Correlation of the Ship Speed and Carbon Dioxide Emissions A Study on Panamax Tankers

Abstract

Keywords: fuel consumption; ship emissions; ship speed; regression analysis

1. Introduction

Energy efficiency and fuel consumption in ships are considered to be crucial issues in the 21st century, due to the environmental awareness has increased with a growing momentum. Increasing population and developing trade lead the world to bigger ships and larger commercial fleets, forming a bigger energy demand. Thus, it is obvious that fuel consumption and consequently ship emissions would be a bigger problem day by day. According to the International Energy Agency (IEA) report, when world energy consumption amounts are examined, 122 EJ of energy was spent in the transport sector in 2023 and 11 EJ of this energy was used by the shipping sector. This

corresponds to approximately 9% of the energy spent in the transport sector. It is predicted that a total of 132 EJ of energy will be spent in the transport sector in 2030 and 12 EJ of this will be used by the shipping sector. When the world CO2 emission amounts are examined, it is seen that the total CO2 emission amount in 2023 is 37723 Mt CO2. While 8213 Mt CO2 of this emission amount belongs to the transport sector, 856 Mt CO2 belongs to the shipping sector. The total CO2 emission amount in 2030 is estimated to be 36170 Mt CO2. It is estimated that 8537 Mt of this amount will belong to the transport sector and 900 Mt of CO2 will belong to the shipping sector (IEA, 2024). On the other hand, even in the most optimistic scenario, fuel demand in the maritime sector is projected to increase by 43.5% in 2050 compared to 2002 (Eyring et al., 2005).

*Corresponding author. *E-mail address: lbilgili@bandirma.edu.tr Published by Yıldız Technical University Press, İstanbul, Türkiye This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Ship-related emissions emerge as a separate and important environmental problem. Although ships emit a large number and variety of emissions (Kollamthodi et al., 2008) only a few of them are worth examining in terms of environmental damage and quantity. According to the latest report of the International Maritime Organization (IMO), shipping activities are responsible for 2.4%, 13-15% and 12-13% of global carbon dioxide equivalent (CO2e), sulphur oxide (SOx) and nitrogen oxide (NOx) production, respectively (Smith et al., 2014). IMO's recent study has shown that greenhouse gas emissions from the shipping sector increased from 977 million tonnes in 2012 to 1,076 million tonnes in 2018, an increase of 9.6% (IMO, 2020a). In addition, it has been determined that 70% of ship emissions occur at 400 km and closer to the shore (Eyring et al., 2010). Efforts to estimate emissions and increase energy efficiency are essential to guarantee a greener future. For this purpose, in addition to many local, national and regional studies, many international rules and regulations have been developed under the leadership of the IMO. Under the International Convention for the Prevention of Pollution from Ships (MARPOL), IMO has prepared several annexes for the monitoring, reduction and control of various shiprelated pollutants. Annex VI is the supplement where ship air pollutants are evaluated and it includes the assessments on ozone-depleting substances (ODSs), particulate matter (PM), and volatile organic compounds (VOCs). Annex VI came into force on 9 May 2005 and is being developed with various updates annually. Restrictions imposed by the IMO for NOx and SOx are presented in Table 1 and Table 2. Table 1 presents the minimum requirements for ships to meet NOx criteria. Ship main engines must be manufactured according to Tier II standards in the current situation. Ships cruising in the North American and United States Caribbean Sea Areas must be subject to Tier III restrictions. Table 2 presents the SOx constraints. Accordingly, under the

