Volatility Compounds . T . . . 61
14 Smith, Bomberger and Haynes First Order Kinetic Equation for
Nonaerated Surface Impoundments m t->
vin
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TABLES (continued)
Number
15 McCord's Steady-State Predictive Model for Nonaerated Surface
Impoundments ................... ..... 65
16 K-Values for Aerated Sis Proposed by Thibodeaux, Parker
and Heck .......................... 66
17 Turbulent Areas and Volumes for Surface Agitators ....... 69
18 McCord's Steady-State Predictive Model for Aerated Sis .... 70
19 Review of Available AERR Landfill Models ........... 73
20 Input Parameters Required for Each Landfill Model in
Table 5-1 .......................... 75
21 Typical Parameter Values and Ranges for the Farmer Landfill
Model as Modified by Shen .................. 82
22 Input Parameters Required for Each Land Treatment AERR Model
86
23 Typical Parameter Values and Ranges for the Thibodeaux-Hwang
Treatment AERR Model .................... 87
24 Input Parameters Required for Recommended Fixed and Floating
Roof Models ......................... 93
25 Recommended Model for Fixed-Roof Tank Breathing Losses .... 9c
26 Recommended Model for Fixed-Roof Tank Working Losses ..... 97
27 Typical Ranges of Input Parameters for Fixed-Roof Tank
Breathing Loss Model ....................
28 Typical Ranges of Input Parameters for Fixed-Roof Tank
Working Loss Model .....................
98
29 EPA/API Recommended Technique for Standing Storage Losses
from External Floating Roof Tanks .............. 103
30 EPA/API Recommended Technique for Withdrawal Loss from
External Floating Roof Tanks ................ 106
IX
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TABLES (continued)
Number Page
31 Typical Range of Input Parameters for Withdrawal Loss from
External Floating Roof Storage Tank Model .......... 107
32 Typical Range of Input Parameters for External Floating Roof
Tank Standing Storage Loss Model .............. 108
33 Input Data for 1962 API Floating Roof Model .......... 110
34 Floating Roof Equations Based on 1978 Pilot Tests ....... Ill
35 Simplified List of Input Parameters Required for Each
Activated Sludge Biological Treatment Model ......... 116
36 Hwang (1980) Activated Sludge Treatment Process AERR Model. . . 122
37 Solution Method for Freeman's Activated Sludge Surface
Aeration AERR Model ..................... 129
33 Application of Various AS AERR Models ............. 136
39 Examples of Routine and Accidental Spill Situations at a Drum
Storage and Handling Facility ................
40 Accidental Spill Fractions for Various Treatment Technologies . 143
41 Storage Pile Particulate Emission Factor Equations Developed
bv MRI ......... ' .................. 143
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ACKNOWLEDGEMENT
This Final Report incorporates comments received from the technical peer
review relative to GCA's selection and judgement of models most appropriate
for evaluating AERR from TSDFs. Dr. Seong T. Hwang, the EPA/OSW Task Officer,
performed technical review of the first and second peer review drafts and
provided valuable insights which are incorporated herein. Additional
technical review and assistance were received from the following: Dr. Charles
Springer, University of Arkansas; Dr. Thomas R. Marrero, University of
Missouri; Dr. John Williams, Northeastern University, Dr. C. Kleinstreuer,
Rensselear Polytechnic Institute; Dr. Donald Mackay, University of Toronto;
and Chemical Manufacturers Association Secondary Emissions Work Group.
Comments have also been received from representatives of other EPA offices:
IERL, MERL, and OAQPS.
The authors wish to thank the following contributors from GCA: Dr. David
Cogley who provided valuable insight relative to vapor diffusion through
soils; Mr. Ron Bell who provided the storage tank summary and other research
efforts; and Mr. Thomas Nunno who provided assistance in review of AERR models
applicable to wastewater treatment systems.
XI
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SECTION 1
INTRODUCTION
BACKGROUND AND PURPOSE
Under contract with EPA's Office of Solid Waste (OSW), GCA reviewed and
evaluated availa-ble mathematical models describing the release rate (i.e. mass
flux) of volatile air emissions from hazardous waste treatment, storage and
disposal facilities (TSDFs). Air emission release rate (AERR) models judged
most suitable for estimating air emissions from TSDFs are identified herein
along with the rationale for each model selection. Other models available in
the technical literature are also described with an indication of their
limitations.
The purpose of this raport is to provide a source of information for all
air emissions release rate models available in the literature. Information
contained in this report incorporates comments made by the peer review group
in January 1983, and the EPA Task Officer. Since AERR models for TSDFs are
continually undergoing development and refinement, and since little field
validation data are available, this document presents the best available
models as of early 1S83.
PROJECT SCOPE AND TECHNICAL APPROACH
Technical efforts were initially limited to an evaluation of existing
AERR models reported in the cechnical literature. A computer-assisted
literature search generated 30 references that appeared suitable for review.
Additional references became evident as the initial 30 technical articles were
evaluated. Telephone surveys were performed to solicit additional information
from EPA personnel, active researchers, other EPA contractors, and trade
associations such as the American Petroleum Institute and the Chemical
Manufacturers Association. A list of the technical references reviewed ror
this report appears in Appendix A.
On OSW's request, AERR models were investigated for the following TSDF
categories:
• Landfills;
• Landfarms (land treatment);
• Surface impoundments;
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• Storage tanks;
• Drum handling and storage;
• Treatment units;
• Waste piles (particulate emissions only).*
Treatment units were segregated at the suggestion of OSW into three generic
types: (1) open tanks with quiescent surface conditions; (2) open tanks with
mixing; and (3) closed-loop treatment units. This approach was developed in
order to reduce the large number of treatment unit processes into a manageable
size for analysis.
No models were found to describe air emissions from drum handling and
storage facilities, although estimates of air emissions can be performed for
known spill quantities using appropriate techniques described later in this
report. GCA developed a general aporoach to describe the potential air
emissions based on estimates of the fractional loss due to accidental spills.
Some effort was devoted to developing criteria for selecting AERR models
most suitable to fulfilling EPA objectives for AERR estimations, and to
provide a uniform basis for comparing different models. These efforts were
terminated when it became apparent that only a limited number of models were
available, and many models had serious limitations. In some cases, only one
model was available to describe a particular type of TSDF. Consequently, the
following basic criteria were used for model selection:
• Emission release phenomenon actually occurring at a TSDF must be
accurately described by the models;
• Input data must be readily obtainable by an Agency engineer either
through published literature or calculation techniques-easily
understood;
• Models must be suitable for use by entry level regulatory engineers
with appropriate guidance through a manual.
Section 2 presents the AERR modeling approaches recommended by GCA based
on the review and evaluation of current research. Rationale for each
selection are also identified. Sections 4 through 8 discuss all AERR models
available for each TSDF-type, indicating deficiencies and the rationale for
not recommending certain models. The status of AERR Model validation efforts
via laboratory and field measurements is provided in Section 3.
*A11 other models address volatile air emissions,
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Section 9 presents the general approach developed by GCA to describe
for drum torage and handling facilities. Section 10 describes methods or
quantifying particulate emissions from storage piles. The remainder of this
introductory section provides a cursory review of the technical background and
discusses tte mass transfer principles that form the basis for virtually all
AERR models.
TECHNICAL INTRODUCTION
Background
Air emissions of volatile hazardous compounds from TSDFs can enter the
atmosphere in two ways: (1) as the result of forced bulk motion on a
macroscopic scale; or (2) as the result of diffusion on a molecular or
turbulent scale. Examples of forced motion include:
• vapor losses during filling of a storage tank;
« vapor movement in a tank or landfill cell due to pressure gradients
created by changes in atmospheric pressure;
convection
due to biogenic gas production in landfills.
i-~ 0-,-Sc;~«s -es> forced motions described above do not depend on
the volatility'of'the Compound; all molecules simply partake in the
macroscopic scale gas motion.
Diffusion of volatile air emissions from a TSDF can generally be thought
of in terms of escape of material through multiple layers, with the last layer
being the lower atmosphere. For example, as illustrated in Figure 1
nonturbulent diffusive transport in a lagoon proceeds through four sta.es
starting with the bulk liquid, to a laminar liquid layer f ^e jquid
surface and then through a similar laminar air layer, and finally, into tn_
atmospnire. The rate oi transfer (diffusion) through all layers combine*,
determines the release rate to the atmosphere. This transfer rate is
expressed in terms of the mass transfer coefficient, as will be Ascribed
later. A compound's volatility, characterized by its solubility, partial
oressure Henry's law constant and diffusivity, provides an indication of the
quanti"' of material in the gas phase which will be subjected to the transfer
process! Additionally, turbulence in any of the layers can significantly
increase the transfer rate.
Generally, transfer rates in one or perhaps two of several layers will be
so low (due to the high resistance in these layers) that these layers will
con rol the overall atmospheric emission release rate. In the example given
for a lagoon, the laminar air or liquid phase (or both for some compounds)
will control the overall transfer rate.
Similarly, in discussing volatile liquids in landfills, it is possible to
describe the process as one of diffusion from bulk waste, through a ««.d
soil region, through dry soil and into a laminar air layer. However, for an>
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BULK GAS
INTERFACE
LAMINAR GAS LAYER
LAMINAR LIQUID^LAYER_
(DIRECTION OF
MASS TRANSFER)
BULK LIQUID
Figure 1. Nonturluilent two-layer model of mass transfer.
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significant burial depth, diffusion of vapors through the overburden of dry
soil will be the most significant factor because the transfer coefficient in
soil will be small. Figure ? shows the probable controlling layer or layers
for different TSUFs.
For an open landfill, precisely which layer will control the overall
release rate will depend on the specific compound of interest and whether, for
example, compounds placed initially on the surface have seeped deeply into the
soil.
SOIL LIQUID AIR
LAGOON X X
BURIAL (LANDFILL) X X
LAND FARM X X X
SPILL ON xa X
IMPERMEABLE
SURFACE
SURFACE DUMP X x
STORAGE TA.NKS xa X
aLiquid phase controlling for dilute aqueous or hydrocarbon
mixture s.
' Figure 2. Controlling layer for diffusion losses from different TSDFs.
All state-of-the-art AERR models reviewed were based on mass
transfer principles. Whenever the concentration of a chemical or compound
varies between two regions there is a natural tendency for mass to be
transferred across the interface, and approach equilibrium within the system.
Each AERR model reviewed was based on the following relationship which
describes diffusion transport across a series of different layers:
Mass flux » (overall mass transfer coefficient) (driving force);
where: " "
Mass flux = net quantity of material transferred across a unit area
normal to the surface in a given unit of time (i.e., grains of
a chemical transferred across one square centimeter of an
air-liquid interface in one second);
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Overall mass transfer coefficient (K) * overall rate of chemical transfer.
The reciprocal of the overall K value* is equal to the sum of
the reciprocals of individual k-values for each region.
Changes in state (liquid-gas) modify this relationship
slightly as described below. The reciprocal of the K-value
is thus defined as the overall resistance to diffusion. The
overall mass transfer coefficient represents the extent of
contribution to mass transfer in each region which the
chemical must pass through;
Driving force * the differences in chemical potential (i.e., chemical
concentration) of the compounds of interest on each side of
the boundary between two regions.
The choice of the most accurate model to represent AERR at TSDFs reduces
to the problem of finding the "best" individual mass transfer coefficient, k,
in each of the regions (soil, liquid, air). The overall mass transfer will, ir.
turn, have a coefficient in the form of a series resistance, — =
K is the overall transfer rate, and ij_ is the equilibrium concentration
ratio in each boundary layer relative to the layer below. For example, at a
liquid-gas interface, ^^ is essentially the Henry's Law constant (Hj_)
divided by the gas constant R and absolute temperature T. For many compounds,
tij_ has been experimentally determined, or can be calculated from other
chemical properties (vapor pressure and solubility).
General Discussion of Available Models
Figure 3 shows for each major reference article investigated during this
study the interface or layer which was considered by the respective
researcheds). In Figure 3, note that an "x" to one side of a specific
interface indicates that side was considered implicitly to be controlling the
overall transfer rate. Figure 3 also shows which forced motions, if any, were
treated by various authors.
The substantial difference between each available model is the method
employed to calculate the individual mass transfer coefficients (k-values).
However, there are also differences in basic assumptions between models. In
some cases, assumptions inherent to certain models do not accurately reflect
the physical phenomenon responsible for air emissions from TSDFs.
Some authors make assumptions which are inappropriate for our purposes as
to which region controls. For example, McCord (1981) bases his approach to
non-aerated lagoons on the theory of water evaporation, where the evaporation
rate of water is gas phase controlled. However, for most .volatile compounds,
*In this report, a capital letter K refers to the overall mass transfer
coefficient and a lower case k refers to the individual phase mass transfer
coefficients.
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Re ferenrr
F,.,,.-.I r m 11 sinus Soil - AM li<|.n.l -
! iqnid - Air Other Interface
2.
10.
11.
1?.
11.
Mackav i Leinonm
FSf>T'7S
Thibndeanx
Parker & Hn l<
AIChK'fll
Smith, Romht^ryer
& Haynes
FST'80
Smith, Bornh.'ryi-r
& Haynes,
ShPn,
JAPCA, 'fi?
Hwang
Rnv. Prop.'H!'
ThihoHeaux,
Hwang
Rnv.
McCord
Haz. Waste Conf . 'Rl
Hartley
Pesticide, ' «><»
Shen,
APCA'SO
S(eenhnis,
BubenRer 6 Converse,
ASAF, ' It
Thibodeaiix,
J. Haz. Mat . '81
Farmer, Yanp, ,
Letey, 1978, 19HO
Liquid -
Surf ,irt,int
Ai r
Figure 3. Interface problems investigated by respecttve researchers for treatment and disposal
AERR models. (A complete list of releirnces is provided In Appendix A.)
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Inl ri I irr Pn>hl«-in5a
Oo
Referem
Fon-fd Kimssions Soil - Ail li«|ui<
- Air Other Interface
14. Thibodeaux
Springer fc Ri l«>v, 1181
IS. tin & Slat.-i ,
Nature* 74
If.. Hackay,
Hat. Assess. »l
Cheat. '81
17. Owens, Edwards,
Ctbbs, Int. .).
Air, Water Pol I.'64
18. Neely, Dou Chemical,
1976
19. Dilling, Tt-lert i I ler,
Katloi
EST'75
70. Dilling
EST'77
71. Hackay & Yum
Water Pol lournal
Canada'80
22. Arnold
Trans of Am. lust.
Chen., 1<>4<.
21. Cohen, Cociliio, M.nKav
EST'78
24. Hackay, MarmiKH
Canadian Journal'71
2V Hackay. WolkoK, ' 71
26. Thibodeaux, Springer
lledden & I..,miry, I9H?
denotes tlie nulhors i nt ri i>f i'l «i i '"> ••* winch phase(s) r.iniKil the ovn.ill Ir.inslcr i«te.
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especially
surface.
in air,
ground.
sssts s
appropriaCe when wastes are plowed or percolate into the
is
ion by Sutton
. Diffusion in air-filled spaces within
aily n the laboratory. Although laboratory-developed correlations
Ascribing k-values are available for both aerated and unaerated surfaces, no
extensiv^data presently exists that places adequate confidence on
extrapolating these correlations to field conditions.
The next section summarizes GCA' s preliminary model selections for each
TSDF category. Later sections provide a more complete literature review
describing each available model in more detail.
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SECTION 2
SUMMARY AND CONCLUSIONS
INTRODUCTION
The mechanisms causing air emissions of volatile compounds from TSDFs
were briefly described in the introduction. The basis for quantifying air
emission release rates (AERR) begins with an accurate description of diffusion
across different regions in a TSDF; i.e., the diffusive transport of air
emissions across soil, liquid and/or air layers.
Diffusive transport can be quantified by determining the mass transfer
coefficient ("k-value") for each region encountered by the potential air
emission. Selecting tne most appropriate AERR model for TSDFs reduces to a
problem of selecting the nose accurate and manageable k-value. Once the best
technique for determining k-values is established for each type of diffusive
transport occurring, the model that most accurately describes the physical
situation at a TSDF can be selected.
This section summarizes techniques available in the literature for
determining individual k-values*, and presents GCA's recommendations for AERR
models based upon our selected k-values. When applicable, recommended model
approaches are presented. Later sections of the report discuss models in more
detail.
It should be noted that the majority of the k-value correlations
presented in this report have not undergone substantial field test validation
or verification. For the most part, k-values were developed from laboratory
experimentation and some limited field studies. Therefore, caution is advised
when applying these correlations to calculate expected emission release
rates. 'Although limited field validation has been performed recently, the
accuracy of all emission release rate models is still unknown..
*In this report, a lower-case letter k refers to the individual mass transfer
coefficients for each region; an upper-case K refers to the overall mass
transfer coefficient obtained from the individual k-values.
10
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AVAILABILITY AND SELECTION OF MASS TRANSFER COEFFICIENTS (k-VALUES)
Several researchers have developed empirical relationships to describe
the mass transfer of contaminants from individual regions or phases, i.e.,
through soil, liquid and air. These mass transfer coefficients can be
categorized according to their applicability to TSDFs as follows:
• Soil (kfinit)—describes molecular diffusion in porous media; i.e.,
landfarms and landfills;
• LiguidCkiinuidl—^) molecular mass transfer (diffusion) within a
stagnant liquid; (b) turbulent diffusion from the surface of a
liquid (impoundment) affected by wind; and (c) turbulent diffusion
enhanced by mechanical aeration;
• Gas Ugas)"(a) turbulent diffusion influenced by wind, and (b)
turbulent diffusion enhanced by mechanical aeration.
Table 1 presents the individual mass transfer coefficients available fro™
the literature reviewed by GCA for each region. When more than one technique
for determining the k-value was available in the literature, GCA s
recommendation of the most appropriate k-value is noted with an asterisk ( ).
Only one technique was available for quantifying the individual liquid and gas
phase k-values for agitatea conditions. Likewise, simplification tecnniques
found in the literature are not shown in Table 1, since these techniques
Provide methods to simplify the calculational effort involved, and do not
represent different approaches to determining k-values. The simplification
techniques are presented later in this report.
The following discussions review in detail all available k-value
relationships shown in Table 1, and describe the theoretical basxs used by GCA
in selecting the most appropriate equation for AERR estimates.
Soil-Phase Mass Transfer Coefficient (kgnj_L»_ksl
Vapor diffusion through air filled pore spaces in soil is a complex
phenomenon which is not amenable to a purely theoretical treatment. To obtain
an effective diffusion coefficient for a particular soil at a known moisture
content, the problem requires that empirical correlations for vapor diffusion
in porous media be evaluated to see if they adequately reflect the many
experimental observations which are available. GCA has reviewed these
correlations for simple systems such as dry sands and for some more complex
systems such as platey minerals and soils of known moisture content. With
presently available data, it should be possible to provide first order
estimates of effective diffusion coefficients. GCA's evaluation of these data
is summarized below.
In order to model AERR from landfills and landfarms, vapor movement
within the soil must be accurately defined. Farmer et al. (1978) and
Thibodeaux (1981a) have both defined the "effective" diffusion coefficient
within soil as a function of the volatile components molecular diffusivity
and the physical characteristics of the respective soil.
11
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TABLE 1. MASSS TRANSFER COKI'KIOIENTS (k's) AVAILABLE IN THE LITERATURE APPLICABLE TO
MODELING TSDF AIK K.MISSION RATES (SEE TEXT FOR TERM DEFINITIONS)
Tranaf.'r phafte
Tranafi'r i od I n i fin ( V
I. Soil (k .,. k >
• R-'l I »
r.irm.-i I I'"H)
on wi»rh hv Millin«fon *i^ Onirh
ibio|t thf> rff«*clK of (toil w*t«r
-n.itiM «
c. Turbulent
Di f f IIY i nn~-
Ai*rat inn
Effect!
1. C.i (k . k,.)
— M'' <:
a. Turbulent
Di ffuiton—
Wind Effecti
Turbulent
Di f f tiflion—
Aerat inn Effects
JU'OUHI (I.II
" |(,S.04
| —•:;:
'" <•> no'1) / n,- ii o
„•-) -- l—.~-'-
\ "2' "?
O.OIHIl') -o
M I'-''-'IM >~"'7' | r ,-r-
riui....i.>.iMx r
Hi, t-.iv -in.l H.il i.i.-u ( It/
ih,>i!> ,nit ,m.i ".ut-.T ' i !!
.tm !l.,ih.. k (|Hfi>i
"' '""•"•I' Il'i77». is
|.i.-s. ni...l h. llu^,^ (|
R«9rH nn FicV'i fir^t lau; of limited
useful n.»st in TSHF nroh|p«<.
Ha^^i) on lahorarnrv wind wavtf tank sru.li
fnr hyilrocarhon v.»l at 1 1 1 tut i«n from aqu.
*-.->lut ton*. 1 ah stiitliea MAV not fullv
r^nr^^enf a*, tttnl «-nvi rrtnm^nt^t c.>n va|«**« for kv ,t< fum
of wind >(M*r<1).
Hrtf^lop^d frow th^'tr^t left I, tf^pf r i«**nt al
.iitil fi**lit «*.rat
rites friMi fli>win* ^tr^anit.
fro«
ftanerf on work of ftuttnn, an4 f
•».-nr« on (h«- -•vrtporacinn of nr
anrf wat^r into air*
na^rci on firia •ravumvnr* fro* thr
rv/tporatinn of water into (h* air.
• RaarH on preliatfnarv *xp*rlMntal inveati-
ftnt ion* for 1 iquiri spheric*! droplet «
f tected into a ga* phaae.
*D«>notpft *:<™A'S rrc(M>»endai jnn.
-------
Pore diffusion, as related to the soil matrix, occurs by the Pick
diffusion mechanism. Within the soil matrix, the effective area for transport
is less than that for uniform pore structures because the diffusion paths are
irregularly shaped channels. Increases in soil moisture will reduce the
air-filled porosity and at the same time increase the diffusion path length.
Therefore, the mass flux for soil-phase diffusion needs to be described in
terms of an "effective" diffusion coefficient which is less than the molecular
diffusion coefficient and dependent upon variables influencing the diffusing
vapor; i.e., moisture content.
The effective diffusion coefficient presented by Farmer (1978) was
formulated from theoretical soil hydraulic conductivity studies of Millington
and Quirk (1961). Based on a theoretical derivation, Millington and. Quirk
presented the following correlation for the effective vapor diffusion
coefficient:
D£ Ea10/3
D~ = ~2
o £.,.
where- D = effective diffusion coefficient in soil;
e
D = air diffusion coefficient;
o
- = air-filled porosity;
"a
f = total porosity.
For dry soil, when ea = eT» this expression reduces to the following:
D , .,,
e _ F 1. 33
= £
D
However, an additional literature review of vapor diffusion in porous media
conducted by GCA indicates that the Millington and Quirk correlation is
limited to a specific soil type. Further, the Millington and Quirk analysis
cannot be of general applicability to the diffusion problem when pores of
different sizes are present. In diffusion, flux is proportional to pore
radius squared. In hydraulic flow, flux is proportional to pore radius to the
fourth power.
In one particularly relevant study, Currie (i960) conducted hydrogen
diffusion experiments with 15 different types of dry porous media and
concluded that the primary influences on the De/Do ratio were porosity,
and particle shape. Differences in particle shape affect the diffusion path.
Therefore, the effective diffusion coefficient in porous media is a function
of internal geometry and porosity.
The empirical equation proposed by Currie was of the form:
D
_e
D
13
-------
where Y and y are constants for a specific type of porous material. Figure 4
is a log-log plot of T)e/r>0 versus e developed by Currie. Figure 4 shows
that the set of data points for a given material lie on a straight line, hut
the slope of the line (value of u) varies with each type of material. The
following values of M were determined from the data on dry soils:
Soil Type
Solid grains (i.e., sand)
Soil crumbs
Kaolin (a type of clay)
Platey minerals (mica, vermiculite)
The value of v has been found to range from 0.8 to 1.0 for the materials
tested. Thus, an equation with two empirical constants (Y and u) is available
to describe the affect of soil porosity (e) on the effective diffusion
coefficient (De) for vapors in dry soil.
Limited data are available for describing the effect of moisture content
on the effective diffusion coefficient in wet soils. Currie (1961) examined
the effect of moisture on some granular materials, and his data fit the
following empirical eauation:
D
e m Y /e \^-~ /£ \c
D~ T a
o
where: e7 = total porosity;
€ a = air-filled porosity;
- =" 4 for granular materials subjected to moisture testing.
This correlation is obtained by combining Currie's dry soil and wet soil
correlations. The complete derivation is provided in Appendix B.
Currie's empirical formula relating De to soil parameters accounts for
experimental observations for all soils tested. The formula allows one to
define De at any specified moisture content provided that the required
parameters can be experimentally evaluated. Taylor (1949), Rolston and Brown
(1976), Lai et al. (1976), and Ball et al. (1981), also present data for
vetted granular soils. Unfortunately clay materials (clayey soils) of the
sort expected to be employed for landfill caps have not been tested.
Although it appears that Currie's work provides a solid empirical base
and adequate general theoretical interpretation for the effect of particle
shape and moisture content on De, there are questions concerning the direct
application of Currie's results to estimation of volatile organic emissions
from landfills. The unsteady state hydrogen diffusion experimentations may
14
-------
-0.8
Loqfc
-0.6 -04
•0.2
i
l
-0.2
-0.4
o
O
-0.6
-0.8
-1.0
O Glass spheres
D Sand
• Carborundum
V Sodium chloride
<8 Barnfield soil crumbs
O Wpburn soil crumbs
e Highfield soil crumbs
A Pumice
A Kaolin (Suprex)
A Kaolin (Peerless No. 2)
4- Celite
X Steel wool
D Perspex flakes
v Verrniculite
v Mica
Figure 4. Dependence of coefficient of diffusion on porosity
log (D/DQ) versus log e (from Currie (I960)).
15
-------
not fully represent a hazardous waste landfill situation since hydrogen is a
small, non-polar molecular structure compared to organics which are more
bulky, and in some cases are polar. In addition, organic vapors are likely to
sorb to the organic material present in most soils.
However, data on vapor diffusion in porous media presented in the
literature indicates that determination of effective diffusion coefficient is
soil-type dependent. At present, GCA suggests that field validation efforts
include an analysis of landfill cap material (i.e., soil type, moisture) such
that kso^i may be properly quantified. Additional laboratory experimentation
for wet soils, especially clays, may provide an improved data base.
