EPA-460/3-76-006
September 1975
                           EXPANSION
                 OF INVESTIGATION
                OF PASSENGER CAR
                 REFUELING LOSSES
       U.S. ENVIRONMENTAL PROTECTION AGENCY
            Office of Air and Waste Management
         Office of Mobile Source Air Pollution Control
           Emission Control Technology Division
              Ann Arbor, Michigan 48105

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                                  EPA-460/3-76-006
              EXPANSION
        OF INVESTIGATION
       OF  PASSENGER CAR
       REFUELING  LOSSES
                       by

Malcom Smith (Olson Research Laboratories) and William Biller (Consultant)

            Scott Environmental Technology, Inc.
                 2600 Cajon Boulevard
             San Bernardino, California 92411

               Contract No. 68-01-0434


           EPA Project Officer: Robert E. Maxwell


                    Prepared for

        U.S. ENVIRONMENTAL PROTECTION AGENCY
             Office of Air and Waste Mangement
          Office of Mobile Source Air Pollution Control
           Emission Control Technology Division
               Ann Arbor, Michigan 48105

                      and

           The Coordinating Research Council, Inc.
               Thirty Rockefeller Plaza
                New York, N.Y.  10020

                  September 1975  U.S. Ernrircr— nl n.1 ?-ot •'•--' ten Agency
                              T -1 <•• i r+ -, t '  •'"   .- • -
                                 o. ^..._.J..
                              Chicago , IL

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                               TABLE OF CONTENTS

                                                                         Page
Summary                                                                   iy
1.0  Introduction                                                          1
      1.1  The Problem                                                     1
      1.2  Program Background                                              2
      1.3  First Year Program                                              2
      1.4  Second Year Program                                             3
      1.5  Third Year Program                                              4
2.0  Laboratory Study                                                      &
      2.1  Experimental Design                                             ;-
      2.2  Derivation of New Regression Model for Estimating
           Displaced Hydrocarbon Loss                                      S
3.0  Field Survey                                                         ^
      3.1  Description of Field Survey                                    ^5
      3.2  Regression Analysis of Temperature Data                        16
      3.3  Frequency of Refueling Operations                              ?4
4.0  Regional Hydrocarbon Refueling Loss Model                            30
      4.1  Derivation of Regional Model                                   30
      4.2  Computer Program of Regional Model                             36
      4.3  Simplified Forms of Regional Model                             50
      4.4  Error and Sensitivity Analysis of the Regional Model           56
References                                                                73
Appendix A   Fuel Inspection Data                                         A-l
Appendix B   Laboratory Data                                              B-l
Appendix C   Standard Error                                               C-l
Appendix D   Sample Temperature Data From the Third Year  Field  Survey     D-l
Appendix E   Multiple Regression of  Field Survey Temperature Data         E-l
Appendix F   Computer Program Listing                                     F-l

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                                    IV
                                  Summary

     This report covers the third year of the program on passenger car
refueling losses undertaken for the Coordinating Research Council and the
Environmental Protection Agency by Scott Environmental Technology, Inc.*
The objective of the third year was the development of a mathematical
model for estimating the total hydrocarbon losses from refueling opera-
tions for an air quality control region over a specified period of time.
In order that the model could be used readily by community planners and
others it was based on relatively easily obtained variables such as aver-
age Reid vapor pressure of the gasolines used in the region and average
underground fuel and ambient temperatures.
     The model requires estimates of losses due to spillage and those
which are displaced from the fuel tank as vapor and entrained fuel drop-
lets during refueling.  The second year program determined through field
studies that spill losses average 0.30 gms/gal of dispensed fuel.  A
mathematical expression for estimating the displaced hydrocarbon losses
was also developed in the second year by the application of stepwise mul-
tiple regression analysis to laboratory measurements of losses under
controlled conditions.  This expression was considered inadequate for use
in developing the regional model because it was based on a small, incomplete
data base and too narrow a range of fuel Reid vapor pressures.  As a result,
the laboratory study was redone in the third year to provide a new, more
comprehensive data base needed for a more reliable expression.  Multiple
regression analysis yielded the following expression:

       L^  =  exp (a + b PVTD + c Ty + d PV + e TQTT)
a   =  -9.1703 x 10"2            d  =  5.4094 x 10"2
b   =   1.1521 x 10"3
c   =  -1.2605 x 10~3
       b   =   1.1521 x 10"3            e  =  1.0725 x 10"4
* Formerly Scott Research Laboratories,  Inc.

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where
    LJ.   =  Estimate of displaced loss, gms/gal .
 •   PV   =  Reid vapor pressure of fuel, psi.
    TD   =  Average dispensed fuel temperature, °F.
    TT   =  Initial tank fuel temperature, °F.

     This expression explained 94. 5% of the variance in the displaced loss
data and had a standard error of '6.6%.  The expression was not, directly
suitable for use in the model because estimation  of dispensed and tank
fuel temperatures wou'id be difficult.  A field study was conducted to
develop an expression, for dispensed fuel temperatures in term*; of more
conveniently determined variables.  Data were obtained in the summer and
spring in the San Bernardino-Ontario area and in  the winter in the
Minneapolis-St.  Paul area.  The following expression was derive1:! through
stepwise multiple regression of a number of variables:
            f -  -1.17523
            g =••   0.80785
            h -   0.22667
where
    T..   =  Underground fuel temperature, °F.
    T.   =  Ambient temperature, °F.
This expression explained 98.9% of the variance and had a 2.47% standard
error of estimate.  The variables T,. and T. are convenient to measure and
                                   U      A
the expression could be used to eliminate T  from the displaced loss equation,
     From the Coordinating Research Council CAPE-5-68 program which studied
the temperatures of automotive fuel systems under different driving patterns
(Reference 7) it was estimated that:
     TT  =  TA + .A T  where    T  = 7°F

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This expression allowed the elimination of T_ from the displaced loss
equation.  The resulting expression gave the displaced hydrocarbon loss
in terms of the desired variables, the Reid vapor pressure and the under-
ground fuel and ambient temperatures.
     The third year field study also provided values for the relative
frequency of refueling operations as a function of the time of day.
     The regional model is shown in the attached table.  Its general
form is a product of three terms.  The first term is the regional average
hydrocarbon refueling loss per gallon of fuel dispensed in the region for
a given hour.  The second term is the fraction of total daily refuelings
which occur in that hour.   By performing a summation of the product of
these two terms over all hours of refueling operations in a day (16 hours),
the total refueling loss per gallon for each day of the period is obtained.
Multiplying by the third term, which is the average number of gallons dis-
pensed per day for the period, and summing over days yields the total
hydrocarbon refueling loss.
     An error analysis of the overall model showed that the inherent error
was about 14%.   A sensitivity analysis indicated average errors of about
18% to be possible from misestimation of the input variables.  It was
further shown that application of the model, or the equations from which
it was derived, to individual  refueling operations could incur substant-
ially larger errors.
     The range of applicability of the model in terms of its input variables
is:
                                        Range of Functions
                                             TA + 7
                                              rt and
                Rvp                   0.81  Ty + 0.23 TA -1.2
                  7                           50-90
                 10                           40 - 80
                 13                           30-70

     A computer program was  written for convenient application of the model.
Simplified forms of the model  suitable for use with desk calculators were
also demonstrated.

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                                      vn
    REGIONAL MODEL FOR HYDROCARBON  REFUELING LOSSES FROM PASSENGER CARS
                        D      H
L;          =  ——  /	  /	    R(h_0  (Li
 I              /ICQ C        '           1    O
L'          =  0.30
 O
                + c/v(d.)  ydj)  +  c^o.^) TU + c



       C1   =  -1.0141  x 10"1                  C5   =  2.6115 x 10~4

       C0   =   5.2740  x 10"2                  Cc   =  9.3072 x 10"4
        f.                                      D

       C.   =  -1.2164  x 10"3                  C7   =  8.6642 x 10~5

       C4   =   6.0649  x ID'4                  c    =  2>431Q x 1Q-5
                                               o


  where

L'          =  Estimated total  hydrocarbon  refueling loss for region over
  '             D days,  pounds.

L1             Estimated average  spill  loss,  gms/gal dispensed.
 O
L'          =  Estimated average  displaced  hydrocarbon loss, gms/gal dispensed,

G           =  Average  daily volume  of  fuel dispensed within the region for
               the period,  gallons.

D           =  Total  integral  days in specified period.

H           =  Total  integral  number of hours of refueling operations per day
               (fixed for period).
R(h.)       =  Fraction of total  daily  refueling operations which occur in
               h.-th hour.

TM          =  Regional average  underground  fuel temperature on a given
               day,  °F.

T.          =  Regional average  ambient temperature for a given hour, °F.

PV          =  Regional average  Reid  vapor pressure on a given day, psi.

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                                      vm
          Regional Model, continued
and where:




  R1  (0600-0700) = 0.0175               Rg   (1400-1500)  = 0.0755



  R2  (0700-0800) = 0.0435               R]Q (1500-1600)  = 0.0770



  R   (0800-0900) = 0.0445               RR  (1600-1700)  = 0.0765



  R4  (0900-1000) = 0.0585               R]9  (1700-1800)  = 0.0835



  R   (1000-1100) = 0.0605               R13  (1800-1900)  = 0.0845



  R   (1100-1200) = 0.0700               R14  (1900-2000)  = 0.0775



  R7  (1200-1300) = 0.0715               R]5  (2000-2100)  = 0.0550



      (1300-1400) = 0.0695               R    (2100-2200)  = 0.0350

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                            1.0  INTRODUCTION


1.1  The Problem
     Compared to motor vehicle tailpipe emissions, a source of hydrocarbon
air pollution which has received little attention is the hydrocarbon losses
that result from the refueling of passenger cars.  The losses encountered
during refueling operations include:
          1.  Displaced fuel tank vapor.
          2.  Entrained fuel droplets in the displaced vapor.
          3.  Liquid spillage from the tank.
          4.  Liquid spillage from the nozzle.
Of these four loss sources, only the first (displaced fuel  tank vapor) has
been estimated for passenger cars.
     During the filling of vehicle fuel tanks, splashing of the fuel
accelerates vaporization and also produces small  droplets which may be
lost by entrainment.  While little work had been  done on this phenomenon
in passenger vehicle-fuel tanks, a considerable amount of work was done by
the petroleum industry on the splash filling of petroleum tanks and trans-
portation equipment (References 1, 2, and 3).
     Reference 3 concludes that faulty tank design or poorly conducted
refueling of petroleum tanks could result in entrainment losses two to
three times greater than the loss due to displaced vapor.  However, this
conclusion cannot be extended to the refueling of automobile gas tanks,
because of the differences in the tank sizes, refueling apparatus, and
other equipment.  A number of methods have been proposed for measuring
the losses experienced in filling petroleum tanks (Reference 4).  The
accuracy of these methods was estimated to be about +25%.
     A frequent cause of liquid spillage is overfilling of the tank,
resulting in fuel being forced back up the fuel fill pipe.   Some vehicles
will "spit-back" liquid fuel even before the tank is full.
     Thus, although the sources of passenger car  hydrocarbon refueling
losses had been recognized, little was known about the magnitude and rela-
tive frequency of occurrence of each of these sources of hydrocarbon loss.

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Before a meaningful assessment of the importance of these losses could
be made, it was necessary to conduct a field survey of gasoline stations
so as to determine the magnitudes and frequency of occurrence of these
refueling losses.

1.2  Program Background
     With mutual concern for the foregoing problem, meetings were held by
the Air Pollution Research Advisory Committee (APRAC) of the Coordinating
Research Council (CRC) and the National  Air Pollution Control Administra-
tion of the U. S. Department of Health,  Education, and Welfare (now the
Office of Air and Waste Management of the Environmental Protection Agency)
to initiate an investigation of passenger car refueling losses.  This
problem fell within the scope of the newly created APRAC-CAPE-9 Committee
which was charged with studies of refueling losses in general.
     On December 18, 1968 Scott Research was awarded a contract to conduct
an "Investigation of Passenger Car Refueling Losses".

1.3  First-Year Program
     The first-year program was conducted in two phases.  The first phase
was an experimental study carried out in the laboratory to determine the
amount of the hydrocarbon losses from displaced vapor and spillage.  The
second pahse was a field survey of service stations to determine the fre-
quency of occurrence of gasoline spills.  The laboratory study was initiated
upon award of the contract.  Go-ahead for the field survey was subsequently
received on April 16, 1969.
     The laboratory study yielded information on the effect of fuel tank
configuration, fill rate, vapor pressure, and fuel and vapor temperatures
on the displaced vapor and entrained droplet losses.  Additional  data were
obtained on the average spill  loss for different fuel  tank configurations
filled at different fueling rates.  The  minimum, maximum,  and average
amounts of nozzle drip were determined by measurement.
     In order to carry out the laboratory study, Scott constructed two
enclosures:  (1) a full-sized SHED (acronym for Sealed Housing for Evaporative
Determinations) to collect spillage from an entire automobile, and  (2)  a

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MINISHED to collect displaced losses from fuel tanks alone.  Measurements
of hydrocarbon concentrations in both SHEDs were made with a flame ioniza-
tion detector (FID).
     The field survey was carried out in two parts.  The first part utilized
Scott employees who filled-out a questionnaire each time they refueled their
automobiles.  This questionnaire was filled-out without the attendant's
knowledge.  In the second part, Scott technicians surveyed several stations
in the San Bernardino area for spillage and nozzle drip under the guise of
determining the average amount of gasoline per fill.  A coded data form
allowed the technician to record number of spills and nozzle drips without
an attendant's knowledge.
     Significant factors contributing to individual and overall  refueling
losses were examined and discussed in the first-year report, but the scope
of the first-year program was limited to the results of exploratory labor-
atory tests and a small sample of survey observations (Reference 5).

1.4  Second-Year Program
     The CAPE-9 Committee concluded that an expanded field survey was
necessary to supplement the relatively small sample size on which the
results of the first-year program were based.   Improvements in the tech-
niques and equipment used to measure displaced losses in the laboratory
were also desired.  On November 19, 1969, the  CRC requested Scott to
propose a one-year extension to the original program.  Scott responded
on December 16, 1969, and program go-ahead was received on June  30, 1970.
     Refueling operations were observed in five major cities during each
of the four seasons.  Detailed information was obtained on the magnitude
and frequency of spill losses in the service station environment.  Data
were obtained at one service station in each city on dispensed fuel,
displaced vapor, underground fuel  and ambient  temperatures during refuel-
ing operations.   Laboratory studies were conducted on the effect on
displaced hydrocarbon losses of:   gasoline volatility (as measured by
Reid vapor pressure), dispensed fuel  temperature, tank fuel  temperature,
displaced vapor temperature, ambient temperature, fuel  tank filler pipe
configuration and refueling procedures.

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     From the field survey data it was estimated that the average total
spill loss was 3.5 grams per refill.  Based on an observed average of 11.5
gallons of gasoline dispensed per refill this estimated spill  loss could
also be expressed as 0.30 grams per gallon dispensed.
     Regression analyses conducted on the laboratory data yielded a math-
ematical expression relating displaced hydrocarbon losses to average
dispensed fuel temperature, average displaced vapor temperature and the
Reid vapor pressure (RVP) of the fuel.  This expression when combined with
the temperature data obtained during the survey and the average RVP for
the fuels used in the survey cities yielded the estimate that the average
displaced loss of hydrocarbon vapors was 57.4 grams per refueling operation
or 5.0 grams per gallon dispensed.  The average total refueling loss based
on the survey and laboratory data was, therefore, estimated at 5.3 grams
per gallon of dispensed gasoline.  On the assumption of a national average
of 13.4 miles per gallon the estimated loss could be expressed as 0.4 grams
hydrocarbon refueling losses per vehicle mile. (Reference 6)

1.5  Third-Year^ Pj-ogram
     The CAPE-9 Committee established as the objective for the third year
program the development of a mathematical model (with associated computer
program) for estimating the total hydrocarbon losses from refueling opera-
tions for a specific air quality region during a specified period of time.
In order that the model be readily used by community planners  and others
it was to be based on relatively easily obtained or estimated  variables
such as ambient temperature, underground fuel  temperature, Reid vapor
pressure and gasoline consumption for the region.  To develop  the model
it was necessary to know the magnitude of spill losses and the mathematical
relationship of hydrocarbon (HC) displaced from the fuel tank  during re-
fueling to the above mentioned variables.  Information on the  frequency
of refueling operations by day of the week and hour of day was also needed.
     The second year program provided a good estimate of spill losses for
use in the model.   However, the mathematical relationship developed in the
second year for displaced HC losses was judged inadequate for  use in the

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model because it was based on an incomplete data set and a too narrow
range of fuel Reid vapor pressures.  The laboratory program was, therefore,
redone in the third year with an improved experimental design.  A new
mathematical expression was derived from the new data by stepwise multiple
regression analysis and related displaced HC losses to average dispensed
fuel temperature, initial vehicle fuel tank temperature and the RVP of the
fuel.
     In order to transform the laboratory expression for displaced HC
vapor losses into a mathematical expression containing the more conven-
iently obtained field variables, underground fuel temperature, ambient
temperature and RVP, additional temperature data were obtained in the
field during actual vehicle refuel ings.  The data were obtained at service
stations in the San Bernardino-Ontario area in summer and spring and in
the Minneapolis-St. Paul area in the winter.  Multiple regression analysis
of the field data led  to an expression relating dispensed fuel temperature
to underground fuel and ambient temperatures.   The substitution of this
expression into the laboratory based  expression eliminated the dispensed
fuel temperature from the expression.   A simple linear expression relating
initial  fuel tank temperature to ambient temperature based on data obtained
during the Coordinating Research Council CAPE-5 program was used to elim-
inate the initial dispensed fuel tank temperature from the expression.  The
resulting transformed expression related the displaced HC vapor losses to
the desired variables,  ambient temperature, underground fuel  temperature
and RVP.   This expression along with the estimate of spill  losses was used
in combination with data on refueling  frequencies obtained in the San
Bernardino-Ontario and  Minneapolis-St. Paul areas to develop the desired
air quality region model.  The detailed program and development of the
model are documented in the following  sections of this report.

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                           2.0  LABORATORY STUDY
     The purpose of the laboratory study was to develop a new, improved
mathematical expression relating displaced hydrocarbon (HC) losses during
refueling to average dispensed fuel  temperature, initial  tank fuel tem-
perature and fuel Reid vapor pressure (RVP).

2.1  Experimental Design
     In the second year program it was determined that the displaced
HC loss could be expressed as a function of the following significant in-
dependent variables:  the fuel RVP,  the average dispensed fuel temperature
and either the average displaced vapor temperature or initial  vehicle tank
fuel temperature.  However, because of an incomplete data base and the use
of fuels with too narrow a range of Reid vapor pressures, the regression
expressions derived in the second-year study were judged  inadequate for
use in developing an air quality region model.  It was, therefore, necessary
in the third year program to completely redo the laboratory study to obtain
a new set of data which would serve as the basis for deriving a more re-
liable mathematical expression.  The experimental design  of the study
provided for both an adequate data base and a sufficient  range of the in-
dependent variables to meet this objective.
     Displaced hydrocarbon losses were measured with the  Scott MINISHED
operating under carefully controlled conditions in the Scott all-weather
room.   The procedures used were those developed during the first two years
of the program and are fully described in References 5 and 6.
     The experimental design is shown in Figure 2-1.  It  is seen that the
controlled variables are average dispensed fuel temperature, initial  tank
fuel temperature, and the fuel RVP.   Five levels each of  dispensed fuel
temperature and initial tank fuel  temperature were used for each of three
levels of RVP.   Each experiment was  replicated so that a  total  of 150
experiments was conducted.  The results from ten of these experiments had
to be  discarded because of instrumentation or other problems,  leaving a
sample of 140 measurements of displaced hydrocarbon vapor loss available
for mathematical  analysis.

