Energetic and Ecological Effects of the Slow Steaming Application and Gasification of Container Ships

Abstract

One of the short-term operational measures for fuel savings and reducing CO₂ emissions from ships at sea is sailing at reduced speed, i.e., slow steaming, while the gasification of the ship represents an important mid-term technical measure. In this study, the energetic and ecological benefits of slow steaming and gasification are studied for a container ship sailing between Shanghai and Hamburg. Resistance and propulsion characteristics in calm water are calculated using computational fluid dynamics based on the viscous flow theory for a full-scale ship, while the added resistance in waves is calculated by applying potential flow theory. The propeller operating point is determined for the design and slow steaming speeds at sea states with the highest probability of occurrence through the investigated sailing route. Thereafter, the fuel consumption and CO₂ emissions are calculated for a selected dual fuel engine in fuel oil- and gas-supplying modes complying with IMO Tier II and Tier III requirements. The results demonstrate a significant reduction in fuel consumption and CO₂ emissions for various slow steaming speeds compared to the design speed at different sea states, and for the gasification of a container ship. For realistic weather conditions through the investigated route, the potential reduction in CO₂ emissions per year could be up to 11.66 kt/year for fuel oil mode and 8.53 kt/year for gas-operating mode. CO₂ emission reduction per year due to gasification under realistic weather conditions could be up to 22 kt/year.

1. Introduction

Global climate change as a significant variation in average weather conditions is currently one of the most important issues. The main cause of climate change is the emission of greenhouse gases (GHG), mostly carbon dioxide (CO₂) and methane (CH₄). Amongst others, climate change is manifested through an increase in the global average temperature, which then leads to an increased rate of evaporation causing intense storms and weather extremes [1]. For that reason, the ratification of the Paris agreement in 2015 has imposed a limit for global average temperature well below 2 °C, and preferably limited to an increase of 1.5 °C compared to preindustrial levels [2]. However, to achieve this aim GHG emissions should be reduced immediately and reach net zero by the middle of the 21st century. It should be noted that 16.2% of global GHG emissions are caused by the transport sector [3] and the reduction in GHG emissions within the transport sector is crucial. Considering that more than 80% of the international trade in goods is carried by sea, maritime transport is the backbone of international trade and the global economy [4]. Consequently, maritime transport is faced with increasing pressure to decarbonize and operate more sustainably. The interest from the stakeholders of the shipping sector concerning deep decarbonization is increasing. However, decarbonization requires financial incentives and policies at international and regional levels [5]. Although during the last decade the world fleet has become more energy efficient, total GHG emissions are continuously growing. A large portion in GHG emissions in the maritime sector comes from container ships, particularly older and less energy efficient ones. Bearing in mind that the container shipping industry is one of the main transport industries in the maritime sector, the GHG emissions reduction for container ships becomes imperative. It should be noted that most of the world fleet is still powered by carbon-based fuels causing the emission of harmful gases. The fourth International Maritime Organization (IMO) GHG study stated that the share of emissions caused by ships in global anthropogenic emissions has increased from 2.76% in 2012 to 2.89% in 2018 [6], and emissions are projected to increase further. In June 2021, IMO adopted amendments to Annex VI of the MARPOL Convention [7] to reduce the carbon intensity of ships and include targets for energy efficiency, to additionally reduce GHG emissions from ships. The newly adopted measures will require all ships to calculate their energy efficiency existing ship index (EEXI) following technical means to improve their energy efficiency and to establish their annual operational carbon intensity indicator (CII) and CII rating. Carbon intensity relates GHG emissions to the transport work of ships. In addition to GHG emissions, the maritime transport industry significantly contributes to the non-GHG emissions, i.e., sulfur dioxides and nitrogen oxides, which are very harmful to the environment as well [8]. IMO has established emission control areas (ECAs), as an important measure to reduce and control SO_x, NO_x, and particulate matter (PM) emissions. With the establishment of ECAs, ship operators must decide whether to comply with ECA regulations, which strategy they should adopt to comply with ECA regulations, and establish the ways to minimize associated costs [9]. The possible solutions are fuel switching, i.e., using fuel with higher sulfur content when sailing outside the ECAs, and fuel with lower sulfur content inside the ECAs, installment of scrubbers, or using clean liquefied natural gas (LNG) as fuel. Although the optimal response strategy to adopt ECA regulations is the ECA evasion strategy when the fuel price ratio is greater than the minimum fuel price ratio (critical threshold), ECA evasion strategy is a decision that the ship will increase its sailing distance outside the ECA to reduce the sailing distance within the ECA. However, an evasion strategy will eventually increase the total emissions of harmful gasses.

Numerous measures have been proposed by IMO from 2011 onward to reduce CO₂ emissions from the maritime transport industry. These measures are categorized as short-term, mid-term, and long-term measures. One of the short-term measures is the reduction in operating speed of ships called slow steaming. The introduction of slow steaming leads to a decrease in fuel consumption and consequently CO₂ emission [10], and is employed by almost all global shipping companies. Although Maersk Lines introduced slow steaming in container shipping, tankers and bulk carriers have adopted it as well [11]. Although slow steaming is associated with environmental benefits, shipping companies often do not recognize slow steaming as a direct measure to increase environmental performance, but whether their customers will be willing to bear the additional costs [12]. In other words, the introduction of slow steaming can increase the round-trip time by 10–20%, depending on the sailing route and port times [13,14], thus reducing the shipping income. An increase in transport time due to slow steaming could lead to an increase in the required number of ships, and in that way the savings in fuel consumption and CO₂ emission could decrease significantly. It should be noted that sailing at a speed lower than the ship design speed changes the operating conditions of the engine that could operate in suboptimal conditions [15]. In inland navigation, slow steaming as an operational measure is less achievable [16] considering that power demands are generally significantly different for upstream and downstream with continuous water level fluctuations.

Another possible short-term measure is the development of technical and operational energy efficiency measures for both new and existing ships. LNG fueled ships seem to be technically the most practical alternative to decrease CO₂ emissions in deep-sea shipping since LNG can replace conventional, more-polluting oil-based fuels, and enable almost complete removal of SO_x and PM emissions with a substantial reduction in NO_x emissions as well [17]. While LNG carriers have used LNG as fuel for a long time, other ship types have recently started to use LNG as fuel. LNG-fueled ships are powered by dual-fuel (DF) two-stroke engines, for example, MAN-gas-diesel or Wartsila-DF, where the former reduces GHGs by 20–24%, NO_x by 25–30%, and SO_x by 92–97% [18].

Degiuli et al. [19] have analyzed fuel oil consumption and CO₂ emissions for engines powered by low sulfur marine gas oil and LNG. They obtained significant savings for slow steaming speed for one of the world’s busiest container ship sailing routes. Namely, the reduction in CO₂ emission is approximately 31% for a speed reduction of 13.6% for an engine powered by low sulfur marine gas oil, and up to 49% for an engine powered by LNG, in comparison to a ship sailing at the design speed and engine powered by low sulfur marine gas oil. Another benefit of LNG fueled engines reflects in the carbon-capture technology onboard ships [20]. In that way, ship-based carbon capture technology becomes a very effective way to reduce emissions for deep-sea LNG fueled ships.

In this paper, the energetic and ecological effects of the slow steaming and gasification of a container ship are studied considering current IMO regulations, performed for the first time to the best of the authors’ knowledge. The results obtained demonstrate important benefits of slow steaming application for fuel oil (FO) and NG fueled modes from an energetic point of view, which is evident from significant fuel savings. The most significant positive ecological effect is achieved by the gasification of the container ship, which is reflected through the vast reduction in CO₂ emission.

