# 40 CFR § 1065.643 - Carbon balance error verification calculations.

This section describes how to calculate quantities used in the carbon balance error verification described in § 1065.543. Paragraphs (a) through (c) of this section describe how to calculate the mass of carbon for a test interval from carbon-carrying fluid streams, intake air into the system, and exhaust emissions, respectively. Paragraph (d) of this section describes how to use these carbon masses to calculate four different quantities for evaluating carbon balance error. Use rectangular or trapezoidal integration methods to calculate masses and amounts over a test interval from continuously measured or calculated mass and molar flow rates.

(a) Fuel and other fluids. Determine the mass of fuel, DEF, and other carbon-carrying fluid streams, other than intake air, flowing into the system, mfluidj, for each test interval. Note that § 1065.543 allows you to omit all flows other than fuel. You may determine the mass of DEF based on ECM signals for DEF flow rate. You may determine fuel mass during field testing based on ECM signals for fuel flow rate. Calculate the mass of carbon from the combined carbon-carrying fluid streams flowing into the system as follows:

(b) Intake air. Calculate the mass of carbon in the intake air, mCair, for each test interval using one of the methods in this paragraph (b). The methods are listed in order of preference. Use the first method where all the inputs are available for your test configuration. For methods that calculate mCair based on the amount of CO2 per mole of intake air, we recommend measuring intake air concentration, but you may calculate xCO2int using Eq. 1065.655-10 and letting xCO2intdry = 375 µmol/mol.

(1) Calculate mCair, using the following equation if you measure intake air flow:

(2) Calculate mCair, using the following equation if you measure or calculate raw exhaust flow and you calculate chemical balance terms:

(3) Calculate mCair, using the following equation if you measure raw exhaust flow:

(4) Calculate mCair, using the following equation if you measure diluted exhaust flow and dilution air flow:

(5) Determined mCair based on ECM signals for intake air flow as described in paragraph (b)(1) of this section.

(6) If you measure diluted exhaust, determine mCair as described in paragraph (b)(4) of this section using a calculated amount of dilution air over the test interval as determined in § 1065.667(d) instead of the measured amount of dilution air.

(c) Exhaust emissions. Calculate the mass of carbon in exhaust emissions, mCexh, for each test interval as follows:

(d) Carbon balance error quantities. Calculate carbon balance error quantities as follows:

(1) Calculate carbon mass absolute error, εaC, for a test interval as follows:

(2) Calculate carbon mass rate absolute error, εaCrate, for a test interval as follows:

t = 1202.2 s = 0.3339 hr

(3) Calculate carbon mass relative error, εrC, for a test interval as follows:

(4) Calculate composite carbon mass relative error, εrCcomp, for a duty cycle with multiple test intervals as follows:

(i) Calculate εrCcomp using the following equation:

(ii) The following example illustrates calculation of εrCcomp, for cold-start and hot-start transient cycles:

(iii) The following example illustrates calculation of εrCcomp for multiple test intervals with varying duration, such as discrete-mode steady-state duty cycles: