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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--> 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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