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      Figure 2-1    Experimental  Design of Laboratory Measurement of
                   Displaced Hydrocarbon Losses
                        INITIAL  TANK FUEL TEMPERATURE C°F)
            30         40      50        60        70        80       90
ui
o:
d
£
a
C/)
CU
C/J
M
a
      30
     40
50
     60
70
     80
      90
X
X
X
X
X

X
X
X
X
X
X
xxx
xxx
X X X
X X X
X X X
X X X

X
X
X
X
X


X
X
X
X
                                                                          ~l
                          1	J
            Legend
                     RVP
                     RVP
                     RVP
                      13
                      10
                       7

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                                    8
     The experimental design represents the optimum desired levels of
each independent variable.  In conducting the actual experiments it was
not always possible to achieve the exact levels required by the design.
For example, heating and dispensing the fuel resulted in some cases in
dropping the RVP from 13 psi to 12.2 psi.  Thermocouple and other instru-
mentation differences also introduced variability.
     Four gallons of fresh fuel were dispensed into the fuel  tank one-half
hour prior to each experiment.  This time was determined to be adequate
to saturate the vapor space and assure that the vapor composition and fuel
RVP in the tank were at the desired values at the beginning of each test.
Ten gallons of fuel were then dispensed during each experiment.  A sample
of the dispensed fuel was obtained for each experiment by the displaced
water method.  In this technique a gasoline sample  is pulled  into a glass
jar by the siphoning action of ice water being displaced from the jar.
The tightly stoppered jars were transported packed  in ice to  an Ethyl
Corporation laboratory for measurement of RVP.  Fresh fuel  was used in
each experiment.   Inspection data for each of the three fuels are given
in Appendix A.
     The data obtained in the 140 valid runs are given in Appendix B.   The
data include the measured values for each run of the independent variables:
average displaced fuel temperature, initial  tank fuel  temperature and fuel
RVP, and the dependent variable, displaced HC loss.   Although not used in
the data analysis the MINTSHED ambient temperature  are also recorded.

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2.2  Derivation of New Regression Model for Estimating Displaced
     Hydrocarbon Losses

     The regression analysis conducted during the second year program
established that an appropriate functional form for the desired model
was obtained by expressing the displaced HC loss as an exponential  func-
tion of the independent variables.  A linear model suitable for the
application of multiple regression techniques was therefore obtained
by regressing the natural logarithm of the displaced HC against linear
combinations of the independent variables, cross products of the variables
and higher power terms.
     Four independent variables were chosen for the analysis.  These
were the three design variables fuel RVP, average dispensed fuel temper-
ature, and the initial tank fuel temperature plus the MINISHED ambient
temperature.  In the initial phases of the analysis all combinations of
first, second, and third order terms of these four variables were examined
using the techniques of stepwise multiple regression analysis.  Four terms
were finally identified as providing an efficient fit to the data.   In the
order of decreasing contribution to reduction in unexplained variance
these were:  the product of RVP and average dispensed fuel  temperature,
initial tank fuel temperature, RVP, and the product of average dispensed
fuel temperature and initial tank fuel temperature.
     A summary of the stepwise regression of these four terms is shown in
Table 2-1.  The correlation matrix is given in Table 2-2.  It is seen from
Table 2-1 that with all four terms included in the regression expression
the multiple correlation coefficient, R between the measured displaced HC
loss and the independent variables has the value R = 0.972.  The coeffi-
                         2
cient of determination, R , which gives the fraction of variance in the
data accounted for by the regression relationship is 0.945.  Thus 94.5% of
the variance has been explained.  It is interesting to note from the Step 1
results that about 85% of the variance is accounted for by  the product of
the average dispensed fuel temperature and the RVP.  It is  also seen from
the first row of the correlation matrix in Table 2-2 that none of the other
terms taken alone correlate nearly as well with the natural logarithm of

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                                     10
Table 2-1  Summary of Stepwise Regression Analysis of Laboratory Displaced
           Hydrocarbon Losses Data
Step Variable
1 Constant
RVDA
2 Constant
RVDA
TK
3 Constant
RVDA
TIC
RV
4 Constant
RVDA
TK
RV
DATK
Model: In
where:






Regression Std. Error of Multiple^ Std. Error
Coefficient Coefficient R R of Estimate
3.7581 x 10"1
1.8126 x 10"3 6.5312 x 10"5 0.921 0.848 0.092
1.2775 x 10~]
1.8380 x 10~3 5.0857 x 10"5
4.0042 x 10~3 4.1926 x 10~4 0.953 0.909 0.072
-6.5063 x 10"2
1.6453 x 10"3 5.6828 x 10~5
5.8259 x 10"3 4.9365 x 10"4
2.0266 x 10~2 3.5367 x 10~3 0.963 0.927 0.065
-9.1703 x 10"2
1.1521 x 10"3 8.9285 x 10"5
-1.2605 x 10"3 1.1507 x 10~3
5.4094 x 10'2 5.9545 x 10"3
1.0725 x 10~4 1.6154 x 10~5 0.972 0.945 0.056
L'D = a + b RVDA + c TK + d RV + e DATKL
L' = Estimate of displaced loss, gms/gal
RVDA = Product of Reid vapor pressure (psi) and average
dispensed fuel temperature, (°F)
TK = Initial tank fuel temperature, (°F)
RV = Reid vapor pressure, (psi)
DATK = Product of average dispensed fuel temperature, (°F),
and tank fuel temperature, (°F)

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                                  11
    Table 2-2   Correlation Matrix of Regression Variables -
                Laboratory Displaced Hydrocarbon Losses Measurements
Variable
Number LNLOSS
1 1.000
2
3
4
5
RVDA
0.921
1.000



TK
0.198
-0.052
1.000


RV
0.423
0.512
-0.579
1.000

DATK
0.284
0.081
0.915
-0.683
1.000
Variable
 Number
   1
   3
   4
   5
Variable
 Symbol
LNLOSS
RVDA

TK
RV
DATK
_ Identification _
Natural logarithm of displaced HC loss,
Product of RVP and average dispensed
 fuel temperatures, psi x °F
Initial tank fuel temperature, °F
RVP, psi
Product of average dispensed fuel and
 initial tank fuel temperatures, (°F)

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                                   12
the displaced loss.  Since the displaced vapor comes into close contact
with the incoming fuel  as it passes out the filler neck and since the fuel
volatility is important in determining the amount of hydrocarbon in the
displaced gases, it would be expected that the dispensed fuel  temperature
and the RVP are of major importance.  The regression analysis  shows that
the impact of each of these variables depends on the magnitude of the
other.  This also appears reasonable in that the vapor pressure of a liquid
increases approximately exponentially with temperature.  The remaining terms
of the expression have no obvious technical interpretation.
     The standard error of estimate for the natural  logarithm of the dis-
placed HC loss is 0.056.  It is shown in Appendix C that this  can be
interpreted as a 5.6% error percentage in the displaced HC loss.  The
ability of the regression to estimate the losses observed in the MINISHED
experiments is shown in Figure 2-2.  It may be concluded from the statis-
tical measures and from an examination of the Figure that the regression
expression provides a good fit to the experimental data:
     The model for displaced hydrocarbon losses derived from the regression
analysis is, therefore:

         Ln L'D  =  a + bPvTD  +  cTT  +  dPy  +  eTDTT                (2-1)
  Where     L n  =  Estimate of displaced hydrocarbon loss, gms/gal
                     of dispensed fuel
            PV   =  RVP of fuel, psi
            TD   =  Average dispensed fuel temperature, °F
            TT   =  Initial tank fuel temperature, °F
            a    =  -9.1703 x 10"2
            b    =   1.1521 x 10"3
            c    =  -1.2605 x 10~3
            d    =   5.4094 x 10"2
            e    =   1.0725 x 10"4

      In using Equation(2-1) certain constraints must be observed.  The re-
gression model should not  be extrapolated beyond the values of the input

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                                      13
   Figure 2-2   Measured Versus EstinBted Displaced Hydrocarbon Losses
     8
en
l/l
t/>
o
-o
QJ
O
•o
o>
•r-   O

•»->   -J
              T      I
I      I       I      I      t
                                                   1	i      t
                    3456


                     Measured   Displaced HC Loss,  gms/gal

-------
                                   14
data.  For example, an RVP of 13 psi should not be used when the dispensed
fuel temperature is greater than 70°F.  Conversely, when the dispensed
fuel temperature is 30°F, the RVP should not be taken as, say 7 psi.
These constraints result not only from the experimental data base but
reflect the fuel RVP's actually provided in the field for the various tem-
perature ranges.
     It is also important to realize that the data base contains no data
at temperatures below 30°F or in excess of 90°F.   Estimates of displaced
vapor loss should not, therefore, be made at extremely low or high temper-
atures since the estimate would be suspect.  There is good reason to
suspect that, as the temperature approaches the initial boiling point of
the fuel, the relationship described by Equation^2-l)vn 11 become invalid.
     In summary the correlation holds for fuels whose RVP's are in the
range 7 to 13 psi while the range of allowable temperatures for a given
RVP are:

              RVP                    Temperature Ranges of
                                    Dispensed and Tank Fuels
             Cpsi)                  	(°H	
               7                          50-90
              10                          40 - 80
              13                          30 - 70

     Other considerations, which will be discussed in more detail in
Section 4.4, further limit the range of applicability of Equation(2-1).
The model applies most accurately to the following situations:
     o  RVP of the tank fuel and the dispensed fuel are the same.
     o  Negligible weathering of tank fuel.
     o  Fuel tank has the same configuration as that used in the study.
     o  Refuel ings which start with a few gallons of fuel in the tank.
         and stop with the tank slightly over half full.

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                                    15
                            3.0  FIELD SURVEY
     The field survey conducted in the third year program had two
objectives:  first, to collect temperature data at service stations
during refueling of vehicles in order to establish a mathematical
relationship between the temperature of dispensed fuel and the ambient
and underground fuel temperatures; second, to determine how the number
of refueling operations per hour varied with time of day and day of
week.  The mathematical relationship and refueling frequency data ob-
tained from the field study were to be used in combination with the
displaced hydrocarbon loss expression obtained from the laboratory
study (Section 2.0) to develop the region wide model (Section 4.0).

3.1  Description of Field Survey
     The field survey phase collected data for three ranges of ambient
temperature, T^:

          1.  Maximum T.  ^  30°F
          2.  60° ^ Maximum T.  ^ 80°F
                              A
          3.  Maximum T^ >>   90°F

For each service station surveyed, at least two dispensers on each of two
islands were instrumented (See Reference 6 for details of experimental
set-up) to measure the dispensed fuel  temperature and the displaced vapor
temperature each time a dispenser was used.   In addition, the following
data were obtained for all refueling operations and all  dispensers:
          1.  Time of day.
          2.  Time between refueling operations.
          3.  Gallons of fuel  dispensed.
          4.  Exposure of dispenser to sun.

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                                    16
     The ambient temperature, relative humidity, and barometric pressure
were continuously measured with instruments mounted in a "cotton-region
type" weather shelter.  The underground fuel temperature was measured
every two hours.
     Data collection operations were conducted for seven days, two shifts
per day, at each of four stations in the San Bernardino-Ontario area during
the summer.  Data were collected in the Minneapolis-St. Paul area for seven
days, two shifts per day, at each of two stations during the month of Jan-
uary to obtain cold weather data.  Finally, because of budget considerations,
data were collected for one week at one station on a one-shift basis in
San Bernardino during the spring to obtain moderate temperature data.
     The stations were selected with respect to two configurational
criteria:  1) canopy vs no canopy, and  2) pump in tank vs pump above-
ground.  It was conjectured that these parameters might be a factor in the
relationship of dispensed fuel  temperature to ambient temperature and under-
ground fuel temperature.  Other factors such as the depth and length of
subsurface fuel lines and the material used to pave the station's apron may
also influence the dispensed fuel temperature but no data were obtained that
would permit an evaluation of these factors.

3.2  Regression Analysis of Temperature Data
     A sampling of temperature data for three selected days corresponding
to summer, spring, and winter are given in Appendix D.  Stepwise multiple
regression analyses were run on 2637 field temperature observations.  The
average dispensed fuel temperature was regressed against underground fuel
temperature, ambient temperature, canopy vs no canopy, pump in tank vs.
pump above ground, gallons of fuel  dispensed, and time between dispenser
use.  The analysis showed that only the underground fuel  temperature and
ambient temperature led to significant reductions in unexplained variance
of the dispensed fuel  temperature.   Therefore, only the temperature vari-
ables were retained for further analysis.   It must be noted, however, that
a much larger program with an appropriate  experimental design, would be
required to provide a definitive conclusion regarding the influence  of the

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                                    17
variables that were dropped.  Such a program should also include addi-
tional configruational variables such as mentioned above.
     Table 3-1 summarizes the stepwise regression and Table 3-2 the
correlation matrix of the temperature variables.  Further details of the
analysis are shown in Appendix E.  It is seen that 98.9% of the variance
in the average dispensed fuel temperature is accounted for with a standard
error of estimate of 2.47°F.  Table 3-1  shows that the underground fuel
temperature alone accounts for 98.2% of the variance.  Addition of the
ambient temperature term appears to be merited in view of the further low-
ering of unexplained variance from 1.8% to 1.1% a large proportional improve-
ment, and the 23% improvement in the standard error of estimate.  The
correlation matrix shows that ambient temperature taken alone can account
for 89% of the variance in the dispensed fuel  temperature.  It also shows,
as would be expected, that the underground fuel  and ambient temperatures
when taken over all  seasons of the year are highly correlated.
     Since the data base used in the regression analysis consisted of three
subsets of data each representing a different city/month combination, it
was of interest to see what regression analyses of these individual  sets of
data would yield.  The results are summarized in Table 3-3 and  given in
more detail  in Appendix E.  The percentage of variance accounted for in the
individual subset analyses are much smaller than for the complete set.   This
result is largely accounted for by the restricted ranges of the variables,
particularly the underground fuel temperature whose standard deviation  was
one to two degrees in each of the subsets.   The standard error  in each  case
is about the same as for the regression  analysis on the total  sample.  From
the more detailed analysis in Appendix E it will  be seen that the ambient
temperature accounts for most of the variance in the dispensed  fuel  temper-
ature for the high and moderate temperature data.  For the low  temperature
subset the underground fuel  temperature  is  again the dominant variable  in
accounting for variance of the dependent variable.   These observations  are
accounted for by the very restricted range  of underground fuel  temperatures
in the high and moderate temperature data and the relatively greater range
of this variable in  the low temperature  subset.

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                                    18
Table 3-1   Summary of Stepwise Regression Analysis  of Third  Year  Field
           Survey Temperature Data
Step Variable Regression
Coefficient
1 Constant -1.21315
UF 1.01714
2 Constant -1.17523
UF 0.80785
AM 0.22667
Std. Error of Multiple,,
Coefficient R R
0.00271 0.991 0.982
0.00530
0.00529 0.995 0.989
Model : DA = a + b UF + c AM
where DA = Estimate of average dispensed fuel temperature,
UF = Underground fuel temperature, °F
AM = Ambient temperature, °F
Std. Error
of Estimate
3.21
2.47
°F

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                                     19
Table 3-2   Correlation Matrix of Regression  Variables  -  Field  Survey
            Temperature Measurements
    Variable
     Number
       1
       2
       3
  DA
1.000
   UF
 0.991
 1.000
  AM
0.946
0.920
1.000
    Variable
     Number
       1
       2
       3
Symbol
  DA
  UF
  AM
            Identification
Average dispensed fuel  temperature.
Underground fuel  temperature, °F
Ambient temperature, °F

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                                     20
Table 3-3  Summary of Stepwise Regression  Analyses  of  Subsets  of Third  Year
           Field Survey Temperature Data
Subset
Minneapolis-
St. Paul
Winter
San
Bernardino
Spring
San
Bernardino
Summer




Variable
Constant
DU
AM
Constant
DU
AM
Constant
DU
AM
Model DA
where DA
DU
AM
ZcTTemp. Regress. Std. Error
Range, °F Coeff. of Coeff .
-11.37380
24-38 1.10383 0.03014
12-45 0.27503 0.01283
33.11020
65-69 0.15295 0.13333
41-76 0.35165 0.01672
38.81367
82-87 0.34232 0.04311
59-97 0.21989 0.00545
= a + b DU + c
= Estimate of average dispensed
= Underground fuel temperature,
= Ambient temperature, °F
Multiple2 Std. Error
R R of Estimate


0.862 0.743 2.77


0.843 0.711 1.95


0.743 0.552 2.05

fuel temperature, °F
°F


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                                    21
    Within each of the three subsets there is little correlation of ambient
and underground fuel temperatures.  This comes about because within each
season there is a relatively small change in average ambient temperature.
The underground fuel temperature is more influenced by the average ambient
temperature than by the day to day variations of ambient about its mean.
This observation together with those of the preceeding paragraph empha-
sizes the importance of including an ambient temperature term in the
regression for the total set even though the underground fuel temperature
is by far the dominant variable.
    The regression expressions for the subsets shown in Table 3-3 bear
little resemblance to the expression in Table 3-1 for the total data set.
To compare how well the expression for the composite agrees with the
expressions for the individual subsets comparative calculations were made
for a spread of temperatures of three standard deviations about the mean
in each temperature regime and are shown in Table 3-4.  It is seen that
the agreement is excellent for the high temperature case.  For the low
temperature case the agreement is close only at the means of the tempera-
ture data.  At the extremes the two expressions are +_ 4°F apart.  In the
moderate temperature case there is a consistent descrepancy of 1 to 3°
over the range of the data.  Part of the reason for these differences is
accounted for by the fact that there are 660 sets of observations for the
low temperature case, 187 sets of observations for the moderate temperature,
and 1790 sets of observations for the high temperature case.  In deriving
the composite equation no attempt was made to compensate for the smaller
number of low temperature and '•till  smaller number of moderate temperature
observations.  Thus the high temperature data weigh  most heavily.   The
low temperature data are the next most dominant which accounts for the good
agreement at the mean of the low temperatures.  The two extreme sets, there-
fore, largely determine the total expression and it is not surprising the
moderate temperature set shows a consistently lower estimated dispensed
fuel  temperature.   To summarize:   the moderate temperature data points
tend to fall  below the plane of the  total  regression expression; the winter
data points show a uniformly wide spread on either side of the plane; the

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                                    22
Table 3-4   Comparison of Dispensed Fuel Temperatures Estimated by Total
            Regression Expression and Individual  Subset Expressions
                                   Temperatures, °F
Temperature
Regime
Low
3S"high
mean
3 alow
Moderate
36-high
mean
36'low
High
3
-------
                                  23
summer data points fall close to the plane; the total regression covers
the overall range of data reasonably well but is not uniformly good for
each of three data subsets.  These differences are to be expected.  The
three subsets represent different service stations in different geographic
locations.  The coefficients of the regression equations are influenced,
therefore, by factors in addition to the underground fuel temperature and
ambient temperature.  These might be depth and length of sub-surface lines,
etc.  The limited number of stations and cities studied prevented includ-
ing such factors in the analysis.
    From the analysis in the preceeding paragraph it is seen despite some
uneven treatment of the three cases the overall expression gives a good
representation of the total data set and, therefore, provides a suitable
expression for developing the regional  model.  This expression is:

         TC  =  a + bTU+cTA'                                        t3^
  where  TD  =  Average dispensed fuel  temperatue, °F
         Ty  =  Underground fuel temperature, °F
         T^  =  Ambient temperature, °F
         a   =  -1.17523
         b   =   0.80785
         c   =   0.22667

    While there may be a temptation to  use the individual  expressions  for
estimates within a given season this practice is not advised.   The individual
expressions are based on very limited data and small  ranges  of the variables
and their generality is far more subject to question than  that of the  overall
expression.

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                                    24
3.3  Frequency of Refueling Operations
     The temperature data were supplemented by the collection of data
yielding the frequency of refueling operations by day of week and by
hour of day, where a refueling day is 16 hours long.   Since data were
collected on a one-shift basis for Station 7, those operational  data were
not included in the frequency of refueling analysis.   Figure 3-1 shows
the frequency functions for operations by day of week for Stations 1
through 6 and Figure 3-2 shows the frequency function for the composite
station.  The dashed line in Figure 3-2 represents the average frequency
for one week of operation.   No day of the week was significantly different
from the average (or even from any other day) as determined by t-testing.
For modeling purposes, then, the days of the week may be taken to be indis-
tinquishable.
     The frequency function for refueling operations  as a function of the
16-hour day for the composite station is shown in Figure 3-3 and tabulated
in Table 3-5.  Again,  Station 7 data have been excluded because  of the
one-shift operation.  The hour-by-hour frequencies in Table 3-5  are used
in the regional model  as shown in the next section.
     Although not directly required for modeling purposes,  it is of some
interest to note the variation in fuel dispensed per  operation.   Figure 3-4
shows the frequency function for the number of gallons dispensed per refuel-
ing operation.   The mean number of gallons is 10.4.   The second-year field
survey which covered other cities gave a value of 11.4 gallons.   Thus, the
average varies  from city-to-city (Reference 6).   It  should, of course, be
kept in mind that the  frequency of fill  by hour and day, and gallons per
fill can vary by locale and also with time for a given location.

