CFR > Title 40 - Protection of Environment > CHAPTER I—ENVIRONMENTAL PROTECTION AGENCY > SUBCHAPTER U—AIR POLLUTION CONTROLS (Parts 1027–1074) > PART 1065—ENGINE-TESTING PROCEDURES > SUBPART G—Calculations and Data Requirements (§1065.601 to §1065.695) > 1065.655—Chemical balances of fuel, intake air, and exhaust.

1065.655—Chemical balances of fuel, intake air, and exhaust.

(a) General. Chemical balances of fuel, intake air, and exhaust may be used to calculate flows, the amount of water in their flows, and the wet concentration of constituents in their flows. With one flow rate of either fuel, intake air, or exhaust, you may use chemical balances to determine the flows of the other two. For example, you may use chemical balances along with either intake air or fuel flow to determine raw exhaust flow.
(b) Procedures that require chemical balances. We require chemical balances when you determine the following:
(1) A value proportional to total work, W, when you choose to determine brake-specific emissions as described in § 1065.650(e).
(2) The amount of water in a raw or diluted exhaust flow, x H2Oexh, when you do not measure the amount of water to correct for the amount of water removed by a sampling system. Correct for removed water according to § 1065.659(c)(2).
(3) The flow-weighted mean fraction of dilution air in diluted exhaust, x dil/exh, when you do not measure dilution air flow to correct for background emissions as described in § 1065.667(c). Note that if you use chemical balances for this purpose, you are assuming that your exhaust is stoichiometric, even if it is not.
(c) Chemical balance procedure. The calculations for a chemical balance involve a system of equations that require iteration. We recommend using a computer to solve this system of equations. You must guess the initial values of up to three quantities: The amount of water in the measured flow, x H2Oexh, fraction of dilution air in diluted exhaust, x dil/exh, and the amount of products on a C1 basis per dry mole of dry measured flow, x Ccombdry. You may use time-weighted mean values of combustion air humidity and dilution air humidity in the chemical balance; as long as your combustion air and dilution air humidities remain within tolerances of ±0.0025 mol/mol of their respective mean values over the test interval. For each emission concentration, x, and amount of water, x H2Oexh, you must determine their completely dry concentrations, x dry and x H2Oexhdry. You must also use your fuel's atomic hydrogen-to-carbon ratio, α, oxygen-to-carbon ratio, β, sulfur-to-carbon ratio, γ, and nitrogen-to-carbon ratio, δ. You may measure α, β, γ, and δ or you may use default values for a given fuel as described in § 1065.655(d). Use the following steps to complete a chemical balance:
(1) Convert your measured concentrations such as, x CO2meas, x NOmeas , and x H2Oint, to dry concentrations by dividing them by one minus the amount of water present during their respective measurements; for example: x H2OxCO2meas x, H2OxNOmeas, and x H2Oint. If the amount of water present during a “wet” measurement is the same as the unknown amount of water in the exhaust flow, x H2Oexh, iteratively solve for that value in the system of equations. If you measure only total NOX and not NO and NO2 separately, use good engineering judgment to estimate a split in your total NOX concentration between NO and NO2 for the chemical balances. For example, if you measure emissions from a stoichiometric spark-ignition engine, you may assume all NOX is NO. For a compression-ignition engine, you may assume that your molar concentration of NOX, x NOx, is 75% NO and 25% NO2. For NO2 storage aftertreatment systems, you may assume x NOx is 25% NO and 75% NO2. Note that for calculating the mass of NOX emissions, you must use the molar mass of NO2 for the effective molar mass of all NOX species, regardless of the actual NO2 fraction of NOX.
(2) Enter the equations in paragraph (c)(4) of this section into a computer program to iteratively solve for x H2Oexh, x Ccombdry, and x dil/exh. Use good engineering judgment to guess initial values for x H2Oexh, x C combdry, and x dil/exh. We recommend guessing an initial amount of water that is about twice the amount of water in your intake or dilution air. We recommend guessing an initial value of x Ccombdry as the sum of your measured CO2, CO, and THC values. We also recommend guessing an initial x dil/exh between 0.75 and 0.95, such as 0.8. Iterate values in the system of equations until the most recently updated guesses are all within ± 1% of their respective most recently calculated values.
(3) Use the following symbols and subscripts in the equations for this paragraph (c):

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x dil/exh = amount of dilution gas or excess air per mole of exhaust.

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x H2Oexh = amount of water in exhaust per mole of exhaust.

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x Ccombdry = amount of carbon from fuel in the exhaust per mole of dry exhaust.

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x H2dry = amount of H2 in exhaust per amount of dry exhaust.

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K H2Ogas = water-gas reaction equilibrium coefficient. You may use 3.5 or calculate your own value using good engineering judgment.

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x H2Oexhdry = amount of water in exhaust per dry mole of dry exhaust.

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x prod/intdry = amount of dry stoichiometric products per dry mole of intake air.

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x dil/exhdry = amount of dilution gas and/or excess air per mole of dry exhaust.

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x int/exhdry = amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust.

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x raw/exhdry = amount of undiluted exhaust, without excess air, per mole of dry (raw or diluted) exhaust.

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x O2int = amount of intake air O2 per mole of intake air.

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x CO2intdry = amount of intake air CO2 per mole of dry intake air. You may use xCO2intdry = 375 µmol/mol, but we
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recommend measuring the actual concentration in the intake air.

