United States Air and Radiation EPA420-R-01-030
Environmental Protection April 2001
Agency M6.EVP007
vxEPA Hot Soak Emissions as a
Function of Soak Time
> Printed on Recycled Paper
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EPA420-R-01-030
April 2001
Hot Soak Emissions as a
Function of Soak Time
M6.EVP.007
Edward L. Glover
U.S. Environmental Protection Agency
Office of Air and Radiation
Office of Transportation and Air Quality
Assessment and Standards Division
NOTICE
77z/s technical report does not necessarily represent final EPA decisions or positions.
It is intended to present technical analysis of issues using data that are currently available.
The purpose in the release of such 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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1.0 INTRODUCTION
MOBILE6 will compute and report (as a user option) hourly emission factors for
start, running, and evaporative emissions. These outputs will be in addition to the
standard daily emission estimates which are currently calculated by MOBILES. The
hourly emission factors will allow the MOBILE6 model to provide more precise output
that accounts for the time of day that vehicle emissions occur.
Hot soaks are one type of evaporative emissions which will be reported on an
hourly basis. They are, by definition, the evaporative hydrocarbon (HC) emissions
which escape from a vehicle during the first hour after the engine is stopped. The
limited data in this analysis suggests that the emissions are not distributed evenly
throughout the hour, but decline as the hour passes. This is likely due to the cooling of
the vehicle and its evaporative system. However, the exact mechanism may include
back purge from the canister to the fuel tank, leaks and permeation effects in the lines,
and canister breakthrough considerations. The reasons why the emissions occurred and
their resulting distribution formed were not investigated in this analysis.
This document (M6.EVP.007) presents an analysis of the rate hot soak
emissions decline over the one hour time period. This information will be used in
MOBILE6 with the hot soak activity information from the document "Soak Length
Activity Factors for Hot Soak Emissions" - EPA Report Number M6.FLT.004, and the
hot soak emission information from the document "Hot Soak Emissions"
(M6.EVP.004).
Structurally, this document is divided into three sections. The first section
briefly describes the data which were analyzed. The second section discusses the
analysis performed on the data. The third section provides the results of the analysis
and shows how they will be applied in the MOBILE6 model.
2.0 DATA
All of the data used to determine the distribution of hot soak emissions as a
function of soak time were collected as part of an EPA study. This study was designed
to be similar to a previous Auto / Oil test program (See SAE Paper 951007 "Real World
Hot Soak Emissions - A Pilot Study"). In the EPA study, 250 vehicles were recruited
and given the standard hot soak test. Only 240 vehicles were used in this analysis since
ten of them received emission control system repairs, and were not representative of the
general fleet. During the test, the hot soak emissions were measured at 10 minute
intervals. Thus, hot soak emission measurements are available at 10, 20, 30, 40, 50 and
60 minute intervals. By definition, the hot soak emissions at time = 0 were assumed to
be 0 grams.
-2-
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Other information was collected during the study in addition to the hot soak
values. This included vehicle identification information, canister type (open bottom,
closed bottom, and unknown), preconditioning prior to the hot soak, and fuel RVP. For
more details on the EPA study please refer to the Final Contractor's (ATL) Report of
Work Assignment 0-2 of EPA Contract 68-C5-0006 "Real World Hot Soak Evaporative
Emissions".
3.0 ANALYSIS
3.1 Hot Soak Fraction
All of the hot soak data (hydrocarbon measurements made in a SHED - sealed
housing for emission detection) were collected at 10 minute intervals during the 60
minute hot soak test. For this analysis, these measurements were transformed into
emission fractions based on the 60 minute test result. This was done by dividing the
individual vehicle hot soak emissions at interval X (i.e., 10 minutes) by the hot soak
emissions at the 60 minute test point (the end of the test). By definition, the zero point
(t=0) was assumed to have a hot soak fraction of 0, and the end of the test (t=60) was
assumed to have a hot soak fraction of 1.0.
Figure 1 shows the hot soak fraction data points versus test time duration. The
figure indicates that many vehicles quickly reach their maximum hot soak emission
value, and emit very little thereafter. Considerable scatter is evident in the figure,
particularly during the early portions of the hot soak test. The reduced scatter at the end
of the test as evidenced in Figure 1, and the slightly concave pattern of the mean hot
soak fractions in Figure 2, suggest that typically hot soak emissions do not occur at or
near the end of the 60 minute test.
3.2 Linear Regressions
A linear regression was performed on the data to determine if test duration,
canister type, preconditioning prior to the hot soak, and fuel RVP significantly affect the
results. The regression results in Appendix A show that test duration and canister type
are statistically significant variables. Preconditioning and fuel RVP were not found to
be significant at a 95% confidence level; although fuel RVP was significant at a 90%
confidence level.
Despite its significance, canister type was eliminated from the analysis because
it is not a variable which will be present in MOBILE6. Thus, analysis by canister type
would prevent the functional relationship from being used in the model. Fleet canister
type information is difficult to obtain, making an accurate default or user defined
MOBILE6 input impractical. However, the vehicle descriptions including canister types
for the data sample are included in the data reports mentioned earlier in this report.
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3.3 Quadratic Fit
Based on Figures 1 and 2, it was decided that a quadratic fit of the hot soak
fraction versus soak time would produce a model which would adequately fit the data,
and be simple to implement in the MOBILE6 model. The quadratic fit was obtained
from a least squares regression of hot soak fraction versus soak time with the regression
intercept fixed at zero. Fixing the zero point was done because the hot soak fraction is
defined to be zero when the soak time is zero. The regression statistics are shown in
Appendix A. The regression equation is:
2
HSFract = 0.0258 * Soaktime + 0.000156 * Soaktime Eqn 1
4.0 Using the Hot Soak Fraction in MOBILE6
The hot soak fractions developed in this analysis will be used in conjunction
with basic hot soak emission values and hot soak activities to predict hourly hot soak
emission rates in MOBILE6.
4.1 Basic Hot Soak Emission Value from MOBILE6
For this illustration the basic hot soak emission value is assumed to be X. It is
based on testing and is an average result which reflects the entire 60 minute hot soak
test. The actual hot soak value will be calculated by the model based on the specific
characteristics of the vehicle class and model year. This calculation will be described in
EPA document M6.EVP.004.
4.2 Hot Soak Fraction
The variable HS Fraction shown in Equation 1 is the cumulative hot soak
fraction at a given time. For example using Equation 1, at a soaktime of 30 minutes,
59.8% of the hot soak emissions have been emitted.
4.3 Hot Soak Activity
Equation 2 is the general equation for hot soak activity. It can be found in the
EPA document "Soak Length Activity Factors for Hot Soak Emissions" - EPA Report
Number M6.FLT.004. This equation calculates the cumulative hot soak activity at a
give time during the test.
Activity(soaktime) = bl - b2 * exp( -b3 * soaktime**b4 ) Eqn 2
-4-
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For example, substituting the coefficients for the 9 to 10 AM Weekday curve
estimates that 44.1 percent of all hot soaks have a soak time of 30 minutes or less.
Activity = 3212.9 - 32.712*exp[4.589 * 30 **-0.001003]
However, a cumulative hot soak activity is not used in the MOBILE6 model.
Instead, the cumulative distribution is broken into one minute intervals, and the amount
of activity for each interval is calculated. This is done by subtracting the previous
activity value from the current value. Mathematically this is:
Interval Activity(t) = Activity(t) - Activity(t-l) Eqn 3
Where t is the time from 1 to 60, and "Interval Activity" represents the fraction
of hot soaks with a soak time between t and t-1.
4.4 Calculating the Hourly Hot Soak Emissions
In the MOBILE6 model, the hot soak emission and activity distributions will be
calculated in one minute intervals ranging from t=0 to t=60 minutes. The overall hot
soak emission (X), the cumulative HS Fraction and the Interval Activity parameters will
be calculated by weighting the three pieces together and summing the product to
produce an overall hourly hot soak emission result.
The hot soak emission value for an individual interval at time = t is calculated
by multiplying the cumulative HS Fraction at time = t, and the Interval Activity at time
= t, and the mean hot soak 60 minute test emission value (X) together using Equation 5.
