 # Ozone-Forming Potential of Reformulated Gasoline(1999)

## Chapter: Appendix C Equation Set for the Complex Model - Phase II RFG

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Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
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## Appendix CEquation Set for the Complex Model—Phase II RFG1

### I.Basic VOC Exhaust Emissions Performance (summer)  where

VOCE= exhaust VOC emissions in milligrams per mile

Yvoc(t) = exhaust VOC performance of the target fuel in terms of percentage change from baseline

VOC(b) = baseline (summer) exhaust VOC emissions (= 907.0 mg/mi; see Table 5-6)

Nv, = [exp v1(t)] ÷ [exp v1(b)]

Hv, = [exp v2(t)] ÷ [exp v2(b)]

w1 = weighting factor for VOC normal-emitter component of fleet (= 0.444)

w2 = weighting factor for VOC higher-emitter component of fleet (=0.556)

v1(t) = normal-emitter VOC equation for target fuel, as defined below

 1 Adapted from 40 CFR 80.45.
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Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×

v2(t) = higher-emitter VOC equation for target fuel, as defined below

v1(b) = normal-emitter VOC equation, defined below, with base-fuel properties as input

v2(b) = higher-emitter VOC equation, defined below, with base-fuel properties as input

exp(n) = the root of Naperian or natural logarithms ( ) raised to the power n.

### II.Consolidated Exhaust VOC Equations

For normal Emitters: For higher emitters: where

OXY = oxygen weight percent of fuel

SUL = sulfur content of fuel, in parts per million by weight

RVP = Reid Vapor Pressure of fuel, in pounds per square inch (gauge), measured at 100° F

E200 = 200° F distillation fraction of the fuel, volume percent

E300 = 300° F distillation fraction of the fuel, volume percent

ARO = total aromatics content of fuel, volume percent

OLE = total olefins content of fuel, volume percent.

Page 228
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×

[NOTE: the value of Yvoc(t) as computed from either of the above equations is modified by linear factoring functions involving deltas (differences between actual and "allowable" values) for E200, E300, and ARO, if any or all of these volume percent values fall outside theft allowable ranges.]

### III.Consolidated non-exhaust VOC equations (Phase II)

For VOC Control Region 1 (south)     For VOC Control Region 2 (north)     where

VOCNEn = total nonexhaust VOC emissions in control region n, grams per mile

VOCDIn = diurnal2 VOC emissions in control region n, grams per mile

 2 See Chapter 4 for definitions. Measured emissions are apportioned over daily trip distances that are assumed in EPA certification procedures.
Page 229
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×

VOCHSn = hot soak2 VOC emissions in control region n, grams per mile

VOCRLn = running loss2 VOC emissions in control region n, grams per mile

VOCRFn = refueling2 VOC emissions in control region n, grams per mile.

### IV.Phase II total VOC emissions performance—summer ozone season   where

VOCSn = total summer VOC emissions in control region n, grams per mile; VOCE, VOCNEn as defined above

VOCS1% = total summer VOC emissions performance of target fuel for VOC control Region 1 (south), in percentage terms relative to baseline level

VOCS2% = total summer VOC emissions performance of target fuel for VOC control Region 2 (north), in percentage terms relative to baseline level.

### V.Summer NOx emissions performance  where

NOx = exhaust NOx emissions in milligrams per mile

YNOX(t) = NOx performance of the target fuel in terms of percentage change from baseline

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Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×

NOx(b) = baseline NOx emissions (=1340 mg/mi, see Table 5-6)

Nn = [exp n1(t)] ÷ [exp n1(b)]

Hv = [exp n2(t)] ÷ [exp n2(b)]

z1 = weighting factor for NOx normal-emitter component of fleet (=0.738)

z2 = weighting factor for NOx higher-emitter component of fleet (=0.262)

n1(t) = normal-emitter NOx equation for target fuel, as defined below

n2(t) = higher-emitter NOx equation for target fuel, as defined below

n1(b) = normal-emitter NOx equation, defined below, with base-fuel properties as input

n2(b) = higher-emitter NOx equation, defined below, with base-fuel properties as input.

### VI.Consolidated NOx equations

For normal emitters: For higher emitters: [NOTE: the value Of YNOX(t) as computed from either of the above equations is modified by linear factoring functions involving deltas (differences between actual and "allowable" values) for SUL, OLE, and ARO,

Page 231
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×

if any or all of these volume percent values fall outside their allowable ranges.]

### VII.Summer toxics emissions performance, Phase II   where

TOXICSn = summer toxics performance, VOC Control Region n, milligrams per mile

TOXICSn% = TOXICS performance of the target fuel in VOC Control Region n, in terms of percentage change from baseline

EXHBZ = exhaust emissions of benzene as computed below, milligrams per mile

FORM = exhaust emissions of formaldehyde as computed below, milligrams per mile

ACET = exhaust emissions of acetaldehyde as computed below, milligrams per mile

BUTA = exhaust emissions of 1,3-butadiene as computed below, milligrams per mile

POM = exhaust emissions of polycyclic organic matter as computed below, milligrams per mile

NEBZn = nonexhaust emissions of benzene, VOC Control Region n, as computed below, milligrams per mile.

