1

The DELTA Model: Improved Evaporative Emissions Modeling for EPA MOVES

DRAFT

October 13, 2011

Jarrod Brown, Philip Carlson

Assessment and Standards Division

Office of Transportation and Air Quality

U.S. Environmental Protection Agency

This report documents the assumptions, data sources, calculations and limitations used to 

estimate on-road vehicle evaporative emissions due to multi-day diurnal cycles using the 

DELTA (Diurnal Emissions Leaving To Atmosphere) model. This new model is associated with 

updates to the EPA MOVES model in conjunction with the proposed Tier 3 rulemaking.

I. Summary

The MOVES 2010a model contains evaporative emissions estimates based on older data 

that could not adequately model emissions beyond one day of diurnals. The DELTA model was 

created to update MOVES 2010a evaporative vapor emissions to extend beyond one day of 

diurnals as well as taking advantage of newer datasets. Curves generated by the DELTAmodel 

would replace the cumTTVcoeffs table found in the default MOVES database, as well as 

including changes to the MOVES Java code to account for new calculations steps included with 

the replacement curves. The DELTA model runs using Python 2.6.2 and associated open source 

libraries; however, it is designed to run internally to the MOVES model and should not require 

interaction from MOVES users.

The DELTA model uses the Wade-Reddy equation for vapor generated from the vehicle 

fuel tank and backpurge factors derived from a previous EPA marine canister study. By 

modeling a single vehicle’s response over the course of multiple diurnals, the DELTA model can 

generate a relationship between tank vapor generated (TVG) and tank vapor vented to the 

atmosphere (TVV) as a TVG – TVV curve. Multiple single vehicle models can then be 

combined to create a single, weighted TVG – TVV curve representative of the entire fleet for use 

in the MOVES model, including specific vehicle standard groups such as Pre-enhanced, 

Enhanced/Tier 1 and Tier 2. 

The results from the DELTA model were compared to multiple day diurnal emissions 

measured as part of the CRC E77 project. It was shown that the DELTA model under ideal 

conditions under-predicts diurnal emissions compared to the real world data seen from E77. 

Further exploration revealed that many of the vehicles in the E77 dataset captured significantly 

less vapor than their rated canister capacity before vapor breakthrough which the DELTA 

modeling was based upon. A supplementary approach was then developed to adjust the DELTA 

model results to account for this non-ideal behavior.
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II. What is the DELTA model?

This section provides background information regarding the current evaporative inputs in 

the MOVES 2010a model and why it they would be updated, what the DELTA model would 

replace in MOVES, and how the DELTA model would function within the MOVES model.

a. Why create the DELTA model?

The MOVES 2010a evaporative emissions estimates were based on IUVP vapor venting 

emission data collected between 1994 and 1996 (please see EPA Development of Evaporative 

Emissions Calculations for the Motor Vehicle Emissions Simulator MOVES2010 – March 2010 

for more information). This data provides SHED evaporative emissions (in grams) for a large set 

of vehicles undergoing a single diurnal cycle. This data was then fit with a quadratic equation as 

shown in Figure 1.

Figure 1 - MOVES 2010a Vapor Venting Curves

Note: These curves apply to a vehicle fleet average of 11 gallons of tank headspace

Although the IUVP data in MOVES 2010a provided a large and robust dataset for one 

day of emissions, it was not capable of modeling evaporative emissions beyond one day of 

diurnal cycling, as desired for future scenarios. Furthermore, using quadratic equations to fit 

diurnal emissions was not accurately representing the actual response of canister breakthrough; 

mainly a prediction of non-zero breakthrough at very low vapor generation not seen in actual 

data due to canister storage capacity. Therefore, the DELTA model was developed in order to 

more accurately represent multiple day canister loading and breakthrough.
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b. What is DELTA replacing in MOVES?

The previous breakthrough emissions equations were contained in the cumTVVcoeffs 

table found in the MOVES database. DELTA would replace these equations with a new set of 

equations generated within the DELTA model. The DELTA model was focused primarily on 

light duty vehicles and therefore this section of the database received the most rigorous changes. 

However, both motorcycles and heavy duty vehicles also benefit from the new calculation of 

multiple day diurnals and allow for the addition of new data sources for diurnal information at a 

later date. The DELTA model also introduces changes to the MOVES Java code in order to take 

into account the nature of multiple day diurnal cycles. These new features (including the DELTA 

equations) can be deactivated if running MOVES using the older evaporative model is desired. 

c. How does the DELTA model function?

The DELTA model is currently written in Python 2.6.2 and uses several extensions to the 

base Python library. Equation fitting was done using a custom Microsoft Excel spreadsheet, 

based on a least-squares approach fitting a rotated hyperbolic section. This process is explained 

in more detail in later sections. More information regarding the MOVES model can be found at 

the EPA MOVES website (http://www.epa.gov/otaq/models/moves/index.htm). It is important to 

note that the DELTA model was written to be run only internally to the MOVES model for the 

generation of TVG – TVV curves. Interaction between the DELTA model and MOVES users is 

not required or expected for evaporative emissions modeling or SIP analyses. A copy of a 

standalone version of the DELTA model source code can be found in Appendix A for review.

III. Modeling a single ideal vehicle

This section begins a walkthrough of the theory behind the DELTA model. Beginning 

with a single vehicle, this section provides information on how vapor is generated during a 

diurnal cycle, how vapor is captured by an evaporative system, how systems may gain capacity 

during the cooling part of a diurnal cycle, and how a diurnal can be extended to multiple days in 

the model.

a. Tank vapor generation - The Wade-Reddy model

The source of diurnal emissions we are concerned about in the DELTA model is 

evaporation of gasoline vapor from a vehicle’s tank during a rise in temperature. The evaporation 

rate is dependent on how much temperature change has occurred, the volatility of the fuel (RVP), 

the ethanol content of the fuel (E0, E10, etc...) and the altitude of the vehicle over sea level. 

