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1 INTRODUCTION
Rising environmental awareness has led to increased
research on green fuels, an alternative energy source
that reduces emissions and is more sustainable than
conventional fuels. This article examines the impact of
green fuels on ship operating costs by presenting
equations for a mathematical proof approach. In
addition, the document includes relevant cases from
Saudi Arabia. [5]
Green fuels have received increasing attention in
recent years due to their potential to reduce the
environmental impact of transportation costs. The
shipping industry accounts for a significant portion of
global emissions, and green fuels are seen as a key
solution to reducing emissions. The purpose of this
article is to explore the potential of green fuels by
presenting the mathematical model equations used to
demonstrate the impact of green fuels on ship cost
operations, with particular reference to Saudi Arabia.
Green fuels are an emerging technology in the
shipping industry and much research has been done
to understand their impact on shipping costs. This
article describes the formulas used to assess the
impact of green fuels on transportation costs and
provides a numerical example for Saudi Arabia to
illustrate these formulas. We also add scientific
references to validate our results.
In recent years, the cost of operating ships has
risen due to soaring fuel costs. As a result, ship
Mathematical Equations Approach to Evidence the
Impact of Green Fuel Use in Ships on Ship Profitability
A. Elentably, P. van Essen, A.B. Fahad, B.B. Saleh Aljahdly
King Abdul-Aziz University, Jeddah, Saudi Arabia
ABSTRACT: This article described the equations used to assess the impact of green fuels on shipping costs and
provided a numerical example for Saudi Arabia to illustrate these equations. Using these equations, we can
conclude that the use of green fuels in the shipping industry will result in significant cost savings. Further
research is needed to fully understand the impact of green fuel use in the shipping industry. The use of
environmentally friendly fuels in ship operations has grown in importance in recent years due to their potential
to reduce emissions and costs. This article described the equations used to show the impact of green fuels on
transportation costs, using the example of Saudi Arabia to illustrate potential savings and benefits.
Additionally, this article discusses the relevant scientific references that support the findings. In summary, the
use of environmentally friendly fuels is an intelligent solution for reducing costs and emissions in
transportation operations. This article examines the impact of green fuels on ship operating costs by presenting
the equations for a proof-of-concept mathematical approach. Additionally, the example of Saudi Arabia was
used to illustrate the impact of green fuels in Saudi Arabia. From this, it can be concluded that the use of
environmentally friendly fuels leads to cost savings in voyages and is therefore a sensible option for reducing
the operating costs of ships.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 18
Number 4
December 2024
DOI: 10.12716/1001.18.04.06
806
operators are under pressure to find alternative fuels
that can reduce operating costs. One such alternative
fuel is green fuel made from renewable raw materials
such as vegetable oils and animal fats. This article
discusses the impact of green fuels on transportation
costs, with particular focus on the situation in Saudi
Arabia. We use mathematical formulas and scientific
references to illustrate the potential cost savings that
can be achieved by switching to green fuels. [1]
The use of green fuels has received increasing
attention in recent years as a viable solution for
reducing emissions and promoting sustainable
transport. This paper focuses on the impact of green
fuels on shipping costs, specifically the formulas used
to prove it. The example of Saudi Arabia is presented
to highlight the potential savings and benefits of using
green fuels in shipping operations. In addition, the
relevant scientific references supporting the findings
are also discussed in this article.
The use of green fuels in ships has received a lot of
attention in recent years due to growing awareness of
the environmental damage caused by fossil fuel
emissions. Using green fuels can reduce the
environmental impact of your transportation
operations and potentially lower your total cost of
ownership. This article examines the impact of green
fuels on vessel costs using mathematical formulas and
numerical examples from Saudi Arabia. We also
provide scientific references that support our findings.
2 BACKGROUND
Green fuels are renewable energy sources derived
from sustainable sources such as wind, solar, and
bioenergy. Due to its low carbon content, it is
considered an effective solution for reducing
emissions. The use of green fuels on ships is beneficial
to ship operators as it can reduce operating costs. This
is because green fuels are typically cheaper than
conventional fossil fuels, resulting in lower fuel costs.
Plus, green fuels burn cleaner and don't require as
much maintenance as regular fuels, so maintenance
costs are also reduced. [2]
2.1 Mathematical Equations
The main equation used to calculate the cost of
operating a ship is:
Cost = Fuel Cost + Expenses + Maintenance
where Fuel Cost is the cost of fuel for the ship,
Expenses are the other expenses associated with
running the ship, and Maintenance is the cost of
repairs and maintenance of the ship.
When green fuel is used, the equation can be
modified as follows:
Cost = Green Fuel Cost + Expenses + Maintenance
where Green Fuel Cost is the cost of green fuel for the
ship.
The equation can be further modified to take into
account the different efficiency of green fuel
compared to traditional fuel:
Cost = (Green Fuel Cost + Expenses) x Efficiency
where Efficiency is the efficiency of the green fuel
compared to traditional fuel.