Liquid-Phase Mass Transfer Coefficient (ki iqujd, kL)
The transfer of a chemical compound within a liquid medium was identified
in Taole 1 for three specific cases; i.e., (1) molecular diffusion within a
stagnant liquid with no wind and no flow effects; (2) diffusion within the
liquid-phase enhanced by cne turbulence caused by wind; and (3) diffusion
within tne liquid-phase enhanced by the turbulence created by mechanical
aeracion. Figure 5 snows tne relationship of the six liquid-phase mass
transfer coefficient correlations presented in the literature as a function of
wina speed. Liquid pnase k-values applicable to TSDFs are highlighted.
Molecular Diffusion — kj_ for No Wind Conditions —
The first case of liquid diffusion has limited applicability to TSDFs,
out is provided for illustrative purposes in Figure 5. This mass transfer
coefficient becomes necessary for the case of open tank storage of a
multicomponent waste, where wind effects are eliminated by a large freeboard.
The situation of no wind is not too unusual for open areas during evening
hours, typically when water temperatures are higher then the surrounding air.
Most mass transfer correlations reviewed incorporate wind speed as a
parameter, nowever, it is likely that emissions release will continue under
low or no wind conditions due to turoulence created by thermal agitation.
Tnioodeaux, et al. (19d2Dj present a method for determining tne mass transfer
coefficients in both phases (liquid and gasJ by use of the Chilton-Colburn
analogy. This analogy permits the evaluation of the mass transfer coefficient
tnrougn the information obtained from the heat transfer phenomenon.
Figure 5 snows that the mass transfer coefficient calculated from this
analogy is greater than tnat predicted by correlations using wind as a
parameter, specifically for the case of low wind speeds (i.e., less than
3 meters per second).
Turbulent Diffusion from Wind and Flow Effects —
In the case of turbulent diffusion, where turbulence is influenced by
variations in wind speed, several researchers have conducted- experiments in
order to develop empirical expressions for determining the liquid-phase mass
transfer coefficient. The results of these correlations are shown in Table 2.
16
-------
0.01
o.ooi
o
o
0.0001
0.00001
O
PICKS LAW - £ (h - 1.0 cm)
(NO WIND, NO FLOW, QUIESCENT STATE)
THIBODEAUX (1982)
(NO WIND, NO FLOW, THERMAL
AGITATION)
MACKAY PLOT OF COHEN AND OTHER
DATA (1981)
(WIND EFFECTS, NO FLOW)
i.e., SURFACE IMPOUNDMENT
OWENS, et al. (1964)-(WITH H = £ f
(WIND AND FLOW EFFECTS)
i.e., TREATMENT SYSTEM
LISS & SLATER (1974)
(OCEAN MOVEMENT)
THIBODEAUX (1979)-(J = 3-0;
POWR = 32.5, a = 0.714;
V = 11 ,970; a = 0.82)
(AERATED LAGOON)
•-'WILL FIND APPLICATION IN TSDF
'©
I
Figure 5,
10 20 30
WIND SPEED, m/S
Ki correlations versus wind speed for
benzene at 25°C.
17
-------
TABLE ?. LIQUID-PHASE MASS TUANSI'KK COEFFICIENT COKKKI.ATIONS FOR WIND AND FLOW TURBULENCE
O.l1)1)
H| k « (U.4 Re SI ('"I ..... .
for O.I I Kf vl()7, UIIIMI' k is in nn/hr ami
— - , is " ~
u e»|><™.fi/ll(0 " )
If R« ^0.11, then k( - '.'.'. tin/In
where:
Hr 3 louphnesa Rcynolils mimluT (dimpns ionles s )
U " wind velocity dm/s) mi-/isiireil «t helphe ?1() il>"V.' e h.
wal tf r aurf ace ( t in)
^ " air klm'B.itic vistosity (cm /sec)
Oo
"i.H.n
k, - (1.1 Ke"
k \-s in Ib mol/f t'-ln
He - riiiiKhn>-» Kryiinlds niimhrr (delernined us .i
i
O. - .liffuitrin cn.'l I ir ient ol rompounrf i in u.il^r ( c in' /sec- )
I ,11,.'*
0_ ....... » JiffiKinn coef f ir irnt ol toluene in water (rm /»iv)
TIIL ( Hi)
(cont inue
-------
TANLE 1 (emit i
Hal k, - Z/.S (I.(.Ml) •'" I."'"' H'"-" (°—' tduardS- ClbbS>
k i .s in c in /11 r
1 = temperature, "C
II - mt>.in velocity ol stream (ft/sec)
II = mean depth of stream (ft)
(valid tor the following .-x|.r rt menl (! .0./41) (I II
(tor fast (lowing or .hallow streams ul.eic II - 0.1-I.K. an,l II ' I).4-2.A)
/ D \
-2(J„('.(,; -0.8i / i.llll \ (Hwang, 1982)
where:
k ' 1.12(1.
(ji( o.t,;H -o.8i / D.,»_,i' 1
oo I T:
\ °2-«^
k is in Ib-tnol/fl -lir
• = temperature ("O
U - surface velocity, ft/sec, normally 0.03-) x wind speed (ft/sec)
" lor natural surfate, and 0.1 ft/sec for outside region
of effect ol aeratois in biological treatment.
H - one-half the effective depth of surfaie impoundment (ft)
o
D * ditlusion coellieient of oxygen in water (rm /sec)
- diffusion coefficient of compound i in water (cm /»ec)
(cout i imed)
-------
c
-------
Ihe first correlation presented in Table 2 wjs developed from laboratory
wind wave tank studies by Cohen, et al. (1978). Cohen et al. developed their
equation for benzene and toluene and indicated kL dependence on wind speed
for velocities between 3 and 10 ra/s (6.7 to 22.4 mph). Below 3 m/s, kL was
influenced by subsurface agitation, while at wind speeds above 10 m/s, kL
increased was due to the presence of spray, bubble entrainment and white
capping. Cohen expressed concern over the direct application of this
correlation to environmental conditions because laboratory tests cannot
accurately predict conditions of fully developed flow. That is, the width of
Cohen's experimental unit may not simulate a larger surface impoundment at a
TSDF.
In applying this correlation to different chemical species, one can refer
to three mass transfer theories stated in the literature:
• Stagnant film tneory;
• Penetration or surface renewal theories; and
• Boundary layer theory.
Tne first case identifies kL as a linear function of diffusivity. However,
other theories of mass transfer, namely, those mentioned above in the second
case, identify tnis dependency to the 0.5 power. The third theory is
generally considered a compromised approacn and identifies the diffusivity
dependency to the two-thirds power. The exact dependence of k^ on
diffusivity remains to be estaolished.
The second equation shown in Table 2 is a reworking of Cohen's
correlation presented by Hwang (1982). The remodeled correlation simply
expresses kL in different units (lb-mol/ft2-hr). Hwang also suggests a
linear dependency to diffusivity.
Equations (3a) and (3b) presented in Table 2 are based on reaeration
stream studies discussed by Owens et al. (1964). Unlike the wind velocity-
dependency analyzed by Cohen, Owens correlations show k^ dependent on stream
velocity and water depth.
Althougn Owens expression suggests hydraulic effects influence k^,
which is in agreement with theoretical models, the direct application of
stream coefficients to surface impoundments is questionable since the degree
of turbulence offered by a flowing stream is much greater than wind induced
turbulence. Thus, Hwang (1982) provides a modification to Owen's correlation
to define the surface velocity of water as a function of wind speed
(Equation (4) in Table 2). This modification is a more accurate
representation of surface impoundment or treatment basin surface actions.
Both correlations also show that k^ is dependent upon water depth for a
flowing system. Note that Hwang's modification also reflects a change in kL
units (Ib-moi/ft2-hr).
21
-------
Mackay (1981) critically reviewed the existing data base for kL
determinations, which included laboratory tank experiments and field
measurements in lakes. Mackay1s data base included the laboratory studies of
Cohen, et al. (1978), Liss and Slater (1974), Kanwisher (1963), and Deacon
(1977). Field studies of Broecker and Peng (1974), Emerson (1975) and
Schwartzenbach, et al. (1974) were also mentioned. Mackay presented what he
considered-as reasonable values of !CL for environmental and laboratory
conditions as a function of wind speed (correlation (5) in Table 2). The data
presented in Table 2 are for benzene at 20°C. As stated by Mackay, it appears
the best correlating approach for estimating k^ for different chemical
species under similar conditions is to use the square root of the diffusivity
ratio. Mackay also mentions that there are theoretical reasons suggesting
that the ratio of Schmidt numbers to the power -0.5 is the best correcting
ratio for both solute diffusivity and temperature. However, he grants no
judgment on this statement.
The turbulent 'KL correlation selected should be based on the degree to
which water is flowing through the system. For nonflow systems, i.e., wind
induced flow, kL as presented by Mackay (1981) appears most appropriate
since he compiled data from several researchers. Selecting the Mackay data,
or rather the plot of Mackay's data, avoids the calculation of a roughness
Reynolds number.
For flowing systems, tr.e correlation presented by Hwang (19S2) based or.
the work of Owens (1964) seems most appropriate. .Whereas, Owens turbulent
k^ is dependent upon the stream velocity, Hwang's approach considers the
effect of the water's surface velocity, which is a function of wind speed.
For large impoundments of water where the mean water velocity may be quite
low, it is the upper surface layer of water directly affected by wind that
will affect ^ the most.
It can be concluded from data presented in the literature, and from
theories of mass transfer, that the liquid phase mass transfer coefficient
depends somewhat on diffusivity. However, the magnitude of this dependency is
not precisely defined by existing research. The mass-transfer coefficient
will be proportional to a power of the molecular diffusivity between 0.5 to
1.0, where the lower number represents conditions of high turbulence and the
higher number represents near stagnant conditions.
Springer (1983) noted that one aspect of ongoing work at the University
of Arkansas involves developing a correlation which etrploys a dimensionless
ratio of fetch to depth. The correlation will be shown to fit data from
earlier stream reaeration studies as well as recent experimental work,
including the "reasonable values" presented by Mackay (1981).
Turbulent Diffusion from Mechanical Mixing—
The third case of liquid phase mass transfer involves turbulent diffusion
created by mechanical aeration. Considerable research has been conducted on
scale models and prototype mechanically agitated water surfaces to determine
the absorption rate of oxygen. Since oxygen absorption is liquid-phase
22
-------
controlling, the reported values can be transformed to yield a liquid-phase
mass transfer coefficient under agitated conditions. The following
relationship is the only correlation appearing within the literature:
6 -20, x / 6, i 4-, "„" i
. _ J(POWR)(1.024) (a)(10 )l g_ I (Thibodeaux, 1978)
kL " 165.04(av)(V) ~
where: kL is in Ib-mol/ft^-hr;
J = oxygen-transfer rating of mechanical aerator (3 Ib 02/hr-hp);
POWR = total power input to aerators (hp)-rated hp x efficiency
(0.65-0.9) ;
6 = temperature (°C);
a = oxygen-transfer correction factor (0.8-0.85);
a = surface area per unit volume of surface impoundment (ft );
V = volume of surface impoundment in region of effect of aerators
Cft3);
D. = diffusion coefficient of compound i in water (cm /sec);
D = diffusion coefficent of oxygen in water (cm2/sec).
°2'H2°
Gas-Phase Mass Transfer Coefficients (kgas) kp)
The final mass transfer region that all chemical compounds must encounter
is diffusion within the gas phase. As illustrated in Table 1, two cases of
gas-phase mass transfer must be considered; i.e., (1) turbulent diffusion
influenced by wind speed, and (2) turbulent diffusion created by mechanical
aeration.
Turbulent Diffusion from Wind Effects
A review of the literature revealed two correlations developed from
experimental field measurements for determining the influence of wind speed on
the gas-phase k-value. These relationships appear in Table 3.
The correlation proposed by Mackay and Matsugu (1973) was developed from
experiments on the evaporation of isopropyl benzene (cumene), gasoline and
water into air. Their research showed that the work of Button (1953), who
assumed that the wind velocity profile follows a power law, could be used to
quantify the rate of evaporation from a smooth liquid surface, and
subsequently obtain an expression for the gas-phase mass transfer
coefficient. The final result of Mackay and Matsugu's research provided the
correlation shown in Table 3 as a function of wind speed and the effective
diameter of the liquid surface.
23
-------
TABLE 3. CAS i'HASK MASS TRANSFER COKI-KICIKNT CORRUGATIONS
[1] k, . - 0.0292 I)0'78 X "0-U Sc °'67 (Mackay, Mataugu, 1973)
u
where: k_ is in m/lir
I*
U • wind speed, m/hr
X " effective pool diameter, m
S " gas Schmidt number (d imenu ionless) , ( a lc u 1 alnl from:
S = u /p D.
c g g i, air
where tig is the absolute viscosity of the gas (g/cm sec), P., is
the density of the gas (g/cm^), and l»i>alr is the moleculai
dittusivity of compound i in air (cur /si-i ) .
121 k - 0 03 I -L?H _ v A"°-us (Harbeck, 1962; as presented
11 "-"J V8 " by Thibodeaux and Parker, 1974)
where: k_ " individual .gas pliase mass transfer coef f icicut
(Ib-mol/ft -hr)
D. , " molecular diffusivity of compound i in air (tin /sec)
i (• E r
D n . " molecular diffusivity of water vapor in air (era /sec)
'o^»^ ^r"
"g = wind velocity measured at 8m above the w.iter surface (miles per hour)
A " surface area of the impoundment (acres)
-------
Hwang (1982) modified the Mackay /MatsuRu correlation to reflect a change
in kr units Ub-mol/ft2-hr). The modification alters the equation
constant to 0.0958 and includes multiplying by the ratio of air s density to
its molecular weight.
The results provided by Harbeck (1962), shown as Equation (2) in
Table 3 were developed entirely on water evaporation measurements from
reservoirs. Theoretically, since water evaporation is gas-phase controlling,
these measurements can provide a measure of the gas-phase mass transfer
coefficient. However, the results obtained by Mackay and Matsugu not only
describe the evaporation of water, but also provide good correlation to the
work of Sutton. Therefore, the selected k-value for the gas-phase (influenced
by wind) is that shown by Mackay and Matsugu.
Turbulent Diffusion from Mechanical Mixing— ^K,,ienr
The literature provided limited information to describe the turbulent
diffusion of a chemical within the gas-phase as a function of mechanical
aeration. However, through limited experimental observations and additional
investigations by Reinhardt (1977), an empirical expression has been developed
to approximate the gas-phase mass transfer coefficient under aerated
conditions. This relationship appears below:
i.air ( }1.42 }-0. 21( } 0. 4( }0. 5 (Reinhardt,
d Re Fr P Sc 19?? as
given by
Hwang, 1982)
where :
kG is in Ib/ft2-hr;
2? = density of the gas (lb/ft3);
D- „,,. = diffusion coefficient of compound i in air (ft /hr) ;
1- ) 3 a. L
d = diameter of aerator turbine or impeller (ft);
(NRe) = gas Reynolds number = Pgd2^/Mg;
- = rotational speed of turbine impeller (rad/sec) ;
ug « absolute gas viscosity (g/cm-sec);
(NFr) * Froude number * d2u/g;
g - gravitational constant (32.17 ft/sec2);
(Np) - power number = Prg/PLd5w3;
Pr * power to the impeller (f t-lbf /sec) ',
25
-------
= density of the liquid (lb/ft3);
" gas Schmidt number = yg/PgDi,air»
Note: (NSH) a Sherwood number - (^-G^^Og^LtaiT atw* therefore;
(NSh) - 0.00039 (NRe)l-42(Np)0.4(Nsc)0.5/(NFBr)0.21
Overall Mass Transfer Coefficient (K-Value)
As described previously, correlations for determining the individual mass
transfer coefficients for the soil, liquid and/or gas-phases have been
developed by several researchers. However, as shown previously in Figure 2,
there are seldom instances where only one phase occurs for a particular TSDF.
Commonly, the mass transfer coefficients for two or more phases must be
calculated to determine the overall mass transfer coefficient (K-value).
The two-phase resistance theory is used to describe transfer within
multiphase systens. The theory describes the relationship between an overall
mass transfer coefficient (K-value) and the individual soil, liquid and/or gas
phase mass transfer coefficients (k-values) identified previously in this
section. Specifically, the reciprocals of the individual mass transfer
coefficients are summed and combined wich the equilibrium concentration
(described by the Henry's Law constant—Hj_) established at either the liquid
or gas interphases, thus describing the overall resistance (1/K) for the
multiphase case. For example, the overall diffusion of a given contaminant
from a lagoon requires the mass transfer of that contaminant through the bulk
of the liquid (k]_j_qui(j) and through the air above the liquid (kgas) . In
terms of the two-phase resistance theory, this multiphase phenomenon can be
described as follows:
1 RT ^as \
K k k H. i C I
liquid gas i \ liquid /
where: K = overall liquid-phase mass transfer coef ficie>nt ;
(Hwang, 1982)
^liquid = individual liquid-phase mass transfer coefficient;
kgas = individual gas-phase mass transfer coefficient;
Hi * Henry's Law constant for compound i in atm-tn^/gmol;
RT - 0.024 atm-m3/gmol (@ 298°K);
Cgas> cliquid z molar densities of the gas and liquid, respectively.
However, one phase frequently dominates the overall mass transfer (or
resistance, 1/K) and therefore controls the rate of mass transfer. The
determining factor for this occurrence has been theoretically and
experimentally found to be dependent upon the value of H^. For example, if
HJ_ is large (more than 10~3), the liquid-phase resistance (l/k]_iqui.cl)
often controls, whereas if Hj_ is small (less than 2 x 10"^), the gas-phase
resistance (1/kgas^ often controls.
26
-------
Special Case for Overall K-Value
For the case of agitated conditions (specifically aerated impoundments),
two distinct zones occur at the liquid surface: (1) turbulent, and (2)
natural (convectLve). To describe this phenomenon using the two-phase
resistance theory, it is necessary to determine the overall mass transfer
coefficient for each distinct zone and sum these values, proportioned to the
affected area of each zone. This can be described as follows:
and
1 _ 1 + _
K (n) k(n) (
L liquid
1 l + -
„ v t,) k i
N K . . .
L liquid
RT
gas i
RT
(k(t))(H.)
gas i
/ c
/ gas
c
\ liquid
(C ^
gas
c
liquid ;
where :
where: KT^n) = overall liquid-phase mass transfer coefficient for the
natural zone ;
K
(t)
overall liquid-phase mass transfer coefficient for the
turbulent zone;
K = area-averaged overall liquid-phase mass transfer
coefficient ;
A = effective surface area of the natural zone;
n
A = effective surface area of the turbulent zone;
A = total surface area of the surface impoundment.
In order to calculate the overall mass transfer coefficient, the
individual k-values for liquid and gas phases must be in similar units. Hwang
(1982) has provided the following conversion method:
lb^nol\_. /cmv Pm (30.48)2
" L Ur/ MW 454
27
-------
where: p = density of mixture (g/cm ) (» 1 for water);
m
MW = molecular weight of mixture (= 18 for water);
re
p . - density of air (Ib/ft );
MW . = molecular weight of air.
SELECTION OF MOST APPROPRIATE AERR MODELS
Once the appropriate mass transfer coefficients are selected, the model
which most accurately reflects the actual emission release phenomena at TSDFs
can be selected. The following paragraphs identify models selected for each
TSDF-type, based on the previous discussion of k-value selection. A more
detailed discussion of each model appears later in this report:.
Surface Impoundment (SI) Model Selection
SI AERR models are required for four typical scenarios encountered in the
field; i.e., steady-state conditions with and without mechanical aeration, ar.d
unsteady-state conditions with and without mechanical aeration. AERR models
for the cases of mechanical and diffused aeration with biological activity are
treated separately in Section 8. Table 4 summarizes the available models
found in the literature and indicates the scenario(s) for which each model is
applicable. GCA's recommended models are footnoted.
Several SI models shown in Table 4 were eliminated from consideration
because they did not completely describe the theoretical conditions
encountered in the field. Specifically, McCord (1981), Smith, et al (1980
and 1981), and Mackay and Wolkoff (1973), were dismissed 'from further
consideration, as described in Table 4.
Shen (1982) modified the original Thibodeaux, Parker and Heck (I981d)
nonaerated, steady-state model by incorporating; (1) the kL relationship
presented by Owens, et al (1964) which is more applicable to flowing streams
(not stagnant surface impoundments), and (2) the most appropriate kg
relationship (in GCA's opinion as described earlier). Shen also suggests a
simplification technique for calculating the Schmidt number based upon the
compound's molecular weight. This simplification technique is described
further in Section 4 of the report.
The Thibodeaux, Parker and Heck (I981d) approach appears most appropriate
for estimating AERR from nonaerated Sis under steady-state conditions i.e.,
fairly continuous inflow of contaminants. For unsteady state nonaerated Sis,
where the contaminant is discharged to the SI as a slug, or pulse injection,
the Mackay and Leinonen (1975) approach appears most appropriate. Section 4
of this report elaborates on each SI model summarized herein.
28
-------
TABLE 4. AERR MODELS FOR SURFACE IMPOUNDMENTS
Model
Applicability
Primary reason
for recommending
or not recommending
Mackay and Wolkoff (1973)
McCord U9rfU
Smith, et ai (1980-31;
Thibodeaux, Parker and
(1961a;a
bnen
Nonaerated
Unsteady state
Macicay and Leinonen (1975;a Nonaerated
Unsteady state
Aerated
Nonaerated
Steady state
Nonaerated
Steady state
Aerated
Nonaerated
Steady state
Nonaerated
Steady state
Not based on two-film
resistance theory
Only unsteady state model
based on two-film
resistance theory
Only considers gas-
phase resistance.
Most chemical compounds
are liquid-phase controlled
Based on two-film
resistance tneory, but
requires complex labora-
tory experiments.
Based on two-film
resistance theory -
recommended for steady-
state conditions
Modified Thibodeaux, Parker
and Heck (1981d) model.
Simplification technique
for Schmidt number is
provided, and kQ value
used is recommended
aDenotes recommended models.
29
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For aerated Sis, only two equations are available. McCord (1981) based
his model on evaporation of water to address diffusion of volatile compounds.
However, the evaporation of water is gas-phase controlling, whereas
volatilization of most chemical compounds is liquid-phase controlling. This
inaccuracy was also noted for McCord1s nonaerated SI model. Only the
Thibodeaux, Parker and Heck (1981d) model accurately describes the aerated SI
in terms of the two-film resistance theory. Thus, Thibodeaux, Parker and Heck
(1981d) is recommended for both aerated and nonaerated Sis under steady state
conditions.
The Mackay and Leinonen (1975) unsteady-state model may also be
applicable to an aerated impoundment. This statement is justifiable by
recalling that the Thibodeaux, Parker and Heck (1981d) model is applicable to
both a nonaerated and aerated SI, and is similar in form. The only difference
is that the aerated impoundment must also consider liquid and gas-phase mass
transfer in the turbulent zone created by mechanical aeration, in addition to
the liquid and gas-phase k-values from the convective (natural.) zone. These
additional considerations can be incorporated into the unsteady-state model,
by using the appropriate overall K-value for both the turbulent and convective
zones.
Landfill Model Selection
Landfill models are required £or two cases: (l) hazardous waste disposal
only, and (2) codisposal of'hazardous waste with solid waste material.
Table 5 summarizes the available models for landfills for no gas generation,
effects of biogas generation, effects of barometric fluctuations and also for
open dumps. GCA1 s recommendations are footnoted.
Limited field validation test data makes the selection of landfill AERR
model difficult at this time. The key to selecting a landfill model is an
accurate description of pore diffusion as it relates to various soil matrices
and moisture contents. As described in the ksoii subsection, tne eirective
diffusivity for pore diffusion may be best described by a power law
relationship to air-filled porosity, which appears to be dependent on soil
type. Limited data for gas diffusion in wet soils complicates a similar power
law relationship.
For now, GCA believes that power law relationship models deserve field
validation. Field testing should include a method of determining the power
law relationship of various soil mixtures and moisture contents which may be
typical of hazardous waste landfill sites.
Accurately determining the effective diffusivity parameter for the AERR
landfill model may only be one of many other potentially major problems to
consider. Other problems include quantifying lateral gas migration, and
adsorption of organic vapors onto soil. Like the effective diffusivity
determination, each of these factors may also be soil specific.
Shen (1980) modified Farmers' original equation, thus introduced some
simplification errors. Shen defined the air emissions of a specific component
30
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TABLE 5. A£RR MODELS FOR LANDFILLS
Model
Applicability
Primary reasons for
recommending or not
recommending
Farmer, et al (1978)a Covered landfills
Shen (1980)
Covered landfills
Thibodeaux (1981a)-
Covered landfills-
with no gas generation
Thibodeaux (1981a)a
Covered landfills-
with biogas generation
Thibodeaux, Covered landfills-
Springer, Riley (19&lb) with barometric
fluctuations
Shen (1981)
Open dump
Experimental data
limited to pure
component
hexachlorobenzene
Simplification of
Fanner's model and
contains over-
simplifications (see
text)
Defines pore
diffusion in terms
of soil porosity
and tortuosity, but
limited for dry,
granular soils
Describes porous
media diffusion with
convective effects
due to biogas
generation
No experimental data
Does not take into
account vertical
structure of the
earth's boundary
layer (Sutton)
Limited to gas
phase diffusion only
aDenotes recommended models.
31
-------
based on its weight percent in the waste mixture. For waste mixtures,
consideration of waste composition on a mole basis and the activity
coefficient is important.
Thibodeaux (198La) also provides a model for codisposal of hazardous
waste with solid waste material to account for the air emissions resulting
from the ascending gases. One may need to correlate the quantity of gases
generated with the type and quantity of material buried and respective soil
properties in order to determine the expected gas velocity. Sufficient data
may exist such that a general correlation can be developed.
Thibodeaux et al. (1981b) also identify air emissions release rate for
landfills which includes the effect of barometric pressure fluctuations.
According to Springer (1983), computer simulation studies have shown that the
effect of barometric pressure fluctuation (pumping) does not average out over
long peri-oas of time, and thus should be considered for annual A£RR
estimates. The effect of internal gas generation also plays an important role
wnen hazaraous waste is codisposed wicn solid waste. The convective effects
created by tne anaerobic gas generation can carry volatile vapors to the soil
surface, tnus increasing the fiux rate.
Open Dump Moaels
Only one equation appeared in tne literature for A£RR fron open dump
sites, proposed by Shen (1981). Shen's equation is not considered accurate
for our purposes because it neglects the vertical structure of the earth's
boundary layer described by the work of Sutton (1953). The starting point for
an appropriate open dump equation should be based on work conducted by
Thibodeaux and Hwang (1982) for landfarming emissions. Assuming solid
material in the open dump that does not intermix or seep into the soil, the
flux rate can be estimated by:
q. = k_.C.X.
