EPA420-P-98-011
- Draft -
Modeling Hourly Diurnal Emissions
and Interrupted Diurnal Emissions
Based on Real-Time Diurnal Data
Larry C. Landman
Document Number M6.EVP.002
May 20, 1998
U.S. EPA
Assessment and Modeling Division
National Vehicle Fuel and Emissions Laboratory
2565 Plymouth Road
Ann Arbor, Michigan 48105-2425
734-214-7939 (fax)
mobile@epa.gov
NOTICE
These reports do not necessarily represent final EPA decisions
or positions. They are intended to present technical analysis
of issues using data which are currently available. The purpose
in release of these reports is to facilitate the exchange of
technical information and to inform the public of technical
developments which may form the basis for a final EPA decision,
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Abstract
This document reports on both the methodology used to analyze
the data from real-time diurnal (RTD) tests on 270 vehicles and on
the results obtained from those analyses. The purpose of the
analysis is to develop a proposal for a model of the hourly
diurnal (and interrupted diurnal) emissions of the in-use fleet.
Since this draft report is a proposal, its analyses and
conclusions may change to reflect comments, suggestions, and new
data.
Please note that EPA is seeking any input from stakeholders
and reviewers that might aid us in modeling any aspect of resting
loss or diurnal evaporative emissions.
Comments on this report and its proposed use in MOBILE6
should be sent to the attention of Larry Landman. Comments may be
submitted electronically to mobile@epa.gov, or by fax to (734)
214-7939, or by mail to "M0BILE6 Review Comments", US EPA
Assessment and Modeling Division, 2565 Plymouth Road, Ann Arbor,
MI 48105. Electronic submission of comments is preferred. In
your comments, please note clearly the document that you are
commenting on, including the report title and the code number
listed. Please be sure to include your name, address,
affiliation, and any other pertinent information.
This document is being released and posted on May 20, 1998.
Comments will be accepted for sixty (60) days, ending July 18,
1998. EPA will then review and consider all comments received and
will provide a summary of those comments, and how we are
responding to them.
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Table of Contents
Page Number
1.0 Introduction 1
2.0 Stratifying the Test Fleets 2
2.1 Evaluating Untested Strata 4
3.0 Evaporative Emissions Represented by the RTD .... 4
4.0 Hourly Diurnal Emissions 6
4.1 Characterizing Hourly Diurnal Emissions ... 6
4.2 Calculating Hourly Diurnal Emissions 10
5.0 Hourly Diurnal Emissions for Gross Liquid Leakers. . 11
6.0 Interrupted Diurnal 15
6.1 Example of an Interrupted Diurnal 15
6.2 Calculating Emissions of an Interrupted Diurnal. 20
6.3 Interrupted Diurnals of Gross Liquid Leakers . 21
7.0 Assumptions Related to Hourly Emissions 21
7.1 Distribution of Hourly Diurnal Emissions ... 21
7.2 Assumptions for Interrupted Diurnals 21
8.0 Other Factors 22
8.1 Temperature Ranges 22
8.2 Estimating Vapor Pressure 23
8.3 Heavy-Duty Vehicles 23
8.4 High Altitude Emissions 24
8.5 Motorcycles 24
8.6 Pre-Control Vehicles 26
8.7 Duration of Diurnal Soak Period 29
8.8 1996 and Newer Model Year Vehicles 29
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Table of Contents (Continued)
Page Number
Appendices
A. Temperature Cycles 30
B. Vapor Pressure 31
C. Modeling 24-Hour Diurnal Emissions 33
D. Hourly RTD Emissions of Gross Liquid Leakers .... 34
E. Estimating Hourly Interrupted Diurnal Emissions . . 35
F. Modeling Hourly Resting Loss Emissions 36
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*** Jd) g1 a {j* % ***
Modeling Hourly Diurnal Emissions
and Interrupted Diurnal Emissions
Based on Real-Time Diurnal Data
Report Number M6.EVP.0 02
Larry C. Landman
U.S. EPA Assessment and Modeling Division
1 . 0 Introduction
In a recently released draft report (entitled "Evaluating
Resting Loss and Diurnal Evaporative Emissions Using RTD Tests,"
originally numbered M6.RTD.001 and then renumbered as M6.EVP.001),
the Environmental Protection Agency (EPA) presented a model for
estimating resting loss and diurnal emissions over the course of c
full day (i.e., 24 hours). (The diurnal emissions are the
pressure-driven evaporative HC emissions resulting from the daily
increase in temperature, while the resting loss emissions are the
evaporative HC emissions not related to pressure changes.) These
estimates were based on the results of 24-hour real-time diurnal
(RTD) tests during which the ambient temperature cycles over one
of three similar 24-degree Fahrenheit ranges. The three ambient
temperatures cycles used in those RTD tests are illustrated below
Figure 1-1
Nominal RTD Temperature Cycles
110
90
in
a>
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3
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70
50
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r '
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_
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*
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12 18
Time (hours)
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May 20, 1998
in Figure 1-1; however, most of the testing was performed using
the 72 to 96 degree cycle. (Many of RTD tests were actually
performed for periods of more than 24 hours. The results after
the 24-hour point are analyzed in M6.EVP.003, "Multi-Day
Diurnals.")
As illustrated in the preceding figure, these three
temperature cycles are parallel (i.e., have identical hourly
increases/decreases). The temperature profiles used in all of the
RTD tests have the ambient temperature rising gradually from the
daily low temperature to the daily high temperature nine hours
later. After which, the ambient slowly returns to the daily low
temperature over the course of the remaining 15 hours. The three
hourly temperature cycles used in this study are given in Appendix
A. The most rapid increase in temperatures occurs during the
fourth hour. For RTD tests that exceed 24 hours, the cycle is
simply repeated. Estimating the effects of alternate temperature
profiles is discussed in Section 8.1.
The cumulative hydrocarbon (HC) emissions were measured and
reported hourly. Subtracting successive cumulative results
produces the hourly emissions. However, using the hourly
emissions requires associating a clock time with each test hour.
The RTD test is modeled after a proposal by General Motors (GM).
(GM's proposal is documented in SAE Papers Numbered 891121 and
901110.) The cycle suggested by GM had its minimum temperature
occurring at 5 AM and its maximum temperature at 2 PM. For
M0BILE5, EPA analyzed 20-year averaged hourly temperatures by
month from Pittsburgh on high ozone days. EPA found that the
minimum daily temperature typically occurred at 6 and 7 AM, while
the maximum daily temperature typically occurred at 3 to 5 PM. For
M0BILE6, EPA proposes to combine the GM and M0BILE5 time estimates
and use (as a default) the daily low temperature occurring at 6 AM,
and the daily high temperature occurring at 3 PM.
In the previous report, EPA proposed a method for estimating
resting loss and diurnal emissions on a daily basis. In this
report, EPA proposes a method for estimating resting loss and
diurnal emissions on an hourly basis. And then, using those
hourly estimates EPA proposes a method to calculate the diurnal
emissions that take place over periods of less than 24 hours.
This document reports both on the methodology used to analyze
the data from these RTD tests and on the results obtained from
those analyses.
2 . 0 Stratifying the Test Fleet
The test data used for these analyses are the same data used
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May 20, 1998
renumbered as M6.EVP.001). The data were obtained by combining
RTD tests performed on 2 70 vehicles tested by the Coordinating
Research Council (CRC) and EPA in separate programs. The
distribution of the fleet is given in Table 2-1.