-------
              Frequency, %

                                                                  Frequency,  %
                                                                        03
 11   —I
    • >—I
en   CD


                                                                    oo
                            if   —,
                                CD
                            UD  =2
                            cn
                            CD  f—'
    oo


                                                  CO
                                                                   00
                                                               II

                                                               oo
                — *
    co
                1

                '
   C  H-
td fD  (N.
«^j  f!j  C^

   O  (-(

                                   ro  i-t
                                   (D  CU
                                   ?^ rt
                                      3
                                      ca
      u>

                                                                   00
                           00   CD
                                                                                       1

-------
                                                        Frequency,
     1
u
(U
s:
fD
fD
7?
                          OJ
                          I
 a\
J_
       CO

        I
2!

 II


00
M
VO
                                                                                                             n
                                                                                                             o
                                                                                                             o
                                                                                                             01
                                                                                                             H-
                                                                                                             cn
                                                                                                             rt
                                                                                                             03
                                                                                                             rt
                                                                                                             h*

                                                                                                             §
                                                                           CD
                                                                           .0
                                                                        w c
                                                                        ^  §
                                                                        u o
                                                                        fD  fD
                                                                        n>  n
                                                                        ?T (B
                                                                           rt
                                                                           p.
                                                                           O
                                                                           3
                                                                           0)
                                                                                                                          fD
                                                                                                                          NJ

-------
  9 -I
            Figure 3-3



    Frequency Function for Refueling

       Operations by Time of Day


              N = 4819

         (Station 7 not included)
   3 -
   7  -
   6  -
 *  c
o  5
e
0)
                                                                                 ro
                                                                                 -j
   4  _
   3  _
   1  _
                 "I	

                  0800
1000
1200
1400
1600
iaoo
2000
                                                                         2200
                                                Time of Day

-------
10 -i '
 9 -
                                                                                  Figure  3-4

                                                                            Frequency Function  for Fuel

                                                                              Dispensed  per  Operation
  8 -
                                                                                    N = 5219

                                                                                Mean  =10.4 gals.
 -i  _
 • 6 —

o

0)
3
u1
                                                                                                            ro
                                                                                                            CO
 4  -
 3  -
 2  _
 1  _
                                             10
T"

 12
                                                             1A
T

 16
                                                                   ,11,
                                                                              18
                                                                                     20
~T

 22
                                                                                                     24

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                                29
Table 3-5   Frequency Distribution of Refueling Operations
            per Hour From Six AM to Ten PM
Interval
#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Hour Beginning at:
6:00 AM
7:00
8:00
9:00
10:00
11:00
12:00
1:00 PM
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
Fraction of Total
Refueling Operations
0.0175
0.0435
0.0445
0.0585
0.0605
0.0700
0.0715
0.0695
0.0755
0.0770
0.0765
0.0835
0.0845
0.0775
0.0550
0.0350
                                                1.0000

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                                   30
            4.0  REGIONAL HYDROCARBON REFUELING LOSS MODEL
     This section derives a model  for estimating hydrocarbon losses from
refueling automobiles in a given geographic area over a specified period
of time.  It makes use of:
        o  Estimates of spilling losses during refueling operations
           obtained during the second year program.
        o  The regression expression derived in the third year
           program for displaced hydrocarbon losses as a function
           of fuel Reid vapor pressure, average dispensed fuel
           temperature, and initial  tank fuel temperatures (Sec-
           tion 2).
        o  The regression expression derived in the third year program
           for average dispensed fuel temperature as a function of
           underground fuel temperature and ambient temperature
           (Section 3).
        o  A relationship between  initial  tank fuel temperature and
           ambient temperature taken from the Coordinating Research
           Council's CAPE-5 program which studied fuel system tempera-
           tures during vehicle operation.
        o  The distribution of refueling operations by hour from 6 AM
           to 10 PM obtained in the third year program field survey
           (Section 3).
The utility and limitations of the model are discussed and its application
illustrated through use of a computer program and a desk calculator.

4.1  Derivation of Regional Model
     The total hydrocarbon losses  from the fueling of automobiles for a
given geographic area over a specified number of days is the grand sum of
the losses from each refueling operation conducted during the time period
of interest.  It is possible to order these losses by day and hour within
the day in which they occur.  We have, therefore:

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                                  31
                 D    H     N(hrd.)
                              ~
      LT  =
       T

where U-  =  Total hydrocarbon refueling losses over D days for the
             region expressed in the same weight units as LR
      LD  =  Loss in arbitrary weight units per unit volume of fuel
       R
             dispensed in n.-th refueling operation during the
             h.-th hour of the d.-th day.
              *                  J
      G   =  Volume of fuel dispensed into vehicle during the
             n.-th refueling in the h.-th hour of the d.-th day.
              K                      I                 J
      D   =  Total integral number of days for period.
      H   =  Total integral number of hours of refueling operations
             per day (assumed the same for each day).
                                                                th
  N (h.d.)  =  Total  number of refuel ings that occurred in the h..-
               hour of the d.-th day.
                            J
To transform this exact model  into a practical, working model  will require
a number of assumptions, each  of which can cause some loss of accuracy.   The
assumptions that are required  and the  derivation of a working model  will  be
given in this subsection.  Subsection  4.3 will discuss the potential  errors
which may be introduced by the assumptions.

     Assumption #1  The loss LR is not a function of volume of fuel
     dispensed.
     Assumption #2  The gallons of fuel dispensed with each refueling
     operation within each hour varies randomly about some mean value
     for that day and hour.
     Assumption #3  The number obtained by averaging the average hourly
     gallons dispensed per refueling operation over all hours of all  days
     within the period may be  substituted for the individual  hourly
     averages.
     Assumption #4  The number of refueling operations per hour is a
     function of hour of the day but not of the day.

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                                      32
     Assumption  #5   The  hourly  average  hydrocarbon  refueling  loss  per
     refueling operation can  be expressed  as  the  sum  of  an  hourly
     average hydrocarbon spill  loss  and an hourly average displaced
     hydrocarbon loss.
     Assumption  #6   The  hourly  average  spill  loss per gallon  of  dispensed
     fuel  varies randomly about a determinable  mean value having no  re-
     lationship  to  hour  of day  or day.
     Assumption  #7   The  hourly  average  displaced  hydrocarbon  loss  can  be
     estimated by a mathematical  expression containing the  hourly  average
     Reid  vapor  pressure, the hourly average  underground fuel  temperature
     and the hourly average ambient  temperature.   (This  assumption contains
     within it the  assumption that region  wide  hourly average values of
     Reid  vapor  pressure and underground fuel temperature can be used  in
     place of values for each service station within  the region.)
     Assumption  #8   The  hourly  average  underground  fuel  temperature  is
     constant within any day.
     Assumption  #9   The  hourly  average  Reid vapor pressure  is constant
     within any day.
Application of Assumptions #1 and #2 to Equation  (4-1) allows the  summation
over n.  to be carried out and the variables LR  and  G  expressed as  hourly
averages over all refuel ings in a given hour.  This operation yields the
following  general form of the model.
               D       H
     U   =  2	   2	      R(hi,d.)  LR (h.,d.)  G (h,,d.)            (4-2)
      '        j=1     i=i          i  J    K   i   j       i   j
 where
LD (h.,d.)=  The average refueling loss of all  refuelings in the h.-th
 K   1  J                                                         1
             hour of the d.-th day in weight per unit volume dispensed.
                          \j
15" (h.,d.) =  The volume of dispensed gasoline per refueling operation
             averaged over all refuelings in the h.-th hour of the
             d^-th day.
              \J
R (h-,d.) =  The number of refueling operations in the h^th hour of
    •   J
             the d.-th day.
                  J

-------
                                  33
     Assumption #3 allows G (h., d.) to be replaced by G and the G to be
                              *    J
factored out of the summation and placed to the left of the summation
signs.  Assumption #4 allows R (h. ,d.) to be replaced by R (h^).
     Application of the Assumption #3 and the remaining assumptions leads
to the desired working model:
                D      H           _    _
                                   _    _
  L'T   = kH  J~~  5~~  RO^) [4 + L£ (TyCdj), WV'  Py(d ))]   (4-3)
               j = I     i.= I
The terms in Equation (4-3) are defined as follows:
  L'T   =  Estimated total refueling loss for region over specified
           period in appropriate weight units.
  k     =  Conversion factor from weight unit used in L1^ and L'D
  G     =  Average  daily volume of fuel dispensed within the region
           for the  period.
  D     =  Total integral  days in specified period.
  H     =  Total integral  number of hours refueling operations  per day.
R(h.)   =  Fraction of total daily refueling operations which occur
           in h.j-th hour.
 L'<-    =  Estimated average spill loss in weight/volume dispensed.
 L's    =  Estimated hourly average displaced hydrocarbon loss  in
           weight per gallon dispensed.
 T.     =  Regional average underground fuel  temperature on a given day,  °F.
 T^     =  Regional average ambient temperature for a given hour, °F.
 Py     =  Regional average Reid vapor pressure on a given day,  psi.
Note that the R(h.) and G" are redefined for convenience (they could have
retained their former interpretation).
     The second year program has established that:
  I     =  0.30 gms/gal                                                      (4-4)

-------
                                    34
     The expression for L' is derived as follows.  From Equation (2-1) of
Section 2 and Assumptions #7 - #9 we can write the following analogous
approximate expression:
     L£    =  exp (a + biyTD + dP"v + cTT + dP"v + e TDTT)                   (4-5)
 where
     T_    =  Regional average dispensed fuel temperature for a
               given hour, °F.
     TT    =  Regional average initial tank fuel temperature for
               a given hour, °F.
The constants a through e are taken as the same as given for Equation (2-1).
Note that this is not a precise application of (2-1) since the exponential
form and the cross product terms do not permit averaging both sides of the
expression in the manner shown (See discussion of Assumption #7 in Section
4.4).
     From Equation (3-1) of Section 3:
     TD    =  f + gTu + hTA                                              (4-6)
Where the constants f, g, and h are the same as for Equation (3-1).  Because
of the linearity of Equation (3-1) there is no difficulty taking averages on
both sides of the equation.
     The Coordinating Research Council APRAC Program on fuel system tempera-
tures, CAPE-5, showed that the fuel tank temperature of an operating vehicle
could vary up to 25° above ambient (Reference 7).  The following simple
relationship is used here:
     TT    =  TA  +AT                                                    (4-7)
If Equations (4-6) and (4-7) are substituted into (4-5) the following expres-
sion is obtained:
 I- (lyd,,)-  exp(Cl + C2Pv(dj) + C^Ovdj) + C^Cd.) +
                                   C7TA
-------
                                 35
  where
     C-!    =  a + c T + ef AT
     C2    =  bf + d
     C3    =  c + ef + eh Al                                             (4-9)
     C4    =  eg
     C5    =  bh
     C6    =  bg
     C?    =  eg
     C8    =  eh
Substituting the appropriate values of the constants from Equations (2-1)
and (3-1) and the value of 7.0 for .AT.  (See discussion of Assumption #11
in Section 4.4).
     C1    =  -1.0141 x 10"1
     C2    =   5.2740 x 10"2
     C3    =  -1.2164 x 10"3
     C4    =   6.0649 x 10"4                                              (4'10)
     C5    =   2.6115 x 10"4
     C,    =   9.3072 x 10"4
      b
     C?    =   8.6642 x 10~5
     Cg    =   2.4310 x 10"5
In deriving Equations (4-4)  and (4-8) the following additional  assumptions
were made.
     Assumption #10  The average spill loss per gallon of fuel
     dispensed is 0.30 gms.
     Assumption #11  Equations (2-1), (3-1) and (4-7) provide a reasonable
     basis for defining L~

-------
                                    36
Equations (4-3), (4-4), (4-8) and (4-10) constitute the model  along with the
frequency distribution of refuel ings given in Table 3-5.  The  model is sum-
marized in Table 4-1.

4.2  Computer Program of the Regional Model
     The regional model applied to a thirty-one day period would require
the calculation of 31 x 16 = 496 values of the moderately complex expression
L' (h.d.) which is itself the exponential  of an eight term polynomial.  Thus
 U   '  w
any extensive use of the model would be greatly aided by use of a computer.
Accordingly, a computer program of the model was constructed and is listed
in Appendix F.  The program allows up to 99 cases to be run in a single
batch operation.  Each case may apply to a different region and cover any
specified time period up to 400 days.
     The program also has three options which are to be specified:
Option 1 allows printing the coefficients of the model's displaced hydro-
carbon loss equation; Option 2 allows a single data card to be used to
cover the period under study rather than a data card for each  day if the
gallons of fuel dispensed per day, the Reid vapor pressure, and the under-
ground fuel temperature are constant over the period; and Option 3 allows
printing out the input data.  Option 2 implies a slight departure from the
model presented in Table 4-1.  The computer program allows a different
value of gallons dispensed to be used for each day while the model uses
only an average value for the period.
     Another feature of the program is that new, improved values for the
basic regression coefficients derived in Section 3, as well as AT and the
average spill loss can be easily inserted without altering other program
steps.   This is possible because the coefficients of the displaced loss
equation of the model, Equation (4-8), are calculated by the computer from
the base regression coefficients and .AT each time a batch of  cases is run.
The data for the base coefficients ..AT, and the average spill  loss are
contained on individual data cards in the program deck (See steps 11  through
16 of the program listed in Appendix F).

-------
                                     37
        Table 4-1    Regional Model for Hydrocarbon Refueling Losses
                         D
4
L's          =  0.30
IjOydj)   =  ExpCCj + C2Pv(d.j) + C3TA(h1,dj) + C^) * Cgtydj) yh^)

                + WWV + C7TA
-------
                                    38
     The input information required to operate the program is as follows:
        o  Number of cases to be run.
        o  Option 1 selection:
             - Option 1=0  Will not print loss equation coefficients.
             - Option 1 = 1  Will print loss equation coefficients.
        o  For each case:
             - The number of days to be covered.
             - Option 2 and 3 selections:
                 - Option 2=0  Gallons dispensed per day, Reid vapor
                                 pressure, underground fuel temperature
                                 are constant over the days to be covered.
                 - Option 2 = 1  Above variables change over the days to
                                 be covered.
                 - Option 3=0  Will not print input data.
                 - Option 3=1  Will print input data.
             - G(d.)»gallons of fuel dispensed in the region for each
                  J  day of the period.
             -Tn(d.)» regional average underground fuel  temperature
                u  J   for each day, °F.
             - Py(dj)» re9i°nal average Reid vapor pressure for each day, psi.
             - T.(h.d.)> regional average ambient temperature for each hour
                A  n J   of each day, °F.

     The ordering and layout of the data input cards is given in Table 4-2.
It is seen that the first card indicates the number of cases to be run and
the Option 1  choice.  The data cards are then grouped by case.  Each case
begins with a card indicating the number of days for that case and the choices
regarding Options 2 and 3.  The data cards follow.   Although each data card
is referenced by the day, it is important that the cards  be ordered by day
as indicated  in Table 4-2.  The program tests for correct ordering.  If the
cards are not in sequence further execution of the program will  be stopped.
In this case  both an error message and the data card which is out of place
are printed.
     As an illustration of the use of the program,  the input and output for
a two case calculation is given here.  The first case is  for a period of 31
days during the summer months while the second case covers 31  days during

-------
                                         39
           Table 4-2    Preparation  and Ordering of  Input Cards For Regional
                       Model  Computer Program
Card
Number
1

Format
3X, 12, 4X, 11


0
0
Information Entered
Number of refueling loss cases to be run
Choice of Option 1
Column
Numbers
4-5
10
                              *****   Case  1  *****

         2X,  13,  2(4X,  II)      o   Number  of days in Case  1                         3-5
                               o   Choice  of Option 2                                10

                               o   Choice  of Option 3                                15

         15,  5X,  F10.0,         o   Day one                                         1-5
          2(5X,  F5.0)           Q   G  (!)5  total ganons dispensed first day        11-20
                               o   Py  (1),  average  regional  Reid vapor pressure,   26-30
                                    (psi)  for  first day
                               o   Tj.  (1),  average  underground fuel temperature,   36-40
                                    (°F),  for  region on  first day

4-31        Assumes 31  days  in  Case  1.   Same format and  variables as Card 3 but
            for each succeeding day  up  to  and  including  last day of case.  Note:
            If Option 2=0  only  one  card  needed for these  variables and columns
            1-5 may be  left  blank.

32       15, IX, 16 F4.0       o   Day one                                          1-5
                               o   T.  (1,1)  average regional temperature, °F,       7-10
                                    for first  hour of first day
                               o   T.  (16,1)  average ambient temperature, °F,      67-70
                                     for  16th  hour of first day.

33-62       Same format Card  32 and  same  variables but for each succeeding day
            up to last day of case.
                              * *  * * *   Case 2,  3, etc.
                                                         *****
            Same set up as  shown  for  Case  1.  Load card groups for each case
            successively.

-------
                                    40
the winter months.   For comparison purposes the number of gallons dispensed
was held constant in both cases at one million gallons per day.   For the
summer case it was assumed that the daily average underground fuel  temper-
ature remained constant at 76°F for the summer period and 30°F for the
winter period.  It was also assumed that the average RVP of the fuels was
constant at 7.5 psi for the summer cases and 12.0 psi for the winter cases.
     The ambient temperatures for the summer months were obtained from the
Weather Service.  However, the temperatures obtained exceeded ninety degrees
and thus were beyond the validity range of the displaced HC loss expression.
In fact, because of the addition of the AT term, the ambient temperature
cannot exceed (90°F -Z\T) without going beyond the range of the model.
Consequently, to obtain a set of temperature data for the illustration each
ambient temperature was reduced by 10°F.  The adjusted ambient temperatures
for the summer case are shown in Table 4-5.  The winter ambient temperature
data were obtained in Minneapolis during the month of January.  Since only
14 days of data were obtained they were replicated to yield 31 days of
winter data as shown in Table 4-8.
     Since it was desired to show the calculated displaced HC loss equation,
Option 1 was set to one.  Because gallons dispensed per day, Reid vapor
pressure, and underground fuel temperature were chosen to be constant within
each of the 31 day  periods, Option 2 was set at zero (or left undesignated
on the card).  It was also desired to printout all the input data for each
case and, therefore, Option 3 was set at one.
     The ordering of the data in the input data cards is illustrated in
Table 4-3 and follows the procedure given set forth in Table 4-2.
     The program outputs are shown in the next seven tables.  Table 4-4
shows the eight computed coefficients of the expression for average dis-
placed hydrocarbon loss (See Equation  (4-10)). Table 4-5 shows the input
data for the summer case.  The calculated hydrocarbon losses are given in
the next two tables.  The first, Table 4-6 gives the hydrocarbon refueling
losses in pounds for each day of the summer period together with the total
period loss and the average loss in grams/gallon dispensed.  The second,
Table 4-7 shows the loss for each hour from 0600 to 2200 hours summed over
the total number of days in the period.  Input data for the winter case is
given in Tables 4-8.  The refueling losses for the winter are shown in Tables
4-9 and 4-10.

-------
                                   41
     The average loss of 5.08 gtns/gal  for the summer  case  is  high  but within
the valid range of the model.  It is noted that  the daily  losses for both
cases do not exhibit large fluctuations.   The larger  fluctuations  in the
case of the hourly losses is partly due to influence  of the hourly refueling
frequencies.