Generally as temperature change, fuel volatility, and altitude increase, vapor evaporation also 

increases. Ethanol effects vary in that vapor evaporation increases as ethanol concentration 

increases until approximately 15% ethanol content. At higher concentrations evaporation 

decreases with increasing ethanol due to nonlinear effects on fuel volatility, with volatility 

returning to E0 levels around 50% ethanol content and decreasing from there.
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In 1989 Samuel Reddy published SAE paper 892089 which characterizes the evaporation 

rates for different temperature ranges, volatilities, altitudes and ethanol concentrations. From 

these results a model of gasoline evaporation rates was created, as seen in Equation 1:

Equation 1 – Wade-Reddy Tank Vapor Generation

Where A, B and C are coefficients based on altitude and ethanol content

The Wade-Reddy model for fuel evaporation is currently used in MOVES in order to 

calculate evaporative emissions for differing locations and fuel properties. DELTA continues to 

utilize the Wade-Reddy model for the RVP and temperature ranges needed for evaporative 

emissions modeling in MOVES. Further information regarding gasoline vapor generation is 

beyond the scope of this document; please refer to SAE 892089 for more details.

b. Tank vapor venting

Vehicle evaporative systems contain a bed of activated carbon in order to capture vapors 

generated from a vehicle fuel tank during diurnal heating. This activated carbon is usually 

contained in a canister present between a vehicle tank vent and the atmosphere. Vapor leaving a 

vehicle fuel tank without being captured by the carbon canister is usually referred to as 

breakthrough. The terms canister, activated carbon, or carbon bed used in the next sections refer 

to this canister of activated carbon. The amount of vapor leaving the fuel tank through this 

canister depends not only on the amount of fuel vapor generated, but also on properties of the 

carbon bed. These properties are briefly explained in the next subsections, an in-depth discussion 

of carbon properties is beyond the scope of this document.

i. Activated carbon properties - butane working capacity

Activated carbon is able to store evaporated fuel vapors through adsorption onto its 

surface. The rate and quantity of this adsorption is affected by properties of the carbon including: 

the extent of carbon bed heel, the number and size of pore sites, the geometry of the carbon 

canister, the presence of channeling in the carbon bed and the material the activated carbon was 

created from. These properties are usually aggregated into the total weight of fuel vapor a 

canister is capable of adsorbing (usually in grams), known as the butane working capacity 

(BWC). The EPA procedure for determining the BWC of a canister can be found in CFR 86.132-

96; the ASTM procedure for determining BWC can be found in ASTM D-5228-92. While we are 

aware that carbon properties may affect canister performance in ways that cannot be captured 

using BWC, we have focused on BWC for the DELTA model at this time. Improvements 

incorporating these properties may be incorporated into a future version of the DELTA model.

ii. Canister loading and non-linear effects

Canister adsorption is also affected by the temperature of the canister as well as the rate 

of vapor loading onto the canister. Activated carbon adsorption rates are inversely proportional 

to the temperature of the carbon bed. As the temperature of the canister rises, the rate of 

adsorption decreases while the rate of desorption increases. This has the effect of lowering the 
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BWC with higher temperatures. This effect is magnified by the exothermic nature of vapor 

adsorption onto the carbon bed. High vapor loading rates (such as those found during onboard 

refueling vapor recovery, ORVR) significantly increase the temperature of the carbon bed, 

reducing the capacity of the vapor storage. Conversely, this effect can increase the effectiveness 

of a canister clean-out event if the canister is heated due to the increased desorption rates at high 

temperatures.

Canister loading does not occur linearly throughout the carbon bed. While it is 

convenient to think of vapor loading into the canister similarly to a glass filling with water (and 

eventually overflowing when the glass is full), fuel vapors form a concentration gradient 

throughout the carbon bed. During short term loading events (such as ORVR), the fuel vapor 

does not have sufficient time to spread into a gradient before a clean-out event takes place. 

However, a diurnal lasting several days provides ample time for some vapor to move beyond the 

front of high concentration near the inlet to the canister. This can cause a ‘bleed’ effect where 

fuel vapor is escaping the canister long before the canister has adsorbed to its rated capacity. 

Differing carbon properties alter the concentration gradient and can affect the rate of bleed to the 

atmosphere.

In the DELTA model canister loading occurs without temperature or bleed effects. Both 

of these effects require input beyond the capabilities of MOVES (canister loading rate, specific 

carbon quality) and would also significantly increase the time to run the DELTA model. 

Methods to incorporate these effects into the next version of the DELTA model are under 

development.

c. Canister backpurge

Durring the cooling phase of a diurnal, fresh air from the atmosphere is drawn back into a 

vehicle fuel tank and across the carbon bed in the canister. This fresh air causes some fuel vapor 

to desorb from the carbon and return to the fuel tank, a process called backpurge, or passive 

purge (as opposed to active purge, where vehicle intake vacuum is used to draw fresh air through 

the canister and into the engine to achieve the same effect). Backpurge essentially creates 

additional vapor capacity within the canister during the cooling phase of a diurnal. The amount 

of additional capacity created is dependent on the magnitude of the temperature change as well 

as the amount of vapor already contained in the canister. Backpurge was studied by EPA as a 

control strategy for marine vehicle evaporative systems lacking active purge (EPA420-R-08-014, 