current situation, the fuel used by a ship cruising in global waters may contain up to 0.5% sulphur by mass. If a ship cruises in an Emission Control Area (ECA) (Baltic Sea, North Sea, North American and United States Caribbean Sea Areas), the ratio is set at 0.1%. In a recent study on the question of whether Annex VI does not include ship-related CO2 emissions, it is stated that especially developed countries accept CO2 as a greenhouse gas (GHGs) rather than a polluting agent. In addition, there is a concern that possible additions for CO2 reduction may lead to "tremendous domestic legal obstacles". Therefore, it was concluded that Annex VI should be left as it is and if necessary, a unique regulation should be prepared for CO2 (Shi, 2016). The deleterious impacts of ship-related emissions on human health and the environment are well-studied (Corbett et al., 2007; Eyring et al., 2010; Kollamthodi et al., 2008; Moldanová et al., 2009) and detailed inventories of these emissions on a regional and global scale were calculated (Alver et al., 2018; Jalkanen et al., 2016; Johansson et al., 2017). It is clear that emissions from ships have a wide variety of harmful impacts to human health and the environment. Considering the development of the global economy, trade volume and the maritime industry, it is obvious that shiprelated emissions and the energy demand of the maritime sector will pose even more serious problems shortly. The majority of these studies focused on emission estimates based on fuel consumption or engine power. Some of them calculate the emission by estimating the possible fuel consumption considering the dynamic sea conditions. It is crucial to calculate the emissions at an early stage, especially in terms of compliance with the IMO criteria. Another important issue is to calculate the fuel consumption (energy demand) and emission amounts empirically. For this purpose, various studies have been carried out to find the correlation between speed, which is the most important output of dynamic marine conditions, and fuel

Ship construction date on or after Tier I Tier II Tier III (ECA)

1. January 2016

Total weighted cycle emission limit (g/kWh) n=Engine’s rated speed (RPM)

IMO: International Maritime Organization; RPM: Revolutions per minute; ECA: Emission Control Area

Table 2. The limits for SOx (IMO, 2015b) Outside an emission control area

4.50% prior to 1 January 2012 3.50% on and after 1 January 2012 0.50% on and after 1 January 2020

1.50% prior to 1 July 2010 1.00% on and after 1 July 2010 0.10% on and after 1 January 2015

consumption/emission. In addition, there are also studies for fuel consumption and emission calculations depending on the dynamic operating conditions. (Beşikçi et al., 2016) developed a fuel consumption methodology based on ship speed, revolutions per minute (RPM), mean draft, trim, cargo quantity, wind and sea effects data by using the noon reports. The authors used the artificial neural networks method for this purpose. (Bialystocki & Konovessis, 2016) developed a fuel consumption prediction algorithm based on current fuel consumption, draft, weather and surface roughness data. The main point emphasized in this study is the effect of weather conditions on fuel consumption. Utilizing the Least Absolute Shrinkage and Selection Operator (LASSO) regression algorithm, (Shengzheng Wang et al., 2018) developed a fuel consumption prediction methodology based on historical fuel consumption, length overall, beam, speed, trim angle, air and sea conditions and swell height data. (Gkerekos et al., 2019) They studied on estimating fuel consumption by using distance, draft, RPM, daily fuel consumption, ship speed, propeller angle, sea current, wave direction, sea and weather conditions and wind direction data in different machine learning methods. (Kee et al., 2018) developed a fuel consumption prediction formula based on distance, working hours and deadweight data by utilizing multiple linear regression methods. Although they are not included in the formula, ship speed and wind speed are among the inputs used. (Graf von Westarp, 2020) investigated the correlation between fuel consumption and speed for a container ship. As a result, depending on the e-function, a direct equation between speed and fuel consumption was found to be valid in container ships. (Ayudhia P. Gusti & Semin, 2016) examined the correlation between speed and fuel consumption and emission values for a container ship cruising between two ports in Indonesia. (Ayudhia Pangestu Gusti & Semin, 2018) also compiled studies on the correlations between ship speed and emission. However, none of these studies found a direct correlation between ship speed and fuel consumption for tankers. An equation, which depends on the ship's speed and without any additional calculation or data, would allow the calculation of fuel consumption and emission amount even when the ship is not cruising. In addition, the simpler the fuel consumption and emission estimation can be achieved, the more useful it will be. In this study, a correlation was developed between the daily speeds and CO2 emissions. For this purpose, the average daily engine load of the ship was calculated based on the speed, and then the specific fuel oil consumption (SFOC) in this engine load was determined and the amount of fuel expected to be spent was reached. Emission calculations were realized depending on the amount of fuel consumed. Since the dynamic external conditions (RPM, weather and sea conditions, cargo amount, wave course) to which the ship is exposed directly affect the speed, no further calculations were realized, assuming that these conditions are included in the calculation over speed. Although it is a well-known fact

