Optimization of Maintenance Schedule for Containerships Sailing in the Adriatic Sea

Abstract

Biofouling attaches to immersed surfaces in between hull cleanings. Due to high speeds and relatively short port times, biofilm often attaches to the immersed surfaces of containerships. In most cases, this type of fouling is not given much importance since it is assumed that it will not cause any fouling penalties. In this paper, the fouling penalties related to fouling with biofilm on the example of the Post Panamax and Post Panamax Plus containership fleets sailing in the Adriatic Sea are assessed. In addition, the investigation is performed for real environmental conditions that a containership can encounter on a sailing route passing through the Adriatic Sea. Thus, the impact of waves and wind is taken into account based on mean values of significant wave height and wind speed for containerships sailing at the design speed along the analyzed route. The procedure for the determination of the detrimental effects of biofilm on the increase in fuel consumption and carbon dioxide emissions is given. Further, the proposed procedure includes the determination of calm water resistance by the Holtrop and Mennen method, the added resistance in waves by Liu and Papanikolaou’s method, spectral analysis using the Tabain’s spectrum for the Adriatic Sea, the wind resistance by the Blendermann method, and added resistance due to biofouling using the Granville method. Thereafter, a time-dependent biofouling growth model proposed by Uzun et al. is incorporated, and the adequate timing for underwater hull cleaning is determined for several hull cleaning costs. The obtained results demonstrate that, from an environmental point of view, proactive hull cleaning should be applied, while, from an economic perspective, optimal timing for underwater hull cleaning is recommended.

1. Introduction

The International Maritime Organization (IMO) included several measures to lower the amount of greenhouse gas (GHG) emissions in 2011. These measures refer to the mandatory Energy Efficiency Design Index (EEDI) for new ships, the Ship Energy Efficiency Management Plan (SEEMP) that should be kept onboard, and a mandatory data collection system for ships of 5000 gross tonnages (GT) and above for collecting the data regarding their fuel oil consumption (FOC). In addition, within SEEMP, the operational performance of ships should be voluntarily self-monitored using the Energy Efficiency Operational Indicator (EEOI) or other indicators [1]. Despite that, the annual emission of GHG caused by the shipping industry has increased from 2012 to 2018 by 9.6%, which raised the portion of the emissions from the shipping industry in the total anthropogenic emissions from 2.76% to 2.89% in 2018. Consequently, the IMO has included the procedure to lower the total annual amount of GHG emissions by at least 50% by 2050, compared to 2008 [2]. The procedure considers several short-term, mid-term, and long-term measures to accomplish these goals [3]. Bouman et al. [4] provided a review of possible measures for the mitigation of GHG emissions within the shipping sector. The measures were divided into six groups: hull design, the economy of scale, power and propulsion, speed, fuels and alternative energy sources, weather routing, and scheduling. However, since the application of alternative fuels, renewable energy sources, and hybrid technologies is still in the early stages of development, the emphasis is directed toward other short- and mid-term measures within the shipping sector [5]. The potential energy efficiency gains were presented in [6], where the authors predicted that by combining speed optimization and weather routing, an energy efficiency gain of up to 60% could be achieved. On the other hand, an energy efficiency gain of up to 10% could be achieved by hull and propeller maintenance. Irena et al. [7] analyzed the cost-effectiveness of a few operational technical measures and the use of alternative energy sources and concluded that the operational and technical measures were more cost-effective than the use of alternative energy sources for reducing GHG emissions. The short-term and mid-term measures are targeted at the abatement of GHG emissions, while long-term measures are targeted at their complete removal [8]. The decrease in GHG emissions is directly related to the decrease in FOC, which is crucial from an environmental and financial point of view, but it also leads to the reduction of fuel costs [9]. One of the measures that is easy to implement is speed reduction, i.e., power reduction [10]. Kalajdžić et al. [11] analyzed the requirements for power reductions on bulk carriers to meet novel energy efficiency measures. Another short-term operational measure that can greatly reduce FOC and consequently lead to significant savings is speed optimization [12]. However, the savings must be greater than the incurred capital and operating costs for ship operators to implement the measure [13]. Since FOC represents a significant portion of operating costs in maritime transport [14], emphasis is given to the prediction of FOC and GHG emissions in the literature review.

The prediction of GHG emissions from a ship is not a straightforward process since FOC depends on many different parameters, as described by Zalacko et al. [15]. The estimation of FOC was assessed by nine methods in [16], where the authors pointed out that the most influential parameters are the engine load factor and specific fuel oil consumption (SFOC). The wind, waves, and sea currents in real conditions such as the ocean environment should be taken into consideration and mathematically modeled [17]. While measures such as speed optimization and route planning depend on parameters over which the ship owner does not have control, the maintenance schedule depends solely on the ship owner’s decision [18].

Significant savings can be achieved by regularly cleaning the hull and the propeller to remove biofouling. In other words, optimization of the maintenance schedule is a viable measure for the reduction of GHG emissions [19]. It is therefore important to correctly predict the impact of biofouling on ship performance [20]. Several different methods have been developed to assess the impact of biofouling, including data-driven models, deterministic methods, and hybrid methods [21]. The data-driven models depend on the data that can be obtained through continuous monitoring. These data are prone to large discrepancies since there is neither a unique guideline nor legal requirements that outline a method or set of rules that must be followed while monitoring FOC during navigation. Additionally, there is always some uncertainty due to human intervention [22] caused by deviations from reported averaged values, accidental errors, or intentionally inaccurate reporting. The large discrepancies in measured data cause large uncertainties in data-driven models, which can be explained through relatively low values of the coefficient of determination, as can be seen in the literature [18,23,24]. Due to this, future trends in fuel consumption cannot be predicted accurately [23]. The deterministic methods rely on either towing tank testing [25], Computational Fluid Dynamics (CFD), or other performance prediction methods [26] to predict ship hydrodynamic performance with fouled hull and propeller surfaces. There are also hybrid methods that combine data-driven and deterministic methods. However, both methods must be validated by comparing the results with onboard-monitored data [27].