-------
                                   42
Table 4-3  Sample Input Data Cards for  Computer Program of Regional  Model

f
V-
<*
V
/
6
&
Jtf
1 	 "C" FOR COMMENT
STATEMENT
1 NUMBER
5
, , , ,2
, , JY

/
2
3
, , , ,4
L ' ' '


l I K^l/

, , , ,/
/J
1 | i i X.
s>
1 1 1 i/~
l 1 1 1
1 1 1 1
1 1 1 1

1 1 1 1
1 1 1 1
lilt
1 l i 1

1 i i i
l 1 l l
l i 1 1
l i i i
l i l l
c
o






























CHPTP AKJ *iT AT FM FNT • fch>
7 10 20 30 40
, , , /I l 1 , , l 1 1 l i 1 I ,. 1 1 1 1 1 1 J 	 L J 	 1 	 1 	 1 	 1 	 1 	 J_.
, , , U\ i i , , / 	 11,1111 i_ _j 	 1 — i — i — i — i — i — i — i — i 	 1 —
	 I^AOAO^ 	 7,.,^T 	 7-£ :
i iV>3\ i I/,/, , i 7iOi , /,^>i i i/ifli i i0i/ i iCM/ i i i<9i/i i ,
// n 3 n ii- 11 7 i? J? f)\ % 1 9 1
, ,&?,£? . i /t^i i i/i/i i /,/, , i / i'J i i lOitxJ — i — \o i/ i — i — i o | / ! — , — .
i |K?J i i 7i^i , i/iTj , /, £>i , , /, ' , , I /i^ l |6|0| i i&l/i l :
// /,(bi , ,£>!/, , ,/,/i , /.^, , i/i/i i i/i/l i i/i^i.. i.. i/i/i i i
, > , ,11,11,1, 1, 	 i 1. 1- .1.. -1.--L 1 1 -1 .-1-...J .- 1 ...
, , , , , , , , JLb&i /sKL/UW&KLA /l&A&s s^.vT i i i i i ,
1,1 Illlll, 1 1 ..i. 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 1 	 ! 	
, , tU\ . , , i /, i t , , , i i i i i i i i. ...i_.j_ j_ j — i — i — i — I — I — 1 — i —
, i , i i i / 1 c/i fJt O, u u U \ i i i i i i/iA-4. \CA i i i i i i i k^iC/ i
, , , U\ , , , / , , , , / i , / , , , i xi, i , , /I 1 i i O i i i / i L/i i i
//, // / *7 i / *7 7*7 / *7\ 1*7 1 &
1 l/lfe?l 1 J_d0\ 1 I/I/I 1 I/I/I J I/I/I t l/I/l 1 I/I/I 1 l/lOl 1 !
y/7. /v7 / <7 7^ J ll \/ \ \ \ \ i i
,11 i i i i i i i i i i i i i i i i i i i i i i i i i i i i

iii i i i i i i i i i ii 	 ii i i i i i i i i i i ._
iii i i i i i i i i i 1 i i i i i i i i i i i l i i i i i i :. _
II) l l 1 1 1 1 1 1 i l 1 1 1 1 1 l l 1 1 1 1 1 1 1 1 1 1 .!._
iii i i i i i i i i i i i i i i i i i i i i i i i i i i i i
11, 1 1 1 1 1 , . Illlll !___!__!__ .!_._! ...J 	 J_._i.._l. _J 	 1 	 1 	 , 	 ,
III 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 , 1 1 —
111 i i i i i i i i i i i l i i i i i 1 l 1 i 1 I 1 1 i i :
III 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 __1 —
III 1 1 1 1 1 1 1 1 1 	 1 1 1 1 1 1 1 1 1 1 1 1 1 	 J — .
1 1 1 1 1 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 — I_I_J — 1_J — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1—
 UD 1-1156
                    VSPER3Y RftfvD

-------
                                 43
Table 4-4   Computer Listing of Coefficients  to  Displaced Hydrocarbon
           Loss Equation  of Regional Model
                  THE CALCULATED  Cctf- f- 1CI tM 8  A*t»

                       C ( J J  =     " . 1 o 1 4'i + 00

                       CCd)  =      ,S27^0-U1

                       CC3)  a     -.Ic'lb^-OcJ
                       CC7;  =

-------
               Table 4-5   Computer' Listing of Input Data for Summer Month  Calculation
?Af
Ft'bL
KvP
    (GAL/OAY)  l^SIA)
1
2
3
4
5
o
7
y
9
10
11
12
13 .
14
1 5
lo
17
16
19.
20
21
22
23
24
25
26
27
26
29
50
31
1
1
1
1
1
1
1
1
I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
•
,
.
,
,
,
,
,
,
,
.
,
*
,
,
.
,
,
•
,
,
,
,
,
•
,
,
•
,
*
,
00
0 +
i) 0 0 +
O'J
00
00
0'.)
00
00
00
00
00
00
0 0
00
C»'J
ou
00
0 0
00
00
00
Ou
00
00
00
00
00
00
iU>
00
00
0 +
0 +
0 +
0 +
06
06
Or>
06
Ob
06
0 + 06
0 +
0 +
0 +
0 +
0 +
0 +
0*
0 +
0 +
0 +
0 +
0 +
0 +
0 +
0 +
0*
0 +
0 +
0 +
0 +
0 +
Oft
06
06
Oft
06
Oo
06
06
06
06
V6
06
06
06
Oo
06
06
06
06
06
0*3
0 + 06
1)4-
0 +
nto
06
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
•
•
*
,
,
,
,
,
.
.
,
f
*
,
»
,
,
,
•
,
*
,
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»
,
,
,
,
,
.
,
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5 1 fv, A L. jj | ' * ^
-* ' * ' L. *» w * W
It "-P.

iGtG F;

76.
7ft.
7ft.
76,
7ft.
7".
76.
76.
7^»
7o.
7ft.
76,
76,
7s*
7ft,
76,
7o.
7i>.
7ft,
7o.
7 '5,
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76,
76.
76.
7ft.
76,
7o,
/o,
7ft.
76,

0600
TO
0700

65,
66.
68.
66,
6b,
68 ,
66,
66,
67,
66,
67.
66,
67.
09,
69.
65.
67,
67.
n 7 .
64.
65,
66,
66,
66.
67.
"67.
67.
66,
65,
64 ,
68 ,
* 1
0 7 0 U
!U
0600

71,
73,
73,
69,
71.
75,
72.
72,
71.
70,
70,
70,
70,
72,
70,
72,
,71 ,
'(I.
70 »
66,
69,
67,
66,
70.
75,
72,
73.
66,
69 ,
66 .
70,

C800
TQ
0900

75.
74,
74,
71,
73,
75.
76.
74,
74,
73,
73,
73.
71.
72.
71.
75.
73,
74,
73,
70,
72,
71,
71,
73,
73,
72,
72,
66,
72,
72,
72.
•f 1 M (•
0900
TU
1000

76,
77,
76,
7b,
76,
76,
76,
76.
76.
76.
76,
76.
72.
75.
7 '4,
77.
75,
75,
75,
72,
77,
75.
72.
75,
77,
76,
77,
69,
75,
75,
76,
>UT 'jl
1000
TO
1100

78.
78.
71.
77.
79,
79.
79.
76.
7H,
76.
79,
79.
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75.
75,
76.
77.
77,
76.
73.
77,
7",
74,
77,
79,
79,
79.
73.
76.
76 ,
79,
U A *
t A f*'1 14 I
1100
TU
1200

61,
60,
72,
77.
76,
79,
60,
76,
60 ,
61 ,
80,
61,
76,
76.
75.
74.
60,
75.
75,
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61.
6 0 *
76,
76.
6U,
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HI,
74,
60,
76 »
60,
* * t
t'\> r i
>N 1 1
IT
MOO

61.
61.
66.
75.
60,
79.
61.
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b i ,
60.
61.
f>2.
76,
76 »
75,
73.
61.
69,
76,
76,
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72,
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62.
61.
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61.
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bO.
( *
' h> !•'*?( h
t i i f t. r
1300
IU
1400

61,
61,
67,
74.
"79.
61,
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76,
ei.
62,
65,
65.
79,
79,
72.
75,
63,
75.
75.
78.
82.
61,
69,
76,
63.
80.
79,
76.
62,
60,
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( A 1 U " i
1400
! U
1500

63.
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69,
76,
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61 -
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63,
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7C,
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60,
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7fr ,
63 ,
HO,
77.

1500
TU
1600
*
61.
83,
72.
75,
60,
79,
60,
60.
HO,
82,
62,
B2,
60,
75,
/2,
75.
60,
75,
66,
76.
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77,
70,
77,
77,
79,
79.
79,
77.
64,
76,

1600
I U
1700

60,
79,
75.
75.
60.
79.
'79,
79.
79.
62,
H2.
60,
69,
76,
74.
76,
76,
77.
67,
76.
60.
69.
72.
76.
60,
79,
60,
76.
60 .
62,
77.

1700
TU
1600

77.
79.
75.
74.
73.
76.
76.
79,
77,
61,
62,
61,
70,
7ft,
75,
76,
76,
76,
69.
76 ,
79,
66,
71.
76,
77,
79.
76.
76.
79.
61.
74.

1600
IU
1900

77,
76,
73,
74.
76.
7^«
7o,
77,
ft ,
79.
H2.
71,
69,
75.
74,
76.
75,
75.
70.
76,
76.
69.
71,
75.
77,
77.
77.
74,
79,
HO ,
74,

1900
TU
2 U 0 0

73.
74,
71.
75,
7a,
73,
73.
74,
74,
75.
70.
69,
70.
74.
72.
72.
73,
72,
69,
74.
74,
69.
70.
73.
7".
75.
74.
72.
75.
77.
73.
«* *
•^ f
2 U 0 0
IU
2100

70,
72,
66,
70,
71,
71.
71.
71.
72.
74.
66,
70,
69.
72.
70.
70.
71,
69.
66,
'71,
72.
66 ,
66.
70,
71,
72.
75.
70.
71,
75,
72,
(* &
T T
2100
TU
2200

69,
69.
66,
70.
69,
69,
69,
70.
71.
72.
66.
69,
67.
71.
69,
70,
70,
69,
66,
7o.
70.
67.
67.
69,
70,
71.
71.
69,
69,
75,
72.

-------
   sassoi
       AVG-K
*OT?I!   = VCi
v-,cit?u   = ssm  of   xvci
'i  t?   AVQ
    *ot   = com  f?   AVO
    »cl   s c,Qrn  ??   AVO
•ptt7ii   = sftui  T;--   AVH
*^2TtT   s c?r'l  fi?   Ava
* o9 qoI   s 9 o n1  61   A V 0
*honn   s com  PI   AVC]
•fcftt   = ccni  n   AVO

    CI   s tSf'l  ^T   >VC1
    IT   s £
-------
                                    46
Table 4-7   Summer Month Refueling Losses  by Hour  Summed  over Month
                UF  L'JSStS  dY  HUUK»  J ,  Mgu.«i)b  OF- HYQKUC

                         MO>-K   1  uJSa  a     bbW.
                         HQut   tl  UOt-S  =
                         HUkj*   .S  L'-SS  s
                         HOu*   a  LUi>!?  =
                         H ' 5 S  s
                         H.-JJX   o  Uybi  =
                         H L' _H   f  U U 3 ">  -
                         w U u -i   9  L 0 3 ^  a   ^ '4 9 u '_•> t
                         ht.HM   9  L'Jo*  s   /^o937,
                         H 0 u n  10  U'.' S S  =   t t 7> J l>,
                         ri'.l'-'^  U  tvSj  s   f?/r.^9,
                         H'jL-.-x  12  L'Jb:3  =
                         H U >.' ^  \ 3  U 0 o i  =
                         nUU.<  1'4  LujS  =   2bHb.
                         H 0 u K  1 b  L n a a  s   1 rt 11 9 »
                         m).J*  16  UJbb  =   11 «06.

-------
              Table 4-8  Computer Listing of Input  Data for Winter Month
3AT
ULL
(UAL/DAY)
                 *****  iNHUl DA!A  » * * *  *

UiNiH.Kfs*o  *  *  * * * *  *  *  * * * * *  AMBlL'Mf Tt-'i-U
                                                                   .KA
OEli
                                                                                             *' *
                                                                                                        *  *
                         Tfc.'1^.   0600 0/00  0800 0900  100" 1100  1200  1300 i/40y  1500 1600  1700 l«0o  1VUO  2000 2100
                                 HJ    iu    TO    io    TO   ru    ru    ru    TO    TO   TU    ru   ru    TU    to    iu
                       IULG  KJ   U700 OHOg  0900 1000  1100 1200  1500  1400 ibOO  IfcOQ 1/00  IflOU lS>oy  dOOQ  2100 2200
1
2
3
a
5
6
7
8
9
10
i 1
12
1 5
14
lb
16
1 7
16
.19
20
21
22
25
24
2b
26
27
23
29
30
31
1 f 0 0 (' t 0 6
1 , 0 U 0 + t Q
1,000+06
1 , V 0 (> + 0 o
1 . 0 V 0 + 0 6
1 . C (' 0 + 0 6
1 ,000 + 06
1 , 0 ') 0 + 0 ^
1 . 0 0 0 + 0 0
1,00 v> +06
1 * 0 0 0 + 0 r>
1 . 0 0 0 + 0 1>
1 . u<>0 + Gh
1 , 0 'J 0 + 0 6
t . 0'.";+C6
t .000+06
1 . TOO + 03
1 . 0 0 0 + (' 6
1 , t) 0 C t U t'
1,000+06
1 , 0 0 0 + 'i b
1,000+06
1 , 0 0 0 + 0 1,
1,000+06
1,000+06
1 , 0 0 0 + 0 b
1 , 0 U 0 + 0 6
1,000+06
1 , 0 0 0 + C' (5
1 , '"» 0 0 + u 6
1 , 0 0 0 + 0 b
J 2,0
12,0
12,0
J 2 , y
12,0
1 2 t 0
12.0
12,0
12,0
12.0
12.0
12,0
12,0
li-", 0
12,0
12,0
12,0
12.0
12,0
12,0
12,0
12,0
12,0
12,0
12.0
12.0
32,0
12.0
12.0
12.0
12,0
3.),
^0,
- 3 'J ,
30,
30.
50.
30.
50,
50.
30,
30,
30.
5(t ,
30.
30,
30.
30.
3'J »
50.
30.
50,
50.
30.
30,
3,'.
50.
3".
50.
30,
50,
50.
0.
16,
17,
17.
20,
32.
37,
54.
16.
23.
2b,
9.
20.
2H,
26 ,
0.
16,
20.
52,
37,
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9,
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16.
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22,
53,
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2o,
28,
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22,
55,
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24,
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20,
26,
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16,
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1.
17,
19,
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25,
33.
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34.
17.
24.
2b,
10.
20,
26.
27,
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If.
23,
35,
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24.
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IV.
1.
17,
25,
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34,
39,
3'4.
13.
24f
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11.
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32,
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24,
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2b,
52,
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24,
24,
26,
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42,
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28.
14,
50.
37,
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2,
17,
20.
5b,
42,
3b.
IV.
25.
26,
14,
50,
37,
36,
2,
1 7,
24,
4,
'17,
25.
23.
5b,
34,
44,
3b,
2u,
26,
29.
1H,
34,
59,
59,
4.
17,
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34,
44,
5b.
20,
2b,
2V,
J. b ,
54,
3V,
59.
a .
17.
25,
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17,
27,
27,
56,
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36.
21,
28,
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21.
5b,
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6,
17,
So,
54.
44,
56,
21,
2B,
2d,
21,
5b,
41.
42.
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17.
27,
10.
iy,
26,
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56,
34,
45.
36,
22,
26,
28,
24.
5b,
4b.
44 ,
10.
16,
56.
3 '4,
45,
56.
22.
2H,
26,
24,
3b,
4b,
4 a ,
10,
JH,
26,
11.
16,
27,
27.
au.
53.
42.
59.
23,
29,
26,
25.
461 ,
46.
45,
11.
16.
40.
53.
42.

^3,
29.
26.
2b,
5H.
4ft,
4b.
1 ) .
16,
27.
12.
18,
27,
27,
UO.
53,
42,
41,
25,
26,
2b,
2b,
5V.
47,
44,
12.
1».
40,
55.
42,
41.
23,
2H.
26,
2b,
3V,
47.
44,
12,
1*.
27,
12.
16.
27,
27.
3V.
55.
40,
39,
25,
26,
26,
26.
56.
44.
42.
12,

39,
53,
4U.
39,
25.
2d.
26,
26,
36,
44.
42,
12.

27,
9.
17,
24.
24,
3M,
32.
36,
59,
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27,
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32.

39,
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26.
27,

40,
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v.
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24,
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22.
22,
57,
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«; 5 .
2'3,
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25.
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57.
56.

17.
37.
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39.
25,
26,
27,
24.
55.
57,
56,
6,
17,
22,
6,
If.
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19,
37.
32.
56,
3V,
22,
26.
27.
22.
32,
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34,
6,
17.
37,
32.
36,
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22.
26,
27,
22,
3d,
3b,
54,
' 6,
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IV,
b.
17,
16,
Ib.
57,
32,
3b,
5V.
22.
26.
26,
20,
3d,
35,
50.
b.
17.
57.
52.
3b,
5V,
22,
28,
26,
20,
32,
55.
30,
b.
17.

4.
IV.

lb.
3b,
3d,
34,
59,

2o,

16,
51,
3d.
27.
4,
IV,
56,
3d.
34,
5V.
22,
20,
2b.
16.
51.
3d,
27,
4,
IV,
lb.

-------
       "IWBv.'Jl 01 *£ =  SS01

       AVO-ti  ^1- i
*f^9    s  SPOT  Ii'   AVO
•g/_t?9    =  fisoi  09   AVO
* ^ M 9    s  «5 s1 P. 1  ft ^   AVO
         =  fiqm  «?   AVO
         s  <5 H 1  ft T    A 7 0
•CJOCK;    ~  ft^n"!  6     A V 0

•hfcc?*    =  «;?(.n  /.     AVC
* P ? i1 /    s  «; <; (n  o     AVO
*t/0l^    =fiSO">c.     I v 0
'SA09    r  c<;n"l  t?     AVG
•f/99    =  fifii'1  f     AVC
* ft I t; 9    s  C f: 01  ?     A V 0
• /. L \ 9    =  s s cn  i     A v o
    /q sassoi 6uii9nj3^  M^uow Jaiuifl   6-t?