2. Materials and Methods

2.1. Ship Resistance and Propulsion Characteristics

The Kriso container ship (KCS) is used as a case study for assessing the impact of speed reduction on fuel consumption and CO₂ emissions. The design speed of KCS corresponds to 22 kn (knots) and the slow steaming speeds range from 18 to 21 kn. The body plan of KCS is presented in Figure 1, and the main particulars are given in

Table 1. The main particulars of KCS.

Main Particulars	Full Scale
Length between perpendiculars, LPP (m)	230
Waterline length, LWL (m)	232.5
Maximum molded breadth at design waterline, BWL (m)	32.2
Depth, D (m)	19
Draft, T (m)	10.8
Displacement volume, ∇ (m3)	52,030
Hull wetted surface area, SW (m2)	9424
Block coefficient, CB	0.6505
Midship section coefficient, CM	0.9849
Longitudinal centre of buoyancy, LCB (% LPP) from midship	−1.48
Vertical centre of gravity, VCG (m)	7.28
Roll radius of gyration, kxx/B	0.40
Pitch radius of gyration, kyy/LPP	0.25
Yaw radius of gyration, kzz/LPP	0.25
Density, ρ (kg/m3)	1026
Propeller diameter, D (m)	7.9
Number of blades, Z	5
Pitch to diameter ratio, P/D	0.997

. KCS represents a typical container ship and a benchmark commonly used in numerous studies related to computational fluid dynamics (CFD) [21,22,23]. The container ship sailing route connects China (Shanghai port, ${\phi }_S$ = 31.303° N, ${\mu }_S$ = 121.667° E) and Germany (Hamburg port, ${\phi }_H$ = 54.542° N, ${\mu }_H$ = 9.915° E) passes through the Mediterranean Sea and is selected for the case study, Figure 2.

Numerical simulations of resistance and self-propulsion tests are carried out utilizing STAR-CCM+. The total resistance of a ship in calm water at the design and slow steaming speeds is obtained in resistance tests, while ship propulsion characteristics are obtained in self-propulsion tests. The governing equations of the applied mathematical model are the Reynolds averaged Navier–Stokes (RANS) equations and the averaged continuity equation [24]:

$$\frac{\partial \left(\rho {\overline{u}}_i\right)}{\partial t}+\frac{\partial }{\partial x_j}\left(\rho {\overline{u}}_i{\overline{u}}_j+\rho \overline{{u^{\prime }}_i{u^{\prime }}_j}\right)=-\frac{\partial \overline{p}}{\partial x_i}+\frac{\partial {\overline{\tau }}_{ij}}{\partial x_j},$$

(1)

$$\frac{\partial \left(\rho {\overline{u}}_i\right)}{\partial x_i}=0,$$

(2)

where $\rho$ is the fluid density, ${\overline{u}}_i$ is the averaged Cartesian components of the velocity vector, $\rho \overline{{u^{\prime }}_i{u^{\prime }}_j}$ is the Reynolds stress tensor, $\overline{p}$ is the mean pressure, and ${\overline{\tau }}_{ij}$ is the mean viscous stress tensor.

To close the set of Equations (1) and (2), the $k-\omega$ shear stress transport turbulence model is applied. The size of the computational domains and the boundary conditions applied on the domain boundaries in the numerical simulations of resistance and self-propulsion tests are the same as is [19], while details on the discretization schemes, mesh refinements, time steps, and stopping criteria are explained in [25,26].

Ship total resistance and propulsion characteristics in calm water are validated against the experimental data available in the literature, and the highest relative deviation is equal to 4.58% for relative rotative efficiency [26]. Ship-added resistance in regular head waves is obtained by the boundary integral equation method (BIEM) [27], and the highest relative deviation from the experimental data is equal to 8.6% [11]. The added resistance for sea states with the highest probability of occurrence on the analyzed sailing route [28] is obtained by means of the spectral analysis using the Bretschneider sea spectrum:

$$S_{\varsigma }\left(\omega \right)=\frac{H_S{}^2}{4\pi }{\left(\frac{2\pi }{T_z}\right)}^4{\omega }^{-5}\exp \left[-\frac{1}{\pi }{\left(\frac{2\pi }{T_z}\right)}^4{\omega }^{-4}\right],$$

(3)

where $H_S$ is the significant wave height and $T_z$ is the zero-crossing period. The term $2\pi /T_z$ corresponds to zero-crossing frequency. The areas of the investigated sailing route are shown in Figure 2, and sea states with the highest probability of occurrence are presented in

Table 2. Sea states.

Sea State, $S{I}_S$	$H_S$, m	$T_z$, s
S0	0	0
S1	0.5	7.5
S2	1.5	8.5
S3	2.5	8.5
S4	3.5	8.5
S5	4.5	8.5
S6	5.5	8.5

.

The total resistance in waves is calculated as the sum of calm water resistance $R_T$ and added resistance in waves $R_{AW}$, as follows:

$$R_{TOT}=R_T(v_S)+R_{AW}(v_S,S{I}_S),$$

(4)

The thrust deduction fraction $t$, wake fraction $w$, and relative rotative efficiency ${\eta }_R$ are obtained in the numerical simulations of the self-propulsion tests in calm water and are assumed to be constant at a certain ship speed for all analyzed sea states.

Based on the thrust deduction fraction depending on ship speed, $t(v_S)$, the required thrust in waves is determined by the following equation:

$$T_P=\frac{R_{TOT}(v_S,S{I}_S)}{1-t(v_S)},$$

(5)

The required thrust depending on the thrust coefficient $K_T$ is defined as follows:

$$T_P=K_T(J)\hspace{0.17em}\rho n^2{D}^4,$$

(6)

The balancing rate of revolution $n_B$ is calculated for each ship speed and sea state, i.e., $n_B=n_B(v_S,S{I}_S)$. Based on the calculated $n_B=n_B(v_S,S{I}_S)$, other propulsion parameters, such as the propeller advance ratio $J_B(v_S,S{I}_S)$ and torque coefficient $10\hspace{0.17em}{K}_{Q_B}(v_S,S{I}_S)$ are determined, as well as propeller efficiency ${\eta }_P$. Finally, the balancing value of the engine torque, taking into account the propeller shafting efficiency ${\eta }_{PS}=0.98$, and the balancing value of brake power are calculated by the following expressions, respectively:

$$Q_B=\frac{K_{Q_B}(v_S,S{I}_S)}{{\eta }_{PS}{\eta }_R(v_S)}\rho \hspace{0.17em}{D}^5{n}_B^2(v_S,S{I}_S),$$

(7)

$$P_{BB}(v_S,S{I}_S)=\frac{\mathsf{\pi }{K}_{Q_B}(v_S,S{I}_S)}{30\hspace{0.17em}{\eta }_{PS}{\eta }_R(v_S)}\rho \hspace{0.17em}{D}^5{n}_B^3(v_S,S{I}_S)=\frac{R_{TOT}(v_S,S{I}_S)\cdot v_S}{{\eta }_{OP}(v_S)},$$

(8)

where ${\eta }_{OP}(v_S)={\eta }_{PS}\hspace{0.17em}{\eta }_R(v_S){\eta }_H(v_S)\hspace{0.17em}{\eta }_P(v_S)$ and ${\eta }_H(v_S)=(1-t)/(1-w)$ are overall propulsion efficiency and hull efficiency, respectively.