Biofouling occurs in between maintenance periods, specifically during port times since the attachment of biofouling is restricted during sailing [28]. In the same paper, the authors argued that in the case of containerships, fouling with biofilm occurs due to their duty cycle, which is characterized by relatively low port times in comparison to other ship types. There are only a few publications that investigate the impact of biofilm on ship propulsion characteristics [20]. Hakim et al. [29] provided a short review of the relationship between the increased ship resistance due to biofouling and the required power. Farkas et al. [30] have estimated the penalties for fouling with biofilm on the example of the Post Panamax (PP) and Post Panamax Plus (PPP) container ship fleets. The authors demonstrated the significance of keeping the hull clean from both an environmental and economic point of view and indicated the disadvantageous impact of biofilm. Dinariyana et al. [31] proposed a decision-support system for scheduling an underwater hull cleaning based on the time-dependent biofouling growth model proposed in [32]. However, the proposed decision support system is based on the simplified added resistance diagrams for biofouling and on the rather simple regression between the equivalent sand grain roughness and fouling rating, and it does not account for the real oceanographic conditions during the ship service.

In this paper, a novel model for the scheduling of underwater hull cleaning is proposed. The study is focused on the impact of fouling with biofilm on FOC for containerships sailing in real conditions in the Adriatic Sea. The study is conducted using deterministic methods, which can predict the impact of biofouling on resistance more precisely than data-driven models. Namely, within data-driven models, it is very difficult to distinguish the impact of biofouling from the impact of other added resistances. This impact is determined for PP and PPP containership fleets along a sailing route passing through the Adriatic Sea. The main contribution of this paper is the assessment of deteriorated ship hydrodynamic performance in real oceanographic conditions, considering added resistance due to biofouling with biofilm, waves, and wind. Further, based on the deteriorated ship hydrodynamic performance and increase in fuel consumption, fouling penalties related to the increased fuel costs can be easily determined. After this assessment, a required time for the occurrence of the analysed fouling conditions is predicted based on the time-dependent biofouling growth model proposed by [32]. A comprehensive model for cleaning scheduling is proposed based on several scenarios for underwater hull cleaning costs.

The rest of the paper is organized as follows: methods are briefly presented in the second section, the case study is given in the third section, and the fourth section shows the obtained results along with the discussion, followed by the conclusions in the final section.

2. Materials and Methods

In this study, the effect of biofilm on the energy efficiency of containerships in the Adriatic Sea is determined using the deterministic method. In addition, the total resistance of the investigated ships in calm water is calculated based on the Holtrop-Mennen method [33], which is proven to be an adequate method for these problems due to its simplicity and accuracy [34]. Further, within the Holtrop-Mennen method, the total resistance in calm water is divided into:

$$R_T=\left(1+\gamma k\right)R_F+R_W+R_B+R_A$$

(1)

where $\gamma$ is the form factor correction, $k$ is the form factor, $R_F$, $R_W$, and $R_A$ are the frictional, wave, and allowance resistances respectively, and $R_B$ is the pressure resistance due to the bulbous bow.

In this paper, it is considered that the transom of the investigated containerships is not immersed. The appendage resistance is assumed to be negligible since it is considerably lower than other resistance components. Additionally, within the IHS Fairplay database [35], there is no data regarding the appendages.

While sailing, the ship encounters wave and wind loads, which cause an increase in resistance. The impact of waves and wind is considered to determine the deterioration of ship performance in real conditions. The added resistance due to the wind $\left(\mathsf{\Delta }{R}_{T\mathrm{wind}}\right)$ is determined by the Blendermann method [36], and the added resistance due to waves $\left(\mathsf{\Delta }{R}_{T\mathrm{wave}}\right)$ is calculated by the method for the estimation of added resistance in regular waves presented in [37]. However, to determine the added resistance in irregular waves, spectral analysis is carried out on the basis of Tabain’s spectrum specific to the Adriatic Sea [38]. The Tabain’s spectrum is a one-parameter wave spectrum depending only on the significant wave height $\left(H_S\right)$:

$$S\left(\omega \right)=0.862\frac{0.0135g^2}{{\omega }^5}\exp \left(-\frac{5.186}{{\omega }^4{H}_S{}^2}\right){1.63}^p$$

(2)

where the parameter $p$ is equal to:

$$p=\exp \left(-\frac{{\left(\omega -{\omega }_{\mathrm{m}}\right)}^2}{2{\sigma }^2{\omega }_{\mathrm{m}}{}^2}\right)$$

(3)

modal wave frequency is calculated as follows:

$${\omega }_{\mathrm{m}}=0.32+\frac{1.8}{H_S+0.6}$$

(4)

and the parameter $\sigma$ is defined as:

$$\sigma =\left\{\begin{array}{c}0.08 \omega \le {\omega }_{\mathrm{m}}\\ 0.1 \omega >{\omega }_{\mathrm{m}}\end{array}\right.$$

(5)

As shown in [39], wave height and period have a larger influence on ship resistance in comparison to wind speed.

