&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

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     -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

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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

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            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)

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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

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                 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)

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     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

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            = 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

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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

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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

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                 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

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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

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                      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

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     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

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     •    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

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                    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

-------
                          Wt.  H/C Volatilized/Wt.  Hydrocarbon Applied


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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

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      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)

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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

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     •    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

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        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

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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

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      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

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                              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

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        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

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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

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       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

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                              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

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     '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

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     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

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        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

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          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

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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

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    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

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        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

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                              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

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                                   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

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              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

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     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

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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

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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

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     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

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                                   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

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     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

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        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

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PRESSURE/VACUUM
      VALVE
                                                             GAUGE  HATCH
 MANHOLE-
                                                                           MANHOLE
NOZZLE (FOR
SUBMERGED FILL
OR  DRAINAGE)
                         Figure 7.  Typical fixed  roof storage tank  (Masser - 1981).

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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

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        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

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                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

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        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

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          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

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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)

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     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

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                                             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

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         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

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                              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

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     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

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       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

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              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

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        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

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     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

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   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
    

    -------
         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
    

    -------
         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
    

    -------
                                            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
    

    -------
    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
    

    -------
    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
    

    -------
                     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
    

    -------
         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
    

    -------
    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
    

    -------
    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
    

    -------
    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
    

    -------
         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
    

    -------
                                      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
    

    -------
         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
    

    -------
    ;«'«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
    

    -------
                                       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
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     Cohen, Yorara, William Cocchio and Donald Mackay.   Laboratory  Study  of Liquid
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     Conway, Richard A.  (ed),  Environmental Risk Analysis for Chemicals.   Van
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                                          149
    

    -------
    Cox, Robert D.,  Jana L. Steinmetz and David L. Lewis.  Evaluation of VOC
    Emissions from Wastewater Systems (Secondary Emissions),  Draft Report.
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    Currie, J. A.  Gaseous diffusion in porous media.   Part  3 - Wet Granular
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    Cuscino,  Thomas A.  Jr.,  Chatten  Cowherd,  Jr.,  and  Russel Bonn. Fugitive
    Emission  Control  of Open Dust  Sources.   Proceedings:   Symposium on Iron and
    Steel  Pollution Abatement Technology  for 1980.  EPA-600/9-81-071.  March 1981.
    
    Danielson,  John A.  Air  Pollution  Engineering Manual, AP-40.   U'S-
    Environmental  Protection Agency,  Research Triangle Park, NC,  May  19/3.
    
    Uilling,  Wendell  L.,  Nancy B.  Tefertiller,  and George J. Kallos.   Evaporation
    Xac^s  and Reactivities of Methylene Chloride, Chloroform,
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     Dilling, Wendell L.   Lnterpnase Transfer Processes II.  Evaporation lates  of
     ,nlorerMe thanes,  Ethanes, Echylenes, Propanes,  and Propylenes fro«=_Dilute
     Aqueous  Solutions.  Comparisons with Theoretical  Predictions.  Environments
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     Ehlers,  Wilfried,  J.  Letey, W. F. Spencer and W.  J.  Farmer.   Lindane  Diffusion
      in Soils:   I. Theoretical  Consideration and  Mechanism of Movement,  Soil
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      Erikson, D.G.  Organic  Chemical Manufacturing,  Volume 3:   Storage,  Fugitive
      and Secondary Sources.   EPA-450/3-80-025.   Research  Triangle Par*,  NC,
      Deceraoer 1980.
    
      Farmer  Walter  J., M. S. Yang and J. Letey,   Land Disposal of Hazardous
      Wages':  Controlling Vapor Movement in Soils.  Fourth Annual Researcn
      Symposium.  EPA-600/9-78-016.  August 1978.
    
      Farmer, Walter  J., Miag-Shyong Yang, and John  Letey.   Land Disposal  of
      Hexachlorobenzene Wastes:  Controlling  Vapor Movement  in Soils.
      EPA-600/2-80-119.  August 1980.
    
      Fryman  R  A   Stripping of Hazardous  Chemicals  from  Surface Aerated Waste
      ? ^t ^s^s   AP^WPCF Specialty Conference on Control o  Specific
      (Toxic)  Pollutants,  Gainesville, Florida, February  13-16  U979).
    
      c eBmaT,  R   A    J M.  Schroy,  J. R. Klieve,  and  S.  R.  Archer, Experimental
        "on'the'R^e  of Air Gripping  of Hazardous Chemicals  f««*-t.
      Treatment Systems,"  73rd  APCA Meeting, Montreal,  Canada,  June 22-27, 1980a.
       Paper No.  80-16.7.
    
    
                                         150
    

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    Freeman,  R.  A.,  Laboratory Study of Biological System Kinetics,  unpublished by
    Catalytic,  Inc.  under contract with EPA,  1980b.
    
    Freeman,  R.  A.,  Comparison of Secondary Emissions from Aerated Treatment
    Systems!  presented at the 1982 Winter AIChE National Meeting, Orlando,
    Florida,  March 3, 1982.  Paper No. 5c.
    