2.2. Selection Procedure for the Main DF Engine Complying with IMO Regulations

Considering the decarbonization trends in maritime transport, the DF engine is currently the most favorable choice. According to MAN propulsion DF engine project guide program [29,30], these engines can run in three fueled modes: FO only; mainly NG with a very small share of the pilot fuel oil (PFO), i.e., $0.5\hspace{0.17em}÷1.5\hspace{0.17em}\%$ of the overall fuel energy income; and fuel-sharing mode (FSM), also referred to as specified dual fuel (SDF) mode, where the ratio between PFO and NG can be selected according to preset values.

The selection DF engine is based on the fact that SMCR (specified maximum continuous rating) must be located within the engine layout diagram (inside of the quadrangle defined by points L₁, L₂, L₃, and L₄), Figure 3. For the SMCR, corresponding break power $P_{SMCR}$ and the rate of revolution $n_{SMCR}$ are calculated as follows:

$$P_{SMCR}=P_D\frac{1+SM}{1-EM},$$

(9)

$$n_{SMCR}=n_{LP}(1-LRM),$$

(10)

where $SM=0.1÷0.2$ and $EM=0.1÷0.15$ are sea and engine margine, respectively, while $LRM=0.04÷0.07$ is light running margine.

Further, $n_{LP}$ is the rate of revolution at the light propeller (LP) curve that is calculated for $P_{LP}=P_{SMCR}$ as follows:

$$n_{LP}=n_D{\left(\frac{P_{SMCR}}{P_D}\right)}^{1/3},$$

(11)

Since SMCR must be within the engine layout diagram, $n_{SMCR}$ must be greater than:

$$n_{SMCR}\ge n_{MCR}\frac{P_{SMCR}}{P_{MCR}},$$

(12)

Because part of the analyzed sailing route passes through ECAs (emission control area), Figure 2, the selected DF engine complies with IMO’s Tier II and Tier III (for ECAs) regulations. It should be noted that Tier II refers to non-ECAs (in the rest of the paper moderate ECAs, MECAs), where according SOx rules [31] mass sulfur fraction in FO and PFO must be $s\le 0.5\hspace{0.17em}\%$, while Tier III refers to ECAs with mass sulfur fraction $s\le 0.1\hspace{0.17em}\%$. Consequently, inside ECAs DF engines must be fueled by the ultra low sulfur fuel oil (ULSFO) with $s_{ULSFO}\le 0.1\hspace{0.17em}\%$, and outside ECAs (MECAs) by the very low sulfur fuel oil (VLSFO) with $s_{VLSFO}\le 0.5\hspace{0.17em}\%$. In general, both ULSFO and VLSFO can be either marine gas oil (MGO), distillate (DM), or residual (RM) marine fuels.

On the other hand, according to the NO_X rules, for ECAs Tier III requirements must be applied for NOx reductions on two-stroke DF engines, which can be fulfilled by two alternative methods: EGR (exhaust gas recirculation) and SCR (selective catalytic reduction). Both alternative methods have two emission-cycle operating modes: Tier II for operation outside NECAs (NO_X ECAs) and Tier III for operation inside NECAs.

For sailing at the design and slow steaming speeds, with the determined SMCR of the selected engine, four optimization variants, concerning the reduction in the specific fuel oil consumption (SFOC) and consequently CO₂ emissions, have been conducted using the MAN computerized engine application system (CEAS). These variants include FO and NG modes complying with Tier II and Tier III regulations (TR-Tier Regulations). In the remaining part of the paper, Tier II and Tier III are indexed by II and III, respectively.

The energy efficiencies for selected fueling mode (FM), depending on the specific fuel consumption at specified TR $\left(SF{C}_{FM,TR}(p_{e_B})\right)$, are determined for NG and FO modes as follows:

$${\eta }_{{}_{NG,TR}}(p_{e_B})=\frac{3600}{SPO{C}_{TR}(p_{e_B})\cdot LH{V}_{FO}+SNG{C}_{TR}(p_{e_B})\cdot LH{V}_{NG}},$$

(13)

$${\eta }_{{}_{FO,TR}}(p_{e_B})=\frac{3600}{SFO{C}_{TR}(p_{e_B})\cdot LH{V}_{FO}},$$

(14)

where $SFO{C}_{TR}(P_{B_B})$, $SPFO{C}_{TR}(P_{B_B})$, and $SNG{C}_{TR}(P_{B_B})$ are specific consumptions of FO, PFO, and NG in a TR mode, respectively, and $LH{V}_{FO}$ and $LH{V}_{NG}$ are lower heating values for FO and NG, respectively.

Based on the $SF{C}_{FM,TR}(p_{e_B})$ values for the operating scenarios obtained using the CEAS, the fuel consumptions (FC) such that FOC (FO consumption), PFOC (pilot FO consumption), NGC (NG consumption), and CDE (carbon dioxide emission), depending on the both balancing mean effective pressure $p_{e_B}(v_S,S{I}_S)$ and brake power $P_{B_B}=P_{B_B}(v_S,S{I}_S)$, can be calculated using the following equations:

$$FC{(v_S,S{I}_S)}_{FM,TR}=SFC{(p_{e_B})}_{FM,TR}\cdot P_{B_B}{(v_S,S{I}_S)}_{TR},$$

(15)

$$CDE{(v_S,S{I}_S)}_{FM,TR}=SFC{(p_{e_B})}_{FM,TR}\cdot C{F}_{FM,TR}\cdot P_{B_B}{(v_S,S{I}_S)}_{TR},$$

(16)

where $C{F}_{FM,TR}$ represents stoichiometric factors depending on the selected FM at specified TR.

2.3. Fuel Savings and CO₂ Emission Reduction

Finally, the fuel savings (FS) and carbon dioxide reduction (CDR), per one kilometer of the sailing route in selected FM at specified TR, for the slow steaming speeds are calculated as follows:

$$FS{(v_S,S{I}_S)}_{FM,TR}=FC{(v_{S_{nax}},S{I}_S)}_{FM,TR}\cdot v_{S_{\max }}{(S{I}_S)}_{TR}-FC{(v_S,S{I}_S)}_{FM,TR}\cdot v_S,$$

(17)

$$CDR{(v_S,S{I}_S)}_{FM,TR}=CDE{(v_{S\max },S{I}_S)}_{FM,TR}\cdot v_{S_{\max }}{(S{I}_S)}_{TR}-CDE{(v_S,S{I}_S)}_{FM,TR}\cdot v_S,$$

(18)

where $S{I}_S$ corresponds to the sea state within TR areas, $v_{S\max }{(S{I}_S)}_{II,III}\le v_D$ is the maximum attainable sailing speed for the installed propulsion system, and $v_S$ is slow steaming speed. It should be noted that $FS{(v_S,S{I}_S)}_{FM,TR}$ and $CDR{(v_S,S{I}_S)}_{FM,TR}$ are calculated concerning the maximum attainable sailing speeds in realistic sailing conditions defined by sea states expected in each segment of the sailing route.

Additionally, the gasification effects on CDR are considered for the ecological valorization of the container ship powered by NG compared to the one powered by FO. Therefore, the corresponding CO₂ emission reduction (CDRG—CDR for gasification) for slow steaming speeds is calculated as follows:

$$CDRG{(v_S,S{I}_S)}_{TR}=\left[CDE{(v_S,S{I}_S)}_{FO,TR}-CDE{(v_S,S{I}_S)}_{NG,TR}\right]\cdot v_S,$$

(19)

The yearly fuel savings ($FO{S}_Y$, $PFO{S}_Y$, and $NG{S}_Y$) and CO₂ emission reductions($CD{R}_{FO,Y}$, $CD{R}_{NG,Y}$, and $CDR{G}_Y$) greatly depend on the engine’s load profile, which is rather predictable because container vessels typically navigate by schedule with transoceanic crossings. For a ship to arrive at the port on time, it is important to maintain a schedule, which sometimes requires operation at higher loads than usual, especially during navigation under harsh weather conditions. Therefore, it is necessary to predict the sea states that will occur during moderate and harsh weather conditions.