Chapter 5). Since this phenomenon also occurs within vehicle canisters the rates derived from 

this study are appropriate for use with onroad vehicles as well, it also served as the basis for 

backpurge in the DELTA model.
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d. Multiple day diurnal emissions for a single ideal vehicle

Modeling a single vehicle requires combining the above three topics (tank vapor 

generation, canister loading, and canister backpurge) in a way that emulates real-world multiple 

day diurnal cycles. This includes calculating the amount of vapor generated during the warming 

phase of a diurnal, loading the canister and accounting for potential breakthrough, and 

calculating additional canister capacity gained through backpurge during the cooling phase of a 

diurnal. The following subsections walk through how the DELTA model would combine these 

topics to calculate multiple day diurnal emissions for a single vehicle.

i. Construction of a TVG - TVV curve

Although it is possible to track diurnal emissions through time, we have decided in the 

DELTA model to associate diurnal emissions with the total amount of vapor generated 

throughout multiple diurnal cycles. In this way, diurnal emissions (tank vapor vented, TVV) 

become a function of the amount of vapor generated in the tank (tank vapor generated, TVG) 

independent of how that vapor was generated. Therefore, the TVG - TVV equation is based 

entirely on canister properties specific to the vehicle being modeled (canister working capacity 

and backpurge characteristics). This allows for the flexibility of differing fuel properties or 

diurnal temperature profiles without having to recalculate entirely new emission equations.

Figure 2 - Ideal Vehicle TVG-TVV Curve

As shown in Figure 2, the model of an ideal vehicle TVG - TVV equation is simple. 

Starting with a clean canister, vapor being generated is entirely captured in the canister, resulting 

in no breakthough emissions. At a point where the amount of vapor generated has reached the 

working capacity of the canister, breakthough begins to occur. The amount of breakthrough after 

this point is equal to the amount of vapor generated beyond this point (due to the canister’s 

inability to adsorb additional vapor beyond its capacity), appearing as a line with slope equal to 

one.
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ii. Using a TVG - TVV curve for multiple diurnals

The DELTA model uses the TVG - TVV curve illustrated in the above subsection III.d.i 

to calculate breakthrough emissions occurring after several diurnal temperature cycles. This is 

accomplished by calculating the total tank vapor generated for a given diurnal, adding that to the 

previous total vapor generation and then using the curve for TVV at this TVG point. The total 

vapor generation is then adjusted in the negative direction to account for the additional capacity 

created by backpurge during the diurnal cooling phase. This process is illustrated in the next set 

of figures.

Figure 3 - TVG-TVV Day 1 Vapor Generation

In Figure 3, the diurnal vapor generation for one day has been calculated and found on 

the TVG - TVV curve. In this example, the vapor is entirely captured by the canister resulting in 

zero breakthough for the first day. Therefore, DELTA would report a value of zero breakthough 

for this vehicle on day one in MOVES.

Figure 4 - TVG-TVV Day 1 Backpurge

In Figure 4, the backpurge has now been calculated and subtracted from the total vapor 

generation (accounting for the additional capacity created by the backpurge during diurnal 

cooling). Calculations for a day two diurnal temperature cycle would begin at this point.
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Figure 5 - TVG-TVV Day 2 Vapor Generation

In Figure 5, the second day of diurnal vapor generation has been calculated and added to 

the previous total vapor generation from the previous day. In this example, the total vapor 

generation has now exceeded the working capacity of the canister and vapor has begun to 

breakthrough. The amount of breakthough is found on the TVG - TVV curve and reported by 

DELTA.

Figure 6 - TVG-TVV Day 2 Backpurge

In Figure 6, the backpurge has now been calculated and subtracted from the total vapor 

generation at the point of the canister capacity. Backpurge can only affect vapor that is actually 

stored in the canister, vapor that is lost due to breakthrough cannot be recovered back into the 

vehicle tank, and therefore cannot be counted either for backpurge or as part of the total vapor 

generation. The DELTA model accounts for the working capacity of the canister and calculates 

where backpurge should begin from accordingly. Calculations for a day three diurnal 

temperature cycle would begin at this point.
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Figure 7 - TVG-TVV Day 3 Vapor Generation

In Figure 7, the third day of diurnal vapor generation has been calculated and added to 

the prvious total vapor generation from the previous days. Again, the amount of breakthrough is 

found using the TVG - TVV curve, and the backpurge is appropriately subtracted from the total 

vapor generation beginning at the working capacity of the canister. This process will continue for 

as many days as desired or necessary for MOVES operation.

Figure 8 - TVG-TVV Vapor Loading and Backpurge Summary

Figure 8 summarizes the calculations completed by DELTA to determine breakthrough 

vapor emissions for a single ideal vehicle. The ability to model a single vehicle is the first step to 

creating a model capable of estimating diurnal evaporative emissions for an entire fleet of 

vehicles. A discussion of how the single vehicle models created in the above section can be 

combined into a single fleet model follows in the next section.
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IV. Modeling an ideal fleet

This section continues the walkthrough of the DELTA model. Using the model of a 

single ideal vehicle explained in section III as a starting point, this section explains how DELTA 

can model breakthrough emissions of an entire fleet. This includes building a fleet average TVG 

- TVV curve, finding and using a fleet average canister size and tank volume, and producing a 

fleet average TVG - TVV curve for use in the MOVES model.

a. Multiple single vehicle models

In order to model a representative fleet for a given vehicle type and model year, multiple 

versions of the single vehicle model (discussed in Section III) are constructed and weighted 

together. This weighted model is used as the fleet average TVG - TVV curve for calculating 

diurnal emissions in the MOVES model. Each single vehicle line depends on that vehicle’s 

canister properties and backpurge characteristics. Properties needed for the calculation of vapor 

generation only (such as tank size) are not included in constructing the multiple vehicle models; 

these properties will be factored into the weighted model at a later point.