Mi Gi i i
where; k^ is tne gas-phase mass transfer coefficient for component i
calculated by the correlation developed by Sutton (1953) and previously
oescrioea unaer kQ subsection; Ci equilibrium vapor concentration of
compound i in g/cm^; and X^ is the mole fraction of compound i in the
waste. Sutton accurately described the gas-phase mass transfer coefficient as
a function ot wina speed, surface roughness, and surface length. For liquid
material in an open dump, the landfarming model described below would be most
appropriate.
Landfarming Model Selection
The selection of an A£RR model for landfarming is relatively
straightforward since only two candidates were found in the literature. The
Hartley (I9b9) model describes A£RR for landfarming operations only as a
surface evaporation problem (i.e., gas phase resistance only). This may be
sufficient for short-term emissions determination following initial spreading,
but for landfarming, where multicomponent waste oil or sludge is generally
32
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incorporated into the soil matrix, one needs to define vapor movement in the
porous soil. In addition, Hartley's evaporation model uses water evaporation
as the basis (reference compound) in determining the AERR for other
compounds. It does not appear correct to compare the rate of evaporation of
volatile compounds to that of water.
The Thibodeaux-Hwang (1982) model correctly identifies the flux rate of a
chemical compound as vapor diffusion through soil medium. The model also
"
accounts for the soil "dry down", the increased — *«•»« "nt"*** £ <£
soil phase. The effect of liquid-phase resistance is considered based on the
assumption that the oil-layer diffusion length is considerably small (i.e. ,
Zn less than soil particle diameter) after the oil waste is incorporated
into the soil. However, one should examine the contribution of liquid-phase
resistance for the initial emission release rates immediately after surface
application where the oil layer thickness may be considerably larger than a
soil particle size.
Although the Thibodeaux-Hwang model most accurately identifies the
soil-phase resistance as a factor in air emissions for landfarming operations,
it does not identify the liquid-phase resistance as probably being most
important, especially for emission rate determination immediately after
application where waste oil may be applied several inches thick. Typically,
waste oil or sludge applied to the soil may contain many organic volatile
compounds. As the liquid diffusion coefficient of a compound is generally
four or five magnitudes smaller than its molecular (gas-phase) diffusion
coefficient, this suggests that the liquid mass transfer coefficient should be
incorporated into the short-term analysis. Assumptions made the
Thibodeaux-Hwang landfarm model include:
• isothermal soil column;
• no vertical liquid movement by capillary action;
• no adsorption by soil particles; and
• no biochemical oxidation.
The use of these assumptions may not be entirely valid for landfarming
operations. Thermal gradients frequently exist in the upper soil layers,
thereby creating the upper movement of heat and water in soil. In addition,
the purpose of landfarming is to employ the microbiological actions of the
upper soil layer to degrade organic material. Thus, biochemical oxidation and
gas generation will influence the air emissions rate.
Very little experimental data are available to verify this model, thus,
factors such as solar radiation effects, gas generation due to biological
activity, and microbiological destruction rates should be quantified when
model verification tests are performed.
33
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Storage Tank Model Selection
Models for storage tanks have long been available through EPA in the
standard air emission estimation handbook, AP-42. Section 7 describes the
state-of-the-art techniques recommended by EPA for fixed-roof and floating
roof tanks. No models were selected for pressure tanks since emissions from
such tanks are not regularly occurring events.
Air emissions from fixed roof tanks occur from breathing losses and
working losses. The best available model for estimating breathing loss
emissions was developed by API (1962) and modified by TRW/EPA (1981). The
TRW/EPA modification was necessary since test results showed the API (1962)
equation over-estimated breathing losses by approximately a factor of four.
The best available model for estimating working loss emissions was developed
by API in 1962. Recent test results show that this model accurately predicts
emiss ions.
The models deemed most applicable to estimating standing storage losses
and withdrawal losses from external floating roof tanks were developed by API
(1980) and modified slightly by EPA (1931). Emissions estimates for internal
floating roof tanks are available in API Publication 2519.
E-nission factor equations in AP-42 are applicable to pure component
liquids. Thus, GCA has provided a method of determining storage tank
emissions for mixtures. In addition, EPA requested that GCA identify
applicable A£RR models for open storage tanks. Details of storage tank AERR
models and these two special cases appear in Section 7.
WASTE TREATMENT PROCESSES
As suggested by OSW, the approach used for properly identifying the
appropriate AERR model for the variety of treatment systems was to categorize
each system into one of three' main topics:
• open tank-no mixing - i.e., no disturbance of air-liquid interface;
• open tank-mixing - i.e., obvious disturbance of air-liquid interface;
• closed system - i.e., no air emissions directly from process during
normal operations.
Table 6 presents each of these categories and lists typical treatment
processes.
34
-------
TABLE 6. WASTE TREATMENT PROCESSES
OPEN TANK-NO MIXING
sedimentation
chlorination
- equalization
- anaerobic treatment
OPEN TANK-MIXING
• Low-rate mixing
- neutralization
• chemical precipitation
flocculation/coagulation
• high-rate mixing
activated sludge process (contact stabilization)
aerated lagoons
ozonation
rotating biological discs
trickling filter
dissolved air flotation
CLOSED TANK SYSTEMS - chemical separation techniques
steam distillation/stripping
extraction
decantation
ion exchange separations
activated carbon systems3
dialysis and electrodialysis
filtration
aPowdered activated carbons can be used in existing tanks, filtration, or
settling equipment (i.e., open tanks).
35
-------
For many treatment processes, some form of reaction, chemical or
biological, will occur within the tank. Assuming steady-state conditions (no
fluctuations in flow or formation of additional chemical compounds) a mass
balance for a specific component can determine the concentration of that
component in the tank. Once the in-tank concentration of the component is
known, air emissions can be estimated by applying one of the surface
impoundment models previously recommended, depending upon whether or not the
tank is agitated. Determining the in-tank concentration of organic compounds,
however, will be related to the following:
• the compound's solubility in water;
• the compound's affinity for the formed sludge, floe, etc., versus
water;
• digestion capability of microbial population within the tank.
Organic compounds removal from wastewater streams by one of the closed
svstems shown in Table 6, is common in che chemical and petrochemical
industries. Aside from system leakage or abnormal operation, there should be
no air emissions from these closed treatment systems. The effluent streams
from these unit operations may go on to further treatment (biological, or
cooling towers and lagoons) or disposal (surface impoundment, or landfarming),
therefore it may be necessary to determine the concentrations of organics in
the respective streams.
Generally, the efficiency of a processing unit (steam stripper, activated
carbon bed, etc.) should be known based on laboratory or pilot scale testing.
However, in the absence of efficiency data, one can calculate a systems
removal efficiency based on chemical engineering principles. For instance,
knowing the design of a stripping tower (i.e. , tray data and flow rates) one
can determine the towers efficiency. Likewise, knowing the absorptive
capacity of carbon for a specific organic compound (generally through
laboratory analysis) and the bed design data, the effluent concentration of
wastewater can be determined.
OPEN TANK WITH MIXING
GCA1s evaluation of open tank treatment processes with mixing focused
mainly on the activated sludge biological treatment process (high rate
mixing). Other processes which might fall into the low rate mixing
subcategory would include neutralization or precipitation process involving
the addition and mixing of a chemical reagent. The emissions from these
processes are best described by application of Thibodeaux's ASI model using
very low power input to identify the area of turbulent mixing. This model is
discussed in detail in Section 4 of this report.
Biological Treatment Systems
Efforts in selecting models for predicting air emission release rates
from activated sludge treatment processes focused on four models given in the
literature:
36
-------
• Thibodeaux (1981d)--Aerated Surface Impoundment (ASI) Model;
• Hwang (1980)—Activated Sludge Surface Aeration (ASSA) Model;
• Freeman (1979)--Activaced Sludge Surface Aeration (ASSA) Model;
• Freeman (1980)—Diffused Air Activated Sludge (DAAS) Model.
All ot the models presented predict the emissions release rate based on
the concentration of compound i (X^> in the aeration basin of the activated
sludge (AS) process. The complexity of the models are generally dependent
upon the information assumed to be unknown. The Thibodeaux U981d) ASI model,
which assumes the concentration X^ is known, is by far the simplest model.
Thibodeaux applies the two-film resistance theory to predict the air stripping
losses due to mass transfer at the air-water interface (aeration basin
surface). Thibodeaux1s model isolates zones for convective and turbulent
mixing and applies appropriate mass transfer expressions for each zone. Thus,
having determined an area-averaged overall mass transfer coefficient (KL; ,
the ASI model applies this to the concentration (Xj_) in the basin to predict
the air emission release rate.
Both the Hwang (1980) and Freeman (1979) ASSA model employ identical mass
transfer expressions to predict emissions from the activated sludge process.
Tnese models differ from tne Tnibodeaux model in that they predict air
emissions based on the influent concentration (So) of the compound
(substrate). The Hwang (1980) ASSA model considers the interaction of;
(1) substrate removal by biodegradation; (2) removal by air stripping; and
(3) adsorption of substrate to the biomass (sludge). Whereas, the Freeman
(1979) ASSA model considers biodegradation and air stripping, but ignores
adsorption of substrate to the biomass. The work of Kincannon (1981,1982),
discussed briefly in Section 8, also indicated that sludge adsorption was not
a major pollutant removal mechanism when biodegradation, air stripping, and
adsorption are considered collectively. However, other studies (Hwang, 1981;
Patterson, 1981) suggest that biosorption removal may be quite significant for
a number of organic priority pollutants. Both ASSA models calculate the
effluent concentration (Se) based upon a steady-state equilibrium reached by
the above competing removal processes. The air emission release rate is then
computed by the ASI mass transfer model.
The different biooxidation rate kinetics equations selected by Hwang and
Freeman lead to major differences in the complexity of each model. Hwang's
ASSA model employs the relatively simple 1st order Grau kinetics to predict
the rate of biooxidation. Freeman selects a biokinetic model developed by
Gerber for refinery wastes, which ties the substrate removal rate to the
biomass concentration, the oxygen concentration, and the substrate
concentration.
Solution of Hwang's model is tedious but workable. In addition, Hwang
has provided biokinetics rate data (values of KI.(S)) for a large number of
organic compounds. Thus, data necessary to develop solutions based on Hwang's
model are reasonably accessible. Conversely, solution of Freeman's model
requires solving three simultaneous nonlinear equations for three unknowns.
37
-------
Hand calculation of the solution is rather cumbersome, thus the solution is
best conducted by a computerized iteration technique. In addition, biokinetic
rate constants for the Geroer Model (3rd order Monod) used by Freeman have
been compiled only for a limited number of compounds (acrylonitrile,
benzene, styrene ). Consequently, application of Freeman's ASSA model
using Gerber kinetics will be limited by this data requirement. In short, the
solution of tne Freeman model is very complex and not well suited to EPA's
intended purposes under this program.
Freeman's (1980) diffused air activated sludge (DAAS) model was the only
model reviewed which adequately models diffused air systems. The DAAS model
is similar to Freeman's ASSA model with the exception of the mass transfer
model for air stripping. In the DAAS model, Freeman predicts the air'
stripping losses based on the mass transfer of the organic compound into the
sparger bubbles as opposed to the surface aeration model which predicts mass
transfer tnrougn the basin surface. Because the DAAS mass transfer model is
slightly more sophisticated than the more empirical surface aeration (ASI)
mass transfer model, Freeman's DAAS is also sligntly more difficult to solve.
Freeman's DAAS model assumes that the mass transfer process is liquid phase
controliea and assumes that transfer occurring at the surface of the basin is
negligible.
Tne cone era in employing these models tor the purpose of predicting air
emission release rates is accuracy. Hwang's ASSA model is based, on limited
laboratory aaa treatment facility data. Efforts to verify tne Hwang model
were only moderately successful. Freeman's diffused air mass transfer model
showed good agreement with verification data based on sterile process
experiments. Freeman's DAAS model has been calibrated to laboratory data,
however, no additional verification has been reported in the literature.
Given the status of model verification presented above, concern, over putting
untested models into general use is warranted.
GCA recommends that the Agency employ the following models for use in air
emission assessments:
• Thioodeaux (1931d) ASI model—for known effluent concentrations;
• Hwang (1980) ASSA model—for unknown effluent concentrations;
• Freeman (1980) DnAS mass transfer model — for known effluent
concentrations;
• Hwang (1930) ASSA model modified after Freeman (1980) DAAS—
for diffused air systems with unknown effluent concentrations.
The Hwang ASSA model is selected over Freeman's model because- the Hwang
model can account for adsorption to wasted sludge, employs simpler bioxidation
kinetics for which rate constant data are available, and is capable of
modeling adsorption of substrate to the biomass. Freeman's DAAS mass transfer
equations are selected for modeling diffused air systems because they are
currently the only reasonable choice. GCA recommends that the DAAS mass
transfer equations be integrated into Hwang's ASSA model for predicting DAAS
38
-------
air emission release rates where the effluent concentration is unknown.
Again, this is recommended to simplify the problem solution and to avoid
costly experiments to determine Gerber's biokinetic rate constants.
WASTE PILES (PART1CULATE EMISSIONS)
EPA requested GCA to survey available information for estimating
particulate emissions from waste storage piles. (Note that all other
information contained in this report pertains to estimating volatile air
emissions). The most approriate approach to estimating waste pile particulate
emissions is the emission factor equations developed from limited field test
data by the Midwest Research Institute (MRI) under contract with EPA. The MRI
correlations have been frequently used by regulatory agencies in estimating
particulate emissions from industrial storage piles (coal, iron ore, gravel,
etc.) and are presented in Section 10 of this report. An emission factor
equation in AP-42 provides a more general approach that does not account for
sice operational procedures.
39
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SECTION 3
AERR MODEL VALIDATION EFFORTS REPORTED IN THE LITERATURE
INTRODUCTION
The AERR models have generally not been validated or calibrated by
comparison with a substantial field data base. Only three test reports or
reference articles reported comparisons between predictive AERR models and
actual field measurements at the end of 1982. Additional reports provided
ambient air monitoring data which cannot be directly applied to the AERR
models without back-calculating the AERR via a dispersion model. However,
some field work aimed at model validation is currently underway
(lERL-Cincinnati with Thibodeaux, et al.) and in the planning stages for 1983
(lERL-Cincinnati with Radian Corooration and OSW - Engineering Science, Inc.).
This section summarizes model validation efforts conducted prior to 1983.
AERR MODEL COMPARISON WITH FIELD DATA
Table 7 lists four reports in which measured AERR were compared with
predictive modeling equations. Test data from the most recent sampling of
surface impoundment air emissions by Thibodeaux, et al. (1982) appear most
promising. Initial comparisons indicate that the predictive model estimates
are within a factor of two to three of the measured emission rate.
Thibodeaux, Parker and Heck (1981d)
The objectives of this report were to develop a measurement technique fo:
volatile organic carbon (VOC) emissions emitted from wastewater treatment
basins and to develon a mathematical model that would predict emission rates.
The concentration-profile (CP) technique was used for determining the flux
rate of methanol, acetone and total hydrocarbon emissions. The following
individual mass transfer correlations were used in the predictive model:
• kff (convective)—Harbeck;
O *.
• kg (turbulent)—Reinhardt;
• k^ (convective)—Cohen;
• k (turbulent)—Thibodeaux, Parker.
40
-------
TABLE 7. AERR MODEL VALIDATION EFFORTS
Test report
Authors (date)
Comparisons made
Measurement of Volatile
Chemical Emissions, from
Wastewater Basins
Evaluation of VOC
Emissions from Waste-
water Systems (Secondary
Emissions) Draft Report
Air Emission Monitoring
of Hazardous Waste
Sites
Suggested Control
Measures to Reduce
Organic Compound
Emissions Associated
with Volatile Organic
Waste Disposal
Thibodeaux, Parker,
Heck (1981d)
Cox, Steinmetz,
Lewis (1982)
Thioodeaux,
Springer, Lunney,
James, Shen (1982)
Ames, Shiroma,
Wang, Lam, O'Brien
(1982)
Development of concentration-
profile technique: comparisons
of measured methanol flux rates
with predictive model
Concentration-profile technique
measurements compared to predic-
tive model for aerated and non-
aerated conditions
Concentration-profile technique
measurements compared to pre-
dictive model for aerated and
nonaerated conditions
Comparisons of measured land-
treatment emission rates with
Hartley and Thibodeaux-Hwang
models
41
-------
Although flux rate measurements were made for methanol, acetone and total
hydrocarbon, only methanol data were used in the predictive model comparison
effort. The authors decided not to use acetone in the comparison because of
uncertain water chemistries at the low concentrations encountered. Chemistry
data with correlation coefficients of less than 0.8 were excluded. The
following flux rate comparisons were reported:
• measured—1.4 to 3.8 ng/cm2-sec (11 to 29 Ib/acre-day);
• predicted—0.37 to 5.9 ng/cm2-Sec (2.8 to 45 Ib/acre-day).
The comparison of all four mass transfer coefficients indicated chat methanol
volatilization is gas-phase controlling.
Cox, Steinraetz and Lewis (1982) - Draft Report
This draft report compares the measured air emissions from two wascewater
treatment facilities to results obtained by using the predictive model. The
CP tecnnique was used to measure chemical flux rates from an aerated and a
nonaerated pond. The following individual mass transfer correlations were
used in the predictive model:
« k., (convective)-~Mackay, Macsugu;
• k, (turbulent)—Reinhardt;
O
• \f-l (convective)—Cohen;
• k^ (turbulent)—Thibodeaux.
A Final Report was not available for review, but the following
preliminary results were noted. Predictive flux rates initially reported
ranged from 15 to 38 percent of measured flux rates for nonaerated conditions,
and from 0.1 to 2.5 percent of measured flux rates for the aerated site.
However, in applying the predictive model equation, the approach used for
calculating the. equilibrium constant was incorrect. The use of Raoult's law
may be only applicable to hydrocarbon mixtures, riot to aqueous solutions.
Henry's law, or the use of an activity coefficient are more correct
approaches. Field data from this report may still be valuable subsequent to
complete peer review and verification of results.
Thibodeaux. et al. (1982)
The work presented in this paper identified the emission rates of two
surface impoundments (one aerated and one non-aerated) at a hazardous waste
facility. Measurements at the site by the CP techniques provided data to
"field test" the emission release rate models for chemicals'in which the mass
transport process is liquid-phase controlled. Additionally, the authors
identified the capability of the CP technique in detecting and quantifying
absorption and vaporization from area source. Comparison of calculated flux
rate versus measured flux rate for 1,1-dichloroethane and benzene were found
to be within a factor of ^2.
42
-------
Ames, et al. (1982)
In an attempt to illustrate the difference between the Hartley and
Thibodeaux-Hwang AERR models for landfarming, this report provided sample
calculations based on experimental data. Figure 6 shows the predictive
results of the two models and also displays the experimental results. The
experimental data were not available to GCA, thus the variables and
assumptions used in the calculations could not be verified.
One limitation of the Hartley model, clearly illustrated in Figure 6, is
the assumption of a maximum emission rate throughout the exposure period. The
Thibodeaux-Hwang model only slightly underpredicts the measured results.
ADDITIONAL DATA AVAILABLE
Additional test reports contain ambient air emissions monitoring data for
hazardous waste facilities. A document prepared by Fred C Hart Associates .
entitled "Development of a Data Base on Air Emissions from Hazardous Waste
Facilities," provided a cursory review of 21 hazardous waste site "ports
received fron, the 10 EPA regions. It is not known if data provided in the
original test reports are adequate for application to the various AERR
models. This data base may need further review.
43
-------
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SECTION 4
REVIEW OF SURFACE IMPOUNDMENT AERR MODELS
INTRODUCTION
previously in Section 2.
...JSfc
aerated) as follows:
. Mackay and Wolkoff (1973) unsteady-state, nonaerated;
. Mackay and Leinonen (1975) unsteady-state, two-film theory,
nonaerated model;
. Thibodeaux, Parker and Heck (1981d) steady-state, two-film theory
one nonaerated and one aerated model ;
. Shen (1982) modification of Thibodeaux, Parker and Heck nonaerated
model ;
• Smith, et al. (1980-81) steady-state, first-order kinetic,
nonaerated model;
. McCord (198D steady-stats, modified Busselt equation, one
nonaerated and one aerated model.
I. addition, tne literature contains a = -^dei C°not1ui table
45
-------
The eight predictive models can be categorized according to their
theoretical basis. Five of tho eight models incorporate the two-film
resistance theory. The three predictive models that are not based on the
two-film resistance theory have been criticized by more recent research. For
example, the two predictive models presented by McCord (1981) are based on the
Nusselt equation, not the two-film resistance theory. The theoretical basis
of water evaporation implied by the Nusselt equation is considered a
unrealistic approach to the volatilization process of most sparingly
(slightly) soluble organics. The Mackay and Wolkoff%(1973) predictive model
is not based on the two-film resistance theory and was essentially revised by
Mackay and Leinonen's 1975 research.
Models which incorporate the two-film resistance theory are considered
the most accurate methods of describing the actual volatilization process, and
subsequent flux rate of an individual compound into the atmosphere,, However,
Che models based on this theory require determining the individual liquid
(kL) and gas-phase (k^) mass transfer coefficients for each compound of
interest. The availability of liquid and gas-phase k-values is limited, and
are primarily based on laboratory experiments or on field measurements of
lakes, rivers, and the ocean. Consequently, the accuracy of all available
state-of-the-art models is somewhat in question due to problems involved with
precisely determining k-values £or specific situations at TSDFs.
Table 8 summarizes input parameters required for each model reviewed by
GCA. Following sections describe all models available for aerated and
nonaeraced surface impoundments.
NONAERATED SURFACE IMPOUNDMENTS
AERR models found in the technical literature for nonaerated Sis are
reviewed below. The summary in Section 2 previously presented GCA's
selections for each SI type.
Mackay and Wolkoff (1973)
Mackay and Wolkoff (1973) proposed a model to quantify the volatilization
of low solubility compounds (hydrocarbons and chlorinated hydrocarbons) from
rivers, lakes and oceans. Their approach was based on equilibrium
thermodynamic principles of water evaporation, in contrast with more recent
research which is based on mass transfer principles of a concentration
gradient across an interface. Mackay and Wolkoff assumed that the AERR could
be calculated on the basis of water evaporation and the ratio of the
contaminant to water in the vapor. This approach assumes that the diffusion
or mixing in the water phase is sufficiently fast so the concentration of the
contaminant at the water-air interface is close to that in the bulk of the
water body. However, recent research on mass transfer rates suggests that
diffusion in the water phase is the rate controlling variable'for most
low-solubility compounds. In other words, current mass transfer theory shows
that the basic assumption in the Mackay and Wolkoff model is inappropriate for
modeling AERR from hazardous waste Sis. Other stated assumptions in the
Mackay and Wolkoff model include:
46
-------
TABLE 8. INPUT PARAMETERS REQUIRED FOR EACH SURFACE IMPOUNDMENT MODEL
Parameter
H> M1( flux rate of compound i across the phase
boundary
Kj L-overall liquid phase mass transfer
coefficient of compound i
k| L individual liquid phase mass transfer
coefficient of compound i
kj G individual gas phase mass transfer
coefficient
R, ideal gas law constant
T, temperature
Hj, Henry's Law Constant
Ci, concentration of compound i at time t
Cio, concentration of compound i at zero time
L, impoundment depth
Pi, equilibrium partial pressure of compound i
in the vapor
pi»> v«P°r pressure of compound i
Ci,, solubility of compound i in water
Qi, rate of air emissions of compound i
K, constant establishing equilibrium between
the liquid and air phases
x£, mole fraction of compound i in the liquid
phase
A, surface area of the disposal facility
MW£, molecular weight of compound i
Mackay Thibodeaux Shen
1975)0 (19Rld)b (1982)c
X
X
X
X
X
X
X
X
X
Smith McCord
(1980-8l)d (I981)e
X
X
X
X
X
X
(continued)
-------
TABLE 8 (coul inued)
oo
Parameter
He*, roughneaa Reynolds number
""benzene- •"'KC"laI ue'Sht "f b''n^">-
Uair, wind apeed
**Sc • 8a* Schaudt number
pg. absolute gas viscosity
p., denaity of gas
°i air« diffusion coefficient of compound i
in air
yair. denaity of air
MU_ ; . mlaciilar weight of air
MackJy Thihodeaun Slien
(I'J/^)" (I98ld)h (I9HJ)C
X
X
X X
X X
X
X
X
X
X
Smith Me Cord
( 1980-81 )<« (1981)«
X
K0.
Q£
KIL, overall liquid phase
•aaa transfer coefficient
H - L, depth of lagoon
P. total pressure
H. average awleculur weight of liquid
Z. length of lagoon surface
Bw, volatilization rate
kyC , volatilization rate of compound c
£,, evaporation ralo at steady stale
K0, initial evaporation rate
L,, aaraunt of compound in lagoon at steady atate
(cent limed)
-------
TABLE 8 (continued)
Mackav Thibodraux Slien Smith McCord
MQ7S)'n MtflM)1' (l<)S?)r (1980-8l)d (19Rl)e
Par ameter \\irt
l.0> initial amount of compound in laj>oon
y
t, weight of percent of compound in water or
lagoon liquid
yp ^ PJ , vapor pressure of the compound
"o " l'air. winH "P*""'1
y
K, amount of compound in fend stream
X
F, feed rate to lapoon
V, operating volume of lagoon
X
sp. gr., specific gravity of liquid waste
NB " N{, flux rate
DB1 " °i>air> Hiffusivity of compound i in air
(cont inued)
-------
NOTES FOR TABLE 8:
MODEL DEFINITIONS—AS PRESENTED IN THE LITERATURE
^lackay and Leinonen - Unsteady-State Predictive Model for Nonaerated
Surface Impoundments.
(1) N. -K.L (C. -P./H.)
(2) I _ 1 ( RT
KiL kiL Hi kiG
(3) C. = C. exp (-K.. t/L)
i 10. iL
(4) P. = C. P. lr
i i is/C.
is
Thibodeaux, Parker and Heck-Steady-State Predictive Model for Nonaerated and
Aerated Surface Impoundments.
(1) 0 . = K, A ( x . - x . * ) MW .
lull L
(2) i- - i- * -1—
^
Shen's Simplification of the Steady-State Predictive Model Proposed by
Thibodeaux, Parker and Heck.
(1) (ERP) . - (18 x 106) K . AC.
i oA i
oA L G
(3) kT - (4.45 x 1
-------
NOTES FOR TABLE 8 (continued):
(2) k
c I
RT
H
-1
e McCord's Steady-State Predictive Model for Nonaerated Surface
Impoundment s•
(1) E.
E L
o s
(2) E = 0.53425 Am § °-22«>
o
(5) K = 0.0334 (F) (%) Up. gr.)
(6) L = 0.0834 (V) U) (sp. gr.)
o
£McCord's Steady-State Predictive Model for Aerated Surface Impoundments
E L
150.315 H ^o V.P. d
v
L
(2) Eo ~ (460-fi; r V sp.gr
0.17678R
1/2
(4)
(5)
0.0834(F)U)(sp.gr.)
(6) L = O.OS34(V)(%)(sp.gr.)
o
51
-------
• The contaminant is truly in solution, not in suspended, collodial,
ionic, complexed, or absorbed form.
• The vapor formed is in equilibrium with the liquid at the interface.
• The water evaporation rate is negligibly affected by the presence of
the contaminant.
Dilling's (1977) preliminary work indicated that the Mackay and Wolkoff
model was inadequate since neither absolute nor relative predicted rates were
in agreement with experimental data.
Mackay and Leinonen (1975)
Mackay and Leinonen (1975) extended Mackay's 1973 research in order to
develop a more realistic AERR estimate for low-solubility compounds from the
entire water body, and not just from the water surface. Mackay and Leinonen
incorporated the work of Liss and Slater (1974) to develop an unsteady-state
model to determine the AERR of a single compound. Liss and Slater applied the
two-film resistance theory to estimate the flux of gases across the air-ocean
interface. Contrary to Mackay's 1973 thermodynamic model theory, Liss and
Slater's 1974 work suggested that for most low-solubility gases, the water
(liquid) phase controls; i.e., the liquid phase offers more resistance to
contaminant transport than through the gas phase.
The details of the Mackay and Leinonen model appear in Table 9. The
model is based on unsteady state conditions; i.e., the chemical contaminant of
interest enters the water body in a discrete slug as a pulse injection. All
other SI models are based on steady state conditions; i.e., a fairly constant
influx of the contaminant into the SI. As in the case of all ottier predictive
models for nonaerated Sis, this model simplifies the actual situation by
assuming well-mixed air and water phases separated by an interface with near
stagnant films of air and water on either side. Thermoclines; i.e., other
rate-limiting diffusion processes at depths in the water body, are not
considered in this model. The Mackay and Leinonen model can be simplified by
assuming that... "if P± is negligible; i.e., the background atmospheric
level of the contaminant is low compared to the local level..." then the
unsteady-state flux equation becomes:
Ni
where: Cj. . Cioexp(-KiLt/L)
1 _ 1 RT
K.T k.T (H.k.^)
iL iL i iG
In 1975, the only technique apparently available to Mackay and Leinonen
for calculating the mass transfer coefficients (k-values for gas and liquid
phases) was the 1974 Liss and Slater work shown below:
kiL
0.5
52
-------
TABLt 9. MACKAY AND LtlNONEN UNSTEADY-STATE PREDICTIVE MODEL
FUK NON AtRATED SURFACE IMPOUNDMENTS
Model Form:
N. = K.T (C. - P./H.)
l iL i 11
where;
1 1 . RT
K.T k.T H. k.
iL iL i iG
C. - C. exp (-K.T t/L)
i 10 ii>
P. = C.P. /C .
1 1 IS IS
Definition of Terms:
N- = mass flux rate of compound i across the phase boundary (mol/m2-hr)
K- = overall liquid phase mass transfer coefficient of compound i (m/hr)
Lt
Ic--. = individual liquid phase mass transfer coefficient of compound i (m/hr)
i. i->
k-G= individual gas phase mass transfer coefficient of compound i (m/hr)
R = ideal gas law constant (8.2 x 10~5 atm-o3/mol-^*0
T - temperature (°K)
H- = Henry's law constant of compound i (atm-m-Vmol)
C = concentration in mol/m3 of compound i at time t (hr)
C- = concentration in mol/m-^ of compound i at zero time
L = impoundment depth (m)
P- = equilibrium partial pressure of compound i in the vapor (atm)
P- = vapor pressure of compound i (atm)
C- = solubility of compound i in water (mol/m-*)
'is
53
-------
and
0.5
kiG
where:
k * liquid phase mass transfer coefficient of C02 • 20 cm/hr
L> 2 (reported to be at the sea surface);
MW - molecular weight of C02 (44 g/g mole);
C02
MW. * molecular weight of compound i;
k = gas phase mass transfer coefficient of ^0 = 3,000 cm/hr
1 2 (reported to be at the sea surface);
MW - = molecular weight of HTO (18 g/g mole).
H00
As described in the following sections, one emphasis of more recent
research has been refinement of techniques for calculating the individual
liquid ar.d gas phase k-values.
Thibodeaux, Parker and Heck (1981d) Including Hwang (1932) and
She- (.1952; Modifications
Thibodeaux, Parker and Heck proposed a steady-state model that assumes a
constant influx of contaminant, as opposed to Mackay and Leinonen's unsteady
state model. The Thibodeaux, Parker and Heck model, shown in Table 10, is
also based on the two-film resistance theory. Empirical relationships for
mass transfer coefficients developed from laboratory and field experiments at
lakes, rivers and oceans were incorporated (Cohen, Cocchio and Mackay-1978;
Mackay and Matsugu-1973 ; Owens, Edwards and Gibbs-1964). Although the
k-values incorporated by Thibodeaux, Parker and Heck represent an improved
data base compared to Mackay and Leinonen's approach, the calculation became
substantially more complex as shown in Table 11. Some of the input
parameters for these k-values are difficult to obtain, calculate or estimate,
and in some cases, require field or laboratory measurement.
Hwang (1982) presented a simplified technique for determining the mass
transfer coefficients for various compounds by referring to a typical compound
whose k-values are known. In his review of several laboratory experiments,
Hwang suggests that the k-values for oxygen and water vapor can be used to
determine the k-value for the compound of interest. In his examples, the
k-values for the reference compounds are based on a temperature of 25°C. The
approach for calculating mass transfer coefficients identified in Hwang's
paper appear in Table 12.
To apply Hwang's simplified equations, the liquid phase mass transfer
coefficient for oxygen and the gas phase mass transfer coefficient for water
vapor must be determined either from: (1) published data; or (2) calculating
from the empirical relationships shown previously in Table 11 (the latter
54
-------
TABLE IU. THIBODEAUX, PARKER AND HECK. STEADY-STATE PREDICTIVE MODEL
FOR NON AERATED SURFACE IMPOUNDMENT
Model Form:
Q.=K1A(x.-x.*)MW.
where;
KL RL KkG
and;
x.* = 0 since y. is negligible in comparison to x^
therefore,
Q. = K A (x.) MW.
-------
TABLE 11. SUMMARY OF EMPIRICAL RELATIONSHIPS TO DETERMINE THE
INDIVIDUAL LIQUID AND GAS PHASE MASS TRANSFER
COEFFICIENTS FOR A NONAERATED IMPOUNDMENT
Liquid Phase Coefficient (kf i .
(, \/MW \ 0.5
LI. 4 Re*U'iy - 5l( M^6ne I (Cohen, Cocchio and Mackay, 1978)
A i /
for 0.11 < Re* <_ 102, where k^ is in cm/hr and
7.07 x 10"3 (Z ) (U )1'25
Re* = ____— ^— — — ^— ^— ^^^——
Va exp (56.fa/U10°'25)
if Re* <- 0.11, then k, = 2. 4 cm/hr
u
where ;
Re* = roughness Reynolds number
Mrt'benzene = nioleculsr weight of benzene (76.1 g/g-mole)
>r.v^ - molecular weight of compound i (g/g-mole)
U10 = wind velocity (cin/s) measured at height ZJ_Q (10 m) above the water
surface (cm)
Va = air kinematic viscosity (cm^/sec)
0 195 ' 2
[2] '^ = (1.3 Re*u>i" - 0*.57)I- - — I (Cohen, et al. as presented
by Hwang, 1982)
where ;
kr^ is in Ib-mol/f t2-hr. (Note: This equation is a modified form of
equation 1 to obtain the k^ value in units of Ib-mol/f t^-hr) .
Re* * roughness Reynolds number (determined as above)
DI HTO * diffusion coefficient of compound i in water (cm2/8ec)
DTOL HoO = diffusion coefficient of toluene in water
(continued)
56
-------
H (continued)
[3J kL = 3.12 (1.024)6"20 U °*67 Ho °'85\U0 u 0) (Owens, Edwards and Gibbs
0 2' 2 / 1964. as presented by
Hwang, 1982)
where;
kL is in Ib-inol/ft2-hr
I= temperature (°C)
U_ = surface velocity, ft/sec, normally 0.035 x wind speed (ft/sec) for
natural surface, and 0.1 ft/sec for outside region of effect
of aerators in the biological treatment.
HQ = effective depth of surface impoundment (ft)
DQ H 0 = diffusion coefficient of oxygen in water (cm^/sec)
Gas Phase Coefficient (kc):
k^ = 0.0^53 U . °'78 N ~U--D7 d -0.11 "air (MacKay and Matsugu, 1973)
G air sc e MVv . °
air
where;
kG is in Ib-mol/ft2-hr
L'a;|_r = wind speed i,m/nr)
Nc_ = gas Schmidt number = '^oX-gD, a;r
^<~ 5 i. , a J. i
-._, - absolute gas viscosity (g/cm-sec)
o
-g = density of gas (g/cm^)
= diffusion coefficient of compound i in air (cm^/sec)
de = effective diameter of the quiescent area of the impoundment
(m) = /AAc\°-5
Ac = area of conveccive (natural) zone of impoundment surface (m )
cair
MWair = molecular weight of air (28.8 Ib/lb-mole)
(continued)
57
-------
TABLE 11 (continued)
[2] k - 0.03 (— J V /A0*05 (Thibodeaux and Parker, 1974)
G \DWA/ 8
where;
kQ is in Ib-mol/ft2-hr
DyA • diffusivity of water vapor in «ir (cm2/sec)
DAA * diffusivity of compound A in air (cm2/sec)
Vo = wind speed at 8 meters above the water surface (miles/hr)
A = surface area of water body (acres)
58
-------
TAIiLL 12. HWANC's (1982) SIMPLIFICATION OF THE EMPIRICAL LIQUID
AND GAS 1'llASli MASS TRANSFER COEFFICIENTS FOR A
NONAKRATEU IMPOUNDMENT
Liquid Phase Coefficient of Compound i (k-[ ^) .
Gas Phase Coefficient of Compound i
°-335
where ;
MW(j = molecular weight of oxygen (g/g-raole)
>i«u Q = molecular weight of water vapor (g/g-mole)
,i_
M'v.1^ = molecular weight of compound i (g/g-raole)
- = temperature of concern ( °C)
ki^Q = liquid-phase mass transfer coefficient of oxygen at 2-5°C
(g-mol/cm^-sec )
Pna5e mass transfer coefficient of water vapor at 25°C
(g-uiol/cm2-sec)
59
-------
case is more accurate). Therefore, from these deterministic equations, the
complex empirical relationships remain a key variable in obtaining either the
liquid and/or gas phase mass transfer coefficients for the compound of
interest.
Shen (1982), using the rate expression proposed by Thibodeaux et al.
(1981d), described a simplifying method for estimating the volatilization rate
of volatile organic compounds from waste lagoons. Shen't modifications
included the use of Owen's correlation for k^ determination and Che use of
Mackay and Matsugu's correlation for kg. Owen's correlation was obtained
from reaeration studies of flowing streams, and thus may not be directly
applicable to stagnant waste lagoons. For .both kL and kg, Shen made some
calculation errors in converting the units of the original correlations.
Thus, correlations snown previously in Table 8 should be modified as shown in
Table 11.
In applying MacKay and Matsugu's correlation, Shen suggests a molecular
weight dependency for Schmidt numoer determinations, such that the following
simplirication could oe employed:
c -0.67
Molecular Weight ££
Less tnan 100 0.7
100-200 0.6
More tnan 200 0.5
Smith, Bomberger and Haynes (1980-1981)
Smith, Eomberger and Haynes proposed a technique for determining an
overall volatilization rate constant based on laboratory measurements. The
volatilization rate constant is essentially the overall K-value that
represents the individual liquid "and gas phase k-val-ues combined. If found
adequate, this approach would eliminate the complex empirical relationships
for determining the individual values proposed by other researeners.
Smith, Bomberger and Haynes essentially expanded on several concepts
presented by Liss and Slater (1974); i.e., (1) mass transfer in the liquid
pnase controls more tnan 95 percent of the volatilization rate if Hc
vtienry's law constant) is greater tnan approximately 3500 torr-LM"1 (G.004i
atm-m-i-mol"1); (2) if tic is less than approximately 10 torr-LM"1-
(1.2 x 10~5 atm-m3-mol~M, mass transter in the gas phase controls more
than 95 perceat of the volatilization rate; and (3) if Hc is between 10 and
3500 torr-LM'l, both gas and liquid phase mass transfer are important.
Smith, Bomberger and Haynes categorized chemicals from these three
classitications as high, low, and intermediate volatility compounds,
respectively. A technique was developed for estimating the. volatilization
rate constant (kvc; for each class ot volatile compounds. Table 13 shows
these three estimation techniques and the model equation presented by
Smith, et al. appears in Table 14.
60
-------
lH H SUMMARY OF TECHNIQUES DEVELOPED BY SMITH, BOMBERGER AND HAYNES
TO LSTiMATi: TIIK VOLATILIZATION RATIi CONSTANT (k^) FOR
HIGH, LOW AND INTERMEDIATE VOLATILITY IMPOUNDS
HUh-Volatility Compounds (Hr > 3.500 torr-LM 1) ;
where ;
k C = volatilization rate constant of compound c (hr )
v
c
v
/k °\ . = ratio of volatilization rate constants for compound c and
V 'lab oxygen measured simultaneously in the laboratory (shown to be a
constant for high-volatility compounds
(k °\ = oxvgen reaeration constant in a real water body (k °\ /L, since
\ v /env ' v ' .
tne second term in the two-film resistance theory model is small
compared to the first for high-volatility compounds
Low-Voiatilitv Compounds lHr " 10 torr-L M L) :
where ;
r. C = volatilization rate constant of compound c (hr )
c/k w\ = ratio of volatilization rate constants for compound c and water
v ' v /lab vapor measured simultaneously in the laboratory (shown to be a
constant for low-volatility compounds)
(k w\ = k. WH /LRT, since the first term in the two-film resistance theory
\ v /env g c
is small compared to the second for low-volatility compounds
k
W = gas phase mass transfer coefficient for water, determined from Pick's
law, i.e., NW - k W (?"- ?W)/RT
g s
where;
(continued)
61
-------
TABLE 13 (continued)
w 2
N » measured water evaporation flux rate (mol/cm -hr)
w
P « saturated partial pressure of water at temperature T
w
P * actual partial pressure of water at temperature T
Intermediate Volatility Compounds (H - 10 to 3500 torr-LM );
Combines the estimation techniques of both high- and low-volatility
compounds.
62
-------
'l/UiLi; l/t. SMITH, liOMJitUChK AND liAYNliS t'iKST OUUtK. KiNEliC EQUATION FOR
NONAERATED SURFACE IMPOUNDMENTS
Model Form:
v dt v
k c . 1 J_ + _RT_ '*
* L >' VoC.
Definition of Terms:
R or — = volatilization rate of compound c from water (mg/l-hr)
v dt
k C = volatilization rate constant of compound c (hr )
v
L = length of impoundment (era)
k. = individual liquid phase mass transfer coefficient of compound c (cra/hr)
= individual gas phase mass transfer coefficient of compound c (cm/hr)
o
R = ideal gas constant (L torr/°K raol)
T = temperature (°K)
H, = Henry's law constant (torr L/mol)
63
-------
The key limitation to the Smith, Boraberger and Haynes approach is that
laboratory determinations ot the ratios (kvc/kv°; and (kvc/kvw)
are compound specific, sophisticated and expensive. Only a very limited
number of compounds have been tested to date. Using other methods for
determining these ratios, i.e., using values of Che diffusion coefficients,
increase the overall uncertainty of this model.
McCord (1981)
A fourth predictive model for estimating the emission rate of volatile
compounds from nonaerated lagoons was presented by McCord (1981). This
steady-state moael, shown in Table 15, was based upon Nusselc's equation which
describes water evaporation rates from a lagoon. Consequently, McCord 's model
is limited to situations where volatilization is controlled by the gas phase
mass transfer. This limitation is similar to that of Mackay and Wolkoff's
(1973) model. It has been shown by more recent research that most
volac i 1 ization is liquid phase controlled. Additionally, McCord assumes that
equilibrium ac tne air-wacer interface follows Raoulc's law. However, for
dilute aqueous solutions, the equilibrium should actually be determined on the
oasis of Henry's law.
A£RATED IMPOUNDMENTS
fniooueaux, Parser, Hec.t Civile)
Ihiooaeaux, Parker and HecK tl'^ola) proposed use of their steady state
model for nonaerated Sis for use with aerated impoundments with some
modifications. The theory of two-film resistance is applicable to an aerated
impoundment if one considers that turbulence, caused by aeration, creates two
distinct zones at the impoundment surface, i.e., CD turbulent, and
(2) convective or natural. The overall liquid phase mass transfer coefficient
for tne entire system muse oe modified to account for each distinct zone,
proportional co che affected area of each zone. The resulting overall K-value
proposea by Tnioodeaux, Parser and Heck, for aerated Sis appears in Taole 16.
As shown previously in Taole 11, empirical relationsnips were developed
oy Thiboaeaux, et al. to estimate individual liquid and gas phase k-values for
a nonaerated (entirely convective zone) SI; i.e., (kL)c and ('<£><.,
respectively. Similar relationships have also been experimentally developed
to account for tne turbulent zone caused by mechanical aeration,. These
empirical equations are shown below:
• . Individual liquid phase coefficient:
, m J(POWR)(l.Q24)9"2Q(a)(106)
^ L T 165.04(a )(v)
64
-------
TABLE 15. McCOKO'S STEADY-STATE PREDICTLVt MODEL FOR
NON AERATED SURFACE IMPOUNDMENTS
Model Form:
where;
t\ o o
0.78
E = 0.53425 A £ <%) (VP) (WJ
o m
L = K
s
1-x
^o + F
L V
o
K = 0.0834(F) (%) (sp.gr. )
L = U.Od3<+(V; (%) Csp.gr.)
o
Definition jf Terms:
E = evaporation rate of a compound at steady state (Ib/hr)
E^ = initial evaporation rate of a compound (Ib/hr)
L° = amount of compound in lagoon at steady state (lb)
L = initial amount of compound in lagoon (lb)
A_ = surface area of lagoon (m"-)
D = diffusivity coefficient of a compound in air (m /hr)
L = a lagoon dimension (m)
% = weignt percent of compound in water or lagoon liquid
V? = vapor pressure of pure compound (atin)
W., = wind velocity (m/sec)
K"= amount of compound in feed stream (Ib/hr)
F = feed rate (^discharge rate) in lagoon (gal/hr)
V = operating volume of lagoon (gal)
sp.gr. = specific gravity of liquid waste
65
-------
TABLE 16. K-VALUES FOR AERATED Sis PROPOSED BY
THIBODEAUX, PARKER AND HECK
Ac *T
K * (K ) + £K )
irf Li C A L* L A
where;
K^ = overall liquid phase mass transfer coefficient for the
entire aerated surface impoundment (also termed the
"area-averaged" coefficient) to be used in the basic
model equation.
(KL)C = overall liquid phase mass transfer coefficient
for the convective zone of the impoundment
1 = 1 + 1
(K ) (k ) K(k )
L c L c G c
AC = effective surface area of the convective zone
A = total surface area of the aerated impoundment
(A=AT+AC)
(KL^T = overall liquid phase mass transfer coefficient
for the turbulent zone of the impoundment.
K = equilibrium constant
(KL) (k) K(k )
T LT T
= effective surface area of the turbulent zone
66
-------
where :
J = oxygen-transfer rating of mechanical aerator (3 Ib 02/hr-hp);
POWR = total power input to aerators (hp)-rated hp x efficiency
(0.65-0.9);
8 = temperature (°C);
a= oxygen-transfer correction factor (0.8-0.85);
av = surface area per unit volume of surface impoundment (ft"1);
V = volume of surface impoundment in region of effect of aerators
(ft3);
Di HoQ = diffusion coefficient of compound i in water (cm2/sec);
DQo HlQ = diffusion coefficient of oxygen in water (cm2/sec)
- ! <-
• Individual gas phase coefficient:
- D 1.42 -0.21 0.4 0.5
U)r - 0.00039 ~g \; ^ (NRe) (NpR) CNp> (N^)
Cg = density of the gas (Ib/Et^)
i air = diffusion coefficient of compound i in air (ft2/hr)
d = diameter of aerator turbine or impeller (ft)
N'P-J = gas Reynolds -lumber = Ogd~-/ug
^ = rotational speed :>f turbine impeller (rad/sec)
Ug = absolute gas viscosity (g/cm-sec)
NpR = Froude number = du.2/g
g = gravitational constant (32.17 ft/sec^)
Np = power number = Pr g/P^^^3
Pr = power to the impeller (ft-lbf/sec)
^L = density of the liquid (Ib/ft^)
Ngc = gas schmidt number = yg/ *'gDi , air
67
-------
Note: Ngh » Sherwood number = (kg)-j d/PgDijair
and therefore, Nsh»o.00039(NRe)l •42(Np)0^(NSc)0-5/(NFR)0.21
Freeman (1979), working with surface aerated waste treatment basins, has
tabulated values published in the literature for estimating; (1) uffective
surface area of the turbulent zone (AT); (2) surface area per unit volume of
surface impoundment (av); and (3) volume of surface impoundment in region of
effect of aerators (V), based on the mechanical aerators horsepower, u. These
parameters are shown in Table 17.
As discussed in the preceeding section, several other researchers have
shown that the individual mass-transfer coefficients for various compounds in
a nonaerated impoundment (convective zone coefficients) can be simplified by
comparison to a typical compound. This simplification process has teen
applied for determining the individual mass transfer coefficients from the
turbulent zone of an aerated impoundment as shown below:
• Individual liquid phase coefficient:
0.25
\ 1
1 .Uz
Individual gas phase coefficient:
, V0.25 0.92
i / 298
P/T^j (kG,H20
However, as noted previously, a key limitation to this simplification
procedure is that the values of kLj0 and kG>H?0 are best determined
by using the complex empirical relationships'sftown earlier.
McCord (1981)
One additional predictive model was proposed by McCord (1981) to estimate
the emission rate of volatile compounds from aerated lagoons. This
steady-state model, based upon Arnold's (1944) studies on the diffusion of
volatile compounds from a liquid surface into air, appears in Table 18.
Discussions in the preceeding section concerning McCord's steady-state
predictive model for nonaerated impoundments showed that the basis for
McCord's model is evaporation of water from the impoundment surface; i.e., gas
phase controlling. Therefore, in reality, this model does not accurately
represent the volatilization rate of most sparingly (slightly.) soluble volatile
organic compounds.
68
-------
TABLE 17. TURBULENT AREAS AND VOLUMES FOR SURFACE AGITATORS*
u , Motor
horsepower,
hp
5
7.5
10
15
20
25
30
4U
50
6U
75
100
Aj,
Turbulent
area, ft2
177
201
227
284
346
415
491
661
855
1,075
1,452
2,206
Effective
depth, ft
10
10
10.5
11
11.5
12
12
13
14
15
16
IB
V, Agitated
volume, ft
1,767
2,010
2,383
3,119
3,983
4,986.
5,890
8,587
11,970
16,130
23,240
39,710
av, Area
per volume
ft2/ft3
0.100
0.100
0.0952
0.0909
0.0870
U.0833
0.0833
0.0769
0.0714
0.0666
0.0625
0.0555
aData for a high speed (1,200 rpm) aerator with bO cm
propeller diameter (d).
69
-------
TABLE 18. McCORD'S STEADY-STATE PREDICTIVE MODEL FOR AERATED Sis
Model Fonn:
E L
E = .° S
s L
o
where;
... _ 150.315 H Lo VP d
c.
(460 * T) r VL .p. gr. w J0.l767ffil/2
0
K = (0.0334)(F)U)(sp.gr.)
L = (0.0334) (V) (%/ (sp. gr.)
Definition of Terms:
E * evaporation rate of a compound at steady-state conditions (Ib/hr)
E = initial evaporation rate of a compound Clb/hr)
o
L = pounds of a comoound in the laeoon at steadv-state conditions
s
L = initial oounds of a comoound in the laaoon
o
T = temperature (8F)
H = amount of water delivered by the aeration pump (jzpm)
r = radius of spherical drops emitted (cm)
V » volume of liquid waste in lagoon (U.S. gal)
L
VP » vapor pressure of the volatile compound at temperature T (atm)
sp. gr. * specific gravity of the liquid waste
d • diffusivity coefficient of a compound in air (cm /sec)
(continued)
70
-------
TARF.E 18 (conM'mipr!)
R = maximum diameter of the aeration spray falling back into the lagoon (m)
K = amount of compound in Che feed stream (Ib/hr)
F = feed rate (= discharge rate) in lagoon (gal/hr)
V = operating volume of lagoon (gal)
% = weight percent of a compound in water or lagoon liquid
71
-------
SECTION 5
REVIEW OF LANDFILL AERR MODELS
INTRODUCTION
Six air emission modeling equations were presented in the literature for
landfill facilities:
• Three models for covered landfills without internal gas generation
(Farmer, Shen, Thibodeaux) ; and
• One model for each of the following scenarios: (L) covered
landfills with internal gas generation (Thibodeaux); (2) covered
landfills with gas generation and barometric pumping effects
(Thibodeaux); and (3) uncovered landfills (Shen).
This" section presents all models for landfills found in the literature.
Tables 19 and 20 respectively summarize available model eauations for
landfills and the necessary input parameters required for each equation. GCA1s
recommendations for landfill models and mass transfer coefficients were
presented previously in Section 2.
Two of the three AERR equations for covered landfills without internal
gas generation were based on laboratory studies conducted by Farmer, et al.,
(1978). Shen (1980) modified Farmer's equation by changing the flux rate to
an emission rate by multiplying by the landfill surface area. In addition, to
determine the AERR for a specific component of the waste, Shen multiplies the
emission rate by the weight fraction of that component in the bulk waste.
Details of both models are provided in this section.
Farmer's laboratory experiments assumed the vapor release of hexachloro-
benzene (HCB) was diffusion controlled within the soil phase because of HCBs
insolubility ia water (i.e., not effected by water movement) and HCBs
resistance to biological activity. However, Thibodeaux's (1981a) equation
takes on a similarity of the two-resistance theory of mass transfer.
Thibodeaux not only describes the vapor movement within the soil phase (as
does Farmer), but also addresses the vapor movement from air-soil interface to
the overlying air. In practice, the air-soil interface transfer should
provide negligible resistance, and thus can be disregarded.
72
-------
TABLE 19. REVIEW OF AVAILABLE AERR LANUFILL MODELS3
(AS PRESENTED IN THE LITERATURE)
A. Farmer, et al. (1978) for covered landfills:
i n / \ *>
(1) J = D (P iU/ /P/) (C -C )/L
o a T s 2
VJ' -s L RT
(4) P = P - - 5
15) ? = 1 - -r
, v*, —
16) r = —
ihen1 a (.IVou) .>loditicat ion of Fanaar's liquation:
A ,
(3) C
31 S Ri
(O ?T » l -
T -<
C. Thibodeaiox' s (1981a) Landfill Equation — Without Internal Gas Generation:
(2) N = Nv . . + N. . . .
A A soil A air-soil
(continued)
73
-------
TABLE 19 (continued)
(3) N. - -^
-------
TABLE 20. INPUT PARAMETERS RFOUIRED FOR EACH LANDFILL MODEL IN TABLE 19
J,
DO-
cs,
C2,
L,
Pa'
PT.
OA,
DB>
P°,
M,
R,
T,
£,
-,
" li!
~,
Wl
Ei
*.
Parameter
vapor flux through soil
diffusion coeff. in air
cone, material in air
cone, of material at soil surface
soil depth
soil air filled porosity
total s:>il porositv
air diffusion coeft. for unknown compound
, air diffusion coeff. for known compound
, vapor pressure
molecular weight
molar gas constant
absolute temperature
soil bul< density
gravimetric soil water content
, density of water
particle density
/W , weignt X of component i in bulk waste
, emission rate of vapor i
, mass flux rate
A
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X .
X
X
Model
B C U E F
•
X
X
X
X
X
X X
X
A
X
X
X
X
X
X
X
X
X
X
XXX
(continued)
75
-------
TABLE 20 (continued)
Parameter
B
Model
C D
> overall soil phase transfer coeff.
0A1» cone, of A in sand chamber filled
pore spaces
0A1> cone, of A in air at distance from
air-soil interface
NA, rate of vapor movement within soil
phase
h, depth of fill cover
DA3, effective diffusivicy of A within
the air-filed soil pore space
"JA1' 'nolecular ciffusivity of A in air
* , tortuosity
*A1» 8as P^ase mass transfer coeff.
Vx, wind speed at 10 m
L, length of ground emission source
V , mean gas velocity in pore spaces
cAli> conc- °f A ac air-soil interface
L, cap thickness
V, superficial velocity through cap
K, permeability of cap material
v, cell gas velocity
P, cell gas pressure
X
X X
X X
X X
X
X
X
X
X
X
X
X
X
X
X
X
(continued)
76
-------
TARLF. 20 (continued)
Parameter
Model
C L)
r, atmospheric pressure
dV , ,
— . volume cone, or vapor
dt
Cp, equilibrium vapor cone
oj, width of open dump
V, wind speed
Fv, correction factor
X
X
X
77
-------
Thibodeaux (1981a) presents another model describing vapor movement in
soil which is subject to the effects of biogenic processes and related gas
generation. .This "sweeping" action provided by the upward movement of
landfill gases provides a parallel transfer motion to the molecular diffusion
of vapor in the soil phase.
Thibodeaux (1981b) further developed his model to include the barometric
pumping effect caused by fluctuations in atmospheric pressure and landfill
cell pressure. Computer simulation tests indicated that the flux rate of
benzene, NA, is influenced only slightly by barometric pressure fluctuations
under conditions of co-disposal, and influenced significantly under conditions
of no internal gas generation (i.e., no co-disposal with municipal refuse).
This statement suggests that for a co-disposal facility, Thibodeaux's
model for landfills with gas generation should be employed. For a landfill
handling strictly hazardous waste, with no expected internal gas generation,
either of two models (Farmer, or Thibodeaux) may be appropriate. However
according to Springer (1983), the effect of barometer pumping is not
reversible and will not average out over a long period of time. An increase
of 10 to 15 percent to emission release rate could be expected.
To determine AERR from an uncovered landfill, Shen (1981) presents the
eqiatio-i based on Pick's Law. This is the only open dump AERR model presented
in the literature and it assumes an insoluble material with vapor movement
that is only air-phase controlled. A review of Thibodeaux's two-resistance-
landfill equation, specifically the rate of vapor movement from the air-soil
interface to overlying air (air-phase resistance) indicates it may be a more
accurate description of vapor movement in the gas phase because it accurately
accounts for wind effects across the earth's boundary i.e., Sutton (1953).
Further development for the open dump case may be warranted.
FARMER, ET AL. (1978) FOR COVERED LANDFILLS
The equation developed by Farmer was intended as a method of assisting a
planner in designing a landfill cover that minimized the escape of
hexachlorobenzene (HCB) or other volatile organic vapors. Alternatively, the
equation could be used to assess the effectiveness of an existing landfill
cover for controlling organic vapor flux to the atmosphere. The equation was
experimentally verified by Farmer for HCB-containing waste in a
laboratory-simulated landfill.
Using Pick's First Law for steady-state diffusion, Farmer describes the
volatilization or vapor loss of HCB, or other compounds, as a diffusion
controlled process. With the assumptions of no degradation from biological
activity, no adsorption of the compound, no transport in moving water and no
landfill gas production, the rate at which a compound will volatize from the
soil surface to the atmosphere will be controlled by the diffusion rate
through the soil cover. To describe molecular diffusion through a soil
surface, Farmer adopted the effective diffusion coefficient suggested by
Millington and Quirk (1961) as shown below:
78
-------
where: De = effective diffusion coefficient in soil;
D0 = diffusion coefficient in air;
Pa = soil air-filled porosity;
FT = total porosity.
This equation describes the effective diffusion coefficient as a power
function of soil porosity. This method may be valid, however, as described
previously in Section 2, additional research indicated the power function may
be soil-tvpe dependent. Thus, this equation appears to be limited to the soil
class with which Millington and Quirk experimented with, namely isotropic soil
The following describes the methods employed by Farmer (1980) to
determine equation parameters, and identifies some simplifications to the
overall equation.
A. Difi'ision coefficients, Do, are available for many compounds,
generally at a specified temperature. The vapor diffusion
coefficient for an unknown compound A can be estimated from a known
compound (B) by the following equation:
1/2
where M«, Mg = molecular weights of compounds A and B,
respect ively.
To d2ternlne the diffusion coefficient at a temperature other than a
temperature listed, the following equation can be used:
1.5
where D^ and D2 are the diffusion coefficients at temperatures
Tl and T2, respectively.
B. Saturation vapor density at the bottom of the soil layer, Cg, can
be obtained based on the ideal gas law:
C = P°M/RT
where: ?° = vapor pressure (mm Hg);
M = molecular weight (g/g-mole);
79
-------
R * molar gas constant (62.36 1-mm Hg/'K-mole)
T - absolute temperature (°K)
Farmer experimented with pure HCB, thus, he calculated the pure
component vapor concentration. For mixtures., the vapor
concentration of a component in the waste becomes the driving force
and this is not equal to the saturation vapor concentration of the
pure component. The vapor concentration for a component in a waste
mixture is calculated by:
C. « — =
i RT
where P. = partial pressure of component i in the waste mixture.
The partial pressure in a liquid mixture is determined as follows:
* o
P. = y. P x-
L 1 *1
where: "• j_ = activity coefficient of component i; and
\i = mole fraction of component i in the liquid.
For hydrocarbon mixtures, Y^_ * l, but for aqueous mixtures the
activity coefficient must be determined.
C. Soil air-filled porosity, Pa, is calculated from the total
porosity, Pj, and the volumetric soil water content, 9, where
?a = PT - e
and 9 * Wfl/o
w
where: W = gravimetric soil water content (g/g) ;
3 = soil bulk density (g/cm^);
ow * density of water = 1 g/cm^.
A worst-case assumption would be completely dry soil, thus, Pa *
Pj, and the flux equation becomes
The addition of any water to the soil will reduce the air-filled
porosity, thus, reduce vapor flux from the soil surface because the
diffusion rate through a liquid is generally several magnitudes less
than diffusion through air.
80
-------
D. The total soil porosity, PT, can be calculated from the soil bulk
density, B, by the following equation:
PT = 1-8/p
where: ft = soil bulk density (g/cm3);
D = particle density (g/cm3).
Particle density is usually taken as 2.65 g/cm3 for most soil
mineral material, while soil bulk density usually varies from
1.0-2.0 g/cm3. Therefore, PT can range from 0.245 to 0.623
cm3/cm3, and (PT)4/3 = 0.153 to 0.532.
Worst-case scenario would be PT 4/3 = 0.532 (from R = 1.0
g/cm3), thus J = 0.532 Do (CS-C2)/L. This flux rate
equation would allow for a worst case estimate of air emissions.
E. Farmer assumed that the concentration of volatilizing material at
the soil surface. C->, is zero. The reasons for this assumption
were stated by Farmer as:
the a-nount of vapor reaching soil surface will be very small;
and
2. the vapor will be rapidly dispersed by wind currents and by
diffusion in air. Thus, the simplified version of Farmer's
equation becomes:
J - Do PT4/3 CS/L
The assumption of C2 = 0, implies worst-case situation
because any increase in C2 will effectively reduce the
concentration gradient (driving force behind vapor flux) and
reduce vapor flux from soil surface.
SHIN'S (1980) MODIFICATION OF FARMER'S EQUATION
Basically, Shen took the simplified version of Farmer's equation for
vapor flux from a soil surface and converted to an emission rate by
multiplying by the exposed area. To determine the emission rate of a specific
waste, component i, Shen multiplied by the weight percent of component i in
the bulk waste (Wi/W). However, weight percent should be replaced by mole
fraction. Additionally, in calculating the emission rate of a specific
compound in a waste mixture, consideration of waste composition and the
activity coefficient is important. This procedure was previously outlined.
Since both Farmer's and Shen's equations are nearly identical, the
parameters Dj_, cs j_, and Pj can be calculated and simplified in similar
manners. For illustrative purposes, Table 21 presents typical parameter
values and ranges for the modified landfill equation.
-81
-------
TABLE 21. TYPICAL PARAMETER VALUES AND RANGES FOR THE FARMER LANDFILL MODEL AS MODIFIED BY SHEN
W. H^
Equation 1. E - 0 C A F f K u lqu.it ion / ", »K M
_j a • ,
Symbol Unita Definitl.." Soui.e of inpui ,,,ir.i.»-tel
D cm2/aec Diffmion , .>,• f f . Cnlc. ft.. a. to,. /
cone .
Pt Dimensionletf Soil poronitv Calc. ficim Fq. 4
L c- Depth of s,>ll Meaaur^ .>r ivpual value
cover assumed
of chrm. assumed
CO DK cm'/aec Known D of ref. Chemical handbook
N) compound
My g/mole MM of ref. Chemical h.iii.ll.unk
compound
Mj g/mole NW of compound Chemical handbook
f mm Hg Vapor pressure Chemical liandboiik
g *** Ht~'|UtI Caa conatant Chemical liaiidlmok
r ' ' ' PM .8
' Fiiuatioii I r • --= Equation 4: P • 1 - -
K
lvpn.il valin- Fxpi-iii'd i.mfp Comaienta
,n H)*1-!!!"1 Methanol high at O.H7; tr ichloroethylene low at
O.OW5 9 20'C
NA in '-Id"1 Methyl chlorid* high at 2.1«> x 10"'; benzene
low at 1.0 x 10"'
inn m' ,'S -S.Oilil in'' HiRhly variable parameter
n.i, 1 H. .'"> <>.»i?
in •>'! I'.
;• il.s ',' Highly variable parameter
NA SO- liii For organic compounds, chtoroawthane is low t
SI, PCB is high t 189
NA VI-IOO For organic compounds, chloronttiane ii tow f
SI, PC» if high 9 It9
JO ' 7SH-1IO Highly variable paraajeter
NA 0.07-7SO PCB low at 0.01), Cyelohexane high at 711
I/cm' Soil hulk drnsity Soil handbook
^/c-1 Fartiele density Soil handbook
">.>>'<
?.
-------
THIBODF.AUX'S (19813, 1981b) LANDFILL EQUATIONS
Thibodeaux (1981a, 1981b) presented three equations for estimating air
emissions from covered landfills; (1) without internal gas generation, (2)
with internal gas generation, and (3) with internal gas generation including
the effect of barometric pumping pressure.
Without Internal Gas Generation
Thibodeaux's equation for covered landfills without gas generation
appears similar to the two resistance theory of mass transfer: i.e., Flux =
(overall transfer coefficient) (concentration gradient). The equation is the
algebraic sum of the two individual phase equations; the rate of vapor
movement within the soil phase, and rate of vapor movement from air-soil
interface to overlying air.
The rate controlling portion of Thibodeaux's flux rate equation is the
rate of vapor movement within the soil phase. The mass transfer coefficient
for vapor diffusion in soil is described for vapor movement through a porous
media. However, other research previously presented in Section 2 indicates
that a more correct expression is to show the effective diffusivity dependency
upon a power function of porosity. This power is a function of soil type and
moisture content. The second portion of Thibodeaux's equation describes the
vapor movement through air, based on the work of Sutton (1953).
With Internal Gas Generation
In addition to molecular diffusion of landfill vapors through soil, there
is a "convective sweep" of chemical vapors toward the surface created by the
formation of landfill gases (COo, H2, Cfy), especially applicable to
co-disposal sites. Therefore, the flux equation contains both a diffusive and
convective term.
Barometric Pumping Effects
Additional work by Thibodeaux, Springer and Riley (1981b) addressed a
third vapor phase transport mechanism in addition to the diffusive and
convective mechanisms previously discussed; the barometric pumping pressure.
Atmospheric pressure fluctuations develop pressure gradients which pump vapors
and gases from landfill cells to the air above. This pumping enhances vapor
phase mass transfer.
Changes in barometric pressure will correspondingly change R (see
Equation E-2, Table 19) to a positive, zero, or negative value (thus effecting
flux rate). For instance:
for < TT, R 0 (air Inflow): NA is suppressed (= 0)
p = 1V) R = 0: NA = DA3PA1/L ^rate of vaPor
movement in soil without gas
generation—see Thibodeaux's
previous equation)
83
-------
p > it , R > 0 (air outflow) : NA is increased due to pressure
gradient driving force.
It was also shown that cell gas pressure, p, will vary with time and is
dependant upon gas generation and the cyclic behavior of fluctuating
atmospheric pressures, such that:
d£ m Vwp Kp(p -IT)
dt e e h Lu
c c c
where: rg » biogas generation rate (cm-Vg-sec) j
py " bulk density of waste (g/cm^)
p = cell gas pressure (atm);
£c = cell porosity;
K = permeability of cap material (cra^-cp/sec-atm);
- atmospheric pressure (atm);
hc = cell depch (cm)
L = cap thickness (cm)
= cell gas viscosity (cp)
Computer simulation tests indicated that the flux rate of benzene, N^,
is influenced only slightly by barometric pressure under conditions of
co-disposal (gas generation) and influenced significantly by barometric
pressure under conditions of no internal gas generation. The air emissions
model equations which incorporate factors for gas generation (and their
related effects on flux rate) should be applied for situations of co-disposal.
SriEN'S (1980) OPEN DUMP EQUATION
The emission rate'equation for open dumps presented by Shen is derived
from Pick's Law and Arnold's (L944) equation for a surface exposed to open
air. A raajor limitation of this model is that it only considers air-phase
diffusion and it does not accarately describe the effect of boundary layer
formation caused by ambient wind, as shown by Thibodeaux in describing the
gas-phase resistance of vapor movement. This limitation suggests further
development of this model is appropriate.
34
-------
SECTION 6
REVIEW OF LAND TREATMENT AERR MODELS
INTRODUCTION
fhe tecanical literature contains two models for calculating air emission
-elease rates (AERR) from landfaming (land treatment) operations. Table 22
summarizes the available equations for land treatment facilities, showing tne
input parameters requirea for each model. Table 23 presents typical parameter
values ana ranges for tne Th ibodeaux-Hwang (1932) AERR model.
me Thiaodeaux-Hwang U*S2) model most accurately defines the physical
situation exiting in a landfann, namely tne mass transfer ot a chemical
o.>cies tr-v.1, a soil-waste mixture. One apparent limitation to this model is
:nac ic decrioes vapor diffusion as being soil-phase controlled, based on tne
assumption tnat tne oil-layer diffusion length is on- the order of a soil
particle size. Tnis assumption may only be valid after a certain exposure
time. For petroleum waste, the sludge material generally subjected to
iandrarming is a multicouponent viscous material. Molecular diffusion
coefficients for this material may be several orders of magnitude less than
tnat for soil-phase diffusion. Thus, the diffusion rate determining factor
will be the application thickness of the waste material. Additionally, it ma,
oe possiole tnat botn phases (soil and oil) will contribute equally to the
diffusion rate of a specific component.
itiItiUUEAUX-H«ANG: MODELING AIR EMISSIONS FROM LANDFARMING
Of PETROLEUM WASTES (I')ti2)
With the assumptions that the soil column is isothermal, that no vertical
novement or waste occurs by capillary action, no adsorption of material occurs
-,n soil particles and tnat no biochemical oxidation occurs, the Thibodeaux-
Hwang model describes the vapor movement of a chemical species from a
soil-waste mixture. This model is applicable to either surface application or
subsurface injection methods of landfarming.
The one key variable in the Thibodeaux-Hwang derivation appears to be the
oil-layer dirfusion length, Zo. This term is related to application rate of
oil waste and thus its value will determine the extent that oil-phase
diffusion will play an important role in the flux rate determination. The
simplified version of the Thibodeaux-Hwang model assumes a low value for
85
-------
TABLE 22. INPUT PARAMETERS REQUIRED FOR EACH LAND TREATMENT AERR MODEL
Parameter
D ., diffusivity «f i in air filled pore spaces
D ., molecular diffuaivity of i in air
ai
D . , diffusivity of i in waste oil
VI
Z , oil-layer diffusion length
o
A interfacial area per unit volume of soil
a
c, soil porosity
t, tortuosity
h , depth of surface injection
A, surface area of application
h , deptn of penetration or plow slice depth
P
M , initial mass of component i
10
t, time
C concentration of i on gas side o: interface
1-8
ri , Henry's Law constant in concentration fora
C ., concentration of i in oil pnase
H, Henry's Law constant
C , solar sar.si.ry of vapor
P, total pressure
:, soil bulk density
-, particle density
E , water evaporation rate
RH, relative humidity
t , vapor pressure of cnemical
p , vapor pressure of water
H molecular weight of cneaical
a
M modelucar weight of water
o
Wi.V, weight fraction of cheaical vn the waste
•Tni bodeaux - Hwang :
(D 1i ' 0., Cif C^/MioH/
(2) Del • Dai '-I'
(3) ' • i - a/;
" T
r T c 1
C*> Ci« l 1 6 D.i Zo Hc \^C.
1 I 2 2 M
ID. a (h+hh-2h fl
y wi a p pa s n
Thibodaaux -
lhuag<
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
2
Hartleyb
X
X
X
X
X
X
X
X
(5) H,. • HCg H)6
bHartley:
86
-------
TABLE 71. TYPICAL PARAMETER VALUES AND RANCKS I-'OR THE TllIBODEAUX-UWANG
LAND TREATMENT AERR MODEL
Symbol Unlts tel.n.non Source of input Pa, a,,,,-, c,
__ , ------
qi g/cn-2-sec fluxra.e ' , ., ! cu 1 ,,t ed f rorc e,,ua, ion H
D cm^/sec diffu.ivity ol l m calculate,! from equal 10,1 .'h
''* air-filled pore spaces
„ cm2/sec molecula, dillusivuy , hemif a 1 handbook or ca leu I..1 e.l
"al cm o{ t in air tri,ni ,,-terence chemical
dimens.onles, .oil porosity ^ U ,,1 at e,l f ro. -qua. lou ^
dinu..,.5l..nle»s tortouslly .onslan. value
hs cra depth of su.Mce injection nv.isured on typical val,,.- ,i,sun. .1
n cm depth of penetration ,u measured or lypual v,ilu.- .iss,n,,e,l
P plow slice depth
00
initial mais of component i measure,!
nlo K
t 8ec time after application measured
c g/cm3 concentration of i on gas calculated from equation .''
'* side of interlace
„ c.3 oil/ Henry1. Law Constant- ,n calculated from equation 5-
C c-3 ,ir concentration form
c g/c«3 cone, of i in oil phase measured
H at.-i.3/«ol Henry1. Law Constant chemical handbook
C R-mol/cm' »ol.r density ol vapor use typ.cal value or calculate
^g • (see comments)
lypiinl value Expected range Comment.
|n-l IO'1 Highly variable Input
parameter
O./, | 0.25 - 0.62
( assumed)
0 0 - 20 cm hs " 0 for surface
appl icat ion
N A (3-10) x 107 highly variable input
1() 8-10 value of hp subscript
may be low shortly after
surface application
N.A. N.A.
N.A. 0-5 x 10*>
N.A. N.A.
N.A. N.A.
M-A,. M.A. highly variable parameter
N A iQ-3 - 10~5 highly variable parameter
I/;. 4*. x lO4 N.A. cg " ll
(cont i nu
-------
TAHI.F 23 (i-oiiL iinit-(l)
oa
00
Symbol Onlta
f/ctt^
g/c»J
Url mil ion
.Miice ot input |,ji JIIH-I ,-r
value Expccced r«nge Commtntt
f.mured or typical v«lut- usbiim'-J
toil bulk density
pirticl.- clun.ity
.oil handbook
so.l l,.,.,,lbook
1-2
atandard at«. prataura la
1 at.
>K
6 0 . Z H
ol a c
Ii el o c i
lo . • (h 2 « li h -2h 2 J
' Ul • p pa i '
•Equation •>. H,. - HCt|_M»'\
•Kqu.tion I. q, • D.j Cig/|hj » (t Uf,tA(hp-h,>C1K>/M,„I' "
bEquatlan 2. Del - Daj t/l
•
cEqu«tion 3. •' • I - B/P
''cqujtton A:
-------
L i e soil particle size thickness, thus for all cases that make use of
this assumption Equation (4) from Table 22 becomes:
Cig = HcCiL
Ci = concentration of component i in gas phase;
H = Henry's Law constant (concentration form);
ClL = concentration of component i in oil phase.
Thibodeaux and Hwang also present a flux rate equation which identifies
tne air emission release rate immediately after waste application:
= K
g
w.iere: q = f^x rate
•< = --as-pnase mass transfer coefficient (cm/s>;
g
^ '"' = vapor concentration of chemical i (g/cm^).
i
ini, equation, assumes no mass-transfer resistance in the soil phase and thus
is applicable only for short periods of time (i.e., immediately after
application, or for spills, and while a liquid pool is still visible). More
importantly, the equation is only valid for a pure compound because it
provides no description of liquid-phase resistance. Here again the
application thickness will be a controlling variable. For use in descr ing
air emission release rates ot a waste material, it is more correct to use an
"era" mass-transfer coefficient. Refinement of this equation may generate a
metnod or quantifying air emissions from drum storage facilities.
Tnis short term emissions estimate model closely correlates to the flux
rate model described by Hartley. The Hartley model does not accurately
uescnoe the physical situation of land application as described later.
Tnere is little experimental data available which can be used to validate
this model in either its complete or simplified forms. The apparent good
agreement with dieldrin test data as shown by Thibodeaux and Hwang (1982) may
not represent true field conditions.
HARTLEY MODtL (1969)
The Hartley model was developed to determine the evaporative loss of pure
volatile compounds. Although it is applicable to land spreading operations,
it is not applicable to landfarming methods. The model assumes that the rate
of mass transfer is controlled by resistance in the gas phase and is
proportional to the saturated vapor concentration. The liquid phase
resistance, which plays an important role for multicomponent liquid mixtures
containing volatile compounds, is completely ignored in the model development.
89
-------
Simply stated, the Hartley model calculation of the flux rate of a
chemical compound is performed on the basis of a known flux rate of a
reference compound. Water is generally taken as the reference compound.
Although the Hartley model represents a simple method of calculating air
emission release- rate of chemical compounds from a soil surface (or any
surface), it does not accurately represent air emissioa release rates of
landfarming application as does the Thibodeaux-Hwang model. Several drawbacks
to the Hartley model include:
• predicts a maximum emission rate throughout volatilization period;
• doesn't account for incorporation of volatile--material within soil;
• not readily extended co complex, raulticomponeht mixtures;
• based on a nonvolatile reference compound (water).
90
-------
SECTION 7
STORAGE TANK AIR EMISSION ESTIMATION TECHNKJJES
INTRODUCTION
Air emissions of volatile compounds from storage tanks at TSDFs are a
function of several -factors including:
• physical and chemical characteristics of the stored liquid;
• tank design;
• tank condition and site conditions; and
• operational characteristics, especially turnover frequency.
Fo- a »iven liquid, tank design influences the emission rate potential. The
five types of storage tanks, which are described later in this section, are:
• fixed roof;
• external floating roof;
• internal floating roof;
• variable vapor space; and
• pressure tanks.
o: t.iri tive designs, vanaDle vapor space and pressure tanks generally proauce
Cue lease air emissions.
In addition to tank design, the true vapor pressure of the material
stored is one of the most significant parameters affecting emissions.
Consequently, the type of tank selected during plant design is partially
dependent on the vapor pressure of the material being stored. According to
Enckson 11980), fixed roof tanks are preferred for storing materials with
vapor pressures up to 34.5 kPa (5 psia) ; floating-roof tanks when vapor
pressures are in the range of 6.9 to 34.5 kPa (1 to 5 psia) ; and pressure
tanks when vapor pressures are greater than 51.7 kPa (7.5 psia). Other
factors such as material stability, safety hazards, health hazards, and
multiple use also influence tank selection for a particular organic liquid.
91
-------
Physical actions on the tank such as changes in temperature or pressure
affect the volatilization rate. Temperature increases from direct solar
radiation and contact with warm ambient air increase volatilization and
emission potential. Danielson (1973) notes that for a free vented tank, winds
may entrain or educt some of the saturated vapors into Che ambient air.
