EPA420-P-99-027
- Draft -
Modeling Hourly Diurnal Emissions
and Interrupted Diurnal Emissions
Based on Real-Time Diurnal Data
Larry C. Landman
Document Number M6.EVP.002
July 1, 1999
U.S. EPA
Assessment and Modeling Division
National Vehicle Fuel and Emissions Laboratory
2000 Traverwood Drive
Ann Arbor, Michigan 48105-2425
734-214-4939 (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,
position or regulatory action.
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ABSTRACT
Evaporative emissions due to changes in ambient temperature
are an important source of hydrocarbons. These diurnal emissions
were described as daily averages in an earlier report
(M6.EVP.001). The current report proposes a model for
distributing these emissions among the hours of the day. This
document reports on both the methodology used to analyze data from
real-time diurnal (RTD) tests on 270 vehicles and the results from
those analyses. 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)
214-4939, or by mail to "MOBILE6 Review Comments", US EPA
Assessment and Modeling Division, 2000 Traverwood Drive, 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.
An earlier draft of this document was released and posted on
May 21, 1998 for stakeholder review. Comments were accepted for
sixty (60) days, ending July 18, 1998. In response to those
comments, we made substantial revisions to both our methodology
and to this document.
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TABLE OF CONTENTS
Page Number
1.0 Introduction 1
2.0 Stratifying the Test Fleets 3
2.1 Evaluating Untested Strata 4
3.0 Evaporative Emissions Represented by the RTD .... 5
4.0 Hourly Diurnal Emissions 7
4.1 Characterizing Hourly Diurnal Emissions .... 7
4.2 Calculating Hourly Diurnal Emissions 11
4.2.1 Carbureted Vehicles 11
4.2.2 Fuel Injected Vehicles 14
4.2.3 Gross Liquid Leakers 17
4.2.4 Summarizing All Strata 20
5.0 Interrupted Diurnal 22
5.1 Example of an Interrupted Diurnal 22
5.2 Calculating Emissions of an Interrupted Diurnal 24
6.0 Assumptions Related to Hourly Emissions 27
6.1 Distribution of Hourly Diurnal Emissions ... 27
6.2 Assumptions for Interrupted Diurnals 27
6.3 Temperature Ranges 28
6.4 Estimating Vapor Pressure 29
6.5 Duration of Diurnal Soak Period 29
11
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TABLE OF CONTENTS (Continued)
Page Number
APPENDICES
A. Temperature Cycles 31
B. Vapor Pressure 32
C. Modeling 24-Hour Diurnal Emissions 34
D. Regressions of Hourly Ratio of Diurnal 36
E. Hourly RTD Emissions of Gross Liquid Leakers .... 43
F. Modeling Hourly Resting Loss Emissions 44
111
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*** D) 1 ***
Modeling Hourly Diurnal Emissions
and Interrupted Diurnal Emissions
Based on Real-Time Diurnal Data
Report Number M6.EVP.002
Larry C . Landman
U.S. EPA Assessment and Modeling Division
1 . 0 Introduction
In a recently released draft report,* the Environmental
Protection Agency (EPA) presented a model for estimating resting
loss and diurnal emissions over the course of a 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 in
Figure 1-1; however, most of the testing was performed using the
72 to 96 degree cycle.** In that 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 are delayed and do not start until
after the daily temperature rise has already begun.
As illustrated in Figure 1-1, 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. Over
the course of the remaining 15 hours, the temperature slowly
returns to the daily low temperature . The three hourly
temperature cycles used in this study are given in Appendix A.
The most rapid increase in temperatures occurs during the fourth
Report numbered M6.EVP.001 is entitled "Evaluating Resting Loss and
Diurnal Evaporative Emissions Using RTD Tests."
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,
entitled "Evaluating Multiple Day Diurnal Evaporative Emissions Using RTD
Tests."
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-2-
DRAFT
hour. For RTD tests that exceed 24 hours, the cycle is simply
repeated. (Estimating the effects of alternate temperature
profiles is discussed in Section 6.3.)
Figure 1-1
Temperature Cycles for Real-Time Diurnal (RTD) Testing
110
90 °
in
o>
3
+-i
re
Q.
E
o>
70
50 °
12
Time (hours)
18
24
The previous document analyzed RTD test results from 270
vehicles. In this document, we analyze the hourly results from
those same tests. This document reports on both the methodology
used to analyze the data from these RTD tests and the results
obtained from those analyses.
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
MOBILES, EPA analyzed 20-year averaged hourly temperatures by
month from Pittsburgh on high ozone days. EPA found that the
minimum daily temperature typically occurred between 6 and 7 AM,
while the maximum daily temperature typically occurred between 3
to 5 PM. Obviously, the local temperature curve depends on local
conditions. However, for MOBILE6, EPA proposes to combine the GM
and MOBILES time estimates and to assign the daily low temperature
to 6 AM, and the daily high temperature to at 3 PM. Applying this
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-3-
DRAFT
proposal to the temperature cycles in Appendix A results in having
the time zero correspond with 6 AM.
2 . 0 Stratifying the Test Fleet
It was necessary to stratify the test fleet for two reasons.
First, different mechanisms are involved in producing the diurnal
emissions for different groups of vehicles, thus, necessitating
different analytical approaches. Second, the recruitment of test
vehicles was intentionally biased to allow testing a larger number
of vehicles that most likely had problems with their evaporative
control systems. This stratified recruitment resulted in the
necessity of separate analyses within each of the recruitment
strata.
The test data used for these hourly analyses are the same
data used in the aforementioned EPA draft report. The data were
obtained by combining RTD tests performed on 270 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
Pre-80 Carbureted
80-85 Carbureted
80-85 Fuel Injected
86-95 Carbureted
86-95 Fuel Injected
Program
CRC
EPA
CRC
EPA
CRC
EPA
CRC
EPA
CRC
EPA
Cars
38
4
0
1 3
0
9
0
8
0
67
Trucks
1 3
2
47
5
3
0
7
0
43
1 1
In that previous draft report, EPA noted that the resting
loss and diurnal emissions from vehicles classified as "gross
liquid leakers" (i.e., 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, those two groups were analyzed
separately in both reports.
The two testing parameters in the EPA programs that were
found (in M6.EVP.001) to affect the 24-hour RTD test results are:
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the Reid vapor pressure (RVP) of the test fuel and
the temperature cycle.
Similarly, the two vehicle parameters that were found to affect
the 24-hour RTD test results are:
the model year range:
1) 1971 through 1979
2) 1980 through 1985
3) 1986 through 1995
the fuel delivery system:
1) carbureted (Garb) or
2) fuel-injected (FI).
Also, since many of the EPA 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).*
This stratification was used in both the analysis of the 24-hour
diurnal emissions and in this current analysis (see Section 4.0).
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 (i.e., less than three percent).
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 MOBILE6, EPA
proposes to estimate the RTD emissions of the (untested) pre-1980
FI vehicles with the corresponding emissions of the pre-1980
For only one of the fuel delivery system/model year range groupings (i.e.,
pre-1980 carbureted vehicles) were 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
were combined into a single ("fail pressure") stratum.
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-5- DRAFT
carbureted vehicles. This should be a reasonable assumption since
any actual differences between the emissions of 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 actually measure the combination (sum) of two
types of evaporative emissions:
1) "Resting loss" emissions are always present and 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 ambient temperature.
That report calculated the hourly resting loss emissions
as being the mean of the RTD emissions from hours 19
through 24 at the nominal temperature for hour 24.
2) "Diurnal" emissions are the pressure-driven emissions
resulting from the daily increase in ambient temperature
(Section 7.2 of M6.EVP.001).
The 24-hour diurnal emissions were calculated by first
adjusting the resting loss value for each hour's ambient
temperature, and then subtracting that temperature-
adjusted resting loss estimate from the full 24-hour RTD
test results.
A special case of each of these two categories consists of
evaporative emissions from vehicles that have significant leaks of
liquid gasoline. We defined these "gross liquid leakers" as
vehicles with resting loss emissions exceeding two grams per hour.
As stated in Section 2, these "gross liquid leakers" were analyzed
separately from the other vehicles. Alternative definitions of
these "gross liquid leakers" are possible; however, with each such
new definition, a new frequency distribution and mean emission
value would have to be determined.
The following graph (Figure 3-1) is an example of hourly RTD
emissions for vehicles that were not gross liquid leakers. For
this example, we averaged the RTD hourly results from 69 1986-95
model year, FI vehicles that had passed both the pressure and
purge tests. All were tested over the 72° to 96° cycle using a
6.8 RVP gasoline. We then plotted the temperature-adjusted hourly
resting loss and diurnal emissions.
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DRAFT
Figure 3-1
An Example of Hourly RTD Emissions
E
SH
o>
c
o
E
LU
O
I
1.0
0.8
0.6
0.4
0.2 -
0.0
Diurnal
Resting Loss
7 10 13 16 19
Duration (hours)
22
This example represents the hourly resting loss and diurnal
emissions of the mean of a single stratum. Each combination of
the five parameters discussed in Section 2.0 can produce a
different graph. 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 construct 86 graphs
for which there are any data (58 are based on the average of no
more than four RTD tests). EPA chose to consolidate those strata
into the smaller number of groups that were actually used. The
selection of both the categorical variables (used to form the
strata) and the analytical variables is discussed in the following
section.
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DRAFT
4 . 0 Hourly Diurnal Emissions
4 . 1 Characterizing Hourly Diurnal Emissions by Strata
In Table 4-1 (below), to normalize the hourly diurnal
emissions (which can vary substantially), we divided each hour's
diurnal emissions by the full (i.e., total 24-hour) diurnal
Table 4-1
Distribution of Hourly Diurnal Emissions
Within the Strata Containing at Least 10 Tests
Purge /
Pressure
Category
Fail ONLY Purge
Fail Pressure
Passing Both
temp
cycle
60. TO. 84
72. TO. 96
82. TO. 106
60. TO. 84
72. TO. 96
82. TO. 106
60. TO. 84
72. TO. 96
82. TO. 106
MYR
Range
86-95
86-95
80-85
86-95
86-95
86-95
86-95
86-95
86-95
Pre-80
80-85
86-95
86-95
86-95
86-95
86-95
86-95
Pre-80
80-85
86-95
86-95
86-95
86-95
86-95
Fuel
Meter
Fl
Fl
CARB
Fl
Fl
Fl
Fl
Fl
Fl
CARB
CARB
Fl
Fl
Fl
Fl
Fl
Fl
CARB
CARB
CARB
Fl
Fl
Fl
Fl
Cnt
1 2
1 7
1 1
1 9
1 7
1 6
1 2
1 1
1 9
33
1 0
20
1 9
1 7
1 2
1 6
32
1 1
38
1 0
70
31
25
22
RVP
6.8
9.0
6.8
6.8
9.0
6.8
9.0
6.8
9.0
6.8
6.8
6.8
9.0
6.8
9.0
6.8
9.0
6.8
6.8
6.8
6.8
9.0
6.8
9.0
Hour During Which
Total 1-
Percen
25%
3.90
4.16
4.24
3.52
4.50
3.99
5.01
4.06
4.08
4.39
4.18
4.31
4.37
4.26
4.57
4.06
5.49
6.32
4.98
5.36
4.62
6.43
4.59
6.73
ourly F
t of F
50%
5.40
5.89
6.50
5.50
6.35
5.74
6.71
5.73
5.60
6.28
6.04
6.04
6.06
5.98
6.29
7.10
7.88
8.46
7.00
7.72
6.73
8.36
6.97
8.06
leaches
ull-Day
75%
7.38
7.86
8.83
7.65
8.02
7.70
8.58
7.54
7.15
8.35
8.10
8.09
7.84
7.79
7.90
9.73
10.36
10.85
9.19
10.10
8.98
10.46
9.56
9.72
Max
Diurnal
Occur
5
6
7
6
7
6
7
7
6
6
6
6
6
7
7
8
8
8
7
9
7
8
7
8
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DRAFT
emissions within each of the strata described in Section 3.0.
Twenty-four of those strata were represented by at least ten
tests. Within each of those 24 strata, we estimated (by
interpolation) the time at which the cumulative hourly diurnal
emissions totaled 25, 50, and 75 percent of the full-days diurnal
emission. We also identified the test hour during which the day's
highest (i.e., peak) hourly diurnal emission occurred. No attempt
was made (in Table 4-1) to estimate the overall mean values.
A visual inspection of these results in Table 4-1 suggests
that:
These strata do not yield a complete representation of the
various technologies (i.e., not all of the combinations of
fuel delivery systems and model year ranges are present),
specifically:
The only strata containing fuel injected vehicles are
exclusively composed of the 1986-95 model year
vehicles.
The only strata containing the Pre-1980 or the 1980-85
model year vehicles are exclusively composed of the
carbureted vehicles.
Thus, we cannot treat as independent variables both the
type of fuel delivery system and the model year range.
Therefore, EPA proposes to select the type of fuel delivery
system (i.e., carbureted versus fuel injected) as the
stratifying variable.
The emissions distribution as indicated by the "four
critical times" (i.e., the number of hours into the tests
that the maximum hourly diurnal emissions occur as well as
the number of hours into the tests necessary for the
cumulative hourly diurnal emissions to total 25, 50, and 75
percent of the full 24-hour diurnal) appear to be effected
by both the temperature cycle and the fuel RVP,
specifically:
The higher temperature cycles often correspond (but not
consistently) with a delay in the occurrence of some of
the four critical times in the distributions.
For the strata of vehicles that passed the pressure
test (either "Fail ONLY Purge" or "Passing Both"), a
higher fuel RVP corresponds with delaying the
occurrence of all four critical times in the
corresponding distributions.
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In the earlier analyses (M6.EVP.001), EPA used the RVP to
estimate the vapor pressure (VP) of the fuel at each point
in the temperature cycle. If we calculate the mean of the
VP at the highest and lowest temperatures, then that
midpoint value incorporates both the temperature cycle and
the fuel RVP. EPA proposes to use that value (in
kiloPascals) as one of the potential variables. (This
variable serves to distinguish among the three temperature
cycles in Appendix A. If RTD testing is performed over
different cycles, then this variable may need to be
modified.)
There appears to be differences among the three purge /
pressure categories, specifically:
As noted above, the four critical times in the
distributions appear to be affected by the fuel RVP in
the strata that passed the pressure test. However, for
the strata of vehicles that failed the pressure test,
those times are fairly insensitive to differences in
fuel RVP.
For the strata of vehicles that passed both the purge
and pressure tests, the occurrence of all four critical
times in the corresponding distributions are delayed
(relative to the strata of vehicles the failed only the
purge test).
Based on these observations, EPA proposes to estimate the
hourly diurnal emissions separately for each of the three
purge / pressure categories.
Therefore, EPA proposes to model the hourly diurnal emissions
(as percentages of the full day diurnal):
separately for the category of "gross liquid leakers" (see
Section 4.2.3),
separately for each of the six combinations of fuel
delivery system (i.e., fuel injected versus carbureted) and
purge / pressure category,
using VP to distinguish among the temperature cycles and
the fuel RVP (for vehicles that are not "gross liquid
leakers"), and
using variables that describe the change in ambient
temperature (discussed on the following page).
These proposals result in modeling the hourly diurnal emissions
separately within each of the following seven strata:
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-10-
DRAFT
1) carbureted vehicles (not "gross liquid leakers") that pass
both the purge and pressure tests,
2) carbureted vehicles (not "gross liquid leakers") that fail
the pressure test,
3) carbureted vehicles (not "gross liquid leakers") that fail
only the purge test,
4) FI vehicles (not "gross liquid leakers") that pass both the
purge and pressure tests,
5) FI vehicles (not "gross liquid leakers") that fail the
pressure test,
6) FI vehicles (not "gross liquid leakers") that fail only the
purge test, and
7) the vehicles classified as "gross liquid leakers" (see
Section 4.2.3) .
Those seven strata can be illustrated in the following table. The
numbering of the cells within the table (1 through 7) coincides
with both the numbering in the preceding list as well as with the
numbering of the seven equations in Section 4.2.
Carbureted
Fuel
Injected
Passing Both
Purge and
Pressure
( 1 )
(4)
Failing the
Pressure
Test
( 2 )
(5 )
Failing ONLY
the Purge
Test
( 3)
( 6)
Gross Liquid
Leakers
(7)
As stated in Section 3.0, the diurnal emissions are the
pressure-driven emissions resulting from the daily increase in the
temperature of both the fuel and the vapor. Although the fuel
temperature is not a readily available variable, it does follow
the daily cycle of the ambient temperature. On 80 of the 119
vehicles that EPA tested using the RTD cycles, EPA measured both
the ambient temperature and the fuel tank temperature. We then
shifted the graph of the tank temperatures to minimize the sum of
the squares of the temperature differences. The amounts of those
shifts are the times (in minutes) by which the fuel tank
temperatures lagged behind the corresponding ambient temperatures.
Those shifts are given below:
Ambient Temperature Cycle
60 to 84° Cycle
72 to 96° Cycle
82 to 106° Cycle
Lag Time
(minutes)
44.4
67.0
108.4
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Since the changes in fuel temperature can lag by one to two hours
behind the corresponding changes in the ambient temperature, EPA
considered the following three variables (and multiplicative
combinations of them to allow for interactions) in modeling the
hourly diurnal emissions:
the change in ambient temperature during that specific
hour,
the change in ambient temperature during the previous
hour, and
the total change in temperature from the start of the
cycle until the start of the previous hour.
Since all three of those temperature terms are actually
differences of temperatures, it was not necessary to convert the
temperature units from Fahrenheit to an absolute temperature. For
the three temperature cycles used, these three temperature
variables are given in Appendix A.
4.2 Calculating Hourly Diurnal Emissions by Strata
EPA proposes to estimate the mean hourly diurnal emissions by
multiplying the full day's diurnal emissions (estimated in the
previous report (M6.EVP.001 and reproduced in Appendix C) by the
hourly percentages predicted in Sections 4.2.1 through 4.2.3 of
this report.
4.2.1 Carbureted Vehicles
As noted in the discussion associated with Table 4-1, within
each of the various strata of carbureted vehicles, the only
combination of temperature cycle and fuel RVP represented by at
least 10 tests was that of the 72 to 96 degree cycle using the 6.8
RVP fuel. That condition persisted even after eliminating the
model year groupings as a stratifying factor. EPA, therefore, had
the option of either performing analyses based on a small number
of carbureted vehicles or applying the results of the analyses of
the FI vehicles directly to the carbureted vehicles. EPA decided
to proceed using the limited test results on carbureted vehicles.
The distribution of the tests is given on the following page in
Table 4-2.
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-12-
DRAFT
Table 4-2
Distribution of RTD Tests of Carbureted Vehicles
Purge/Pressure
Category
Fail ONLY Purge
Fail Pressure
Passing Both
temperature
cycle
60 to 84
72 to 96
82 to 106
60 to 84
72 to 96
82 to 106
60 to 84
72 to 96
82 to 106
RVP
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
Number
of Tests
4
6
1 9
6
5
4
4
8
45
8
6
4
4
9
59
9
6
4
EPA chose to use stepwise* linear regressions to identify the
variables that were the most influential in determining the shape
of the hourly diurnal emissions. The mean hourly diurnal
emissions were calculated within each of the 18 sub-stratum
determined by the purge/pressure category, the temperature cycle,
and fuel RVP. The emissions were positive for hours one through
18, and were zero for hours 19 through 24. The emissions for each
hour were divided by the full (i.e., total 24-hour) diurnal
emissions to calculate the percentage (ratio) of the total diurnal
the percentage for hour 19 always zero). Therefore, each
The stepwise regression process first uses the Pearson Product-Moment to
select the independent variable that has the highest correlation with the
"Ratio of Hourly Diurnal." The difference between the best linear estimate
using that variable and that "Ratio of Hourly Diurnal" (i.e., the residuals)
is then compared with the set of remaining variables to identify the
variable having the next highest correlation. This process continues as
long as the "prob" values do not exceed 5%, thus, creating a sequence of
variables in descending order of statistical correlation.
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purge/pressure stratum contained 19 hourly percentages for each of
six combinations of temperature cycles and fuel RVP (for a total
of 114 results). Within each purge/pressure stratum, a stepwise
linear regression of those 114 hourly diurnal ratios was performed
to estimate the "Ratio of Hourly Diurnal" as a linear function of the
temperature variables (from page 10) and multiplicative
combinations of them, as well as, multiplicative combinations of
them with the VP term (calculated as the midpoint of the VP at the
highest and lowest temperatures of the day in kiloPascals). The
stepwise regression process produced the following three equations
that predict the ratios of hourly diurnal emissions from
carbureted vehicles :
For Carbureted Vehicles Passing Both Purge and Pressure Tests: ( 1 )
Ratio of Hourly Diurnal = 0.007032
+ 0.000023 * [ ( Midpoint VP ) *
( Change in Ambient During Previous Hr )
( Change in Ambient Prior to Previous Hr ) ]
+ 0.003586 * ( Change Prior to Previous Hr )
0.001111 * ( Sqr of Change During Previous Hr )
For Carbureted Vehicles Failing the Pressure Test: ( 2 )
Ratio of Hourly Diurnal = 0.010549
+ 0.001138 * [ ( Change During Previous Hr ) *
( Change in Ambient Prior to Previous Hr ) ]
+ 0.001758 * ( Change Prior to Previous Hr )
+ 0.001765 * ( Sqr of Change During Current Hr )
For Carbureted Vehicles Failing ONLY the Purge Test: ( 3 )
Ratio of Hourly Diurnal = 0.006724
+ 0.000023 * [ ( Midpoint VP ) *
( Change in Ambient During Previous Hr )
( Change in Ambient Prior to Previous Hr ) ]
+ 0.003966 * ( Change Prior to Previous Hr )
0.001122 * ( Sqr of Change During Previous Hr )
+ 0.000019 * [ ( Midpoint VP ) *
( Sqr of Change During Current Hr ) ]
- 0.000018 * [ ( Midpoint VP ) *
( Change Prior to Previous Hr ) ]
-------
-14-
DRAFT
More details can be found in Appendix D which contains the
regression tables and graphs comparing the actual and predicted
hourly ratios. The solid lines in each of the graphs in Appendix
D are not regression lines; they are unity lines. (That is, if
the predicted values exactly matched the actual values, then the
points of predicted versus actual pairs would exactly lie on those
lines.) EPA proposes to use equations (1) through (3) to predict
the ratios of hourly diurnal emissions of the carbureted vehicles
that were not gross liquid leakers. EPA then proposes to multiply
those percentages by the full (24-hour) diurnals estimated by
using the corresponding equations in Appendix C to obtain the
hourly emissions (in grams of HC).
4.2.2 Strata of FI Vehicles
The distribution of the tests of fuel injected vehicles is
given below in Table 4-3. This table is similar to the previous
table on the distribution of the tests of carbureted vehicles
(Table 4-2).
Table 4-3
Distribution of RTD Tests of FI Vehicles
Purge/Pressure
Cateaory
Fail ONLY Purge
Fail Pressure
Passing Both
temperature
cycle
60 to 84
72 to 96
82 to 106
60 to 84
72 to 96
82 to 106
60 to 84
72 to 96
82 to 106
RVP
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
6.8
9.0
Number
of Tests
1 5
21
21
21
1 8
1 6
1 3
21
23
21
1 8
1 4
1 7
33
73
33
26
22
-------
-15- DRAFT
For the strata of fuel injected vehicles, the analytical
approach was similar to that used for the carbureted vehicles.
That is, the mean hourly diurnal emissions were calculated within
each of the 18 sub-stratum determined by the purge/pressure
category, the temperature cycle, and fuel RVP. The emissions were
positive for hours one through 18, and were zero for hours 19
through 24. The percent of the total diurnal emissions
represented by each hour was calculated for hours one through 19
(with the percentage for hour 19 always zero). Therefore, each
purge/pressure stratum contained 19 hourly percentages for each of
six combinations of temperature cycles and fuel RVP (for a total
of 114 results).
Within each of the three purge/pressure strata, a stepwise
linear regression of those 114 hourly diurnal ratios was performed
to estimate the "Ratio of Hourly Diurnal" as a linear function of the
temperature variables (from page 10) and multiplicative
combinations of them, as well as, multiplicative combinations of
them with the VP term (calculated as the midpoint of the VP at the
highest and lowest temperatures of the day in kiloPascals). The
stepwise regression process produced the following three equations
that predict the ratios of hourly diurnal emissions from fuel
injected vehicles:
For Fuel Injected Vehicles Passing Both Purge and Pressure Tests: ( 4 )
Ratio of Hourly Diurnal = 0.008001
+ 0.001961 * ( Change Prior to Previous Hr )
+ 0.000535 * [ ( Change During Previous Hr) *
( Change in Ambient Prior to Previous Hr ) ]
- 0.000060 * [ ( Midpoint VP ) *
( Sqr of Change During Previous Hr ) ]
+ 0.005964 * ( Change During Current Hr )
+ 0.000056 * [ ( Midpoint VP ) *
( Change in Ambient Prior to Previous Hr ) ]
-------
-16- DRAFT
For Fuel Injected Vehicles Failing the Pressure Test: ( 5 )
Ratio of Hourly Diurnal = 0.006515
+ 0.001194 * [ ( Change During Previous Hr ) *
( Change in Ambient Prior to Previous Hr ) ]
+ 0.001963 * ( Change Prior to Previous Hr )
+ 0.001329 * ( Sqr of Change During Current Hr )
+ 0.000574 * ( Sqr of Change During Previous Hr )
For Fuel Injected Vehicles Failing ONLY the Purge Test: ( 6 )
Ratio of Hourly Diurnal = 0.007882
+ 0.000855 * [ ( Change During Previous Hr ) *
( Change in Ambient Prior to Previous Hr ) ]
+ 0.000084 * [ ( Midpoint VP ) *
( Change in Ambient Prior to Previous Hr ) ]
+ 0.006960 * ( Sqr of Change During Current Hr )
- 0.000160 * [ ( Midpoint VP ) *
( Sqr of Change During Current Hr ) ]
0.001172 * ( Change Prior to Previous Hr )
+ 0.000118 * [ ( Midpoint VP ) *
( Change in Ambient During Current Hr ) ]
+ 0.000825 * ( Sqr of Change During Previous Hr )
More details can be found in Appendix D which contains the
regression tables and graphs comparing the actual and predicted
hourly ratios. The solid lines in each of the graphs in Appendix
D are unity lines. (That is, if the predicted values exactly
matched the actual values, then the points of predicted versus
actual pairs would exactly lie on those lines.) EPA proposes to
use equations (4) through (6) to predict the ratios of hourly
diurnal emissions of the fuel injected vehicles that were not
gross liquid leakers.
In the observations following Table 4-1, it was noted that
the shape of the hourly distribution curve (i.e., the ratios not
the actual magnitude) for FI vehicles that failed the pressure
test seemed insensitive to changes in the fuel RVP. The
regression in Appendix D confirms that observation. The
regression table indicates that more than 95 percent of the
variability in the hourly diurnal emissions can be explained using
only the variables involving changes in the temperature. (A
-------
-17- DRAFT
similar condition holds true for carbureted vehicles that failed
the pressure test.)
4.2.3 "Gross Liquid Leaker" Vehicles
In the previous report (M6.EVP.001), vehicles classified as
"gross liquid leakers" were analyzed separately from the other
vehicles due to both:
the large differences in both 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 4.2.1 and 4.2.2 were repeated for
the vehicles identified as being gross liquid leakers. The hourly
RTD results for those test vehicles are given in Appendix E.
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 E, we attempt to compensate (as explained
in the footnote in Appendix E) for what appears to be simply an
artifact of the test procedure. The modified RTD evaporative
emissions were then converted to diurnals by assuming that the
hourly resting loss for these vehicles is completely independent
of ambient temperature, subtracting that amount (8.52 grams per
hour which is the average RTD emissions of hours 19 through 24)
from each hour's modified RTD emissions, and then dividing by the
total diurnal to yield the hourly percentages in Table 4-4 on the
following page.
-------
-18-
DRAFT
Table 4-4
Distribution of Hourly Diurnal Emissions
of Gross Liquid Leakers
(Hourly Emissions as Percent of 24-Hour Diurnal)
Hour
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
Time of Day
6 - 7 AM
7 - 8 AM
8 - 9 AM
9 - 10 AM
10 - 11 AM
11 AM - Noon
Noon - 1 PM
1 - 2 PM
2 - 3 PM
3 - 4 PM
4 - 5 PM
5 - 6 PM
Emissions
1.82%
3.64%
7.27%
8.63%
9.19%
9.80%
9.64%
9.61%
7.95%
7.50%
5.89%
5.09%
Hour
1 3
1 4
1 5
1 6
1 7
1 8
1 9
20
21
22
23
24
Time of Day
6 - 7 PM
7 - 8 PM
8 - 9 PM
9 - 10 PM
10 - 11 PM
11 PM - Midnight
Midnight - 1 AM
1 - 2 AM
2 - 3 AM
3 - 4 AM
4 - 5 AM
5 - 6 AM
Emissions
4.53%
2.99%
1.95%
1.73%
1.48%
1.28%
0 %
0 %
0 %
0 %
0 %
0 %
A stepwise linear regression of those hourly diurnal ratios
(for hours 1 through 19) was performed to estimate the "Ratio of
Hourly Diurnal" as a linear function of the temperature variables
(from page 10) and multiplicative combinations of them, as well
as, multiplicative combinations of them with the VP term
(calculated as the midpoint of the VP at the highest and lowest
temperatures of the day in kiloPascals). The stepwise regression
process produced the following equation that predict the ratios of
hourly diurnal emissions from vehicles with gross liquid leaks:
For "Gross Liquid Leaker" Vehicles:
Ratio of Hourly Diurnal = 0.021349
+ 0.010137 * ( Change During Previous Hr )
+ 0.002065 * ( Change Prior to Previous Hr )
(7)
More details can be found in Appendix D which contains the
regression table and graph comparing the actual and predicted
hourly ratios. A second graph comparing the actual and predicted
hourly ratios appears in Figure 4-1 in which equation (7) is
plotted as a solid line and the data from Table 4-4 as a bar
chart. Based on those two graphs which depict close matches
between the predicted and actual ratios of hourly diurnal
emissions, EPA proposes to use equation (7) to predict the ratios
of hourly diurnal emissions of the gross liquid leakers.
-------
-19-
DRAFT
Figure 4-1
Distribution of Hourly Diurnal Emissions
from "Gross Liquid Leakers"
12%
E >
u Ğ
_ Q
re
3
Q
0)
O)
4%
3 0)
I "
1 Q)
0.
0%
7 10 13
Duration (hours)
1 6
In the earlier report (from Section 10.2 of M6.EVP.001), it
was determined that the mean 24-hour diurnal emissions from "gross
liquid leakers" (for any of the three temperature cycles in
Appendix A and independent of the fuel RVP) was 104.36 grams.
Multiplying the hourly ratios in equation (7) by that value
produces, on the following page, equation (7a) which predicts the
mean hourly diurnal emissions (in grams of HC) for vehicles that
are gross liquid leakers.
For "Gross Liquid Leaker" Vehicles:
(7a)
Hourly Diurnal Emissions (grams of HC) =
+ 2.22798
+ 1.057897 * ( Change During Previous Hr )
+ 0.215503 * ( Change Prior to Previous Hr )
-------
-20- DRAFT
In that earlier report, we predicted the full 24-hour diurnal
emissions from vehicles that were not gross liquid leakers for all
temperature cycles in which the hourly changes in temperatures are
proportional to the cycles in Appendix A. Unfortunately, the
corresponding data on the "gross liquid leakers" were limited
(i.e., practically all of the tests were performed using the same
temperature cycle), and we did not make similar predictions for
the gross liquid leakers. However, if we apply equation (7a) to
each hour of any temperature cycle (with the hourly changes in
temperatures proportional to the cycles in Appendix A) and then
add these hourly predictions together, we obtain equation (7b):
Total 24-Hour Diurnal Emissions (grams) ( 7 b )
= 40.10367 + ( 2.616201 * Diurnal_Tem pe ratu re_Range )
Where the Diurnal_Temperature_Range is the difference of the daily
high temperature minus the daily low temperature.
Note, equation (7b) predicts a 24-hour total diurnal emission
of 40.10 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 for gross liquid leakers
as increasing linearly from zero to 66.27 grams (i.e., the value
predicted by the equation for a diurnal temperature range of 10
degrees).
