Introduction
The regulatory framework for pollutants from marine engines includes nitric oxides (NO_{x}) and sulfur oxides (SO_{x}), with limitations referring both to the globe and to specific geographical areas (Emission Control Areas  ECA_{S}^{[1]}). These regulations are reported in Annex VI of the MARPOL Convention, and date since 2008 (MEPC.176(58)). Further, the International Maritime Organization (IMO) intends to impose new regulations associated with Greenhouse Gases (GHGs). In particular, in comparison to 2008 levels, IMO has brought to discussion a reduction in carbon dioxide (CO_{2}) emissions per transport work (Energy Efficiency Design Index  EEDI) of 40% by 2030 and of 70% by 2050 (MEPC.304(72), as an average across international shipping.
In this context, a module for the calculation of the mass flow rate of CO_{2}, NO_{x} and SO_{x} emissions from the ship main engine was developed by the NTUA team during VesselsLife.com. The module builds on a (background) preprocessing step, which: (i) Considers about 10,000 bulk carriers of all subclasses using the Seaweb database; (ii) Generates a new database of about 24,000 loading conditions; (iii) Calculates geometry/hydrodynamic parameters and Lightship using validated formulas; (iv) Calculates engine brake power – speed (P, n) at the engine Maximum Continuous Rating (MCR); (v) Selects automatically a twostroke marine Diesel engine using envelopes of MAN engines, digitized in the course of this study; (vi) For each of the 24,000 cases, following a procedure prescribed by MAN, the engine SFOC is automatically calculated, for prototype conditions, as per ISO 3046 (the procedure has been automated and can be readily executed for any point on the propeller curve – "real" SFOC); (vii) A regression analysis is performed, arriving at a proper representation of SFOC ("calculated" SFOC), based on input data (principal design/operational ship data), available to the ship operator; (viii) Proper corrections for nonISO conditions are implemented, to account for different fuel types, air intake temperature and sea cooling water inlet temperature; (ix) Finally, CO_{2}, NO_{x} and SO_{x} mass flow rates are calculated by multiplying engine’s power with the "calculated" SFOC and proper emission factors, as derived from the combustion stoichiometry and NO_{x} chemistry. In summary, the present module constitutes an accurate, effective and easy to use computational tool for the calculation of CO_{2} emissions  important for forthcoming regulations, as well as NO_{x} and SO_{x} emissions  central to the in force regulations.
The report is structured as follows.
· First, the model development is highlighted.
· Second, a presentation of results in terms of calculated CO_{2}, NO_{x} and SO_{x} mass flow rates, for a number of representative cases, spanning the entire spectrum of bulkcarrier subclasses.
· Finally, a summary of the present work is presented.
Emissions Module Development
The module developed uses data obtained from the Seaweb database (https://ihsmarkit.com/products/seawebmaritimereference.html). In particular, data for 10,350 Bulkcarriers of the global fleet were collected, including all subclasses: Handysize, Handymax, Panamax, Capesize and Very Large Bulk Carriers (VLBCs). Ships built after 2005 were considered, accounting for new designs, with different loading conditions (Deadweight – DWT).
Based on this data, a new database, of 24,000 operating points, has been generated, accounting for different ship loading conditions: (i) full load condition  70%, (ii) ballast condition  20%, (iii) random condition  10%, without considering slow steaming. Hull fouling has been taken into account, ranging between 0% (clean hull) and 25% (drydock condition), in the frame of a normal distribution. Slow steaming was not considered in the present implementation.
The sequence of calculations performed is summarized as follows.
(1) Selection of loading condition (DWT) and fouling level.
(2) (i) Calculation of ship geometry: length (L), breadth (B), and depth (D); (ii) Calculation of hull form coefficients: block coefficient (C_{b}), prismatic coefficient (C_{p}), midship section coefficient (C_{m}), and waterplane coefficient (C_{w}); (iii) Calculation of Lighship (Papanikolaou 2009). (iv) Calculation of ship resistance, propeller selection (Molland 2012, Carlton 2012, Charvalos 2020).
(3) Calculation of engine Power and speed (P, n) at MCR, automatic selection of engine from a generated engine library (Molland 2012, Carlton 2012, MAN technical papers 2013, 2018, 2019).
(4) For each of the 24,000 operating points: automatic calculation of the "real" SFOC, for reference conditions (ISO 3046), following MAN guidelines (MAN technical papers 2013, 2018, 2019).
(5) Regression analysis using the "real" SFOC values of the 24,000 operating points, resulting in proper formulas for a "calculated" SFOC function, in terms of proper input parameters; the values of these parameters are readily available to the ship operator, during ship operation.
Two approaches were considered, a reference and an extended one, differing only in the number of input parameters. In the reference approach, the input parameters correspond to operational ship data, while the additional input parameters of the extended approach are characteristics of the main engine geometry. Two correlations were thus introduced:
reference approach: (1)
extended approach: (2)
The following input parameters are considered in (1) and (2):
(a) Displacement (D  tn)
(b) Operational speed (V  kn)
(c) Operational break power (P – kW)
(d) Draft at loading condition (T – m)
(e) Engine number of cylinders (z  #)
(f) Cylinder bore (b  m)
(g) Piston stroke (s  m)
The present regression analysis yielded the values of coefficients included in formulas (1) and (2), as presented in Table 1 and Table 2, for the reference and the extended approach, respectively.
Table 1. Reference approach: Calculated values of coefficients
c_{0} 
b_{1} 
b_{2} 
b_{3} 
b_{4} 
 
