## 2 Analysis and Literature Review of Clearance in Port Channels and Basins
### Mathematical Model
Emissions are calculated according to the formula that includes fuel consumption, actual engine power used and the relative magnitude of specific emissions. Thus, the carbon dioxide emissions are calculated according to the following formula [15; 47]:  
\[CO_{2}=q_{LP}\cdot\Delta CO_{2}, \tag{10}\]  
where \(\Delta CO_{2}\)--carbon dioxide coefficient, which for petroleum products (diesel, fuel oil) is between 3.0 and 3.5 and for LNG between 2.5 and 2.9. Figure 5: Relative vessel speed (\(v^{\prime}\)) versus relative engine power (\(N^{\prime}\)). The Sulphur oxide content can be calculated using the following formula [14; 15]:  
\[SO_{x}=q_{LP}\cdot\Delta SO_{x}, \tag{11}\]  
where \(\Delta SO_{x}\)--Sulphur oxide coefficient, which depends on the type of fuel; for petroleum products, it ranges from 0.001 to 0.035 and for LNG it is around zero. The carbon monoxide content can be calculated using the following formula [41]:  
\[CO=\int\limits_{0}^{t}N_{av}\cdot\Delta CO\cdot dt, \tag{12}\]  
where \(\Delta CO\)--carbon monoxide coefficient, which depends on the type of engine [42]. The amount of nitrogen oxides generated is calculated using the following formula [41]:  
\[NO_{x}=\int\limits_{0}^{t}N_{av}\cdot\Delta NO_{x}\cdot dt, \tag{13}\]  
where \(\Delta NO_{X}\)--nitrogen oxide coefficient, depending on the engine type. The particulate matter generation is calculated using the following formula [48]:  
\[PM=\int\limits_{0}^{t}N_{av}\cdot\Delta PM\cdot dt, \tag{14}\]  
where \(\Delta PM\)--the particulate matter coefficient, which depends on the type of engine and the type of fuel, and is up to 10 g/kWh for petroleum products and close to zero for LNG fuels [48]. The emission factors and sizes of marine engines depend on the type of engine and the type of fuel used. For marine engines, average emission factors and relative values are given in Table 2 (as an example) [11]. Thus, the reduction of emissions from engines depends on the type and design of the engine, the type of fuel used and the engine's operating conditions (maneuvering mode). Fuel consumption depends on the operating mode of the engine, especially the modes of transitional mechanisms. The qualifications and experience of ship crews and port pilots greatly influence the amount of emissions from ships [15; 38; 48; 49]. The power of engines used in ships has a significant influence on the generation of individual emissions. Emission factors and relative magnitudes are shown in Table 3 (as an example) [11; 49; 50]. \begin{table}
\begin{tabular}{l l l} \hline
**Types of Emission** & **Petroleum Products** & **LNG** \\ \hline \(CO_{2}\)—depending on the amount of fuel & 3.2 & 2.5 \\ \(SO_{x}\), \%—depending on the amount of fuel & 0.1 & 0.0–0.1 \\ \(NO_{x}\), g/kWh & 10 & 4 \\ \(CO\), g/kWh & 5 & 3 \\ \(PM\), g/kWh & 0.5 & 0.0–0.1 \\ \hline \end{tabular}
\end{table} 
Table 2: Average emission factors for marine engines by fuel type. Thus, shipping emissions depend on the type of fuel, the quality of the engine and its power. Knowing how much fuel is consumed in shipping, what type of emissions are emitted and what their quantities are, it is possible and necessary to look for opportunities and methods to reduce the impact on the environment.