Operating conditions also affect storage tank emissions; i.e., frequency
of filling (turnover rate), vapor tightness of the tank, and volume of the
vapor space. Fixed-roof tanks maintained completely full limit the volume of
vapor space and, thus, emissions. When the turnover rate is long; i.e.,
extensive time periods between filling/emptying cycles, the free space in a
tank becomes more saturated with vapor from the ITquid. Thus, during filling
of the tank or during breathing cycles, a larger concentration of vapors
exists in the air-vapor mixture vented ,to the atmosphere. Danielson (1973)
states that vapor tightness of the tank can influence the evaporation rate,
and a lack of tight vapor seal allows increased emissions. Proper seal
maintenance for floating tanks is necessary to limit vapor losses.
The American Petroleum Institute (API), EPA and others have developed
empirical equations for fixed and floating roof tank emissions based on field
test data. Masser (1981) notes that emissions from pressure tanks occur only
when the design pressure is exceeded, when the tank is filled improperly, or
wher. abnormal vapor expansion occurs. Because these are not regularly
occurring events, and pressure tanks are not a significant source of emissions
under normal operating conditions, no equations were found available for
estimating air emissions from pressure tanks.
Table 24 summarizes the recommended equations for fixed and floating
roof tanks, showing the input parameters required for each model. Following
sections describe these models in more detail, and also describe additional,
non-recommended models found in the literature. Special case consideration
for open tanks and storage of mixtures is also presented.
FIXED ROOF TANKS
A typical fixed roof tank is shown in Figure 7. Air emissions from
fixed roof tanks occur from breathing losses and working losses. Masser
(1981) defines breathing loss (Lg) as vapor expulsion due to vapor expansion
and contraction from changes in tank temperature and ambient barometric
pressure. Breathing losses occur in the absence of any liquid level change in
the tank.
The combined loss from periodic filling and emptying is called working
loss (Ly). When a tank is filled, vapors are expelled from the tank when
the pressure inside the tank causes opening of the relief valve. Emptying
loss occurs when air drawn into the tank during liquid removal becomes
saturated with organic vapor, expands, and exceeds the capacity of the vapor
space.
In 1962, the American Petroleum Institute published API Bulletin 2518
which contained equations for estimating breathing losses and working losses
from fixed roof tanks. These equations were used extensively by regulatory
92
-------
TABLE 24. INPUT PARAMETERS REQUIRED FOR RECOMMENDED FIXED AMD
FLOATING ROOF MODELS
M,
P,
D,
H,
AT
Fp
c,
KG
K -
V,
N,
p~
^ C"
^,
c,
WL
Parameter
molecular weight of vapor in storage tank
true vapor pressure at bulk liquid conditions
tank diameter
average vapor space height
, average ambient diurnal temperature change
, paint factor
adjustment factor for small diameter tanks
, product factor
, turnover factor
, seal factor
average wind speed
seal related wind speed exponent
, vapor pressure function
, secondary seal factor
average tnroughput
shell clingage factor
, average organic liquid density
A
X
X
X
X
X
X
X
X
Model
B C
X X
X
X
x x
X
X
X
X
X
D
x
X
MODEL DESIGNATIONS
A. Fixed Roof Tank Breathing Losses (API-1962, modified by TRW/EPA).
L - 2.26 „ 10- H
b. Fixed Roof Tank Working Losses (API-1962). •
LV = 2.40 x 10~2 MPKN KC
C. £xternal and Internal Floating Roof Tank Standing Storage Loss (API/EPA,
1980).
Ls - Ks VNP*DMKCEF
D. External and Internal Floating Roof Tank Withdrawal Loss.
(0.943)QCWL
L. .= D
93
-------
PRESSURE/VACUUM
VALVE
GAUGE HATCH
MANHOLE-
MANHOLE
NOZZLE (FOR
SUBMERGED FILL
OR DRAINAGE)
Figure 7. Typical fixed roof storage tank (Masser - 1981).
-------
agencies in the past to estimate air emissions from fixed roof tanks.
However test results reported by EPA (1979), the Western Oil and Gas
Association (WOGA) (1977), and the German Society for Petroleum Science and
Carbon Chemistry (DGMK), showed that the 1962 API equation for breathing
losses over-estimated air emissions by roughly a factor of four. However,
work i,in losses estimated by the 1962 API equation were found to be fairly
accurate.
Under EPA contract, TRW (1981), updated the breathing loss equation for
fixed roof tanks based on the more recent test data. The revised equation
provides breathing loss emission estimates which are 72 percent less than
obtained by estimating emissions using the 1962 API equation. EPA s Office of
Emission Standards Engineering Development (ESED) reported to GCA that: the
revised equation for breathing losses, prepared by TRW, and the 1962 API
equation for working losses are the best available equations for fixed roof
scora-e tanks. These equations are incorporated into a revised edition of
EPA's pmission factor handbook, AP-42 (April 1981). The revised AP-42
equations appear in Tables 2> and 26 for breathing and working losses,
respectively, from fixed roof tanks.
The fixed roof working loss Uw) is the sura of the loading and
unloading losses. Special tank operating conditions may result in losses
which are significantly greater or lower than the estimates provided by
lfl,;« :i ana -ust be evaluated on a site-specific basis. The total losses
from a fixed roof storage tank are equal to the sum of the breathing losses
(Lg) and working losses (L^).
Typical values for input parameters to the fixed roof tank equations
appear in Tables 27 ana 28, for breathing and working losses, respectively.
EXTERNAL AND INTERNAL FLOATING ROOF TANKS
External Floating Roof Tanks
Standing storage loss, the major element of evaporative loss, results
from wind induced effects acting on the top of an external floating roof
tank. The types of seals used to close the annular-vapor space between the
floating roof and the tank wall dictate the nature of wind effects.
l-igurt; 6 depicts a typical external floating roof storage tank.
Standing storage loss emissions from external floating roof tanks are
controlled by either a primary seal, alone, or a primary and a secondary
seal. Three basic types of primary seals used on external floating roofs
are- (1) mechanical (metallic shoe); (2) resilient (nonmetallic); and.(1)
flexible wiper. Resilient seals are mounted to eliminate the vapor space
between the seal and liquid surface (liquid mounted), or to allow a vapor
space between the seal and liquid surface (vapor mounted). A primary seal
closes the annular space between the edge of the floating roof and the tank
wall. Some primary seals are protected by a metallic weather shield. Two
configurations of secondary seals currently in use are: (1) shoe mounted; and
(2) rim mounted. Although there are other seal system designs, Masser (1981)
indicates that the systems described here comprise the majority in use today.
95
-------
TABLE 25. RECOMMENDED MODEL FOR FIXED ROOF TANK BREATHING LOSSES
(TRW UPDATE OF 1962 API MODEL)
2.26
where:
LJJ * fixed roof breathing loss (Ib/year)
M * molecular weight of vapor in storage tank (Ib/lb mole).
See AP-42, Table 4.3-1.
P = true vapor pressure at bulk liquid conditions (psia).
See note 1.
D = tank diameter (ft).
H = average vapor space height, including roof volume correction (ft).
See Note 2.
'. T = average ambient diurnal temperature change (°F).
Fp = paint factor (dimensionless). See AP-42, Table 4.3-2.
C * adjustment factor for small diameter tanks (dimensionless).
See AP-42, Figure 4.3-4.
K£ = product factor (dimensionless). See Note 3.
Notes: (1) True vapor pressures for organic liquids can be determined from
AP-42, Figures 4.3-3 or 4.3-6, or AP-42, Table 4.3-1.
(2) The vapor space in a cone roof is equal in volume to a cylinder
which has the same base diameter as the cone and is one third the
height of the cone.
(3) For crude oil, Kc * 0.65. For all other organic liquids,
96
-------
TABLE 26. RECOMMENDED MODEL FOR FIXED ROOF TANK
WORKING LOSSES (1962 API MODEL)
Ly = 2.40 x 1CT2 MPKNKC
where:
LW = fixed roof working loss (lb/103 gal throughput).
M = molecular weight of vapor in storage tank (Ib/lb mole).
See AP-42, Table 4.3-1.
P = true vapor pressure at bulk liquid conditions (psia).
See Note 1.
KN = turnover factor (dimensionless). See AP-^2, Figure 4.3-7.
Kc = product factor (dimensionless). See Note 2.
Notes: (1) True vapor pressures for organic liquids can be determined from
AP-42 Figures 4.3-5 or 4.3-6, or AP-42 Table 4.3-1.
(2) for crude oil, RC=U.OH. For all other organic liquids,
97
-------
TABLE 27. TYPICAL RANGES OF INPUT PARAMETERS FOR FIXED ROOF TANK
BREATHING LOSS MODEL:
2.26 x 10
0.68
1.73 U0.51 AT0.50
D H AT
Typical range of values
Parameter
symbol
Parameter
description/units
For 95% of
compounds
For 50% of
compounds
M Molecular weight of vapor
in storage tank (Ib/lb
mole)
32-190
True vapor pressure at bul* 0.00004-6.9@60°Fa
Liquid conditions (psia)
Tank diameter (feet)
14.7-98b
Average vapor space height 7-3Jb
(ft)
Average ambient diurnal
temperature change (°F)
_+20° from average
daily temp.c
Paint factor (dimensionless) 1.0-1.58a
Adjustment factor for small 0.4-1.Oa
diameter tanks
Product factor
(dimensionLess)
0.65-1.03
70-130*
1.0 - 4.0a
16-55b
19-33b
_+10° from average
daily temp.c
1.2-1.43
0.7-1.03
0.65-1.0a
aEstimated from a review of data presented in AP-42.
bEstimated from a review of data presented in Erikson (1980).
c£ngineering judgement.
98
-------
TABLE 28. TYPICAL RANGES OF INPUT PARAMETERS FOR FIXED ROOF
TANK WORKING LOSS MODEL:
LU = 2.40 x 10~2 MPKNKC
Parameter
symbol
Typical range of values
Parameter
description/units
For 95% of
compounds
For 50% of
compounds
M Molecular weight of vapor 32-1903
in storage tank (Ib/lb mole)
P True vapor pressure at bulk 0.00004-6.9^60°Fa
liquid conditions (psia)
Turnover factor
(diinensionles s)
Product factor
(dimensionless)
0.22-1.03
0.84-1.0b
7U-1303
1.0-4.Oa
0.3-0.83
N.A.
ited from.a review of data presented in AP-42.
Kc for crude oil = 0.84, K.c for all other organic liquids = 1.0. An
average value of 0.95 is expected to be a good average value with high
precision.
99
-------
o
o
TANK GAUGE
PONTOON
MANHOLE
SEAL
ENVELOPE
ROOF LEG
SUPPORT
AUTOMATIC
BLEEDER VENT
PRIMARY
SHOE SEAL
Figure 8. Typical external floating roof storage tank (Masser - 1981)
-------
Withdrawal loss is another source of emissions from external floating
roof tanks. This loss is the vaporization of liquids that cling to the tank
wall and are exposed to the atmosphere when a floating roof is lowered by
withdrawal of liquid.
Internal Floating Roof Tanks
An internal floating roof storage tank has a permanently fixed roof and a
cover inside the tank that either floats on the liquid surface (contact), or
rests on pontoons several inches above the liquid (noncontact). Figur.s 9
and 10 illustrate the contact and noncontact design of internal floating roof
storage tanks.
Internal floating roof tanks generally have the same sources of emissions
as external floating roof tanks; i.e., standing storage and working losses.
Fittina losses through deck fittings in the roof, roof column supports, or
other openings, can also account for emissions from internal floating roof
tanks.
Typical internal floating roofs incorporate two types of primary seals,
resilient foam filled and wiper. Similar to those employed in external
floating roof tanks, these seals close the annular vapor space between the
•=>d"e of the floating roof and the tank wall.
Recommended Emission Estimation Techniques for Floating Roof Tanks
EPA's Office of ESED recommends in Supplement No. 12 to AP-42 the use of
API's February 1980 Bulletin 2517, Evaporation Loss from External Floating
Roof Tanks. According to McDonald (1982), EPA currently suggests two changes
to the API equations presented in AP-42 for volatile organic liquid storage,
• Change the product factor, Kc, from 10 to 1;
• Disregard the secondary seal factor, Ep.
Based on the above changes, Table 29 shows EPA's currently recommended
equation for standing storage losses from external floating roof canks.
For estimating standing storage losses from internal floating roof tanks,
£PA recommends the approach identified in API's June 1983 Bulletin 2519,
Evaporation Loss from Internal Floating-Roof Tanks. Standing losses «"»
internal floating roof tanks are derived by summing the losses estimated from
the rim seal area, deck fittings, and deck seams.
101
-------
Center Vint
Pwipherol Roof Vent/
Inspection Hatch
l/4 inch diameter
SS Ground Cables
Primary Seal
Access Port
Tan* Support Column with
Column Wei!
Figure 9. Ncncontact internal floating roof tank.
Center Vent
Penpherol Roof Vent/
Inspection Hatch
'/4incti diameter
SS Ground Cities
Primary Seal
Access Port
Rim Plate
— Rim Pontoons
Rim Pontoons
Support Column with
Column Well
Vapor Space
Figure 10. Contact internal floating roof tank.
1,02
-------
TAIiLK 29. Kl'A/AI'I KKCOMMKNOI;!) fKCIINKJUli FOR STANDING STOKAGK
NOSSliS FROM KXTKKNA1. KLOAITNC ROOF TANKS
Ls = KSVNP*DMKC
where: LS = standing storage loss (Ib/yr)
Ks = seal factor (lb-mole/(ft (mi/hr)Nyr)). See Note 1.
V = average wind speed at tank site (rai/hr). See Note 2.
N = seal related wind speed exponent (dimensionless). See Note 1.
P* = vapor pressure function (dimensionless). See Note 3.
PA
0.5
i / P \
?* =
L
I .
P = true vapor pressure at average actual organic liquid storage at
temperature (psia)
PA = average atmospheric pressure at tank location (psia)
D = tank diameter (ft)
M = average vapor molecular weight (Ib/lb-mole). See Note 4.
Kc = product factor (dimensionless). See Note 5.
Notes: (1) For petroleum liquid storage: Kg and N for both primary only
and primary/secondary seal systems are found in AP-42, Table 4.3-3
(2) If tne wind speed at the tank site is not available, wind speed
data from the nearest local weather station may be used as an
approximat ion.
(continued)
103
-------
TABLE 29 (continued).
Notes (continued).
(3) P* can be calculated or read directly from AP-42 Figure 4.3-8.
True vapor pressures for organic liquids can be determined from
AP-42 Figures 4.3-5 or 4.3-6, or AP-42 Table 4.3-1. If average
actual organic liquid storage temperature, Ts, is unknown, the
average storage temperature can be estimated from the average
ambient temperature TA(F) (available from local weather
service data), adjusted by the tank paint color factor. See AP-42
Table 4.3-4.
(4) The "molecular weight of the vapor, M, can be determined by AP-42
Table 4.3-1, analysis of vapor samples, or by calculation from the
liquid composition. A typical value of 64 Ib/lb-mole can be
assumed for gasoline, and a value of 50 Ib/lb-mole can be assumed
for U.S. midconcinental crude oils.
(5) For all petroleum liquids except crude oil: K£ = 1.0
For crude oil: *".£ = 0.4
For all volatile organic liquids: K£ = 1.0
104
-------
Withdrawal losses from external floating roof tanks are determined by the
EPA/API equation shown in Table 30. The total loss from floating roof tanks
in Ib/yr is estimated by the following equation:
LT(lb/yr) - Ls(lb/yr) + Lw(lb/yr)
where: LT = total loss;
Ls = standing storage loss;
Ly = withdrawal loss.
The equation presented in Table 30 for external floating roof tanks was
modified in API Publication 2519 for use in estimating withdrawal losses from
internal float ing. roof tanks. The improvement in withdrawal loss estimate is
obtained if the type and number of columns are known.
Tables 31 and 32 show typical ranges of values for input parameters to
external floating roof model recommended by EPA.
OTHER STORAGE TANK MODELS
Several other models for storage tanks were found in GCA1 s literature
search and through discussions with EPA and API. However, these approacnes,
as descrinen below, are not considered state-of-the-art techniques.
Storage Tank Model Developed in the USSR
Moryakov, et al. (1979) presents a model developed in the USSR for
estimating storage tanks emissions, but it appears to have two major
drawbacks. First, the model is based on tests conducted in a northern clima.e
and has not been thoroughly validated through field measurements. Moryakov
reported that further experimental verification is required before tne model
can be used directly for southern climate zones.
The second major drawback is that the model -does not account for what the
authors termed small breathing losses. These losses are the equivalent of
API's breathing losses for fixed roof tanks and standing storage losses for
floating roof tanks. In the U.S., breathing losses are considered signi.ican.
sources of emissions, and in some cases may exceed working losses or
withdrawal losses.
In addition to the above drawbacks, the USSR model was developed to
estimate emissions of petroleum products only. It is not known if the model
is applicable for estimating emissions of volatile organic liquids.
105
-------
TABLE 30. EPA/API RECOMMENDED TECHNIQUE FOR WITHDRAWAL LOSS FROM
EXTERNAL FLOATING ROOF TANKS
(0.943)
LW * 5
where: Lw * withdrawal loss (Ib/yr).
Q * average throughput (barrel (bbl)/yr; 1 bbl * 42 U.S. gallons).
C * shell clingage factor (bbl/1000 ft2). See AP-42, Table 4.3-5.
WL = average organic liquid density (Ib/gal). See Note 1.
D = tank diameter (ft).
N'otes: (1) If W^ is not known, an average value of 6.1 Ibs/gallon can be
assumed for gasoline. An average value cannot be assumed for
crude oil, since densities are highly variable.
(2) The constant, 0.9^3, has dimensions of (1000 ft3 x. gal/bbl2).
106
-------
TABLE 31. TYPICAL RANGE OF INPUT PARAMETERS FOR WITHDRAWAL LOSS FROM EXTERNAL
FLOATING ROOF STORAGE TANK MODI'.L:
Parameter
model
Q
C
H<
Parameter
description/units
Average throughput (bhl/yr)
Shell clingage factor
(bbl/1000 ft
ge
2)
Average organic liquid
density (Ib/gal)
Tank diameter (ft)
Typical range ot values
For 95* of
compounds
6.0 x lO^ - 5-0 x
0.0015 - 0.6
N. A.
For 50% of
compounds
0.0015 - 0.6
N.A.
30 - 100
45 - 85
Comments
Average throughput varies greatly.
Clingage factor varies signifi-
cantly dependent on the product
stored and the shell condition.
An average value of 6.1 Ib/gal
can be assumed for gasoline. An
average value cannot be assumed
for crude oil or volatile organic
liquids, since densities are
highly variable (Masser - 1981).
Variance between tank sizes it too
great to select a constant.
i • i • n i
. „„ o -130 m3 tank turned over an average
times per year and an B,J->•
-------
o
00
TABLE 32. TYPICAL RANGES OK INPUT PARAMETERS FOR EXTERNAL FLOATING ROOF TANK STANDING
STORAGE LOSS MODEL:
Ls = KSVNI>*!1MK,:
Parameter
symbol
f*
Typical range of values
Parameter
description/units
For 95% of
compounds
Seat factor
Average wind speed at t
-------
Qutdated/Nonrecommended Models for Floating Roof Tanks
1962 API Bulletin 2517 presented equations for estimation standing
loss'and withdrawal loss for floating roof tanks. The equations did
not dirrerentiate between internal and external floating roof: tanks. Input
parameters for the API Bulletin 2517 equations appear in Table 33.
in 1978, the Chicago Bridge "d^^ny^
seal. EPA's Office of ESED does not presently recommend use of these
equat ions .
SPECIAL CONSIDERATIONS
Storage of Mixtures
instead of the pure compound vapor pressure.
The true vapor pressure of a mixture is the summation of partial
pressures of each component in the stored liquid:
'i-S'i-
where- P° = vapor pressure of mixture;
' ' m
P. = partial pressure of component i;
x. = mole fraction of component i in the liquid;
i
= activity coefficient of component i in the liquid;
' i
p° = vapor pressure of pure component i.
The activity coefficient corrects for deviations from Raoult's Law to
account for liquid interactions. For hydrocarbon mixtures it is enera
l ii
by Lyman, et al. (1982).
It should be noted that by using the vapor pressure of the mixture in the
storage tank models, the missions estimate will.be as total volatile organic
c«boJ (VOC). The concentration of component i in the vapor phase is the
109
-------
TABLE 33. INPUT DATA FOR 1962 API FLOATING ROOF MODEL
Standing storage loss Withdrawal loss
Molecular weight of vapor in storage Density of stored liquid
tank
True vapor pressure at bulk conditions Tank construction factor
Tank diameter Tank diameter
Average wind velocity
Tank type factor
Seal factor
Paint factor
Crude oil factor
110
-------
TABLE 34. FLOATING ROOF EQUATIONS BASED ON 1978 PILOT TESTS
(NOT RECOMMENDED FOR USE)
LT =
LS + LF
Vn M D
(14.7)
1 +
(1 -
P
14.7
0.5
}
2
2205
Vn M
(14.7) 1
1 + (1 -
P 0.5
14.7 )
2 2205
where: L_ -
LWD
LS =
LF =
M =
P
D
V
K
L,, = O.OJ0198DTHd 1/2205
'rt D
total loss (mg/yr) ;
= withdrawal loss (mg./yr);
seal loss (mg./yr) ;
fitting loss (mg/yr);
molecular weight of product vapor (Ib/lb-mole); 78.1 Ib/lb-mole
for VOC;
= true vapor pressure of product (psia); 2 psia assumed;
= tank diameter (ft);
= average wind speed for the tank site (mph); 10 mph assumed
average wind speed ;
= seal factor
« fitting factor
» seal wind speed exponent
= fitting wind speed exponent
= product withdrawal shell clingage factor
= fitting multiplier
= turnovers (per yr),
= tank height (ft),
= density of stored liquid at bulk liquid conditions (Ib/gal;
use 8.0).
Ill
-------
partial pressure o£ component i (P^ divided by the vapor pressure of the
mixture (Pm). Thus, the emission rate contribution for component i is
determined by multiplying the calculated emission rate for the mixture by the
vapor phase mole fraction of component i.
Open Storage Tanks
Generally, it is unusual to find pure volatile organic liquids stored in
open tanks. However, it may be possible that certain wastes such as sludges
are stored in open tanks prior to treatment or disposal. The mechanisms of
molecular and turbulent diffusion will control the process of evaporation.
Thus, the methods for determining an emission rate for this type of storage
becomes similar to that developed for surface impoundments.
The major difference between a surface impoundment and an open storage
tanks is the potential for a greater freeboard effect. For a substantial
freeboard (i.e., greater than the fetch), the wind effect on the liquid
surface becomes negligible, thus the emission rate controlling step becomes
the molecular diffusion of component i in the waste sludge.
112
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SECTION 8
AIR EMISSION ESTIMATION TECHNIQUES
FOR WASTEWATER TREATMENT PROCESSES
INTRODUCTION
The purpose of this section is to identify AERR models which can be used
for quantifying air emissions of volatile compounds from hazardous waste
rrea'rren.- svst^ms. The approach used for identifying the appropriate AERR
nociPl was to categorize each treatment system into one of these main
categories:
• open tanks with no nixing;
• opcr. tanks with T.ixing; and
• closed systems.
In the case where all volatile species in the waste stream have been
identified, and their effluent concentrations measured, AERR models for
aerated or nonaerated surface impoundments could be applied to open tank
Processes depending upon system dynamics (i.e., aerated or nonaerated) For
Closed svstem wastewater treatment processes, it can be assumed that asiae
^,n svstem leakage or operational abnormalities, there are no air emissions.
rV concentration of effluent contaminants can be calculated based on process
unit efficiency. Such calculations are provided in the literature out will
no: be discussed in this report.
Limited data are available regarding the removal efficiency and effluent
concentrations for organic pollutants subjected to various biological
treatment systems. If outlet concentrations are not available for the subject
facility, these limited data may provide a rough cut estimate of the in-tank
concentration for a specific compound. However, caution is advised since it
is likely such data were developed for single component waste streams.
interactions of multicomponent waste streams will affect the system removal
ef ficiency.
Emissions estimation techniques have been developed for biological
treatment processes when only inlet concentrations are known. These models
tak, into consideration pollutant removal by degradation adsorption and air
stripping. A formal discussion of each model is provided in this section.
113
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OPEN TANK SYSTEM-NO MIXING
Typical wastewater treatment systems that fall into the category of open
tank-no mixing are:
• sedimentation;
• chlorination;
• equalization.
No AERR Models were located that specifically described air emissions from
these treatment systems. However, it can be assumed that these systems fall
into a broader category of nonaerated surface impoundments. Treatment systems
that fall into the open tank-no mixing category represent plug flow systems.
Therefore, applying the nonaerated surface impoundment model one needs to
accurately define the in-tank concentration of the specific compound in
question.
As described in Section 4, Mackay and Leinonen (1975) presented a surface
impoundment model for plug flow, where the in-tank concentration was defined
by:
= C *»v^ —V r /T
\* • W - »• rf \. "^ * T ' '
10 iL
where:
Cj_ * concentration of compound i at time t (mol/ta-3) ;
G£O = initial concentration of compound i (niol/m3) ;
KJ_L = overall liquid phase mass transfer coefficient (m/hr) ;
t = residence time (hr);
L = impoundment depth (m).
This is a simple, first-order decay method for calculating the in-tank
concentration, however, the term KJ_L only accounts for a compound's loss by
volatilization. A more correct application would be to define the effects of
sorption and probably chemical conversion.
OPEN TANK-MIXING: BIOLOGICAL TREATMENT SYSTEMS
GCA* s evaluation of open tank treatment processes with mixing focused
mainly on the activated sludge biological treatment process (high rate
mixing). Other processes, which might fall into the low rate mixing
subcategory, include neutralization or precipitation involving the addition
and rapid mixing of a chemical reagent. The emissions from these processes
are best described by application of Thibodeaux's Aerated Surface Impoundment
(AS I) model using very low power input to identify the area of^turbulent
mixing. This model was previously discussed in detail in Section 4.