Table 2-1
Distribution of Test Vehicles
Vehicle Type
Proaram
Cars
Trucks
Pre-80 Carbureted
CRC
38
1 3
EPA
4
2
80-85 Carbureted
CRC
0
47
EPA
1 3
5
80-85 Fuel Injected
CRC
0
3
EPA
9
0
86-95 Carbureted
CRC
0
7
EPA
8
0
86-95 Fuel Injected
CRC
0
43
EPA
67
1 1
In that previous draft report, EPA noted that the resting
loss and diurnal emissions from vehicles classified as gross
liquid leakers (vehicles identified as having substantial leaks of
liquid gasoline, as opposed to simply vapor leaks) are
significantly different from those of the remaining vehicles.
Based on that observation, the analyses in that previous report
were performed separately for those two groups. That separation
of analyses will be continued throughout this report.
The two testing parameters in the EPA programs that were
found (in M6.EVP.001) to affect the RTD test results are:
the Reid vapor pressure (RVP) of the test fuel and
the temperature cycle.
Similarly, the two vehicle parameters that were found to affect
the RTD test results are:
the model year range:
1) 1971 through 197 9
2) 1980 through 1985
3) 1986 through 1995
the fuel delivery system:
1) carbureted (Carb) or
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May 20, 1998
Also, since many of the vehicles were recruited based on the
pass/fail results of two screening tests (i.e., canister purge
measured during a four-minute transient test and pressurizing the
fuel system using the tank lines to the canister), each of those
resulting stratum was further divided into the following three
substrata:
vehicles that passed both the purge and pressure tests,
vehicles that failed the purge test, but passed the
pressure test, and
vehicles that failed the pressure test (including both
the vehicles that passed the purge test as well as those
that failed the purge test).*
2 . 1 Evaluating Untested Strata
As noted in M6.EVP.001, no pre-1980 model year, FI vehicles
were recruited because of the small numbers of those vehicles in
the in-use fleet.
Since the FI vehicles lack a carburetor bowl, they also lack
the evaporative emissions associated with that. This suggests
that the resting loss and diurnal emissions of the pre-1980 FI
vehicles are likely to be no higher than the corresponding
emissions of the pre-1980 carbureted vehicles. For M0BILE6, EPA
proposes to estimate the RTD emissions of the (untested) pre-1980
FI vehicles with the corresponding emissions of the pre-1980
carbureted vehicles. This should be a safe assumption since any
actual differences between these strata should be balanced by the
relatively small number of these FI vehicles in the in-use fleet.
3 . 0 Evaporative Emissions Represented by the RTD Test
As described in M6.EVP.001, the results from the real-time
diurnal (RTD) tests can be used to model the following two
categories of evaporative emissions:
1) "Resting loss" emissions are always present and
relatively weakly related to the ambient temperature
(see Section 7.1 of M6.EVP.001) as opposed to diurnal
emissions which are related to the rise in temperature.
That report calculated the hourly resting loss emissions
to be the mean of the RTD emissions from hours 19
through 24 at the nominal temperature for hour 24.
For only one of the fuel delivery system/model year range groupings (i.e.,
pre-1980 carbureted vehicles) was there sufficient data to distinguish
between the vehicles that failed both the purge and pressure tests and
those that failed only the pressure test. Therefore, these two substrata
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May 20, 1998
6.8 RVP gasoline. We then plotted the calculated hourly resting
loss and diurnal emissions.
The preceding graph is representative of the hourly resting
loss and diurnal emissions of the mean of a single stratum. Each
combination of the following five parameters (previously discussed
in Section 2.0) can produce a different graph:
the model year range,
the fuel delivery system,
the RVP of the test fuel,
the temperature cycle, and
the results of the purge and pressure tests.
In the database used for these analyses, there are:
five combinations of fuel delivery system and model year
range,
six combinations of temperature cycle and fuel RVP, and
three combinations of results of the purge and pressure
tests.
Therefore, using the available data, we could theoretically
construct almost 90 such graphs. (Actually, there are only 86
graphs for which there are any data, of which 58 are based on the
average of no more than four RTD tests.) An alternative approach,
involving a single graph is discussed in the following section.
4 . 0 Hourly Diurnal Emissions
4 . 1 Characterizing Hourly Diurnal Emissions by Strata
Diurnal emissions (either on a daily or hourly basis) can
vary substantially among vehicles within a single stratum and more
so among different strata. In an attempt to normalize the hourly
diurnal emissions, we calculated the percentage of the full (i.e.,
total 24-hour) diurnal emissions that is emitted each hour.
Graphing these percentages of hourly diurnal emissions against
time seemed to pictorially produce very consistent results among
the various strata, suggesting that averaging the hourly
percentage of daily diurnal emissions (across all of the tested
strata) would produce a representative result.
To test our hypotheses that the percent of daily diurnal
emitted hourly was independent of vehicle and test parameters, we
coded the RTD results to distinguish among:
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May 20, 1998
model year ranges,
fuel delivery system (i.e., carbureted versus FI),
pressure test results (i.e., pass versus fail),
temperature cycle, and
RVP of the test fuel.
This coding resulted in dividing the hourly results on 684 RTD
tests into 138 strata (many of them with only one or two tests).
Within each of those strata, we averaged the calculated diurnal
emissions for each of the first 19 hours. (We had previously
defined the average RTD emissions from hours 19 through 24 to be
the resting loss emissions. Therefore, the calculated diurnal
emissions was zero for hour 19.) We then regressed that hourly
percentage of the full diurnal's emission against those six coded
variables plus four other variables related to the hourly
temperature change, the total temperature change since the start
of the test, and products of those temperature changes. The
result of that regression analysis is given (on the following
page) as Table 4-1. The analysis indicates that none of those six
vehicle and test parameters is statistically significant (at any
level of significance) in estimating the hourly percentage of
diurnal emissions. Additionally, the correlation coefficients
were calculated, and they were all zero confirming the lack of
significance of those six variables.
Since the possibility existed that our analysis was skewed
because we had applied equal weighting to each of those 138 test
grouping even though some were represented by as many as 3 9 test
while most were represented by only a few tests. Therefore, the
regression analysis was repeated but restricting the sample to
only those test strata containing at least four tests (reducing
the analysis to only 40 strata), at least six tests (reducing the
analysis to only 26 strata), and at least 10 tests (reducing the
analysis to only 22 strata). In every case, those same six
variables were determined to be statistically not significant.
We, therefore, proceeded with calculating a (representative)
hourly percentage of diurnal emissions for all vehicles that are
not gross liquid leakers by averaging the individual hourly
percentages. (Gross liquid leakers will be analyzed separately.)
Table 4-2 is a listing of those resulting percentages in tabular
form.
Later in the report (Section 6.1), we will repeat the
regression analysis using the temperature variables from this
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Table 4-1
Regression of Diurnal Emissions
(Vehicles Other Than Gross Liquid Leakers)
Dependent variable is:
No Selector
Percent of 24-Hour Diurnal
2736 total cases of which 114 are missing
R squared = 49.9% R squared (adjusted) = 49.7%
s = 0.0431 with 2622 - 11 = 2611 degrees of freedom
Source
Regression
Residual
Sum of Squares
4.82643
4.85250
df
1 0
261 1
Mean Square
0.482643
0.001858
F-ratio
260
Variable
Constant
Coefficient
0.028265
s.e. of Coeff
0.0105
t-ratio
2.69
prob
0.0072
Fuel RVP
0.000000
0.0007
0.000
1 .0000
Hourly
Temperature
Change
0.000986
0.0008
1.19
0.2328
Total
Temperature
Change
-0.002850
0.0005
-5.64
0.0001
Hou rly*T otal
Temperature
Changes
0.000635
0.0000
11.0
0.0001
Square of Total
Temperature
Change
0.000241
0.0000
13.1
0.0001
Car vs Truck
0.000000
0.0018
0.000
1 .0000
Model Year
Range
0.000000
0.0014
0.000
1 .0000
Carbureted vs
FI
0.000000
0.0021
0.000
1 .0000
Pressure Test
0.000000
0.0018
0.000
1 .0000
Temperature
Cycle
0.000000
0.0001
0.000
1 .0000
Presenting the data from Table 4-2 in a bar chart format
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From the data in Table 4-2 and Figure 4-1, we make the following
observations:
Although the daily ambient temperatures do not peak
until the end of the ninth hour of the test (i.e., at
3 PM), the average hourly diurnal emissions peak during
hour seven (from noon to 1 PM) . That is, the mode of
this distribution occurs during the seventh hour.