Figure 9 - Multiple Individual Vehicle TVG-TVV Models

Individual vehicle models are weighted together in DELTA using fractional percentages 

of the user’s choice. For the MOVES model, we formed each average model year fleet from 

individual vehicles models of the top 30 selling vehicles of that model year. Data for canister 

properties were determined from EPA certification data for these vehicles. These models were 

then weighted together based on the volume of sales for each vehicle within a given model year. 

This produces a single TVG - TVV curve representing a weighted average of all individual 

vehicle models within that vehicle type and model year.
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Figure 10 - Combined/Weighted Fleet Average TVG-TVV Model

This curve no longer has the characteristic rise at a specific canister capacity. This is due 

to some vehicles beginning to break through while others remain at zero breakthrough; caused by 

differences in canister properties expressed in the individual vehicle models. The method for 

handling the average canister breakthrough point on the weighted TVG - TVV curve is discussed 

in the next subsection.

b. Fleet average canister size and tank volume

The same methodology for calculating single vehicle breakthrough emissions (as 

discussed in section III.d.ii) can be used with the fleet average TVG - TVV curve developed in 

the previous subsection. However, unlike the single vehicle models, there are multiple canister 

capacities and tank volumes that comprise the weighted curve for the fleet. Since tank size is 

used in the calculation of TVG and canister capacity is used in the calculation of backpurge and 

TVV (for determining when breakthrough will occur as well as what value of TVG backpurge 

will occur from), these values must also be aggregated from each of the single vehicle models. 

DELTA uses the same weighting factors applied to the single vehicle TVG – TVV curves to 

calculate a single weighted tank size and canister size based on the individual tank and canister 

sizes found in the fleet. These weighted average tank and canister sizes are then used in the fleet 

average model in a similar way to how they would be applied in the single vehicle models. A 

summary of this method can be found in the figure below.
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Figure 11 - Fleet Average TVG-TVV Summary

We are aware that using a single average tank and canister capacity to represent an entire 

vehicle may be over-simplified in some circumstances. Cases such as a small number of 

passenger vehicles modeled in the same group as a large number of pickup trucks may produce 

larger breakthrough than expected due to a large average tank size producing high amounts of 

vapor while coupled with less storage due to a smaller average canister capacity. One vehicle 

breaking through significantly before other vehicles in the aggregate model may also cause 

higher than expected breakthrough due to a small but non-zero fleet average TVG – TVV line 

occurring well before the average canister capacity of the fleet is reached. Usually, tank volume 

and canister capacity are well correlated over an entire model year fleet and therefore the tank 

volume and canister capacity simplifications should largely not affect results. However, this is an 

area under consideration for improvement in the next version of the DELTA model.

c. Producing a fleet average curve equation for MOVES

The EPA MOVES model requires the average tank size, the average canister capacity, 

the backpurge percentage and a fleet average TVG – TVV curve from DELTA as inputs to its 

evaporative emissions module for on-road vehicle emissions modeling. Most of these can be 

converted directly to MOVES format as single numbers, however; the TVG – TVV curve must 

first be converted to a continuous equation before use in the MOVES model. A rotated hyperbola 

was identified as the most similar continuous equation to the fleet average TVG – TVV lines 

created by the DELTA model, and is of the form:

Equation 2 - Generic Form of Hyperbolic Section

A least-squares approach was used to determine the six variables needed to fit the TVG –

TVV curve to this form of the hyperbolic equation. Special care should be taken to fit the values 

of the curve less than 200 grams TVG; an iterative least-squares algorithm has been shown to 

provide less than ideal fits for this region of the TVG – TVV curve.
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The results of the DELTA model fitted TVG – TVV curve as well as other data points 

discussed earlier in this subsection for all model years 1974 and later can be found in the 

MOVES database table cumTVVcoeffs. In addition to DELTA modeling results and legacy 

evaporative coefficients, the cumTVVcoeffs table also contains vapor leak rates and leak 

prevalence; topics which are beyond the scope of this document.

V. Comparison of an ideal fleet to E77 diurnal data

This section compares the ideal models described in the previous section to real world 

diurnal data obtained through the CRC E77 project. As part of this project, several vehicles were 

tested in an evaporative SHED over three days with the resulting evaporative emissions reported 

on a continuous basis in ten minute intervals. In this section, the inputs used for the DELTA 

modeling of the E77 test vehicles are discussed, the results of the DELTA model are compared 

to those from the E77 multiple day evaporative shed results, and data supporting DELTA underpredicting vehicle breakthrough emissions are discussed. For more information regarding the 

CRC E77 project, including test procedures, specific vehicle information and more detailed 

results, please see E77-2c at (http://crcao.org/publications/emissions/index.html).

a. Constructing DELTA inputs from the E77 vehicle fleet

The total set of vehicles used in this comparison was comprised of 21 vehicles and 47

individual tests, divided into three subsets based on emission certification class. Of the 47 tests, 9 

tests were considered pre-enhanced (vehicles pre-1996), 23 tests were considered Tier 

1/enhanced (vehicles 1996-2003) and 15 tests were considered Tier 2 (vehicles 2004+). A tank 

volume headspace average of 10.5 gallons, a backpurge value of 35%, and equal weighting 

between vehicles was used for all three subsets. Vehicle canister capacities used in the DELTA 

model follow in the tables below: The vehicle canister capacities were derived from EPA vehicle 

certification data and evaporative family codes.

