40 C.F.R. § 1065.656

Current through September 30, 2024

Section 1065.656 - Hydrogen-based chemical balances of fuel, DEF, intake air, and exhaust

(a)General. Chemical balances of fuel, DEF, 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 hydrogen-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, 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. 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 two of the following quantities: the amount of hydrogen in the measured flow, x_H2exhdry, the fraction of dilution air in diluted exhaust, x_dil/exhdry, and the amount of intake air required to produce actual combustion products per mole of dry exhaust, x_int/exhdry. 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 carbon mass fraction, w_C, hydrogen mass fraction, w_H, oxygen mass fraction, w_O, sulfur mass fraction, w_S, and nitrogen mass fraction, w_N; you may optionally account for diesel exhaust fluid (or other fluids injected into the exhaust), if applicable. Calculate w_C, w_H, w_O, w_S, and w_N as described in paragraphs (d) and (e) of this section. You may alternatively use any combination of default values and measured values as described in paragraphs (d) and (e) of this section. Use the following steps to complete a chemical balance:

(1) Convert your measured concentrations such as x_H2meas, x_NH3meas, x_CO2meas, x_COmeas, x_THCmeas, x_O2meas, x_H2meas, x_NOmeas, x_NO2meas, and x_H2Oint, to dry concentrations by dividing them by one minus the amount of water present during their respective measurements; for example: x_H2Omeas, x_H2OxO2meas, x_H2OxNOmeas, and x_H2Oint. If the amount of water present during a "wet" measurement is the same as an 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 combustion engine, you may assume all NO_X is NO. For a lean-burn combustion 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% NO_2. 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)(5) of this section into a computer program to iteratively solve for x_H2exhdry, x_dil/exhdry, and x_int/exhdry. Use good engineering judgment to guess initial values for x_H2exhdry, x_dil/exhdry, and x_int/exhdry. We recommend guessing an initial amount of hydrogen of 0 mol/mol. We recommend guessing an initial x_int/exhdry of 1 mol/mol. We also recommend guessing an initial x_dil/exhdry of 0.8 mol/mol. Iterate values in the system of equations until the most recently updated guesses are all within ±1% or ±1 [MICRO]mol/mol, whichever is larger, 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 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.
x_{H2O[emission]meas}	Amount of H₂O in sample at emission-detection location; measure or estimate these values according to § 1065.145(e)(2) .
x_Ccombdry	Amount of carbon from fuel and any injected fluids in the exhaust per mole of dry exhaust.
x_Hcombdry	Amount of hydrogen from fuel and any injected fluids in the exhaust per mole of dry exhaust.
x_dil/exh	Amount of dilution gas or excess air per mole of exhaust.
x_dil/exhdry	amount of dilution gas and/or excess air per mole of dry exhaust.
x_Hcombdry	Amount of hydrogen from fuel and any injected fluids in the exhaust 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_CO2int	Amount of intake air CO₂ per mole of intake air.
x_CO2intdry	amount of intake air CO₂ per mole of dry intake air; you may usex_CO2intdry = 375 [MICRO]mol/mol, but we recommend measuring the actual concentration in the intake air.
x_H2Oint	Amount of H₂O in the intake air, based on a humidity measurement of intake air.
x_H2Ointdry	Amount of intake air H₂O per mole of dry intake air.
x_O2int	Amount of intake air O₂ 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 usex_CO2dildry = 375 [MICRO]mol/mol, but we recommend measuring the actual concentration in the dilution gas.
x_H2Odil	Amount of dilution gas H₂O per mole of dilution gas.
x_H2Odildry	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.
w_C	Carbon mass fraction of the fuel (or mixture of test fuels) and any injected fluids.
w_H	Hydrogen mass fraction of the fuel (or mixture of test fuels) and any injected fluids.
w_O	Oxygen mass fraction of the fuel (or mixture of test fuels) and any injected fluids.
w_S	Sulfur mass fraction of the fuel (or mixture of test fuels) and any injected fluids.
w_N	Nitrogen mass fraction of the fuel (or mixture of test fuels) and any injected fluids.

(4) Use the equations specified in this section to iteratively solve for x_int/exhdry, x_dil/exhdry, and x_H2exhdry. The following exceptions apply:

(i) For x_H2exhdry multiple equations are provided, see table 2 to paragraph (c)(6) of this section to determine for which cases the equations apply.

(ii) The calculation of x_O2exhdry is only required when x_O2meas is measured.

(iii) The calculation of x_NH3exhdry is only required for engines that use ammonia as fuel and engines that are subject to NH₃ measurement under the standard setting part, for all other engines x_NH3exhdry may be set to zero.

(iv) The calculation of x_CO2exhdry is only required for engines that use carbon-containing fuels or fluids, either as single fuel or as part of the fuel mixture, and for engines that are subject to CO₂ measurement under the standard setting part, for all other engines x_CO2exhdry may be set to a value that yields for x_Ccombdry a value of zero.

(v) The calculation of x_COexhdry and x_THCexhdry is only required for engines that use carbon-containing fuels and for engines that are subject to CO and THC measurement under the standard setting part, for all other engines x_COexhdry and x_THCexhdry may be set to zero.

(vi) The calculation of x_N2Oexhdry is only required for engines that are subject to N₂O measurement under the standard setting part, for all other engines x_N2Oexhdry may be set to zero.

(5) The chemical balance equations are as follows:

x_Ccombdry = x_co2exhdry + x_coexhdry + x_THCexhdry - x_co2dil·x_dil/exhdry - x_co2int·x_int/exhdry

Eq. 1065.656-1

When measuring	Guess . . .	Calculate . . .
(i) x_O2meas	x_int/exhdry andx_H2exhdry	(A) x_H2exhdry using Eq. 1065.656-7.
		(B) x_O2exhdry using Eq. 1065.656-16.
(ii) x_H2meas	x_int/exhdry andx_dil/exhdry	(A) x_H2exhdry using Eq. 1065.656-6.
		(B) [Reserved]

Fuel	Atomic carbon, oxygen, and nitrogen-to-hydrogen ratios CA,H[XI],O[THETA],S3/4,N [OMEGA]
Hydrogen	C₀H₂O_oS_oN_o.
Ammonia	C₀H₃O_oS_oN₁.