## 2 Materials and Methods
### Uncertainty Analyses  
Uncertainty analyses were presented according to the procedure presented in the previous literature [20]. It is known that the relative (\(\Delta A\)) and the absolute (\(\delta A\)) uncertainty of a considered parameter \(A\) are related by Equation (1)  
\[\Delta A=(\delta A/A)\times 100\% \tag{1}\]  
It can be assumed that for measured parameters \(A\) and \(B\), the rules for the uncertainty calculation are described by Equations (2)-(5).  
\[(A\pm\delta A)+(B\pm\delta B)\cong(A+B)\pm(\delta A+\delta B), \tag{2}\]  
\[(A\pm\delta A)-(B\pm\delta B)\cong(A-B)\pm(\delta A+\delta B), \tag{3}\]  
\[(A\pm\Delta A)\times(B\pm\Delta B)\cong(A\times B)\pm(\Delta A+\Delta B), \tag{4}\]  
\[(A\pm\Delta A)/(B\pm\Delta B)\cong(A/B)\pm(\Delta A+\Delta B). \tag{5}\]  
Moreover, if the final parameter \(Q\) is obtained by the multiplication of measured parameter \(A\) and number \(N\), \(Q=N\times A\), then the absolute uncertainty of \(Q\) is described by Equation (6):  
\[\delta Q\approx|N|\times\delta A \tag{6}\]  
Figure 1: Scheme of a technical-scale installation used for combustion of liquid fuels. MB—main burner (liquid fuels: FADR and HFO), PB—pilot burner (fuel: natural gas), PA—primary air, SA—secondary air, W—water for cooling, I—combustion chamber, II—dust separator, III—exhaust gas cooler, IV—chimney, V—exhaust gas sampling point, VI—O\({}_{2}\) measurement in raw exhaust gas. Reprinted from [24] (upon permission of Elsevier, License Number 5656340853661).  
Moreover, if the measured parameter \(A\) is changed in time due to stochastic variation (i.e., fluctuation in a certain average value), then the final value of absolute uncertainty of an analyzed parameter, \(\delta A\), includes the uncertainty related to the measuring system \(\delta A_{measuring}\) and the uncertainty related to the measured parameter fluctuation \(\delta A_{fluctuations}\). Thus, in such cases, the \(\delta A\) is calculated from Equation (7)  
\[\delta A=\sqrt{\delta A_{fluctuations}^{2}+\delta A_{measuring}^{2}} \tag{7}\]  
Based on these rules, the uncertainty was calculated from the equations presented below, in terms of the following parameters:  
* energy density: \[\Delta E_{d,\;LHV}=\Delta\rho+\Delta LHV\] (8) \[\Delta E_{d,\;HHV}=\Delta\rho+\Delta HHV\] (9)
* the energy for fuel heating and fuel pressurization: \[\Delta E_{heat}=\frac{\delta T_{fuel}+\delta T_{room}}{T_{fuel}-T_{room}} \times 100\%\] (10) \[\Delta E_{pressure}=\Delta\rho+\Delta\rho\] (11)
* nominal fuel feed: \[\dot{\Delta m}_{100\text{kW}}=\Delta LHV\] (12)
* power loss: \[\Delta P_{loss}=\dot{\Delta m}_{100\text{kW}}+\frac{\delta E_{heat}+\delta E_ {pressure}}{E_{heat}+E_{pressure}}\times 100\%\] (13) The relative and absolute uncertainty of analyzed parameters are presented in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & \multicolumn{2}{c}{**FADR**} & \multicolumn{2}{c}{**HFO**} \\ \hline  & **Absolute Uncertainty** & **Relative Uncertainty** & **Absolute Uncertainty** & **Relative Uncertainty** \\ \hline Density, kg/m\({}^{3}\) & 1 & 0.11 & 1 & 0.1 \\ HHV, kJ/kg & 87 & 0.22 & 87 & 0.2 \\ LHV, kJ/kg & 120 & 0.33 & 120 & 0.3 \\ C, w.\% & 1 & 1.31 & 1 & 1.16 \\ H, w.\% & 0.50 & 4 & 0.54 & 4 \\ N, w.\% & 0.05 & 6 & 0.03 & 6 \\ S, w.\% & 0.05 & 31 & 0.05 & 8 \\ Ash content, w.\% & 0.04 & 14 & 0.04 & 6 \\ Ignition temperature, \({}^{\circ}\)C & 1 & 0.4 & 1 & 0.4 \\ E density (LHV), GJ/m\({}^{3}\) & 0.142 & 0.4 & 0.146 & 0.4 \\ E density (HHV), GJ/m\({}^{3}\) & 0.155 & 0.4 & 0.156 & 0.4 \\ \(E_{heat}\), kJ/kg & 2.85 & 3 & 5.13 & 3 \\ \(E_{pressure}\), kJ/kg & 10.8 & 1.8 & 6.4 & 1.0 \\ \(E_{total}\), kJ/kg & 13.7 & 1.9 & 11.5 & 1.4 \\ \(P_{loss}\), kW & 0.044 & 2.3 & 0.033 & 1.7 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The relative and the absolute uncertainty of analyzed parameters.