Of the seven regression analyses performed (and displayed in
Appendix D), the simplest equation (in terms both of number of
variables and complexity of the variables) is the equation that
predicts the hourly diurnal emissions of gross liquid leaking
vehicles. This most likely results from the simplicity of the
primary mechanism that produces the emissions for the vehicles in
this stratum (i.e., a significant leakage of liquid fuel).
4.2.4 Summarizing All Strata
Examining the seven stepwise regression analyses in Appendix
D (one for each of the strata identified on page 10), we note that
not every possible variable described on page 11 (along with their
multiplicative combinations) were found to be statistically
significant in one or more of those analyses; only 11 variables
and products of variables were found to be statistically
significant:
Delta (change) in previous hour's temperature,
Delta (change) in current hour's temperature,
-------
-21- DRAFT
Total (change in temperature) prior to previous hour,
Square of the delta in previous hour's temperature,
Square of the delta in current hour's temperature,
Product of the delta in previous hour's temperature times
the total (change in temperature) prior to the previous
hour,
Product of the VP times the delta in current hour's
temperature,
Product of the VP times the total prior to the previous
hour,
Product of the VP times the square of the delta in previous
hour's temperature,
Product of the VP times the square of the delta in current
hour's temperature, and
Product of the VP times the delta in previous hour's
temperature times the total prior to the previous hour.
On further examination of Appendix D, we note that some of those
variables are statistically significant in most of the strata:
The total (change in temperature) prior to the previous
hour, possibly combined with its interaction (i.e.,
product) with the midpoint VP, is statistically significant
in all seven strata.
The product of the delta in previous hour's temperature
times the total (change in temperature) prior to the
previous hour, possibly combined with its interaction
(i.e., product) with the midpoint VP, is statistically
significant in the six strata that do not include gross
liquid leakers.
The square of the delta in the previous hour's temperature,
possibly combined with its interaction (i.e., product) with
the midpoint VP, is statistically significant in the five
strata that do not include either gross liquid leakers or
carbureted vehicles that failed the pressure test.
The square of the delta in the current hour's temperature,
possibly combined with its interaction (i.e., product) with
the midpoint VP, is statistically significant in the four
strata of vehicles that failed either the pressure or the
purge test but which are not gross liquid leakers.
This "universality" of the variable "total (change in temperature)
prior to the previous hour" will be the basis for a critical
assumption in estimating interrupted diurnals (in Section 5.2)
-------
-22- DRAFT
5 . 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.
5 . 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, uses a
6.8 RVP fuel, and experiences a daily temperature profile of the
standard 72° to 96° F cycle from Appendix A). For those
conditions, we will assume the following vehicle activity:
1. The vehicle soaks overnight and into the early morning.
2. Shortly after 9 AM (corresponding to the fourth hour of
the RTD test), the vehicle is driven for 30 minutes.
The vehicle reaches its destination and is parked by
10 AM. (That is, the entire drive takes place during
the fourth hour of the RTD test.)
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
evaporative emissions would occur for only limited periods.
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 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). 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.)
-------
-23- DRAFT
3. While the vehicle was being driven, the temperature in
its fuel tank rose by about 20 degrees Fahrenheit*.
After the vehicle stops and until this elevated fuel
temperature drops to become equal to the ambient air
temperature, the vehicle will be experiencing what is
referred to as "hot soak" emissions.
In MOBILES (and MOBILE4.1), 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, in MOBILE the
entire hot soak emissions will be credited to the first
hour (see reports M6.EVP.004 and M6.FLT.004). Thus, in
this example, from 11 AM to noon, only resting losses
will be calculated.
4. At noon, we assume the fuel temperature has cooled to
the ambient temperature of 93.1° F (from the temperature
profile). The hourly diurnal emission will resume but
in the modified form of an "interrupted diurnal" due to
the effects of the drive on canister loading and fuel
temperature. To modify the hourly diurnal emissions, we
will make the following assumption:
The pressure that is driving the 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.
This suggests that the interrupted diurnal emissions
will end once the ambient temperature returns to its
starting point (i.e., 93.1° F in this example).
From the temperature profile, the ambient
temperature will return to 93.1° at 5:25 PM. We
will assume that after 5:25 PM, there are only
resting loss emissions.
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 duration, fuel tank temperature increases as a function of
the trip duration. 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
with an increase in tank temperature of about 30 degrees Fahrenheit.
-------
-24- DRAFT
Therefore, we need to modify the estimated hourly
diurnal emissions so that the modified values are
zero after 6 PM (i.e., from test hour 13 through
24). In the following section (Section 5.2), EPA
proposes a method of modifying the hourly diurnal
emissions following such an interruption to the soak
period.
5 .2 Calculating Emissions of an Interrupted Diurnal
Based on the discussions in the preceding sections, EPA
proposes to make the following three key assumptions in estimating
interrupted diurnals:
The ambient temperature at the beginning of the interrupted
diurnal (i.e., the end of the hot soak) will be used as the
starting temperature for that interrupted diurnal.
In Section 4.2.4, we commented on the "universality" of the
variable "total (change in temperature) prior to the
previous hour." In those analyses of diurnals that were
not interrupted, that variable was calculated by
subtracting the daily low temperature (i.e., the starting
temperature of the full day's diurnal) from the temperature
at the start of the previous hour. EPA proposes for
interrupted diurnals that the daily low temperature in that
subtraction be replaced with that new starting temperature.
The estimate of hourly diurnal emissions from that
interrupted diurnal will be modified so that they cease
once the ambient temperature drops below that new starting
temperature.
In the preceding paragraphs, we analyzed one theoretical
situation in which the diurnal emissions (following the morning
drive) resumed at noon when the ambient temperature reached 93.1°F
and, then, continued until the temperatures declined to that
93.1°F (at 5:25 PM). Using the 72° to 96° F temperature cycle
given in Appendix A, we can repeat those calculations for
interrupted diurnals that begin at each hour of the day. Those
results appear in Table 5-1 (on the following page).
While the starting temperatures (the second column in Table
5-1) would vary with the daily temperature cycle, the time at
which each (interrupted) diurnal ends would be unchanged for any
of the three temperature cycles in Appendix A or for any cycle
based on those three. Table 5-1, therefore, provides the time
intervals during which diurnal emissions could occur following an
interruption to the soak period.
-------
-25-
DRAFT
Table 5-1
Starting and Ending Times and Temperatures
For Interrupted Diurnals
For the 72° to 96° Fahrenheit Cycle
Diurnal
Time
Midnight thru
6 AM*
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
Noon
1:00 PM
2:00 PM
3 PM thru
Midnight
Begins
Temperature
72.0°
72.5°
75.5°
80.3°
85.2°
89.4°
93.1°
95.1°
95.8°
N/A***
Time
Diurnal
Ends
Midnight**
Midnight**
Midnight**
10:18PM
8:06PM
6:44PM
5:25PM
4:17PM
3:24PM
N/A* * *
Therefore, EPA will modify the predicted hourly emissions of
full day's diurnals (from equations (1) through (7)) using the
following four-step process:
1.) In each of the seven regression equations (in Sections
4.2.1 through 4.2.3), the variable "Change Prior to Previous
Hr" appears. For an interrupted diurnal, that variable
is calculated by subtracting the temperature at the
start of the interrupted diurnal from the temperature at
the beginning of the previous hour. This step will
produce an estimate of the percent of the full day's
diurnal occurring each hour of the interrupted diurnal.
In Section 4.2.1, it was noted that diurnal emissions are zero for hours
19 through 24 (i.e., midnight through 6AM) . Thus, any diurnal that
begins between midnight and 6AM effectively begins at 6AM, and that
diurnal is actually a full 24-hour diurnal.
In the previous footnote, it was noted that diurnal emissions are zero
after midnight. Thus, even if the ambient temperature has not returned
to the temperature at which the (interrupted) diurnal began, the diurnal
effectively ends by the following midnight.
Any interrupted diurnal that begins while the ambient temperatures are
declining (i.e., 3 PM or later) does not exist (has zero emissions).
-------
-26- DRAFT
2.) Those hourly percentages would then be modified so that
any negative estimates would be changed to zero, and any
estimates for hours beyond the "Time Diurnal Ends" column
in Table 5-1 would be replaced by zero.
3.) The total 24-hour diurnal emissions are then predicted
using the regression equations from Appendix C.
4.) Finally, the hourly (interrupted) diurnal emissions are
estimated by multiplying the predicted full 24-hour
diurnal emissions by the individual hourly percentages.
To illustrate the use of this four-step process, we return to
the example in Section 5.1.
Both Table 5-1 and the discussion at the end of Section 5.1
indicate that the interrupted diurnal emissions would begin
at noon and continue until 6 PM. For each of those six
hours, we can use Appendix A to construct a table of hourly
temperatures and changes in temperatures. (We will assume
that the changes in temperature prior to noon are zero.)
Those temperature values are given in Table 5-2 on the
following page.
Using the changes in temperature in Table 5-2 we use
equation (4) (to estimate hourly emissions from FI vehicles
that pass both the pressure and purge tests) to calculate
the estimated percentages of the full 24-hour diurnal
emissions that occur each hour of this interrupted diurnal.
Those hourly fractions are given (as percentages) in the
seventh column of Table 5-2.
For the purpose of that example, we assumed a 1986-95 model
year, FI vehicle that passed both the purge and pressure
tests, that used a 6.8 RVP fuel, and where the daily
temperature profile was the standard 72° to 96° F cycle
from Appendix A. The equation in Appendix C predicts the
full 24-hour diurnal in this case would be 2.55 grams (per
day) .
Multiplying the predicted full 24-hour diurnal (2.55 grams)
emissions by the six hourly percentages then produces the
estimated hourly emissions (in grams) which appear as the
eighth column of Table 5-2. (The negative value for the
second hour is then rounded up to zero.)
-------
-27-
DRAFT
Table 5-2
Example of Calculating Hourly Diurnal Emissions
From an Interrupted Diurnal
Time
Of Day
Noon - 1PM
1PM - 2PM
2PM - 3PM
3PM - 4PM
4PM - 5PM
5PM - 6PM
Initial
Temp
(° F)
93.1
95.1
95.8
96.0
95.5
94.1
Final
Temp
95.1
95.8
96.0
95.5
94.1
91.7
Change in
Previous
Hr Temp
0
2.0
0.7
0.2
-0.5
-1 .4
Change in
Current
Hr Temp
2.0
0.7
0.2
-0.5
-1 .4
-2.4
Change
Prior to
Previous
0
0.0
2.0
2.7
2.9
2.4
Hourly
Diurnal
(pet)
0.80%
-0.06%
1.16%
1.35%
1.23%
0.66%
Hourly
Diurnal
(grams)
0.020
0.000
0.030
0.034
0.031
0.017
EPA believes that while this approach is not perfect (as
evidenced by the prediction of negative emissions during the
second hour that needed to be rounded up to zero), it does provide
a reasonable estimate of hourly diurnal emissions during an
interrupted diurnal; therefore, EPA proposes to use this method in
MOBILE6.
6 . 0 Assumptions Related to Hourly Emissions
Several basic assumptions related to estimating hourly
emissions were made in this analysis due to the lack of test data.
6 . 1 Distribution of Hourly Diurnal Emissions
In Section 4, the key assumption is that once the hourly
diurnal emissions are divided by the full 24-hour diurnal
emissions, the distribution (within each of the seven strata
identified on page 10) of those fractions is a function of the
temperature change variables and the midpoint VP.
As a direct result of that assumption, the hourly diurnal
emissions (in grams) can be predicted by simply multiplying the
estimated full 24-hour diurnal emissions (from Appendix C) by the
fractions calculated in Section 4.2. EPA proposes using those
products to estimate the diurnal emission from each individual
hour.
6.2 Assumptions for Interrupted Diurnals
The discussion of interrupted diurnals (in Sections 5.1 and
5.2) requires a number of assumptions. Three of these assumptions
are stated at the beginning of Section 5.2.
-------
-28- DRAFT
The fourth assumption deals with estimating how much time
must elapse following the driving cycle for the diurnal to resume.
It is an accepted fact that interrupting the diurnal with a trip
will result in a temporary increase in fuel tank temperature. The
time required after the trip for the fuel temperature to return to
(i.e., achieve equilibrium with) the ambient temperature depends
on many factors (e.g., duration of the trip, fuel delivery system,
fuel tank design, fuel tank materials, air flow, etc.). However,
EPA proposes to continue the approach used since MOBILE4.I 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 MOBILE6.)
6.3 Temperature Ranges
All of the tests used in this analysis were performed using
one of the three temperature cycles in Appendix A. Thus, all of
the resting loss data were measured at only three temperatures
(i.e., 60, 72, and 82 °F). In Appendix F, we present regression
equations (developed in M6.EVP.001) to estimate hourly resting
loss emissions at 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 MOBILES.)
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°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
of temperature, averaging 9.16 grams per hour, (from report
number M6.EVP.009, entitled "Evaporative Emissions of Gross
Liquid Leakers in MOBILE6").
In a similar fashion, the equations developed in this report
to estimate hourly diurnal emissions theoretically could also be
-------
-29- DRAFT
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 MOBILES.)
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 the linear interpolation of the predicted
value for the ten-degree cycle and zero.
6.4 Estimating Vapor Pressure
EPA proposes using 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 relationships
between the vapor pressure and the temperature. 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.
6 . 5 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, vehicles could soak
for longer periods of time. Estimating diurnal emissions when the
soak period is a multiple of 24 hours will be analyzed in report
M6.EVP.003. For the purpose of this analysis, a full 24-hour
diurnal takes place between 6 AM and 6 AM of the following day
(with hourly diurnal emissions of zero between midnight and 6 AM) .
If a diurnal period extends beyond 6 AM, then the emissions during
the hours beyond 6 AM will be calculated using equations (1)
through (7) (in Sections 4.2.1 through 4.2.3).
EPA's proposal on classifying a diurnal that follows a
diurnal of less than 24 hours is based on EPA's hypothesis of why
-------
-30- DRAFT
a single-day diurnal is different from a multiple-day diurnal.
EPA believes that as the time progresses (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 interrupted diurnal is
almost equivalent to a full 24-hour diurnal, EPA proposes to treat
the subsequent days as if the first day's diurnal were a complete
(i.e., a full-day) diurnal.
To determine the meaning of an interrupted diurnal being
"almost equivalent" to a full 24-hour diurnal, we applied the
equations (1) through (6) to various combinations of fuel RVP,
temperature cycle, and starting time of an interrupted diurnal.
This analysis determined that:
Interrupted diurnals that began at 10 AM (i.e., the
start of the fourth hour of the RTD test) exhibited only
about one-third of the emissions of the full 24-hour
diurnal.
Interrupted diurnals that began at 9 AM (i.e., the start
of the third hour of the RTD test) exhibited only about
one-half of the emissions of the full 24-hour diurnal.
Interrupted diurnals that began no later than 8 AM
(i.e., at least by the start of the second hour of the
RTD test) exhibited at least 80 percent of the emissions
of the full 24-hour diurnal.
Based on these observations, if a vehicle's first day's incomplete
(i.e., interrupted) 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. Otherwise, we treat the subsequent day as the
first day of the diurnal.
-------
-31-
DRAFT
Appendix A
Temperature Cycles (°F)
Hour
0
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
20
21
22
23
24
Temperati
60-84°F
60.0
60.5
63.5
68.3
73.2
77.4
81.1
83.1
83.8
84.0
83.5
82.1
79.7
76.6
73.5
70.8
68.9
67.0
65.2
63.8
62.7
61.9
61.3
60.6
60.0
jres Cyclinc
72-96°F*
72.0
72.5
75.5
80.3
85.2
89.4
93.1
95.1
95.8
96.0
95.5
94.1
91.7
88.6
85.5
82.8
80.9
79.0
77.2
75.8
74.7
73.9
73.3
72.6
72.0
) Between
82-1 06°F
82.0
82.5
85.5
90.3
95.2
99.4
103.1
105.1
105.8
106.0
105.5
104.1
101.7
98.6
95.5
92.8
90.9
89.0
87.2
85.8
84.7
83.9
83.3
82.6
82.0
Change in
Previous Hr
Temp (°F)
...
0.0
0.5
3.0
4.8
4.9
4.2
3.7
2.0
0.7
0.2
-0.5
-1 .4
-2.4
-3.1
-3.1
-2.7
-1 .9
-1 .9
-1 .8
-1 .4
-1.1
-0.8
-0.6
-0.7
Change in
Current Hr
Temp (°F)
...