The total resistance under the analysed wave and wind conditions is determined with the following equation:

$$R_{TW}=R_T+\mathsf{\Delta }{R}_{T\mathrm{wind}}+\mathsf{\Delta }{R}_{T\mathrm{wave}}$$

(6)

Additionally, more details regarding the analyzed wave and wind conditions are given in the third section.

Furthermore, to take the effect of biofilm on ship hydrodynamic performance into account, the Holtrop-Mennen method is modified so that the roughness allowance is calculated using the Granville similarity law scaling method [40] and roughness functions for biofilm [41]. It should be noted that there are three roughness functions for biofilm, depending on the percentage of surface coverage with biofilm $\left(\%SC\right)$:

• for $\%SC$ > 25%:

$$\mathsf{\Delta }{U}^{+}=\left\{\begin{array}{l}\frac{1}{\kappa }\ln \left(0.27767k^{+}\right) \mathrm{for} k^{+}\ge 3.61\\ 0 \mathrm{for} k^{+}<3.61\end{array}\right.$$

(7)

for 10% < $\%SC$ < 25%:

$$\mathsf{\Delta }{U}^{+}=\left\{\begin{array}{l}\frac{1}{\kappa }\ln \left(1.14492+0.0988k^{+}\right) \mathrm{for} k^{+}\ge 4.5\\ 0 \mathrm{for} k^{+}<4.5\end{array}\right.$$

(8)

for $\%SC$ < 10%:

$$\mathsf{\Delta }{U}^{+}=\left\{\begin{array}{l}\frac{1}{\kappa }\ln \left(1.06492+0.05332k^{+}\right) \mathrm{for} k^{+}\ge 4\\ 0 \mathrm{for} k^{+}<4\end{array}\right.$$

(9)

where $\kappa =0.42$ is von Karman constant, and $k^{+}$ is the roughness Reynolds number, which is calculated as:

$$k^{+}=\frac{k{u}_{\tau }}{\nu }$$

(10)

In Equation (10) $u_{\tau }$ is the friction velocity, $\nu =1{.1882·10}^{-6}{ \mathrm{m}}^2/\mathrm{s}$ is the kinematic viscosity, and $k$ is the roughness length scale estimated by the equation given in [42]:

$$k=0.055h\sqrt{\%SC}$$

(11)

where $h$ is the average biofilm height

This allows a more reliable prediction of the effect of biofilm or other types of biofouling on the ship hydrodynamic performance in comparison to a roughness allowance, which is determined based only on the equivalent sand grain roughness $\left(k_S\right)$ [43]. The roughness functions for biofilm are used in several studies in the literature [19,20,44].

Within the Holtrop Mennen method, roughness allowance $\left(\mathsf{\Delta }{C}_A\right)$ is equal to zero for a smooth hull, while for a fouled hull, the equation based on $k_S$ is proposed. In this study $\mathsf{\Delta }{C}_A$ is calculated as a difference between the frictional resistance coefficient for a fouled and a smooth flat plate with a length equal to the ship length, defined by the Schoenherr friction line. Finally, the added resistance due to biofilm on the hull is determined with the following equation:

$$\mathsf{\Delta }{R}_A=\frac{1}{2}\rho v^{2}S\mathsf{\Delta }{C}_A$$

(12)

where $\rho =1026{ \mathrm{kg}/\mathrm{m}}^3$ is the sea density, $v$ is the ship speed, and $S$ is the wetted surface area. Obviously, $\mathsf{\Delta }{R}_A$ is equal to zero for a smooth hull.

After the total resistance under real sailing conditions is calculated for, a smooth and fouled hull, the effective power and propulsive efficiency are determined as follows:

$$P_E=R_{TW}v$$

(13)

$${\eta }_P=\frac{P_E}{0.8P_{MCR}}$$

(14)

where $P_{MCR}$ is the maximum continuous rating of the installed diesel engine, which is reduced by 20% to account for engine and sea margin [45]. Thus, the denominator in Equation (14) represents the brake power $\left(P_B\right)$ for a smooth hull. It should be noted that ${\eta }_P$ are the same for a smooth and fouled ship since in this study only fouling of the hull surface is analysed [46]. Once $P_B$ for a certain fouling condition is calculated, FOC and CO₂ emissions are determined with the following equations:

$$FOC=SFOC\cdot P_B$$

(15)

$${\mathrm{CO}}_2 \mathrm{emission}=C\cdot FOC$$

(16)

where $C=3{.206 \mathrm{g} \mathrm{CO}}_2/ \mathrm{g} \mathrm{Marine} \mathrm{Diesel} \mathrm{Oil} \left(\mathrm{MDO}\right)$ is the carbon conversion factor.

The SFOC depends on several parameters, including the engine load, speed, optimization strategy, and environmental conditions. In this study, SFOC values are obtained for an engine optimized for high load and ISO conditions, which is also done in [47]. In addition, the SFOC values are determined for MAN B&W S90ME-C [45] using the polynomial trendline presented in Figure 1. According to [45], the obtained values should be increased by 6% due to the tolerance. Based on the analysis of the data from the IHS database, 278 containerships in total having a breadth of 40 m or higher are powered by the MAN B&W S90ME-C. Therefore, this engine is chosen for further analysis as a representative engine. Further, depending on the number of cylinders, $P_{MCR}$ of these engines varies from 30.5 MW to 73.2 MW, which largely corresponds to $P_{MCR}$ of the containerships analyzed.

In Figure 2. the benefit of the proposed method over the existing methods is presented, and it is reflected by considering added resistance due to wind and waves.

