1

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.
2

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 MOBILE5. 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.
3

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. 
4

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:

HS Fract = 0.0258 * Soaktime + 0.000156 * Soaktime Eqn 1 2

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.
5

Activity(soaktime) = b1 - 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(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
6

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.
Figure 1

Fraction of HS Emissions vs Test Length

TIME

0 10 20 30 40 50 60

Hot Soak Fraction

1.0

.8

.6

.4

.2

0.0

Figure 2

Mean HS Emission Fraction

TIME

0. 10. 20. 30. 40. 50. 60.

Hot Soak Fraction

1.0

.8

.6

.4

.2

0.0

Mean

Upper 95% CL

Low 95% CL

MEAN

7
8

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_$ (f1.0).

-> 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

 Median .2100 Variance .0343 Max 1.0200 S E Skew .1571

 5% Trim .2441 Std Dev .1853 Range 1.0200 Kurtosis 4.5601

 95% CI for Mean (.2423, .2894) IQR .1300 S E Kurt .3130

 HS_PERC

 By TIME 20

 Valid cases: 240.0 Missing cases: .0 Percent missing: .0

 Mean .4687 Std Err .0104 Min .1800 Skewness 1.4434

 Median .4300 Variance .0260 Max 1.0000 S E Skew .1571

 5% Trim .4549 Std Dev .1613 Range .8200 Kurtosis 1.9371

 95% CI for Mean (.4482, .4892) IQR .1400 S E Kurt .3130

 HS_PERC

 By TIME 30

 Valid cases: 240.0 Missing cases: .0 Percent missing: .0

 Mean .6276 Std Err .0083 Min .3100 Skewness 1.0080

 Median .5950 Variance .0164 Max 1.0600 S E Skew .1571

 5% Trim .6198 Std Dev .1282 Range .7500 Kurtosis 1.0257

 95% CI for Mean (.6113, .6439) IQR .1300 S E Kurt .3130

 HS_PERC

 By TIME 40

 Valid cases: 240.0 Missing cases: .0 Percent missing: .0
9

 Mean .7686 Std Err .0059 Min .5300 Skewness .8471

 Median .7500 Variance .0085 Max 1.1600 S E Skew .1571

 5% Trim .7649 Std Dev .0919 Range .6300 Kurtosis 1.2231

 95% CI for Mean (.7569, .7803) IQR .1075 S E Kurt .3130

 HS_PERC

 By TIME 50

 Valid cases: 240.0 Missing cases: .0 Percent missing: .0

 Mean .8853 Std Err .0033 Min .6700 Skewness .0098

 Median .8800 Variance .0026 Max 1.0000 S E Skew .1571

 5% Trim .8849 Std Dev .0514 Range .3300 Kurtosis 1.5568

 95% CI for Mean (.8788, .8919) IQR .0650 S E Kurt .3130

 HS_PERC

 By TIME 60

 Valid cases: 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.
10

-> USE ALL.

-> COMPUTE filter_$=(test_seq = 17).

-> VARIABLE LABEL filter_$ 'test_seq = 17 (FILTER)'.

-> VALUE LABELS filter_$ 0 'Not Selected' 1 'Selected'.

-> FORMAT filter_$ (f1.0).

-> 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) .

 * * * * M U L T I P L E R E G R E S S I O N * * * *

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 Sum of Squares Mean Square

Regression 4 88.71651 22.17913

Residual 1435 21.23650 .01480

F = 1498.69575 Signif F = .0000

---------------------- Variables in the Equation -----------------------

Variable B SE B 95% Confdnce Intrvl B Beta

TIME .014461 1.8771E-04 .014093 .014830 .893783

CAN -.020136 .002674 -.025381 -.014891 -.087556

FUEL_RVP -3.19716E-04 1.7195E-04 -6.57019E-04 1.75872E-05 -.021644

PRECOND -.004923 .008094 -.020800 .010954 -.007070

(Constant) .233692 .014555 .205140 .262244

----------- in ------------

Variable T Sig T
11

TIME 77.041 .0000

CAN -7.531 .0000

FUEL_RVP -1.859 .0632

PRECOND -.608 .5431

(Constant) 16.055 .0000

 * * * * M U L T I P L E R E G R E S S I O N * * * *

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
12

 

 

-> 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 Method.. QUADRATI

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 Mean Square

Regression 2 763.37082 381.68541

Residuals 1498 22.01098 .01469

F = 25976.34126 Signif F = .0000

-------------------- Variables in the Equation --------------------

Variable B SE B Beta T Sig T

TIME .025772 .000326 1.387091 78.938 .0000

TIME**2 -.000156 6.5297E-06 -.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.
Soak time Activity % Activity Fract Delta Act Fract Emission HS Average Wt Emiss

