Determination of Demand for LNG in Poland

Abstract

This study was aimed at improving the energy efficiency of the distribution of liquefied natural gas (LNG) as shipping fuel in the southern Baltic Sea. The objective of this study was to determine the demand for LNG for maritime shipping by analyzing the distribution of the resource from the water side (ship-to-ship). LNG was chosen due to the location of the LNG terminal in Świnoujście within the analyzed water area, where a problem has arisen in the southern part of the Baltic Sea regarding fuel supply for vessels due to the lack of developed infrastructure along the coast. An analysis was conducted to optimize the size of the LNG fleet and infrastructure facilities. Seeking compliance with Annex VI to the MARPOL 73/78 Convention, adopted by the International Maritime Organization (IMO), shipowners see potential in the switch from conventional fuels to LNG. As one of the alternative solutions, it will contribute to reducing harmful emissions. Determination of the LNG distribution volume requires the identification of LNG storage facility locations, specifying the number of LNG-powered ships (broken down by type) and the number of LNG bunkering ships. The first part of this study contains a detailed analysis of the number of sea-going ships that provide services in the southern part of the Baltic Sea and the world’s number of LNG bunkering ships. The database contains a set of the characteristics required to determine the optimal demand for LNG, where LNG bunkering vessels are capable of supplying fuel within the shortest possible time and covering the shortest possible distance to LNG-powered ships. The characteristics include the type of ship, requested LNG volume, the speed of LNG bunkering ships, the distance between LNG facilities, and the loading rate (the volume of fuel received per time unit). Based on the collected data, the volume of LNG distribution was determined using MATLAB R2019a software. The remainder of this study contains a description of the conducted research and results of an analysis of the traffic density in the Baltic Sea. The results were obtained on the basis of data from the Statistical Yearbook of Maritime Economy and IALA IWRAP Mk2 2020 software. The number of LNG-powered ships and number of LNG bunkering ships were specified, and the demand for LNG for the area under analysis was determined.

1. Introduction

Reducing environmental pollution is at the top of the agenda for many organizations, commissions, and national governments. The use of fossil fuels in transportation is one of the major causes of increased emissions of sulfur oxides (SO_x) and nitrogen oxides (NO_x); therefore, directives and regulations regarding LNG as fuel for maritime vessels have been introduced (

Table 1. Directives and regulations concerning LNG [1,2,3,4,5].

Regulation	Date of Adoption	Characteristics
MARPOL Annex VI	19 May 2005	SO2: 0.50% (except Sulphur Emission Control Areas–SECA). 0.10% in SECA. NOx: Tier I: for engines produced from 1 January 2000; engine power ≤ 130 kW: 17.0 g/kWh and engine power > 130 kW: 14.4 g/kWh. Tier II: produced from 1 January 2011; engine power ≤ 130 kW: 14.4 g/kWh and engine power > 130 kW: 7.7 g/kWh. Tier III produced from 1 January 2016 in ECA (Emission Control Areas); engine power ≤ 130 kW: 3.4 g/kWh and engine power > 130 kW: 2.0 g/kWh. Particulate matter (PM) emissions from 1 January 2016. Tier III requirements.
Directive 2014/94/UE	22 October 2014	SO2 content in fuels used by ships: SECA: limited to 0.10% until 1 January 2015. Non SECA: from 1 January 2020 and limited to 0.50%.
Directive RED II	11 December 2018	Not directly applicable to LNG, and it promotes the use of renewable energy, which influences the development of alternative fuels, including LNG-related technologies.
FuelEU Maritime	25 July 2023	A 2% reduction in greenhouse gas (GHG) intensity by 2025. A 6% reduction by 2030. A 13% reduction by 2035. A 26% reduction by 2040. A 59% reduction by 2045. A 75% reduction by 2050.
European Union’s Emissions Trading System	1 January 2024	From 2024, shipping will be covered by an emissions trading scheme, which means that ships will have to buy emission permits for CO2.

).

As a major emitter of harmful substances to the atmosphere, the maritime transport industry is required to comply with restrictions on emissions in the ECA. The ECA is a general category that includes the areas of the Baltic Sea, the North Sea, the area around North America (including the US and Canada), and the areas around the US Caribbean Islands (Puerto Rico and the US Virgin Islands), which have stricter emissions regulations for various pollutants, including sulfur oxides (SO_x), nitrogen oxides (NO_x), particulate matter, and volatile organic compounds (

Table 2. Emission control areas.

Area	Date Adoption	Effective Date	Date of Applicability	Oxides
Baltic Sea	26 September 1997	19 May 2005	19 May 2006	SOx
North Sea	22 July 2005	22 November 2006	22 November 2007	SOx
US Caribbean Islands	26 July 2011	1 January 2013	1 January 2014	SOx PM NOx
The area around North America	26 March 2010	1 August 2011	1 August 2012	SOx NOx

).