-------
                                   49
Table 4-10   Winter Month  Refueling Losses by Hour Summed Over Month
      3iJ-if->A"5'i =   i^dfl ,
                        H o v' K   s  u o b .5 s   i a 9 a c ,
                                9  L 0 S » s   1 o 5 U 0 ,

                        ri 0 J ^  13  I.' •' a S -   \ b >4 S 5 ,
                        HOu-<  le:  LOSd =   17b^'4,
                        hOuK  13  U'.'bS =   i/'yl.'i,
                        H 'J v.H  1 H  I- '-• bos   1

                        MOlH  lt>  L.U58 *

-------
                                    50
Section 4.3   Simplified Forms of the Regional  Model
     As indicated in the last section the Regional  model  involves  a  large
enough number of calculations to make the use  of  a  computer  very desirable.
In deriving the model  it was necessary to sacrifice some  accuracy  through
the use of averages.  If this process is  carried  further  the model can  be
simplified to the point that the use of electronic  calculators  becomes
practical.  The first simplification that can  be  made  is  to  use regional
hourly average ambient temperature averaged over  the days of the period
and regional average values of L,(d.) and Pu(d.)  over  the period.
                                U  J       V   J
Thus:                  D
      TA(h.)  =
      Tu      •  ~n   L-    W                                       I4'12'
                 1   2_   VV                                       (4-13)
In this case the model  becomes
                             H
      4      =  45^6     EJI    R(hi>  tLj  + UD  (V  V W3

A final simplification  can be made by employing  the  average  of  the  hourly
average ambient temperatures
      TA
to give:
      4'

-------
                                    51
      The additional primes on the total loss in Equations (4-14) and
(4-16) are to emphasize that these are, in effect, estimates of previous
estimates.  Each additional substitution of an average further reduces
the accuracy of the estimate. _
      It  should be noted that T~A may be obtained by applying (4-11) and
then(4-15) or (4-15) followed by (4-11).  Both give the same result.  Thus
T. may be interpreted as the average over the period of the daily average
 M
temperature (for the 16 hour period).
      If the period covered by the calculation is no more than a month,
the use of (4-14) will  lead to only slightly increased error.  The Reid
vapor pressures of the gasolines supplied to an area will not vary by much
in the period of a month.  Underground fuel  temperatures would be expected
to vary only a few degrees.  The ambient temperature will show the greatest
variation from day to day.   But the variation will  be predominantly random
within a month period,  and Equation (4-14) accounts for the more systematic
diurnal variation in ambient temperature.  Detailed sample calculations,
employing Equations (4-14)  and (4-16) for the winter and summer condition
examples treated in the last section are given in the following paragraphs:
      In the summer case it was assumed for the 31  day period that G =
1,000,000 gals/d, PV = 7.5 psi, and T.. = 76°F.  The hourly average summer
month temperatures calculated from Table 4-3 are given in Table 4-11 along
with their standard deviations.
      The agreement between the computer runs and the Equation (4-16)
calculations for the fully averaged case is not as  good, but even here
results only differ by 1% which is less than the error in the displaced
loss equations.
      The loss calculated by Equation (4-16) would  be expected to tend
somewhat below the result calculated by the more precise methods since the
exponential equation would give greater weight to temperatures higher than
the mean temperature.
      It can be concluded that Equations (4-14) and (4-16) are useful cal-
culations in estimating regional  losses

-------
                                    52
 Table 4-11   Average Ambient Temperatures for Thirty One Day Periods
              Summer and Winter
                  Summer Period
                      Winter Period
Hour
Beginning:
0600
0700
0800
0900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
Average
Temperature
°F
66.5
70.4
72.6
75.3
77.0
78.2
78.2
78.7
78.2
77.8
77.3
76.6
75.4
72.7
70.5
69.5
Standard
Deviation
°F
1.3
1.9
1.6
2.0
2.2
2.5
3.9
4.1
4.2
4.0
3.9
3.5
3.1
2.0
2.0
1.6
Average
Temperature
°F
21.2
21.0
21.4
23.4
25.4
27.0
28.7
29.9
30.6
30.7
30.0
26.6
27.4
26.3
25.4
24.6
Standard
Deviation
°F
10.3
10.0
9.8
10.4
11.1
11.3
10.7
10.6
10.9
10.7
9.9
9.9
9.6
9.8
9.8
9.9
Grand Average    74.7
3.8
                                  0)
26.2
3.3'
    (1) Standard deviation of the hourly averages from the Grand Average

-------
                                     53
Applying Equation 4-16 first to show the relative value of the terms in

the exponential expression for UJ1 we have for the L^L1 exponent polynomial





     C,      =  -0.10141                          =  -0.10141


     C2?v    =   5.274 x 10"2 x 7.5               =   0.39555



     C,T.    =  -1.2163 x 10"3 x 74.7             =  -0.09086
      «5 rt


     C.f     =   6.0649 x 10"4 x 67               =   0.04609



     C5FVTA  =   2.6115 x 10"4 x 7.5 x 74.7       =   0.14631



     cJij..  =   9.3072 x 10"4 x 7.5 x 67         =   0.53051
      o V U



     C7Vu  =   8-6642 x 10"5 x 74<7 x 67        =   O-4^188


     Cf     =   2.4310 x 10"5 x  (74. 7)2          =   0.13565
                                                      1.55372
     LjJ1      =  exp. 1.55372                     =  4.73 gms/gal



     L' + L"1 =  0.30 + 4.73                      =  5.03 gms/gal
      ^    U



                             31 x 5.03   =  344,000 Ibs in 31 days
                    roc
                   4bo.b

-------
                                   54
     Carrying through the calculation with. Equation(4-14)yields:
Hour
Index
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Hour
Beginning
0600
0700
0800
0900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
Loss, gms/gal
Displaced
4.330
4.513
4.622
4.760
4.850
4.915
4.915
4.943
4.915
4.894
4.867
4.829
4.766
4.627
4.518
4.470
Total
4.630
4.818
4.922
5.060
5.150
5.215
5.215
5.243
5.215
5.194
5.167
5.129
5.066
4.927
4.818
4.770
R(h.)
0.0175
0.0435
0.0445
0.0585
0.0605
0.0700
0.0715
0.0695
0.0755
0.0770
0.0765
0.0835
0.0845
0.0775
0.0550
0.0350
Loss x R
(gms/gal )
0.0810
0.2094
0.2190
0.2960
0.3116
0.3651
0.3729
0.3644
0.3938
0.3999
0.3952
0.4283
0.4280
0.3818
0.2650
0.1670
31 Days*
Hourly Loss
(Ibs)
5536
14311
14967
20229
21295
24952
25485
24903
26913
27330
27009
29271
29250
26093
18111
11413
                                                      5.0784
      * [Loss x
Y o-,   1,000,000
A O I /\   ,«>. w >•
                                              347069
     The same calculation can be performed for the winter case starting with
the averaged ambient temperatures shown in Table 4-10.  The results of both
the summer and winter calculation are summarized in Table 4-12 which compares
them with the computer results shown in the last section.  It is seen that
Equation (4-14) agrees within one percent of the results calculated by computer
employing the full  model.  This result would have been suspected for the
summer case since as indicated by the low standard deviations in Table 4-2
the temperature profiles do not disagree much from day to day.  However,
they disagree substantially more in the winter case and the agreement is
still  excellent.

-------
                                   55
Table 4-12   Comparison of Results  From Computer Run and Short Calculations

Hour
Index
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16






Summer
Total Loss,
Computer
5537
14321
14969
20229
21289
24961
25504
24945
26937
27375
27049
29281
29261
26115
18119
11406
347297


Computer
Eq. 4-14
Eq. 4-16
Month
lbs/31 days
Eq. 4-14
5536
14311
14967
20229
21295
24952
25485
24903
26913
27330
27009
29271
29250
26093
18111
11413
347069
Average Refueling
Summer
5.08
5.08
5.03
Winter
Total Loss,
Computer
3586
8927
9147
12152
12704
14829
15271
14942
16300
16630
16453
17824
17913
16333
11541
7313
211864
Loss - Grams/Gal
Winter
3.10
3.09
3.07
Month
lbs/31 days
Eq. 4-14
3588
8895
9118
12107
12651
14767
15213
14884
16230
16562
16391
17781
17856
16282
11501
7289
211109






-------
                                    56
Section 4.4  Error and Sensitivity Analysis of the Regional Model
     This section examines the basis of the regional model so that its
utility and limitations may be appreciated by the potential user.  The
analysis will examine each of the underlying assumptions and how they
affect the accuracy and applicability of the model.
     Assumption #1   The loss LR for a given refueling operation is not
a function of fuel dispensed:
     This assumption was used to set the basis for maintaining the separa-
tion of the fuel dispensed variable, G, from the loss variable, LD, in
                                                                 K
Equation(4-2)and those that follow.  Thus, the total loss, LRG, is then
directly proportional to the volume of fuel dispensed per operation.  The
second year program showed good proportionately between measured displaced
HC losses and gallons dispensed when the dispensed fuel and fuel tank tem-
peratures were the same.  However, further analysis leads to the conclusion
that the assumption is not strictly correct (Reference 8) for those condi-
tions in which there is a temperature difference between the dispensed
fuel and the vehicle tank fuel.  It is correct, however, even with temper-
ature differences, both for very small amounts of dispensed fuel and complete
filling of the tank.  Calculations show that the dependence of LD on volume
                                                                K
of fuel dispensed may be as much as 10 percent in an individual refueling
where the tank is only partially filled.
     The displaced loss equation derived in Section 2   was based on partial
fillings.   Ten gallons of fuel were added to a 22 gallon tank containing 4
gallons of fuel.  Thus the vapor volume above the original fuel level  was
only 56% depleted.  The effect of dispensed fuel  volume was probably near
maximum in this case, so that the resulting displaced loss expression tends
to be in error for cases of complete refuel ings or the addition of only
small amounts of fuel when a temperature difference exists.  Since the third
year field survey showed the tank was filled in about two thirds of the re-
fueling operations observed, there may be some bias in the displaced loss
portion of the model.  Its magnitude is difficult to judge without more ex-
perimental data.  It will  be reduced by the averaging process of the model
since the effect can both increase or decrease losses depending upon whether
the incoming fuel  is hotter or colder than the vehicle tank fuel.   The aver-
age error is estimated to be + 3%.

-------
                                    57
      Part of the Loss, L , is made up of spill  loss which is very unlikely
                         R
to be related to amount of fuel dispensed.  So long as average gallons dis-
pensed per refueling does not vary substantially from region to region or
period to period within a region, that is so long as gallons dispensed is
a good general index of number of refuel ings, no significant error results
from this approach.  As pointed out in Section 3.3 the mean number  of
gallons dispensed was 10.4 gallons in the third  year program and 11.4 gal-
lons in the second year program.  This would lead to about 10% change in
spill losses on a per gallon dispensed basis and about a 1« error in the
total loss.  Note that this error is compounded  by changes in spill  loss
per refueling that may occur from one region to  the next.  Spill losses
are treated more fully in the discussion  of Assumption #10.

     Assumption #2  The gallons of fuel  dispensed for each refueling oper-
ation within each hour varies randomly about some mean value for that day
and hour:
     This assumption coupled with the first is needed to break away  from
the individual refueling operations of Equation  (4-1) and get to the region
wide hourly averages used in Equation (4-2) while maintaining the separa-
bility of G and LR.  The assumption seems to be  a reasonable one and,
therefore, does not appear to contribute  to error.

     Assumption #3  The number obtained  by averaging hourly gallons  dis-
pensed per refueling operation over all  hours of all  days within the
period may be substituted for the individual hourly averages:
     This assumption allows a single value of gallons dispensed per  refuel-
ing to be used and allows G expressed as  total gallons dispensed per day
to be factored out and placed to the left of the summations in the model.
The data obtained in the field surveys were not  analyzed to determine the
presence of any effect of hour of day, or day of week, or day during the
period.   It seems unlikely, however, that there  exists any significant and
persistent effect of hour and day that would impact on the model.  The
question, hov/ever, merits further investigation.  If an effect were  found,
it would be no great complication to bring G back within the summations.
As was pointed out in Section 4.2 the computer model  provides for a  varia-
tion in G by day.

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                                    58
     Assumption #4  The number of refueling operations per hour is a
function of the hour of the day but not of the day:
     This assumption allows the substitution in Equation (4-3) of the fre-
quency factos R(h.) for the R(h.,d.) values of Equation(4-2).  This assump-
                  1             I  J
tion is supported by the analysis of the field survey data discussed in
Section 3.3.  As was pointed out the values assigned to the R(h.) may
require alteration from time to time to fit particular situations.  It
may be necessary in some situations to vary the R(h.) according to day.
The assumption, however, currently included in the model  appears reason-
ably justified by the third year survey data.

     Assumption #5  The hourly average hydrocarbon refueling loss per
refueling operation can be expressed as the sum of an hourly average
hydrocarbon spill loss and an hourly average displaced hydrocarbon loss.
     This assumption is adequately supported by the work conducted in the
first and second year programs which shows that the two kinds of losses
can be treated independently.

     Assumption #6  The hourly average spill loss per gallon of dispensed
fuel varies randomly about a determinate mean value having no relationship
to hour of day or day.
     This assumption combined with Assumption #5 is necessary first to ex-
press the overall loss as the sum of a spill loss and a displaced loss and
second to substitute a single value independent of hour and day for the
spill loss.  The second year program did not analyze for an effect of hour
of day or day.  However, the assumption appears to be reasonable and no
significant error is expected to result from its use.

     Assumption #7  The regional  hourly average displaced hydrocarbon loss,
Up can be estimated by a mathematical  expression containing the hourly
average RVP, the hourly average underground tank temperature,  and the
hourly average ambient temperature. [This assumption contains  within it
the assumption that region wide hourly average values of Reid  vapor pres-
sure and underground fuel  temperature  can be used in place of  values for
each service station within the region.)

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                                     59
     This assumption allows a substantial simplification of the expression
for L'.  The analysis in Sections  2  and  3  show that the displaced HC
loss from an individual refueling can Be expressed as a function of RVP,
T.. and T..  It must next be determined what errors may result from the use
of regional average values for these variables for each hour.  Equation(4-17)
applies to each individual refueling operation:
                      N(h.,dj)
"k
                               L' CTu(n|c.h1.dj),TA(nk.h1.dj).

                             Pv(nk,h.,d..)]                               (4-17)
The assumption seeks to substitute in place of Equation 4-17:

     "^W  =  LD [Wdj)> VN-'V' Vhi'dj)]                  (4

Since L^ is an exponential function, Equation (4-18)  cannot hold exactly.
To see how well the two equations do agree in practice, consider 27 service
stations within the region in which P.,, Ty, and T.  at some given hour take
on all combinations of two extreme and a mean values  for each  variable.
These values are given by:

                                  !v      Iu     ]A
        Upper Extreme             10      80     85
        Average                    9      75     80
        Lower Extreme              8      70     75

The Reid vapor pressures of gasolines supplied to a given region might
easily vary this much.   The underground tank temperature is presumed to
range over 10°F because of local  differences within the region.   It is
assumed the range in ambient conditions over the region within a given
hour is also 10°F.   The displaced HC loss per refill  was calculated for
each of the 27 different combinations of values using Equation (4-1$.  The
values are shown in Table 4-13.   It is seen the average of the 27 calcu-
lated displaced HC  losses is 6.19 gms.  The displaced loss calculated

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                                   60
Table 4-13   Comparison of Average of Displaced Loss with Displaced Loss

             Calculated from Averages of Independent Variables  PU>T>TA
    pv           Tu
    10            80             85                  8.19
    10            80             80                  7.70
    10            80             75                  7.25

    10            75             85                  7.51
    10            75             80                  7.07
    10            75             75                  6.67

    10            70             85                  6.89
    10            70             80                  6.50
    10            70             75                  6.15

     9            80             85                  7.05
     9            80             80                  6.64
     9            80             75                 -6.26

     9            75             85                  6.50
     9*           75*            80*                 6.13*
     9            75             75                  5.79

     9            70             85                  5.99
     9            70             80                  5.66
     9            70             75                  5.36

     8            80             85                  6.07
     8            80             80                  5.72
     8            80             75                  5.40

     8            75             85                  5.62
     8            75             80                  5.31
     8            75             75                  5.02

     8            70             85                  5.20
     8            70             80                  4.93
     8            70             75                  4.67

                                        Average      6.19
                           - IX
  * average values of variables

-------
                                    61
using the regional average values of the variables is underlined in the
table and is 6.13 gms/gal.  This value is within 1% of the more correct
average.  Because of the randomness of the variables there is a strong
central tendency of the calculated losses, and this tends to account for
the closeness of the results.  Thus Equation (4-18) appears to be a good
approximation of (4-17) and the average hourly values can be used in
Equation (4-8 ) with little loss of accuracy.
     It should be noted that because of the exponential nature of the
displaced loss equation, the result obtained by using the hourly averages
will always be slightly low.

     Assumption #8  The hourly average underground fuel temperature is
constant within any day:
     The underground fuel temperatures are generally stable over a day
at any one location and in fact may vary only a few degrees in the course
of a month.  Use of this assumption allows the substitution of T..(d.) in
place of T..(h.,d.).  Furthermore, it is unlikely that significant error
would be encountered if a constant value of T.. were used for periods of
up to a month.
     Assumption #9  The hourly average Reid vapor pressure is constant
within the day:
     The Reid vapor pressures of the gasolines supplied to a given loca-
tion vary slowly over the course of the year between the highest values in
the winter and the lowest values in summer and essentially not at all  within
a given day.  As with the underground fuel temperature, the average Reid
vapor pressure for a given region can reasonably be considered constant for
periods up to a month.

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                                    62
     Assumption #10  The average spill loss per gallon of fuel dispensed
is 0.30 gms:
     This value was determined from the second year field survey.  As
indicated in the discussion of Assumption #1, spill loss is not funda-
mentally proportional to gallons of fuel dispensed.  Thus as gallons
dispensed per refueling varies from region to region the value of the
spill loss per gallons dispensed should be adjusted accordingly.  In addi-
tion to this source of error, which can be as much as 1%, the spill loss
per refueling can vary from region to region.  Table 4-14 summarizes
results of the second year report (Reference 6) for five cities.  The
spill loss for individual cities is seen to vary from a low of 0.16
gms/gal to a high of 0.49 gms/gal.  If these data are an indication of
the potential spread, possible errors to the model could be as much as
± 7% for winter losses +_ 4% for summer losses.

     Assumption #11  Equations (2-1), (3-1) and (4-7) provide a reasonable
basis for defining Li.
     These equations are the basis for the average displaced hydrocarbon
loss Equation (4-8) used in the model.  The equations will  be considered
separately and then in terms of their combined effect on the accuracy and
applicability of Equation (4-8).
     Equation (2-1), developed from the third year laboratory study, was
shown in the earlier discussion to strictly apply to partial tank fillings
in which somewhat more than half the empty space in the tank was filled.  A
resulting +_ 3% error in the model was estimated when applied to a distribu-
tion of refueling operations.  This bias could not be totally avoided since
it was desirable to achieve separation of the variables G and Li.
                                                               K
     Another effect that was not taken into account in the experimental
design was that of dispensing a fuel of a given volatility into a vehicle
tank containing a fuel of a different volatility.   Conditions of different
dispensed fuel temperature and vehicle tank fuel temperature, which were
studied in the program, generate vapor pressure differences between the
incoming fuel and the fuel  in the tank which have the same kind of impact
as differences in Reid vapor pressure.  The RVP differences both enhance

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                                       63
          Table 4-14   Summary of Total  Spill  Losses  from Second  Year Survey*
   City
                               Average Spill
 No.    Average   No.  of Ref.    Spill   Loss
 of     Refill,   Operations    Loss,   Freq.,
Cases  (Gallons)  With Spills   (Grams)   %	  (Gms/Refill)
                             Average Spill  Loss
                                        (Gms/gal)
Los Angeles
Houston
Chiago
New York
Atlanta
1005
1287
1234
1515
1378
11.8
12.8
11.7
10.0
11.5
392
480
321
546
372
8.6
17.0
9.8
9.5
6.7
39.0
37.3
26.0
36.0
27.0
3.3
6.3
2.6
3.4
1.8
0.28
0.49
0.22
0.34
0.16
Composite    6419
          11.5
2111
10.6    32.9
3.5
0.30
  *Reference 6

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                                    64
and detract from the effects of temperature on vapor pressure.   In the
regional model the effect will, to a large extent, be diminished through
the averaging process of the model.  Furthermore, the effect will  be
diminished by the tendency of motorists to remain with a favored brand.
From these considerations the probable error is estimated as +_3%.
     The weathering of fuel in vehicle tanks will also lead to  differences
in volatility between incoming fuel and fuel in the tank.  It would tend to
generate a systematic negative error because the effect is in one direction.
However, there is not sufficient information available at this  time to de-
termine the magnitude of the possible error.  As a practical matter only
one value of RVP appears in Equation (2-1).  A two valued equation would be
difficult to incorporate into a regional  model.  Thus, even if  the average
degree of weathering were known it is not certain whether the values of the
RVP entered into the model should be for the weathered fuels in vehicle
tanks or that of the dispensed fuels or some weighted average.
     A third simplification was involved in the experimental program which
led to Equation (2-1).  A single fuel tank configuration was used.  The
second year program did show differences between two commonly used fuel
tank types that varied from 0 to 30%.  The greatest differences occurred at
high temperatures.  Thus, a systematic error can be generated if the fuel
tank used in the laboratory study is different from the average of the
vehicle population of the region.  Since the tank studied was a common type
it is estimated that the resulting average error in the regional model is
+_ 10%.  It could be higher at the upper temperature bound of the equation.
     Given in addition to the above considerations, the high coefficient
                   2
of determination (R  = 94.5%) and the estimated 5.6% regression error per-
centage for Equation (2-1), it can be concluded that it provides a practical
basis for the regional model.  However, these same considerations  also indi-
cate the equation is much less applicable to individual refueling  operations.
     Considering next Equation (3-1), it appears to provide an  acceptable
method of eliminating the dispensed fuel  temperature from the model  and sub-
stituting the more readily measured underground fuel  and ambient temperatures.
                                                         p
The expression has a high coefficient of determination (R  = 98.9%). and a
small standard error of estimate of 2.47°F.  The analysis in Secion  3 shows

