40 C.F.R. § 1065.655

Current through September 30, 2024

Section 1065.655 - Carbon-based chemical balances of fuel, DEF, 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. See § 1065.520(f) for information about when to use this carbon-based chemical balance procedure. 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. Note that chemical balance calculations allow measured values for the flow rate of diesel exhaust fluid for engines with urea-based selective catalytic reduction.

(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(f) .

(2) Raw exhaust molar flow rate either from measured intake air molar flow rate or from fuel mass flow rate as described in paragraph (f) of this section.

(3) Raw exhaust molar flow rate from measured intake air molar flow rate and dilute exhaust molar flow rate, as described in paragraph (g) of this section.

(4) 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. Note that you may not use the water measurement methods in § 1065.257 to determine x_H2Oexh. Correct for removed water according to § 1065.659 .

(5) The calculated total dilution air flow when you do not measure dilution air flow to correct for background emissions as described in § 1065.667(c) and (d) .

(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 intake air humidity and dilution air humidity in the chemical balance; as long as your intake 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 mixture's atomic hydrogen-to-carbon ratio, [ALPHA], oxygen-to-carbon ratio, [BETA], sulfur-to-carbon ratio, [GAMMA], and nitrogen-to-carbon ratio, [DELTA]; you may optionally account for diesel exhaust fluid (or other fluids injected into the exhaust), if applicable. You may calculate [ALPHA], [BETA],[GAMMA], and [DELTA] based on measured fuel composition or based on measured fuel and diesel exhaust fluid (or other fluids injected into the exhaust) composition together, as described in paragraph (e) of this section. You may alternatively use any combination of default values and measured values as described in paragraph (e) of this section. 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 NO_X and not NO and NO₂ separately, use good engineering judgment to estimate a split in your total NO_X 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 NO_X is NO. For a compression-ignition engine, you may assume that your molar concentration of NO_X, 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 NO_X emissions, you must use the molar mass of NO₂ for the effective molar mass of all NO_X species, regardless of the actual NO₂ fraction of NO_X.

(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 performing the chemical balance calculations in this paragraph (c):

TABLE 1 OF § 1065.655 - SYMBOLS AND SUBSCRIPTS FOR CHEMICAL BALANCE EQUATIONS

x_dil/exh	Amount of dilution gas or excess air per mole of exhaust
X_dil/exh	amount of dilution gas or excess air per mole of exhaust.
x_Ccombdry	amount of carbon from fuel and any injected fluids in the exhaust per mole of dry exhaust
x_H2dry	amount of H₂ in exhaust per amount of dry exhaust
K_H2Ogas	water-gas reaction equilibrium coefficient; you may use 3.5 or calculate your own value using good engineering judgment
x_H2Oexhdry	amount of H₂ O in exhaust per dry mole of dry exhaust
x_prod/intdry	amount of dry stoichiometric products per dry mole of intake air
x_dil/exhdry	amount of dilution gas and/or excess air per mole of dry exhaust
x_int/exhdry	amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust
x_raw/exhdry	amount of undiluted exhaust, without excess air, per mole of dry (raw or diluted) exhaust
x_O2int	amount of intake air O₂ per mole of intake air
x_CO2intdry	amount of intake air CO₂ per mole of dry intake air; you may use x_CO2intdry = 375 [MICRO]mol/mol, but we recommend measuring the actual concentration in the intake air
x_H2Ointdry	amount of intake air H₂ O per mole of dry intake air
x_CO2int	amount of intake air CO₂ per mole of intake air
x_CO2dil	amount of dilution gas CO2 per mole of dilution gas
x_CO2dildry	amount of dilution gas CO₂ per mole of dry dilution gas; if you use air as diluent, you may use x_CO2dildry = 375 [MICRO]mol/mol, but we recommend measuring the actual concentration in the intake air
x_H2Odildry	amount of dilution gas H₂ O per mole of dry dilution gas
x_H2Odil	amount of dilution gas H₂ O per mole of dilution gas
x_{[emission]meas}	amount of measured emission in the sample at the respective gas analyzer
x_{[emission]dry}	amount of emission per dry mole of dry sample
x_{H2O[emission]meas}	amount of H₂ O in sample at emission-detection location; measure or estimate these values according to § 1065.145(e)(2)
x_H2Oint	amount of H₂ O in the intake air, based on a humidity measurement of intake air
[ALPHA]	atomic hydrogen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids
[BETA]	atomic oxygen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids
[GAMMA]	atomic sulfur-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids
[DELTA]	atomic nitrogen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids

(4) Use the following equations to iteratively solve for x_dil/exh, x_H2Oexh, and x_Ccombdry: