EPA420-P-98-018
June 1998
Hot Soak Emissions as a
Function of Soak Time
Edward L. Glover
Assessment and Modeling Division
Office of Mobile Sources
U.S. Enviromental Protection Agency
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 of releasing 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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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.
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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 SFLED - 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.
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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:
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.
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Activity(soaktime) = bl - b2 * exp( -b3 * soaktime**b4 ) Eqn 2
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-1) 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© = 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
5
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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. 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'
o .6.
o
03
LL .4'
^
05
<£ .2<
0
^ 0.0,
c
Figure 1
Fraction of HS Emissions vs Test Length
) 10 20 30 40 50 60
TIME
Figure 2
Mean HS Emission Fraction
1
.6'
'*=
O
03
iV 4'
^:
03
0 „
C/) 2'
0
I 00,
=•=
=!=
0. 10. 20. 30. 40. 50. 60.
TIME
Mean
T Upper 95% CL
1 Low95%CL
a MEAN
-------
Appendix A
Statistical Results
-> USE ALL.
-> COMPUTE filter_$=(test_seq = 17).
-> VARIABLE LABEL filter_$ 'test_seq = 17 (FILTER)1.
-> VALUE LABELS filter_$ 0 'Not Selected' 1 'Selected'
-> FORMAT filter_$ (fl.O).
-> FILTER BY filter_$.
-> EXECUTE .
-> EXAMINE
-> VARIABLES=hs_perc BY time
-> /PLOT NONE
-> /STATISTICS DESCRIPTIVES
-> /CINTERVAL 95
-> /MISSING LISTWISE
- > /NOTOTAL.
HS_PERC
By TIME
Valid cases:
10
240 .0
Missing cases:
Percent missing:
.0
Mean .2659 Std Err .0120 Min
Median .2100 Variance .0343 Max
5% Trim .2441 Std Dev .1853 Range
95% CI for Mean (.2423, .2894) IQR
.0000 Skewness 2.0959
1.0200 S E Skew .1571
1.0200 Kurtosis 4.5601
.1300 S E Kurt .3130
HS_PERC
By TIME
Valid cases:
20
240 .0
Missing cases:
Percent missing:
.0
Mean .4687 Std Err .0104 Min
Median .4300 Variance .0260 Max
5% Trim .4549 Std Dev .1613 Range
95% CI for Mean (.4482, .4892) IQR
.1800 Skewness 1.4434
1.0000 S E Skew .1571
.8200 Kurtosis 1.9371
.1400 S E Kurt .3130
HS_PERC
By TIME
Valid cases:
30
240 .0
Missing cases:
Percent missing:
.0
Mean .6276 Std Err .0083 Min
Median .5950 Variance .0164 Max
5% Trim .6198 Std Dev .1282 Range
95% CI for Mean (.6113, .6439) IQR
.3100 Skewness 1.0080
1.0600 S E Skew .1571
.7500 Kurtosis 1.0257
.1300 S E Kurt .3130
HS_PERC
By TIME
Valid cases:
40
240 .0
Missing cases:
Percent missing:
.0
-------
Mean .7686 Std Err .0059 Min
Median .7500 Variance .0085 Max
5% Trim .7649 Std Dev .0919 Range
95% CI for Mean (.7569, .7803) IQR
.5300 Skewness .8471
1.1600 S E Skew .1571
.6300 Kurtosis 1.2231
.1075 S E Kurt .3130
HS_PERC
By TIME
Valid cases:
50
240 .0
Missing cases:
Percent missing:
.0
Mean .8853 Std Err .0033 Min
Median .8800 Variance .0026 Max
5% Trim .8849 Std Dev .0514 Range
95% CI for Mean (.8788, .8919) IQR
.6700 Skewness .0098
1.0000 S E Skew .1571
.3300 Kurtosis 1.5568
.0650 S E Kurt .3130
HS_PERC
By TIME
Valid cases:
60
240 .0
Missing cases:
.0 Percent missing:
.0
>Note # 17570. Command name: EXAMINE
>The number of unique data values for this cell is equal to one. The cell
>will be included in any boxplots produced but other output will be omitted.
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-> USE ALL.
-> COMPUTE filter_$=(test_seq = 17).
-> VARIABLE LABEL filter_$ 'test_seq = 17 (FILTER)'.
-> VALUE LABELS filter_$ 0 'Not 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) .
'Selected'
* * * *
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
Sum of Squares
88.71651
21 .23650
Mean Square
22.17913
.01480
F =
1498 .69575
Signif F =
.0000
Variable
TIME
CAN
FUEL_RVP
PRECOND
(Constant)
Variables in the Equation
3 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
in
Variable
T Sig T
10
-------
TIME 77.041 .0000
CAN -7.531 .0000
FUEL_RVP -1.859 .0632
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.
12
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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 Averaae
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
13
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