of the Maritime University of Szczecin
Akademii Morskiej w Szczecinie
2015, 44 (116), 83–89
ISSN 1733-8670 (Printed) Received: 01.09.2015
ISSN 2392-0378 (Online) Accepted: 16.10.2015
DOI: 10.17402/061 Published: 07.12.2015
Voyage optimization for a Very Large Crude Carrier oil tanker:
a regional voyage case study
Aliakbar Safaei, Hassan Ghassemi
, Mahmoud Ghiasi
Amirkabir University of Technology, Department of Maritime Engineering Tehran, Iran, e-mails: {alisafaei123; gasemi, mghiasi}@aut.ac.ir
corresponding author
Key words: optimum route, sea condition, ship movements, criteria move, operational cost, fuel
consump-tion
Abstract
In line with the ambition of ship-owners to preserve capital and reduce operational costs, the selection of an optimum, safe and secure route for an envisaged voyage has always been a challenge for ship-owners, masters, and engineers. Due to the many complexities and parameters that affect the selection of an optimal route, the topic has become very interesting to many researchers. Each of the parameters affecting the process of route selection has its own values and weights, and these values change depending on specific situations and objectives. This sensitivity to context increases the difficulty selecting the optimum route. In this research, the optimization of a tanker-sized VLCC voyage for predefined and different routes is addressed in order to identify the optimum route. To reduce the number of variable parameters, major values have been assigned to the ship profile and sea conditions. The time domain analysis and the solution of equations of motion are then performed. The proposed route is designed by using a Bezier curve, and this route is then optimized with the objective of decreasing fuel consumption using the Fletcher-Powell method. The resulting optimized route shows a 3.7% savings in fuel consumption.
Introduction
Nowadays, the role of maritime transportation in the global economy is known to everyone. In particular, it is clear that a global economy based on world-wide production could not be achieved without safe, secure and very economical maritime transportation. In turn, the shipping industry is based on the advantages of the economy of scale, new technologies, a completely competitive market, and operational flexibility. This prevailing competi-tive environment, particularly in tramp shipping, acts as a powerful incentive for the charterer or ship-owner to minimize all operational cost ele-ments. Depending on current oil prices, fuel costs represent 30% to 40% of daily ship operational expenses, and have always been considered as a vital economic factor by charterers, ship-owners, engine makers, and ship designers.
In this respect, for a voyage from origin point A to destination point B, being able to select the best
route in terms of reduced fuel consumption, high safety and security of passage is a considerable competitive advantage for a charterer or ship-owner.
It is worth mentioning that the optimum route is not always the shortest. This is so because in the process of selecting the optimum route entails simultaneous consideration of many variables; such variables as the safety and security of the voyage, fuel consumption, weather conditions, wave condi-tions, currents, wind, the ship’s structural design and speed all play a role and have different values and weighting factors. In the other words, all of the effective variables are optimized by the optimum route. Moreover, the optimum route is subject to change over the course of the whole voyage due to changes in the effective variables, conflicting variables or uncertainty of conditions.
Several extensive studies have been performed in the area of this study. Chen (Chen, 2013)
evalu-ated and optimized sea routes by considering weather conditions. He first studied all existing ways of selecting routes as a function of weather conditions, and then investigated the feasibility of using all available equipment and technologies to select optimal, safe and efficient maritime routes. Kobayashi et al. (Kobayashi, Asajima & Sueyoshi, 2011) studied optimized route for ocean going vessels. Ocean currents, winds, and waves in the time domain were the main variables. By solving the equations in the time domain, as well as study-ing maneuverability equations for the vessel, opti-mized routes were developed for an ocean going container ship.
Catalani (Catalani, 2009) examined the schedul-ing and route optimization for the voyages in the western Mediterranean. He used the Fadden func-tion for optimizafunc-tion and chose voyage paths with the help of the Catalani geographic information system. Journée and Mejijers(Journée & Mejijers, 1980) optimized the routes to allow a ship to per-form at its highest level, and described operational costs associated with changing course.
