Table 1 to Paragraph (c)(3) of § 1065.656-Symbols and Subscripts for Chemical Balance Equations
x[emission]meas | Amount of measured emission in the sample at the respective gas analyzer. |
x[emission]exh | Amount of emission per dry mole of exhaust. |
x[emission]exhdry | Amount of emission per dry mole of dry exhaust. |
xH2O[emission]meas | Amount of H2O in sample at emission-detection location; measure or estimate these values according to § 1065.145(e)(2) . |
xCcombdry | Amount of carbon from fuel and any injected fluids in the exhaust per mole of dry exhaust. |
xHcombdry | Amount of hydrogen from fuel and any injected fluids in the exhaust per mole of dry exhaust. |
xdil/exh | Amount of dilution gas or excess air per mole of exhaust. |
xdil/exhdry | amount of dilution gas and/or excess air per mole of dry exhaust. |
xHcombdry | Amount of hydrogen from fuel and any injected fluids in the exhaust per mole of dry exhaust. |
xint/exhdry | Amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust. |
xraw/exhdry | Amount of undiluted exhaust, without excess air, per mole of dry (raw or diluted) exhaust. |
xCO2int | Amount of intake air CO2 per mole of intake air. |
xCO2intdry | amount of intake air CO2 per mole of dry intake air; you may usexCO2intdry = 375 [MICRO]mol/mol, but we recommend measuring the actual concentration in the intake air. |
xH2Oint | Amount of H2O in the intake air, based on a humidity measurement of intake air. |
xH2Ointdry | Amount of intake air H2O per mole of dry intake air. |
xO2int | Amount of intake air O2 per mole of intake air. |
xCO2dil | Amount of dilution gas CO2 per mole of dilution gas. |
xCO2dildry | Amount of dilution gas CO2 per mole of dry dilution gas; if you use air as diluent, you may usexCO2dildry = 375 [MICRO]mol/mol, but we recommend measuring the actual concentration in the dilution gas. |
xH2Odil | Amount of dilution gas H2O per mole of dilution gas. |
xH2Odildry | Amount of dilution gas H2O per mole of dry dilution gas. |
A | Effective carbon content of the fuel and any injected fluids. |
[XI] | Effective hydrogen content of the fuel and any injected fluids. |
[PHI] | Effective oxygen content of the fuel and any injected fluids. |
Xi | Effective sulfur content of the fuel and any injected fluids. |
[OMEGA] | Effective nitrogen content of the fuel and any injected fluids. |
wC | Carbon mass fraction of the fuel (or mixture of test fuels) and any injected fluids. |
wH | Hydrogen mass fraction of the fuel (or mixture of test fuels) and any injected fluids. |
wO | Oxygen mass fraction of the fuel (or mixture of test fuels) and any injected fluids. |
wS | Sulfur mass fraction of the fuel (or mixture of test fuels) and any injected fluids. |
wN | Nitrogen mass fraction of the fuel (or mixture of test fuels) and any injected fluids. |
xCcombdry = xco2exhdry + xcoexhdry + xTHCexhdry - xco2dil·xdil/exhdry - xco2int·xint/exhdry
Eq. 1065.656-1
Eq. 1065.656-2
Eq. 1065.656-3
Eq. 1065.656-4
Eq. 1065.656-5
Eq. 1065.656-6 (see table 2 of this section)
Eq. 1065.656-7 (see table 2 of this section)
Eq. 1065.656-8
Eq. 1065.656-9
Eq. 1065.656-10
Eq. 1065.656-11
Eq. 1065.656-12
Eq. 1065.656-13
Eq. 1065.656-14
Eq. 1065.656-15
Eq. 1065.656-16 (see table 2 of this section)
Eq. 1065.656-17
Eq. 1065.656-18
Eq. 1065.656-19
Eq. 1065.656-20
Eq. 1065.656-21
Eq. 1065.656-22
Eq. 1065.656-23
Table 2 to Paragraph (c)(6) of § 1065.656-Chemical Balance Equations for Different Measurements
When measuring | Guess . . . | Calculate . . . |
(i) xO2meas | xint/exhdry andxH2exhdry | (A) xH2exhdry using Eq. 1065.656-7. |
(B) xO2exhdry using Eq. 1065.656-16. | ||
(ii) xH2meas | xint/exhdry andxdil/exhdry | (A) xH2exhdry using Eq. 1065.656-6. |
(B) [Reserved] |
Eq. 1065.656-24
Eq. 1065.656-25
Eq. 1065.656-26
Eq. 1065.656-27
Eq. 1065.656-28
Where:
wC = carbon mass fraction of the fuel and any injected fluids.
wH = hydrogen mass fraction of the fuel and any injected fluids.
wO = oxygen mass fraction of the fuel and any injected fluids.
wS = sulfur mass fraction of the fuel and any injected fluids.
wN = nitrogen mass fraction of the fuel and any injected fluids.
A = effective carbon content of the fuel and any injected fluids.
MC = molar mass of carbon.
[XI] = effective hydrogen content of the fuel and any injected fluids.
MH = molar mass of hydrogen.
[PHI] = effective oxygen content of the fuel and any injected fluids.
MO = molar mass of oxygen.
Xi = effective sulfur content of the fuel and any injected fluids.