A subcategory of the ECAs are SECAs, which focus solely on regulating SO_x emissions. In the SECAs (Baltic Sea, North Sea, and English Channel), ships are required to use ultra-low sulfur fuels or to use technologies such as exhaust-gas-cleaning systems (scrubbers) to meet these standards. Measures aimed to ensure that only marine fuels that meet this requirement are used in the maritime transport have become a priority. Therefore, the creation of an environment fostering the development of alternative fuels followed.

The use of LNG as fuel for maritime vessels is widely viewed as a transitional option to meet the stringent EU and IMO regulations in the context of long-term decarbonization [6]. With the goal of reducing or completely eliminating CO₂ production (related to the emissions from fossil fuel use such as oil, hard coal, and lignite) in the shipping industry, the use of LNG as a transitional fuel is associated with the following:

• Lower CO₂ emissions compared to traditional marine fuels;
• The efficiency of LNG in trapping heat in the atmosphere compared to CO₂, which is a very potent greenhouse gas;
• Alternative technologies and fuels—their ongoing development aims to eliminate CO₂ (e.g., ammonia, hydrogen, biofuels, and hybrid propulsion technologies utilizing electricity from renewable sources);
• Legal regulations.

Expanding LNG infrastructure—maritime vessels must make significant changes to their fuel systems to comply with new regulations. These changes could include the following:

• Switching to more expensive, lower-sulfur fuels, such as marine diesel oil [7,8,9];
• Installing scrubbers and other devices on board to reduce sulfur emissions into the atmosphere [10,11];
• Fully transitioning to LNG [12,13,14].

LNG as a shipping fuel has been gaining supporters worldwide and is considered the most advanced new technology in the shipbuilding industry. Compared to conventional fuels, the use of LNG as marine fuel makes it possible to reduce the following [15,16]:

• Sulfur oxide emissions by ca. 90–95%;
• Carbon dioxide emissions by ca. 20–25%.

The most important of the criteria mentioned above is the possibility of bunkering LNG on key shipping routes. The existing LNG-bunkering infrastructure is poorly developed and situated along the coast. The ultimate LNG-bunkering infrastructure should comprise facilities, LNG-powered ships, and LNG bunkering vessels capable of meeting the demand in SECA while adhering to the principles of rational management [17].

The ongoing rapid development in the maritime transport is observed in all its branches. The demand for energy is continuously growing, accompanied by efforts aimed at reducing greenhouse gas emissions causing environmental damage. Consequently, the demand for LNG is on an upward trend and stimulates the development of the LNG distribution network. The LNG distribution network comprises the following components:

• Infrastructure facilities, such as LNG terminals;
• LNG-powered ships;
• LNG carriers;
• LNG bunkering ships.

LNG is a natural gas in a liquid state. The liquefaction technology reduces its volume and enhances the safety of transport and consumption [18,19,20]. In the process of liquefaction, LNG changes its physical state from a gas to liquid as a result of the application of appropriate pressure and temperature below critical limits [21,22]. During the process, the natural gas is cleansed from water, carbon dioxide, and nitrogen, and any solid particles it contains are removed. Considering its volume, which is ca. 600 times smaller than when it is in the gaseous state, the advantages include low cost and high safety of transport. LNG is not explosive, it is safe [23], and it can be transported from distant locations [24]. Since it can effectively cover energy demand in regions without direct access to a gas infrastructure, the volume of LNG traded globally is growing [25,26,27].

The utilization of LNG in various sectors of the global economy is backed with environmental and security concerns aimed at further diversification of gas supplies [28,29]. Compared to conventional fuels, the use of LNG as marine fuel reduces SO_X, CO₂, NO_X, and PM emissions [30,31,32,33]. An increasing number of newly built LNG-powered ships leaves enterprises with a business opportunity to build LNG facilities and offer fuel supplies.

Considering its common use and the many benefits that it offers, LNG is an active link in the supply chain. A classic supply chain model comprises consecutive stages in a prearranged order, which ensures streamlined and effective flow of goods [34]. A standard LNG supply chain model consists of the following main stages:

• Extraction and transfer from deposits to liquefaction facilities through a pipeline system in the gas exporting country;
• Liquefaction, storage, and loading at the loading terminal;
• Transportation by sea, onboard methane carriers, and in insulated cryogenic tanks [35,36,37];
• Discharge and regasification at imports terminal [38,39];
• Delivery to end users through a pipeline system or in tank containers (by rail or road) [40].