Roh (Roh, 2013) also investigated a ship’s op-timum route under the impact of sea conditions in an effort to reduce the vessel’s fuel consumption. He reduced costs by using economic approach based on up-to-date sea conditions and estimated fuel consumption, developing a method consisting of three steps. The first step entails the collection of sea condition data at the desired time. In the second step, the vessel’s fuel consumption as a function of sea conditions is estimated. In the third step, the economic path with minimum fuel consumption is estimated on the basis of the previous two steps. The first step entails gathering information through analysis of satellite data and weather information over the past few months. The method used to implement the second step involves the calculation of the increase in the ship’s resistance, and calculat-ing the reduction of the ship’s speed due to increas-ing resistance. Then the amount of power needed to compensate for this loss of speed is estimated, along with the additional fuel required for this power. In the third step, the Isochrone method is used to choose the optimal route. This method can be manually programmed by the person setting the route. The method generates a series of connected points that ship can move through over a limited period of time by starting from a given point and passing all possible directions. These points depend on the ship’s performance and the sea conditions. Because of problems like the inability to account for islands, the procedure has been modified in this paper. The concept of modeling a ship’s operating
parameters to minimize fuel consumption in real weather conditions was presented by Cepowski (Cepowski, 2015).
Mathematical models using cross-flow drag ex-pressions in lateral force and yaw moments to reduce fuel consumption have been developed by Oltman and Sharma (Oltman & Sharma 1984). Takashina (Takashina, 1986) also proposed a model using harmonic functions with β and r' that lead to power savings. A unique expression based on adopting each hydrodynamic component instead of conventional polynomial terms was also developed by Karasuno et al. (Karasuno et al., 2001).
Nonaka et al. (Nonaka et al., 1981) carried out circular motion tests (CMTs) with a 3 m model of a SR-108 container ship. This study investigated several motion tests and developed some algo-rithms for minimizing energy consumption. Yumuro (Yumuro, 1987) carried out similar re-search with a 4 m model of the “Esso Osaka” VLCC, and did Yoshimura (Yoshimura, 1988) with a 3 m model of PCC. Recently, the authors also performed almost the same tests with a Fishery Research Ship model (Yoshimura, 2007). All of them tried to fit mathematical equations to the models for reducing the fuel usage of a vessel.
Because of a lack of research conducted on oil tankers, this article estimates the behavior of an oil tanker in waves, analyzing the ship’s behavior according to the ship movements’ criteria, with a focus on reducing fuel consumption and selecting the optimal route. In the sections that follow, the equations governing the issue and the terms of solving differential equations are described.
Ship case study and chosen route
A VLCC-sized tanker, one of the most deployed oil tankers in the oil transportation industry, was selected as the design of the ship to be studied. Table 1 and Figure 1 summarize the specifications for the ship as studied. The voyage from Khark Island to the port of Bandar Abbas was the chosen
Table 1. Characteristics of the ship that was evaluated
Specific characteristic Value Symbol Unit
Total length 320 Loa m
Model width 60 Bmld m Model height 30 Dmld m Draft 20 D m Propeller diameter 15 Dp m Propeller pitch 12 Pp m Projected area 12,000 AAl m2
Transverse projected area 1,500 AAT m2
Gross tonnage 200,000 GT –
Nominal tonnage 300,000 T Ton Operational velocity 12 VS Knot
route, and the duration of the voyage was assumed to be about 3 days. The ports of origin and destina-tion are shown in Figure 2, as well as the primary and optimized routes without the mandatory parts, which are same for both the starting and ending parts of the routes.
Figure 1. The VLCC tanker
Figure 2. Navigation path
Evaluating wind, waves and currents
The 5-day averages of sea current were drawn from the weather forecast world maps. In addition, wind and wave predictions were taken from the Sail
Wx source. This information contains wind direc-tion and velocity, and significant wave heights at specified time intervals. Wind velocity and direc-tion, and the height and direction of waves are shown in Figures 3 and 4, respectively.