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                                    65
it spans quite well the two geographic areas and three months  in  which  data
were collected.  Because the data were collected for a limited number of
service stations and areas its generality cannot be fully judged.  However,
its use is not likely to lead to significant error since  the analysis shows
the main factor in dispensed fuel temperature to be the underground fuel
temperature.  It alone can account for almost 99% of the  observed variance
in dispensed fuel  temperature.  While there may well  be other  factors as
discussed earlier for given service stations configurations  and locations,
the form of Equation (3-1) and its simplicity make it very suitable for
the regional model .
     Equation(4.7) which relates initial  fuel  tank temperature  to  ambient
temperature is of a particularly simple form.  It reflects the lack of
information concerning the factors determining the effect of ambient con-
ditions and vehicle operation on fuel tank temperatures.   The  termz\T
in the equation is the average increment above ambient for all  cars in  a
region over the specified period.  The discussion given under  Assumption #7
shows that the model handles average values quite well.   It  would be expect-
ed, however, that AT is a function of the vehicle population,  the driving
patterns, time of refueling, and ambient temperature.   The impact of all
these factors could vary with the region and time of year.   There is insuf-
ficient information available, however,  to estimate these effects.   The
Coordinating Research Council's CAPE 5-68 project (Reference 7) obtained
data on fuel system temperatures for a number of cars  in  the summer and fall
of 1969.  These data were subsequently analyzed by Scott  and applied to
driving patterns in four cities.  (Reference 9).   Using the  Scott treatment
the temperature increment for each of the cities  was  estimated  to be as
follows:
                    City
                Los Angeles                        6.4
                Chicago                           6.1
                Houston                           6.3
                New York                          6.8
                 Average                          6.4

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                                    66
These calculations show little variation in^^.1 among the four cities.
A value of .A T of 6 to 7 is the best current estimate for use in the
regional model.
     It is of interest to determine the sensitivity of the model  to the
choice of .Z\T.  The table below shows the average refueling loss for the
winter and summer cases with Z^. T varying 5°F above and below the optimum
value of 7°F.
                                    Average Refueling Loss
             AT                          (gms/gal)
             (°F)                   Summer          Winter
              12                     5.25            3.13
               7                     5.08            3.10
               2                     4.92            3.07

It is seen that for the summer period the 5° change results in about a
+_ 3% change while for the winter period the change is about +_ 1%.  The
model, therefore, appears to be relatively insensitive to the precise
choice of /\ T.
     The above  considerations lead to the conclusion that the form of
Equation (4.7)  with Z\ T = 6° to 7° is a good first approximation and
will not lead to substantial error.
     The discussion of the base equations which give rise to the  average
estimated displaced hydrocarbon loss expression Equation (4-8),  lead to
the general conclusion that the model rests on a sound basis and  should
give reasonably accurate answers.   It would not be appropriate,  however,
to apply any of the three base equations nor the composite equation to
a single refueling operation.
     The regression error or error of estimate in Equation (4-8)  is a
combination of  the errors in the base equations.   The errors combine
approximately as follows:
Equation (2-1)  has the form:

      In L^   =  a + bPvTD + cTT + dPy + eTDTT

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                                    67
The following approximation can then be made of the overall  standard  error
of estimate when Equations (3-1) and (4-7)  are substituted  into (2-1) to
yield Equation (4-8):

     E (InL^) = E2(lnL^) + (bP E(TD))2 + (cE (Ty))2 + (eE(TD)E(TT))2       (4-19)
where
      E(lnLrj) =  The standard error of estimate for  Equation  (4-8)
      E(lnL') =  The standard error of estimate for Equation (2-1)
      E(TD)   =  The standard error of estimate for Equation (3-1)
      E(TT)   =  The standard error of estimate for Equation (4-7)
The regression analyses give EOnl^) = 0.056, and E(TQ)  = 2.5.   Addition-
ally it is assumed that E(Ty) = 7 which is  almost certainly too high.  It
is further assumed that the error in the term TpTy is reasonably approxi-
mated by product of the respective standard errors of estimate.  If  these
values are substituted into Equation (4-19) along with the  appropriate
constants from Equation (2-1) we have:
                                             Squares
     E(lnLJ)     =  0.056                3.136 x 10"3
     bPvE(TD)    =  0.0287               0.827 x 10"3
     cE(Ty)      =  0.0088               0.079 x 10"3
     eE(TD)E(TT) =  0.00188              0.004 x 10"3
                                         4.046 x 10"3
     E(L')       =   N/4.046 x 10"3  =  0.064
Thus the percentage error in going from the displaced loss equation given
by Equation (2-1) to that given by Equation (4-8)  only increases  from
5.6% to 6.4%.  It can also be seen from the above  tabulation that a large
error of estimate assumed for TT does not have a large impact on  the
overall error.  This further supports the use of Equation (4-7).

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                                   68
     There is also room for a large error in the term T_.TT so that the
estimate E(TD)E(TT) is reasonably safe.
     In addition to the model error there is the possible error resulting
from selecting incorrect values of the variables to be input to the model.
The sensitivity of the model to changes in the variables has already been
partially explored in the previous discussion.  To further explore the
sensitivity, calculations were performed to show the effects of misesti-
mates of all the variables acting simultaneously and individually.  For
this purpose it was sufficient to use Equation (4-16),the most abreviated
form of the model.
     The results are shown in Table  4-15  and  4-16  for both warm and
cold 31 day periods. In Table 4-15, the middle values in each of the two
cases were taken as the estimated values of the variables.  It is assumed
the set of values just above the middle values are correct in one situation
and those below are correct in the other situation.
     It is seen in the warm temperature case a +_ 31% error was incurred
in the estimate of grams loss per gallon and a -37 to + 48% error in the
estimate of pounds lost over the 31 day period.  In the cold temperature
case the error in grams lost per gallon was +_ 27%.  These are substantial
errors and indicate the need for care in estimating the input values.   Of
course, it is unlikely that all the variables would err in the same direc-
tion by the amounts shown.
     The effects of misestimates of individual variables in Table 4-16
show errors ranging from 0.6 to 11.5%.  The model  is most sensitive to
misestimates of Reid vapor pressure and underground fuel temperature but
the somewhat lower sensitivity to the ambient temperature is accounted
for by the smaller change allowed in that variable.  The model  is least
sensitive to the,AT value.  The gallons dispensed per day was not in-
cluded in the table since the resulting model error in this case is equal
to the percentage error in the estimate of gallons dispensed.
     The error and sensitivity analysis discussed  in this section is sum-
marized in Table 4-17.  The combination of all the estimated errors
intrinsic to the model was estimated to be 14%. This estimate was obtain-
ed by assuming the variances from each source of error are additive.   If

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                           69
Table 4-15   Sensitivity Analysis of Refueling Loss Model-
             Combined Effect of Variables
                                        Total  Refueling Loss
pv
9
8
7
13
12
11
Tu
73
65
57
38
30
22
TA
70
65
60
35
30
25
AT
12
7
2
12
7
2
G/106
1.10
1.00
0.90
1.10
1.00
0.90
Gms/gal
6.09
4.23
3.21
3.98
3.14
2.56
Pounds (31 days)
458,000
289,000
197,000
299,000
214,000
157,000

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                          70
Table 4-16   Sensitivity Analysis of Refueling  Loss  Model
             Effect of Individual Variables
Variable
Altered
_
Pv
!u
TA
AT
. P
V
8
9
8
8
8
T
U
65
65
73
65
65
T
A
65
65
65
70
65
7
7
7
7
12
Refueling Loss
(Gms/gal)
4.23
4.78
4.69
4.43
4.35
^Difference
-
11.5
9.8
4.5
2.8
12
13
12
12
30
30
38
30
30
30
30
35
7
7
7
7
3.14
3.40
3.48
3.22
-
7.6
9.8
2.5

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                                       71
          Table 4-17   Summary of Error and  Sensitivity  Analysis of
                       the Regional  Model
 Errors Intrinsic to Model
   o  Dependence of displaced HC loss  on  volume  dispensed
   o  Lack of representativeness of fuel  tank  used  to  obtain
      displaced HC loss data for a  given  region
   o  Differences in volatility of  dispensed fuel and  fuel  in  tank
         - Base difference  in Rvp
         - From weathering  of fuel  in  tank
   o  Incorrect dependence  of spill  loss  on gallons dispensed
      (due to incorrect estimate of average gallons dispensed
      per refueling)
   o  Incorrect estimate of average spill  loss per  refueling for
      a given region
   o  Substitution of average values of independent variables  in
      displaced HC loss equation instead  of taking  average  of
      losses
   o  Unexplained variance  in L^ (Eqn.  4-8)
   o  Overall,  combined error
   + 3%

   + 10%

   + 3%
   no info

   + 1%

   +_ 5%

    -1%
   6.4%
    14%
Errors from Incorrect Choice  of Input  Variable
   o  Reid vapor pressure,  1  Ib error
   o  Underground fuel  tank temperature,  8°F  error
   o  Ambient temperature,  5°F  error
   o  ,ZVT,  5°F error (not  strictly an input  variable)
   o  Gallons dispensed,  10%  error
   All variables in  error in  same direction
   + 10%
   + 10%
   ±4%
   + 2%
    10%
 +21-32%
  (Gms/gal)
 +26-47%
(Total  pounds)

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                                    72
it is assumed that the errors from the incorrect choice of input vari-
ables occur randomly, about 18% error is estimated for this source.   The
overall estimate of the standard error for the use of the model  is  about
23%.  It should be emphasized, however, that while the user cannot  do
much about the intrinsic errors in the model, he can use care  in deter-
mining the input variables and thus take maximum advantage of  the model's
inherent accuracy.
     As a final consideration it should be noted that the ranges of the
input variables are restricted by the constraints placed on the  original
input variables to the displaced HC loss expression Equation (2-1).

                                     Range of Functions
               Rvp                          T Y
                 K                           and
              (psi)                0.81 TJJ + 0.23 TA -1.2
                7                          50-90
               10                          40-80
               13                          30 -  70

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                                   73
                                  REFERENCES
1.  "Tentative Methods of Measuring Evaporation  Loss  From Petroleum Tanks
    and Transportation Equipment";  API  Bulletin  2512;  July 1957.

2.  "Evaporation Loss in the Petroleum  Industry  -  Causes  and  Control";
    API Bulletin 2513; February 1959.

3.  "Evaporation Loss From Tank Cars, Tank Trucks,  and Marine Vessels";
    API Bulletin 2514; November 1959.

4.  "Comparative Methods for Evaluation of Conservation Mechanisms  for
    Evaporation Loss"; API Bulletin 2522.

5.  "Investigation of Passenger Car Refueling  Losses"; Scott  Research
    Laboratories, Inc., March 6, 1970.

6.  "Investigation of Passenger Car Refueling  Losses,  Second  Year Program";
    Malcolm Smith, Scott Research Laboratories,  Inc.,  September  1,  1972.

7.  "Time-Temperature Histories of Specified  Fuel  Systems"; CAPE 5-68,
    APRAC, Coordinating Research Council,  New  York, October 15,  1969

8.  Private Communication; R. A. Nichols,  Parker-Hannifin Corp.

9.  "Mathematical Expressions Relating  Evaporative  Emissions  From Motor
    Vehicles Without Evaporative Loss Control  Devices  to  Gasoline
    Volatility"; W.  F. Biller, M.  Manoff,  et.al, SAE  Paper 720700 SAE
    National West Coast Meeting, August 1972.

-------
     APPENDIX A




FUEL INSPECTION DATA

-------
                                    A-2
                                Tatle. A-l
                           Fuel Inspection Data
  (Measurements Made by the Ethyl Corporation, Long Beach, California)
Sampl e
6-31
7
7.2
35.0
2.0
63.0
Sampl e
16-61
10
9.7
35.0
2.0
63.0
Sampl e
32-111
13
12.2
29.0
2.0
69.0
Nominal RVP, psi
Measured RVP, psi

FIA, % Aromatics
     % Olefins
     % Saturates

Distillation Data, °F
     Initial Boiling Point           98                97             84
      5% Evaporated                 122               114             93
     10% Evaporated                 137               125            103
     15% Evaporated                 150               134            111
     20% Evaporated                 165               143            118
     30% Evaporated                 187               162            135
     40% Evaporated                 208               182            154
     50% Evaporated                 228               204            173
     60% Evaporated                 252               228            195
     70% Evaporated                 284               255            222
     80% Evaporated                 320               284            256
     90% Evaporated                 360               310            298
     95% Evaporated                 391               337            340
     Final  Boiling Point            428               398            382
Recovery,  percent                    98.8              98.0           97.0
Residue, percent                      1.0               0.6            0.6
Loss, percent                         0.2               1.4            2.4

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  APPENDIX B




LABORATORY DATA

-------
                       TABLE  H-l.   LABORATORY DATA


        ******** TEMPERATURE  -  DEGREES  FAHRENHEIT *********           DISPLACED
 CASE      AVERAGE       INITIAL      MINI-SHED    AVERAGE      RVP        LOSS
NUMBER    DISP FUEL    TANK  FUFL      AMBIENT      VAPOR      (PSI)     (GMS/GAL)


                                                    91         6.8        4. 3 7
                                                    94         6.1        4.48
                                                    90         6.1        4.90
                                                    92         6.8        4.52
                                                    88         6.8        4.34
                                                    93         6.6        4.34
                                                    90         6.6        4.12
                                                    90         6.6        3.79
                                                    89         6.6        3.39
                                                    90         6.2        3.91
                                                    89         6.2        3.21
                                                    80         7,1        3.06
                                                    82         7.1        3.56
                                                    80         7.0        3.42
                                                    79         6.9        3.52
                                                    82         6.7        4.00
                                                    82         6.7        4.21
                                                    84         6.4        4.39
                                                    79         6.4        4.44
                                                    70         6.8        3.93
                                                    72         6.8        4.18
                                                    74         6.8        4.04
                                                    72         6.8        3.93
                                                    71         6.8        3.60
                                                    71         6.8        3.58
                                                    71         6.1        3.20
                                                    71         6.7        3.18
                                                    68         7.0        3.04
                                                    65         7.0        2.82
                                                    60         7.2        2.65
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
85
81
87
84
80
76
76
68
64
73
60
60
67
66
70
74
78
75
82
82
85
80
80
72
73
68
68
64
58
58
83
89
. ._ . 88
84
80
85
89
83
82
87
84
76
78
76
71
74
77
BO
76
70
70
72
70
63
70
68
68
68
63
60
89
91
88
88
85
90
89
86
86
89
8d
76
80
76
76
80
79
79
76
70
70
70
70
70
71
70
72
70
' 70
56

-------
                 TABLE B-L  (CONTINUED).   LABORATORY DATA
        ******** TEMPERATURE - DEGREES  FAHRENHEIT *********
 CASE      AVERAGE      INITIAL      MINI-SHED    AVERAGE     RVP
NUMBER    DISP FUEL    TANK FUFL      AMBIENT       VAPOR     (PSI)
                               DISPLACED
                                 LOSS
                               (GMS/GAL)
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
56
56
60
64
66
70
76
81
79
85
69
12
73
70
60
63
59
57
71
72
68
63
56
55
53
4&
45
46
42
46
                          60
                          60
                          60
                          60
                          60
                          60
                          60
                          61
                          49
                          50
                          50
                          50
                          50
                          52
                          55
                          54
                          52
                          53
                          45
                          45
                          45
                          44
                          41
                          42
                          42
                          41
                          41
                          47
                          46
                          46
58
53
58
59
70
70
71
70
50
50
50
50
50
52
52
52
49
50
43
43
42
42
40
41
40
40
40
46
46
46
59
58
61
63
64
65
70
71
58
55
53
54
56
57
56
56
54
56
52
55
52
51
47

-------
TABLE 3-1 (CONTINUED).   LABORATORY DATA
CASE AV
NUMBFR DIS
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
	 8 7 	
88
89
90
ERAGE
P FUFL
50
55
59 	
61
66
68
74
72
73
70
64
61 	
60
54
51
48
53
49
52
53
61
60
63
66
71
76
77
78
75
68
TEMPERATURE - DEGREES  FAHRENHEIT
       INITIAL     MINI-SHED    AVERAGE     RVP
      TANK FUEL      AMBIENT       VAPOR     (PSD
                                                      DISPLACED
                                                        LOSS
                                                      (GMS/GAL)
         46
         48
         47
         48
         48
         40
         48
         61
         61
         62
         65
         64
         63
         6?
         61
         61
         66
         64
         66
         65
         66
         66
         66
         66
         66
         66
         74
         72
         73
         75
                       47
                       48
                       47
                       40
                       47
                       48
                       46
                       62
                       62
                       62
                       60
                       59
                       60
                       59
                       58
                       60
                       68
                       66
                       66
                       66
                       66
                       66
                       67
                       66
                       66
                       69
                       79
                       79
                       78
                       79
51
52
52
54
54
54
58
66
65
63
63
61
61
59
58
58
66
62
63
64
64
o5
69
68
70
71
80
76
76
/9
9.9
9.8
9.8
10.0
10.0
9.9
9.9
9.9
10.0
10.0
10.0
10. 0
9.7
9.7
9.7
9.7
9.8
9.Q
9.8
9.8
10.0
10. 0
9.8
9.8
9.7
9.7
9.7
9.7
9.6
9.7
3.55
3.76
4.06
4.05
4.59
4.53
5.26
5.74
5.24
5.01
4.41
4.29
3.89
3.79
3.60
3.39
3.94
3.52
3.06
3.63
4.28
4.49
4.75
4.93
5.45
6. 18
6.09
6.48
6.04
5.40
CO
-fi

-------
TABLE B-l (CONTINUfcD).   LABURAT'JRY DATA
TEMPERATURE - DEGREES  FAHRENHEIT  *********
                   MINI-SHEC    AVERAGE     RVP
                     AMBIENT       VAPOR     (PSI)
                       81
                       80
                       80
                       70
                       68
                       63
                       68
                       68
                       67
                       69
                       65
                       57
                       55
                       57
                       57
                       59
                       59
                       60
                       59
                       58
                       58
                       46
                       47
                       46
                       46
                       47
                       46
                       46
                       47
                       47
CASE
NUMBER
91
92
93
94
95
96
97 """
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
AVERAGE
DISP FUEL
68
63
63
70
70
66
64
56
52
55
47
51
41
41
43
- 52
50
56
58
63
68
68
62
59
53
50
48
41
36
34
INITIAL
TANK FUEL
77
76
76
72
71
70
65
65
64
68
65
60
58
57
57
59
58
59
57
54
54
46
47
45
45
45
45
48
49
49
                                                     DISPLACED
                                                       LOSS
                                                     (GMS/GAL)
76
77
77
70
70
69
68
67
69
71
68
58
56
59
57
62
61
62
60
61
62
54
52
51
50
49
49
48
46
47
9. 7
9.6
9.6
12.6
12.6
12.9
12.9
12.8
12.8
12.9
12.9
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.5
12.2
12.2
12.2
12.2
12.3
12.3
12.4
12.4
12.5
5.35
4.95
4.73
7.10
8.08
7.16
6.97
5.64
5.02
5.29
4.18
4.52
3.68
3.97
3.97
4.70
4.99
5.96
6.05
5.96
6.69
5.90
5.28
5.41
4.52
4.38
4.12
3.67
3.27
3.14
                                                                      ta
                                                                      I
                                                                      Ln

-------
                 TABLE  Q-l  (CONTINUED).  LABORATORY DATA
                 TEMPERATURE  -  DEGREES FAHRENHEIT *********           DISPLACED
 CASF ....  . AVERAGE       INITIAL      MINI-SHED    AVtRAGE      RVP        LOSS
NUMBER    DISP FUEL     TANK  FUEL      AMBIENT      VAPOR      (PSI)     (CMS/GAL)
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
42
40
31
35
36
43
47
53
5R
58
64
61
54
5i
47
42
40
35
33
38
50
41
41
43
42
40
40
40
40
39
40
	 31
30
31
31
32
33
31
36
37
48
39
30
40
39
39
38
38
38
3 I
37
30
27
28
30
29
31
26
31
30
50
4?
40
42
42
42
43
41
46
40
43
34
27
30
28
26
26
22
25
24
12.5
12.5
12.5
12.2
12.2
11.9
11.9
12.6
12.6
12.5
12.5
12.4
12.5
12.5
12.6
12.6
12.7
12.6
12.6
12.6
3.76
3.54
3.35
3.52
3.65
3.87
4.21
4.56
5.21
4.73
5.68
5.13
4.11
3.70
3.87
3.47
3.68
3. 13
3.07
3.19

-------
  APPENDIX C




STANDARD ERROR

-------
                                     C-2
                       Standard Error as Percent Error

     In computing the standard error of the estimate for a logarithmic
fit, the residuals are given as the natural log of the measured loss,
In l_m, minus the natural log of the regression estimate, In L'.  Let
that residual be denoted by R so that
                                     R = in Lm - in L'

In units of grams/gallon, let the residual  be
Then
Denoting the residual  as R% in percentage units,
                                    R% =  Lm   x   100  =   100  (1-e   ).

