Division 3.4.3 Chemical balance procedure

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:

1. (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 NO_x are measured and not NO and NO₂ separately, good engineering judgement shall be used to estimate a split in the total NO_x concentration between NO and NO₂ for the chemical balances. The molar concentration of NO_x, 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 NO_x emissions, the molar mass of NO₂ for the effective molar mass of all NO_x species, regardless of the actual NO₂ fraction of NO_x, shall be used;

2. (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;

3. (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

4. (d)

   The following equations [(7-84) to (7-101)] shall be used to iteratively solve for x _dil/exh, x _H2Oexh and x _Ccombdry:

   $x_{\mathrm{dil/exh}}=1-\frac{x_{\mathrm{raw/exhdry}}}{1+x_{\mathrm{H2Oexhdry}}}$	(7-84)
   $x_{\mathrm{H2Oexh}}=\frac{x_{\mathrm{H2Oexhdry}}}{1+x_{\mathrm{H2Oexhdry}}}$	(7-85)
   $x_{\mathrm{Ccombdry}}=x_{\mathrm{CO2dry}}+x_{\mathrm{COdry}}+x_{\mathrm{THCdry}}-x_{\mathrm{CO2dil}}\times x_{\mathrm{dil/exhdry}}-x_{\mathrm{CO2int}}\times x_{\mathrm{int/exhdry}}$	(7-86)
   $x_{\mathrm{H2dry}}=\frac{x_{\mathrm{COdry}}\times \left(x_{\mathrm{H2Oexhdry}}-x_{\mathrm{H2Odil}}\times x_{\mathrm{dil/exhdry}}\right)}{K_{\mathrm{H2Ogas}}\times \left(x_{\mathrm{CO2dry}}-x_{\mathrm{CO2dil}}\times x_{\mathrm{dil/exhdry}}\right)}$	(7-87)
   $x_{\mathrm{H2Oexhdry}}=\frac{\alpha }{2}\left(x_{\mathrm{Ccombdry}}-x_{\mathrm{THCdry}}\right)+x_{\mathrm{H2Odil}}\times x_{\mathrm{dil/exhdry}}+x_{\mathrm{H2Oint}}\times x_{\mathrm{int/exhdry}}-x_{\mathrm{H2dry}}$	(7-88)
   $x_{\mathrm{dil/exhdry}}=\frac{x_{\mathrm{dil/exh}}}{1-x_{\mathrm{H2Oexh}}}$	(7-89)
   $x_{\mathrm{int/exhdry}}=\frac{1}{2\times x_{\mathrm{O2int}}}\left[\left(\frac{\alpha }{2}-\beta +2+2\gamma \right)\left(x_{\mathrm{Ccombdry}}-x_{\mathrm{THCdry}}\right)-\left(x_{\mathrm{COdry}}-x_{\mathrm{NOdry}}-2x_{\mathrm{NO2dry}}+x_{\mathrm{H2dry}}\right)\right]$	(7-90)
   $x_{\mathrm{raw/exhdry}}=\frac{1}{2}\left[\left(\frac{\alpha }{2}+\beta +\delta \right)\left(x_{\mathrm{Ccombdry}}-x_{\mathrm{THCdry}}\right)+\left(2x_{\mathrm{THCdry}}+x_{\mathrm{COdry}}-x_{\mathrm{NO2dry}}+x_{\mathrm{H2dry}}\right)\right]+x_{\mathrm{int/exhdry}}$	(7-91)
   $x_{\mathrm{O2int}}=\frac{\mathrm{0,209820}-x_{\mathrm{CO2intdry}}}{1+x_{\mathrm{H2Ointdry}}}$	(7-92)
   $x_{\mathrm{CO2int}}=\frac{x_{\mathrm{CO2intdry}}}{1+x_{\mathrm{H2Ointdry}}}$	(7-93)
   $x_{\mathrm{H2Ointdry}}=\frac{x_{\mathrm{H2Oint}}}{1-x_{\mathrm{H2Oint}}}$	(7-94)
   $x_{\mathrm{CO2dil}}=\frac{x_{\mathrm{CO2dildry}}}{1+x_{\mathrm{H2Odildry}}}$	(7-95)
   $x_{\mathrm{H2Odildry}}=\frac{x_{\mathrm{H2Odil}}}{1-x_{\mathrm{H2Odil}}}$	(7-96)
   $x_{\mathrm{COdry}}=\frac{x_{\mathrm{COmeas}}}{1-x_{\mathrm{H2OCOmeas}}}$	(7-97)
   $x_{\mathrm{CO2dry}}=\frac{x_{\mathrm{CO2meas}}}{1-x_{\mathrm{H2OCO2meas}}}$	(7-98)
   $x_{\mathrm{NOdry}}=\frac{x_{\mathrm{NOmeas}}}{1-x_{\mathrm{H2ONOmeas}}}$	(7-99)
   $x_{\mathrm{NO2dry}}=\frac{x_{\mathrm{NO2meas}}}{1-x_{\mathrm{H2ONO2meas}}}$	(7-100)
   $x_{\mathrm{THCdry}}=\frac{x_{\mathrm{THCmeas}}}{1-x_{\mathrm{H2OTHCmeas}}}$	(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.