Figure 4. The waves height and direction (IOC-UNESCO)
This study made use of 3-hr updates for wind direction and velocity and for significant wave height and direction. Other data was updated every 6 hours. The geographic coverage ranged from 05020.45 western up to 05606.9 western, and from 2913.85 northern to 2707.20 northern.
Governing equations
A stationary coordinate system starting from the ship’s center of gravity was used to solve the equa-tions of motion corresponding to the ship’s coordi-nates. The coordinates system is shown in Figure 5. The basic equations used to solve for the ship’s transverse and longitudinal movements, and for the ship’s yaw rotation, are listed below (Kobayashi, Asajima & Sueyoshi, 2011):
Primary Route Optimized Route
R P H vr x y c c vr y x FX FX FX X m m v u vr X m m u m m cos sin 0 0 (1)
A R P H x y c c x y FY FY FY FY r m m v u ur m m v m m sin cos 0 0 (2)
IzzJzz
rFNH FNPFNRFNA (3)where m is the ship’s mass or displacement; mx and my are additional mass in the x and y directions,
respectively; Izz and Jzz are mass moments of inertia
and additional mass moment of inertia around the z axis; u and v are ship’s velocity in the direction of the x- and y-axis. respectively; uc0 and vc0 are the
current velocity components in direction of the x-axis and y-x-axis; r is the rotational velocity; is yaw
angle; u , are u and v are time derivatives; Fv XH, FYH, FNH – FXP, FYP, FNP – FXR, FYR, FNR – FXA, FYA, FNA – are longitudinal forces in x-direction,
trans-verse forces in Y direction, and yaw moments around Z, respectively, caused by the hull, propel-ler, radar and wind; RAW is additional resistance
caused by waves; and Xvr is the hydrodynamic
derivative.
Forces acting on the body
The forces acting on the body of the ship based on the above equations, which are used to solve maneuvering equations, are as follows (Kobayashi, Asajima & Sueyoshi, 2011):
1 2 2 1 H XH R LdU H F (4) H YH LdU Y F 2 2 1 (5) H NH LdU N F 2 2 2 1 (6) 4 2 2 1 FX v FX r FX vr FX v X F H vv rr vr vvvv (7) 3 2 2 r Y F r v Y F r v Y F r Y F v Y F Y F rrr vrr vvr r v H (8) 3 2 2 3 r N F r v N F r v N F v N F r N F v N F N F rr vrr vvr vvv r v H (9) where R is the ship’s resistance, X'H1, Y'H, N'H are
non-dimensional forces and moments applied on the ship’s wetted area due to suave and yaw in x, y and z axes, respectively; and the other parameters are hydrodynamic derivatives.
Propeller forces and fuel consumption
In this study, lateral forces and moments on the propeller on direct routes given are minimal and therefore are not considered. Also, propeller longi-tudinal force is expressed using the following equations:
t
T FXP 1 (10) 0 0 P P N FY (11)where t is the propeller thrust reduction factor, and
T is the propeller thrust that can be evaluated from
the following equations:
t PK D n T 2 4 (12) 2 2 1 0 cJ c J c Kt (13) P P D n u J (14)
where n is the propeller revolution, KT is the thrust
coefficient, J is the advanced coefficient, c0, c1 and
c2 are propeller characteristic coefficients, and up is
the current velocity. The propeller torque is also evaluated from the following equations:
Q P K D n Q 2 5 (15) 2 2 1 0 d J d J d KQ (16)
where KQ is the torque coefficient and d0, d1 and d2
are propeller characteristic coefficients. We also need the main engine power to evaluate the fuel consumption, which can be calculated by following equations: t DHP BHP (17) Q n π 2 DHP (18)
where BHP is the main engine nominal horse power, DHP is the main engine actual horse power, and t is the power transition coefficient. For fuel consumption in time units we use the following equation:
FOCR BHP
FOC
(19)
where FOCR is the fuel consumption rate. Finally, the total fuel consumption is evaluated by integrat-ing over the time domain.
FOCdt
FOC (20)
Wave forces and moments
The forces and moments for waves are calcu-lated from the following equations:
A XA T A A XA V A C F 2 2 1 (21)Figure 6. Force and moment coefficients caused by wind by yaw angle (Fujiwara, Ueno & Nimura, 2001)
A YA L A A YA V A C F 2 2 1 (22)
A NA T A A NA V AC F 2 2 1 (23)where A is the air density, VA is the wind relative
velocity, AT is the transverse projected area, AL is
the longitudinal projected area, A is the wind relative direction, and CXA, CYA, CNA are forces and
moment coefficients around the x, y and z axes. These coefficients can be evaluated by curves presented in Figure 6.
Additional resistance by waves
Sasaki et al. (Sasaki, Motsubara & Yoshida, 2008) provided the following equations for evaluat-ing the additional resistance caused by waves. These formulae are used for seas with significant wave height less than 3 m.
0.8
2 2 2 1 1 2 1 fcp W nB AW C g C F H BB R (24)
0.5 gB V F S nB (25)
2 2 1 2 1 1 Pf Pf fcp C C B (26) 46 . 0 1 C (27) 3 . 0 when , 0 . 2 2 Bfcp C (28)
0.3
, when 0.3 60 0 . 2 2 Bfcp Bfcp C (29)where RAW is the additional resistance caused by
waves, is the water density, g is earth gravity acceleration, FnB is Froude number, HW is the
specific wave height, B is the ship’s width, Bfcp is
Blunt coefficient, VS is the ship velocity, and CPf is
prismatic geometry coefficient. Solutions and results
There are various methods to optimize the sail-ing route, such as solvsail-ing differential first-order functions, the Newton-Raphson method, and all other practices based on the gradient method. Although the gradient is not measurable using statistical methods, approximation methods can be used. The method used here is the Fletcher-Powell method (Fletcher & Powell, 1963). Also, the fol-lowing cost estimate was used:
J = FOC (30) [deg] [deg] [deg] CX A [ – ] CY A [ – ] CNA [ – ]
where FOC is the fuel consumption integrated over a defined route using the Bezier curve for N–1 degrees, where N is the number of points. This method also uses some fixed variables. The Bezier curve is shown in Figure 7.
Figure 7. Bezier curve
The optimal path from a solution of the govern-ing equations usgovern-ing the methods described was identified for the 5th of July, 2015. A comparison between the primary and optimal route for fuel consumption, distance, and travel time is illustrated in Figures 8–10, respectively. As can be seen, although the distance between the two ports on the optimal route increases slightly, fuel consumption decreases by 3.7%, and travel time decreases by about 1%. Thus, it can be concluded that fuel consumption is directly affected by weather condi-tions. This was our first stage, which considered fuel consumption and travel time for local route optimization. In our next study, we will address seakeeping as well as economic issues for ocean-going routes.
Figure 8. Fuel consumption
Figure 9. Distance changes
Figure 10. Travel time
Conclusions
In this paper, we addressed the reduction of fuel consumption using route optimization with consid-eration of sea and weather conditions by solving the maneuvering equations of a ship in a defined time domain. In the case study defined in this article, a VLCC tanker is assumed to be sailing from Khark Island to the Port of Banda Abbas. The specific route is optimized by applying the Bezier curve and the Fletcher-Powell method to the governing equa-tions. The conclusions are as follows:
a) A new method for choosing a sailing route con-sidering weather conditions can be developed and optimized by the Fletcher-Powell method. This method could be used for other vessels and routes.
b) The computer simulation showed a considerable decrease in fuel consumption of 3.7%. Although the distance and time increased, the results showed a decrease in fuel consumption.
For proposed future studies, an equation or sta-tistical method combined with experimental data could be developed, taking into consideration crew performance impact factors in order to calculate a more accurate result.
Acknowledgments
This research was supported by the Marine Re-search Center (MRC) of AUT and the National Iranian Tanker Company (NITC) whose works are greatly acknowledged. The authors would grateful-ly like to thank the reviewers for their comments that helped us to improve the manuscript.
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