MS = molar mass of nitrogen.
[OMEGA] = effective nitrogen content of the fuel and any injected fluids.
MN = molar mass of nitrogen.
Example for NH3fuel:
A = 0
[XI] = 3
[PHI] = 0
Xi = 0
[OMEGA] = 1
MC
MH
MO
MS
= 14.0067 g/mol
= 0 g/g
wH
wO
wS
wN
Eq. 1065.656-29
Eq. 1065.656-30
Eq. 1065.656-31
Eq. 1065.656-32
Eq. 1065.656-33
Where:
wC = carbon mass fraction of the fuel and any injected fluids.
wH = hydrogen mass fraction of the fuel and any injected fluids.
wO = oxygen mass fraction of the fuel and any injected fluids.
wS = sulfur mass fraction of the fuel and any injected fluids.
wN = nitrogen mass fraction of the fuel and any injected fluids.
MC = molar mass of carbon.
[ALPHA] = atomic hydrogen-to-carbon ratio of the fuel and any injected fluids.
MH = molar mass of hydrogen.
[BETA] = atomic oxygen-to-carbon ratio of the fuel and any injected fluids.
MO = molar mass of oxygen.
[GAMMA] = atomic sulfur-to-carbon ratio of the fuel and any injected fluids.
MS = molar mass of sulfur.
[DELTA] = atomic nitrogen-to-carbon ratio of the fuel and any injected fluids.
MN = molar mass of nitrogen.
Example:
[ALPHA] = 1.8
[BETA] = 0.05
[GAMMA] = 0.0003
[DELTA] = 0.0001
MC
MH
MO
MS
= 14.0067
Eq. 1065.656-34
Eq. 1065.656-35
Eq. 1065.656-36
Eq. 1065.656-37
Eq. 1065.656-38
Where:
wC = carbon mass fraction of the mixture of test fuels and any injected fluids.
wH = hydrogen mass fraction of the mixture of test fuels and any injected fluids.
wO = oxygen mass fraction of the mixture of test fuels and any injected fluids.
wS = sulfur mass fraction of the mixture of test fuels and any injected fluids.
wN = nitrogen mass fraction of the mixture of test fuels and any injected fluids.
N = total number of fuels and injected fluids over the duty cycle.
j = an indexing variable that represents one fuel or injected fluid, starting with j = 1.
mj = the mass flow rate of the fuel or any injected fluid j. For batch measurements, divide the total mass of fuel over the test interval duration to determine a mass rate.
wCmeasj = carbon mass fraction of fuel or any injected fluid j.
wHmeasj = hydrogen mass fraction of fuel or any injected fluid j.
wOmeasj = oxygen mass fraction of fuel or any injected fluid j.
wSmeasj = sulfur mass fraction of fuel or any injected fluid j.
wNmeasj = nitrogen mass fraction of fuel or any injected fluid j.
Example for a mixture of diesel and NH3fuel where diesel represents 15% of energy:
N = 2
= 0.5352 g/s
m2
wCmeas1
wHmeas1
wOmeas1
wSmeas1
wNmeas1
wCmeas2
wHmeas2
wOmeas2
wSmeas2
= 0.822447 g/g
= 0.0581014 g/g
wH
wO
wS
wN
Table 3 to Paragraph (e)(4) of § 1065.656-Default Values of A,[XI],[THETA],Xi , and [OMEGA]
Fuel | Atomic carbon, oxygen, and nitrogen-to-hydrogen ratios CA,H[XI],O[THETA],S3/4,N [OMEGA] |
Hydrogen | C0H2OoSoNo. |
Ammonia | C0H3OoSoN1. |
Eq. 1065.656-39
Where:
nexh = raw exhaust molar flow rate from which you measured emissions.
nint = intake air molar flow rate including humidity in intake air.
Example:
nint
xint/exhdry
xraw/exhdry
xH20exhdry
Eq. 1065.656-40
Where:
nexh = raw exhaust molar flow rate from which you measured emissions.
j = an indexing variable that represents one fuel or injected fluid, starting with j = 1.
N = total number of fuels and injected fluids over the duty cycle.
mj = the mass flow rate of the fuel or any injected fluid j.
wCj = carbon mass fraction of the fuel (or mixture of test fuels) and any injected fluid j.
wHj = hydrogen mass fraction of the fuel (or mixture of test fuels) and any injected fluid j.
Example:
= 312.013 mmol/mol = 0.10764 mol/mol
MC
MH
= 6.45541 mmol/mol = 0.00645541 mol/mol
xHcombdry1
m1
m2
wC1
wC2
wH1
= 0.177553 g/g
N = 2
= (xraw/exhdry - xint/exhdry) · (1 - xH20exh) ·ndexh + nint
Eq. 1065.656-41
Example:
nint
= 7.930 mol/s
xraw/exhdry
= 0.1544 mol/mol
xint/exhdry
= 0.1451 mol/mol
xH20exhdry
= 32.46 mmol/mol = 0.03246 mol/mol
ndexh
= 49.02 mol/s
nexh
= (0.1544 - 0.1451) · (1 - 0.03246) · 49.02 + 7.930 = 0.4411 + 7.930 = 8.371 mol/s
40 C.F.R. §1065.656