1 0.0000 0.0000 0.0442 0.0256 100 0.1133

2 4.4196 0.0442 0.0598 0.0510 100 0.3047

3 10.3965 0.1040 0.0423 0.0760 100 0.3217

4 14.6290 0.1463 0.0328 0.1007 100 0.3301

5 17.9073 0.1791 0.0268 0.1251 100 0.3347

6 20.5828 0.2058 0.0226 0.1492 100 0.3372

7 22.8427 0.2284 0.0196 0.1730 100 0.3383

8 24.7988 0.2480 0.0172 0.1964 100 0.3387

9 26.5230 0.2652 0.0154 0.2196 100 0.3384

10 28.0644 0.2806 0.0139 0.2424 100 0.3378

11 29.4580 0.2946 0.0127 0.2649 100 0.3369

12 30.7295 0.3073 0.0117 0.2871 100 0.3357

13 31.8987 0.3190 0.0108 0.3090 100 0.3344

14 32.9808 0.3298 0.0101 0.3306 100 0.3329

15 33.9877 0.3399 0.0094 0.3519 100 0.3313

16 34.9293 0.3493 0.0088 0.3729 100 0.3297

17 35.8135 0.3581 0.0083 0.3935 100 0.3279

18 36.6468 0.3665 0.0079 0.4139 100 0.3261

19 37.4348 0.3743 0.0075 0.4339 100 0.3243

20 38.1822 0.3818 0.0071 0.4536 100 0.3224

21 38.8929 0.3889 0.0068 0.4730 100 0.3204

22 39.5704 0.3957 0.0065 0.4921 100 0.3185

23 40.2176 0.4022 0.0062 0.5109 100 0.3165

24 40.8370 0.4084 0.0059 0.5293 100 0.3145

25 41.4311 0.4143 0.0057 0.5475 100 0.3124

26 42.0017 0.4200 0.0055 0.5653 100 0.3104

27 42.5507 0.4255 0.0053 0.5829 100 0.3083

28 43.0796 0.4308 0.0051 0.6001 100 0.3062

29 43.5898 0.4359 0.0049 0.6170 100 0.3041

30 44.0826 0.4408 0.0048 0.6336 100 0.3020

31 44.5592 0.4456 0.0046 0.6499 100 0.2998

32 45.0205 0.4502 0.0045 0.6659 100 0.2977

33 45.4676 0.4547 0.0043 0.6815 100 0.2955

34 45.9013 0.4590 0.0042 0.6969 100 0.2934

35 46.3223 0.4632 0.0041 0.7119 100 0.2912

36 46.7314 0.4673 0.0040 0.7266 100 0.2891

37 47.1292 0.4713 0.0039 0.7410 100 0.2869

38 47.5164 0.4752 0.0038 0.7551 100 0.2847

39 47.8934 0.4789 0.0037 0.7689 100 0.2825

40 48.2609 0.4826 0.0036 0.7824 100 0.2804

41 48.6192 0.4862 0.0035 0.7956 100 0.2782

42 48.9689 0.4897 0.0034 0.8084 100 0.2760

43 49.3102 0.4931 0.0033 0.8210 100 0.2738

44 49.6437 0.4964 0.0033 0.8332 100 0.2716

45 49.9696 0.4997 0.0032 0.8451 100 0.2694

46 50.2884 0.5029 0.0031 0.8567 100 0.2672

47 50.6002 0.5060 0.0031 0.8680 100 0.2649

48 50.9054 0.5091 0.0030 0.8790 100 0.2627

49 51.2044 0.5120 0.0029 0.8896 100 0.2605

50 51.4972 0.5150 0.0029 0.9000 100 0.2583

51 51.7842 0.5178 0.0028 0.9100 100 0.2561

52 52.0656 0.5207 0.0028 0.9198 100 0.2539

53 52.3416 0.5234 0.0027 0.9292 100 0.2516

54 52.6124 0.5261 0.0027 0.9383 100 0.2494

55 52.8783 0.5288 0.0026 0.9471 100 0.2472

56 53.1393 0.5314 0.0026 0.9556 100 0.2450

57 53.3957 0.5340 0.0025 0.9638 100 0.2428

58 53.6475 0.5365 0.0025 0.9716 100 0.2405

59 53.8951 0.5390 0.0024 0.9792 100 0.2383

60 54.1385 0.5414 0.4586 1.0000 100 45.8615

100.0000 1.0000

63.1797

13

Appendix B - Sample Calculation