Table 1 - Pre-enhanced DELTA Model Input

Model / ID Weighting Factor Canister Size

6915 0.1111 41

6919 0.1111 90

6922 0.1111 90

6925 0.1111 47

6926 0.1111 57

6927 0.1111 50

6970 0.1111 68

6973 0.1111 68

6985 0.1111 75
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Table 2 - Enhanced/Tier 1 DELTA Model Input

Model / ID Weighting Factor Canister Size

7001 0.0435 20

7006 0.0435 30

7015 0.0435 153

7033 0.0435 40

7046 0.0435 82

7088 0.0435 121

7091 0.0435 142

7131 0.0435 98

7150 0.0435 49

7461 0.0435 115

7463 0.0435 100

7476 0.0435 40

7508 0.0435 121

7551 0.0435 80

7556 0.0435 163

7562 0.0435 90

7667 0.0435 50

7672 0.0435 60

7703 0.0435 100

7713 0.0435 163

7753 0.0435 80

7794 0.0435 62

7859 0.0435 40
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Table 3 - Tier 2+ / ZEV DELTA Model Inputs

Model / ID Weighting Factor Canister Size

7059 0.05556 161

7099 0.05556 172

7130 0.05556 121

7142 0.05556 153

7170 0.05556 121

7197 0.05556 172

7229 0.05556 90

7289 0.05556 153

7252 0.05556 70

7429 0.05556 200

7462 0.05556 40

7516 0.05556 203

7531 0.05556 100

7725 0.05556 60

7803 0.05556 203

7558 0.05556 40

7696 0.05556 120

7871 0.05556 120

The DELTA model was run three times, using each of the above tables as a set of 

individual vehicle inputs. The model was run for a temperature range of 65-105F, an altitude of 

sea level (14.7psi) and a fuel RVP of 10psi. The resulting TVG – TVV curves produced by the 

DELTA model can be seen in Figure 12 below.
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Figure 12 - DELTA Model Results for Pre-Enhanced, Enhanced and Tier 2 Fleet Averages

Note that diurnal temperature, altitude and fuel RVP do not affect the shape of the TVG –

TVV curves, only the output from those curves. Although the values for these variables in the 

model have been selected to most closely match those found in the E77 vehicle data; a 

comparison using the TVG – TVV curves as a basis should not be affected by changes in these 

inputs (as changes would only impact TVG itself, not the relationship between TVG and TVV).

b. Comparison to E77 vehicle fleets

The E77 vehicle fleet data was first reconstructed in a form that is easily comparable to 

the TVG – TVV curves produced by the DELTA model. The data from E77 was originally of the 

form: total canister breakthrough weight vs. time (specifics on how this data was obtained, 

including detailed descriptions of the test setup can be found in the E77 report). This data 

includes backpurge events and a dependence on temperature that is not useful for comparison 

with the TVG – TVV curves produced by the DELTA model. An example of the original E77 

data can be seen in Figure 13 below.
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Figure 13 - Untransformed E77 Vehicle Breakthrough Data

The Wade-Reddy equation was used to approximate the amount of vapor generation for 

every point in the original E77 data since the altitude, fuel RVP, and temperature of the 

emissions shed were known for all datapoints. Using the results from the Wade-Reddy equation 

as the TVG for the E77 data, the canister breakthrough weight was then reconstructed to 

represent the TVV for that vehicle. Firstly, the portions of canister breakthrough weight data that 

occurred during diurnal cooling (the backpurge events) were removed. Secondly, the portions of 

canister breakthrough weight data that occurred during diurnal heating were shifted to fill the 

gaps formed by the removal of the diurnal cooling data. Finally, the remaining portions of the 

canister breakthough weight data were matched with the proper TVG point based on the 

temperature of the shed at the time they were recorded. This process creates a TVG – TVV curve 

that is comparable to the TVG – TVV curve produced by the DELTA model, as seen in Figure 

14 below.
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Figure 14 - Transformed E77 Vehicle Breakthrough Data

Note the above figure represents the reconstructed version of the original E77 data for the 

vehicle shown previously in Figure 14. A script carrying out the process described above 

automatically can be found in Appendix B to this document.

By applying this reconstruction process to every vehicle in the E77 fleet, a cloud of TVG 

– TVV points was generated for each subset of E77 vehicles: pre-enhanced, enhanced/Tier 1, and 

Tier 2 (each characteristic rise in TVV seen in the following plots represents one set of vehicle 

test data). These point clouds were then compared to the TVG – TVV lines generated by the 

DELTA model. These comparisons are seen in the following figures.
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Figure 15 - Pre-enhanced E77 / DELTA Model Comparison
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Figure 16 - Enhanced/Tier 1 E77 / DELTA Model Comparison
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Figure 17 - Tier 2/ZEV E77 / DELTA Model Comparison

From the figures above it was apparent that the DELTA model based on ideal canister 

size was under-predicting breakthrough emissions for all but a few cases of the E77 vehicles. A 

discussion of these results can be found in the next subsection.

c. Discussion of non-ideal canister behavior in the E77 vehicle fleet

The comparisons shown by the figures in the previous subsection indicate a large underprediction of breakthrough emissions when using the DELTA model based on ideal canister 

capacities and canister behavior. A more thorough analysis of E77 vehicle breakthrough was 

completed to explain the differences seen between the ideal model and what was happening in 

real world testing. It is important to note that the preconditioning procedure performed on the 

