### U.S. Code of Federal Regulations

Regulations most recently checked for updates: Jan 29, 2023

(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. 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*

(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, χ

(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**x**x**x*, and amount of water, *x**x**x*

(1) Convert your measured concentrations such as, *x**x**x**x**x**x**x**x**x*

(2) Enter the equations in paragraph (c)(4) of this section into a computer program to iteratively solve for *x**x**x**x**x**x**x**x*

(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

Amount of dilution gas or excess air per mole of exhaust | |
---|---|

amount of dilution gas or excess air per mole of exhaust. | |

amount of carbon from fuel and any injected fluids in the exhaust per mole of dry exhaust | |

amount of H | |

water-gas reaction equilibrium coefficient; you may use 3.5 or calculate your own value using good engineering judgment | |

amount of H | |

amount of dry stoichiometric products per dry mole of intake air | |

amount of dilution gas and/or excess air per mole of dry exhaust | |

amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust | |

amount of undiluted exhaust, without excess air, per mole of dry (raw or diluted) exhaust | |

amount of intake air O | |

amount of intake air CO | |

amount of intake air H | |

amount of intake air CO | |

amount of dilution gas CO2 per mole of dilution gas | |

amount of dilution gas CO | |

amount of dilution gas H | |

amount of dilution gas H | |

amount of measured emission in the sample at the respective gas analyzer | |

amount of emission per dry mole of dry sample | |

amount of H | |

amount of H | |

α | atomic hydrogen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids |

β | atomic oxygen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids |

γ | atomic sulfur-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids |

δ | 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**x**x*

(5) The following example is a solution for *x**x**x*

(d) *Carbon mass fraction of fuel.* Determine carbon mass fraction of fuel, *w**w*

*w*

*M*

*M*

*M*

*M*

*M*

*M*

*M*

*M*

*M*

*M*

*w*

(e) *Fuel and diesel exhaust fluid composition.* Determine fuel and diesel exhaust fluid composition represented by α, β, γ, and δ as described in this paragraph (e). When using measured fuel or diesel exhaust fluid properties, you must determine values for α and β in all cases. If you determine compositions based on measured values and the default value listed in Table 2 of this section is zero, you may set γ and δ to zero; otherwise determine γ and δ (along with α and β) based on measured values. Determine elemental mass fractions and values for α, β, γ, and δ as follows:

(1) For liquid fuels, use the default values for α, β, γ, and δ in Table 2 of this section or determine mass fractions of liquid fuels for calculation of α, β, γ, and δ as follows:

(i) Determine the carbon and hydrogen mass fractions according to ASTM D5291 (incorporated by reference in § 1065.1010). When using ASTM D5291 to determine carbon and hydrogen mass fractions of gasoline (with or without blended ethanol), use good engineering judgment to adapt the method as appropriate. This may include consulting with the instrument manufacturer on how to test high-volatility fuels. Allow the weight of volatile fuel samples to stabilize for 20 minutes before starting the analysis; if the weight still drifts after 20 minutes, prepare a new sample). Retest the sample if the carbon, hydrogen, oxygen, sulfur, and nitrogen mass fractions do not add up to a total mass of 100 ± 0.5%; if you do not measure oxygen, you may assume it has a zero concentration for this specification. You may also assume that sulfur and nitrogen have a zero concentration for all fuels except residual fuel blends.

(ii) Determine oxygen mass fraction of gasoline (with or without blended ethanol) according to ASTM D5599 (incorporated by reference in § 1065.1010). For all other liquid fuels, determine the oxygen mass fraction using good engineering judgment.

(iii) Determine the nitrogen mass fraction according to ASTM D4629 or ASTM D5762 (incorporated by reference in § 1065.1010) for all liquid fuels. Select the correct method based on the expected nitrogen content.

(iv) Determine the sulfur mass fraction according to subpart H of this part.

(2) For gaseous fuels and diesel exhaust fluid, use the default values for α, β, γ, and δ in Table 2 of this section, or use good engineering judgment to determine those values based on measurement.

(3) For nonconstant fuel mixtures, you must account for the varying proportions of the different fuels. This paragraph (e)(3) generally applies for dual-fuel and flexible-fuel engines, but it also applies if diesel exhaust fluid is injected in a way that is not strictly proportional to fuel flow. Account for these varying concentrations either with a batch measurement that provides averaged values to represent the test interval, or by analyzing data from continuous mass rate measurements. Application of average values from a batch measurement generally applies to situations where one fluid is a minor component of the total fuel mixture, for example dual-fuel and flexible-fuel engines with diesel pilot injection, where the diesel pilot fuel mass is less than 5% of the total fuel mass and diesel exhaust fluid injection; consistent with good engineering judgment.

(4) Calculate α, β, γ, and δ using the following equations:

*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.

*m*

*j*. For applications using a single fuel and no DEF fluid, set this value to 1. For batch measurements, divide the total mass of fuel over the test interval duration to determine a mass rate.

*w*

*j*.

*w*

*j*.

*w*

*j*.

*w*

*j*.

*w*

*j*.

*N*= 1

*j*= 1

*m*

*w*

*w*

*w*

*w*

*w*

*M*

*M*

*M*

*M*

*M*

(5) Table 2 follows:

(f) *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
*

*n*

*m*

*n*

*m*

(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
*

*m*

(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.* Calculate *n
*

*n*

*n*

*n*

*n*

*x*

*x*

*x*

(3) *Fluid mass flow rate calculation.* This calculation may be used only for steady-state laboratory testing. You may not use this calculation if the standard-setting part requires carbon balance error verification as described in § 1065.543. See § 1065.915(d)(5)(iv) for application to field testing. Calculate *n
*

*m*

*n*

*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.

*m*

*j*.

*w*

*j*.

*N*= 1

*j*= 1

*m*

*w*

*M*

*n*

(g) *Calculated raw exhaust molar flow rate from measured intake air molar flow rate, dilute exhaust molar flow rate, and dilute chemical balance.* You may calculate the raw exhaust molar flow rate, *n
*

*n*

*n*

*n*

*n*

*n*

(1) *Crankcase flow rate.* If engines are not subject to crankcase controls under the standard-setting part, calculate raw exhaust flow as described in paragraph (e)(1) of this section.

(2) *Dilute exhaust and intake air molar flow rate calculation.* Calculate *n
*

*n*

*x*

*x*

*x*

*n*

*n*