The median of this distribution occurs during the ninth
hour. That is, the diurnal emissions that occur
through the first nine hours are approximately half (57
percent) of the full day's diurnal emissions.
Almost 43 percent of the full day's diurnal emissions
occur in the morning (i.e., between 6 AM and noon).
Approximately 98 percent of the full day's diurnal
emissions occur from 6 AM through 8 PM (i.e., from hours
one through 14).
Most (53 percent) of the full day's diurnal emissions
occur during the four-hour period from 10 AM through
2 PM (i.e., test hours five through eight).
Almost 19 percent of the full day's diurnal emissions
occur during the cool-down period (i.e., test hours 10
through 24).
While these observations are not used in the following
analyses, they are useful in gaining a perspective of the
distribution of the diurnal emissions. All of these observations
are based on data from tests in which daily temperature cycled
over a 24-degree range. Other temperature cycles are discussed in
Section 8.1.
4.2 Calculating Hourly Diurnal Emissions by Strata
In the previous report (M6.EVP.001), we developed equations
that would predict the full day's diurnal emissions based on the
RVP of the fuel, on the temperature cycle, and on the vehicle
grouping (fuel delivery system plus model year range). In that
report, we used both the RVP of the fuel and the ambient
temperature to estimate the vapor pressure (VP). (The formula
used to estimate VP is given in Appendix B. The VP coincides with
RVP at 100° F.) The VP was then used to create a new parameter
that was used as the variable on which diurnal emissions were
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(VPhigh - VPLOW) * (VPhigh + VPLOW) I 2
Where
VPhigh is the VP associated with the day's high
temperature.
VPlow is the VP associated with the day's low
temperature.
For each of the six vehicle groups and each of the three purge /
pressure recruitment groups, we created an equation that would
model the full day's diurnal emissions. (Those equations are
reproduced in Appendix C.)
Therefore, to estimate the mean hourly diurnal emissions,
MOBILE will first use the equations in Appendix C to estimate the
full day's diurnal emissions, then multiply that value by the
hourly percentages from Table 4-2.
5 . 0 Hourly Diurnal Emissions for Gross Liquid Leakers
In the previous report (M6.EVP.001), vehicles classified as
gross liquid leakers were analyzed separately from the other
vehicles due to both:
the order of magnitude difference in resting loss and
diurnal emissions, as well as,
the mechanisms that produce those high emissions.
For these vehicles, the primary source of the evaporative
emissions is the leakage of liquid (as opposed to gaseous) fuel.
Therefore, we would expect the diurnal emissions from these
vehicles to be less sensitive to changes in ambient temperature
than the diurnal emissions from vehicles that do not have
significant leaks of liquid gasoline.
The analyses in Sections 4.1 and 4.2 were repeated for the
vehicles identified as being gross liquid leakers. The hourly RTD
results of those test vehicles is given in Appendix D. These
tests indicate that several of the higher emitting vehicles
exhibited unusually high emissions during the first one or two
hours of the test (relative to their emissions for the next few
hours). One possible explanation is that during the first two
hours of the RTD test, the analyzer was measuring gasoline vapors
that resulted from leaks that occurred prior to the start of the
test. These additional evaporative emissions (if they existed as
hypothesized) would have resulted in a higher RTD result than this
vehicle would actually have produced in a 24 hour period. In the
last column of Appendix D, we attempt to compensate for what
appears to be simply an artifact of the test procedure. The
modified RTD evaporative emissions were then converted to diurnals
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May 20, 1998
completely independent of ambient temperature, subtracting that
amount (8.52 grams per hour) from each hour's modified RTD
emissions, and then dividing by the total diurnal to yield the
hourly percentages in Table 5-1.
Table 5-1
Distribution of Hourly Diurnal Emissions
of Gross Liquid Leakers
(Hourly Emissions as Percent of 24-Hour Diurnal)
Hour
Time of Day
Emissions
Hour
Time of Day
Emissions
1
6 - 7 AM
1 .82%
1 3
6 - 7 PM
4.53%
2
7 - 8 AM
3.64%
1 4
7 - 8 PM
2.99%
3
8 - 9 AM
7.27%
1 5
8 - 9 PM
1 .95%
4
9 - 10 AM
8.63%
1 6
9 - 10 PM
1 .73%
5
10 - 11 AM
9.19%
1 7
10 - 11 PM
1 .48%
6
11 AM - Noon
9.80%
1 8
11 PM - Midnight
1 .28%
7
Noon - 1 PM
9.64%
1 9
Midnight - 1 AM
0 %
8
1 - 2 PM
9.61%
20
1 - 2 AM
0 %
9
2 - 3 PM
7.95%
2 1
2 - 3 AM
0 %
1 0
3 - 4 PM
7.50%
22
3 - 4 AM
0 %
1 1
4 - 5 PM
5.89%
23
4 - 5 AM
0 %
1 2
5 - 6 PM
5.09%
24
5 - 6 AM
0 %
A comparison of the values in Table 5-1 with the
corresponding values in Table 4-2 (or Figure 5-1 with Figure 4-1)
indicates that the distribution of emissions for the gross liquid
leakers is flatter than for the other vehicles, achieving most of
the peak value by the third hour (i.e., after a temperature rise
of approximately eight degrees Fahrenheit), and then maintains
that high level of emissions until the ambient drops to within 15
to 2 0 degrees of the initial temperature. This tends to confirm
the hypothesis that the diurnal emissions from vehicles with
significant leaks of liquid gasoline are less sensitive to changes
in ambient temperature than the diurnal emissions from vehicles
that do not have significant leaks of liquid gasoline.
We calculated (from Appendix A) both the hourly change in
temperature as well as the total change in temperature for each of
the first 18 hours of the RTD test, and then regressed the diurnal
emissions from Table 5-1 against those two variables. From this
empirical (i.e., data driven) approach, we obtain the regression
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Table 5-2
Regression of Diurnal Emissions
(Gross Liquid Leakers)
Dependent variable is
Percent of 24-
Hour Diurnal
No Selector
R squared = 98.0%
R squared (adjusted) = 97.8%
s = 0.0048 with 18
-3=15 degrees of freedom
Source Sum of Squares df
Mean Square
F-ratio
Regression
0.017169 2
0.008584
371
Residual
0.000347 1 5
0.000023
Variable
Coefficient s.e. of Coeff
t-ratio
prob
Constant
0.008958 0.0025
3.62
0.0025
Hourly
Temperature
0.007383 0.0004
17.9
0.0001
Change
Total
Temperature
0.003053 0.0002
20.3
0.0001
Change
This regression analysis produces the following equation that
predicts hourly diurnal emissions from the sub-fleet of gross
liquid leakers:
Hourly Diurnal Emissions (grams of HC)
100.29 * [ 0.008958
+ ( 0.007383 * Hourly_Temperature_Change )
+ ( 0.003053 * Total_Tem peratu re_Change ) ]
If the equation produces a negative value, then zero will be used.
Where 100.29 is the average 24-hour diurnal for gross liquid
leakers (from Section 10.2 of M6. EVP. 001) . Omitting the 100.29
produces the estimate of percent of daily diurnal (instead of
actual grams). Graphing that linear equation as a solid line with
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May 20, 1998
Total 24-Hour Diurnal Emissions (grams)
= 100.29 * ( 0.2 + ( 0.03333 * Diurnal_Te m pe rat u re_Range ) )
Where 100.29 is the average 24-hour diurnal for gross liquid
leakers (from Section 10.2 of M6.EVP.001), and where the
Diurnal_Temperature_Range is the difference of the daily high
temperature minus the daily low temperature.