Interval Hot Soak(t) = Cumulative HS Fraction(t) * Interval Activity(t)*X Eqn 5
Where X is the average hot soak emissions for a 60 minute test.
The hourly hot soak emissions are calculated by summing the 60 individual
Interval Hot Soak(t) values.
Hourly Hot Soak = SUM [Interval Hot Soak(t)] Eqn 6
where t ranges from 0 to 60 minutes.
A sample calculation spreadsheet illustrating the hot soak calculation for the 9 to
10 AM weekday case is shown in Appendix B. In the example calculation, the one hour
average hot soak (X) is assumed to be 100 grams. This is not the actual value which
will be used in MOBILE6. It is shown as a round number (100) for illustration only.
-5-
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For this example when 100 grams is used for the overall average hot soak after 60
minutes, the resulting hourly soak with emission fraction and activity fraction weighting
is 63.179 grams.
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1.0-
.8'
0 .6'
ts
2 A
LL .4'
_*:
0 9
C/) -2'
£ 0.0,
C
Figure 1
Fraction of HS Emissions vs Test Length
•
i
I
I
•
>
) 10 20 30 40 50 60
TIME
-7-
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Appendix A
Statistical Results
-> USE ALL.
-> COMPUTE filter_$=(test_seq = 17).
-> VARIABLE LABEL filter_$ 'test_seq = 17 (FILTER)'.
-> VALUE LABELS filter_$ 0 'Not Selected' 1 'Selected'
-> FORMAT filter_$ (fl.O).
-> FILTER BY filter_$.
-> EXECUTE .
-> EXAMINE
-> VARIABLES=hs_perc BY time
-> /PLOT NONE
-> /STATISTICS DESCRIPTIVES
-> /CINTERVAL 95
-> /MISSING LISTWISE
-> /NOTOTAL.
HS_PERC
By TIME 10
Valid cases:
240.0 Missing cases:
.0 Percent missing:
.0
Mean
.2659 Std Err
.0120 Min
.0000 Skewness 2.0959
1.0'
.8'
r
U_ .4'
_*:
CO
& .2-
=c o.o,
Figure 2
Mean HS Emission Fraction
=
=•=
=s=
0. 10. 20. 30. 40. 50. 60.
TIME
Mean
T Upper 95% CL
1 Low95%CL
n MEAN
Median
5% Trim
.2100 Variance
.2441 Std Dev
.0343 Max
.1853 Range
1.0200 S E Skew
1.0200 Kurtosis
.1571
4 .5601
-------
95% CI for Mean (.2423, .2894)
IQR
.1300 S E Kurt
.3130
HS_PERC
By TIME
Valid cases:
20
240.0
Missing cases:
Percent missing:
. 0
Mean .4687 Std Err .0104 Min
Median .4300 Variance .0260 Max
5% Trim .4549 Std Dev .1613 Range
95% CI for Mean (.4482, .4892) IQR
.1800 Skewness 1.4434
1.0000 S E Skew .1571
.8200 Kurtosis 1.9371
.1400 S E Kurt .3130
HS_PERC
By TIME
Valid cases:
30
240.0 Missing cases:
Percent missing:
. 0
Mean .6276 Std Err
Median .5950 Variance
5% Trim .6198 Std Dev
95% CI for Mean (.6113, .6439)
.0083 Min
.0164 Max
.1282 Range
IQR
.3100 Skewness 1.0080
1.0600 S E Skew .1571
.7500 Kurtosis 1.0257
.1300 S E Kurt .3130
HS_PERC
By TIME
Valid cases:
40
240.0 Missing cases:
Percent missing:
. 0
Mean .7686 Std Err .0059 Min
Median .7500 Variance .0085 Max
5% Trim .7649 Std Dev .0919 Range
95% CI for Mean (.7569, .7803) IQR
.5300 Skewness .8471
1.1600 S E Skew .1571
.6300 Kurtosis 1.2231
.1075 S E Kurt .3130
HS_PERC
By TIME
Valid cases:
50
240.0 Missing cases:
Percent missing:
. 0
Mean .8853 Std Err .0033 Min
Median .8800 Variance .0026 Max
5% Trim .8849 Std Dev .0514 Range
95% CI for Mean (.8788, .8919) IQR
.6700 Skewne s s .0098
1.0000 S E Skew .1571
.3300 Kurtosis 1.5568
.0650 S E Kurt .3130
HS_PERC
By TIME
Valid cases:
60
240.0 Missing cases:
. 0
Percent missing:
. 0
>Note # 17570. Command name: EXAMINE
>The number of unique data values for this cell is equal to one. The cell
>will be included in any boxplots produced but other output will be omitted.
-9-
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-> USE ALL.
-> COMPUTE filter_$=(test_seq = 17).
-> VARIABLE LABEL filter_$ 'test_seq = 17 (FILTER)'.
-> VALUE LABELS filter_$ 0 'Not Selected1 1 'Selected'
-> FORMAT filter_$ (fl.O).
-> FILTER BY filter_$.
-> EXECUTE .
-> REGRESSION
-> /MISSING LISTWISE
-> /STATISTICS COEFF OUTS CI R ANOVA
-> /CRITERIA=PIN(.05) POUT(.10)
-> /NOORIGIN
-> /DEPENDENT hs_perc
-> /METHOD=ENTER time can fuel_rvp precond
-> /RESIDUALS HIST(ZRESID) NORM(ZRESID) .
* * * *
MULTIPLE
REGRESSION
* * * *
Listwise Deletion of Missing Data
Equation Number 1 Dependent Variable.. HS_PERC
Block Number 1. Method: Enter TIME CAN
FUEL RVP PRECOND
Variable(s) Entered on Step Number
1.. PRECOND
2 . . TIME
3.. CAN
4.. FUEL RVP
Multiple R .89825
R Square .80686
Adjusted R Square .80632
Standard Error .12165
Analysis of Variance
DF
Regression 4
Residual 1435
F =
1498.69575
Sum of Squares
88.71651
21.23650
Signif F = .0000
Mean Square
22 .17913
.01480
Variable
TIME
CAN
FUEL_RVP
PRECOND
(Constant)
- Variables in the Equation
B SE B 95% Confdnce Intrvl B
.014461
- .020136
-3 .19716E-04
- .004923
.233692
1.8771E-04 .014093
.002674 -.025381
1.7195E-04 -6.57019E-04
.008094 -.020800
.014555 .205140
.014830
-.014891
1.75872E-05
.010954
.262244
Beta
.893783
-.087556
-.021644
-.007070
Variable
TIME
CAN
FUEL RVP
T Sig T
77.041 .0000
-7.531 .0000
-1.859 .0632
-10-
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PRECOND -.608 .5431
(Constant) 16.055 .0000
**** MULTIPLE REGRESSION ****
Equation Number 1 Dependent Variable.. HS_PERC
End Block Number 1 All requested variables entered.
Residuals Statistics:
Min Max Mean Std Dev N
*PRED .2560 1.0746 .6694 .2483 1440
*RESID -.3512 .7089 .0000 .1215 1440
*ZPRED -1.6649 1.6319 .0000 1.0000 1440
*ZRESID -2.8872 5.8271 .0000 .9986 1440
Total Cases = 1440
Hi-Res Chart # 13:Histogram of *zresid
Hi-Res Chart # 14:Normal p-p plot of *zresid
-11-
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-> GET
-> FILE='D:\MOBILE6\EVAP\EMIS\AOH95_2.SAV'
-> EXECUTE .
-> * Curve Estimation.
-> TSET NEWVAR=NONE .
-> CURVEFIT /VARIABLES=hs_perc WITH time
-> /NOCONSTANT
-> /MODEL=QUADRATIC
-> /PRINT ANOVA
-> /PLOT FIT.
MODEL: MOD 8.
Dependent variable.. HS_PERC
Listwise Deletion of Missing Data
Multiple R .98589
R Square .97197
Adjusted R Square .97194
Standard Error .12122
Analysis of Variance:
DF Sum of Squares
Regression
Residuals
2
1498
763.37082
22.01098
Method.. QUADRATI
Mean Square
381 .68541
.01469
F =
25976.34126
Variable
TIME
TIME**2
Signif F = .0000
Variables in the Equation
B SE B Beta
.025772 .000326
-.000156 6.5297E-06
T Sig T
1.387091 78.938 .0000
-.419536 -23.875 .0000
Notes:
* Equation was estimated without the constant term; Rsq is redefined.