Additionally, after the gains related to the cleaning of biofilm are determined, it is equally important to determine when certain fouling conditions will occur in order to adequately time the cleaning schedule. This would allow the development of a comprehensive model for cleaning scheduling, which could be very beneficial for shipowners and ship operators. Within the literature, there are numerous optimization methods that are based on artificial intelligence [48], fuzzy logic, adaptive neuro-fuzzy inference systems [49], and others that are especially useful within multi-objective optimization problems. For example, Hou et al. [50] used the Kriging-based response surface method and multi-objective optimization algorithm for hull shape optimization of a small underwater vehicle. The model proposed in this paper is a single objective optimization problem and, as such, does not require the utilisation of the previously mentioned complex algorithms.

Uzun et al. [32] proposed a time-dependent biofouling growth model based on the static immersion of various flat plates coated with the typical antifouling coatings across several locations in the world seas. The authors proposed a parameter fouling rating, based on the antifouling performance index, which can be determined as follows:

$$FR=0.2\cdot \%SC+0.5\cdot \%S{C}_{\mathrm{NS}}+15\cdot \%S{C}_{\mathrm{C}}$$

(17)

where $\%S{C}_{\mathrm{NS}}$ is the area covered by non-shell organisms shorter than 5 mm, while $\%S{C}_{\mathrm{C}}$ is the area covered by calcareous fouling higher than 5 mm.

Since the main aim of this study is to propose a comprehensive model for the cleaning schedule depending on the different scenarios of the cleaning costs, the authors decided to only account for biofilm, i.e., slime fouling. Namely, the fouling penalties in the case of non-shell organisms, or calcareous fouling on the hull surface are very high [51], and it is obvious that their presence cannot be tolerated, i.e., it is not economically justified to keep this type of fouling on the wetted surface of a ship in service. If only biofilm fouling is present on the wetted surface of a ship, based on Equation (17), the maximum FR is achieved if the entire wetted surface is fouled with slime, and it is equal to 20. In this study, the highest analysed %SC is equal to 50%, meaning that the highest FR is equal to 10.

The time-dependent biofouling growth model proposed by Uzun et al. [32] accounts for growth and saturation at the maximum rating point, and it is a Gaussian-type fit of a correlation between FR and time:

$$FR=a{e}^{\left[-{\left(\frac{t - t_0}{\tau }\right)}^2\right]}$$

(18)

where $a$ is the maximum rating, $t_0$ is the time that the rating reaches the maximum point, and $\tau$ is the coating performance parameter.

In fouling with biofilm, $a$ is equal to 20, while the other parameters are provided within [32] for the Mediterranean Sea and fouling with biofilm and are equal to $t_0=271.9 \mathrm{days}$ and $\tau =99.31$.

3. Case Study

In this paper, the PP and PPP containership fleets are studied. The PP containerships carry up to 4000–6000 TEU with a breadth of approximately 40 m. PPP containerships carry up to 6000–8500 TEU with a breadth of approximately 43 m [52]. The input data used in this paper are taken from the IHS Fairplay database [35], which represents the standard database for the calculation of the EEDI reference line [53]. For the purpose of this study, data regarding the length between perpendiculars, breadth, draught, depth, speed, deadweight, displacement, gross tonnage, and maximum continuous rating are required. After discarding the ships with insufficient data, the remaining ships are classified into containership classes. Additionally, some data for the remaining ships is erroneous, and to discard ships with such data, a criterion based on ${\eta }_P$ is set. Thus, all ships with propulsive efficiencies greater than 0.8 are excluded from further consideration, leaving a total of 101 PP and 160 PPP containerships for the analysis.

The wave and wind data for the analyzed route through the Adriatic Sea are taken from the high-resolution interactive wind and wave atlas, World Waves Atlas (WWA). Within the WWA, the data obtained by satellite measurements are validated with buoy measurements and afterward reanalyzed using numerical wave modeling [54]. The data refer to the period July 1992–January 2016. In order to achieve adequate high temporal resolution and systematic and high-resolution data, measurements are combined with the 3rd generation wave model WAM for deep-sea waves. The WAM is run every day by the European Centre for Medium-Range Weather Forecasts (ECMWF), and it is calibrated with satellite measurements. The WWA database contains data for 39 uniformly distributed locations in the Adriatic Sea (Figure 3). The ten wave parameters and two wind parameters are available for each location at six-hour intervals, meaning that a total of 34,460 data outputs are at disposal. It should be noted that some data logs have missing data, which should be excluded before processing and analyzing the wave statistics [55].

In this study, wave and wind statistics at 11 locations in the Adriatic Sea are taken into account, representing the approximate sailing route of the containerships. Data outputs consist of significant wave height, mean wave direction, wind speed, and wind direction, and the number of data outputs for all analysed locations along with their longitude and latitude are presented in

Table 1. Analyzed locations for the Adriatic Sea.

Latitude	Longitude	Number of Data Outputs
45	13	31,724
44.5	13.5	32,519
44	14	33,013
43.5	14.5	33,104
43	15.5	33,300
42.5	16.5	33,443
42	17.5	33,520
41.5	18	33,460
41	18.5	33,735
40.5	19	33,771
40	19	33,875

.