 
 
 
 
Table 2. Extended approach: Calculated values of coefficients
c_{0} 
b_{1} 
b_{2} 
b_{3} 
b_{4} 
b_{5} 
b_{6} 
 
 
 
 
 
 
 
The error of the present regression analysis has been quantified in terms of a mean deviation of the resulting ("calculated") SFOC values from the "real" values, in the entire set of 24,000 operating points:
(3)
Values of 1.25% and 1.20% have been calculated for the error of the reference and the extended approach, respectively, illustrating the high accuracy of both approaches.
Finally, to account for nonISO conditions, proper corrections were implemented for type of fuel, air intake temperature and inlet temperature of sea cooling water, following MAN guidelines (MAN technical papers 2013, 2018, 2019). It is noted that ISO conditions consider Marine Diesel Oil (MDO) as the reference fuel, with corrections for Heavy Fuel Oil (HFO) and Low Sulfur Heavy Fuel Oil (LSHFO) implemented in the present work.
Mass flow rates of CO_{2}, NO_{x} and SO_{x} are calculated based on the engine’s power, the "calculated" SFOC and proper emission factors, accounting for the combustion stoichiometry and NO_{x} chemistry (Entec 2002):
(4)
The following input parameters are considered in (4):
(a) Engine power (P  kW)
(b) Engine corrected "calculated" SFOC
(c) Emission factor (EF – )
Thus, (4) calculates emission mass flow rates, , in .
Emission factor values are presented in Table 3.
Table 3. Emission factor (EF) values used for calculating CO_{2}, NO_{x} and SO_{x} mass flow rates
CO_{2} 
3.114 (tn CO_{2 }/tn fuel) 
NO_{x} 
0.092 (tn NO_{x }/tn fuel) 
SO_{x} 
2.023 x S mass fraction in fuel 
Results
Emission mass flow rates for CO_{2}, NO_{x} and SO_{x} were calculated for several representative cases, across the entire spectrum of all bulkcarrier subclasses. The present cases were generated by considering the following combinations of input parameters, for each subclass: (a) the minimum values, (b) the average values, and (c) the maximum values; the corresponding range of the input parameters is presented in Table 4.
Next, results are presented for the reference and the extended approach of the present work. It is noted that in all cases HFO of a sulfur content of 2.7% was considered.
Table 4. Range of input variables
Displacement (tn) 
Speed (kn) 
Draft (m) 
Power (kW) 
Air Inlet Temperature (°C) 
Cooling Water Temperature (°C) 

min 
max 
min 
max 
min 
max 
min 
max 
min 
max 
min 
max 

Handysize 
25417 
42921 
11.0 
14.0 
5.0 
10.71 
2208 
6734 
20 
50 
5 
35 
Handymax 
42931 
65765 
11.3 
14.5 
7.5 
12.9 
2965 
9659 