### VIII.Emissions equations for individual ozone-season toxics—(1) benzene Page 232
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× where

YBEN(t) = exhaust benzene performance of the target fuel in terms of percentage change from baseline

BENZ(b) = baseline (summer) exhaust benzene emissions (=53.54 mg/mi, from Table 5-6)

Nb = [exp b1(t)] ÷ [exp b1(b)]

Hb = [exp b2(t)] ÷ [exp b2(b)]

W1 = weighting factor for toxics normal-emitter component of fleet (=0.444)

W2 = weighting factor for toxics higher-emitter component of fleet (=0.556)

b1(t) = normal-emitter benzene equation for target fuel, as defined below

b2(t) = higher-emitter benzene equation for target fuel, as defined below

b1(b) = normal-emitter benzene equation, defined below, with base-fuel properties as input

b2(b) = higher-emitter benzene equation, defined below, with base-fuel properties as input.

### IX.Consolidated benzene equations

For normal emitters: For higher emitters: where BEN = benzene content of target fuel, volume percent, and all other terms are as defined above.

Page 233
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×

### X.Emissions equations for individual ozone-season toxics—(2) formaldehyde  where

YFORM(t) = exhaust formaldehyde performance of the target fuel in terms of percentage change from baseline

FORM(b) = baseline (summer) exhaust formaldehyde emissions ( = 9.70 mg/mi, see Table 5-6)

Nf = [exp f1(t)] ÷ [exp f1(b)]

Hf = [exp f2(t)] ÷ [exp f2(b)]

f1(t) = normal-emitter formaldehyde equation for target fuel, as defined below

f2(t) = higher-emitter formaldehyde equation for target fuel, as defined below

f1(b) = normal-emitter formaldehyde equation below, with base-fuel properties as input

f2(b) = higher-emitter formaldehyde equation below, with base-fuel properties as input.

### XI.Consolidated formaldehyde equations

For normal emitters: For higher emitters: where MTB = methyl tertiary-butyl ether content of target fuel, weight percent oxygen, and all other terms are as defined above.

Page 234
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×

### XII.Emissions equations for individual ozone-season toxics—(3) acetaldehyde  where

YACET(t) = Exhaust acetaldehyde performance of the target fuel in terms of percentage change from baseline

ACET(b) = baseline (summer) exhaust acetaldehyde emissions (=4.44 mg/mi, see Table 5-6)

Na = [exp a1(t)] ÷ [exp a1(b)]

Ha = [exp a2(t)] ÷ [exp a2(b)]

a1(t) = normal-emitter acetaldehyde equation for target fuel, as defined below

a2(t) = higher-emitter acetaldehyde equation for target fuel, as defined below

a1(b) = normal-emitter acetaldehyde equation below, with base-fuel properties as input

a2(b) = higher-emitter acetaldehyde equation below, with base-fuel properties as input.

### XIII.Consolidated acetaldehyde equations

For normal emitters: For higher emitters: Page 235
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×

where ETB = ethyl tertiary-butyl ether content of target fuel, weight percent oxygen and ETH = ethanol content of target fuel, weight percent oxygen, and all other terms are as defined above.

### XIV.Emissions equations for individual ozone-season toxics—(4) 1,3-butadiene  where

YBUTA(t) = Exhaust 1,3-butadiene performance of the target fuel in terms of percentage change from baseline

BUTA(b) = Baseline (summer) exhaust 1,3-butadiene emissions (=9.38 mg/mi, see Table 5-6)

Nd = [exp d1(t)] ÷ [exp d1(b)]

Hd = [exp d2(t)] ÷ [exp d2(b)]

d1(t) = normal-emitter 1,3-butadiene equation for target fuel, as defined below

d2(t) = higher-emitter 1,3-butadiene equation for target fuel, as defined below

d1(b) = normal-emitter 1,3-butadiene equation below, with base-fuel properties as input

d2(b) = higher-emitter 1,3-butadiene equation below, with base-fuel properties as input.

For normal emitters: For higher emitters:

Page 236
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× where OXY = oxygen content of target fuel, weight percent, and all other terms are as defined above.

### XVI.Polycyclic organic matter, mass emissions (milligrams per mile) Terms are as defined above.

### XVII.Non-exhaust benzene emissions (milligrams per mile) where terms are defined as under Part III above, but "BZ" refers only to the benzene component of evaporative emissions.

For VOC Control Region 1:    For VOC Control Region 2: Page 237
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×    All terms are as defined above.

[NOTE: For purposes of comparing weight percent vs. volume percent of oxygen, approximate conversion values are the following: for MTBE as oxygenate, Wm = Vm × 0.18, and for ethanol as oxygenate, We = Ve × 0.35, where W is weight percent and V is volume percent.]

Page 238
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
×
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Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
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Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× Page 228
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
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Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
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Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
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Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× Page 232
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× Page 233
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× Page 234
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× Page 235
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× Page 236
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× Page 237
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
× Page 238
Suggested Citation:"Appendix C Equation Set for the Complex Model - Phase II RFG." National Research Council. 1999. Ozone-Forming Potential of Reformulated Gasoline. Washington, DC: The National Academies Press. doi: 10.17226/9461.
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The Committee on Ozone-Forming Potential for Reformulated Gasoline was asked whether the existing body of scientific and technical information is sufficient to permit a robust evaluation and comparison of the emissions from motor vehicles using different reformulated gasolines based on their ozone-forming potentials and to assess the concomitant impact of that approach on air-quality benefits of the use of oxygenates within the RFG program. As part of its charge, the committee was asked to consider (1) the technical soundness of various approaches for evaluating and comparing the relative ozone-forming potentials of RFG blends, (2) technical aspects of various air-quality issues related to RFG assessment, and (3) the sensitivity of evaluations of the relative ozone-forming potentials to factors related to fuel properties and the variability of vehicle technologies and driving patterns.

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