In general, the time interval of one transport cycle between two terminals ${\tau }_{ORT}$ (one round trip) contains time intervals of the ship being at berth ${\tau }_{PS}$ (loading and unloading intervals, so-called port staying time), and two navigation intervals ${\tau }_{OT}$ depending on the ship loading condition (so-called one trip). It should be noted that the effects of a ship being at berth and during its maneuvering on the fuel consumption and CO₂ emission have been ignored since fuel consumption and CO₂ emissions are the most conspicuous during the sail [32]. In further analysis, navigation intervals in a full loading condition are considered only, taking into account different IMO regulations for certain parts of the sailing route.

Furthermore, based on the realistic environmental conditions that can be experientially predicted based on logbooks for container ships on the particular sailing route, the overall sailing route can be divided into segments with respect to the sea states that will occur during one year. In that context, the occurrence of moderate (MWC) and harsh weather conditions (HWC) is defined for the analyzed sailing route, denoted as $S{I}_{MWC}$ and $S{I}_{HWC}$ for moderate and rough sea states, respectively.

The total number of round trips per year $N_{ORT}$, depending on the assumed weather conditions defined by the weather conditions factor $f_{WC}$ and slow steaming speed, is determined as follows:

$$N_{ORT}=\frac{{\tau }_{SY}}{{\tau }_{ORT}(v_S,f_{WC})}=\frac{{\tau }_{SY}}{2\left[{\tau }_{PS}+{\tau }_{OT}(v_S,f_{WC})\right]},$$

(20)

where ${\tau }_{SY}=365.25\hspace{0.17em}\hspace{0.17em}$ days is the number of days of the sidereal year, ${\tau }_{PS}$ is the port staying time, and ${\tau }_{OT}(v_S,f_{WC})$ is the sailing time between ports, which depends on the ship speed $v_S$ and appearing $f_{WC}$.

Taking into account the predicted time intervals ${\tau }_{HWC}$ of the HWC and ${\tau }_{MWC}$ of the MWC, $f_{WC}$ is defined as $f_{WC}={\tau }_{HWC}/{\tau }_{SY}=1-{\tau }_{MWC}/{\tau }_{SY}$.

By assuming that there are no constraints for attainable sailing speed (up to the design speed) under MWC, $N_{ORT}$ for one realistic operating profile of a ship is defined as follows:

$$N_{ORT}=N_{ORT}(v_S,S{I}_{MWC})+f_{WC}{\tau }_{SY}\left[\frac{1}{{\tau }_{OR{T}_{HWC}}(v_S,S{I}_{HWC})}-\frac{1}{{\tau }_{OR{T}_{MWC}}(v_S,S{I}_{MWC})}\right],$$

(21)

where $N_{ORT}(v_S,S{I}_{MWC})$ is the number of ORT per year under MWC, and it is defined as follows:

$$N_{ORT}(v_S,S{I}_{MWC})=\frac{{\tau }_{SY}}{{\tau }_{OR{T}_{MWC}}(v_S,S{I}_{MWC})},$$

(22)

The times required for one trip under MWC and HWC, ${\tau }_{O{T}_{MWC}}$ and ${\tau }_{O{T}_{HWC}}$, respectively, are defined as follows:

$${\tau }_{O{T}_{MWC}}(v_S,S{I}_{MWC})=\frac{L_{TOT}}{v_S(S{I}_{MWC})},$$

(23)

$${\tau }_{O{T}_{HWC}}(v_S,S{I}_{HWC})=\frac{L_{TOT}}{v_S(S{N}_{FS})}+{\displaystyle \sum _{I_{CS}=(1+N_{FS})}^{N_{CS}}\left[\frac{L_{I_{CS}}}{v_{\max }(S{I}_{CS})-v_S(S{N}_{FS})}\right]},$$

(24)

where $L_{TOT}$ is the total length of a route, $L_{I_{CS}}$ is the length of the part of the route with extreme sea states under HWC constraining the design sailing speed $S{I}_{CS}$, $S{N}_{SF}$ is the highest sea state that does not constrain the sailing speed, $N_{FS}$ is the number of sea states that do not constrain the sailing speed, $N_{CS}$ is the number of sea states under HWC limiting sailing speed ($N_{CS}>N_{FS}$), $v_S(S{I}_{FS})$ is the sailing speed without constrains for all $S{I}_{FS}\le S{I}_{CS}$, and $v_{\max }(S{I}_{CS})$ is the maximum attainable sailing speed for $L_{I_{CS}}$.

To calculate the fuel savings ($FO{S}_{OT}$, $PFO{S}_{OT}$, and $NG{S}_{OT}$) and CO₂ emission reduction in FO-fueled mode $CD{R}_{OT,FO}$ and NG-fueled mode $CD{R}_{OT,NG}$, and $CDR{G}_{OT}$ during the one trip and for the specified slow steaming speed $v_S$, the following equations are used:

$$F{S}_{OT}{(v_S,S{I}_S)}_{FM}={\displaystyle \sum _{j_{II}=1}^{n_{II}}FS{(v_S,S{I}_S)}_{FM,II}\cdot L_{j_{II}}}+{\displaystyle \sum _{j_{III}=1}^{n_{III}}FS{(v_S,S{I}_S)}_{FM,III}\cdot L_{j_{III}}},$$

(25)

$$CD{R}_{OT}{(v_S,S{I}_S)}_{FM}={\displaystyle \sum _{j_{II}=1}^{n_{II}}CDR{(v_S,S{I}_S)}_{FM,II}\cdot L_{j_{II}}}+{\displaystyle \sum _{j_{III}=1}^{n_{III}}CDR{(v_S,S{I}_S)}_{FM,III}\cdot L_{j_{III}}},$$

(26)

$$CDR{G}_{OT}(v_S,S{I}_S)={\displaystyle \sum _{j_{II}=1}^{n_{II}}CDRG(v_S,S{I}_S)\cdot L_{j_{II}}}+{\displaystyle \sum _{j_{III}=1}^{n_{III}}CDRG(v_S,S{I}_S)\cdot L_{j_{III}}},$$

(27)

where $L_{j_{II}}$ and $L_{j_{III}}$ are lengths of the sailing route segments where $S{I}_S$ occur in MECAs (indexed by II), and ECAs (indexed by III).

Further, to evaluate the length of the sailing route, the route between Shanghai (index S) and Hamburg (index H), assumed to be equal for the westbound and eastbound trip, is divided into $n_S$ straight line segments on the geographical map (Mercator chart), Figure 2. Thus, the route length is defined by:

$$L_{SH}=L_{HS}={\displaystyle \sum _{i=1}^{n_s+1}{L}_{i,i+1}},$$

(28)

where index i denotes the initial node of the j^th route segment, and through that route segment the latitude ${\phi }_j$ depends on the longitude ${\mu }_j$ and is expressed as follows:

$${\phi }_j({\mu }_j)={\phi }_{i+1}+\frac{{\phi }_{i+1}-{\phi }_i}{{\mu }_{i+1}-{\mu }_i}\left({\mu }_j-{\mu }_i\right);\hspace{0.17em}\hspace{0.17em}\left[{\phi }_i\le {\phi }_j(\mu )\le {\phi }_{i+1};\hspace{0.17em}\hspace{0.17em}{\mu }_i\le {\mu }_j\le {\mu }_{i+1}\right],$$

(29)