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x H2Ointdry = amount of intake air H2O per mole of dry intake air.

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x CO2int = amount of intake air CO2 per mole of intake air.

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x CO2dil = amount of dilution gas CO2 per mole of dilution gas.

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x CO2dildry = amount of dilution gas CO2 per mole of dry dilution gas. If you use air as diluent, you may use xCO2dildry = 375 µmol/mol, but we recommend measuring the actual concentration in the intake air.

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x H2Odildry = amount of dilution gas H2O per mole of dry dilution gas.

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x H2Odil = amount of dilution gas H2O per mole of dilution gas.

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x [emission]meas = amount of measured emission in the sample at the respective gas analyzer.

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x [emission]dry = amount of emission per dry mole of dry sample.

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x H2O[emission]meas = amount of water in sample at emission-detection location. Measure or estimate these values according to § 1065.145(e)(2) .

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x H2Oint = amount of water in the intake air, based on a humidity measurement of intake air.

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α = atomic hydrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

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β = atomic oxygen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

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γ = atomic sulfur-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.

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δ = atomic nitrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
(4) Use the following equations to iteratively solve for x dil/exh, x H2Oexh, and x Ccombdry :
(5) The following example is a solution for x dil/exh, X H2Oexh, and x Ccombdry using the equations in paragraph (c)(4) of this section:

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α = 1.8

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β = 0.05

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γ = 0.0003

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δ = 0.0001
(d) Carbon mass fraction. Determine carbon mass fraction of fuel, w c, using one of the following methods:
(1) You may calculate w c as described in this paragraph (d)(1) based on measured fuel properties. To do so, you must determine values for α and β in all cases, but you may set γ and δ to zero if the default value listed in Table 1 of this section is zero. Calculate w c using the following equation:
Where:
wC, = carbon mass fraction of fuel.
MC = molar mass of carbon.
α = atomic hydrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
MH = molar mass of hydrogen.
β = atomic oxygen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
MO = molar mass of oxygen.
γ = atomic sulfur-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
MS = molar mass of sulfur.
δ = atomic nitrogen-to-carbon ratio of the mixture of fuel(s) being combusted, weighted by molar consumption.
MN = molar mass of nitrogen.
Example:
α = 1.8
β = 0.05
γ = 0.0003
δ = 0.0001
MC = 12.0107
MH = 1.01
MO = 15.9994
MS = 32.065
MN = 14.0067
wC, = 0.8205
(2) You may use the default values in the following table to determine w c for a given fuel:
Table 1 of § 1065.655 —Default Values ofα, β, γ, δ, andw c, for Various Fuels
Fuel Atomic hydrogen, oxygen, sulfur, andnitrogen-to-carbon ratios CHαOβSγNδ Carbon mass fraction, w c g/g.
Gasoline CH1.85O0S0N0 0.866
#2 Diesel CH1.80O0S0N0 0.869
#1 Diesel CH1.93O0S0N0 0.861
Liquefied Petroleum Gas CH2.64O0S0N0 0.819
Natural gas CH3.78O0.016S0N0 0.747
Ethanol CH3O0.5S0N0 0.521
Methanol CH4O1S0N0 0.375
Residual fuel blends Must be determined by measured fuel properties as described in paragraph (d)(1) of this section.
(e) Calculated raw exhaust molar flow rate from measured intake air molar flow rate or fuel mass flow rate. You may calculate the raw exhaust molar flow rate from which you sampled emissions,n exh, based on the measured intake air molar flow rate, n int, or the measured fuel mass flow rate, m fuel, and the values calculated using the chemical balance in paragraph (c) of this section. Note that the chemical balance must be based on raw exhaust gas concentrations. Solve for the chemical balance in paragraph (c) of this section at the same frequency that you update and record n int orm fuel.
(1) Crankcase flow rate. If engines are not subject to crankcase controls under the standard-setting part, you may calculate raw exhaust flow based on n int orm fuel using one of the following:
(i) You may measure flow rate through the crankcase vent and subtract it from the calculated exhaust flow.
(ii) You may estimate flow rate through the crankcase vent by engineering analysis as long as the uncertainty in your calculation does not adversely affect your ability to show that your engines comply with applicable emission standards.
(iii) You may assume your crankcase vent flow rate is zero.
(2) Intake air molar flow rate calculation. Based onn int, calculaten exh as follows:
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 = 3.780 mol/s
xint/exhdry = 0.69021 mol/mol
xraw/exhdry = 1.10764 mol/mol
xH20exhdry = 107.64 mmol/mol = 0.10764 mol/mol
nexh = 6.066 mol/s
(3) Fuel mass flow rate calculation. Based on m fuel, calculate n exh as follows:
Where:
nexh = raw exhaust molar flow rate from which you measured emissions.
mfuel = fuel flow rate including humidity in intake air.
Example:
mfuel = 7.559 g/s
wC = 0.869 g/g
MC = 12.0107 g/mol
xCcombdry = 99.87 mmol/mol = 0.09987 mol/mol
xH20exhdry = 107.64 mmol/mol = 0.10764 mol/mol
nexh= 6.066 mol/s

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[73 FR 37331, June 30, 2008, as amended at 73 FR 59334, Oct. 8, 2008; 75 FR 23051, Apr. 30, 2010]