This equation predicts a 24-hour total diurnal emission of
20.06 grams for a day during which the temperatures do not change.
This is not reasonable since diurnal emissions result from the
daily rise in ambient temperatures. Therefore, EPA proposes to set
the 24-hour diurnal equal to zero for a diurnal temperature range
of zero degrees Fahrenheit. For diurnal temperature ranges between
zero and ten degrees Fahrenheit, EPA proposes to calculate the 24-
hour diurnal as increasing linearly from zero to 53.48 grams (i.e.,
the value predicted by the equation for a diurnal temperature range
of 10 degrees).
6 . 0 Interrupted Diurnal
Many vehicles do not actually experience a full (i.e., 24-
hour) diurnal. That is, their soak is interrupted by a trip of
some duration. This results in what this report refers to as an
"interrupted diurnal." The following example illustrates such an
interrupted diurnal.
6 . 1 Example of an Interrupted Diurnal
For the purpose of this example, we will use the type of
vehicle and conditions in Figure 3-1 (i.e., a 1986-95 model year
FI vehicle that passes both the purge and pressure tests, that
uses a 6.8 RVP fuel, and where the daily temperature profile is
the standard 72° to 96° F cycle from Appendix A). For those
conditions, we will assume the following vehicle activity:
1. The vehicle soaks over night.
2. Shortly after 9 AM (corresponding to the fourth hour of
the RTD test), the vehicle is driven (for 15 to 50
minutes). The vehicle reaches its destination and is
parked by 10 AM. (That is, the entire drive takes place
during RTD test hour 4.)
3. The vehicle remains parked until the following morning.
The resting loss emissions would continue throughout the entire
24-hour period of this example. However, the other types of
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May 20, 1998
1. The first segment of this example (from 6 AM through 9
AM) corresponds to the first three hours of the RTD
test. Therefore, the diurnal emissions are represented
by the first three hours in Figure 3-1.
2. The evaporative emissions associated with the morning
drive are the "running loss" emissions (for that vehicle
stratum, fuel RVP, and temperature cycle) and the
continuing resting loss emissions. Thus, the running
loss emissions replace the diurnal emissions for the
fourth hour (from 9 AM through 10 AM). Due to the
limitations of the activity data (see M6.FLT.006), we
will allocate the entire hour interval (rather than
fractional intervals) to running loss emissions even if
the actual drive is much shorter than one hour. (Since
running loss emissions are calculated as a function of
distance, rather than of time, this approach will not
change the total running loss emissions. Also, since
MOBILE6 will not report emissions for intervals smaller
than one hour, this approach will not change the
calculated emissions.)
3. While the vehicle was being driven, the temperature in
its fuel tank was gradually rising by about 10 to 3 0
degrees Fahrenheit*. After the vehicle stops and until
this elevated fuel temperature drops to become equal
with the ambient air temperature, the vehicle will be
experiencing what is referred to as "hot soak"
emissions.
In M0BILE5 (and M0BILE4.1), EPA determined the time
required to stabilize the temperatures was two hours.
Therefore, the hot soak emissions replace the diurnal
emissions for the fifth and sixth hours (from 10 AM
through noon). For calculation purposes, the entire hot
soak emissions will be credited to the first hour.
4. At noon, the hourly diurnal emission will resume but in
a modified form due to the heating of the fuel that is
* In SAE Paper Number 931991 (referenced in Appendix B), the authors discuss
the increase in tank temperatures as a function of trip duration. The
data presented in that report (in Table 4) suggest that for trips of over
five minutes in length, fuel tank temperature increases as a function of
the trip length. A 15 minute trip would be associated (on average) with
an increase in tank temperature of about 12 to 13 degrees Fahrenheit. A
30 minute trip would be associated with an increase in tank temperature of
about 20 degrees Fahrenheit, while a one hour trip would be associated
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May 20, 1998
associated with the drive. To modify the hourly diurnal
emissions, we will make the following assumptions:
At the beginning of the driving cycle, the ambient
temperature was 80.3° F (from Appendix A), and the
effect of the drive was to increase the fuel tank
temperature to 95° F (what would be expected from a
trip just under 20 minutes in length). By the end
of the hot soak period (noon), we are assuming that
the falling fuel tank temperature will have reached
equilibrium with the rising ambient temperature
(which would have climbed to 93.1° F by noon).
The pressure that is driving these interrupted
diurnal emissions (starting at noon) results from
the fuel being heated to above the temperature which
occurred at the end of the hot soak (in this
example, 93.1° F) . Therefore, had the ambient
temperature not risen above 93.1° F, there would
have been no further diurnal emissions for the
remainder of that day, only resting loss emissions.
5. Calculating emissions of an interrupted diurnal:
This suggests that the interrupted diurnal emissions
will end once the ambient temperature returns to its
starting point (i.e., 93.1° F) . Since the ambient
temperature will return to 93.1° at 5:25 PM, we will
assume the after 5:25 PM, there are only resting
loss emissions. Therefore, we need to modify the
hourly diurnal emissions so that the modified values
are zero after 6 PM (i.e., from test hour 13 through
24) .
One such method of modifying the hourly diurnal
values is to create a function that closely
approximates the hourly emissions (in a fashion
similar to what was done in Table 5-2).
For the analysis that produced Table 5-2, we only needed to
consider the temperature change within the given hour and the
total change (above the initial temperature) to closely estimate
the hourly diurnal emissions from vehicles having significant
leaks of liquid gasoline. It is likely that the reason such a
simple model was so successful was that the primary mechanism of
the diurnal emissions of such vehicles (i.e., the leakage of
liquid gasoline) is a fairly simple process. Attempting to model
the diurnal emissions from vehicles that were not gross liquid
leakers required a more complicated set of (independent) variables
and produced hourly estimates that were not as close to the values
in Table 4-2. The regression analysis that required the least
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DRAFT
May 20, 1998
yet produced one of the best fits (of predicted versus actual) is
given in Table 6-1.
Table 6-1
Regression of Percent of Total Diurnal Emissions
(Non-Gross Liquid Leakers)
Dependent variable is
Percent of 24-
Hour Diurnal
No Selector
R squared = 95.8%
R squared (adjusted) = 95.3%
s = 0.0110 with 18
-3=15 degrees of freedom
Source Sum of Squares df
Mean Square
F-ratio
Regression
0.041867 2
0.020933
1 72
Residual
0.00183 1 5
0.000122
Variable
Coefficient s.e. of Coeff
t-ratio
prob
Constant
0.01 102 0.0042
2.6
0.0201
Hourly
Temperature
Change
0.000819 0
12.1
0.0001
Times Total
Temperature
Change
Square of Total
Temperature
0.000152 0
12.4
0.0001
Change
From Table 6-1, we obtain the following equation predicting hourly
diurnal emissions:
Percent Hourly Diurnal Emissions (as percent of 24-hour diurnal)
0.01102
+ 0.07383 * Hourly_Temperature_Change * Total_Temperature_Change
+ 0.000152 * Square of Total_Temperature_Change
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May 20, 1998
for the non-leakers. However, because data are not available for
interrupted diurnals, EPA proposes to use this equation to
estimate the hourly diurnal emissions of the interrupted diurnal
of the non-leakers. (For the vehicles classified as gross liquid
leakers, EPA proposed in Section 5.0 to use the corresponding
equation for both situations.)