that speed is a decisive dependant for emissions, to the best knowledge of the authors, there is no direct link between these two variables. The novelty of this study is to provide a quick equation to measure the relationship of speed and emission. This study used data from a Panamax tanker. Panamax tankers have maximum dimensions determined by the Panama Canal Authority due to the size of the canal they pass through. These tankers have dimensions of approximately 275 meters (950 feet) in length, 31 meters (106 feet) in width and 11 meters (39.5 feet) in depth (Autoridad del Canal de Panamá, 2022).

2. Materials And Methods

Regression analysis is used in many subjects in the maritime industry. (Lepore et al., 2017) used variable selection methods, penalized regression methods, latent variable methods and tree‐based ensemble methods regression techniques to analyze the data collected from the shipping industry scenario and C02 emission estimation in their study. (Öztürk & Başar, 2022) used MLRA (multiple linear regression analysis) method in their studies, and estimated ship fuel consumption with RPM, trim, mean draft, weather condition data. (Uyanık et al., 2020) estimated the fuel consumption of a container ship with data such as main engine rpm, main engine cylinder values, scavenge air, shaft indicators using Multiple Linear Regression, Ridge and LASSO Regression, Support Vector Regression, Tree-Based Algorithms, Boosting Algorithms methods. (Cepowski & Drozd, 2023) used data such as rotational speed, draught, trim, hull fouling time, wind speed, wave height, and seawater temperature of a container ship and examined the hierarchical effects of these parameters on fuel consumption using artificial neural networks and multiple nonlinear regression methods. In this study, Microsoft Excel was used to perform regression analysis. Design speed of the Panamax tanker used in this study is 14 knots and the base SFOC value is 169 g/kWh. These values are obtained from the booklets published by the ship's main engine manufacturer. Daily speed values for each day were obtained from the logs and the average daily engine load was calculated first. For this purpose, the following equation, which is called as Propeller Law and presented in was utilized: 

SFOC values were calculated in accordance with these engine loads after engine loads, which were calculated depending on daily speed. For this, the equation, which is presented below, obtained from the study below (MorenoGutiérrez et al., 2015) was utilized:

this purpose, first, a dependent variable symbolized by y and an independent variable symbolized by x is determined (Rawlings et al., 1998). The mathematical expression of regression analysis is given by (Ye et al., 2017) as follows:

After that, SFOC value is calculated based on the related engine load with the help of the following equation. The SFOCbase value is given by the main engine manufacturer and has been measured as 169 g/kWh for the ships used in this study. SFOC = SFOCrelative ×SFOCbase

Thus, firstly, the engine load depending on the average speed value of that day and then the SFOC value of the ship can be calculated depending on the variable engine load. Then, the total fuel consumption can be calculated. After calculating the fuel consumption, emission estimates can be estimated. In this study, only CO2 emissions were evaluated. Emission estimations can be calculated via the following equation (Trozzi, 2010): ETrip=FC×EF(5) where; ETrip

The emission factor for CO2, which is 3114 g/kg fuel for LSHFO, was taken from (IMO, 2020a). Thus, based on the fuel consumption data obtained with the help of the equations presented above, the estimation of mentioned emissions can also be realized. These fuel consumption and emission data were processed with the help of regression analysis and formulas were developed to calculate the fuel consumption and emission amounts depending on the speed variable. Regression analysis is to explain the relationship between two variables with the help of a mathematical formula. For

The main purpose of such equations established in the regression analysis is to explain one variable through other variables. Regression analysis is a method developed to find the correlation or relationship between dependent or independent variables by finding the coefficients expressed by β (Bilgili, 2018).