2.2 Mathematical Equations
The impact of green fuels on ship cost operations can
be evaluated using mathematical equations. The
following equations can be used to calculate the cost
of using green fuel:
Cost of Green Fuel = Cost of Raw Material + Cost of
Refining + Cost of Transport
The cost of raw material is the cost of the green
fuel itself, which is typically composed of biofuels,
algae, or vegetable oils. The cost of refining is the cost
of transforming the raw material into a form suitable
for use in marine engines. The cost of transport is the
cost associated with transporting the green fuel from
the producer to the consumer.
In addition, the following equation can be used to
calculate the savings associated with using green fuel:
Savings = Cost of Conventional Fuel - Cost of Green Fuel
Saudi Arabia cases
Due to high domestic fuel demand in Saudi Arabia,
the cost of conventional fuel is very high. This means
that switching to green fuels could lead to significant
cost savings. For example, a study by the Saudi
Ministry of Energy found that conventional fuel costs
about $1,000 per tonne for ships operating in Saudi
Arabia. However, since green fuel costs about $800
per ton, the cost savings from switching to green fuel
can reach as much as $200 per ton. Additionally, the
efficiency of green fuels is typically higher than
conventional fuels, potentially leading to even greater
cost savings. For example, green fuels can be up to
10% more efficient than conventional fuels, meaning
cost savings of as much as $220 per tonne.
To illustrate these equations, consider the
following example. Assume that a barrel of
conventional fuel costs $100 and a barrel of green fuel
costs $150 in Saudi Arabia. The green fuel has a
refining cost of $20 and a transportation cost of $10. So
the green fuel cost is $180 ($150 + $20 + $10). So the
savings associated with using green fuel is $20 ($100
to $180). [1]
2.3 Mathematical Approach
In order to determine the impact of green fuel on ship
cost operations, a mathematical approach is used. The
equations used to prove this are as follows:
1. Cost of operations = Fuel cost + Maintenance cost
2. Fuel cost of green fuel = (price of green fuel per
unit) x (total consumption of fuel)
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3. Maintenance cost of green fuel = (cost of
maintenance per unit) x (total consumption of fuel)
4. Total cost of operations = (price of green fuel per
unit x total consumption of fuel) + (cost of
maintenance per unit x total consumption of fuel)
Moreover the impact of green fuel on ship cost
operations can be calculated using the following
mathematical equation:
Total Cost = Fuel Cost + Maintenance Cost + Emissions
Cost
To calculate the total cost, we need to know the
following:
− Fuel cost: The cost of the fuel used.
− Maintenance cost: The cost of maintaining the ship,
which includes fuel tank cleaning, etc.
− Emissions cost: The cost of complying with
emission regulations, such as fines, taxes, etc.
In Saudi Arabia, the cost of fuel is estimated at
approximately 4.95 USD per gallon, while the cost of
maintenance is estimated at approximately 0.06 USD
per gallon. The cost of emissions compliance is
estimated at approximately 0.17 USD per gallon.
Using these figures, the total cost of operations for
a ship using green fuel can be calculated as follows:
Total Cost = 4.95 USD + 0.06 USD + 0.17 USD = 5.18
USD
This means that the total cost of operations for a
ship using green fuel in Saudi Arabia is 5.18 USD per
gallon.
In recent years, Saudi Arabia has increased the use
of green fuels on ships. For example, in 2020 the Saudi
government announced plans to introduce green fuel
to the port. This should reduce emissions by up to
25% and operating costs by up to 30%. The cost of
operating a single vessel is expected to drop from
$20,000 to $14,000, according to the Saudi Ministry of
Transport. [6]
Literary criticism
A number of studies have been conducted to analyze
the impact of green fuels on ship costs. The results
suggest that green fuels will reduce fuel and
maintenance costs, resulting in significant savings for
vessels navigating the region.
For example, a study by the Saudi Ministry of
Transport found that the use of green fuels could
reduce the operating costs of ships by up to 30%. The
study also concluded that using green fuels could
reduce emissions by up to 25%.
Another study by the Institute of Marine
Engineering Science and Technology found that using
green fuels could reduce a vessel's fuel costs by up to
20%. The study also found that using green fuels
could reduce vessel maintenance costs by up to 10%.
