## 4 Tool Application to Evaluate Pollutant Emissions
### Carbon Balance Method
#### 4.2.1 Demonstration of the Carbon Balance Method  
The basic assumption of the Carbon Balance method implies that the exhaust gas components are in the form of CO, CO\({}_{2}\), and HC (HydroCarbon). Consequently, the flowrate of wet exhaust gases is defined by the following equation [16]:  
\[\dot{m}_{exh,~{}wet}~{}=~{}\dot{m}_{fuel}\left[\frac{\frac{1.4 Full_{mix,~{} comu,Full_{mix,~{}comt}}}{\frac{1.180}{\left(\frac{1.4 Full_{mix,~{} comu,Full_{mix,~{}comt}}}{\frac{1.4 Full_{mix,~{}comt}}}{\frac{1.4 Full_{mix,~{} comt}}}{\frac{1.4 Full_{mix,~{}comt}}}{\frac{1.4 Full_{mix,~{}comt}}}{\frac{1.4 Full_{mix,~{} comt}}}{\frac{1.4 Full_{mix,~{}comt}}}}}}{\left.+0.08936 Fuel_{mix~{}comt}-1\right]\right] (14)  
This formula is based on the principle for which the carbon-inlet quantity is equal to the carbon-outlet quantity: Carbon in = Carbon out. The following sections will clearly define the meaning of the two quantities.  
_Carbon in_  
The carbon-inlet quantity is calculated through the following formula:  
\[Carbon_{in}=\dot{m}_{fuel}~{}Fuel_{mix~{}cont~{}c} \tag{15}\]  
where \(\dot{m}_{fuel}~{}[\mathrm{kg/h}]\) is the net fuel flowrate and \(Fuel_{mix~{}cont~{}c}~{}[\%\) mass] is the carbon content in the fuel mixture, which is calculated as follows:  
\[Fuel_{mix~{}cont~{}c}~{}= \tag{16}\] \[= \left\{ \begin{array}{ll}\frac{Fuel_{all~{}cont~{}c}~{}=}{Fuel_{ all~{}cont~{}c}[BSFC_{Fuel~{}al-lus}+BSFC_{Pilot~{}al}]}&\text{if Fuel gas duration injection }<1~{}\mu s\\ \frac{Fuel_{all~{}cont~{}cBSFC_{Pilot~{}al}+Fuel_{gas~{}cont~{}c}BSFC_{Pilot~{} gas}}}{BSFC_{total}}&\text{if Fuel gas duration injection }\geq 1~{}\mu s\end{array} \right.\]  
in which:  
\(Fuel_{oil~{}cont~{}c}~{}[\%\) mass] is the carbon content in the primary fuel, provided by fuel tests;  
\(BSFC_{Fuel~{}oil-loss}~{}[\mathrm{g/kWh}]\) is the brake-specific fuel consumption minus losses and is calculated through the following formula:  
\[BSFC_{Fuel~{}oil-loss}=\frac{10^{3}\dot{m}_{fuel}}{P_{engine}}=\frac{10^{3} \dot{m}_{fuel,total}-60\frac{m_{fuel,loss}}{t_{fuel~{}loss}}}{P_{engine}} \tag{17}\]  
where:  
\(\dot{m}_{fuel}~{}[\mathrm{kg/h}]\) is the net fuel flowrate;  
\(\dot{m}_{fuel,total}~{}[\mathrm{kg/h}]\) is the fuel flowrate, losses included;  
\(m_{fuel,loss}~{}[\mathrm{g}]\) is the mass of fuel lost;  
\(P_{engine}~{}[\mathrm{kW}]\) is the engine power;  
\(t_{fuel~{}loss}~{}[\mathrm{min}]\) is the losses measurement time. _BSFC\({}_{\text{Pilot oil}}\)_ [g/kWh] is the brake-specific pilot fuel consumption, which is calculated with the following formula:  
\[BSFC_{\text{Pilot oil}}\ =\ \frac{\dot{m}_{\text{Pilot oil}}}{P_{\text{eng}}} \tag{18}\]  
in which \(\dot{m}_{\text{Pilot oil}}\) [g/h] is the pilot fuel flowrate and \(P_{\text{eng}}\) [kW] is the engine power. _Fuelgas cont \(\subset\)_ [% mass]: fuel gas carbon content;  
_BSFC\({}_{\text{Fuel gas}}\)_ [g/kWh] : brake-specific fuel gas consumption, equal to \(BSFC_{\text{Fuel gas}}\ =\ \frac{10^{3}\dot{m}_{\text{gas}}}{P_{\text{engine}}}\) where \(\dot{m}_{\text{gas}}\) [kg/h] is the gas flowrate and \(P_{\text{eng}}\) [kW] is the engine power. _BSFC\({}_{\text{total}}\)_ [g/kWh] is the total brake-specific fuel consumption, which is calculated through the following formulae:  
\[BSFC_{\text{total}}\ =\ \left\{ \begin{array}{cl}BSFC_{\text{Fuel oil-loss}}\ +\ BSFC_{\text{Pilot oil}}&\text{if Fuel gas duration injection}\ <\ 1\ \mu s\\ BSFC_{\text{Fuel gas}}\ +\ BSFC_{\text{Pilot oil}}&\text{if Fuel gas duration injection}\ \geq\ 1\ \mu s\end{array} \right.