The differential length of the route segment in the Cartesian coordinate system is defined by the $\mathrm{d}{L}_j=\sqrt{{(\mathrm{d}{x}_j)}^2+{(\mathrm{d}{y}_j)}^2+{(\mathrm{d}{z}_j)}^2}$, where $\mathrm{d}{x}_j$, $\mathrm{d}{y}_j$, and $\mathrm{d}{z}_j$ are contained Cartesian differential segments, thus the length of the route segment $L_j=L_{i,i+1}$ is defined by the following integral:

$$L_{i,i+1}=r_E{\displaystyle \underset{{\mathsf{\mu }}_i}{\overset{{\mathsf{\mu }}_{i+1}}{\int }}\sqrt{{\left\{\frac{\mathrm{d}}{{\mathrm{d}\mathsf{\mu }}_{\mathrm{j}}}\left[\cos {\phi }_j({\mu }_j)\cos {\mu }_j\right]\right\}}^2+{\left\{\frac{\mathrm{d}}{{\mathrm{d}\mathsf{\mu }}_{\mathrm{j}}}\left[\cos {\phi }_j({\mu }_j)\sin {\mu }_j\right]\right\}}^2+{\left\{\frac{\mathrm{d}}{{\mathrm{d}\mathsf{\mu }}_{\mathrm{j}}}\left[\sin {\phi }_j({\mu }_j)\right]\right\}}^2}{\mathrm{d}\mathsf{\mu }}_{\mathrm{j}}},$$

(30)

where $r_E=6367.5\hspace{0.17em}\mathrm{km}$ is the mean Earth radius (taking into account the average geoid undulation on the sea surface, which is assumed 100 m) obtained by numerical integration.

Finally, based on the calculated values of $N_{OR{T}_Y}$, the total fuel savings and CO₂ emission reductions per year for a FO- and NG-fueled ship, can be calculated as follows:

$$F{S}_Y{(v_S,f_{WC})}_{FM}=2N_{ORT}(v_S, f_{WC})\cdot F{S}_{OT}{(v_S,f_{WC})}_{\mathrm{FM}},\hspace{0.33em}\hspace{0.17em}\mathrm{t}/\mathrm{year},$$

(31)

$$CD{R}_Y{(v_S,S{I}_S)}_{FM}=2N_{ORT}(v_S, f_{WC})\cdot CD{R}_{OT}{(v_S, f_{WC})}_{FM},\hspace{0.33em}\hspace{0.17em}\mathrm{t}/\mathrm{year},$$

(32)

$$CDR{G}_Y(v_S,S{I}_S)=2N_{ORT}(v_S, f_{WC})\cdot CDR{G}_{OT}(v_S, f_{WC}),\hspace{0.33em}\hspace{0.17em}\mathrm{t}/\mathrm{year},$$

(33)

As NG-fueled mode includes simultaneous consumption of PFO and NG, for energy efficiency valorization it is more appropriate to compare total fuel energy consumption in relation to FO mode. For this purpose, the energy efficiency ratio (EER) between FO- and NG-fueled modes for one year is introduced as follows:

$$EER=\frac{FO{C}_Y(v_S,S{I}_S)\cdot LH{V}_{FO}}{PFO{C}_Y(v_S,S{I}_S)\cdot LH{V}_{FO}+NG{C}_Y(v_S,S{I}_S)\cdot LH{V}_{NG}},$$

(34)

Although the economic aspects of slow steaming are not considered within this paper, their impact on the yearly freight income is worth mentioning, which is a key parameter for the evaluation of the economic effects. The freight income efficiencies ratio (FIER) between freight incomes achievable at slow steaming and those achievable at maximum attainable sailing speeds on the sailing route during one year is defined as:

$$FIER=\frac{N_{ORT}(v_S,S{I}_S)}{N_{ORT}(v_{S\max },S{I}_S)},$$

(35)

3. Results and Discussion

3.1. Ship Resistance and Balancing Propulsion Characteristics

The numerical results obtained are presented within this section. The total resistance of a ship in calm water and propulsion characteristics at the design and slow steaming speeds are shown in

Table 3. The total resistance of a ship and propulsion characteristics in calm water (S0).

S0	18 kn	19 kn	20 kn	21 kn	22 kn
$R_T$, kN	692.56	842.81	970.02	1089.54	1204.01
$w$	0.233	0.230	0.228	0.225	0.223
$t$	0.159	0.153	0.147	0.128	0.134
${\eta }_R$	0.996	0.997	1.000	1.000	1.001
${\eta }_H$	1.096	1.100	1.105	1.125	1.115
$T_P$, kN	823.82	995.05	1136.79	1267.39	1390.31

.

$R_T$$w$$t$${\eta }_R$${\eta }_H$$T_P$ The added resistance in regular waves is calculated for sea states with the highest probability of occurrence on the selected sailing route, Table 2, and the results for the added resistance are shown in

Table 4. Added resistance in waves for various ship speeds and sea states.

	$R_{AW},\hspace{0.33em}\mathrm{kN}$
VS, kn	18	19	20	21	22
Sea state
S1	6.035	6.17	6.34	6.56	6.81
S2	60.268	61.94	63.83	65.93	68.25
S3	167.435	172.06	177.31	183.14	189.61
S4	328.192	337.25	347.52	358.95	371.61
S5	542.511	557.49	574.48	593.36	614.29
S6	810.412	832.79	858.17	886.38	917.65

. Thereafter, the total resistance in waves is determined as the sum of the total resistance in calm water and the added resistance in waves, Figure 3.

Based on these results, the required thrust in waves is determined. After that, the balancing rate of revolution $n_B=n_B(v_S,S{I}_S)$ is calculated and thereafter other balancing propulsion parameters $J_B(v_S,S{I}_S)$, $K_{T_B}(v_S,S{I}_S)$, and $10K_{Q_B}(v_S,S{I}_S)$ of a propeller operating in waves are calculated. The results obtained are presented in

Table 5. Propulsion characteristics for various sailing speeds and sea states.