In each location, the mean values of significant wave height, wave direction, wind speed at 10 m height, and wind direction are calculated. Additionally, in considering all 11 locations, the mean values of the previously mentioned wave and wind statistics are calculated for the analyzed sailing route through the Adriatic Sea. Thus, the mean value of the significant wave height is equal to $H_S$ = 0.8671 m and the mean wave direction is equal to 187.5°. It should be noted that all directions are incoming (opposite to the direction of flow) and measured clockwise from the north. The mean wind speed is equal to 5.3769 m/s, and the mean wind direction is 180.5°. Further, considering the ship’s course along the analyzed sailing route, the relative mean wave and wind direction for a ship sailing from point A to point B are equal to 53° and 46°, respectively. The relative mean wave and wind direction for a ship sailing from point B to point A are equal to 127° and 134°, respectively (Figure 3). The value of 180° corresponds to head waves in the ship coordinate system.

The effect of biofilm on the energy efficiency of containerships while sailing in the Adriatic Sea is investigated for seven fouling conditions presented in

Table 2. Analyzed fouling conditions.

Fouling Condition	$\mathit{h}$, µm	$\mathit{\%}\mathit{S}\mathit{C}$, %	$\mathit{k}$, µm	$\mathit{F}\mathit{R}$	t, days
R1	300	50	116.67	10	189.2
R2	300	35	97.62	7	170.1
R3	300	25	82.50	5	155.0
R4	300	15	69.90	3	135.1
R5	300	5	36.90	1	100.0
R6	300	2.5	26.09	0.5	81.2
R7	300	0.75	14.29	0.15	52.2

. In Table 2, besides the main data related to the fouling conditions $\left(h, \%SC, k, FR\right)$, the time needed for the occurrence of certain fouling conditions is given and is calculated based on Equation (18). To propose an adequate model for underwater hull cleaning, it is of the utmost importance to determine a fouling condition where the fouling penalty will be equal to zero. As can be seen from the roughness functions for the biofilm presented in equations (7–9), if $k^{+}$ value is below a certain threshold value, $\mathsf{\Delta }{U}^{+}=0$, meaning that the fouling penalty will also be equal to zero. However, for the investigated containerships and sailing route, the fouling condition R7 does not cause any fouling penalty, meaning that all investigated ships could sail without an increase in fuel consumption. Consequently, for other ship types or other sailing routes, the fouling condition that does not cause any fouling penalty would be different, and therefore the appropriate mildest fouling condition must be determined.

4. Results and Discussion

In the method given in the second section, firstly, the effect of biofilm on FOC and carbon dioxide emissions is calculated for a smooth surface and the seven fouling conditions presented in Table 2. Due to biofilm, FOC and carbon dioxide emissions will increase if the speed is kept constant along the sailing route, or speed will decrease if the brake power is kept constant. In addition, since fouling with biofilm is usually neglected, within this study, the increase in FOC and carbon dioxide emissions due to biofilm is determined. It should be noted that for R1 fouling condition, one PP and two PPP containerships cannot achieve their design speed due to the increase in ship resistance. These ships are excluded from further analysis as they cannot achieve the design speed, and therefore their FOC would not be comparable with the FOC of ships that can achieve the design speed. The effect of biofilm on energy efficiency is presented as an increase in brake power, FOC, and carbon dioxide emissions, which are determined using the

$$\mathsf{\Delta }\varphi =\frac{{\varphi }_{\mathrm{R}}-{\varphi }_{\mathrm{S}}}{{\varphi }_{\mathrm{S}}}\cdot 100\%$$

(19)

where $\varphi$ represents either brake power, FOC, or carbon dioxide emissions, and S and R denote smooth and fouled surface conditions, respectively. The obtained increases in brake power and effective power will be the same since it is assumed that ${\eta }_P$ will be the same for a smooth and fouled ship. Since the carbon conversion factor is constant, the resulting increases in FOC and CO₂ emissions will also be the same.

The obtained $\mathsf{\Delta }{P}_B$ and ΔFOC caused by the fouling with the investigated fouling conditions and calculated for sailing under real conditions in the Adriatic Sea from point A to point B and vice versa, are presented in

Table 3. The obtained increases in $P_B$ for PP and PPP containership classes.

$\mathbf{Average} {\Delta }{\mathit{P}}_{\mathit{B}}$, %
Sailing Route	A-B		B-A
Surface Condition / Containership Class	PP	PPP	PP	PPP
R1	19.648	20.586	19.190	20.203
R2	17.677	18.492	17.264	18.147
R3	15.871	16.647	15.500	16.336
R4	8.224	8.615	8.032	8.454
R5	2.715	3.038	2.658	2.982
R6	1.139	1.672	1.116	1.640
R7	0	0	0	0
Standard Deviation of  ${\Delta }{P}_B$, %
Sailing Route	A-B		B-A
Surface Condition / Containership Class	PP	PPP	PP	PPP
R1	0.841	0.774	0.906	0.782
R2	0.754	0.721	0.818	0.725
R3	0.711	0.661	0.777	0.664
R4	0.374	0.373	0.404	0.373
R5	1.493	1.321	1.463	1.297
R6	1.306	1.360	1.280	1.335
R7	0	0	0	0

and

Table 4. The obtained increases in FOC for Post Panamax and Post Panamax Plus containership classes.