Returning to the example at the beginning of Section 6.1, we
make the following observations:
Requiring the estimated hourly emissions of the
interrupted diurnal to drop to zero once the ambient
temperature drops to the starting temperature results in
a shortened period of emissions for the interrupted
diurnal.
Since diurnal emissions are dependent upon rising
ambient temperatures to induce the pressure-driven
evaporative emissions, the diurnal must begin while the
air temperature is increasing (i.e., prior to 3 PM) .
As corollaries to this observation:
There can be no interrupted diurnal emissions
following a drive that ends after 1 PM.
A daily activity consisting of several trips, with
each period of inactivity between the trips no
more than two hours and the final trip ending
after 1 PM, will produce no diurnal evaporative
emissions. (However, there will be running loss
and hot soak emissions associated with each trip.)
6 .2 Calculating Emissions of an Interrupted Diurnal
In the preceding paragraphs, we analyzed one situation in
which the hot soak (following a period of vehicle operation) ended
during the fifth hour (i.e., between 10 and 11 AM). EPA then
proposed a method for calculating the hourly emissions that would
have resulted from the abbreviated diurnal cycle that began at 11
AM. Repeating this procedure for (interrupted) diurnals beginning
at each hour of the day produces seven interrupted diurnals plus
the full-day diurnal. The values for each of the interrupted
diurnals are given in Appendix E. (The values for the full 24-
hour diurnal were simply copied from Table 4-2.) To estimate the
grams of evaporative emissions emitted in any given hour, M0BILE6
will multiply the appropriate percentage from Appendix E times the
full 24-hour diurnal's emission (calculated in Appendix C for each
vehicle stratum and for each combination of ambient temperature
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May 20, 1998
6 .3 Interrupted Diurnals of Gross Liquid Leakers
In Section 5.0, we estimated the hourly diurnal emissions
from vehicles with gross leaks of liquid gasoline as a linear
function of both the temperature change during that hour and the
total temperature change up through that hour.
The basic premise in the preceding section was that the base
temperature for calculating interrupted diurnals is the ambient
temperature at the beginning of the diurnal period, which is also
the end of the hot soak period. For each hour of the interrupted
diurnal, we calculate both the temperature change during that hour
and the total temperature change from the beginning of the
interrupted diurnal through that hour. The regression equation
following Table 5-2 will then produce the hourly emissions of the
interrupted diurnal of gross liquid leakers.
7 . 0 Assumptions Related to Hourly Emissions
Two basic assumptions related to estimating hourly emissions
were made in this analysis:
the distribution of hourly diurnal emissions being
independent of vehicle and test parameters (except for
leaker status)
and
the approach used in Section 6 on estimating diurnals
following an interruption (i.e., a trip).
7 . 1 Distribution of Hourly Diurnal Emissions
In Section 4, we assumed that the distribution of hourly
diurnal emissions (as a percentage of the full day's diurnal
emission) for non-leakers is independent of all of the vehicle and
test parameters. Thus, all that is necessary to obtain the hourly
diurnal emissions is to multiply percentages in Table 4-2 by the
full day's diurnal (calculated in Appendix C) for non-leakers.
For gross liquid leakers, the equation following Table 5-2 will
generate the hourly diurnal emissions.
7.2 Assumptions for Interrupted Diurnals
The discussion of interrupted diurnals (in Section 6)
requires a number of assumptions.
First, interrupting the diurnal with a trip will result in an
increase in fuel tank temperature. However, the amount of that
temperature rise is dependent not only upon the duration of the
trip (see footnote on page 14) but also on other parameters (e.g.,
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DRAFT
May 20, 1998
flow, etc.). Similarly, the time necessary for the elevated fuel
temperature to decrease to equal the rising ambient temperature is
dependent on factors such as the actual temperature cycle (see the
discussion on temperature cycles in Section 6.2), fuel tank
design, fuel tank materials, and air flow. EPA proposes to
continue the approach used since M0BILE4.1 of assuming that
exactly two hours is necessary to stabilize the temperatures.
(Also, this approach of rounding off the vehicle activity periods
to whole hours is also consistent with the vehicle activity data
that will be used in M0BILE6.)
8 . 0 Other Assumptions
In this report, EPA proposes using the total 24-hour diurnal
emissions as a basis for calculating the diurnal emission from
each individual hour. Another set of assumptions indirectly
affected the calculation of hourly emissions by directly affecting
the calculation of the full (24-hor) diurnal emission.
8. 1 Temperature Ranges
All of the tests used in this analysis were performed using
one of the three temperature cycles in Appendix A. This results
in all of the resting loss data being measured at only three
temperatures (i.e., 60, 72, and 82 °F). In Appendix F, we
presented regression equations (developed in M6.EVP.001) to
estimate hourly resting loss emissions at theoretically any
temperature. We will limit that potentially infinite temperature
range as we did in the previous version of MOBILE, specifically:
1) We will assume, for vehicles other than gross liquid leakers,
there are no resting loss emissions when the temperatures are
below or equal to 40°F. (This assumption was used
consistently for all evaporative emissions in M0BILE5.)
For temperatures between 40°F and 50°F, EPA proposes to
interpolate between an hourly resting loss of zero and the
value predicted in Appendix F for 50°F.
2) We will assume, for vehicles other than gross liquid leakers,
that when the ambient temperatures are above 105°F that the
resting loss emissions are the same as those calculated at
105 0 F.
Since vehicles classified as gross liquid leakers were not handled
separately in MOBILES, we will now make a new assumption
concerning the resting loss emissions of those vehicles as relates
to temperatures. Specifically:
3) For the vehicles classified as gross liquid leakers, we will
assume the resting loss emissions are completely independent
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DRAFT
May 20, 1998
In a similar fashion, the equations developed in this report
to estimate hourly diurnal emissions theoretically could also be
applied to any temperature cycle. EPA proposes to limit those
functions by making the following assumptions:
1) Regardless of the increase in ambient temperatures, there are
no diurnal emissions until the temperature exceeds 40°F.
(This assumption was used consistently for all evaporative
emissions in M0BILE5.)
For a temperature cycle in which the daily low temperature is
below 40°F, EPA proposes to calculate the diurnal emissions
for that day as an interrupted diurnal that begins when the
ambient temperature reaches 40 °F.
2) The 24-hour diurnal emissions will be zero for any
temperature cycle in which the difference between the daily
high and low temperatures (i.e., the "diurnal temperature
range") is no more than zero degrees Fahrenheit. For
temperature cycles in which the diurnal temperature range is
between zero and ten degrees Fahrenheit, the 24-hour diurnal
emissions will be linear interpolation of the predicted value
for the ten-degree cycle and zero.
8.2 Estimating Vapor Pressure
EPA is proposing to use the fuel's RVP and the Clausius-
Clapeyron relationship to calculate the fuel's vapor pressure at
each ambient temperature (see Figure B-l). This approach is the
equivalent of attempting to draw a straight line based on only a
single point since RVP is the vapor pressure calculated at a
single temperature (100° F). Since two different fuels could have
the same vapor pressure at a single temperature, it is possible
for two fuels to have the same RVP but different vapor pressure to
temperature curves. However, the two vapor pressure curves would
yield similar results near the point where they coincide (i.e., at
100° F). Thus, at temperatures where ozone exceedences are likely
to occur, this assumption should produce reasonable estimates of
diurnal emissions.
8.3 Heavy-Duty Vehicles (HDGVs)
The analyses in this report were based only on RTD tests of
light-duty gasoline-powered vehicles (LDGVs) and light-duty
gasoline-powered trucks (LDGTs). Since the data did not indicate
a significant difference between the RTD emissions from LDGVs and
LDGTs, they were combined in a single group of analyses.
Since no RTD testing was performed on any HDGVs, we will use
the same approach that was used in the earlier version of MOBILE.
That is, the ratio of diurnal emissions of the HDGVs to those of
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DRAFT
May 20, 1998
evaporative emission standards. Translating that sentence into an
equation yields:
DIhdgv = DIldgt * [ ( 1.5 * 0.875 ) + ( 2.0 * 0.125 ) ]
= 1.5625 * DIldgt
Where, DIhdgv is the full day's diurnal
emissions from the HDGVs.
DIldgt is the full day's diurnal
emissions from the corresponding
LDGTs.
EPA proposes to use this equation to estimate the mean of the
24-hour diurnal emissions from HDGVs. EPA also proposes to
calculate the hourly diurnal emissions by multiplying that
estimated 24-hour diurnal emission value by the percentages in
Table 4-2 to predict the hourly diurnal emissions from HDGVs.
EPA proposes to use the corresponding formula for resting
losses (obviously changing Dl to "hourly resting losses").
8.4 High Altitude Evaporative Emissions
EPA proposes to continue to use the multiplicative adjustment
factor of 1.30 (from previous version of MOBILE) to adjust both
the hourly resting loss and 24-hour (and hourly) diurnal emissions
for high altitude.
8.5 Motorcycles (MC)
RTD evaporative emission tests were not performed on
motorcycles (MC). In M0BILE5, the resting loss and diurnal
emissions from motorcycles were modeled using carbureted vehicles
equipped with open-bottom canisters. EPA proposes to continue
that approach to continue in M0BILE6.
We first identified the 109 RTD tests of carbureted vehicles
equipped with open-bottom canisters (all 1988 or earlier model
years), and calculated both the hourly resting loss (associated
with the test's low temperature) and the full-day's diurnal for
each of those 109 tests. The diurnal emissions were then
regressed against both the vapor pressure product term (from
Section 4.2) and the age of each test vehicle. As illustrated in
Table 8-1, each of those variables is statistically significant.
MOBILE6 will use the linear regression equation generated by that
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DRAFT
May 20, 1998
Table 8-1
Regression of Diurnal Emissions
(Simulated Motorcycle Fleet)
Dependent variable is:
No Selector
Diurnal
R squared = 59.0% R squared (adjusted) = 58.3%
s = 10.20 with 109 - 3 = 106 degrees of freedom
Source Sum of Squares
Regression 15892.9
Residual 1 1024.5
df
2
1 06
Mean Square
7946.46
104.005
F-ratio
76.4
Variable Coefficient
Constant -36.7971
age 0.855491
VP_Product 0.058251
s.e. of Coeff
4.5620
0.1 894
0.0051
t-ratio
-8.07
4.52
11.5
prob
0.0001
0.0001
0.0001
Translating that regression analysis into an equation yields:
24-Hour Diurnal Emissions (grams) for Motorcycles
= -36.7971 + ( 0.855491 * Vehicle.Age )
+ ( 0.058251 * VP_Product_Term )
EPA proposes to use this equation to estimate the mean of the 24-
hour diurnal emissions from motorcycles.
For M0BILE6, EPA proposes to multiply the estimated 24-hour
diurnal emissions from those vehicles (calculated from the
preceding equation) by the percentages in Table 4-2 to predict the
hourly diurnal emissions from motorcycles.
Similarly, the hourly resting loss emissions were regressed
against both the temperature at which those values were calculated
(i.e., the daily low temperature) and the age of each test
vehicle. As illustrated in Table 8-2, only the vehicle age is
statistically significant. It is possible that temperature was
not found to be statistically significant simply due to the fact
that most of the resting loss emissions were calculated at a
single temperature (72 °F). Since temperature should be an
important factor in determining resting loss emissions, EPA
proposes to use for MOBILE6 the linear regression equation
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DRAFT
May 20, 1998
Table 8-2
Regression of Hourly Resting Loss Emissions
(Simulated Motorcycle Fleet)
Dependent variable is:
No Selector
Hourly
Resting Loss
R squared = 5.6%
s = 0.1346 with
R squared (adjusted) = 3.8%
109 - 3 = 106 degrees of freedom
Source
Regression
Residual
Sum of Squares df
0.1 14078 2
1.92123 1 06
Mean Square
0.057039
0.018125
F-ratio
3.15
Variable
Constant
age
Temperature
Coefficient s.e. of Coeff
0.044345 0.1572
0.006134 0.0025
0.000859 0.0022
t-ratio
0.282
2.45
0.399
prob
0.7784
0.01 59
0.6909
Translating that regression analysis into an equation yields:
Hourly Resting Loss Emissions (grams) for Motorcycles
= 0.044345 + ( 0.006134 * Vehicle.Age )
+ ( 0.000859 * Temperature )
EPA proposes to use this equation to estimate the hourly resting
loss emissions from motorcycles.
8.6 Pre-Control Vehicles
Non-California vehicles prior to the 1972 model year were not
required to meet an evaporative emission standard. These
uncontrolled vehicles would simply vent vapors to the atmosphere
as pressure built up. Since that situation is similar to that of
a controlled vehicle with a vapor leak, we hypothesized that the
resting loss and diurnal evaporative emissions of the pre-1972
vehicles would be comparable to the emissions of the pre-1980
vehicles that had failed the pressure test.
To characterize the hourly resting loss emissions from these
pre-control vehicles, we proceeded in a similar fashion to the
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DRAFT
May 20, 1998
pre-1980 vehicles in our study that both had failed the pressure
test and were tested over the full range of fuels and temperature
cycles. Possibly due to that small sample size, a regression of
those data produced a slope of resting loss versus temperature
that was not statistically different from zero. Since most of the
RTD tests (i.e., 37 of 47) that were performed on the 34 candidate
vehicles were run over the same temperature cycle (i.e., 72 to 96
degrees), the variable "temperature" would not make a useful
independent variable to analyze those 47 resting loss results.
We, therefore, decided to use the same slope (0.002 812) that was
developed in that earlier report. However, the variable "age" was
found to be statistically significant. Combining the results of
regressing the data against age with the previously calculated
temperature slope yields the following equation:
Hourly Resting Loss (grams) = -0.768438
+ ( 0.002812 * Temperature )
+ ( 0.040528 * Vehicle Age in Years )
EPA proposes to use this equation to estimate the hourly resting
loss emissions from pre-control vehicles.
To characterize the full day's diurnal emissions from these
pre-control vehicles, we proceeded in a similar fashion to the
approach in the previous report. In the preceding paragraph we
noted that only two of the candidate vehicles (i.e., pre-1980
vehicles that failed the pressure test) were tested over the full
range of fuels and temperature cycles. Attempting to analyze the
resting loss emissions of those two vehicles as a function of
temperature did not produce usable results. However, the
corresponding analysis for diurnal emissions as a function of the
vapor pressure product term produced satisfactory results, as shown
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DRAFT
May 20, 1998
Table 8-3
Regression of Diurnal Emissions
(Simulated Pre-Control Fleet)
(Based on Two Vehicles)
Dependent variable is:
No Selector
Diurnal
R squared = 92.3%
s = 5.503 with 6
R squared (adjusted) = 90.4%
-2 = 4 degrees of freedom
Source
Regression
Residual
Sum of Squares df
1456.41 1
121.136 4
Mean Square
1456.41
30.284
F-ratio
48.1
Variable
Constant
VP_Product
Coefficient s.e. of Coeff
-6.52265 6.1 75
0.051 15 0.0074
t-ratio
-1.06
6.93
prob
0.3504
0.0023
As previously stated, the diurnal emissions from these tests
are almost exclusively from tests performed over a single
temperature cycle using a single fuel RVP (i.e., 6.8 psi RVP fuel
over the 72 to 96 degree cycle). Thus, using a variable for vapor
pressure with the full set of 47 tests would not be productive.
