# Commission Delegated Regulation (EU) 2017/654 of 19 December 2016 supplementing Regulation (EU) 2016/1628 of the European Parliament and of the Council with regard to technical and general requirements relating to emission limits and type-approval for internal combustion engines for non-road mobile machinery, Division 3.4.3: Chemical balance procedure

Extent: E+W+S+N.I.

The calculations for a chemical balance involve a system of equations that require iteration. The initial values of up to three quantities shall be guessed: the amount of water in the measured flow, x H2Oexh, fraction of dilution air in diluted exhaust gas (or excess air in the raw exhaust gas), x dil/exh, and the amount of products on a C1 basis per dry mole of dry measured flow, x Ccombdry. Time-weighted mean values of combustion air humidity and dilution air humidity in the chemical balance may be used; as long as combustion air and dilution air humidity 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, their completely dry concentrations, x dry and x H2Oexhdry shall be determined. The fuel atomic hydrogen-to-carbon ratio, α, oxygen-to-carbon ratio, β and carbon mass fraction of fuel, w C shall also be used. For the test fuel, α and β or the default values in Table 7.3 may be used.
Use the following steps to complete a chemical balance:
(a) Measured concentrations such as, x CO2meas, x NOmeas, and x H2Oint, shall be converted 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 gas flow, x H2Oexh, it has to be iteratively solved for that value in the system of equations. If only total NOx are measured and not NO and NO2 separately, good engineering judgement shall be used to estimate a split in the total NOx concentration between NO and NO2 for the chemical balances. The molar concentration of NOx, x NOx, may be assumed to be 75 % NO and 25 % NO2. For NO2 storage after-treatment systems, x NOx may be assumed to be 25 % NO and 75 % NO2. For calculating the mass of NOx emissions, the molar mass of NO2 for the effective molar mass of all NOx species, regardless of the actual NO2 fraction of NOx, shall be used;
(b) Equations (7-82) to (7-99) in paragraph (d) of this point have to be entered into a computer program to iteratively solve for x H2Oexh, x Ccombdry and x dil/exh. Good engineering judgment shall be used to guess initial values for x H2Oexh, x Ccombdry, and x dil/exh. Guessing an initial amount of water that is about twice the amount of water in the intake or dilution air is recommended. Guessing an initial value of x Ccombdry as the sum of the measured CO2, CO, and THC values is recommended. Guessing an initial x dil between 0,75 and 0,95, such as 0,8 is also recommended. Values in the system of equations shall be iterated until the most recently updated guesses are all within ± 1 % of their respective most recently calculated values;
(c) The following symbols and subscripts are used in the equation system of paragraph (d) of this point where x unit is mol/mol:
Symbol
Description
x dil/exh
Amount of dilution gas or excess air per mole of exhaust gas
x H2Oexh
Amount of H2O in exhaust per mole of exhaust gas
x Ccombdry
Amount of carbon from fuel in the exhaust per mole of dry exhaust gas
x H2Oexhdry
Amount of water in exhaust per dry mole of dry exhaust gas
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 gas
x int/exhdry
Amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust gas
x raw/exhdry
Amount of undiluted exhaust, without excess air, per mole of dry (raw or diluted) exhaust gas
x O2intdry
Amount of intake air O2 per mole of dry intake air; x O2intdry = 0,209445 mol/mol may be assumed
x CO2intdry
Amount of intake air CO2 per mole of dry intake air. x CO2intdry = 375 μmol/mol may be used, but measuring the actual concentration in the intake air is recommended
x H2Ointdry
Amount of the intake air H2O 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 air is used as diluent, x CO2dildry = 375 μmol/mol may be used, but measuring the actual concentration in the intake air is recommended
x H2Odildry
Amount of dilution gas H2O per mole of dry dilution gas
x H2Odil
Amount of dilution gas H2O 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 water in sample at emission-detection location. These values shall be measured or estimated according to point 9.3.2.3.1.
x H2Oint
Amount of water in the intake air, based on a humidity measurement of intake air
K H2Ogas
Water-gas reaction equilibrium coefficient. 3,5 or a different value might be calculated using good engineering judgement.
α
Atomic hydrogen-to-carbon ratio of the mixture of fuel(s) (CHαOβ) being combusted, weighted by molar consumption
β
Atomic oxygen-to-carbon ratio of the mixture of fuel(s) (CHαOβ) being combusted, weighted by molar consumption
(d) The following equations [(7-84) to (7-101)] shall be used to iteratively solve for x dil/exh, x H2Oexh and x Ccombdry:
x dil/exh = 1 − x raw/exhdry 1 + x H2Oexhdry
(7-84)
x H2Oexh = x H2Oexhdry 1 + x H2Oexhdry
(7-85)
x Ccombdry = x CO2dry + x COdry + x THCdry − x CO2dil × x dil/exhdry − x CO2int × x int/exhdry
(7-86)
x H2dry = x COdry × x H2Oexhdry − x H2Odil × x dil/exhdry K H2Ogas × x CO2dry − x CO2dil × x dil/exhdry
(7-87)
x H2Oexhdry = α 2 x Ccombdry − x THCdry + x H2Odil × x dil/exhdry + x H2Oint × x int/exhdry − x H2dry
(7-88)
x dil/exhdry = x dil/exh 1 − x H2Oexh
(7-89)
x int/exhdry = 1 2 × x O2int α 2 − β + 2 + 2 γ x Ccombdry − x THCdry − x COdry − x NOdry − 2 x NO2dry + x H2dry
(7-90)
x raw/exhdry = 1 2 α 2 + β + δ x Ccombdry − x THCdry + 2 x THCdry + x COdry − x NO2dry + x H2dry + x int/exhdry
(7-91)
x O2int = 0,209820 − x CO2intdry 1 + x H2Ointdry
(7-92)
x CO2int = x CO2intdry 1 + x H2Ointdry
(7-93)
x H2Ointdry = x H2Oint 1 − x H2Oint
(7-94)
x CO2dil = x CO2dildry 1 + x H2Odildry
(7-95)
x H2Odildry = x H2Odil 1 − x H2Odil
(7-96)
x COdry = x COmeas 1 − x H2OCOmeas
(7-97)
x CO2dry = x CO2meas 1 − x H2OCO2meas
(7-98)
x NOdry = x NOmeas 1 − x H2ONOmeas
(7-99)
x NO2dry = x NO2meas 1 − x H2ONO2meas
(7-100)
x THCdry = x THCmeas 1 − x H2OTHCmeas
(7-101)
At the end of the chemical balance, the molar flow rate is calculated as specified in points 3.5.3 and 3.6.3.

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Source: https://www.legislation.gov.uk/eur/2017/654/annex/VII/division/3/division/3.4/division/3.4.3 (the official version)
Page: https://openlegislation.uk/eu-regulation-2017-654/annex-VII/division-3/division-3.4/division-3.4.3
Contains public sector information licensed under the Open Government Licence v3.0. Source: legislation.gov.uk, The National Archives.