0.5
3.0
4.8
4.9
4.2
3.7
2.0
0.7
0.2
-0.5
-1 .4
-2.4
-3.1
-3.1
-2.7
-1 .9
-1 .9
-1 .8
-1 .4
-1.1
-0.8
-0.6
-0.7
-0.6
Change
Prior to
Previous Hr
...
0.0
0.5
3.5
8.3
13.2
17.4
21.1
23.1
23.8
24.0
23.5
22.1
19.7
16.6
13.5
10.8
8.9
7.0
5.2
3.8
2.7
1.9
1.3
0.6
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).
For cycles in excess of 24 hours, the pattern is repeated.
-------
-32-
DRAFT
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, fuels with similar Reid
vapor pressures (RVP) were tested, and their vapor pressures (in
kiloPascals) at three temperatures were measured. The results of
those tests are given in the following table:
Nominal
RVP
7.0
9.0
Measured
RVP
7.1
8.7
Vapor Pressure (kPa)
75° F
30.7
38.2
100° F**
49.3
60.1
130° F
80.3
96.5
** The VPs at 100° F are the fuels' RVPs (in kiloPascals).
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:
A B
RVP
8.7
7.1
13.5791
13.7338
-2950.47
-3060.95
C. Lindhjem and D. Korotney, "Running Loss Emissions from Gasoline-Fueled
Motor Vehicles", SAE Paper 931991, 1993.
-------
-33-
DRAFT
Figure B-l
Comparison of Vapor Pressure to Temperature
100
re
a.
2!
3
(A
(A
0)
O
Q.
re
1 0
RVP 8 .",
'RVP 7.1
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
13.773
13.554
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
A = Ln( 6.89286 * RVP ) - ( B / 310.9
-------
-34-
DRAFT
Appendix C
Modeling 24-Hour Diurnal Emissions
As Functions of Vapor Pressure (kPa) and RVP (psi)
(Reproduced from M6.EVP.001)
In each of the following 18 strata, 24-hour diurnal emissions
are modeled using four constants:
A ,B, C, D. Where,
24-Hour Diurnal (grams) =
= A
+ B * RVP (in psi)
+ C * [(Mean VP) * (Change in VP)]
+ D * [(Mean VP) * (Change in VP)]2 / 1,000
For each of the 9 strata, the four constants used to model
diurnal emissions are given below in the following table.
Within each cell of this table, the four constants are listed
vertically (i.e., with "A" at the top and "D" at the bottom).
Fuel Delivery
Carbureted
Model Year
Range
1972-79*
1980-1985
1986-
1995**
Fail
Pressure
Test
-0.29374
-0.62160
0.039905
0
-1.22213
-0.62160
0.039905
0
18.97709
-1.81237
0
0.017098
Fail Only
Purge Test
21.94883
-2.23907
0
0.02990
16.69934
-2.23907
0
0.02990
13.90647
-2.14898
0.021368
0
Pass Both
Purge and
Pressure
21.13354
-2.42617
0
0.024053
15.50536
-2.42617
0
0.024053
8.37118
-0.767027
0
0.005934
The B, C, and D values are based on 1980-85 carbureted
vehicles.
The B, C, and D values are based on 1986-95 FI vehicles.
-------
-35-
DRAFT
Appendix C (Continued)
Modeling 24-Hour Diurnal Emissions
As Functions of Vapor Pressure (kPa) and RVP (psi)
(Reproduced from M6.EVP.001)
In each of the following 18 strata, 24-hour diurnal emissions
are modeled using four constants:
A ,B, C, D. Where,
24-Hour Diurnal (grams) =
= A
+ B * RVP (in psi)
+ C * [(Mean VP) * (Change in VP)]
+ D * [(Mean VP) * (Change in VP)]2 / 1,000
Fuel Delivery
Fuel Injected
Model Year
Range
1972-79*
1980-1985
1986-1995
Fail
Pressure
Test
-0.29374
-0.62160
0.039905
0
7.11253
-1.25128
0.036373
0
14.19286
-1.81237
0
0.017098
Fail Only
Purge Test
21.94883
-2.23907
0
0.02990
7.48130
-0.701002
0
0.010466
9.93656
-2.14898
0.021368
0
Pass Both
Purge and
Pressure
21.13354
-2.42617
0
0.024053
5.6211 1
-0.701002
0
0.010466
5.85926
-0.767027
0
0.005934
* The three untested strata of Pre-1980 FI vehicles were
represented using the Pre-1980 model year carbureted
vehicles (which were themselves based on the 1980-85 model
year carbureted vehicles).
-------
-36-
DRAFT
Appendix D
Regression of Ratio of Mean Hourly Diurnal Emissions
Carbureted Vehicles Passing Both Purge and Pressure Tests
Dependent variable
No Selector
R squared = 91.6%
s = 0.0146 with
Source
Regression
Residual
Variable
Constant
VP * Previous
* Total Prior
to Previous
Total Prior to
Previous
Sqr_Delta
Previous
is:
Ratio of Hourly Diurnal
R squared (adjusted) = 91.4%
114 - 4 = 110 degrees of freedom
Sum of Squares
0.257692
0.023597
Coefficient s.e.
0.007032 0
0.000023 0
0.003586 0
-0.001111 0
df
3
1 10
of Coeff
.0033
.0000
.0002
.0002
Mean Square
0.085897
0.000215
t-ratio
2.15
23.1
20.7
-5.01
F-ratio
400
prob
0.0336
<. 0.0001
<. 0.0001
<. 0.0001
Plotting Predicted Versus Actual Values
20%
* v*/ * I
' '
0% 10% 20%
Predicted Hourly Diurnal (pet)
-------
-37-
DRAFT
Appendix D (continued)
Regression of Ratio of Mean Hourly Diurnal Emissions
Carbureted Vehicles Failing the Pressure Test
Dependent variable is:
No Selector
R squared = 95.1
s = 0.0119 with
Source
Regression
Residual
Variable
Constant
Previous *
Total Prior
to Previous
Total Prior to
Previous
Sqr_Delta
Current
Ratio of Hourly Diurnal
% R squared (adjusted) = 95.0%
114 - 4 = 110 degrees of freedom
Sum of Squares
0.300208
0.015505
Coefficient s.e.
0.010549 0
0.001138 0
0.001758 0
0.001765 0
df
3
1 10
of Coeff
.0029
.0000
.0001
.0002
Mean Square
0.100069
0.000141
t-ratio
3.60
37.4
1 1 .8
10.4
F-ratio
710
prob
0.0005
<. 0.0001
<. 0.0001
<. 0.0001
Plotting Predicted Versus Actual Values
20%
o
Q.
re
Q 1 0 %
o
I
15
3
+Ği
O
<
ki
'*
0% 10%
Predicted Hourly Diurnal (pet)
20%
-------
-38-
DRAFT
Appendix D (continued)
Regression of Ratio of Mean Hourly Diurnal Emissions
Carbureted Vehicles Failing ONLY the Purge Test
Dependent variable is:
No Selector
Ratio of Hourly Diurnal
R squared = 93.5% R squared (adjusted) = 93.1%
s = 0.0124 with 114 - 6 = 108 degrees of freedom
Source
Regression
Residual
Variable
Constant
VP * Previous
* Total Prior
to Previous
Total Prior to
Previous
Sqr_Delta
Previous
VP * Sqr_Delta
Current
VP * Tot Prior
to Previous
Sum of Squares
0.236796
0.01659
Coefficient
0.006724
0.000023
0.003966
-0.001 122
0.000019
-0.000018
df
5
108
s.e. of Coeff
0.0030
0.0000
0.0004
0.0003
0.0000
0.0000
Mean Square
0.047359
0.000154
t-ratio
2.23
27.1
10.1
-4.05
3.14
-2.24
F-ratio
308
prob
0.0276
<. 0.0001
<. 0.0001
<. 0.0001
0.0022
0.0272
Plotting Predicted Versus Actual Values
20%
u
Q.
Q 10%
3
O
I
0 % 10 %
Predicted Hourly Diurnal (pet)
20%
-------
-39-
DRAFT
Appendix D (continued)
Regression of Ratio of Mean Hourly Diurnal Emissions
Fl Vehicles Passing Both Purge and Pressure Tests
Dependent variable is:
No Selector
Ratio of Hourly Diurnal
R squared = 85.2% R squared (adjusted) = 84.5%
s= 0.0188 with 114-6 = 108 degrees of freedom
Source
Regression
Residual
Variable
Constant
Total Prior to
Previous
Previous *
Total Prior
to Previous
VP * Sqr_Delta
Previous
Delta Current
VP * Tot Prior
to Previous
Sum of Squares
0.220626
0.03832
Coefficient
0.008001
0.001961
0.000535
-0.000060
0.005964
0.000056
df
5
108
s.e. of Coeff
0.0046
0.0006
0.0000
0.0000
0.0015
0.0000
Mean Square
0.044125
0.000355
t-ratio
1.75
3.33
5.61
-8.75
4.1 1
4.47
F-ratio
124
prob
0.0834
0.0012
<. 0.0001
<. 0.0001
<. 0.0001
<. 0.0001
Plotting Predicted Versus Actual Values
20%
o
Q.
re
c
^
3
Q
3
O
I
re
3
+-i
O
10%
0%
0% 10%
Predicted Hourly Diurnal (pet)
20%
-------
-40-
DRAFT
Appendix D (continued)
Regression of Ratio of Mean Hourly Diurnal Emissions
Fl Vehicles Failing the Pressure Test
Dependent variable
No Selector
R squared = 95.9%
s = 0.0118 with
Source
Regression
Residual
Variable
Constant
Previous *
Total Prior
to Previous
Total Prior to
Previous
Sqr_Delta
Current
Sqr_Delta
Previous
is:
Ratio of Hourly Diurnal
R squared (adjusted) = 95.7%
114 - 5 = 109 degrees of freedom
Sum of Squares
0.350423
0.015068
Coefficient s.e.
0.006515 0
0.001194 0
0.001963 0
0.001329 0
0.000574 0
df
4
109
of Coeff
.0029
.0000
.0002
.0003
.0003
Mean Square
0.087606
0.000138
t-ratio
2.25
33.9
12.9
5.04
2.03
F-ratio
634
prob
0.0267
<. 0.0001
<. 0.0001
<. 0.0001
0.0449
Plotting Predicted Versus Actual Values
20%
o
Q.
re
c
^
3
Q
3
O
I
re
3
+-i
O
1 0 %
0%
kn:
si
0% 10%
Predicted Hourly Diurnal (pet)
20%
-------
-41-
DRAFT
Appendix D (continued)
Fl Vehicles Failing ONLY the Purge Test
Dependent variable is:
No Selector
Ratio of Hourly Diurnal
R squared = 95.6% R squared (adjusted) = 95.3%
s= 0.0120 with 114-8 = 106 degrees of freedom
Source
Regression
Residual
Variable
Constant
Previous *
Total Prior
to Previous
VP * Tot Prior
to Previous
Sqr_Delta
Current
VP * Sqr_Delta
Current
Total Prior to
Previous
VP * Delta
Current
Sqr_Delta
Previous
Sum of Squares
43.7687
1.29117
Coefficient
0.007882
0.000855
0.000084
0.006960
-0.000160
-0.001 172
0.000118
0.000825
df
2
3
s.e. of Coeff
0.0030
0.0001
0.0000
0.0007
0.0000
0.0004
0.0000
0.0004
Mean Square
21.8844
0.43039
t-ratio
2.66
7.87
8.82
10.7
-10.0
-2.88
2.98
2.06
F-ratio
50.8
prob
0.0090
<. 0.0001
<. 0.0001
<. 0.0001
<. 0.0001
0.0048
0.0036
0.0419
Plotting Predicted Versus Actual Values
20%
TO
C
D
b
10%
0% 10%
Predicted Hourly Diurnal (pet)
20%
-------
-42-
DRAFT
Appendix D (continued)
Regression of Ratio of Mean Hourly Diurnal Emissions
"Gross Liquid Leaker" Vehicles
Dependent variable
No Selector
is:
Ratio of Hourly Diurnal
R squared = 96.2% R squared (adjusted) = 95.7%
s = 0.0070 with 19 - 3 = 16 degrees of freedom
Source
Regression
Residual
Variable
Constant
Delta Previous
Total Prior to
Previous
Sum of Squares
0.019576
0.000783
Coefficient s.e.
0.021349
0.010137
0.002065
df
2
1 6
of Coeff
0.0032
0.0006
0.0002
Mean Square
0.009788
0.000049
t-ratio
6.67
16.90
10.30
F-ratio
200
prob
< 0.0001
< 0.0001
< 0.0001
Plotting Predicted Versus Actual Values
12%
o
Q.
re
c
3
Q
3
O
I
re
3
6%
0%
'.*
0%
6%
12%
Predicted Hourly Diurnal (pet)
-------
-43-
DRAFT
Appendix E
Hourly Real-Time Diurnal (RTD) Emissions (in grams)
From Six Gross Liquid Leakers
Hour
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
20
2 1
2 2
2 3
2 4
5002
4.56
4.71
6.12
7.93
9.55
1 1.29
9.41
9.78
7.14
6.06
5.35
4.18
3.66
3.08
2.89
2.83
2.97
2.76
2.91
2.82
3.01
3.06
3.01
2.96
5082
2.23
2.41
3.18
4.00
4.63
5.14
5.39
5.1 1
4.73
4.36
4.30
4.10
3.51
2.76
2.55
2.23
2.22
2.20
2.18
2.09
2.06
2.09
1.97
2.13
Vehicle
9049
11.88
8.79
10.24
11.74
11.62
1 1.19
10.99
9.74
9.04
8.02
7.42
6.91
6.91
6.25
5.63
5.78
5.09
4.91
4.93
4.89
4.70
5.02
4.78
4.88
Numl
9054
10.99
11.24
9.78
13.05
14.28
14.69
14.00
16.08
15.05
14.06
14.85
15.53
14.93
15.03
14.60
13.93
16.37
14.65
11.54
11.30
11.12
9.89
10.36
9.28
D G r --
9087
27.67
28.50
24.65
25.98
25.06
24.61
25.70
25.22
24.21
23.36
20.95
19.67
18.50
17.58
16.57
16.31
13.59
15.29
13.86
13.46
13.69
13.62
13.04
17.05
9111
55.95
46.77
44.26
44.32
45.49
47.67
48.07
47.46
42.41
43.84
36.43
33.72
32.96
25.79
21.55
21.24
20.46
19.64
17.60
16.85
16.52
15.89
15.82
16.40
Mean
18.88
17.07
16.37
17.84
18.44
19.10
18.93
18.90
17.10
16.62
14.88
14.02
13.41
1 1.75
10.63
10.39
10.12
9.91
8.84
8.57
8.52
8.26
8.16
8.78
Modified*
10.48
12.45
16.37
17.84
18.44
19.10
18.93
18.90
17.10
16.62
14.88
14.02
13.41
1 1.75
10.63
10.39
10.12
9.91
8.84
8.57
8.52
8.26
8.16
8.78
Mean emissions for the first two hours have been
"MODIFIED" (see Section 4.2.3) to fit the following
assumed pattern:
The diurnal emissions (i.e., RTD minus resting loss
of 8.52) during the first hour were assumed to be
one-half the diurnal emissions during the second
hour.
The diurnal emissions during the second hour were
assumed to be one-half the diurnal emissions during
the third hour.
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DRAFT
Appendix F
Modeling Hourly Resting Loss Emissions
As Functions of Temperature (°F)
In each of the following 12 strata, resting loss emissions (in
grams per hour) are modeled using a pair of numbers (A and B),
where:
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
Carbureted
Fuel Injected
Model Year
Range
Pre-1980
1980-1985
1986-1995
Pre-1980*
1980-1985
1986-1995
Pass Pressure
Test
0.05530
-0.05957
-0.07551
0.05530
-0.09867
-0.14067
Fail Pressure
Test
0.07454
-0.02163
0.05044
0.07454
0.02565
-0.10924
* 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
C = 0.002632 + (24 * Low Temperature)
+ (11.3535 * Diurnal_Temperature_Range)
Where the Diurnal_Temperature_Range is the difference of the daily
high temperature minus the daily low temperature.
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