Notes:
* Equation was estimated without the constant term; Rsq is redefined.
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Appendix B - Sample Calculation
Soak time
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Activity %
0.0000
4.4196
10.3965
14.6290
17.9073
20.5828
22.8427
24.7988
26.5230
28.0644
29.4580
30.7295
31.8987
32.9808
33.9877
34.9293
35.8135
36.6468
37.4348
38.1822
38.8929
39.5704
40.2176
40.8370
41.4311
42.0017
42.5507
43.0796
43.5898
44.0826
44.5592
45.0205
45.4676
45.9013
46.3223
46.7314
47.1292
47.5164
47.8934
48.2609
48.6192
48.9689
49.3102
49.6437
49.9696
50.2884
50.6002
50.9054
51.2044
51.4972
51.7842
52.0656
52.3416
52.6124
52.8783
53.1393
53.3957
53.6475
53.8951
54.1385
100.0000
Activity Fract
0.0000
0.0442
0.1040
0.1463
0.1791
0.2058
0.2284
0.2480
0.2652
0.2806
0.2946
0.3073
0.3190
0.3298
0.3399
0.3493
0.3581
0.3665
0.3743
0.3818
0.3889
0.3957
0.4022
0.4084
0.4143
0.4200
0.4255
0.4308
0.4359
0.4408
0.4456
0.4502
0.4547
0.4590
0.4632
0.4673
0.4713
0.4752
0.4789
0.4826
0.4862
0.4897
0.4931
0.4964
0.4997
0.5029
0.5060
0.5091
0.5120
0.5150
0.5178
0.5207
0.5234
0.5261
0.5288
0.5314
0.5340
0.5365
0.5390
0.5414
1.0000
Delta Act Fract
0.0442
0.0598
0.0423
0.0328
0.0268
0.0226
0.0196
0.0172
0.0154
0.0139
0.0127
0.0117
0.0108
0.0101
0.0094
0.0088
0.0083
0.0079
0.0075
0.0071
0.0068
0.0065
0.0062
0.0059
0.0057
0.0055
0.0053
0.0051
0.0049
0.0048
0.0046
0.0045
0.0043
0.0042
0.0041
0.0040
0.0039
0.0038
0.0037
0.0036
0.0035
0.0034
0.0033
0.0033
0.0032
0.0031
0.0031
0.0030
0.0029
0.0029
0.0028
0.0028
0.0027
0.0027
0.0026
0.0026
0.0025
0.0025
0.0024
0.4586
Emission
0.0256
0.0510
0.0760
0.1007
0.1251
0.1492
0.1730
0.1964
0.2196
0.2424
0.2649
0.2871
0.3090
0.3306
0.3519
0.3729
0.3935
0.4139
0.4339
0.4536
0.4730
0.4921
0.5109
0.5293
0.5475
0.5653
0.5829
0.6001
0.6170
0.6336
0.6499
0.6659
0.6815
0.6969
0.7119
0.7266
0.7410
0.7551
0.7689
0.7824
0.7956
0.8084
0.8210
0.8332
0.8451
0.8567
0.8680
0.8790
0.8896
0.9000
0.9100
0.9198
0.9292
0.9383
0.9471
0.9556
0.9638
0.9716
0.9792
1.0000
HS Average
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
Wt Emiss
0.1133
0.3047
0.3217
0.3301
0.3347
0.3372
0.3383
0.3387
0.3384
0.3378
0.3369
0.3357
0.3344
0.3329
0.3313
0.3297
0.3279
0.3261
0.3243
0.3224
0.3204
0.3185
0.3165
0.3145
0.3124
0.3104
0.3083
0.3062
0.3041
0.3020
0.2998
0.2977
0.2955
0.2934
0.2912
0.2891
0.2869
0.2847
0.2825
0.2804
0.2782
0.2760
0.2738
0.2716
0.2694
0.2672
0.2649
0.2627
0.2605
0.2583
0.2561
0.2539
0.2516
0.2494
0.2472
0.2450
0.2428
0.2405
0.2383
45.8615
63.1797
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