E77 vehicles to ensure adequate purge between tests, while meant to emulate a standard FTP

cycle, was performed on public roads with variable weather conditions. This real-world 

preconditioning may have contributed to the non-ideal behavior seen in the data. For each test 

conducted in the E77 multi-day diurnal study, the canister breakthrough point (which was 

determined as the point at which more than 2% of the total canister capacity had escaped the 

vehicle canister) was compared against the theoretical capacity for the canister on that particular 

vehicle. The results of this analysis are shown in the following tables, separated by certification 

class.
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Table 4 - E77 Tier2/ZEV Premature Breakthrough

Test # Veh # Fuel RVP 

(psi nominal)

Breakthrough 

Point (g)

Canister 

Capacity (g)

Difference 

(g)

% of Rated 

Capacity

7059 212 10 161 172 -11.05 93.58%

7099 212 9 135 172 -37.05 78.47%

7130 211 9 132 121 11 109.09%

7142 215 10 171 153 17.55 111.44%

7170 211 10 90 121 -30.9 74.44%

7197 212 9 139 172 -33.05 80.79%

7229 215 9 90 153 -63.45 58.65%

7289 215 9 136 153 -17 88.89%

7252 211 9 70 121 -50.9 57.90%

7429 213 10 200 203 -2.74 98.65%

7462 210 10 40 115 -75.32 34.69%

7516 213 9 222 203 19.26 109.50%

7531 210 9 100 115 -15.32 86.72%

7725 210 9 60 115 -55.32 52.03%

7803 213 9 237 203 34.26 116.90%
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Table 5 - E77 Enhanced/Tier 1 Premature Breakthrough

Test # Veh # Fuel RVP 

(psi nominal)

Breakthrough 

Point (g)

Canister 

Capacity (g)

Difference 

(g)

% of Rated 

Capacity

7001 205 10 20 107 -87.0 18.70%

7006 204 10 30 121 -90.9 24.81%

7015 207 10 194 153 40.6 126.43%

7033 204 9 40 121 -80.9 33.09%

7046 205 9 82 107 -25.0 76.67%

7088 204 9 128 121 7.1 105.87%

7091 207 9 142 153 -11.5 92.54%

7131 205 9 98 107 -9.0 91.63%

7150 207 9 49 153 -104.5 31.93%

7461 209 10 115 121 -5.9 95.12%

7463 208 10 100 163 -62.8 61.44%

7476 206 10 40 112 -71.6 35.84%

7508 209 9 128 121 7.1 105.87%

7551 206 9 80 112 -31.6 71.68%

7556 208 9 129 163 -33.8 79.26%

7562 221 10 90 153 -63.5 58.65%

7667 221 9 50 153 -103.5 32.58%

7672 207 10 60 153 -93.5 39.10%

7703 206 9 100 112 -11.6 89.61%

7713 208 9 142 163 -20.8 87.25%

7753 209 9 80 121 -40.9 66.17%

7794 207 10 62 153 -91.5 40.40%

7859 221 9 40 153 -113.5 26.07%

Premature breakthrough occurred in tests at a wide range of ambient lab temperatures and 

humidity. Note that although the tests occurred in a controlled evaporative SHED, 

preconditioning occurred on surface streets meant to emulate an FTP dynamometer cycle where 

ambient conditions could affect the state of the canister. Premature breakthrough occurred at 

levels as low as 19% of the ideal canister capacity for a vehicle, with the average vehicle 

breakthrough occurring at 72% of ideal canister capacity. The under-estimation of fleet 

breakthrough emissions is due to the fact that the DELTA model is reliant on ideal canister 

capacity for breakthrough calculations; because the fleet performed at only 72% of ideal canister 

capacity, the DELTA model cannot properly account for the non-ideal behavior. A method of 

correcting the DELTA model to more correctly reflect the non-ideal behavior of a real-world 

fleet follows in the next section.
24

VI. Correcting DELTA for non-ideal behavior

As described in the previous section, the data from the E77 program shows that 

evaporative emission control systems on many vehicles are not operating as an ideal model 

would predict. EPA believes there are a number of reasons why this non-ideal behavior may be 

occurring. While evaporative emission canister technology is relatively simple, deterioration of 

the charcoal in the canister can occur for a variety of reasons including if the canister is exposed 

to liquid or repeated dusty conditions. This type of deterioration could result in permanent 

reduction in vapor storage capacity of the canister. In addition, canisters in the real-world may 

not experience as much purge as canisters tested under the certification procedures. While the 

vehicles tested in the E77 program were prepped for testing by driving under real-world 

operation meant to simulate certification pre-conditioning, it appears that some of the canisters 

may not have been purged by the real-world operation as much as canisters prepped in the 

laboratory that are following the certification procedures. Lower purge levels in the real-world 

could lead to temporary reduction in vapor storage capacity until the vehicles are driven for 

sufficient distances to purge the canister more completely.

To address the fact that the E77 program results show some evaporative emission control 

systems do not operate ideally, EPA developed a modified approach for modeling evaporative 

emissions in the DELTA model. This modified approach relies on the basic relationship 

between tank vapors vented (TVV) and tank vapors generated (TVG) upon which the DELTA 

model is based, as shown below.

TVV = TVG – (theoretical capacity)

For the purposes of this analysis, the theoretical capacity of the evaporative emission canister 

replaces the real-world capacity of the evaporative emission canister. Table 4 and 
25

Table 5, presented earlier, contain the estimated real-world capacity of the evaporative emission 

canisters for each of the Tier 1 and Tier 2 vehicles tested in the E77 program. The following 

equation shows the modified relationship between the TVV and TVG terms.

TVV = TVG – (real-world capacity)

It should be noted that TVV will be zero if TVG is less than or equal to the real-world capacity 

of the evaporative emission canister.