Proper operation of the supply chain and the end user price of LNG, which depends on the structure of costs in the supply chain, are affected by a number of factors, such as the following (Figure 1):

• Extraction. The price of natural gas varies depending on the geological conditions, characteristics of deposits, distance to the terminal, and labor costs. This factor has a significant impact on the global costs of natural gas extraction [41].
• Liquefaction. The costs of liquefaction depend on the costs of investments in LNG terminals, the technologies used, and the logistics of natural gas [42].
• Regasification and storage. The costs of regasification depend on the technologies applied at LNG terminals and the costs of LNG logistics. The storage process, including, without limitation, the location of infrastructure facilities (either offshore or on land) and the manner of storage, has a significant impact on the costs of LNG distribution [43,44].
• The costs of transportation are a considerable component of the LNG purchase price [45,46,47] as they constitute 10–30% of the end user price. The costs of transportation are determined by many factors, including, inter alia, the costs of chartering a sea-going ship (which depend on the situation on the natural gas market and are closely linked to economic fluctuations), fuel costs, and charter fees, which constitute 80–90% of the costs of LNG transportation. Hence, crude oil prices indirectly influence the prices of LNG through harbor fees, freight charges, canal tolls, and insurance premiums [48].

The technical aspects of the LNG distribution chain are related to the possibility of applying a variety of solutions for LNG-carrier-loading systems [49]. Technical parameters are of key importance in the entire logistic process in terms of hazards to people and the environment [50]. Another important aspect of the LNG distribution process, in view of the development of the infrastructure and sea-going fleet, is the optimization of the supply chain [51,52,53], which is one of the determinants of the end user price of LNG.

Considering its low cost and extraordinary potential to improve the global environmental performance, LNG is a highly valuable product. Investments in LNG terminals and transmission pipelines to ensure LNG supplies from multiple sources contribute to the global diversification of LNG sources and destinations [54]. Construction of LNG terminals is also strategic for the final price of LNG, the process of selection of LNG suppliers, and national economic security, which relies on uninterrupted supplies of energy sources [55].

The unit cost of fuel is of key importance to end users. The import costs determine the end-user price, which is an inherent part of the supply chain [56,57,58].

The growing supply of natural gas is directly driven by demand, which, according to the statistical data (of 2021), is on a global upward trend. Demand for natural gas has risen by 60% and is double that for crude oil [59].

Commodity markets have a great impact on the final price of gas [60]. Trade in natural gas is conducted at virtual trading points (VTPs), and they are characterized by dynamic price fluctuations, with multiple price changes occurring during a trading day. Virtual transactions are settled through the gas supplies in the network of pipelines throughout Europe. The major European VTPs include the Dutch TTF, the German Gaspool, and the British NBP.

Expanding the use of LNG in the maritime economy sector strongly relies on modernization of the existing fleet [61,62]. The forecast for the development of LNG-powered sea-going ships is optimistic. Conversion of the fleet seems to be promising as it will make it possible to conduct the following:

• Strengthen the reliability of supplies in an emergency, such as in the blockage of trade or the outbreak of a conflict;
• Operate the sea-going fleet depending on the current demand regardless of the destination;
• Increase the national energy security through reducing the dependency of supplies on foreign shipping companies;
• Make savings on freight charges.

A spike in demand for LNG is observed in the SECAs [63,64]. Compliance with environmental regulations requires the implementation of state-of-the-art measures, such as bunkering networks that use the following bunkering methods [65,66,67,68]:

• Port-to-Ship—the process of loading fuel on to a ship directly from port facilities, such as bunkering in ports, port basins, or on the roads, at favorable weather conditions;
• Ship-to-Ship—the supply of fuel during the ship’s voyage at sea (which can be used if port facilities are not available);
• Truck-to-Ship—one of the advantages of this fuel transfer method is mobility since a lorry can access any location within a port, but a downside is that several lorries may be required to fill up a tank;
• Onshore facility—an inconvenience of this type of fuel transfer lies in the fact that LNG facilities are situated in ports that may not be located at the main fairways where LNG-powered ships operate;
• Container–ship—the container is connected directly to the ship, and fuel loading method entails using a specially designed container or fuel tank.

LNG bunkering methods have also been discussed in terms of regulations and technical arrangements. The analyses described in the literature cover LNG carriers, LNG bunkering ships, and LNG ports that are already providing or are planning on developing distribution networks to provide bunkers to LNG-powered ships [69].

An analysis of the literature on the distribution of LNG as marine fuel and the related infrastructure facilities shows that little attention has been paid to the following:

• Solutions related to the LNG distribution model;
• The size of the LNG fleet in SECAs and other sea areas;
• Demand for LNG as marine fuel in SECAs and other sea areas;
• Optimization of LNG distribution in terms of time frames and costs in SECAs and other sea areas;
• Optimization of the LNG distribution network.

Restrictions imposed by the EU require business entities providing services in SECAs to implement measures aimed at reducing air pollution. As a low-emission fuel, LNG has become a focal point of development in the entire energy sector. The authors will describe the condition of the existing LNG infrastructure and set directions for the development of LNG as shipping fuel.