    Gerber, V.  Y., V. M. Sharafutdinov and A. Ya. Gerceridov, Kinetics of
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    (USSR) _12:  826 (1976).
    
    German Society for Petroleum Science and Carbon Chemistry (DGMK) and the
    Federal Ministry of the Interior  (BMI).  Measurement and Determination of
    Hydrocarbon Emissions  in  the Course of Storage and Transfer  in Above- Ground
    Fixed  Cover Tanks With and Without Floating Covers.  BMI-DGMK Joint Projects
    4590-10 and 4590-11;  translated for EPA  by Literature Research Company,
    Annandale, VA.
    
    Grau,  P., M.  Dohanyos, and  J. Chudoba, Kinetics  of Multicomponent Substrate
    Removal by Activated  Sludge, Water Research,  Pergamon Press,  Vol. 9, 637,  1975.
    
    Hartley, G. S.   Evaporation  of  Pesticides, published  in  Advances  in Chemistry
    Series'86, American  Chemical  Society,  Washington, D.C.,  1969.  pp.  115-134.
    
    Hillenbrand,  E.,  JRB  Associates,  McLean,  VA,  private  communication  based  on
    the  Draft Report,  "Failure  Incidents  Analysis:   Evaluation  of Storage  Failure
    Points,"  submitted  to EPA Office  of  Solid  Waste.  March  1982.
    
     Hwang, Seong  T.   Treatability and Pathways of Priority Pollutants in  the
     Biological  Wastewater Treatment.   Paper  presented  at  the American Institute  of
     Chemical  Engineers Symposium,  Chicago, November  1980.
    
     Hwang, S.  T.   Toxic Emissions from Land  Disposal Facilities.  Environmental
     Progres_s,  Vol.  I, No. 1.  February 1982.
    
     ICF,  Inc.,  Clement Associates,  Inc.  and SCS Engineers,  Inc., "RCRA Risk/Cost
     Policy Model Project," Phase 2 Report Submitted  to EPA,  Office of Solid Waste,
     June  15,  1932.
    
     Kincannon,  Donald F. and Enos L. Stover, Stripping Characteristics of Priority
     Pollutants During Biological Treatment.  Paper presented at the Secondary
     Emissions Session of  74th Annual AICHE Meeting,  New Orleans.  November 1981.
    
     Kincannon, Donald F., et al.  Predicting Treatability of Multiple Organic
     Priority Pollutants  in Wastewater from  Single Pollutant Treatability Studies.
     Paper presented at the  37th Purdue Industrial Waste Conference, Purdue
     University,  West Lafayette, Indiana.  May 1982.
    
     Lai,  Sung-Ho, James  M. Tiedje, and A. Earl Erickson.  In situ Measurement of
     Gas Diffusion Coefficient  in Soils.   Soil Science Society  Proceedings.  40.
      1976.
                                          151
    

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    Liss, P. S. and P.  G. Slater.   Flux of Gases Across Che Air-Sea Interface.
    Nature,  Vol.  247.  January 1974.
    
    Lyman, Warren J. , William F.  Rechl and David H. Rosenblatt, Handbook of
    Chemical Property Estimation Methods.  McGraw-Hill, New York, 1982.
    
    Mackay,  Donald and Aaron W. Wolkoff.  Rate of Evaporation of Low-Solubility
    Contaminants from Water Bodies to Atmosphere.  Environmental Science and
    Technology, Vol.  7, No. 7.  July 1973.
    
    Mackay,  Donald and Ronald S.  Matsugu.  Evaporization Rates of Liquid
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    Contaminants froTi Water Bodies to Atmosphere.  Environmental Science and
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    Mac
    -------
    Murphy, B.  L.,  et al.   Outer Continental Shelf Oil Spill Probability
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    Material Spills.  New Orleans, LA.  April 25-28, 1976.
    
    Nelson, R.  W., G. W. Gee, and D. W. Mayer.  Control of Radon Emissions from
    Uranium, Mill Tailings by Multilayered Earth Barriers.  Transcripts of
    American Nuclear Society, 38.  1931.
    
    Owens, M., R. W. Edwards, and J. W. Gibbs.  Some Reaeration Studies in
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    Patterson, J. W.  and P. S.  Kodukala.  Biodegradation  of Hazardous Organics
    Pollutants.  Chemical Engineering  Progress.  April  1981.
    
    Rolston, D.  E.  and  B. D.  Brown.  Measurement  of  Soil  Gaseous  Diffusion
    Coefficients  by  a  Transient-State  Method  with  a  Time-dependent  Surface
    Condition.   Soil  Science  Society  American Journal,  40.   1976.
    
     Shen,  Thomas T.   Emission Estimation  of  Hazardous  Organic  Compounds from Waste
     Disposal Sites.   Presented  at the  73rd  Annual  Meeting of  the  Air Pollution
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    -------
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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
    

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                                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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              nur
    U.S. Environmental Fraction  Agency.
    Region V, Library
    230 South Dc-"»:.r.n Otrset ^
    Chicago,  Illinois  <»06G4 "
    

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