Because vehicles have a variety of canister capacities, and the E77 program results show 

that many vehicles experience breakthrough of the evaporative emission canisters at less than the 

theoretical working capacity, EPA decided to use the equation noted above and develop a 

modified approach for the whole vehicle fleet that would attempt to factor in both of these 

conditions into the modeling. The following sections describe the development of the equations 

used in the DELTA model for the Tier 2 and Tier 1 vehicle fleets based on the E77 program 

results. EPA’s approach for modeling pre-enhanced vehicles in the DELTA model is presented 

as well.
26

a. Tier 2 vehicles

The first step in this approach was to divide the modified equation by TVG. This results 

in the following equation:

TVV/TVG = 1 – (real-world capacity)/TVG

Next, the “real-world capacity” term in the equation was replaced by a new term equal to 

the real-world fraction of theoretical capacity multiplied by the theoretical canister capacity. For 

example, as noted in Table 4, test number 7099 on vehicle number 212 in the E77 program had a 

real-world capacity of approximately 135 grams and a theoretical capacity of 172 grams. 

Therefore, the real-world fraction of theoretical capacity would be 0.785 (i.e., 135 grams divided 

by 172 grams). The equation with the replaced term is as follows:

TVV/TVG = 1–[(real-world fraction of theoretical capacity)*(theoretical capacity)]/TVG

This equation can be rearranged as follows:

TVV/TVG = 1 – (real-world fraction of theoretical capacity)/(TVG/theoretical capacity)

This equation can be represented as follows for graphing purposes where the y-axis represents 

(TVV/TVG) and the x-axis represents (TVG/theoretical capacity):

y = 1 – (real-world fraction of theoretical capacity)/x

Putting the equation in this rearranged form “normalizes” the emission results on 

TVG/theoretical capacity and allows each test/vehicle combination from the E77 program to be 

compared on the same basis. This rearrangement also removes the impact of the differences in 

theoretical capacity and real-world capacity which exist for each test/vehicle combination that 

would otherwise occur in any comparison of TVV and TVG. Based on this equation, a graph 

was be made for each test/vehicle combination in the E77 program by calculating and graphing 

TVV/TVG (on the y-axis) as a function of TVG/theoretical capacity (on the x-axis). (It should 

be noted that the TVV/TVG value is zero if TVG/theoretical capacity is less than or equal to the 

real-world fraction of theoretical capacity.) 
27

Figure 18 presents this relationship for one test/vehicle combination from the E77 

program for test 7099 on vehicle 212, which is a Tier 2 vehicle. For this test/vehicle 

combination, canister breakthrough occurred at 0.785 of the theoretical capacity of the canister. 

At that point, the ratio of TVV/TVG rises as TVG/theoretical capacity increases. All such 

graphs asymptotically approach a TVV/TVG value of 1.00 as the value of TVG/theoretical 

capacity increases to higher and higher levels.

Figure 18 - Graph for Test 7099/Vehicle 212
28

Figure 19 shows the results for all 15 test/vehicle combinations for Tier 2 vehicles in the 

E77 program (as presented in Table 5). For the E77 program, there were five Tier 2 vehicles 

tested, with three different tests performed on each vehicle with different fuels, resulting in 15 

test/vehicle combinations. Of the 15 test/vehicle combinations, breakthrough occurred earlier 

than the theoretical canister capacity would suggest on 10 of the test/vehicle combinations. The 

remaining 5 test/vehicle combinations that behaved ideally (i.e., breakthrough occurred at or 

above the theoretical canister capacity) are shown in Figure 19 with curves that start to increase 

at a value of 1.0 for TVG/theoretical canister capacity.

Figure 19 - Graphs for All Tier 2 Vehicles

Based on the results for each of the test/vehicle combinations from the E77 program, the 

TVV/TVG values were averaged across all 15 test/vehicle combinations to result in a single 

graph representing all of the Tier 2 vehicles. EPA is using the Tier 2 vehicle dataset from the 

E77 program as a representation of the entire Tier 2 vehicle fleet
29

Figure 20 shows the resulting average graph of all test/vehicle combinations for Tier 2 

vehicles from the E77 program.

Figure 20 - Average Tier 2 Vehicle Graph

This average curve for Tier 2 vehicles was then converted back into the form needed for 

the DELTA model of TVV versus TVG. First, the x-axis values were multiplied by the average 

theoretical canister capacity of the Tier 2 vehicles tested in the E77 program to obtain TVG 

values. The average theoretical canister capacity value was determined to be 152.8 grams, a 

value slightly higher than Tier 2 vehicles certified with EPA which averaged from approximately 

136 to 150 grams over model years 2004 through 2010. Next, the y-axis values were multiplied 

by the associated TVG values at each point (as determined in the first step) to obtain TVV 

values. Figure XX shows the resulting TVV (on the y-axis) versus TVG (on the x-axis) curve 

for the Tier 2 fleet for the DELTA model.
30

Figure 21 also shows the TVV versus TVG curve as it currently exists in the 

MOVES2010a model for Tier 2 vehicle.

Figure 21 - TVV versus TVG for Tier 2 Fleet

The x and y values from the resulting graph of TVV versus TVG for the Tier 2 fleet were 

then curve-fit based on an equation of the following form in order to provide inputs for the 

DELTA model:

Table 6 shows the values of the constants determined for the equation based on the curvefit analysis of the TVV versus TVG curve for the Tier 2 fleet.