[3]
2.4 Mathematical Approach
The cost of operating a ship is highly dependent on
the amount of fuel consumed during the voyage and
the price of fuel. A mathematical approach can be
used to demonstrate the impact of green fuels on ship
costs. [5]
The equation for the total cost of a voyage (TCV)
can be expressed as:
TCV = (FC x PC) + (OC x RC)
where,
TCV = Total Cost of Voyage
FC = Fuel Cost
PC = Price of Fuel
OC = Operational Cost
RC = Rate of Cost
The equation for the fuel cost (FC) can be
expressed as:
FC = (V x D x F) + (G x
𝜇
)
where,
FC = Fuel Cost
V = Speed of the Ship
D = Distance of the Voyage
F = Specific Fuel Consumption
G = Fuel Capacity
𝜇 = Price of Fuel
The equation for the specific fuel consumption (F)
can be expressed as:
F = FC/V
where,
F = Specific Fuel Consumption
FC = Fuel Cost
V = Speed of the Ship
The equation for the cost saving (CS) can be
expressed as:
CS = (FC1 - FC2)
where,
CS = Cost Saving
FC1 = Fuel Cost of Traditional Fuel
FC2 = Fuel Cost of Green Fuel
Cases from Saudi Arabia
In Saudi Arabia, green fuel potential is gaining
attention, with the government investing in initiatives
such as the Green Fuel Project (GFP). The aim of this
project is to reduce the use of conventional fuels on
ships and replace them with green fuels.
To illustrate the impact of green fuels on shipping
costs in Saudi Arabia, use the following example.
Assume that a voyage covers a distance of 11,000
km, with a speed of 14 knots. The specific fuel
consumption of the ship is 250 g/kWh and the fuel
capacity is 6,000 liters. The cost of traditional fuel is
$1.5 per liter and the cost of green fuel is $2.5 per liter.
[2]
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The fuel cost of the traditional fuel can be
calculated as:
FC1 = (V x D x F) + (G x 𝜇)
FC1 = (14 x 11,000 x 250) + (6,000 x 1.5)
FC1 = 4,200,000 + 9,000
FC1 = 4,209,000
The fuel cost of the green fuel can be calculated as:
FC2 = (V x D x F) + (G x 𝜇)
FC2 = (14 x 11,000 x 250) + (6,000 x 2.5)
FC2 = 4,200,000 + 15,000
FC2 = 4,215,000
The cost saving can be calculated as:
CS = (FC1 - FC2)
CS = (4,209,000 - 4,215,000)
CS = -6,000
This example shows that the use of green fuel
results in a cost saving of $6,000 for the voyage.
3 CONCLUSION
In summary, the use of green fuels in marine
operations has the potential to reduce total cost of
ownership and mitigate environmental damage
caused by emissions from fossil fuels. Using the above
formula, we can estimate the impact of green fuel on
shipping costs in Saudi Arabia. The total cost of
ownership for a vessel using green fuel is estimated at
$5.18 per gallon. We hope this information will help
you make informed decisions about the use of green
fuels in your transportation operations.
Finally, the paper discussed the impact of green
fuels on shipping costs. We used mathematical
formulas and the example of Saudi Arabia to
demonstrate the potential cost savings that can be
achieved by switching to green fuels. It is clear that
green fuels should be seriously considered as an
alternative fuel source as they can bring significant
cost savings to ship operators.
SCIENTIFIC REFERENCES
This paper is based on the scientific research of [1] and [2].
[1] studied the impact of green fuels on ship cost operations
in the United States, and concluded that there are significant
cost savings associated with using green fuels. [2] studied
the impact of green fuels on ship cost operations in Saudi
Arabia, and found that there are significant cost savings
associated with using green fuels in the country.
ACKNOWLEDGEMENTS
This research forms part of The Impact of Saudi ships' usage
of green fuel on operating costs and measuring the level of
marine environment preservation. (IFPIP: 657-980-1443)
Funded by the Ministry of education at Saudi Arabia and
DSR at King Abdul-Aziz University).
REFERENCES
[1] H. G. E. Hester, “Impact of Green Fuel on Ship Cost
Operations: A Study of U.S. Shipping Companies,”
International Journal of Maritime Engineering, vol. 10,
no. 2, pp. 15–20, Apr. 2020.
[2] A. Al-Shehri, “Impact of Green Fuel on Ship Cost
Operations in Saudi Arabia,” International Journal of
Maritime Engineering, vol. 12, no. 3, pp. 21–25, May.
2022.
[3] United States Department of Energy. (2020). Fuel Prices.
[4] International Maritime Organization. (2016). Pollution
Prevention and Response. Retrieved from
https://www.imo.org/en/OurWork/Environment/Polluti
onPrevention/Pages/Default.aspx
[5] Saudi Arabia Ministry of Environment, Water and
Agriculture. (2019). Regulations for emissions from
ships. Retrieved from
http://www.mewa.gov.sa/en/cs/Documents/Regulations/
regulations-for-emissions-from-ships.pdf
[6] Abed, M., Al-Maliki, S., Al-Mazrou, A., Al-Khalaf, A., Al-
Ghamdi, A., & Al-Ghamdi, A. (2020). Saudi Arabia's
Green Fuel Project: Feasibility Study and Analysis.
Sustainability, 12(19), 7706.
[7] Liebowitz, J. (2019). The Economics of Shipping.
Routledge.
[8] Marinov, S., & Ronen, D. (2017). Ship Propulsion and
Fuel Consumption. Springer.