$\mathbf{Average} {\Delta }\mathit{F}\mathit{O}\mathit{C}$
Sailing Route	A-B		B-A
Surface Condition / Containership Class	PP	PPP	PP	PPP
R1	21.715	22.863	21.581	22.763
R2	19.376	20.346	19.215	20.219
R3	17.283	18.185	17.110	18.046
R4	8.773	9.200	8.646	9.094
R5	2.870	3.212	2.829	3.172
R6	1.202	1.765	1.186	1.742
R7	0	0	0	0
Standard Deviation of  $\mathsf{\Delta }FOC$, %
Sailing Route	A-B		B-A
Surface Condition / Containership Class	PP	PPP	PP	PPP
R1	1.017	0.940	1.049	0.957
R2	0.888	0.849	0.919	0.861
R3	0.821	0.762	0.856	0.770
R4	0.408	0.405	0.427	0.406
R5	1.578	1.397	1.557	1.380
R6	1.378	1.436	1.360	1.418
R7	0	0	0	0

. Since a large number of data points were obtained, only the average values and standard deviations of all $\mathsf{\Delta }{P}_B$ and ΔFOC calculated for PP and PPP containerships are shown.

In Table 3 and Table 4, it can be seen that slightly higher increases in $P_B$ and FOC for all fouling conditions are obtained for PPP containerships. The obtained $\mathsf{\Delta }{P}_B$ are up to 19.648% for PP and up to 20.586% for PPP containerships. Additionally, the obtained $\mathsf{\Delta }{P}_B$ are higher for the sailing route from point A to point B than vice versa. This can be attributed to the fact that the total resistance under the analysed wave and wind conditions is higher in a case when the ship sails from point B to point A, while the added resistance due to biofilm is the same for both sailing routes. As a result of this of this, the increase in $P_B$ and FOC is lower for the sailing route from point B to point A. The obtained ΔFOC are higher than the obtained increases in $\mathsf{\Delta }{P}_B$ for both containership classes and for all investigated fouling conditions and both sailing routes. These increases are up to 21.715% for the PP containership class and up to 22.683% for the PPP containership class. This can be attributed to the fact that due to the presence of biofilm, the engine load increases, leading to a higher SFOC since, for the smooth surface condition, the engine load is already higher than 80%, Figure 1.

In Table 3 and Table 4 the obtained standard deviations of the increases in $P_B$ and FOC are given as well. The highest standard deviations are obtained for fouling conditions R5 and R6. These fouling conditions affect ship hydrodynamic performance and yet have a very low $k$ value. Due to this $k^{+}$ value is lower and for some ships it can even be below the threshold value for which $\mathsf{\Delta }{U}^{+}=0$, meaning that the impact of biofilm on the ship hydrodynamic performance is irrelevant, while for other ships $k^{+}$ value is above the threshold and the presence of biofilm affects the ship hydrodynamic performance, causing the higher values of standard deviation.

The obtained average FOC per route along with the standard deviation of FOC for both PP and PPP containership classes and both sailing routes are presented in Figure 4. The impact of biofilm on ΔFOC per route is evident in Figure 4. Thus, for fouling condition R1 and the sailing route from point B to point A, the average ΔFOC is equal to 24.6 t for PP containership classes and 33 t for PPP containership classes. The obtained ΔFOC are slightly lower for the sailing route from point A to point B than vice versa. During the sailing in the Adriatic Sea from point A to point B, even for fouling condition R6, ΔFOC is equal to 1.4 t for PP and 1.9 t for PPP containership classes.

After the average FOC values are calculated, CO₂ emissions can be estimated using Equation (16). In

Table 5. The obtained average CO₂ emissions and increase in CO₂ emissions per route for PP and PPP containership classes.

Average CO2 Emissions, t
Sailing Route	A-B		B-A
Surface Condition / Containership Class	PP	PPP	PP	PPP
S	348.35	457.88	356.49	466.99
R1	426.02	562.11	435.50	572.75
R2	416.13	549.04	425.31	559.34
R3	408.84	539.18	417.82	549.23
R4	379.04	498.18	387.48	507.57
R5	358.90	471.15	367.13	480.29
R6	352.82	464.11	361.00	473.21
R7	348.35	457.88	356.49	466.99
Average ∆CO2 Emissions, t
Sailing Route	A-B		B-A
Surface Condition / Containership Class	PP	PPP	PP	PPP
R1	77.68	104.23	79.01	105.76
R2	67.78	91.16	68.82	92.34
R3	60.50	81.30	61.33	82.24
R4	30.69	40.30	30.99	40.58
R5	10.56	13.27	10.64	13.30
R6	4.47	6.23	4.51	6.21
R7	0	0	0	0

, the obtained average values of CO₂ emissions per route along with the obtained ΔCO₂ emissions for both PP and PPP containership classes and both sailing routes are shown. However, for the investigated fouling conditions, average ΔCO₂ emissions are up to 79.01 t/route for PP containership classes, and up to 105.76 t/route for PPP containership classes. The obtained results demonstrate the importance of hull cleaning from an environmental point of view.

Additionally, except from an environmental point of view, it is very important to demonstrate that, from an economic perspective, underwater hull cleaning is a very important measure as well. In this study, the costs related to fouling penalties are related to the increased fuel costs, and it is assumed that hull cleaning will be performed during the port time, which is equal to 0.71 days [56], meaning that there will not be any additional costs related to hull cleaning except the cost of the underwater hull cleaning itself. The fuel costs are estimated based on the average MDO price of 640 $/t [57]. In Figure 5, the obtained average savings in fuel costs per route (S) related to underwater hull cleaning are presented with respect to the time required for the occurrence of certain fouling conditions. It is clear that S are higher for PPP containerships than for PP containerships, which is expected since ΔFOC are higher as well. Thus, the highest obtained S for a PP containership is equal to 15,640 $/route, while for a PPP containership, it is equal to 20,960 $/route. However, it should be noted that the underwater hull cleaning would be more expensive for PPP containerships than for PP containerships due to the larger wetted surface area.