$V_S, \mathrm{kn}$	$S{I}_S$	$T_P, \mathrm{kN}$	$n_B, \mathrm{rpm}$	$J_B$	$K_T$	$10K_Q$	${\eta }_P$	$Q_B, \mathrm{MNm}$	$P_B, \mathrm{MW}$
18	S0	823.819	69.479	0.7766	0.1539	0.2986	0.6369	1.2941	9.4159
	S1	830.999	69.611	0.7751	0.1546	0.2996	0.6367	1.3033	9.5005
	S2	895.511	70.782	0.7623	0.1612	0.3080	0.6348	1.3854	10.2689
	S3	1022.987	73.025	0.7388	0.1730	0.3231	0.6294	1.5471	11.8311
	S4	1214.215	76.229	0.7078	0.1884	0.3428	0.6190	1.7886	14.2781
	S5	1469.152	80.238	0.6724	0.2058	0.3648	0.6035	2.1089	17.7199
	S6	1787.826	84.892	0.6356	0.2237	0.3874	0.5840	2.5069	22.2860
19	S0	995.053	74.818	0.7640	0.1603	0.3068	0.6351	1.5402	12.0672
	S1	1002.337	74.942	0.7627	0.1609	0.3077	0.6349	1.5494	12.1597
	S2	1068.181	76.048	0.7516	0.1665	0.3149	0.6327	1.6329	13.0044
	S3	1198.195	78.174	0.7312	0.1768	0.3280	0.6272	1.7974	14.7143
	S4	1393.223	81.225	0.7037	0.1904	0.3454	0.6175	2.0432	17.3791
	S5	1653.248	85.068	0.6719	0.2060	0.3651	0.6033	2.3693	21.1064
	S6	1978.276	89.560	0.6382	0.2224	0.3858	0.5855	2.7748	26.0239
20	S0	1136.788	79.436	0.7598	0.1624	0.3096	0.6343	1.7519	14.5732
	S1	1144.220	79.555	0.7586	0.1630	0.3104	0.6341	1.7613	14.6735
	S2	1211.589	80.621	0.7486	0.1681	0.3169	0.6319	1.8467	15.5911
	S3	1344.580	82.672	0.7300	0.1774	0.3288	0.6268	2.0149	17.4439
	S4	1544.055	85.628	0.7048	0.1899	0.3447	0.6179	2.2663	20.3215
	S5	1810.029	89.368	0.6753	0.2044	0.3630	0.6049	2.6000	24.3319
	S6	2142.494	93.761	0.6437	0.2198	0.3825	0.5885	3.0150	29.6034
21	S0	1267.393	83.759	0.7589	0.1629	0.3102	0.6342	1.9514	17.1162
	S1	1275.027	83.875	0.7578	0.1634	0.3109	0.6340	1.9611	17.2249
	S2	1344.083	84.911	0.7486	0.1681	0.3169	0.6319	2.0486	18.2161
	S3	1480.428	86.911	0.7313	0.1767	0.3279	0.6272	2.2211	20.2145
	S4	1684.934	89.800	0.7078	0.1884	0.3428	0.6191	2.4789	23.3107
	S5	1957.612	93.468	0.6800	0.2021	0.3601	0.6072	2.8212	27.6135
	S6	2298.463	97.794	0.6500	0.2167	0.3786	0.5920	3.2471	33.2533
22	S0	1390.309	87.881	0.7600	0.1623	0.3095	0.6344	2.1431	19.7227
	S1	1398.176	87.995	0.7590	0.1628	0.3101	0.6342	2.1531	19.8402
	S2	1469.121	89.011	0.7503	0.1672	0.3157	0.6324	2.2430	20.9077
	S3	1609.264	90.974	0.7341	0.1753	0.3261	0.6281	2.4204	23.0582
	S4	1819.419	93.818	0.7119	0.1864	0.3403	0.6206	2.6854	26.3832
	S5	2099.650	97.439	0.6854	0.1994	0.3568	0.6097	3.0375	30.9939
	S6	2449.954	101.723	0.6566	0.2135	0.3746	0.5955	3.4756	37.0235

and Figure 4, Figure 5 and Figure 6.

In Figure 4 the obtained values of the propeller rate of revolution for different sailing speeds and sea states are given. It can be seen that at higher speeds and for harsh sea states due to an increase in the balancing rate of revolution, lower propeller efficiency is obtained, Figure 5, due to an increase in balancing propulsion parameters, Figure 6.

It should be noted that the highest propeller efficiency is obtained at the lowest speed and for calm water conditions. Based on the advance and torque coefficients, the propeller rotation rate and brake power are determined. The propeller rate of revolution and brake power for the analyzed sea states at sailing speed in the range 18–22 kn are presented in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9, and it can be seen that a significant decrease in $n$ and $P_B$ is obtained at the slow steaming speeds. Namely, the decrease in brake power at the slow steaming speed of 18 kn ranges approximately from 47% for S6 to 52% for S0 compared to the design speed of 22 kn, while the decrease in the propeller rate of revolution is around 16.6% for S6 and 21% for S0.

3.2. Selection of DF Engine and Determination of FC and CDE

Based on the MAN propulsion DF engine project guide program [29,30], the MAN B&W 8S70ME-G10.5.GI engine with a maximum continuous rating (MCR) of $P_{MCR}=27.44\hspace{0.17em}\mathrm{MW}$ at $n_{MCR}=91\hspace{0.17em}\mathrm{rpm}$ is selected, which can be seen in Figure 7 as point L1. The specified maximum continuous rating (SMCR) of the selected DF engine, characterized by brake power $P_{SMCR}=26.684\hspace{0.17em}\mathrm{MW}$ at $n_{SMCR}=90.4\hspace{0.17em}\mathrm{rpm}$, is determined based on the estimated continuous service rating for propulsion on the sailing route between Shanghai and Hamburg via the Suez Canal. The following parameters have been taken into account: $SM=EM=0.15$, $LRM=0.07$, and propeller design point calculated for the design speed $V_D=22\hspace{0.33em}\mathrm{kn}$, specified with $P_D=19.723\hspace{0.33em}\mathrm{MW}$ and $n_D=87.881\hspace{0.33em}\mathrm{rpm}$.

In the NG fueling mode, the engine consumes mainly NG (which is assumed as fuel gas consisting of 100% methane, CH₄) and PFO in an amount corresponding to about 1.5% overall energy income. In FO mode, the engine consumes ULSFO inside ECAs and VLSFO outside ECAs. In NG mode, the PFO engine consumes ULSFO inside ECAs and VLSFO outside ECAs. LHV for these fuels are assumed as follows: $LH{V}_{FO}=LH{V}_{PFO}=42.7\hspace{0.17em}\mathrm{MJ}/\mathrm{kg}$ for FO and PFO, and $LH{V}_{NG}=50\hspace{0.17em}\mathrm{MJ}/\mathrm{kg}$ for NG. The carbon conversion factors $C{F}_{FM,TR}$ for analyzed fuels are: $C{F}_{FO}=3.206\hspace{0.17em}{\mathrm{kg}}_{{\mathrm{CO}}_2}{/\mathrm{kg}}_{\mathrm{FO}}$ for VLSFO and ULSFO, and $C{F}_{NG}=2.75\hspace{0.17em}{\mathrm{kg}}_{{\mathrm{CO}}_2}{/\mathrm{kg}}_{\mathrm{NG}}$ for NG [33].

Because of NO_X rules, EGRBP technology that is applicable for engines whose bores are $\le 70\mathrm{cm}$ is selected, i.e., the selected engine is specified by the extension 8S70ME-G10.5.GI-EcoEGR.

At higher speeds and in harsh sea states, the DF engine cannot balance propulsion loads during continuous operation due to the operational characteristics of the DF engine selected, Figure 8, Figure 9 and Figure 10. Namely, at higher continuous propulsion loads, the engine operating point must be in areas 1 and 2, as presented in Figure 7. Consequently, for S6 the investigated ship could not achieve 20, 21, and 22 kn, and for S5 the ship could not achieve 21 and 22 kn, Figure 9. Limiting operation conditions that cannot be exceeded during continuous operation of the selected DF engine follow: $P_{B\max }\le P_{SMCR}$, $n_{B\max }\le n_{MCR}$ and $p_{e_{B\max }}\le p_{e_{SMCR}}$.

For the selected engine and SMCR, depending on the Tier II and Tier III specified rules for FO- and NG-fueled modes, using the MAN CEAS tool [34], SFOC and SNGC are obtained. SFOC and SNGC depend on the engine power and rotation rate, and these values are determined for appropriate balancing mean effective pressures for the expected sailing conditions, Figure 11. From Figure 11, it is clear that both SFOC and SNGC are within ECAs (Tier III) for FO- and NG-fueled modes are higher compared to MECAs (Tier II), and that minimal SFOC and SNGC are obtained for mean effective pressures in the range from 1.5 to 1.7 MPa.

To properly compare the energy efficiency of FO- and NG-fueled modes, SPFOC should be taken into account for NG-fueled mode. Consequently, energy efficiencies of FO- and NG-fueled modes are determined using Equations (13) and (14) and based on the corresponding specific fuel consumptions.