Table 6 - Modeling Inputs for Tier 2 Vehicles

Constant Value for the

Tier 2 Fleet

A -0.071

B -1.20

C 1.15

D 3.12

E 187

F 20
31

b. Enhanced/Tier 1 vehicles

For Enhanced/Tier 1 vehicles, EPA followed a similar approach to that described above 

for deriving the equations used for modeling evaporative emissions with the DELTA model. 

Table 4 shows the breakthrough points for the test/vehicle combinations from the E77 program 

for Enhanced/Tier 1 vehicles. For the E77 program, there were seven Enhanced/Tier 1 vehicles 

tested, with three different tests performed on each vehicle with different fuels plus an additional 

two tests on one of the vehicles, resulting in 23 test/vehicle combinations. 

Figure 22 presents the TVV/TVG versus TVG/theoretical capacity results for all 23 test/vehicle 

combinations for Enhanced/Tier 1 vehicles in the E77 program. Of the 23 test/vehicle 

combinations, breakthrough occurred earlier than the theoretical canister capacity would suggest 

on 20 of the test/vehicle combinations. The remaining 3 test/vehicle combinations that behaved 

ideally (i.e., breakthrough occurred at or above the theoretical canister capacity) are shown in 

Figure 22 with curves that start to increase at a value of 1.0 for TVG/theoretical canister 

capacity.

Figure 22 - Graphs for All Enhanced/Tier 1 Vehicles

Based on the results for each of the test/vehicle combinations from the E77 program, the 

TVV/TVG values were averaged across all 23 test/vehicle combinations to result in a single 

graph representing all of the Enhanced/Tier 1 vehicles. EPA is using the Enhanced/Tier 1 

vehicle dataset from the E77 program as a representation of the entire Enhanced/Tier 1 vehicle 

fleet. 
32

Figure 23 shows the resulting average graph of all test/vehicle combinations for 

Enhanced/Tier 1 vehicles from the E77 program.

Figure 23 - Average Enhanced/Tier 1 Vehicle Graph

This average curve for Enhanced/Tier 1 vehicles was then converted back into the form needed 

for the DELTA model of TVV versus TVG. First, the x-axis values were multiplied by the 

average theoretical canister capacity of the Enhanced/Tier 1 vehicles tested in the E77 program 

to obtain TVG values. The average theoretical canister capacity value was determined to be 

134.6 grams, a value slightly higher than the estimated average of Enhanced/Tier 1 vehicles 

certified with EPA between model year 1999 and 2003 of approximately 123 grams. Next, the 

y-axis values were multiplied by the associated TVG values at each point (as determined in the 

first step) to obtain TVV values. 
33

Figure 24 shows the TVV versus TVG curve as it currently exists in the MOVES2010a 

model for Enhanced/Tier 1 vehicles. It also shows the resulting TVV (on the y-axis) versus TVG 

(on the x-axis) curve for the Enhanced/Tier 1 fleet for the DELTA model.

Figure 24 - TVV versus TVG for Enhanced/Tier 1 Fleet
34

The x and y values from the resulting graph of TVV versus TVG for the Tier 1 fleet were 

then curve-fit based on an equation of the following form in order to provide inputs for the 

DELTA model:

Table 7 shows the values of the constants determined for the equation based on the curvefit analysis of the TVV versus TVG curve for the Tier 1 fleet.

Table 7 - Modeling Inputs for Enhanced/Tier 1 Vehicles

Constant Value for the

Enhanced/Tier 1 Fleet

A -0.125

B -1.34

C 1.90

D 2.70

E 115

F 23

c. Pre-enhanced vehicles

For pre-enhanced vehicles, EPA did not collect any emissions data in the E77 program. 

Because the basic technologies use on pre-enhanced vehicles to control evaporative emissions 

are similar to those used on Enhanced/Tier 1 vehicles and Tier 2 vehicles, we believe the same 

type of issues such as canister deterioration and limited purge would result in similar evaporative 

emission trends as those found on vehicles tested in the E77 program. For the purposes of this 

analysis, we believe that pre-enhanced vehicles would have a similarly shaped curve of 

TVV/TVG versus TVG/theoretical capacity as Enhanced/Tier 1 vehicles because their 

evaporative emission control systems are closer in design to those of Enhanced/Tier 1 vehicles.

Based on the average curve of TVV/TVG versus TVG/theoretical capacity for 

Enhanced/Tier 1 vehicles, EPA converted the values back into the form needed for the DELTA 

model of TVV versus TVG as described earlier. First, the x-axis values were multiplied by the 

average theoretical canister capacity of pre-enhanced vehicles certified with EPA to obtain TVG 

values. The average theoretical canister capacity value was determined to be 72.8 grams for 

vehicles certified with EPA between model year 1978 and 1995. Next, the y-axis values were 

multiplied by the associated TVG values at each point (as determined in the first step) to obtain 

TVV values. 
35

Figure 25 shows the resulting TVV (on the y-axis) versus TVG (on the x-axis) curve for 

the pre-enhanced fleet for the DELTA model. It also shows the TVV versus TVG curve as it 

currently exists in the MOVES2010a model for Pre-Enhanced vehicles.

Figure 25 - TVV versus TVG for Pre-Enhanced Fleet

The x and y values from the resulting graph of TVV versus TVG for the pre-enhanced 

fleet were then curve-fit based on an equation of the following form in order to provide inputs 

for the DELTA model:

Table 8 shows the values of the constants determined for the equation based on the curvefit analysis of the TVV versus TVG curve for the pre-enhanced vehicle fleet.

Table 8 - Modeling Inputs for Pre-Enhanced Vehicles

Constant Value for the

Pre-Enhanced Vehicle 

Fleet

A -0.25

B -1.00

C 1.25

D 0.2

E 85

F 70
36