where

VOCE= exhaust VOC emissions in milligrams per mile

Y_{voc}(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)

N_{v}, = [exp v_{1}(t)] ÷ [exp v_{1}(b)]

H_{v}, = [exp v_{2}(t)] ÷ [exp v_{2}(b)]

w_{1} = weighting factor for VOC normal-emitter component of fleet (= 0.444)

w_{2} = weighting factor for VOC higher-emitter component of fleet (=0.556)

v_{1}(t) = normal-emitter VOC equation for target fuel, as defined below

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Appendix C
Equation 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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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.

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[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.

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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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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,

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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

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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.

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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.

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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:

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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.
XV. Consolidated 1,3-butadiene equations
For normal emitters:
For higher emitters:

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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:

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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.]

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