However, as with the resting loss emissions, we used the preceding
coefficient (0.05115) to estimate diurnal emissions (based on the
vapor pressures) and then regressed the calculated residuals
against vehicle age. These two regression analyses yield the
following equation:
24-Hour Diurnal (grams) = -40.6751 2
+ ( 0.05115 * VP_Product_Term )
+ (1.41114 * Vehicle_Age_in_Years )
EPA proposes to use this equation to estimate the 24-hour diurnal
emissions from pre-control vehicles.
For M0BILE6, EPA proposes to multiply the estimated 24-hour
diurnal emissions from those vehicles (calculated from the above
equation) by the percentages in Table 4-2 to predict the hourly
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DRAFT
May 20, 1998
8 .7 Duration of Diurnal Soak Period
The analyses in this report were based on diurnals of 24
hours or less in length. In the real-world, the soak period could
run for longer periods of time. Estimating diurnal emissions when
the soak period is a multiple of 24 hours will be analyzed in
report number M6.EVP.003.
EPA's proposal on how to classify a diurnal that follows an
interrupted diurnal is based on EPA's hypothesis of why a single-
day diurnal is different from a multiple-day diurnal. EPA
believes that as the days progress (during a multiple day
diurnal), the vehicle's evaporative canister becomes more heavily
loaded (with a possible back purge occurring during the night
hours). Therefore, if the first day's less than full diurnal is
almost equivalent to a 24-hour diurnal, EPA proposes to treat the
subsequent days as if the first day's diurnal were a complete
diurnal. From Appendix E, the regression equation predicts that
(interrupted) diurnals that begin no earlier than 9 AM, produce
less than one-half the emissions of the corresponding full day's
diurnal. Therefore, If a vehicle's first day's incomplete diurnal
begins no later than 8 AM, EPA proposes to treat the subsequent
days as if the first day's diurnal were a complete diurnal.
8 . 8 1996 and Newer Model Year Vehicles
Starting with the 1996 model year, EPA began certifying some
of the new LDGVs and LDGTs using the RTD test. Estimating the
resting loss and diurnal emissions from these vehicles will be
analyzed in report number M6.EVP.005.
For M0BILE6, EPA proposes to multiply the estimated 24-hour
diurnal emissions from those vehicles (to be calculated in
M6.EVP.005) by the percentages in Table 4-2 to predict the hourly
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May 20, 1998
Appendix A
Temperature Cycles (°F)
Hour
Temperati
60°-84°F
jres Cycling
72°-96°F*
Between
82°-106°F
Change in
Temperature
0
60.0
72.0
82.0
...
1
60.5
72.5
82.5
0.5
2
63.5
75.5
85.5
3.0
3
68.3
80.3
90.3
4.8
4
73.2
85.2
95.2
4.9
5
77.4
89.4
99.4
4.2
6
81.1
93.1
103.1
3.7
7
83.1
95.1
105.1
2.0
8
83.8
95.8
105.8
0.7
9
84.0
96.0
106.0
0.2
1 0
83.5
95.5
105.5
-0.5
1 1
82.1
94.1
104.1
-1.4
1 2
79.7
91.7
101.7
-2.4
1 3
76.6
88.6
98.6
-3.1
1 4
73.5
85.5
95.5
-3.1
1 5
70.8
82.8
92.8
-2.7
1 6
68.9
80.9
90.9
-1.9
1 7
67.0
79.0
89.0
-1.9
1 8
65.2
77.2
87.2
-1.8
1 9
63.8
75.8
85.8
-1.4
20
62.7
74.7
84.7
-1.1
2 1
61.9
73.9
83.9
CO
o
1
22
61.3
73.3
83.3
1
o
CD
23
60.6
72.6
82.6
i
o
24
60.0
72.0
82.0
1
o
CD
* The temperature versus time values for the 72-to-96 cycle are
reproduced from Table 1 of Appendix II of 40CFR86.
These three temperature cycles are parallel (i.e., identical
hourly increases/decreases). The temperatures peak at hour nine.
The most rapid increase in temperatures occurs during the fourth
hour (i.e., a 4.9° F rise).
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DRAFT
May 20, 199?
Appendix B
Vapor Pressure
Using the Clausius-Clapeyron Relationship
The Clausius-Clapeyron relationship is a reasonable estimate
of vapor pressure over the moderate temperature range (i.e., 60°
to 106°F)* being considered for adjusting the diurnal emissions.
This relationship assumes that the logarithm of the vapor pressure
is a linear function of the reciprocal (absolute) temperature.
In a previous EPA work assignment, similar RVP fuels were
tested, and their vapor pressures (in kilo Pascals) at three
temperatures were measured. The results of those tests are given
in the following table:
Nominal
Measured
Vapor Pressure (kPa)
RVP
RVP
75° F
100° F**
130° F
7.0
7.1
30.7
49.3
80.3
9.0
8.7
38.2
60.1
96.5
** The VPs at 100° F are the fuels' RVPs (in kilo Pascals).
Plotting these six vapor pressures (using a logarithm scale for
the vapor pressure) yields the graph (Figure B-l) on the following
page.
For each of those two RVP fuels, the Clausius-Clapeyron
relationship estimates that, for temperature in degrees Kelvin,
the vapor pressure (VP) in kPa will be:
Ln(VP) = A + (B / Absolute Temperature), where:
RVP A B
8.7 13.5791 -2950.47
7.1 13.7338 -3060.95
* C. Lindhjem and D. Korotney, "Running Loss Emissions from Gasoline-Fueled
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DRAFT
May 20, 1998
Figure B-l
Comparison of Vapor Pressure to Temperature
100
re
a.
J*
a>
3
in
in
a>
o
Q.
re
>
1 0
*
" ^
4
~ - RVP 8.1
0.0030 0.0031 0.0032 0.0033
Reciprocal of Temp (1/°K)
0.0034
We will assume that the specific fuels used in the vehicles that
were tested in this analysis had vapor pressure versus temperature
curves similar to the curves for these to two test fuels.
Extrapolating the trends in either the "A" or "B" values to fuels
with nominal RVPs of 6.3, 7.0, and 9.0 psi; and then requiring the
lines (in log-space) to pass through the appropriate pressures at
100°F, yields the linear equations with coefficients:
RVP
6.3
6.8
9.0
13.810
1 3.773
1 3.554
B
-3121.05
-3085.79
-2930.67
We will use the above to estimate vapor pressures for the 6.3,
6.8, and 9.0 psi RVP fuels.
In general, given the fuel RVP, we can approximate A and B with
these equations:
B = -3565.2707 + ( 70.5114 * RVP )
and
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May 20, 1998
Appendix C
Modeling 24-Hour Diurnal Emissions
As Functions of Vapor Pressure (kPa)
In each of the following 18 strata, 24-hour diurnal emissions
modeled using a triple of numbers:
A
B
C. Where,
24-Hour Diurnal (grams) = A + B * [(Mean VP) * (Change in VP)]
+ C * [(Mean VP) * (Change in VP)p / 1,000,000
Fuel Delivery
Model Year
Ranae
Fail
Pressure
Test
Fail Only
Purae Test
Pass Both
Purge and
Pressure
Carbureted
Pre-1980
1 1 .4367
0
0.026810
8.8657
0
0.026810
4.63506
0
0.026810
1980-1985
-4.6034
0.0374
0
6.9618
0
0.018974
3.0719
0
0.014217
1986-1995*
9.9392
0
0.009876
1 0.0559
0
0.005993
4.5033
0
0.002850
Fuel Injected
Pre-1980**
1 1 .4367
0
0.026810
8.8657
0
0.026810
4.63506
0
0.026810
1980-1985
0.2134
0.0326
0
4.3700
0
0.006868
3.9001
0
0.004744
1986-1995
4.7661
0
0.009876
5.7386
0
0.005993
2.0690
0
0.002850
* "C" value based on 1986-95 FI vehicles.