The energy efficiency depending on the sailing speed and sea states for FO- and NG-fueled engines in Tier II and Tier III modes are shown in Figure 12. It should be noted that in Tier II mode, the energy efficiencies are higher by approximately 5% compared to Tier III mode, for both FO- and NG-fueled modes. Additionally, energy efficiencies for the same engine loads and tier mode slightly vary for different fueled modes, Figure 13.

3.3. Fuel Savings and CO₂ Reductions for Slow Steaming

Based on the calculated values of brake power for various sea states for the design and slow steaming speeds, savings for FO- and NG-fueled modes are obtained using Equation (17), Figure 14. The corresponding CDR for FO- and NG-fueled modes are obtained using Equation (19), Figure 15. Note that the highest FOS and CDR values are obtained for the engine powered by FO for S4. For an engine powered by NG, maximum values of both NGS and corresponding CDR in gas mode also occur for S4. In addition, CDR in gas mode is approximately 25% lower compared to CDR in FO mode.

By the gasification of the ship (NG-fueled mode), the most positive ecological effects are obtained. CO₂ emission reduction for Tier II and Tier III modes at various sailing speeds and sea states per 100 km of the sailing route are presented in Figure 16. It can be seen that CO₂ emission reduction for the NG fueled ship compared to the FO fueled ship ranges from 3.8 to 10.6 tons/100 km, which are rather significant amounts.

3.4. Sailing Route between Shanghai and Hamburg

The sailing route between Shanghai and Hamburg via Malacca Strait, Suez Canal, Gibraltar, and La Manche is divided into 49 segments (based on straight lines on the Mercator map). Based on the numerical integration of Equation (30), the length of each segment is obtained, and the sum of their lengths according to Equation (28) represents the total length of the sailing route, $L_{TOT}=20,108\hspace{0.17em}\mathrm{km}\triangleq 10,857.5\hspace{0.17em}\mathrm{NM}$, Figure 17.

A minor part of the sailing route passes through ECAs (the part between the entrance at La Manche (LM) and the estuary of the Elbe River, Hamburg (H)), with a length of about $L_{LMH}=L_{III}=1470.43\hspace{0.17em}\mathrm{km} \doteq 7.33\%\hspace{0.17em}{L}_{TOT}$, whilst the major part of the sailing route passes through MECAs (between Shanghai (S) and La Manche) with length about $L_{SLM}=L_{II}=18637.57\hspace{0.17em}\mathrm{km} \doteq 92.67\%\hspace{0.17em}{L}_{TOT}$. For these parts of the sailing route, IMO Tier III and Tier II regulations are applied, respectively. Furthermore, these route parts are characterized by rather different sea states that occur during a year under MWC and HWC, Figure 18. It should be noted that in Figure 18, SI_S% presents the percentage of the route length with sea state SI_S, for either Tier II or Tier III areas.

Thus, under HWC, extreme sea states categorized as S5 and S6 occur along about 16% and 30% of the route length with Tier II regulations, respectively. Sea state categorized as S5 occurs along about 18% of the route length with Tier III regulations. In other words, in those conditions, the achievement of sailing speeds higher than maximum attainable speeds for S5 and S6 with an installed propulsion plant will not be possible.

On the other hand, sea states higher than S4 do not appear under MWC at all, which means that in such weather conditions there will be no constraints in achieving the design speed. Taking into account that under MWC $N_F=4$ and $S{I}_{\max }=S4$, and that under HWC $N_S=6$ and $S{I}_{\max }=S6$, the corresponding intervals of one trip are calculated based on Equations (23) and (24), Figure 19.

It should be noted that under HWC, sea states S5 and S6 occur on the route length $L_{S5}$ and $L_{S6}$, respectively, with maximum attainable ship speed for S5$V_{S\max }(S5)\le 20.393\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$, and for S6 $V_{S\max }(S6)\le 19.163\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$. Engine brake power and mean effective pressure must be less than the corresponding values for SMCR. Therefore, for $V_{S\max }(S5)$ the balancing engine parameters are $P_{B_B}=25.614\hspace{0.17em}\mathrm{MW}$, $n_{B_B}=91\hspace{0.17em}\mathrm{rpm}$, and $p_{B_B}=1.9548\hspace{0.17em}\mathrm{MPa}$; for $V_{S\max }(S6)$ the balancing engine parameters are $P_{B_B}=26.608\hspace{0.17em}\mathrm{MW}$, $n_{B_B}=90.264\hspace{0.17em}\hspace{0.17em}\mathrm{rpm}$, and $p_{B_B}=2.05\hspace{0.17em}\hspace{0.17em}\mathrm{MPa}$.

From Figure 19, it is evident that for sailing speeds less than 19.163 kn, the time interval of one trip is equal for HWC and MWC. Additionally, for sailing speeds higher than 19.163 kn the time interval of one trip under HWC increases compared to MWC, with an increase in a range from 1.21% for $V_S=20\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$ to 5.42% for $V_S=22\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$. These are significant parameters for scheduling the arrival time at ports for container ships, as well as port staying intervals. Within this study, port staying intervals are assumed based on the information and integrated data of similar container ships operating with a different pattern [35], which is ${\tau }_{PS}=36\hspace{0.17em}\hspace{0.17em}\mathrm{h}$ for a 3600 TEU container ship.

Considering that the investigated ship is intended for direct shipping between Shanghai and Hamburg, its operating profile for one round trip depends on the predefined sailing speeds and is determined according to Equation (20), Figure 20. It should be noted that for the sailing speed of 18 kn, time spent in sailing increases by approximately 2.3% sailing speed compared to the design speed.

Further, to obtain the number of round trips per year, which is a very important parameter for the evaluation of the energetic and ecological effects of slow steaming, it is necessary to define a realistic navigation scenario in which the ship operating profile will be adequately assumed. Therefore, for the realistic navigation scenario, it is assumed that HWCs last for two months per year, meaning that $f_{WC}=1/6$. The number of round trips per year $N_{ORT}(v_S,S{I}_{RWC})$ under realistic weather conditions (RWC), and $N_{ORT}(v_S,S{I}_{MWC})$ under MWC calculated based on Equations (21) and (22), respectively, along with the number of round trips per year under HWC, calculated as $N_{ORT}(v_S,S{I}_{HWC})=N_{ORT}(v_S,S{I}_{RWC})-N_{ORT}(v_S,S{I}_{MWC})$, are shown in Figure 21.

3.5. Impact of Slow Steaming on Fuel Savings and CO₂ Emission Reduction

To evaluate the effect of slow steaming on the fuel savings and CO₂ emission reductions, Equations (25) and (26) are used and the fuel savings per one trip for FO- and NG-fueled modes under MWC and HWC are obtained, Figure 22 and Figure 23. For the evaluation of the effect of slow steaming on PFOS per one trip under MWC and HWC, Equation (25) is employed. Under RWC, the effect of slow steaming on PFOS per one trip is calculated based on Equation (25) and modified as follows: $PFO{S}_{RW}=f_{WC}PFO{S}_{HW}+(1-f_{WC})PFO{S}_{MW}$, Figure 24.

In relation to the design speed under MWC and maximum attainable service speed under HWC, the highest FOS are achieved at minimum predefined slow steaming speed, and one can see that these amounts for both FO and NG are rather significant, especially under navigation in MWC. Since the savings calculated for PFOS are relatively small compared to FOS and NGS, they are presented separately in Figure 23. The real effect of PFOS at slow steaming speed is considered when overall energy consumption is compared between FO- and NG-fueled modes. Additionally, Figure 23 shows that small negative values of PFOS are obtained at higher sailing speeds.

Finally, based on Equation (33), the yearly FS for FO, PFO, and NG are evaluated and presented in Figure 25 for FO and NG. Again, due to small values of PFOS, they are not presented in Figure 25. It is evident that FOS and NGS per year are quite large, so it appears that the application of slow steaming with the aim of fuel consumption reduction presents the right choice.