In Figure 5, the dependence on savings and time, i.e., $S=f\left(t\right)$ is given as well. In order to predict the return on the investment of the underwater hull cleaning adequately, the cleaning costs must be equated with the achieved savings due to cleaning over time:

$$\mathrm{cleaning} \mathrm{costs}={\displaystyle {\mathsf{\int }}_{t_{\mathrm{R}7}}^{t_{\mathrm{RI}}}S\left(t\right)} \mathrm{d}t$$

(20)

where the cleaning costs is varied depending on the scenario, $t_{\mathrm{R}7}$ is the time when biofilm fouling starts causing fouling penalties, and $t_{\mathrm{RI}}$ is the time needed to achieve a return on investment.

As it is recommended in the recent studies published in the literature, fouling with biofilm must not be ignored [20], and in this study, the return on investment is determined for the scenario when underwater hull cleaning is performed as soon as a slime starts causing fouling penalty. This scenario could be related to the proactive grooming technique, which is recommended for coping with climate issues, i.e., increasing ship energy efficiency [58]. However, it should be noted that the timing of underwater hull cleaning could be determined for some other scenario, for example, to achieve the lowest possible rate of return on the investment.

In

Table 6. The time needed to achieve the return on the investment.

Cleaning Costs, $	PP		PPP
	${\mathit{t}}_{\mathbf{RI}}$, days	N	${\mathit{t}}_{\mathbf{RI}}$, days	N
15,000	47.2	32	40.2	28
30,000	54.2	37	47.3	33
45,000	59.7	40	53.0	37
60,000	64.3	44	57.7	40
75,000	68.2	46	61.7	43

, the time obtained to achieve a return on the investment related to different costs of underwater hull cleaning and the number of trips required to achieve a return on the investment are presented. However, from the obtained results, it is clear that underwater hull cleaning is a very cost-effective tool since the obtained $t_{\mathrm{RI}}$ are lower than $t_{\mathrm{R}1}=52.2 \mathrm{days}$ for one scenario in the case of PP and two scenarios in the case of PPP containerships. It should be noted that if proactive hull cleaning is done, the cost of underwater hull cleaning will be significantly lower, as only 0.75% of the wetted surface should be cleaned in the case of investigated ships. Important assumptions within this study are as follows: the underwater hull cleaning will not cause an increase in hull roughness fouling will be completely removed; and the antifouling coating efficiency will not decrease after the underwater hull cleaning. It should be mentioned that the biofouling growth model does not consider the impact of seasonality [32]. In addition, the proposed model does not consider the variation in cleaning costs with respect to the wetted surface area, different seasons, or market environments due to a lack of available data. Therefore, the authors decided to present cleaning costs as a discrete variable using five levels rather than consider it a continuous variable within the study.

In Table 6, it is evident that if the cleaning costs are higher than $15,000 in the case of a PP containership and higher than $30,000 in the case of a PPP containership, $t_{\mathrm{RI}}$ will be longer than $t_{\mathrm{R}7}=52.2 \mathrm{days}$, meaning that slime will start to affect the ship hydrodynamic performance and increase fuel costs. To find an optimal timing for underwater cleaning, the following equation should be solved:

$$\mathrm{cleaning} \mathrm{costs}={\displaystyle {\mathsf{\int }}_{t_{\mathrm{OPT}}}^{t_{\mathrm{OPT}}+t_{\mathrm{R}7}}S\left(t\right)} \mathrm{d}t$$

(21)

where $t_{\mathrm{OPT}}$ is the optimal timing for underwater cleaning, which for previously mentioned scenarios should be added to $t_{\mathrm{R}7}=52.2 \mathrm{days}$.

The authors used the generalized reduced gradient method for nonlinear optimization. The objective function, which was the difference between cleaning costs and increased fuel costs, was minimized. In that way, the optimal timing for underwater cleaning was determined. The optimization was performed in MS Office Excel using the add-in program Solver. More details regarding the nonlinear optimization using the generalized reduced gradient method can be found in [59].

In

Table 7. Optimal timing for underwater cleaning.

Cleaning Costs, $	PP				PPP
	${\mathit{t}}_{\mathbf{OPT}}$, days	N	${\mathit{t}}_{\mathbf{OPT}}+{\mathit{t}}_{\mathbf{RI}}$, days	N	${\mathit{t}}_{\mathbf{OPT}}$, days	N	${\mathit{t}}_{\mathbf{OPT}}+{\mathit{t}}_{\mathbf{RI}}$, days	N
15,000	0	0	52.2	35	0	0	52.2	36
30,000	0.9	1	53.2	36	0	0	52.2	36
45,000	4.2	3	56.5	38	0.4	0	52.6	37
60,000	7.8	5	60.0	41	3.2	2	55.5	39
75,000	11.6	8	63.8	43	6.3	4	58.5	41

, the obtained optimal timing for underwater cleaning, depending on the different cleaning costs, is presented. From the obtained results, it is clear that $t_{\mathrm{OPT}}$ are lower than $t_{\mathrm{RI}}-t_{\mathrm{R}7}$, which is expected since the fouling penalties increase with time. This highlights the importance of solving Equation (21) and finding the optimal timing for underwater cleaning. Once the obtained $t_{\mathrm{OPT}}$ is added to $t_{\mathrm{R}7}$ for PP containerships, the obtained results demonstrate that cleaning should be performed after 35 trips if the cleaning costs are equal to $15,000 and after 43 trips if the cleaning costs are equal to $75,000. For PPP containerships, cleaning should be performed after 36 trips if the cleaning costs are equal to $15,000 and after 41 trips if the cleaning costs are equal to $75,000.