For small R, e~R^ 1-R.   Thus,  R% %slOOR.

Each residual is thus convertible to an approximate  error  percentage.
Therefore, the standard  error of the estimate  is  in  units  of percentage
error.

-------
                       APPENDIX  D




SAMPLE TEMPERATURE DATA FROM  THE THIRD YEAR  FIELD SURVEY

-------
                                     D-2
 TABLE 0
           THIRD YEAR FIELD SURVEY TEMPERATURE DATA
STATION!  2
TIME
655
701
748
752
816
833
837
839
902
9Q5
911
916
930
945
951
957
L015
L017
L1Q5
L107
1114
1127
L134
1139
1151
L157
L153
1201
1203
1219
i,244
1253
1303
L3Q5
L310
L31B
1339
L35n
L353
64
64
64
64
64
64
64
64
65
65
65
65
> 66
66
66
66
67
67
70
70
71
72
72
73
73
73
73
74
74
75
76
76
77
77
78
7*
80
81
81
SAN BF.KV!A«DIMO
« tt tt O 0
UNlQE^GROUN
FUEL
83,7
83,7
83.9
83,9
64,0
83,8
84,0
84,0
33,9
63,9
84,0
83,8
84,0
83,6
84,0
b3.5
33,6
83,6
04,0
84,0
84,0
84,0
84,0
84,0
B4.0
84,0
84.0
84,0
84,0
84,0
84,0
84,0
84,0
84,0
84,0
84,0
84,0
84,0
84,0
•< ONTA^I
* * TEMPERATURES
,"» ««#rj
AVG,
73,0
82,0
82,5
71, C
82,5
75,5
83,5
85,o
83,0
84,0
81, C
83,5
83,5
86,0
85,o
Bl.s
84,5
75 , 5
85,0
84,5
84,rj
82,5
84,0
84,5
84,0
83,5
82,5
84,0
82,5
83,o
64 , o
85,0
84,5
84,.5
84,0
85,0
85,o
87,0
86,5
JSPENSED
INITIAL
65,0
78,0
74,0
68,0
73,0
68,5
80,0
82,0
70, Q
73,0
72,0
76,0
73,5
85,0 '
71,5
78,0
75,5
74,0
P5 , 0
77,0
77,0
76,0
84, Q
86,0
00,0
77,0
83,0
83,5
79,0
84,0
79,5
81,0
83,0 .
81,5
83,5
82,0 '
84,5
85,0
86,5
0 DA
» DEC
FUEL***
PPAL
76,0
84,0
84,0
75,0
P4,0
79,5
84,5
85,5
P6 , 0
86,0
82.5
85 , o
^4 ,5
86,0
P6 i 0
«2.0
«5iO
78,5
85,0
84,0
M i 5
f?4 , 5
84,5
84,5
84 i 0
• 82,0
63,0
54,0
84,0
85,5
85,0
P5.Q
84,5
36,0
84,5
86,0
'86,0
• 87,5
861 5
                                                     8 25 72
                                                *«DlSPLACFD
                                                AVG,  INITIAL
                                                                   FJMAL
71,5
78,0
78, n
70,5
81,0
70,0
81,0
82, n
72,5
75,5
75,5
85,5
79,5
79,0
81.5
75, r.
35.0
77,0
83,0
82,5
82,0
80,0
82,5
81,0
81,0
79, 0
82,0
84, n
84,0
80,5
80,5
86,0
83,0
85,0
84,5
81,5
85.0
87,5
89,0
67,0
74,0
74,0
67,5
73,0
68,0
74,5
PO.O
70,0
72,0
74,0
74,5
76,0
76,0
74,0
73,0
78,0
7-2,5
32,0
75,0
75,0
77,0
80,5
80,0
80,0
77,0
«2,D
81--.0
80,0
82,0
83,0
81,0
84,0
82,0
84,0
81,0
84,0
87,0
68,5
75,0
81,5
80,0
72,5
83,5
73,0
83,0
83,5
76,0
78,0
76,5
82,5
82,0
BO, 5
B4.0
76,0
84.5
82,5
83,5
83,5
83,0
82,0
83,0
82,0
81,0
75,0
82,0
84,0
85,0
79,5
79,0
85,5
82,5
86,0
88,0
82,0
86,0
88,0
89,0

-------
                                     D-3
 TABLE 0*1   CONTINUED
    STATION!  2
SAN.BER^'A«DINO - ONTARIO
DATEI  a 25 72
       *«#»**»*»«* TEMPERATURES,  DEC. F«»««««»»#»»
FIME   AMBJENT  UNDERGROUND  •••OlSPENSbO F.UF.L***    «<*D I5PLACED  VAP03*«
                  FUEL      AVG,  IMITIAL" FINAL    AVG,   INITIAL   FINAL
L400
1407
Hll
L413
L420
L422
1.427
L5Q5
L528
L53S
L543
[546
[549
L550
16QQ
1612
1617
,621
,626
.629
.65n
.653
,7Q4
.707
.713
1717
.721
.726
.732
.737 '
^740
.742
.855
.858
.9Q4
.9Q9
.915
i926
,928 .
81
82
82
62
81
81
82
8?
83
83
83
83
83
83
84
84
84
84
84
84
83
83
82
82
82
82
82
81
80
60
79
79
74
74
74
74
73
72
72
84,0
34,0
84,0
84,0
34,0
64,0
84,0
84,0
84,0
94,0
34,0
34,0
84,0
54,0
84,0
83,9
84,0
83,8
84,0
84,0
33,5
94, Q
83,4
93,4
84,0
33,3
44,0
33,2
84,0
83,1
83,1
94,0
83,0
84,0
83,0
83,0
^4 , 0
-34,0
93,0
86,5
86,0
88,0
88,0
86,n
86,5
85,5
85,5
86,5
85,5
87,5
86, n
86,0
67 , o
85,5
86,0
86,5
88,Q
86, n
85,o
87,5
87,5
86,5
87,5
85,5
65,5
' 86,0
86,0
85,5
85,5
86,0
86,0
85,5
84,o
84,0
86,0
85,5
66,0
84,5
85,0 '
84,0
87,0
83,0 •
05, JD
85,0
86,0
85,0
87,0
84,0
86,5
83,0
86,0
86,5
86,0
85,5
86,0
88,0
08,0
80,0
88,0
88,0
86,0
86,5
85,0
86,0
66,0
86,0
85,0
82,5
86,0
84,0
78,0
78,0
78,0
82,0
76,0
85,5
7.8,0
88,0
86,0
83,0
ea.o
86,Q
86,5
85,0
86,0
87,Q
85,5
ft8,0
86,0 •
86,0
fi7,5
85,5
86,0
86,0
88,0
86,0
85,0
87,5
88,0
85,5
87,5
85,5
Q x c
O 1 3
85 , 5
86,0
85,5
86,0
86,0
86,5
86,5
84,0
85,0
86,5
87* 0
87,0
85,5
87,5
80,5
86,5
87,5
86,0
86,5
86,0
86,5
89,5
87, 0
87,5
98,5
88,5
91, n
90,0
88,5
89,5
91,0
87,5
90, D
89,0
88,5
89,0
88,5
92,0
86,5
87,5
87,0
85,0
86,0
86,0
86,0
85,0
84,0
84, n
83,0
85,0
82,0
78,0
84,5
83,0
86,0
86,0
84,0
85,0
87,0
86,0
87,0
88,5
86,5
34,0
91,0
87,0
86,0
86,0
90,5
89,5
09,5
82,5
88,0
' 88,5
89,0
86,5
86,0
86 , 0
86,0
85,0
83,5
85,0
75,0
85,0
81,0
84,0
78,0
76,0
79,0
81,5
78,0
89,5
80,0
86,5
88,0
86,0
' 87,5
86,0
86,5
90,0
87,0
88,0
103.0
88,0
90,0
90,0
89,0
89,0
90,0
86,5
92,0
88,0
88,0
87,5
9n,o
91,5
86,0
87,0
88,0
86,5
86,0
88,0
86,5
'86,0
84,5
85,5
84,0
87,0
82,5
78,0

-------
                                        D-4


 TABLE D - i   CONTINUED

    STATIONS 2    SASJ BERVARDIN1 - ONTARIO    DATEl  8 25  7?
       «*»»*#ttft*»» TEMPERATURES*  DEC" F*«*»***tt*»»
TIME  AMBlEMT  UNDERGROUND  «*«DISPENRED FUF.L*«»    **DlSPLACED  VAP03««
                  FUEL      AVG,  INITIAL  FINAL    AVG,   INITIAL   FJMAL
        72
1935    72
1939    71
194B    71
1955    70
2000    7Q
2009    70
2021    69
2035    69
2040    68
2047    68
2054    63
211?    6B
'34,0
33,0
$3 , 0
33,0
33,0
33,0
83,0
93,0
83, 0
3 4 , 0
83 , Q
33,0
43,0
86,
85,
86,
86,
85,
85,
86,
85,
84,
63,
8*3,
85,
83,
5
n
5
5
3 '
3
5
0
n
5
5
5
n
n5
79
32
75
78
RO
79
no
78
P3
73
B2
82
• 0
• o<
• 0
,0
• °
, 5
,o
,0
• 0
,0
,0
iO
iO
16
. P4
*6
H8
P6
R5
R7
«6
?5
?6
«5
"5
ft 4
.0
»0
.5
iO
.0
• 5
i5
iO
• 0
• 0
, o
, Q
• 0
84
81
84
81
83
83
80
80
79
81
80
83
79
,5
,n
,5
,c
,5
,5
,0
.5
• 0
,5
,n
,0
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76
74
77
78
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78
77
78
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77
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85!o
62,0
H5.0
85,0

13 ',0
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-------
D-6
 TABLE 0 r 2

    STATION? 6

       * * * 0
TIME  AMBIENT
CONTINUED

   MINNEAPOLIS - ST PAUL
     DATE!   1  21  73
1714
1731
1740
1751
1759
1800
16Q5
1820
1823
1827
i63n
1846
1852
1857
1901
1938
1940
S.94?
1947
1950
1956
20Q6
2010
2014
2024
2030
?039
2047
2050
2100
2103
2120
2140
2142
2146
2154
28
28
28
25
28
23
28
28
28
2»
2*
2B
28
28
2f
28
28
28
28
28
28
28
28
28
28
23
28
28
28
28
28
28
28
28
28
28
# •»«»««« TEMPERATURES*  DEC  F
U'-lDE^GROUN"  «*»D I SPFNSED FUEL*»*>
   FUEL      AVG,  INITIAL  FINAL
                           *»»*
                           VAPCR««
                           L  FJMAL
36,0
36,0
36,0
36,0
36,0
36,0
36,0
36,0
36,Q
36, n
35,8
36,0
35,9
36.0
36,0
35,7
35,7
35,7
35,7
35,6
35,6
35,5
35,5
35,4
35,4
35,3
35,2
35,2
35,1
33,0
35,0
35,0
35,0
35,0
35,0
35,0
34,5
35,0
35,0
35 , Q
34,5
35,5
34 , e,
35,5
34 , 5
34,5
33,0
34,5
33,3
35,0
35,5
•33,o
34,5
35,5
35,0
35,0
35,5
35,0
34,5
35,0
34,5
34,5
34,0
35,0
35,o
35,0
35,0
35,0
35,Q x
35,0
34,5
33,5
33,0
32,0
34,0
35,5
33,0
34,0
32,5
33,5
32,0
31,0
31,0
31,5
31,0
32,5
35,0
31,0
31,5
35,5
32,5
34,0
35,5
34,0
34,0
33,0
32,0
33,0
32,5
31,0
34,0
34,0
35,0
33,0
• 33,0
32,0
33,5
33,5
35,0
35,0
35,0
35,0
34,5
' 35,0
35,0
?5,5
35,0
35,0
34,0
35,0
34,0
34,5
35,5
34,0
35,0
35,5
35,0
35,5
35,5
35,0
35,0
35,5
34,0
34,5
34,0
34,5
35,0
35,0
35,0
35,5
35,0
34,5
34,5
33,5
35,5
33,0
•33, n
33,5
33,5
44,5
36,5
38,5
32,5
34,0
31,0
33,5
33,5
32,5
35, n
35,0
36,5
36,5
32,5
38,5
' 36,0
37,5
33,5
36, n
34,5
37,5
33,5
35, n
34,0
35,5
34,0
37,5
35,5
34,5
32,5
33,5
33,0
33,5
33,0
35, b
31,5
42,5
33,0
34,5
30,0
29,5
29,5
29,5
33,0
30,0
35,0
32,0
30, U
35,5
30,5
30,0
36,5
31,5
34,0
30,0
30,5
33,0
30,5
30,5
32,0
32,0
34, b
34,0
34,5
35,0
31,5
33,5
39,0
33,5
32,5
32,5
33,5
46,0
36,5
39,0
32,5
34,0
31,0
33,5
34,0
33,0
34,0
35,5
36,5
36,5
32,5
38,5
35,5
33,0
33,5
36,5
34,0
36,5
33,5
34,5
33,0
35,5
34,0
37,5
36,0
34,0
33,0
33,5

-------
                                      D-7
 TA31.E D - 3   THIRD YF.AR FIELD SURVEY TEMPERATURE OATA
    STATION I  7
TIME
 735
 8Q6
 813
 813
 854
 902
 9Q3
 933
 936
 941
1000
lOOfl
1023
1035
1041
1047
1048
1125
1123
1204
1211
1212
1239
1243
1249
1251
1310
1317
1320
<* * » »
AMBIENT

47
47
47
47
47
47
47
47
47
4 a
r
49
49
49
49
49
49
49
. 49
49
49
50
50
50
50
50
50
50
» « « *
UNnr^r.Rt
F'JEU
67,6
67,0
66,0
66,0
67,9
6? , 0
6? , 0
66,1
68,0
65,0
65,0
67 ',0
6B.O
66,4
66,4
66.4
67.0
6^,0
67,0
67,0
6^,0
67,0
68,0
6P.O
66,5
6^,0
6$, 0
66,5
BERNARDINO - ONTARIO    DATES

   « « TEMPERATURES!  D^G F
   ,O  #««^ISPF.NSL'3
      AVG,  INITIAL
55,5
57,0
56,0
53,0
56,Q
58,5
53,0
57,0
59,5
62,0
61,5
58,0
58,0
61,0
61,0
63,n
57,0
56,5
58,5
56,0
57,5
61,0
57,0
58,0
60,5
57,5
58,5
60,5
58,5
49,5
50, n
51,0
50,0
53,0
53,5
50,0
52,5
52,5
56,0
56,0
52,0
53,5
54,5
55,0
60,0
54,0
52,0
52,0
51,5
53,0
54,0
54,0
54,0
54,0
53,5
54,0
55,5
54,0
                                           56,5
                                           60,0
                                           60,0
                                           55,0
                                           57,0
                                           60,0
                                           54,5
                                           59, C
                                           *0»0
                                           64,0
                                           62i5
                                           61,0
                                           59,0
                                           62,0
                                           63,0
                                           63,5
                                           61,0
                                           57,0
                                           60,0
                                           57,0
                         0
                         0
                                            61,
                                            63,
                                            58,0
                                            60iQ
                                            62,0
                                            58,0
                                            59,0
                                            63iO
                                            60.0
S 3 27
AVG,
51,5
54.0
55,5
53,5
51 , 5
55, C
51,0
55.0
37,0
57,5
56,5
57,5
55,5
57,5
61, n
60,5
55,5
53,5
57,0
53,0
57,0
56,0
54,5
58,0
55,5
55,0
56,5
59.0
65,0
73
IMJTlAL
50,0
51,0
52,0
53,0
51,0
52, -0
51,0
52,5
51,5
54,0
53,5
55,0
54,0
53,5
56,0
53,0
54,0
52,0
53,5
52,5
53,0
54,0
53,0
54,0
53,0
53,0
54,0
55,5
54,0

FINA!
52,0
57,0
58,0
54,0
52,0
.56,0
51,0
57,0
59,0
59,5
57,5
60.0
57,0
59,0
62,5
62,5
57,0
55,0
59,0
54,0
59,0
58,5
55,0
60,0
56,0
57,0
57,5
61,0
65,0

-------
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-------
                     APPENDIX E




MULTIPLE REGRESSION OF FIELD SURVEY TEMPERATURE DATA

-------
                                E-2
In the following tables, the variables are indentified as follows
         DA  =  Average dispensed fuel temperature
         UF  =  Underground fuel  temperature
         AM  =  Ambient temperature

-------
                           E-3

                        Table E-l

                Statistics for Total Sample

PROBLEM CODE                   REFFLD
NUMBER OF CASES                  2637
NUMBER OF ORIGINAL VARIABLES       3       	 	
NUMBER OF VARIABLES ADDED          7
TOTAL NUMBER  OF  VARIABLES         10
NUMBER_OF SUB-PROBLEMS             3
THE VARIABLE  FORMAT IS   { 37X, F3 . 1 , 2 IX, F 3. I , IX, F 3. 0)
  VARIABLE         MEAN        STANDARD DEVIATION
  	 DA   I         69.72316           23.74181
     UF   2         69.74094           23.12682
     AM   3         64.22638           23.20882
    A-U   4         -5.52289       .  _   9.26426_
 CORRELATION  MATRIX

 V ARI A B L E	1	    2          _3	4	
  NUMBER

 ..._	1_	1«.000	   0.991       0.946 ___-_(>• l.P 5
     2                    1.000      "0.920     -0.192
     3                                1.000      0.208
 	4	      	  ..   _      	       1.000
  COVARIANCE MATRIX

  VARIABLE       1           2           3    	4	
   NUMBER                        "~

 	1	563.674     544.017    521.045     -23.076
      2                  534.850    493.842-41.097
      3                             538.649      44.725
      4                                          85.826

-------
                                  E-4
                               Table E-2
                     Regression Data for Total Sample
 STEP NUMBER    1
.VARIABLE ENTERED^ _._;

 MULTIPLE R
 STD. ERROR OF EST.

