Appendix C
Equation Set for the Complex Model—Phase II RFG^{1}
I. Basic VOC Exhaust Emissions Performance (summer)
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
v_{2}(t) = higher-emitter VOC equation for target fuel, as defined below
v_{1}(b) = normal-emitter VOC equation, defined below, with base-fuel properties as input
v_{2}(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.
[NOTE: the value of Y_{voc}(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 = diurnal^{2} 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. |
VOCHSn = hot soak^{2} VOC emissions in control region n, grams per mile
VOCRLn = running loss^{2} VOC emissions in control region n, grams per mile
VOCRFn = refueling^{2} 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 NO_{x} emissions performance
where
NO_{x} = exhaust NO_{x} emissions in milligrams per mile
Y_{NOX}(t) = NO_{x} performance of the target fuel in terms of percentage change from baseline
NO_{x}(b) = baseline NO_{x} emissions (=1340 mg/mi, see Table 5-6)
N_{n} = [exp n_{1}(t)] ÷ [exp n_{1}(b)]
H_{v} = [exp n_{2}(t)] ÷ [exp n_{2}(b)]
z_{1} = weighting factor for NO_{x} normal-emitter component of fleet (=0.738)
z_{2} = weighting factor for NO_{x} higher-emitter component of fleet (=0.262)
n_{1}(t) = normal-emitter NO_{x} equation for target fuel, as defined below
n_{2}(t) = higher-emitter NO_{x} equation for target fuel, as defined below
n_{1}(b) = normal-emitter NO_{x} equation, defined below, with base-fuel properties as input
n_{2}(b) = higher-emitter NO_{x} equation, defined below, with base-fuel properties as input.
VI. Consolidated NO_{x} equations
For normal emitters:
For higher emitters:
[NOTE: the value Of Y_{NOX}(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,
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
where
Y_{BEN}(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)
N_{b} = [exp b_{1}(t)] ÷ [exp b_{1}(b)]
H_{b} = [exp b_{2}(t)] ÷ [exp b_{2}(b)]
W_{1} = weighting factor for toxics normal-emitter component of fleet (=0.444)
W_{2} = weighting factor for toxics higher-emitter component of fleet (=0.556)
b_{1}(t) = normal-emitter benzene equation for target fuel, as defined below
b_{2}(t) = higher-emitter benzene equation for target fuel, as defined below
b_{1}(b) = normal-emitter benzene equation, defined below, with base-fuel properties as input
b_{2}(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.
X. Emissions equations for individual ozone-season toxics—(2) formaldehyde
where
Y_{FORM}(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)
N_{f} = [exp f_{1}(t)] ÷ [exp f_{1}(b)]
H_{f} = [exp f_{2}(t)] ÷ [exp f_{2}(b)]
f_{1}(t) = normal-emitter formaldehyde equation for target fuel, as defined below
f_{2}(t) = higher-emitter formaldehyde equation for target fuel, as defined below
f_{1}(b) = normal-emitter formaldehyde equation below, with base-fuel properties as input
f_{2}(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.
XII. Emissions equations for individual ozone-season toxics—(3) acetaldehyde
where
Y_{ACET}(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)
N_{a} = [exp a_{1}(t)] ÷ [exp a_{1}(b)]
H_{a} = [exp a_{2}(t)] ÷ [exp a_{2}(b)]
a_{1}(t) = normal-emitter acetaldehyde equation for target fuel, as defined below
a_{2}(t) = higher-emitter acetaldehyde equation for target fuel, as defined below
a_{1}(b) = normal-emitter acetaldehyde equation below, with base-fuel properties as input
a_{2}(b) = higher-emitter acetaldehyde equation below, with base-fuel properties as input.
XIII. Consolidated acetaldehyde equations
For normal emitters:
For higher emitters:
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
Y_{BUTA}(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)
N_{d} = [exp d_{1}(t)] ÷ [exp d_{1}(b)]
H_{d} = [exp d_{2}(t)] ÷ [exp d_{2}(b)]
d_{1}(t) = normal-emitter 1,3-butadiene equation for target fuel, as defined below
d_{2}(t) = higher-emitter 1,3-butadiene equation for target fuel, as defined below
d_{1}(b) = normal-emitter 1,3-butadiene equation below, with base-fuel properties as input
d_{2}(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:
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:
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, W_{m} = V_{m} × 0.18, and for ethanol as oxygenate, W_{e} = V_{e} × 0.35, where W is weight percent and V is volume percent.]