114
-------
Major research and development efforts of models to predict hazardous
chemical air emissions from biological treatment processes have been conducted
by Hwang and Freeman. The following discussion of AERR models developed by
these two researchers identifies basic similarities in approach and
differences in model details. In addition, Thibodeaux's ASI model is
discussed in the context to which it cnn he applied to the activated sludge
(AS) biological tr.eatment process. In summary, four basic models to predict
air emissions release rates from the AS process are discussed as follows:
• Thibodeaux (1981d)—ASI model;
• Hwang (1980)—activated sludge surface aeration (ASSA) model;
• Freeman (1979)—ASSA model;
• Freeman (1980 )--c i. E f us-: d air activated sludge (DAAS) model.
Cable 35 summarizes input parameters required for each model reviewed by
GC-'-.. The following sections discuss these models in detail.
All of th= models presented predict the air emissions rate based on the
concentration of compound i in the aeration basin of the activated sludge (AS)
orocess. For a well mixed system, the basin concentration of a specific
co-pound is assumed equal to the effluent concentration. Models which predict
emissions based on the influent concentration (S0 or Cj_) of the compound
tend to be very complex compared to models which assume a known effluent
concentration (Se). Three of the four models reviewed can be applied to
surface aeration AS systems, whereas only the Freeman DAAS is directly
applicable to diffused air systems. In general, the Hwang ASSA model tends to
be both adequate and simple to apply compared to Freeman's model.
Hwang (1930) Activated Sludge Surface Aeration
Hwang's Activated Sludge (AS) treatment AERR model employs techniques
presented earlier for predicting emissions from aerated surface impoundments
•m ler steady state conditions (Thibodeaux, Parker, and Heck, 1981). The model
b.- Thibodeaux ". t al., predicts the air emission rate of a compound based on
th- concentration of the compound (substrate concentration, SP) within the
impoundment. Hwang notes that for AS treatment systems, AERR models should
consider removal of the compound by: (1) biological oxidation; (2) air
stripping; and (3) adsorption to wasted sludge. Thus, Hwang's model predicts
the effluent concentrations that result when the mass balance for the compound
across the AS process is satisfied. The emission rate from the process is
then predicted by the aerated surface impoundment equation. Note that if the
pollutant's effluent concentration for an AS process is known, the emission
release rate for that pollutant can be calculated directly by the aerated
surface impoundment equation. This is based on the complete mix assumption
that the effluent concentration adequately represents the concentration of the
compound in the aeration tank.
115
-------
TABLE 35. SIMPLIFIED LIST OF INPUT PARAMETERS REQUIRED FOR EACH ACTIVATED
SLUDGE BIOLOGICAL TREATMENT MODEL3
Tl,, I.O.I,-.-I,,. Hu.-lilK
<19Hld)h U»80)c
Parameter ^ ASI «odel ASSA Model
Air minion rate of hazardous substance i 0; Qj
Overall mas* transfer coefficient Kj. *«
Total surface are* of basin *» As
Mole fraction of compound i in the liquid X, X;
Mole fraction of compound i ac equilibrium X, Xj
Molecular weight of compound i *V\ ^\
£;:!u*nt concentration of compound i Se
Inf! i«nc concentration of ^O^OOuna i S-,
Re-.-c^'^:.^. ''.w'scere-'-cl ef'-w'-tr--^^'
•j-j^i:criS'. Je-ve:~e
Concentration o: micro-orzan nrrr; in ^ps-.~
'" . sv
C1
"
Torcen t ra t ion cf sj":s:ra:e comoo-r.': ;r re-vale; ^r
Adsorption constants Kl- KT
Maximum concentration of »u!>strjce on sludge *
Stripoing rate constant ^a
"cnc en t ra t ion if * ic ro-qr£3" LSITS in recv.le
r --ncen: ra t *5n ^f -i i : ro-orz a-,: ST.S .n .nrlueit
. ^n:encrat i in o- _-.x.ii-> i- 'nc.ienc
Jjncencracion of oxy2en in effluent 'lasin/
Concentration of oxv^en in recycle
"eec flow rate
Effljen: flow rate
Ri»cyc le f low rate
Diameter of r»|tion of effect f»r m««s transfer
in the turbulent tone
(1979)d
ASSA nodel
Fri-rt«jin ( 19HD)
Hif fused air
mtit transfer
nedel
MV,
(continued)
116
-------
TABLE 35 (continued)
Hn
Mass transfer coefficient for orKanic , ompound
turbulent zone, convective zone
Mass transfer coefficient for oxygen
t'irhiil»nt zone, convective zone
Cerber's biokinetic rate constants
Number of aerators in basin
Oxygen transferred to basin
R ? t P of orcani- ,1 i t i-,n.M ranc-=
5j:e ol mirro-orcar i sir £r(.u".
e ' a c t o ~ , i ^ ~ •' '
. 1 i "ir!^ sj"s:^3te ,->^^iimi
11 s i factor,
c i a ' area p.
->i f fusivi t-. jf cnmp.i.ina i m u?te-
Acceleration of K--avitv
r.verall mass transfer coef'.cienc to
fr">tn lioni^
", iec'ilar jeieb: of iir
M . i p,; . i,r we ight .it jatc-
.
(I98!tl>h (19XO)r
,\>!l mcii.-I ASSA mo.IP I
1-reem.in ( IWD*
ri»r:. - ' ^
P, wer inp.it tr !iqu:T per u.-it v >!,)"
Volume of bubble
ont inu..«i)
Sc
117
-------
TABLE 35 (continued)
Parameter
Thibodeaux Hwang
(1981d)b (I980)e
ASI wxlel ASSA Model
Frttiun
(1979)d
ASSA Model
Freewn (1980)*
diffused air
m»st transfer
•Odtl
Superficial liquid velocity
Rise velocity of » bubble swam
Terminal velocity of * single rising bubble
Hole fractions of compound in gas
Mole fraction of compound in ga> as it enters
bottom of basin
Mole fraction of compound in gaa as it hr*>ak*
tH» *urf*ce of the h**tn
ToCa! r'.sf time ^>f huh^lt? in Sa^:"., h'>-irs
V . s c o s i z -J 7 f 11 a u i d
0«»ns t f. of eas
5ers i:v of I i.su id
Surface :£"S,or o' '.cuic
y
n
a
"i
"8
-1
a?araiT«cers usec in corputvns nass transfer coefficients -ioc inclmied '-See Section <* Cor details*
h_
'Thibodeaux (1981d) ASI model
CHwang (1980) ASSA model
Q - K, A (X - X 1 MV.
'i L > 1 I i
:J r >T): . f I -r 'V t
S c -ic
Iv witn adsoroci^n :c slu^ae
-hers h
o -K.^ • g ( l-r ) t = ( 1 -
0
.r 1 1 i >n S ) «< , X' ( l-r )u
c r
(continued)
118
-------
TABLE 35 (continued)
Freeman (1979) ASSA model
(1) For substance balance
where X - C_
V
(2) For micro-organism balance
/*
(31 For oxygen balance
- °
where Xn = Or
Ks * co °o
go co °o
/MV
\*l °o * Ko2 Ks * co °o
ar '1930: DAAS model mass transfer equations
where
-6 K rM
B kg
(p' v:
-6 K MV,1
0.09 cm
1.9 ft, sec * 2
(p/v) "*
- 0.42
1/3
(3600) 1
MW,
H,0
119
-------
Figure 11 presents a schematic of the continuous AS process and defines
the terms used by Hwang and others* Hwang describes the dynamics of substrate
removal in the AS process by employing the following material balance:
Input in
Influent
QFSo -
Remova 1 by :
+
Biodegradation
*\ S/ ..6 TT ,
I So
(2) Air
stripping
(K S V) + Q
a e v
h(3)
1
Sludge
wastage.
KI x* s
e
* KT sr * KI sc
Output in
Effluent
- (QF - V Se
where:
X * sludge concentration in reactor (ug/l);
X' = maximum concentration of substrate on sludge (jg/1)
^l(s) = Grau equation rate constant, n=l (I/day).
Upon simplification and rearrangement;
(S - S )
o e
i ( ^ x s
K s) e
(1+r) t + K (1+r) S t
c a e c
W(l+r)
Kl X'
Further rearrangement of the above equation yields the two solution methods
presented in Table 36. The first method presented in Table 36 predicts air
emissions from the AS process by requiring the solution of a quadratic
equation in order to obtain Se. The second solution method is based on the
assumption that adsorption to the waste sludge is negligible which is true in
many instances.
Biodegradatiorx Kinetics —
Hwang evaluated the four biodegradat ion kinetic models listed below wich
respect to the AS process:
1.
2.
dS
First order kinetics: - -JT a k. X S
dS
Monod (1942) kinetics: - -T-
.
u X
3. Grau (1975) kinetics:
-|| -
j x(f-J '•
where n - 1
JC
4. Hwang (1980) kinetics: - -
X S
(1
S) S
120
-------
No2 AND N.
L-CL-, • ^ ^ AFRATFn
FEED >
FT (Q_) '
T F
B f¥ ^
_ ^A )
c fs°)
°i °
^ BASIN
RECYCLE
FR ^r(^F^
BR }Se|
J ™ 1
BASIN DISCHARGE 1^R F'^J "^^^
PA (Q ) ~"""""<"1'"1
% '^
>
r^^ P vx-
1 c' ft
°E
Fw (Qw)
B / w ~ \
\ " /
. cjj (sj)
rt *
•A'
NOTE: FREEMAN'S NOTATION FI, BI, CIt Oz,
ETC., WITH THE CORRESPONDING HWANG'S
NOTATION IN PARENTHESES.
Figure 11. Model of activated sludge system,
121
-------
TABLE 36. HWANG (1980) ACTIVATED SLUDGE TREATMENT PROCESS A£RR MODEL
Model Form:*
Q. - 4047 x 104 MW. KL{ A x£
where x. • (Se) MWH 0/10 MW.
T
K. . • (K. .) -£+(*)_ —
Ul Li C T Ll T -
A A.
— * (K,-JT-
A ^lT A
for significant absorption to waste sludge:
t
- b * b~+4aS(l*KS)
. M \ o T r
e 2 a
where b = 1 - K S * K S + -l s ' '>r)t ' l*K S ) * k ''!*r)t '1-K S ) » K X' (i*r)
loTr S cTr a cTr 1
c
a - K, (1 * Or) -:.SJ c + (l*r) k t )
1 S c a c
se ;rg adsorption :o wasce s 1-jdee ^ X ' smal I ^ '
o
_ , . .
De : inic ions:
Q. • er-ission rate of chemical t (g/s)
MW - molecular weight of chemical i (g/z mole)
1C » overall mass transfer coefficient o^" chemical i expressea in
liquid phase concentration (gmol/cnT- s)
A • surface area of the impoundment expressed in acres (Subscript c
denotes the conveccive area of the surface impoundment; subscript T
denotes the turbulent area)
x » mole fraction of component i in the liquid phase
4047 x 10"* • denotes the factor needed to convert the surface area expressed
in acres to cm'
X • sludge concentration in reactor (ug/1)
X* • nuxivun concentration of substrate (compound i) on sludge (ug/1)
k., , " Grau equation rate constant nml (I/day)
S » initial substrate concentration (yg/1)
o
k - area averaged overall air stripping rate constant (I/day)
3 Note: K . may be converted to k as described earlier under
surface impoundments
122
-------
The suitability o£ each biokinetic model was tested by Hwang with data from
the following sources:
• EPA, Cincinnati, Ohio; Batch experiments using over 50 pure priority
pollutants at initial concentrations of 5 and 10 mg/L.
• Union Carbide Corporation; Continuous flow reactors, two in series,
for BOD degradation of wastewater.
• Catalytic, Inc.; Continuous flow reactor using synthetic mixtures of
pure components; BOD analyzed.
• J. WPCF; Continuous flow reactor for biodegradation of benzidine in
wastewater.
Hwang noted that increased initial concentrations resulted in decreased
removal efficiencies, thus eliminating the first order kinetics model from
consideration. Grau kinetics and Hwang kinetics proved superior to Monod or
first order kinetics in fitting the data. The difference between the Grau and
Hwang kinetics was determining whether the plot of Xt/So (So-Se) versus
l/Se yields a straight line through the origin of the plot. Hwang found
that in most cases the Grau kinetics model (n=l) adequately described
biodegration kinetics. Thus, tne rate of organic (substrate) removal is
expressed as:
li
dt
'l(s)
X S
wh e r e:
dS/dt = rate of substrate removal (ug/l/day);
X = biomass concentration (ppm);
S = substrate concentration (usually Se) (ug/D;
S0 = initial substrate concentration (yg/1);
kl(s) = Grau kinetics rate constant (n=l) (I/day).
Determination of Biokinetics Rate Constants—
In order to apply the above biokinetics model to an AS system one must
know the Grau kinetics rate constant ki(s) specific to the substrate
compound of concern. Determination of the biokinetic rate constant k^(s)
can be accomplished by fitting laboratory or field data to the Grau kinetics
material balance;
Xt
S (S -S )
o o e
Cl(s)
123
-------
Plotting Xt/S0 (S0-Se) versus l/Se, should yield a straight line
through the origin at a slope of l/k]_(s). Hwang has developed values for
Grau's kj.(s) for most of the 129 priority pollutants based on; (1)
laboratory and field data cited above; and (2) estimates based on observed
similarities between compounds extended to include untested compounds.
Air Stripping Kinetics—
The expression for air stripping of volatile compounds (substrate) from
the AS treatment basin is given as:
" dt " ka S
(for single component substrate system)
where:
ka = air stripping rate constant, I/day.
Hwang employs the area-averaged mass transfer model used by Thibodeaux
(1931d), where the overall mass transfer coefficient
-------
S = substrate concentration in the liquid, yg/1;
Sr = concentration of total substrates minus substrate S under
consideration, Pg/1;
K^, KT = adsorption constants;
X' = the maximum amount of the substrate adsorbed on sludge, ug/1.
Similarly, for a multicomponent substrate system the above equation
becomes:
KT ST x' T
[B'ST] = 1 + K S
(for multicomponent substrate system).
Note that the AS treatment system AERR model presented in Table 36 includes
tne sludge adsorption term for single component systems.
Kincannon et al. (1981,1982) investigated the importance of each
pollutant mechanism (air stripping, sorption and biodegradation) from
iab-scal" activated sludge treatment systems and found that sorption was not
ar. important mechanism for any of the priority pollutants analyzed. Although
sorne'"excen^ions applied, tne most predominate removal mechanism was found to
be consistent with chemical classification. For instance, biodegradation
r-raoval was predominate for nitrogen compounds, phenols and oxygenated
compounds. Aromatics were removed from wastewater by a combination of
biodegradation and air stripping, while halogenated hydrocarbons were removed
by air stripping.
Determination of Adsorption Rate Constants
Hwang also presents a method for determining the adsorption rate
constants? The above two equations can be rearranged and linearized as
r?T= -r^ (r)+ x-
[B.
(single component)
_ __1
[B.S] =
(multicomponent).
The values of KT and XT' are determined by plotting 1/[B.ST] versus
I/ST for single component substrates. Similarly, a plot of 1/lB.S] versus
1/S can be prepared for multicomponent substrate systems. Data presented
by Hwang may be used to develop these rate constants. In addition, Hwang has
provided a listing of these rate constants for the priority pollutants based
on work sponsored by EPA.
125
-------
Freeman (1979) Activated Sludge Surface Aeration Model
Freeman's original AS treatment AERR model appears very similar to the
work of Thibodeaux (198Ld) and Hwang (1980). The major difference between the
Freeman and Hwang AS models are Che biodegradation kinetics used. In
addition, Freeman does not address adsorption of substrate onto the wasted
sludge, assuming that adsorption is not a major removal mechanism for organic
pollutants. This is a reasonable assumption based on the most recent work of
Kincannon mentioned previously.
Freeman uses Thibodeaux 's aerated surface impoundment AERR model, based
on the two-film resistance theory, to predict the emissions from the AS basin
knowing the concentration of substrate in the basin. However, in order to
predict the concentration of substrate, Freeman writes the material balance
around the basin for the substrate, C, the micro-organisms, B, and oxygen, 0,
as follows:
C F + ? C_ = Cn F + N +• r V (for compound A)
Li. i\t\ UU 3 3
••• FR BR
' °0 F0
(for biomass B)
(f°r
Figure 11, shown previously, illustrates the material balance equations
presented above and provides a comparison with the Hwang (1980) model. Note
that the substrate material balance given above does not consider substrate
lost to wasted sludge.
Mass Transfer —
Freeman also employs Thibodeaux1 s aerated surface impoundment model for
prediccing the air stripping losses based on mass transfer ac the air-water
interface. Like Hwang, Freeman isolates zones for convective and turbulent
mixing and applies appropriate mass transfer expressions for each. The fina
form of Freeman's mass transfer expression describing the stripping of a
substrate X from an AS reactor is shown below:
N =
A -
N D
K X
MW
Freeman used similar analogies to predict the rate of oxygen transfer
into the AS basin as:
N,
NTTD
)*(*.-
Note that in Freeman's formula the turbulent area is given as 1TD2/4 where D
is the diameter of the region of effect for a given surface aerator.
Estimates on regions of turbulence for various sized surface aerators were
presented earlier in Section 4. Essentially, all aspects of the mass transfer
expression given above are identical to that in the Hwang ASSA model.
126
-------
Biokinetics— . ,
To represent the biological oxidation process, Freeman selected a model
developed by Gerber et al. (1976) as shown below:
kl
B + A^ . %
-
k5
BA02 > B + P
where:
B = micro-organisms;
A = substrate;
02 - dissolved oxygen;
P = products.
Assuming that the last step is rate determining, and the basin is
completely mixed, Freeman predicts the rate of oxygen uptake as:
k, B C 0
5 o o o
+K0 RS * Co°o
where :
In relating the oxidation of compound A to oxygen uptake and-'bioraass
growth, Freeman writes the following:
t 02 + s A—»B + H20 + O>2 + products
where:
t and s are stoichiometric constants based on assumptions made about the
molecular structure of the biomass in the above equation.
127
-------
ttased on the above equation, the rate of biomass growth (rg) and the
rate of substrate (compound A) removal (r^) can be shown as follows:
Thus, the final expression for the rate of substrate utilization would be:
t k,. B CO
5 o o o
r
_ _
A is k_ 0 fK Ko + C 0 + K C \ MW I'
_2 o 02 s oo 02 o) \ 02/
\ kL /
Similarly, Freeman's expression for the value of biomass growtn would be:
C 0 -i- K C U MW
Model Solution
Solution of the above system of equations requires the following data:
• process flow rates (feed, recycle, effluent) and basin dimensions;
• physical data and energy input data for calculating mass transfer
coefficients;
* biokinecic rate constants for the compound being considered (which
can be obtained by methods discussed later).
One key difference between the solution method for Freeman's ASSA model and
the Hwang ASSA model presented earlier is the extent of data assumed to be
known at the start of the problem. The Hwang model works with a known bionass
concentration and assumes that sufficient oxygen is maintained in the aeration
basin to support biological growth. On the other hand, Freeman's model
considers the interaction of the substrate (the compound being removed),
bioraass, and oxygen material balances, thus Freeman's model can be used to
predict emissions when less information is known. However, the solution
procedure for Freeman's model is inherently more difficult, as it requires the
solution of three simultaneous nonlinear equations to determine three unknowns
(B0, C0, and Oo) by iterative method. The solution method is¥briefly
outlined in Table 37. Freeman recommends that the solution be conducted by
application of a small personal computer. Computerized solution will tend to
save time and calculational errors will be avoided.
128
-------
TABLE 37. SOLUTION METHOD FOR FREEMAN'S ACTIVATED SLUDGE SURFACE AERATION AERR MODEL
1. Ueterni
r , ,h,.|pncP ami >..nv. ,,nv muii
, A f, nr,,i.,,is t,. ,!,.• terrain.- v.il,,,-s of s toichomet ric constants t «nd • in the following
2. Estimate Stoichio«try of Bl.>loRH-«l Decomposition of Compound A to product* t,. .K terrain
equal ion:
t02*lA*B» »2° * a)2 * Products
3. Obtain blokinetic r«t« constants Hi rough laboratory tests (see text).
4. Write Material Balance Equation for substiate. mic ro-org-ni smf., and oxyKi-n .is I., low
For substrate balance
CjF( + ffCf
N "II2 T / N '!>' 1
N -i- Kf (X ) «|A - - I
i. a a | S '• /
Bo co °o
MU
s k \ n
(r°o* VKs » S % * Ko2 co) '
For •icro-organiam balance
BF
00
For oxygen balance
• Fr°r ' °« F0 '
^~ S «0 co °o
?".-.«.* S % * «o, S.
12 2
/
L b '°2 °2
where X_
Sel
ect valve, for B0. C0. and 00 and solve the m.trr.al balance equation.. Kepe.t as necessary
until th* solution converge..
-------
Biokinetic Rate Constant Determination—
According to Freeman, determination of biokinetic rate constants to fit
the Gerber kinetics model can be conducted in one of two ways. By following
die work of Gerber, laboratory experiments can be conducted at considerable
cost and the data may be plotted to.directly determine Gerber'a; rate
constants. Freeman estimates that this method could cost in the range of
$50,000 to $100,000 per compound to develop the appropriate kinetics data.
The cost would tend to be dependent on the compounds characteristics
(biodegradability, volatility, etc.).
Another method used by Freeman in experiments with acrylonitrile (AN)
involved calibration of the entire model based on laboratory experiments
measuring feed AN and AN emissions. In order to apply this calibration method
Freeman measured or calculated all variables in the equations shown in
fable 37 except the biokinetic rate constants. The rate constants were then
determined by "fitting" the model predictions to the measured results under
varying conditions. One drawback to this method was that Freeman apparently
assumed Gerber's values for kQ? and kg were applicable to AN
biokinetics. While Freeman's assumption may or may not be correct, the model
should be accurate at least within the range of testing done by Freeman.
Freerrar. (1950) Diffused Air (Subsurface) Activated Sludge Model
In later wor*. Freeman (1930) developed a significant modification to Che
initial AS modal to more adequately describe the mass transfer phenomena
taking place in diffused air AS systems. Diffused air systems are commonly
employed in laboratory bench testing and occasionally used in actual field
applications. Freeman's Diffused Air Activated Sludge (DAAS) model, also
called the subsurface aeration model, focuses on the mass transfer of the
compound into the air bubbles released by the spargers as the bubbles rise to
the surface. This is quite different from the models discussed earlier, since
tne area across wr.ich mass transfer takes place is the surface area of the
buboles, not the oasir. surface area. Note that this model is better suited to
the activated sludge diffused air application than other models discussed.
Aside from the variation in mass transfer expressions the DAAS model should be
considered identical to Freeman's earlier AS model, thus only mass transfer
aspects of the model will be discussed.
Mass Transfer--
If it is assumed that the concentration of compound i in the air diffuser
source is negligible, than Freeman's expression for the concentration of
compound i in an air bubble as it reaches the surface is:
m X.
1 - exp
-6k 9 MW .
x air
°B Pgm
where:
m = distribution coefficient;
X^_ * mole fraction of compound i in liquid (ppra);
130
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kx = overall mass transfer coefficient to the bubble from the liquid
(g-mole/hr-cm2);
6 = rise time of bubbles (hours);
MWair = molecular weight of air (28.8 g/g-mol);
Dg = mean bubble diameter (cm);
Pg = density of air (g/cm3);
y2 = mole fraction of compound i in the gas bubble as it breaks the
surface.
The mean bubble diameter required above may be estimated according to the
following equation by Calderbank (1967):
n = 4. 15
(p/v)0'4
1/2
i + 0.09 cm
wnere:
~= liquid surface tension (g/s-);
~ I = liquid density (g/cm-');
P/V = power input to liquid per unit volume of basin (g-cm^/s-^-cm3);
r1'= gas holdup fraction in basin.
The power input per unit volume (P/V) to the basin could be estimated from
diffuser system pjwer use or from the superficial gas velocity as follows:
P/V = VG PL g .
whe re:
Vj = superficial gas velocity (cm/s);
g = acceleration due to gravity (980.6 cm/s').
The gas holdup fraction is estimated by Towell (1965) as:
0.9 + 2 V
Vj
Note that VQ is simply the gas volumetric flow rate divided by the surface
area of the tank and 0.9 is an approximation of the terminal gas velocity
(Vt) in feet per second.
131
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In the application of the above described diffusional air mass transfer
model, Freeman assumes the overall transfer is controlled by the liquid film
Thus:
1 1 1 1 e
^^™" ** ^"^"^™ ^ ' "•" 35 ^-»-» i rt ^ I A f O & \7 J) I 11 A f\ T ^
Ki * , LWL LOLkLCV/lLU^i-'LlV *
mk k, k, e
x g I 1 *
Freeman uses Calderbank's (1967) relationship for the liquid film mass
transfer coefficient in the following form:
H2 VKi ~ °-) Wig !/3
(Sc) = 0.62
Other Activated Sludge Models
g_
P 2
1
Ar?.oru- che nu:-v?r :>us ocr.er -iif^rts n nodeling air emissions from the AS
process, the vor'< of -mkash et a 1 . (13SI), and Brown and Weiucraus (1^82)
-sh^'jlc be r - i e rencea for COTID le t ;nes s .
Publicly O-.v-.e-i Treatment '.-.'crks (POI^'s 1 —
U'orK c.Tn.-ia:;e- '->;/ Iv'ika-h en al. C1931), describing the fate of organic
--''".? "'•-"- ^ i;"' °"rW;, cresen'T a svs tr.~.at ic aooroach tovar^s ""ooel devel opT.er, : .
Tr-.s sc-^y ^^ — d, as ji.d ii'van^, cist air stripping, biode^rada t ion and
id:?roti^n. :o ^.->-.is; •'.'ere -'.e z'r ^ : ^B associated with p>n:achlorop'«enol (?C?)
r-=-o/aL in :n- AS proves?. Air -=:rippi-.g was found to be responsible for
re-oval of less than 0.0- percent of the PC? applied, while adsorption onto
biomass accounted for less than 0.3 percent of the PCP. Important conclusions
of this study are summarized below:
• At substrate concentrations below the inhibitorv threshold, the
ec-iil ibr iur. concentration of a growth limiting substrate can be
descrioea oy Monod kinetics as follows:
'- S
m
K + S
where:
- = specie.; cell ?rowf. rate (day ~^);
^.m = maximum growth rate achievable;
Ks » saturation constant (mg/1);
S = substrate concentration (mg/1) also [Sg (Hwang)] or [Co
(Freeman) ].
• At much lower substrate concentrations (S < < Ks), as is the case
for most POTWs, the Monod equation reduces to simple first order
kinetics:
132
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y s
JH
K
s
Under steady state conditions P is equal to the reciprocal of the sludge
retention time. (1/SRT) plus decay (d) thus:
= 1/SRT + d = —
K
S
rearranging:
K K d
S = — (1/SRT) + —
Urn Urn
Vukash et a!., found" very good correlation with first order kinetics shown
a^ove for ?C? concentrations below inhibitory levels (< 350 ;ag/l).