Panamax 
65833 
93883 
11.6 
14.5 
10 
14.42 
4437 
11693 

Capesize 
93898 
225860 
11.6 
14.5 
12 
18.03 
4646 
21129 

VLBC 
229150 
445554 
11.6 
14.5 
14 
22.79 
10308 
36521 
Reference Approach
Three series of calculations were performed for the reference approach, corresponding to combinations of the minimum, average and maximum values of the input parameters; the input data are presented in Tables 5, 6 and 7, respectively. The calculated emission mass flow rates for the three series are presented in Figures 16.
Table 5. Minimum values of input variables

Displacement (tn) 
Speed (kn) 
Draft (m) 
Power (kW) 
Air Inlet Temperature(°C) 
Cooling Water Temperature (°C) 
Handysize 
25417 
11.0 
5.0 
2208 
20 
5 
Handymax 
42931 
11.3 
7.5 
2965 
20 
5 
Panamax 
65833 
11.6 
10 
4437 
20 
5 
Capesize 
93898 
11.6 
12 
4664 
20 
5 
VLBC 
229150 
11.6 
14 
10308 
20 
5 
Figure 1. Reference approach: CO_{2} mass flow rate (tn/hr) versus engine power P (kW) for the minimum values of the input data.
Figure 2. Reference approach: NO_{x}  SO_{x} mass flow rate (kg/hr) versus engine power P (kW) for the minimum values of the input data.
Table 6. Average values of input variables

Displacement (tn) 
Speed (kn) 
Draft (m) 
Power (kW) 
Air Inlet Temperature(°C) 
Cooling Water Temperature (°C) 
Handysize 
37837 
13.7 
8.74 
4591 
35 
20 
Handymax 
52138 
14.1 
9.67 
6029 
35 
20 
Panamax 
74879 
14.4 
11.37 
7778 
35 
20 
Capesize 
141025 
14.4 
13.52 
11441 
35 
20 
VLBC 
275495 
14.4 
16.28 
18705 
35 
20 
Figure 3. Reference approach: CO_{2} mass flow rate (tn/hr) versus engine power P (kW) for the average values of the input data.
Figure 4. Reference approach: NO_{x}  SO_{x} mass flow rate (kg/hr) versus engine power P (kW) for the average values of the input data.
Table 7. Maximum values of input variables

Displacement (tn) 
Speed (kn) 
Draft (m) 
Power (kW) 
Air Inlet Temperature(°C) 
Cooling Water Temperature (°C) 
Handysize 
42921 
14.0 
10.71 
6734 
50 
35 
Handymax 
65765 
14.5 
12.90 
9659 
50 
35 
Panamax 
93883 
14.5 
14.42 
11693 
50 
35 
Capesize 
225860 
14.5 
18.03 
21129 
50 
35 
VLBC 
445554 
14.5 
22.79 
36521 
50 
35 
Figure 5. Reference approach: CO_{2} mass flow rate (tn/hr) versus engine power P (kW) for the maximum values of the input data
Figure 6. Reference approach: NO_{x}  SO_{x} mass flow rate (kg/hr) versus engine power P (kW) for the maximum values of the input data.
Figures 16 verify that emission mass flow rates are increasing with the ship size, while NO_{x} emissions are consistently higher than SO_{x} emissions.
Extended Approach
Three series of calculations were performed for the extended approach, corresponding to combinations of the minimum, average and maximum values of the input parameters; the basic input data of Tables 5, 6 and 7 are maintained, while the supplementary inputs are presented in Tables 8, 9 and 10. The calculated emission mass flow rates for the three series are presented in Figures 712.
Table 8. Extended approach: Supplementary input variables  minimum values

Cylinders 
Stroke(m) 
bore (m) 
Handysize 
5 
1.77 
0.40 
Handymax 
5 
2.00 
0.45 
Panamax 
5 
2.40 
0.50 
Capesize 
5 
2.40 
0.50 
VLBC 
5 
2.21 
0.50 
Figure 7. Extended approach: CO_{2} mass flow rate (tn/hr) versus engine power P (kW) for the minimum values of the input data.
Figure 8. Extended approach: NO_{x}  SO_{x} mass flow rate (kg/hr) versus engine power P (kW) for the minimum values of the input data.
Table 9. Extended approach: Supplementary input variables  average values