Furthermore, to estimate the possible economic value that can be obtained by the application of the proposed method, the costs caused by biofouling are calculated for optimal timing for underwater cleaning and for cleaning twice annually (

Table 8. The possible economic value which can be obtained using the proposed method.

Cleaning Costs, $	PP	PPP
	$	$
15,000	454,086	589,919
30,000	403,453	537,504
45,000	360,364	486,261
60,000	322,241	442,094
75,000	288,401	406,533

). In the table above, it can be seen that higher savings can be achieved for PPP than for PP containership. However, it should be highlighted that the cleaning costs for a PPP containership would surely be higher than for a PP containership due to the larger wetted surface area. From the obtained results, it is clear that significant savings can be achieved if the maintenance schedule is optimized, i.e., up to $454,000 for a PP containership and $590,000 for a PPP containership.

It should be noted that the time-dependent biofouling growth model proposed by Uzun et al. [32] is based on the static immersion of coated flat plates. To increase the reliability and practicability of the biofouling growth model for real applications, dynamic immersion tests should be performed according to the duty cycle of a certain merchant ship. These tests could more reliably simulate the actual working conditions of a certain merchant ship and would probably extend the time that the fouling rating reaches the maximum point as well as the time when biofilm fouling starts causing fouling penalties. Consequently, the possible economic values related to the application of the proposed method would be lower.

5. Conclusions

In this paper, a comprehensive model for cleaning scheduling is proposed based on several scenarios for the costs of underwater hull cleaning. The applicability of the proposed model is demonstrated in the example of Post Panamax and Post Panamax Plus containerships sailing in the Adriatic Sea, and the optimal timing for underwater hull cleaning is determined for different cleaning costs. Additionally, the performed research demonstrated the reductions in CO₂ emissions that can be achieved if proactive hull cleaning is applied. The obtained results are calculated for the case of sailing under real conditions in the Adriatic Sea. The real sailing conditions include the impact of waves and wind on the total resistance, which is estimated based on the wave and wind statistics for the analysed route passing through the Adriatic Sea. In this study, the authors wanted to balance operational and maintenance costs. The increase in operational costs is related to the increase in fuel costs due to increased fuel consumption since it is assumed that the ship will sail at the same speed regardless of biofouling occurrence. The maintenance costs are related only to the hull cleaning costs. It is considered that hull cleaning will be performed during port time, meaning that there will not be any additional costs related to hull cleaning except the cost of the underwater hull cleaning itself. Due to a lack of data related to cleaning costs, the authors decide to present cleaning costs as a discrete variable using five levels rather than consider it a continuous variable within the optimization process.

The main conclusions drawn from this research are as follows:

• A new, comprehensive model for the prediction of the optimal timing for underwater hull cleaning is developed. This model includes the assessment of fuel consumption for both smooth and fouled ships. It accounts for waves and wind, as well as the engine load through specific fuel oil consumption, and it incorporates the time-dependent biofouling growth model proposed in [30].
• The new model is applied to Post Panamax and Post Panamax Plus fleets from the IHS Fairplay database for a smooth surface and a surface fouled with biofilm. However, the proposed method can be employed for different ship types and fouling conditions.
• Fuel oil consumption and CO₂ emissions are calculated for a smooth surface and seven fouling conditions. The increases in CO₂ emissions per route are up to 79.01 t, and up to 105.76 t for Post Panamax and Post Panamax Plus containerships, respectively. These increases represent the potential CO₂ emissions savings that can be achieved if proactive hull cleaning is applied.
• The variations in the obtained increases in CO₂ emissions per route due to biofilm presence are observed among the containership classes as well as among the sailing routes. This emphasizes the significance of taking into account real sailing conditions (i.e., wave and wind conditions) as well as the engine load within the method for the estimation of energy efficiency gains due to hull cleaning.
• This study indicates that the biofilm on the immersed surfaces should be cleaned. However, from an environmental perspective, proactive cleaning should be applied, meaning that as soon as the slime starts to cause a fouling penalty, it should be cleaned. Further, from an economic perspective, depending on the cleaning costs, it is demonstrated that proactive cleaning may not be the best solution and that certain fouling penalties should be tolerated to achieve the highest financial savings.

The proposed method and potential energy efficiency gains due to hull cleaning can be utilized in future studies related to low-carbon shipping. Specifically, the proposed method can be utilized for obtaining the input data for the analysis of the potential energy savings due to hull cleaning on a yearly basis for all merchant ships sailing through the Adriatic Sea. In that way, environmental benefits on a larger scale would be noticed, which could put pressure on ship owners or ship operators to keep their ships free of biofouling. Additionally, future studies regarding the application of the proposed model for cleaning scheduling on examples of different ship types and routes would be beneficial to analyze the differences in the optimal timing for underwater hull cleaning. Application of the proposed model to different sailing routes would require adequate wave energy spectra and exploitation of wind and wave statistics for the route. Additional investigations related to the biofouling growth model, especially related to the impact of seasonality on biofouling growth, would be beneficial. In order to increase the reliability and practicability of the biofouling growth model for real applications, dynamic immersion tests should be performed according to the duty cycle of a certain merchant ship. Further studies regarding the costs related to hull cleaning would be beneficial to determine the dependence of cleaning costs on the wetted surface area that must be cleaned, as well as the impact of market environments and seasonality on the cleaning costs.