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
-------
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
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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.
-------
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
-------
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
-------
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
-------
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)
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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
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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).
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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
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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; =
-------
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.
-------
"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.
-------
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.
-------
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.)
-------
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
-------
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.
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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).
-------
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
-------
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
-------
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
-------
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)
-------
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
-------
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.
-------
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
-------
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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)
-------
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
-------
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)
-------
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
-------
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