Cylinders 
Stroke (m) 
bore (m) 
Handysize 
6 
2.00 
0.44 
Handymax 
6 
2.15 
0.49 
Panamax 
6 
2.48 
0.52 
Capesize 
7 
2.82 
0.59 
VLBC 
7 
3.25 
0.74 
Figure 9. Extended approach: CO_{2} mass flow rate (tn/hr) versus engine power P (kW) for the average values of the input data.
Figure 10. Extended approach: NO_{x}  SO_{x} mass flow rate (kg/hr) versus engine power P (kW) for the average values of the input data.
Table 10. Extended approach: Supplementary input variables  maximum values

Cylinders 
Stroke (m) 
bore (m) 
Handysize 
8 
2.25 
0.50 
Handymax 
7 
2.50 
0.60 
Panamax 
8 
2.50 
0.60 
Capesize 
8 
3.26 
0.70 
VLBC 
8 
3.72 
0.95 
Figure 11. Extended approach: CO_{2} mass flow rate (tn/hr) versus engine power P (kW) for the maximum values of the input data.
Figure 12. Extended approach: NO_{x}  SO_{x} mass flow rate (kg/hr) versus engine power P (kW) for the maximum values of the input data.
Figures 712 verify that emission mass flow rates are increasing with the ship size, while NO_{x} emissions are consistently higher than SO_{x} emissions, in agreement with the results of the reference approach.
Summary
The present document has briefly presented a computational module, developed by the NTUA team in the course of VesselsLife.com, for calculating main ship emissions, in particular NO_{x}  SO_{x}, pertinent to the in force regulations, and CO_{2}, central to the forthcoming regulations for GHG emissions, in the frame of EEDI. The present development is applicable to all bulkcarrier subclasses. It builds on a preprocessing step for calculating the main engine SFOC for prototype ISO 3046 conditions ("real" SFOC). Using regression analysis, two correlations of a "calculated" SFOC are derived, using independent variables readily available to ship operators, such as ship’s displacement, draft, operation speed and engine power. Proper corrections for nonISO conditions have been implemented, to account for different fuels, and air and cooling water initial temperature. Mass flow rates for CO_{2}, NO_{x}and SO_{x}are calculated based on the engine’s power, "calculated" SFOC and proper values of emission factors. Results of calculated emissions have been presented for representative cases, spanning the entire spectrum of bulkcarrier subclasses. Overall, the present development has produced an accurate, computationally cost effective and easy to use tool, for calculating ship emissions.
References
1. Carlton, J. 2012. “Marine propellers and propulsion.” ButterworthHeinemann publications.
2. Charvalos, G. 2020. “Investigation of tribological properties of mechanical systems of conventional merchant vessels.” Diploma thesis, Dept. of Naval Architecture and Marine Engineering, National Technical University of Athens.
3. Entec UK Limited. 2002. “Quantification of emissions from ships associated with ship movements between ports in the European Community”.
4. https://ihsmarkit.com/products/seawebmaritimereference.html
5. MAN, technical papers. 2013. “Basic principles of ship propulsion.” MAN Energy Solutions.
6. MAN, technical papers. 2018. “Basic principles of ship propulsion.” MAN Energy Solutions.
7. MAN, technical papers. 2019. “Propulsion trends in bulk carriers.” MAN Energy Solutions.
8. MEPC.176(58). 2008. “Amendments to the Annex of the Protocol of 1997 to amend the International Convention for the Prevention of Pollution from Ships, 1973, as modified by the Protocol of 1978 Relating Thereto (Revised MARPOL Annex VI).” IMO, London, UK.
9. MEPC.304(72). 2018. “Initial IMO strategy on reduction of GHG emissions from ships.” IMO, London, UK.
10. Molland, A. 2011. “Ship resistance and propulsion.” Cambridge University Press.
11. Papanikolaou, A. 2009. “Ship Design, methodologies of Preliminary Design, Part I.” Simeon Publications.
12. Papanikolaou, A. 2009. “Ship Design, methodologies of Preliminary Design, Part II.” Simeon Publications.
[1]The existing ECAs include the Baltic Sea, the North Sea, the North American ECA (including most of US and Canadian coast) and the US Caribbean ECA (including Puerto Rico and the US Virgin Islands) MEPC.176(58).