 ANALYSIS OF VARIANCE
                              (N = 2637)
    0.9908
    3.2148
         REGRESSION
         RESIDUAL
  OF
   1
2635
SUM OF SQUARES	ME_AN_SQUARE_. .. _ F  RATIO
 1458609.000    1458609.000   141133.933
   27232.527         10.335
                  VARIABLES IN EQUATION

'""VARIABLE	   COEFFICIENT  STQ. ERROR""IFTO"R~EMCJVE


"  (CONSTANT         -1.21315 )
      UF  2           1.01714     0.00271  141133.9375  (2)










 STEP NUMBER    2
_V A.R I A 8L E^ _ENT E RE D	3	

 MULTIPLE R                0.9946
.S.TD._..ERROP_QF_EST.. .._  _..  2.4674	

 ANALYSIS OF  VARIANCE
	                DF   _SUM OF  SQUARES	MEAN[...SQUARE	F_RATIC
         REGRESSION      2     1469805.000    734902.500   120709.875
         RESIDUAL      2634       16036.242         6.088


                  VARIABLES IN EQUATION

   VARIABLE      COEFFICIENT  sib. ERROR   F TO REMOVE


   (CONSTANT         -1.17523 )
      UF  2           0.80785     0.00530   23195.3789  (2)
      AM  3           0.22667     0.00529    1839.0271  (2>

-------
                              E-5
                         Table E-3

         Statistics for Moderate Temperature Sample
  "PRO BLEW "COOL                  SPRING
  NUMBER OF CASES                   187
  NUMBER OF ORIGINAL  VARIABLES       3       _  	
  NUMBER OF VARIABLES ADDED          I
  TOTAL NUMBER  OF  VARIABLES          4
  NUMBER OF SUB-PROBLEMS             2               _
  THE VARIABLE  FORMAT IS   ( 37X , F3 . 1 , 2 I X , F 3.Y, IX , F~3. 0)
    VARIABLE         MEAN       STANDARD  DEVIATION
       DA   1         63.97861           3.61106
    " " " UF   2         66.95920           1.07839 "
       AM   3         58.65775           8.60168
      A-U   4         -0.30209           8.57029
 CORRELATION  MATRIX


 VARIABLE       1           2           3	        4
  NUMBER               ~~ * """


   _ 1_	  i.OOO      0.123       0.842	O-J3?
     2      "   - -  --   -     i.OOO  " "*" 6.092    "  -0.03~3

     3                                1.000       0.992
   __ 4	 ___                                      I.OOO
 COVARIANCE MATRIX


 VARIABLE      1           2           3     	4	
  NUMBER


     1        13.040       0.478     26.148      25.671
     2                     1.163      0.853      -6.309
     3                               73.989      73.138
	4  .                                         73.450

-------
                                  E-6
                               Table E-4

                      Regression Data for Moderate
                      Temperature Sample (N - 187)
 STEP  NUMBER    1
 VARIABLE ENTERED	 3	

 MULTIPLE R                0.8418
 STD.  ERROR OF EST.        1.9543
ANALYSIS OF VARIANCE
    	               .OF    SUM OF  SQUARES	J4EAN_SQUARE	_F_ RATIO
         REGRESSION       1        1718.S42      1718.842      450.051
         RESIDUAL       185         706.554         3.819
                  VARIABLES IN EQUATION
   VARIABLE      COEFFICIENT  STD. ERRDR   F TO REMOVE
   (CONSTANT         43.24840 )
      A")  3           0.35341     0.01666     450.0508  (21
 STEP NUMBER    2
 VARIABLE ENTERED     2
 MULTIPLE R                0.8431
 STD.  ERROR OF EST.        1.9526
 ANALYSIS OF VARIANCE
	                  OF    SUM OF  SQUARES    MEAN  SQUARE    F RATIO
         REGRESSION       2        1723.860       3ol.930      226.068
         RESIDUAL       184         701.537         3.813
                  VARIABLES IN EQUATION
   VARIABLE      COEFFICIENT  STD. ERROR   F TO REMOVE
   (CONSTANT         33.11020 )
      UF  2           0.15295     0.13333       1.3160  (2)
      AM  3           0.35165     0.01672     442.5522  (2)

-------
                             E-7



                           Table  E-5

              Statistics for High Temperature Sample


 PROBLEM CODE                  SUMMER
 NUMBER Of  CASES                  1790
 NUMBER OF ORIGINAL  VARIABLES       3            	
"NUMBER OF VARIABLES  ADDED          1
 TOTAL  NUMBER OF VARIABLES          4
 NUMBER OF SUB-PRUBLEMS             2
 THE  VARIABLE FORMAT  IS   (37X,F3.1,1IX»F3.1f1X,F3.0)
   VARIABLE         MFAN        STANDARD  DEVIATION
      DA  1         84.88658            3.05335
      UF  2         84.4597b            1.20224
      AM  3         78.04139            9.51606
     A-U  4         -6.42408            9.15581
   CORRELATION MATRIX

   VARIABLE       1         _  2      _    3   	4
    NUMBER           ~"	  "             ~" " "     ""

    	1	   1.000       0.37«       0.732   _   0.711
       2                    1.000       0.356""     6.239
       3                                1.000       0.992
       4                                            1.000
   COVARIANCE MATRIX

   VARIABLE       1           2           3     	4
    NUMBER

   	1    _    9.354       1.391     21.307      19.913
       2                     1.445      4.075       2.629
       3                               90.555      66.469
   	4	 _.                                    83.829

-------
                                E-8
                             Table E-6

                         Regression Data for High
                       Temperature Sample (N = 1790)
STEP NUMBER     1
VARIABLE ENTERED     3

MULTIPLE R                0.7321
STU. ERROR OF  EST.        2.0838
ANALYSIS OF VARIANCE
                        DF    SUM OF SQUARES	MEAN^SQUARE	F  RATIO
     	REGRESSION       1        8969,254       8969.254    2065.512
        RESIDUAL      1788        7764.191          4.342
                  VARIABLES IN EQUATION

  VARIABLE       COEFFICIENT  STO. ERROR   FTO~R~E MO vF
  (CONSTANT         66.52361 )
     AM  3           0.23530     0.00518    2065.5134 (2)
STEP NUMBER     2
VARIABLE  ENTERED     2
MULTIPLE R                0.7428
STD. ERROR  OF  EST.        2.0486
ANALYSIS OF  VARIANCE
                        DF    SUM OF  SQUARES     MEAN SQUARE     F  RATIO
        REGRESSION       2        9233.816       4616.906     1100.109
        RESIDUAL      1787        7499.629          4.197
                  VARIABLES IN EQUATION

  VARIABLE"       COEFFICIENT  STD/ ERROR" ' F~fo~RTMOvT
  (CONSTANT         38.81367 )
     UF  2           0.34232     0.04311      63.0399 (2)
     AM  3           0.21989     0.00545    1629.6946 (2)

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                           E-9
                        Table E-7

                    Statistics for Low
                    Temperature Sample
PROBLEM CODE                   WINTER
NUMBER OF  CASES                  660
NUMBER OF  ORIGINAL VARIABLES       3      	
NUMBER OF  VARIABLES ADDED          1
TOTAL NUMBER  OF VARIABLES          4
NUMBER OF  SUB-PRCBLEMS             2
THE VARIABLE  FORMAT IS   ( 37X, F 3 . 1 , 2 IX , F 3 . iTfxVF 3~. 6T
  VARIABLE         MEAN        STANDARD DEVIATION
     DA   1         30.22575            5.44865
    " UF   2         30.62665            3.58264
     AM.   3         28.33434            8.41652
    A-U   4         -2.29237            8.95500
  CORRELATION MATRIX

  VARIABLE       1_       2           1   	4_ __
   NUMBER   " '    - -  - -        -	- -

   	1         1.000       0.750       0.467      0.139
      2~	             "  1.000       0.058     -0.~346
      3                                1.000      0.917
      4                                           1.000
  COVARIANCE MATRIX

  VARIABLE       1_     	 _ 2 	 3	4	
   NUMBER

      1_     - 29.688     14.647      21.405       6-760
    ""2                   12.335       1.742 ~" -11.093
      3                               70.838      69.098
                                                  80.192

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                               E-10
                             Table E-8

                       Regression Data for Low
                     Temperature Sample (N = 660)
 STEP NUMBER     1
 VARIABLE ENTERED
 MULTIPLE R                0.7503
 SJD.  ERROR OF  EST.        3.6046    	

 ANALYSIS OF VARIANCE
                         OF    SUM  OF  SQUARES    _MEANJSQUARE__   F  RATt?
         REGRESSION       1        11014.758"     11014.753647.733
         RESIDUAL       658         8549.473         12.993


                   VARIABLES IN EQUATION

"""VARIABLE       COEFFICIENT  STO.  ERROR"" "F"Hfo~Te~MG"v"E~


 ""{"CONSTANT   "     -4.72371  )      	
      UF  2           1.14115      0.03919    847.7375 (2)





 STEP  NUMBER     2
.VARIABLE ENTERED     3	

 MULTIPLE R                0.8619
_STp. _ERROR OF  ESI.        2.7670	

 ANALYSIS OF VARIANCE
		      	OF    SUM  OF  SQUARES	MEAN SQUARE     F  RATIO
         REGRESSION       2        14534.117       7267.059     949.175
         RESIDUAL       657         5030.113          7.656


                   VARIABLES IN EQUATION

  VAR I A B~L E       C 0 E F F'l C I "E N f"~" S T 0 .  E R ROR   F"~t"0
   (CONSTANT
      UF  2
      AM  3
-11.37380  )
  1.10383
  0.27503
0.03014
0.01233
1341.6296  J2)
 459.6748  (2)

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       APPENDIX F




COMPUTER PROGRAM LISTING

-------
          Table F-l   Computer Program Listing
 1*   C     REFUELING LUSSES  AKEA  MODELt   MALCOLM SMITH? 4/lb//4
 2*   C
 3*   L          REVISED BY IN,  F.  BILLtK   9/lb//b
 a*   c
 b*         INTEGER OPTlt UPT2»  OPT3
 6*         DIMENSION K(16)»  REGlb)»  IEMP(3)» PV1400)» UF(400)t  AK(16»400)f
 /*        1ND(400)» C(8)» HCLOSS(16»40U) »  IUT[)AY(400) » TUTHR(16)»
 b*   C
 9*   C  COEFFICIENTS OF BASt  fcUUATIONS  ON  NtXF SIX DATA CARUb
11*         DA I A «tG/-9.r/03fc-^»l.lb21t-5»-i . 2bObt-3 f 5 , a094E-7/
13*         DATA K/.Ol7b?.Oa3bt ,0a«5».058bf .Obobf . 0 7t . 0 7 lb» . 069b» . 07bb» . 077 » . 0
14*        176bt ,083b».0«4b».(H/b»,Obb» .Oib/
Ib*         DATA DfcLT/  7.0/
16*         DATA SPIL/  0.3/
17*         ICHD=b
1H*         1PKI=6
19*         E = <2. 716^81828
2 0 *   C
*   C
37*         WRITEUPRTt  1010)
i
ro

-------
               Table F-I  continued


       1010 FURMATCl't bXt "THE CALCULATED COEFFICIENTS  ARE:'/)
39*         DO 60 I=lt8
40*      60 WRITEdPRl tlOlb)ItC(I)
41*    lOlb FORMATUIXt>C('»I1»') = 'fEJ3.b/)
42*      20 CONTINUE
43*         DU 999 IJ=ltNTIMES
44*         TOTAL=0,
4b*         TUTGAL=0
46*   C
47*   C  NDAYS = NUMBER OF DAYS OVER WHICH LOSS  IS  TO bE  ESTIMATED
48*   C
49*   C
bO*   C     OPT2 = 0  MEANS GALLONS PER DAY (GDAY)t REID  VAPOR  PRESSURE  lPV)t
bl*   C               UNDERGROUND FUEL TEMPERATURE  (UF)t  ARE  CUNSTANl  OVER
b2*   C               NDAYS
b3*   C     OPT2 = I  MEANS THEY ARE VAKIAtiLE OVER  NDAYS
b4*   C
5b*   C     OPT3 = 0  WILL NOT PRINT INPUT DATA
bb*   C     OPT3 = 1  HILL PRINT INPUT DATA
b/*   C
b8*         READUCRDt  1000) NDAYSt OPT2t OP13
b9*    1000 FURMAH2Xt  I3t 2(4Xt ID)
60*         DU 10 1=1»NUAYS
61*      10 TUTDAY(1)=0.
62*         DO Ib I=ltl6
63*      15 TOTHH(I)=0.
64*   C
6b*   C  READ IN FUR EACH DAY (UNE CARD PER DAY): UAYt  NDU)J  GALLONS  PER DAYt
66*   C  GDAY(J). REID  VAPOR PRESSUREt PVU)» UNDERGROUND FUEL  1EMPERAIURE  IN
67*   C  DEG Ft UFU).  IF PARAMETERS CONSTANT OVER NUAYSt  USE  ONE  CARD
6tt*   C
69*         IFCOPT2 .fcfc. 0) GO TO 2b
70*         DO 21 J = It NDAYS
71*         READUCRDt  1020) ND(J)t GUAYCJ)t PVCJJt UFU)
72*      21 CONTINUE
73*    1020 FURMATtlbt  bXt FlO.Ot ?(bXt F5.0))
74*   C
7b*   C     TES'T FOR CORRECT SEQUENCE OF"  INPUT CARDS
76*   C
77*         DU 24 J = It NDAYS
78*         IF(NUU) ,NE. J) GO TU 27
         24 CONTINUE

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80*
81*
82*
83*
84*
8b*
86*
8/*
88*
89*
90*
91*
92*
93*
94*
95*
96*
9/»
98*
99*
100*
101*
102*
103*
104*
lOb*
106*
10/»
108*
109*
110*
111*
112*
113*
il«»
ll'i*
116*
117*
lib*
119*
120*
121*
• GU TU 3b
27 wRlTEdHRTt 6000) Jt N!)(J)t GDAY(J)t PV(J)t UF(J)
6000 FORMAmi GDAYtPVtUF JNPUT CARDS NUT IN SEUUENCE1/
1 Ibt Ibt FlO.Ot 2(bXt Fb.O))
STOP
2b READdCRDt 102b) GOA YC t P VC » UF C
102b FURMAHlOXt FlO.Ot 2(bX» Fb.O))
OU 26 I =1» NUAYS
GDAY(I) = GDAYC
PVd) = PVC
26 UFd) = UFC
C
t RtAD IN FOR tACH HOUR OF hACh DAY THt AMBIENT TEMP. IN
C
3b RtADCICRDt 1 030) ( ND( J ) » (AM(I»J)r 1 = 1» 16)» J = It
1030 FURMATdbt 1X» 16FiJ,0)
C
C ItST FUR CORRECT vSfcQUtNCt OF INPUT CARDS
C
00 28 J = It NDAYS
IF(NO(J) ,Nt. J) GO TO 29
28 CONTINUE
GU 10 36
29 tSRITEdPRTt 6010) J» ND(J)t AM(ItJ)
6010 FURhAK'l AM(I,J) INPUT CAKDS NUI IN StUUtNCE'/
1 I3t 13 t 16F4.0)
STOP
C
C PRINT INPU1 DATA IF CALLED FUR bY OPflUN 3 = 1
C
36 IFCOPT3 .EO. 0) GO TO a5
WRITEdPRl t7000)
7000 FORMATC ' 1 » t T4Q»5( « * l)t
-------
                      laoie r-i

122*'   C "
123*   C  COMPU1E HYDROCARBON REFUELING LUSS FOK tACH HOUH OF  EACH  DAY
124*   C
             DO 70 J = 1» NDAYS
             DO 65 I = It 16
127*      65 HCLObSUtJ)  = I.SP1L + E**(C(1) t C(2)*PVCJ) * C C 5) * AM ( 1 » J ) f
128*        1 C(a)*UKJj  + C(b)*PV(JJ*AM(ItJ) * C(6)*PV( J)*UK J)  t
129*        2 C(7)*AM(1»J)*UKJ) * C ( 8) * AM ( 1 1 J) * AM ( 1 » J) ) )
130*        i +K(I)*UOAY(J)/<»b3.6
131*      70 CUNTlNUt
132*   C
133*   C  COMPUTE DAILY LOSS TOTALS
134*   C
13b*         DU 80 I=1»NDAYS
136*         DO 80 J=i»l6
13^*      80 H)rUAY(l) = TQH)AY(l)+HCLGSS(J»I)
136*   C
139*   C  COMPUTE T01AL LOSS OVhK SPECIFIED PERIOD
Ul*         DO 90 1 = 1»NOAYS
142*      90 TUUL=IOTAL-»-rOTDAY(I)
143*    1040 F-UHMAH IHl/bXt 'SUMMARY OF LOSSES BY DAY*  IN  POUNDS  Of  HYDROCARBONS
144*        !«/)
145*    1050 FUHMAf C20Xf 'DAY «»I3»» LOSS =«tF8.0)
146*         WK1?E(1PKT»1040)
147*   C
148*   C  OUTPUT LOSS BY DAY IN POUNDS OF" HYDROCARBONS
149*   C
150*         DO 100 I=lfNUAYS
151*     100 WRITEtlPRT* I0b0)lt IUTDAYII)
152*    1060 FORMAT t/5Xt "IHh TOTAL LOSS OVER  THE  'rUt'-DAY  PERIOD  =i»F«.0)
153*   C
154*   C  OUTPUT TOIAL LOSS OVER SPECIFIED PERIOD  OF  TIME
155*   C
156*         WRI IEUPRI » 1060)NDAYS»TOTAL
157*   C
158*   C  COMPUTE AVERAGE LOSS IN GRAMS/GALLON
159*   C
160*         00 105 I=ltNDAYS
161*     105 TUTGAL=TOTGAL* GDAY(l)
162*         AVGE=TUTAL/10TGAL*453.6
163*    106'j FORMAU/5X» 'THt AVERAGE LOSS =ifF5.2»> GMS/GAL1)

-------
                 Table F-l Continued
164*   C
165*   C  OUTPUT OVERALL AVERAGE LOSS  IN  GRAMS  PEK  GALLON
166*   C
167*         WKITE(IPRT»106b)AVGE
166*    1070 FURMATUHl/bXf "SUMMARY OF LOSSES BY  HOURt  IN POUNDS OF HYDROCARBON
169*        ISl/)
170*         wHlftCIPRT»i070)
171*   C
If**   C  COMPUTE HOURLY LOSSES SUMMED OVER  ALL  DAYS
175*   C
174*         DC) 110 I = ltl6
17b*         DO 110 J=i»NDAYS
176*     110 TUTHR(I)=TOTHRCmHCLOSSU»J)
177*    1080 FURMAf(20X»'HOUR  "tI2»l LOSS =»»F8.0)
178*   C
179*   C  OUTPUI LOSS tJY HOURr SUMMED  UVER ALL  UAYSt  IN POUNDS UF HYDKOCARbONS
180*   C
181*         DO 120 I=ltl6
ia
-------
                                   TECHNICAL REPORT DATA
                           (Please read Instructions on the reverse before completing)
1. REPORT NO.
 EPA-460/3-76-006
4. TITLE ANDSUBTITLE
 Expansion of Investigation of  Passenger Car
 Refueling Losses
                                                           B. REPORT DATE
                                                             September 1975
                                                           6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
                                                           8. PERFORMING ORGANIZATION REPORT NO.
 Malcom Smith (Olson Research  Laboratories)
 and William Biller (consultant)
9. PERFORMING ORGANIZATION NAME AND ADDRESS
  Scott Environmental Technology,  Inc.
  2600  Cajon Boulevard
  San Bernardino, CA 92411
12. SPONSORING AGENCY NAME AND ADDRESS
 Environmental Protection Agency,  OMSAPC
 Ann Arbor.  MI 48105 and
 Coordinating Research Council, Inc.
 New York,  NY 10020	
                                                           3. RECIPIENT'S ACCESSION"NO.
                                                            PB-247  786
                                                           10. PROGRAM ELEMENT NO.
                                                           11~ CONTRACT/GRANT NO

                                                             68-01-0434
                                                           13. TYPE OF REPORT AND PERIOD COVERED
                                                             FINAL _£1972 t.o_l£75J	
                                                           T~4.~SPONSORi"NG~~AGENcY CODE
15. SUPPLEMENTARY NOTES
  Prepared for both EPA and  the Coordinating Research Council, Inc. ui.der  the jointly
  Funded APRAC CAPE 9 Project
16. ABSTRACT
  This  report describes a model for predicting total  regional hydrocarbon  emissions
  from  refueling operations.   Actual refueling emissions were measured under laboratory
  controlled conditions using a mini-SHED.  Resultant data led to the development of a
  "laboratory model" giving  refueling emissions  as  a  function" of fuel RVP,  dispensed,
  fuel  temperature, and initial vehicle tank temperature.  A field survey  was conducted
  to determine temperature conditions and refueling frequency as a function of time of
  day and season.  The laboratory model was then generalized using the field data to
  create a regional model giving total refueling losses for a given time period as a
  function of average daily  fuel sales in the region, average RVP of fuel  used in
  the region, average hourly ambient temperature, and average daily underground tank
  temperature.
17.
                                KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
  Air Pollution
  Gasoline Vapor
  Hydrocarbons
                                              b.IDENTIFIERS/OPEN ENDED TERMS
                                               Refueling Operations
                                               Mobile Sources
                                               Hydrocarbon Emissions
                                                                         c. COSATI Field/Group
18. DISTRIBUTION STATEMENT

  UNLIMITED
                                              19. SECURITY CLASS (ThisReport)

                                                IINCTASSTFTFJ)	
21. NO. OF PAGES

      116
                                              20. SECURITY CLASS (Thispage)
                                                UNCLASSIFIED
                                                                         22. PRICE
                                                                            $5.50
EPA Form 2220-1 (9-73)
                                            116

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