4. Discussion

(Graf von Westarp, 2020) carried out a study on the data of 3 ships, searching for a general speed-fuel consumption formula based on dynamic variable conditions. According to the results of the study, the relationship between speed and fuel consumption was found exponential. Accordingly, the results of the study conducted by the current study and the results of (Graf von Westarp, 2020) are partially compatible. The graphics obtained in the current study (Fisg. 1, 2) are almost exactly compatible with the SFOC curves presented by the ship's main engine manufacturer. The data from the main engine manufacturer shows that SFOC values are decreasing rapidly to a certain level, but then the acceleration reverses and fuel consumption starts to increase although the speed continues to decrease. For this reason, the results obtained in the current study do not change in any way either exponentially or linearly, but as a peculiar graphic. (Moreira et al., 2021) showed that it is possible to predict the ship speed and fuel consumption using only sea conditions data without using variables

such as RPM and torque using an artificial neural network. (Pelić et al., 2023) investigated the effects of slow steam on fuel consumption and CO2 emissions in their study. They calculated the reduction in fuel consumption between 72.36% and 76.25% at a speed of 12 knots. When compared to a speed of 23 knots, CO2 emissions were found to be four times less. (Taskar et al., 2023) calculated fuel savings using the speed optimization algorithm for two case ships in different seasons at three different ship speeds. It was observed in the study that fuel savings of up to 6% could be achieved. It was stated that combining slow steaming with speed optimization would support higher fuel savings and emission reductions. In addition, various studies have been carried out to realize cost estimations, which is the second important issue affected by fuel consumption. These studies generally focus on estimating to perform realistic cost calculations by considering the relationship between speed and fuel consumption. (Notteboom, 2006) assumed that fuel consumption increased with the increase in speed. This increase is exponential and more consistent with the results of (Graf von Westarp, 2020). (Ronen, 1982) conducted a study on the effect of fuel prices on the optimum speed of the ship and examined the effects of optimum speed on fuel cost instead of developing a speed-fuel consumption formula. Similarly, (Corbett et al., 2009; Psaraftis & Kontovas, 2010; Ronen, 2011) studies have also focused on fuel costs and route optimization, mostly through the relationship between speed optimization and fuel consumption.

5. Conclusion

Increasing commercial activities and energy demand are accelerating a process that results in the growth of the number and size of ships. Energy demand for ships means more need for fuel. Depending on this energy demand, ship emissions, which are already known to be a major problem, are expected to increase shortly if adequate measures are not taken. Therefore, estimating fuel consumption and emissions and determining whether these values comply with international restrictions have gained great importance.

Table 4. Speed-dependent fuel consumption and emission formulas Variable dependent

y = 7E-05×5 – 0.0005×4 – 0.0078×3 – 0.0491×2 + 0.0338× + 61.803 y = 0.0002×5 – 0.0015×4 – 0.0247×3 – 0.1559×2 + 0.1074× + 196.47

In addition, estimating the fuel consumption as simply as possible depending on the dynamic conditions will provide important preliminary data to the relevant subjects such as route and speed optimization by providing accurate and realistic calculations of the fuel costs during the operation. In particular, the relationship between speed and fuel consumption has been studied in several studies, and despite some important progress, it has not been possible to develop a direct and effective correlation. The emission estimation is based on a well-known and frequently applied method, which includes SFOC calculations and utilization of emission factors. The reason for using regression analysis method is to reach a single-variable equation to estimate the target values. This study aims to calculate fuel consumption on a single variable (speed) that is indirectly linked to other variables (RPM, air and sea conditions, cargo amount, wave course). In addition, emissions from fuel consumption can also be achieved depending on speed (Table 4). The evaluation criteria for the success of this study is to reach a reliable equation to estimate the speed-emission relationship. The equation has a R2 value as 0.9941, which means the expected success is met. Employing this equation, when the estimated speed of the ship is determined, average fuel consumption and emissions can be calculated. In this way, the speed-fuel consumption relationship, which has not been answered clearly for a long time, has become evident and simple equations, which are ready for use, have been developed. The results are also compatible with the engine load-SFOC curves given by the ship's main engine manufacturer.

Data Availability Statement

The published publication includes all graphics and data collected or developed during the study.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

Financial Disclosure

The authors declared that this study has received no financial support.

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