On the other hand, for the assessment of the effect of slow steaming on CDR for FO- and NG-fueled modes per one trip under MWC and HWC, Equation (26) is used, and the results obtained are presented in Figure 26 and Figure 27, respectively.

From these figures, it is evident that the highest values of CDR for both fueled modes are achieved for lower slow steaming speeds. For example, in FO mode, the CDR obtained for a sailing speed of 18 kn is more than 2 kt per one trip under MWC and around 1.7 kt per one trip under HWC.

For the assumed ship operating profile per year under RWC, CDR for FO- and NG-fueled modes based on the slow steaming speed are calculated using Equation (32), Figure 28. It should be noted that the significant CDR for the FO and NG mode could be obtained if the ship operator decides to sail at a slow steaming speed. Thus, for the analyzed sailing route under RWC at a sailing speed of 18 kn, CDR is approximately 11.66 kt/year for FO mode and 8.53 kt/year for NG mode. It should be noted that CDR values presented do not show the real reductions in CO₂ emission for FO- and NG-fueled ships. In other words, it seems that the reductions are larger for slow steaming speeds at FO mode compared to NG-fueled mode, because the CDR values obtained correspond to reductions at lower speeds with respect to the maximum attainable speed under RWC for a particular fueling mode.

3.6. Impact of Ship Gasification on Energy Efficiency and CO₂ Emission Reduction

The overall energy consumption for FO (ECFO) and NG (ECNG) fueled mode are evaluated, as well as the energy efficiency ratio (EER) between FO and NG mode, based on Equation (34). The values obtained are presented in Figure 29 and Figure 30 (left), and it is evident that there are no noticeable differences between these fueling modes. It is evident that under RWC the number of round trips per year is reduced by approximately 16.5% if slow steaming is applied, and by 18.2% for the design speed. Consequently, FIER is reduced by 16.5% as well, Figure 30 (right).

On the other hand, the ship gasification has a strong influence on CDR compared to a classical FO powered ship, which is shown in Figure 31 for one round trip under MWC and HWC depending on the sailing speed. The results presented were obtained using Equation (33). It should be noted that under MWC the highest CO₂ emission reductions are achieved at higher sailing speeds, i.e., the maximum value of 1.428 kt per one trip for the design speed. Since under HWC at higher sea states the maximum attainable sailing speeds are $V_{S\max }(S5)\le 20.393\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$ and $V_{S\max }(S6)\le 19.163\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$, the maximum value of CO₂ emission reduction is achieved for 19 kn and equal to 1.425 kt per one trip.

Finally, CDRG per year for various sailing speeds is calculated using Equation (33) under MWC, HWC, and RWC, Figure 32. The results obtained demonstrate positive ecological effects for ship gasification. The CDR values obtained are rather high, ranging from 10.04 kt per year for 18 kn to 21.93 kt per year for the design speed.

4. Conclusions

In this study, the energetic and ecological benefits of slow steaming and gasification are investigated for a container ship sailing between Shanghai and Hamburg. Resistance and propulsion characteristics in calm water are determined by means of computational fluid dynamics based on the viscous flow theory for a full-scale ship. The added resistance in waves is calculated by applying potential flow theory. The propeller operating point is determined for the design and slow steaming speeds at sea states with the highest probability of occurrence along the investigated sailing route. The fuel consumption and CO₂ emissions are then calculated for the selected DF engine in fuel oil and gas supplying modes complying with IMO Tier II and Tier III requirements.

The main balancing engine parameters of the selected DF engine characterized with SMCR are determined for different ship speeds in the range $18÷22\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$ at sea states with the highest probability of occurrence on the selected sailing route. It should be noted that for the highest sea states S5 and S6, which occur under HWC, maximum attainable sailing speeds are considered referent ones. Since container ships usually sail by schedule, it is important to predict the realistic weather conditions during one trip, so that ship arrives at a port on time. Within this paper, realistic environmental conditions are predicted experientially based on logbooks for container ships on the investigated sailing route. Thus, for the analyzed sailing route, HWC occur during one-sixth of the sidereal year. The number of round trips per year is calculated considering the attainable ship speed and port staying intervals, and it is equal to 6.857 for the lowest slow steaming speed and up to 8.211 for maximum attainable speed $V_S\le 22\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$. In other words, the number of round trips per year decreases by 16.5% for the lowest slow steaming speed in comparison to the design speed, which consequently causes the same reduction in yearly freight income.

In the context of the energetic and ecological effects of the slow steaming for FO- and NG-fueled modes, fuel consumption and CO₂ emission reduction are calculated per one kilometer of the route segment for slow steaming speeds in comparison with maximum attainable speeds for both ECAs and MECAs. In addition, fuel consumption and CO₂ emission reduction are calculated for the entire route based on route segments with MWC, HWC, and RWC.

The results show significant savings in fuel consumption for both FO- and NG-fueled modes, with maximum savings corresponding to the lowest slow steaming speed $V_S=18\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$ under MWC, i.e., 547 t/OT and 641 t/OT for FO- and NG-fueled mode, respectively. The savings under HWC are somewhat lower, i.e., 451 t/OT and 529 t/OT for FO- and NG-fueled mode, respectively. On the other hand, savings for PFO are rather low and for $V_S=18\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$ are equal to 0.91 t/OT and 0.8 t/OT under MWC and HWC, respectively. Based on the results obtained for savings in fuel consumption, a significant reduction in CO₂ emission is achieved for both FO- and NG-fueled modes. CO₂ emission reductions for $V_S=18\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$ under MWC are up to 2.1 kt/OT and 1.51 kt/OT for FO- and NG-fueled mode, respectively. Under HWC, CO₂ emission reductions are up to 1.7 kt/OT and 1.24 kt/OT for FO- and NG-fueled mode, respectively. The savings in fuel consumption under RWC for $V_S=18\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$ are equal to 3.63 kt/year and 3.1 kt/year for FO- and NG-fueled mode, respectively. The corresponding CO₂ emission reductions are equal to 11.7 kt/year and 8.5 kt/year.

The gasification of a ship powered by a DF engine leads to a significant CO₂ emission reduction in comparison to FO-fueled mode at the same sailing speeds. This is especially pronounced under HWC with maximum attainable speed $V_S\le 19.23\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$, where CO₂ emission reduction is equal to 1.45 kt/OT. Under MWC, the highest CO₂ emission reduction is obtained for the design speed, and it is equal to 1.43 kt/OT. Under the estimated RWC, CO₂ emission reduction per year for maximum attainable speed $V_S\le 22\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$ is up to 22 kt/year, which is approximately 114.3% higher in comparison to the lowest slow steaming speed $V_S=18\hspace{0.17em}\hspace{0.17em}\mathrm{kn}$. From the energetic point of view, ship gasification does not lead to significant savings. Namely, the differences between the results obtained for FO- and NG-fueled modes are in the range −0.012% to 0.015% for all investigated speeds.

Finally, it can be concluded that the introduction of slow steaming can lead to significant savings in fuel consumption and CO₂ emission for both FO- and NG-fueled modes. Furthermore, ship gasification leads to significant reductions in CO₂ emission compared to the FO-fueled mode for the same sailing speed. However, by introducing slow steaming, the number of round trips per year is reduced as well. This leads to a reduction in yearly freight income and a relative increase in energy consumption and CO₂ emissions due to an increased number of ships to keep the yearly transport work constant. For that reason, part of future work will be an economic analysis of the slow steaming introduction for a container ship powered by NG under the estimated RWC.