** The untested stratum of Pre-1980 FI vehicles was represented
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-34- DRAFT
May 20, 1998
Appendix D
Hourly RTD Emissions (in grams) of Gross Liquid Leakers
Vehicle
Number
Hour
5 0 0 2
5 0 8 2
9 049
9054
9 0 8 7
9 111
Mean
Modified*
1
4.56
2.23
1 1 .88
10.99
27.67
55.95
1 8.88
10.48
2
4.71
2.41
8.79
1 1 .24
28.50
46.77
1 7.07
12.45
3
6.12
3.18
10.24
9.78
24.65
44.26
16.37
16.37
4
7.93
4.00
1 1 .74
13.05
25.98
44.32
1 7.84
1 7.84
5
9.55
4.63
1 1 .62
14.28
25.06
45.49
1 8.44
1 8.44
6
1 1 .29
5.14
11.19
14.69
24.61
47.67
19.10
19.10
7
9.41
5.39
10.99
14.00
25.70
48.07
1 8.93
18.93
8
9.78
5.1 1
9.74
16.08
25.22
47.46
1 8.90
1 8.90
9
7.14
4.73
9.04
15.05
24.21
42.41
17.10
17.10
1 0
6.06
4.36
8.02
14.06
23.36
43.84
16.62
16.62
1 1
5.35
4.30
7.42
14.85
20.95
36.43
14.88
14.88
1 2
4.18
4.10
6.91
15.53
19.67
33.72
14.02
14.02
1 3
3.66
3.51
6.91
14.93
18.50
32.96
13.41
13.41
1 4
3.08
2.76
6.25
15.03
17.58
25.79
1 1 .75
1 1 .75
1 5
2.89
2.55
5.63
14.60
16.57
21 .55
1 0.63
1 0.63
1 6
2.83
2.23
5.78
13.93
16.31
21 .24
1 0.39
1 0.39
1 7
2.97
2.22
5.09
16.37
13.59
20.46
10.12
10.12
1 8
2.76
2.20
4.91
14.65
15.29
1 9.64
9.91
9.91
1 9
2.91
2.18
4.93
1 1 .54
13.86
17.60
8.84
8.84
2 0
2.82
2.09
4.89
1 1 .30
13.46
16.85
8.57
8.57
2 1
3.01
2.06
4.70
11.12
13.69
16.52
8.52
8.52
2 2
3.06
2.09
5.02
9.89
13.62
15.89
8.26
8.26
2 3
3.01
1 .97
4.78
10.36
13.04
1 5.82
8.16
8.16
2 4
2.96
2.13
4.88
9.28
17.05
16.40
8.78
8.78
* Mean emissions for the first two hours have been
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DRAFT
May 20, 1998
Appendix E
Estimating Hourly Interrupted Diurnal Emissions
Diurnal Begins
Time:
6 AM*
7 AM
8 AM
9 AM
10 AM
11 AM
Noon
1 PM
2 PM
Temperature:
72.0°
72.5°
75.5°
80.3°
85.2°
89.4°
93.1°
95.1°
95.8°
Diurnal Ends
Time:
6:00AM
5:10AM
1:16AM
10:18PM
8:06PM
6:44PM
5:25PM
4:17PM
3:24PM
Duration (h r):
24.000
22.167
17.273
10.111
10.111
7.742
5.417
3.286
1.400
Time od Day
Pro
portion
of Full
Day's
Diurnal
Allocated to
Each Hour
1
6-7 AM
1.89%
0%
0%
0%
0%
0%
0%
0%
0%
2
7-8AM
2.45%
1.98%
0%
0%
0%
0%
0%
0%
0%
3
8-9AM
5.13%
5.09%
3.34%
0%
0%
0%
0%
0%
0%
4
9-10 AM
8.36%
8.65%
6.42%
3.43%
0%
0%
0%
0%
0%
5
10-11AM
11.24%
11.26%
8.82%
5.49%
2.81%
0%
0%
0%
0%
6
11AM - Noon
13.78%
13.79%
11.14%
7.47%
4.44%
2.43%
0%
0%
0%
7
Noon - 1PM
14.93%
12.57%
10.15%
6.86%
4.21%
2.53%
1.49%
0%
0%
8
1-2PM
13.08%
10.69%
8.53%
5.64%
3.42%
2.09%
1.37%
1.15%
0%
9
2-3 P M
9.85%
9.88%
7.83%
5.11%
3.05%
1.87%
1.28%
1.13%
1.11%
1 0
3-4PM
6.69%
8.20%
6.36%
3.99%
2.29%
1.42%
1.09%
1.09%
0%
1 1
4-5 P M
4.31%
5.72%
4.23%
2.41%
1.29%
0.90%
1.00%
0%
0%
1 2
5-6 P M
2.97%
2.93%
1.91%
0.84%
0.47%
0.73%
1.41%
0%
0%
1 3
6-7 P M
2.09%
0.95%
0.38%
0.04%
0.41%
1.31%
0%
0%
0%
1 4
7-8 P M
1.32%
0.37%
0.08%
0.19%
1.03%
0%
0%
0%
0%
1 5
8-9 P M
0.75%
0.44%
0.30%
0.64%
0%
0%
0%
0%
0%
1 6
9-10PM
0.53%
0.87%
0.70%
1.01%
0%
0%
0%
0%
0%
1 7
10-11PM
0.35%
0.73%
0.74%
0%
0%
0%
0%
0%
0%
1 8
11PM - Midnite
0.26%
0.74%
0.90%
0%
0%
0%
0%
0%
0%
1 9
Midnite - 1AM
0.00%
0.00%
0.00%
0%
0%
0%
0%
0%
0%
20
1- 2AM
0.00%
0.00%
0.00%
0%
0%
0%
0%
0%
0%
21
2-3AM
0.00%
0.00%
0%
0%
0%
0%
0%
0%
0%
22
3-4AM
0.00%
0.00%
0%
0%
0%
0%
0%
0%
0%
23
4-5AM
0.00%
0.00%
0%
0%
0%
0%
0%
0%
0%
24
5-6AM
0.00%
0.00%
0%
0%
0%
0%
0%
0%
0%
Percentage of Full Day's Diurnal Emissions:
100.0%
94.9%
71.8%
43.1%
23.4%
13.3%
7.6%
3.4%
1.1%
Number of Hours of Positive
Diurnal
Emissions:
1 8
1 7
16
1 3
1 0
8
6
3
1
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DRAFT
May 20, 1998
Appendix F
Modeling Hourly Resting Loss Emissions
As Functions of Temperature (°F)
In each of the following 12 strata, resting loss emissions
per hour) are modeled using a pair of numbers (A and B), whe
Hourly Resting Loss (grams) = A + ( B * Temperature in °F )
B = 0.002812 (for ALL strata) and
"A" is given in the following table:
Fuel Delivery
Model Year
Ra n a e
Pass Pressure
Test
Fail Pressure
Test
Carbureted
Pre-1980
0.05530
0.07454
1980-1985
-0.05957
-0.02163
1986-1995
-0.07551
0.05044
Fuel Injected
Pre-1980*
0.05530
0.07454
1980-1985
-0.09867
0.02565
1986-1995
-0.1 4067
-0.1 0924
* The untested stratum (Pre-1980 FI vehicles) was represented
using the Pre-1980 model year carbureted vehicles. (See
report M6.EVP.001 for additional details.)
These equations can then be applied (in each stratum) to each of
the hourly temperatures in Appendix A to obtain the resting loss
emissions released in a 24 hour period. If we use an alternate
temperature profile in which the hourly change in temperature is
proportional to the cycles in Appendix A, we find that:
24-Hour Resting Loss (grams) = (24*A) + (B*C)
Where A and B are given above, and where
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