Appendix 2 - Proof of the SO₂/CO₂ Ratio Method

1 The SO₂/CO₂ ratio method enables direct monitoring of exhaust gas emissions to verify compliance with emissions limits set out in table 1 in paragraph 1.3 of these guidelines. In the case of EGC systems that absorb CO₂ during the exhaust gas cleaning process it is necessary to measure the CO₂ prior to the cleaning process and use the CO₂ concentration before cleaning with the SO₂ concentration after cleaning. For conventional low alkali cleaning systems virtually no CO₂ is absorbed during exhaust gas cleaning and therefore monitoring of both gases can be undertaken after the cleaning process.

2 Correspondence between the SO₂/CO₂ ratio can be determined by simple inspection of the respective carbon contents per unit mass of distillate and residual fuel. For this group of hydrocarbon fuels the carbon content as a percentage of mass remains closely similar, whereas the hydrogen content differs. Thus it can be concluded that for a given carbon consumption by combustion there will be a consumption of sulphur in proportion to the sulphur content of the fuel, or in other words a constant ratio between carbon and sulphur adjusted for the molecular weight of oxygen from combustion.

3 The first development of the SO₂/CO₂ ratio considered its use to verify compliance with emissions from 1.5% sulphur fuel. The limit of 65 (ppm^footnote/%) SO₂/CO₂ for 1.5% sulphur in fuel can be demonstrated by first calculating the mass ratio of fuel sulphur to fuel carbon, which is tabulated in table 1 in this appendix for various fuels and fuel sulphur contents; including 1.5% sulphur for both distillate and residual fuels. These ratios were used to solve for the corresponding SO₂ and CO₂ concentrations in exhaust, which are tabulated in table 2 of this appendix. Molecular weights (MW) were taken into account to convert mass fractions to mole fractions. For the 1.5% sulphur fuels in table 2, the amount of CO₂ is set first at 8% and then changed to 0.5% to show that there is no effect due to changes in excess air. As expected, the absolute SO₂ concentration changes, but the SO₂/CO₂ ratio does not. This indicates that the SO₂/CO₂ ratio is independent of fuel-to-air ratios. Therefore, SO₂/CO₂ ratio can be used robustly at any point of operation, including operation where no brake power is produced.

3.1 Note that the SO₂/CO₂ ratio varies slightly from distillate to residual fuel. This occurs because of the very different atomic hydrogen-to-carbon ratios (H:C) of the two fuels. Figure 1 illustrates the extent of the SO₂/CO₂ ratios' sensitivity to H:C over a broad range of H:C and fuel sulphur concentrations. From Figure 1, it can be concluded that for fuel sulphur levels less than 3.0% sulphur, the difference in S/C ratios for distillate and residual fuel is less than 5.0%.

3.2 In the case of using non-petroleum fuel oils, the appropriate SO₂/CO₂ ratio applicable to the values given in regulations 14.1 and/or 14.4 of MARPOL Annex VI will be subject to approval by the Administration.

Table 1: Fuel properties for marine distillate and residual fuel*

* Based on properties in the IMO NO_x Monitoring Guidelines, resolution MEPC.103(49).

Table 2: Emissions calculations corresponding to 1.5 % fuel sulphur

SO₂/CO₂ ratio vs % sulphur in fuel

4 Correspondence between 65 (ppm^footnote/%) SO₂/CO₂ and 6.0 g/kWh is demonstrated by showing that their S/C ratios are similar. This requires the additional assumption of a brake-specified fuel consumption value of 200 g/kWh. This is an appropriate average for marine diesel engines. The calculation is as follows:

• brake-specific SO₂ = 6.0 g/kW-hr
• MW_S = 32.065 g/mol
• MW_SO2 = 64.064 g/mol
• BSFC = 200 g/kW-hr
• % carbon in 1.5% sulphur fuel (from table 1) = 85.05% (distillate) or 87.17% (residual)
• 
• 

Note 1: The S/C mass ratios calculated above, based on 6.0 g/kWh and 200 g/kWh BSFC, are both within 0.10% of the S/C mass ratios in the emissions table (Table 2). Therefore, 65 (ppm^footnote/%) SO₂/CO₂ corresponds well to 6.0 g/kWh.

Note 2: The value of 6.0 g/kWh, hence the 200g/kWh brake-specified fuel consumption is taken from MARPOL Annex VI as adopted by the 1997 MARPOL Conference.

5 Thus, the working formulas are as follows:

For complete combustion =

For incomplete combustion =

* Note: Gas concentrations must be sampled or converted to the same residual water content (e.g. fully wet, fully dry).