Point Pr?ce-- ''as tester Treafv^nt—
A studv don>-> -,»' Srowr. and Weintraub (1982) indicated that the rate of
^•iistrate renoval c^uld be predicted bv pseudo first order kinetics of the
i?llo'»'ing forr:
s - sp
removal rate = = k S
X t e
v
where:
SQ = influent COD concentration;
S, = effluent COD concentration;
X. = mix^-i liq".or volatile suspended solids (MLVSS);
Q = flow rate:
V = reactor volume;
t = residence time = "/O;
k = coefficient of substrate removal.
The laboratory results from testing several paint process water constituents
apparently fit the model shown above extremely well. Substrate concentrations
ranged up to 600 ppm in some tests.
The results of the above investigations were included to illustrate the
point that one single biokinetic model may not be the only model capable of
fitting hiodegradation rate data. Furthermore, the number of biokinetic rate
expressions is almost as vast as the number of investigators conducting
133
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research. No single biokLnetic model is currently viewed as the best model,
although the Monod model and first order models have been in general use for
somo t
A. noted earlier, Hwang investigated four biokinetic models before
selecting Grau kinetics for use in his model. He expressed concern (Hwang
1932) that a model for complete mix systems would be based on the influent_
concentration. While this is contrary to basic assumptions for complete mixed
reactors [Rx is usually f(Se)l, Hwang notes that it apparently works better
than other commonly accepted models.
Similarly, Freeman (1982) noted that in hi- ~d.ling work ?« °u
biokinetic rate expressions are commonly ^P1^^." d«^ ^del could be
the data. Freeman indicates that any «"™£l'^e7tJe Berber model for
biomass concentration and sufficient oxygen.
5 - —e. :i—. --i. -
9 s u-pl Lc i '-•; ',
« model accuracy;
underlying assumptions.
T^ following dlscus^n will -cus on the above . issues , Briefly presenting
' - -els ressncei ear.ier.
eri-5
'•'^a-/:aXL"l;;y'" ess 'he extent to wnicn nodels are adequately flexible, i
n orscr to assess .he ex.. fA, w-ich :hev were intended and
L3 necessary to '--stand .h, ;ir - tan ^ ^ applicacion of; (I) Che
those :or wnich we v,isn -o anp.y c e model. (2) the Hwang actwatec
Thibodeaux aerated -"ac^ impoundment AS mod^ ^^ ^^ ^d ^}
slu,3a ,urfa= « ««^-r J ^ ^^ [oAAS) nodel . These models run the
Freeman di^-iseu ai. ac.i a - requires a known concentration ot
.ambit from th e simp e AS «o del -ic^^ q^^ ^ ^^ ^.^
of plant design and operating parameters
f,r rpaulatory agencies or consultants may desire to
Engineers working or regulat ory «g faciUcies. Conventional surface
assess emissions from p ^ «J « ^ ^owev.r , energy efficient DAAS
aerator design lagoons -il .be ?™™1* Q£ each of the four models to
g a'umstances is sho,n in Tab. 33. ,s
134
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shown in fable 3B, the Hwang ASSA Model tends to be very flexible except in
predicting emissions from oxygen limited systems, or systems operating under
unconventional circumstances. Of course, only the Freeman DAAS model
adequately handles circumstances involving diffused air systems. Note that
where sludge adsorption is determined to be substantial only the Hwang ASSA
model is adequate. In addition, the Hwang model also finds greater immediate
application to many organic compounds because adequate biokinetics rate data
have been developed for the Hwang (Hwang 1980) model as compared to the
Freeman ASSA Model.
Model Simplicity--
One underlying problem in predicting AERR from the AS process is the
complex nature of the solution method required. In comparison to other AERR
models, the AS models are among the most complex to solve. The Thibodeaux ASI
nodel is, of course, relatively simple, whereas the Freeman ASSA and DAAS
models requires tne assistance of a small computer for practical purposes. A
somewhat subjective ranking of the complexity of the models on a scale of 1 to
10 (10 being the most complex solution) is given below:
Complexity
Mode I . rating
Tiibode.-3.ix ASI 1
Hwang ASSA I
(without sludge adsorption)
Hwang ASSA ^
(with sludge adsorption)
Freeman ASSA 8
Freeman DAAS 10
Realizing thac most of the AS models presented require time consuming solution
techniques, the Hwang ASSA model with sludge adsorption is probably the most
complex model an evaluator Could be expected to employ without the aid of a
small computer.
The issue of model simplicity must be viewed with regard to problem
application. For example, given the concentration of compound i (Se) in the
aeration basin, the ASI model is the logical, simple choice. Use of other
models under these circumstances would be poor judgement and likely lead to
conflicting information. Similarly, application of the Freeman ASSA model for
a compound for which no biodegradation kinetics data have been generated would
be difficult. However, use of any ASSA model to predict diffused aerator-
emissions would be in error. Thus, in this case, the additional complexity of
Freeman's subsurface diffused air mass transfer expression is justifiable.
Also, the increased complexity of Freeman's ASSA model is justifiable for very
high substrate loading conditions, or for modeling an oxygen starved reactor.
135
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TAHI.K IK. APPLICATION OK VARIOUS ,VTI V/VH-.O SI.HUCI--. AKKR MODELS
Appl icat ions
Surface aeral i«n
Civon: So Given- Sr,
Model
Given: St, convtMition.il Oxygen I'roi -i-ss
only systfiii 1 imitfl i "
All conditions
-------
tt is doubtful that such model flexibility will be required for modeling air
emissions from planned facilities on a regular basis. While Freeman's models
do have valuable use under certain circumstances, it is clear that they were
developed for research and design purposes rather than fulfilling analytical
needs .
Model Accuracy —
The Thibodeaux AS I model was tested by Cox, et al. (1982) and shown to
underpredict benzene emissions as indicated in Section 3. However, it was
noted by Hwang* that calculational errors were made in assuming application of
Raoult's Law. When applying Henry's Law", the corrected model predictions were
found to be within a factor of 2 to 3 to the measured results. Additional
model verification was also conducted by Thibodeaux (1981) for methanol.
These measured results showed reasonable agreement with predicted emissions.
Tests conducted for the Thibodeaux ASI model are largely applicable to
the mass transfer portion of the Hwang ASSA models since they are identical in
this respect. Freeman's ASSA model also employs the same mass transfer terms
and would be similar in accuracy. Biokinetic rate data and sludge adsorption
data were collected for input to the Hw.ing model. No complete testing of the
fully assembled model has been conducted to date. However, if the individual
elements are based on test data it can be rationalized that the total model
be reliable.
Freeman (1980, 1982) also conducted laboratory experiments to verify the
mass transfer portions of his DAAS model separate from the biokinetics model.
Using air stripping experiments with sterile reactors, Freeman (1980) found
that the subsurface diffused air model predicted the material balance for
acrylonitrile to within 3.2 percent. Freeman (1982) also calibrated the
Gerber biokinetics model, using the DAAS mass transfer model, for
acrylonitrile and for other organic compounds.
Model Assumptions —
Complete Mix Reactor—One basic underlying assumption of all the models
investigated is the complete mix reactor assumption." This assumption is basic
to most conventional AS process modeling and will not be disputed. However,
GCA notes that there may exist some contradiction between the complete mix
modeling assumption and the turbulent/convec tive zone mass transfer concept
used in the ASI and ASSA models. In reviewing these models, GCA questioned
the necessity of considering the convective zone mass transfer since the
transfer from the turbulent zone should be substantially greater. However,
Hwang* pointed out that for large area lagoons the area of convective mass
transfer could be very large (inferring low mixing might result). Thus, in
this application the complete mix assumption may not be completely accurate.
*Telecon with Tom Nunno of GCA, 15 September 1982.
137
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Mass Transfer—Assumptions regarding the governing mechanisms of mass
transfer are summarized as follows:
• ASI and ASSA models reviewed assume that mass transfer takes place
at the surface according to the two-film resistance theory. In
addition, these models generally assume that the concentration of
compound i (X^) in the air is neglibible to that in the liquid.
• Freemans DAAS model assumes that mass transfer takes place at the
diffused air bubble interface and that, again, the initial
concentration (X^) is zero and increases until equilibrium is
reached. The Freeman DAAS model also assumes that the overall mass
transfer rate (KL) is equal to the liquid phase mass transfer
coefficient (k^) because the gas phase mass transfer coefficient
is assumed' to be very large. In addition, the DAAS model assumes
that mass transfer which cakes place at the surface is small
compared to subsurface mass transfer and, thus, is negligible.
Biokinetics Model—The biokinetic rate expressions employed in the Hwang
and Freeman models are quite different in structure, complexity, and
underlying assumptions. The Hwang model relies on Grau kinetics which assumes
adequate oxvgen in the basin. The Freeman model uses Gerber kinetics which
considers oxygen requirements in trie oiokinecic expression. As mentioned
earlier, it is difficult to judge the relative merits of biokinetic models.
However, it is likely that the Gerber model would be valid under a greater
range of conditions than :he Grau model.
Sludge Adsorption—Only the Hwang ASSA Model considers adsorption of
substrate to the sludge competing with other substrate removal mechanisms.
Freeman's ASSA and DAAS models both assume that adsorption of substrate is
negligible. While this assumption may be valid for many organic-compounds
based on the work of Kincannon, adsorption has been shown to be significant in
several instances (Hwang 1981, Patterson 1981).
Model Selection
The Hwang ASSA model is preferred to Freeman's model because the Hwang
model is most easily applied, employs simpler bioxidation kinetics for which
rate constant data is available, and is capable of modeling adsorption of
substrate to the biomass. Freeman's DAAS mass transfer equations are
recommended for modeling diffused air systems because they are currently the
only reasonable choice. The DAAS mass transfer equations could be integrated
into Hwang's ASSA model for predicting DAAS air emission release rates where
the effluent concentration is unknown. This is recommended to simplify the
problem solution and to avoid costly data collection required to use Freeman's
biokinetic model.
Based on the factors discussed above GCA recommends that EPA select the
following models for the applications listed below:
138
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Application Selected model
Surface aeration— Thibodeaux AST model
eEfluent or aeration basin
concentration (Se) known
Surface aeration—influent Hwang ASSA model
concentration (So) known
Diffused aeration—Se known Freeman DAAS model
Diffused aeration—So known Hwang (modified after Freeman)
The basis for selecting the Thibodeaux ASI and Hwang ASSA models for
applications to surface aerated treatment systems includes considerations of
simplicity, accuracy and ease of application. It is believed that these
models will adequately predict emissions from the majority of most AS
treatment systems and are acceptable for use by most permitting engineers. In
addition, the availability of biokinetic rate data for Grau kinetics makes the
Hwang ASSA model particularly attractive for general use. Because the Hwang
ASSA model does not apply well to subsurface diffused air systems, it is
recommended that for modeling diffused air systems the Hwang model be modified
to incorporate diffused air mass transfer mechanisms similar to that described
by Freeman (19SO). Freeman's diffused air mass transfer model could be
incorporated into the Hwang model without substantial .effort. This
modification would permit the application of Freeman's mass transfer
expression integrated with the Grau kinetics and sludge adsorption
considerations of Hwang's model.
139
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SECTION 9
AIR EMISSIONS FROM DRUM STORAGE AND HANDLING FACILITIES
INTRODUCTION
Drum storage and handling facilities encompass diverse operations and
sources of air emissions. Sources of routine air emissions include the
storage of volatiles in lagoons or storage tanks. Air emission release rate
estimation techniques for these activities are described in other sections of
this report. The otner important air emissions category is thought to be
accidental spills.
The purpose of this section is to identify data necessary for estimating
air emissions attributed to accidental spills at drum storage and handling
facilities. Tnis section proviaes a general description of a arum storage ana
handling facility and also sorre spill rate data for hazardous waste treatment
facilities and petroleum handling facilities. At present, no data specific to
air emissions from drum handling and storage facilities have been found.
DESCRIPTION OF DRUM STORAGE AND HANDLING FACILITIES
At drum storage and handling facilities, waste material, most commonly
solvents, may arrive by tank, car or tank truck, as well as in drums. Material
mav then be pumped to storage tanks, lagoons, or other drums for storage.
Materials are segregated by type until enough are collected for reprocessing
or disposal either onsite or offsite with removal again either by tank car, or
tank truck, and less commonly, in drums.
Drums are removed from a tractor trailer on arrival with a fork lift and
are conveved to and from the drum storage building, ideally a locked mecal
building with louvered gables where storage occurs on concrete pads. Drams
which are storea directly on the ground may freeze to the surface, thus, are
subject to rupture during removal.
A number of other operations may also occur. Damaged drums will usually
be replaced either upon arrival or upon later inspection. Material may have
to be resampled to check compatibility parameters such as flash point, acidity
or chloride content. Drums may be intentionally burst if this is the most
effective way of removing contents of damaged barrels.
140
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SOURCE OF VOLATILE AIR EMISSIONS
It is useful to classify emissions as routine or accidental, and to
further classify routine emissions as either continuous or intermittent.
Examples of each category are shown in Table 39. Note that routine
continuous air emissions are from sources (lagoons and -"rage tanks) for
which air emission release rate models have been previously discussed It
also appears that intermittent routine emissions cannot be very significant
since they involve only one drum at a time over limited time periods.
To describe total facility emissions there are two approaches depending
on available data:
. Total facility emissions, in barrels* lost per barrel handled;
• With an accurate description of onsite lagoons and storage tanks,
air emissions from these sources can be calculated directly and tne
supplemented by the accidental spill rate, again parameterized by
barrels lost per barrel handled.
The remainder of this discussion assumes the second course.
LITERATURE SURVEY
No examples have been found in the literature corresponding directly to
spill rate data at drum storage and handling facilities. Nevertheless, we
mention some recent work which is relevant.
Hillenbrand, et al. (1982) have surveyed Pollution Incident ^Porting
System (PWS) and Spill Prevention, Control, and Countermeasures (SPCC) data
/or EPA The stud/is restricted to tank fanns and chemical plant tanks
"eater than 100,000 gallons. Data consists mainly of gasoline and fuel oil,
but also include spill reports on non-fuel products, organic and inorganic
materials The report categorized over 3,000 spills by cause (pipe rupture,
: r^lfuncSn, etc.) and'quantity . Unfortunately, they have not een ao.e
to give a spill rate based on the total amount of material handled (i.e.,
"exposure variable") .
Also under EPA contract, ICF, SCS and Clement Associates (1982) have
surveyed release rates and costs for waste treatment technologies. As par. °
this work, estimates were made of routine and accidental spillage based
apparently on "best judgment." Some loss fraction estimates for accident
spills for various treatment processes are shown in Table 40.
This report also notes that a December 1980 study by F. G. Bercha and
Associates estimated a spill loss fraction of 2.45 x 10 * for hazardous
waste loading and unloading operations.
*The term barrels is used in this section as a unit of volume whether or not
material is in drums, tanks, etc.
141
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TABLE 39. EXAMPLES OF ROUTINE AND ACCIDENTAL SPILL'SITUATIONS
AT A DRUM STORAGE AND HANDLING FACILITY
Routine
Accidental
Continuous
Lagoon emissions
e Storage tank breathing
and working losses
Intermittent
• Open pouring
• Sampling open drums
• Intentional drum
bursting
• Drum rupture by transfer
operations
• Dropped drun
• Tank or drum overflow
• "Spontaneous" drum
failure
* Pipe rupture or pump
malfunction
• Faulty hose coupling
142
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TABLE 40. ACCIDENTAL SPILL FRACTIONS FOR VARIOUS
TREATMENT TECHNOLOGIES3
Accidental
spill fraction
(amount spilled/
Technology amount handled)
Chemical stabilization
Chemical precipitation
Chemical destruction
Chemical coagulation
Filter press
Centri £uge
Vacuum filter
Evaporat ion
Air stripping
Steam stripping
Solvent extraction
Leaching
Distillat ion
Electrolytic decomposition
Reverse osmosis
Carbon adsorption, PAC
Ion exchange
Average
1.5 x 10
2.6 x 10"
1.1 x 10
2.6 x 10
-3
-5
-4
1.1 x 10~4
2.2 x 10~"*
1.1 x IQ~*
7. 7 x 10*"4
1.3 x 10""4
2.1 x icf*
1.6 x 10~4
3.0 x 10~4
2.1 x 10
2.2 x 10
1.9 x 10"
4.3 x 10"
4.3 x 10
-4
-9
3.0 x 10~4
aFrom "RCRA Risk/Cost Policy Model Project;"
ICF, Inc., SCS Engineers, Inc., and Clements
Associates, Inc., 1982.
143
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Murphy, et al. (1981) presented data for oil spills occurring at the
MiLEord Haven Terminal over an 18-year period. The loss fraction attributable
to terminal operations (faulty hose couplings, pumps, valves, etc.) are
4 x 10-5.
Until we have the pertinent data in hand we cannot confirm that any of
the figures above are relevant to drum handling and storage facilities. Yet
these figures do represent what is considered acceptable in operations with a
number of similar steps. Our best estimate, therefore, is that the spill rate
at drum handling and storage facilities is between 1 and 100 barrels per
100,000 barrels handled.
OTHER CONSIDERATIONS
The amount spilled is not Che same as the amount of volatile released to
the atmosphere. Absorbent material will be added, at least to significant
spills, when spills are discovered during inspection. Spills on a concrete
surface, as opposed to ground, will be -ore amenable to cleanup. Since
individual spills occur randomly, spills that are not noticed at the time of
the occurrence will tend to grow in number linearly with time in the interval
between inspector! periods.
Many handling operations occur in outdoor areas. The rate at which
material volatilizes before it can be cleaned up will then depend on
temperature and wind conditions. Similarly, for indoor spills, volatilization
rates will depend primarily on temperature and ventilation conditions.
Finally, hunan factors such as management attitudes and worker training and
indoctrination must be important in determining the accidental spill rate.
144
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SECTION 10
PARTICULATE EMISSIONS ESTIMATION
TECHNIQUES FOR WASTE PILES
INTRODUCTION
Particulate air emissions from waste piles occur at several points in the
storage cycle:
• transfer of material to and from the pile;
• wind erosion;
• maintenance and traffic activities on the pile.
Particulate emissions from waste piles are influenced by the following factors
• moisture content;
• rainfall;
• duration of storage;
• compaction of pile;
• amount and size of aggregate fines.
A method of estimating particulate emissions from waste piles is
available in EPA publication AP-42. Cuscino, et al. (1981) presents emission
factor equations empirically developed by Midwest Research Institute (MRI).
Both methods describe emissions of particles smaller than 30 urn in diameter
based on a particle density of 2.5 g/cnv.
AP-42 EMISSION FACTOR EQUATION FOR STORAGE PILES
The quantity of suspended particulate emissions from waste piles may be
estimated by the following equation:
0.33
E =
PE>2
(A)
145
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where: E = emission race, pounds per ton of material placed in storage;
PE = Thornwaite's precipitation - evaporation index from
Figure 12.
This equation only considers geographic variations in precipitation/
evaporation. Emission factor equations developed by MRI based on test data
allow for variances in facility operations.
MRI EMISSION FACTOR EQUATIONS FOR STORAGE PILES
The emission factor equations empirically developed by MRI for
uncontrolled storage piles are shown in Table 41. These equations were
developed from limited testing of storage piles at iron and steel facilities
(i.e. coal, iron pellets, coke, slag, etc.). However, the use of these
predictive equations may provide for greater accuracy than the single value
emission factor equation (from AP—+2). Input parameters for the MRI equations
account for source variability.
The diversity of materials handled and differences in handling operations
suggest that additional source testing may increase the precision of the
predictive equations. The estimation accuracy for the storage pile
maintenance anc storage pile wind erosion equations are unknown due to limited
test iata.
146
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;«'«A . ?.. '
Figure 12. Map of Thornlhwaite's Precipitation-Evaporation Index values for
state climatic divisions. (From AP-42) .
-------
TABLE 41. STOKAUK PILE PARTIO/LATE EMISSION FACTOR EQUATIONS
DEVELOPED BY MKI
Batch load-in or load-out:
0.0018
Continuous load-in:
2 ,„. 0.33
pounds per ton of material transfered
5 / \5/ \ 107 « pounds per ton of material loaded
0 0018
Active storage pile mainteriar.ee and traffic:
0.10K. (•J~~5J ("233) = Pouncis Per Con °f material put througn storage
Active stDra^e pile wind erosion:
0.05 I-,—TJ (TJJ) ("^j ("QQ) = pounds per ton of material put
through storage
Parameters
s 3 silt content of aggregate (/»)
u = mean wind speed at 4ra above ground (mph)
h = drop height (ft)
M = unbound moisture content of aggregate (%)
Y * dumping device capacity (cu. yd.)
K s activity factor
d * number of dry day per year
D * duration of material storage (days)
f * percentage of time wind speed exceeds 12 mph measured at one foot
above the ground.
148
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APPENDIX A
REFERENCES
American Petroleum Institute, Evaporation Loss Committee. Evaporation Loss
from External Floating Roof Tanks. Bull. 2517 (revised), Washington, DC,
February 1980.
American Petroleum Institute, Evaporation Loss Committee. Evaporation Loss
from Fixed Roof Tanks. Bull. 2518, Washington, DC, June 1962.
American Petroleum Institute, Evaporation Loss Committee. Evaporation Loss
from Internal Floating Roof Tanks. Bull. 2519 (revised), Washington, DD,
June 1983.
Ames, et al. Suggested Control Measure to Reduce Organic Compound Emissions
Associated with Volatile Organic Waste Disposal. Air Resources Board, State
of California, Industrial Strategy Development Branch. August 20, 1982.
Arnold, J. H., Unsteady-State Vaporization and Absorption. Transaction of
American Institute of Chemical Engineers 40, 361-379. 1944.
Ball, B. C., W. Harris and J. R. Burford. A Laboratory Method to Measure Gas
Diffusion and Flow in Soil and Other Porous Materials. Journal of Soil
Science, 32. 1981.
Brown, J.A. and M. Weintraub. Bioxidation of Paint Process Wastewater.
Journal WPCF, Vol. 54, No. 7, pp. 1127-1130, July.1982.
Calderbank, P. H. "Mass Transfer," Chapter 6 of Mixing, edited by V. W. Uhl
and J. B. Gray, Academic Press, New York, 1967.
Chicago Bridge and Iron Company, Plainfield, IL. Hydrocarbon Emission Loss
Measurements on a 20 foot Diameter Pilot Test Tank with an Ultraflote and a
CBI Weatheraaster Internal Floating Roof. R-0113/R-0191, June 1978.
Cohen, Yorara, William Cocchio and Donald Mackay. Laboratory Study of Liquid
Phase Controlled Volatilization Rates in Presence of Wind Waves.
Environmental Science and Technology, Vol. 12, No. 5. May 1978.
Conway, Richard A. (ed), Environmental Risk Analysis for Chemicals. Van
Nostrand Reinhold Company, New York, 1982.
Compilation of Air Pollutant Emission Factors (AP-42), U.S. Environmental
Protection Agency. Research Triangle Park, N.C. April 1981.
149
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155
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APPENDIX B
DERIVATION OF CURRIE WET SOIL CORRELATION
FOR EFFECTIVE DIFFUSIVTTY
CURRIE (1960) DRY SOIL CORRELATION
D~~ * E
O
where D - diffusion coefficient in dr/ soil;
D0 = air diffusion coefficient ;
£ = soil porosity;
Y,y = constants for a specific type of soil.
Cl~RP.II (1561) VEI 5011 CG5.?ZlAIIJx.i
n
w
V \ V)
where D = diffusion coefficient in wet soil;
D,, = -diffusion coefficient in air-filled soil;
~-a = air-filled soil porosity;
cv = incer-crusb pore spaces;
- a soil specific constant.
Derive D,7:
for dry soils, sa » EX
where ET - total porosity
D-D Y e» - D Y e_w
O O T
156
-------
D = D
v o
substituting DV into wet soil correlation;
check for dry soil,
D = D y £T
o T
157
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TECHNICAL REPORT DATA .
(Please reed Instructions on the reverse before completing)
1. REPORT NO. 2-
EPA-450/3-84-020
4. TITLE AND SUBTITLE .... j. • a •
Evaluation and Selection of Models for Estimating Air
Emissions from Hazardous Waste Treatment, Storage,
and Disposal Facilities
7. AUTHORIS)
Marc Breton, Thomas Nunno, Peter Spawn, William Farino,
and Robert Mc.Innes
9. PERFORMING ORGANIZATION NAME AND ADDRESS
GCA Corporation Technology Division
213 Burlington Road
Bedford, Massachusetts 01730
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Enission Standards and Engineering Division
Research Triannle Park, North Carolina 27711
3. RECIPIENT'S ACCESSION NO.
5. REPORT DATE
December 1984
6. PERFORMING ORGANIZATION CODE
10. PROGRAM ELEMENT NO.
11. CdNfRACTAiRANt NO.
68-02-3168
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/200/004
15 SUPPLEMENTARY NOTES
16. ABSTRACT
Mathematical models describing the release rate of volatile air
emissions from hazardous waste treatment, storage, and disposal facilities
were compiled and reviewed. Mathematical modeling techniques which predict
volatile air emissions release rates from landfills, landfarms, surface
impoundments, storage tanks, wastewater treatment processes, and drum
handling and storage facilities were assessed. Existing field test valida-
tion efforts were also reviewed.
The purpose of this report is to provide a source of current informa-
tion available on this subject area. A guidance manual of practice will
ultimately be prepared to assist regulatory engineers and others in apply-
ing the recommended models. Since many new papers in this area are continu-
ally being published, this selection of modeling techniques may be considered
present state-of-the-art as of spring 1983. Field validation scheduled to be
conducted in 1983 and 1984 under EPA and private directives should provide
additional information regarding model precision.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
COSATi Fieid'Group
Air Pollution
Pollution Control
Hazardous Waste TSDF
Volatile Organic Compounds (VOC)
Air Emission Models
lir Pollution Control
18. DISTRIBUTION STATEMENT
Release unlimited, Available from NTIS,
5285 Port Royal Road, Springfield, VA
22161
19. SECURITY CLASS (This Report!
UNCLASSIFIED
21. NO. 0*
AGE!
128
20. SECURITY CLASS (Tins page)
UNCLASSIFIED
22. PRICE
EPA F»m> 2220-1 (R«v. 4-77) mevioui COITION is OMOUKTt
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oots
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