The remainder of this study is organized as follows. Section 2 provides a review of the literature and the key components of distribution of LNG as a shipping fuel. In Section 3, models and methods of the proposed solution to the problem of LNG distribution are discussed. Section 4 contains a classification of the results obtained from an analysis of the proposed universal distribution model of LNG as shipping fuel for LNG-powered ships in the southern part of the Baltic Sea based on the data from the Statistical Yearbook of Maritime Economy and the IALA IWRAP Mk2 software, which were sampled using MATLAB Mk2 software. In Section 5, the results are discussed and final conclusions are formulated.

2. Materials and Methods

Optimal distribution of LNG as marine fuel in a selected sea area relies on optimal routing, and this is construed as a combination of two interdependent values, namely the routes of sea-going ships and the availability of distribution facilities. In order to find a solution, the size of the LNG fleet and the number of distribution facilities must be defined and arranged in a way that ensures a streamlined operation of the LNG distribution network. Several stages of data analysis must be implemented in order to find the best cost-optimized solution. The problem of routing in the distribution network can be considered in terms of cost effectiveness (e.g., the cost of transportation between locations, the cost of distribution, or the cost of profit); bunkering lead times (frequency of bunkering and time windows); and the sequence of providing bunkers to specific LNG-powered ships, route lengths, and the location and range of service of LNG storage facilities.

A method that can be applied to solve this problem is Mixed Integer Linear Programming (MILP). This method is an optimization tool used in supply chain management [70,71,72]. The LNG supply chain can be analyzed in terms of LNG transportation planning, storage management, distribution planning, cost optimization, or risk management. The implementation of MILP in the MATLAB Mk2 environment allows for the simulation of real input data, enabling the determination of the best solution aligned with the actual situation. The solution can also include economic aspects related to optimal routing, cost minimization, and the timing of LNG distribution operations. This research employed a MILP model that included the following assumptions:

• The price of LNG in 2023 (Figure 2);
• A period of 12 × 30 days;
• The distances from LNG-powered vessels were determined with the anchorage boundary every 0.5 Nm;
• Distribution was by waterway.

The calculations were conducted in the MATLAB Mk2 environment. For the considered LNG distribution optimization task (i.e., finding the minimum cost), the objective function f(x) was defined over the set f(x) → MIN.

$$f\left(x\right)={\sum }_{a=1}^{NU}{\sum }_{b=1}^{NB}{vb}_{a,b}\ast {kb}_{a,b}\ast t_{a,b}+{\sum }_{c=1}^{NP}{kp}_c\ast {vp}_c+{\sum }_{c=1}^{NE}{Ep}_c\ast {ep}_c\to MIN,$$

(1)

where

NU—the number of LNG-powered vessels;

NB_v—the number of LNG bunkering vessels;

NP_v—the number of ports;

NE—emissions;

vb_a,u—the quantity of LNG transported from LNG bunker vessel a to LNG-powered vessel b;

kb_a,u—the cost of transporting LNG from LNG bunker vessel a to LNG-powered vessel b;

t_a,b—the time required for LNG bunker vessel a to reach LNG-powered vessel b;

kp_c—the cost of storing LNG at port p;

vp_c—the quantity of LNG stored at port p;

Ep_c—the emission cost associated with transportation or operations at port p;

ep_c—the amount of emissions at port p.

The input data for a selected LNG NP port with capacity c are defined by the following sequence:

NP = {NP₁, NP₂, …., NP_c}.

(2)

LNG bunker vessels NB_b from Population B were assigned to the selected LNG storage facility NP_c from set NP:

NP_c → NB_b.

(3)

A probabilistic algorithm was developed, defining the set of LNG-powered vessels NU_c,b for the areas served by the LNG bunker vessels NB_b in a specified LNG port NP_c:

$${NP}_c=\left({\mathrm{N}\mathrm{U}}_{{\mathrm{c}}_1,{\mathrm{b}}_1},\mathrm{N}{\mathrm{U}}_{{\mathrm{c}}_2,{\mathrm{b}}_1}\dots {\mathrm{N}\mathrm{U}}_{{\mathrm{c}}_{\mathrm{n}},{\mathrm{b}}_{\mathrm{n}}}\right).$$

(4)

Identification of the minimum number of LNG-powered vessels NU reporting a demand for fuel was calculated as follows:

$$NU=\sum _{\mathrm{b}\in \mathrm{K}}{\displaystyle \frac{d_{\mathrm{k}}}{{\mathrm{v}}_{\mathrm{u}}}},$$

(5)

where

d_k—the fuel demand of the LNG-powered vessels;

v_u—the cargo capacity of the LNG bunkers.

The capacity v_u of LNG bunker vessels was determined by the defined capacity p_i of the LNG facilities at ports p. The limit on the capacity of the LNG bunker vessels was that it must not exceed the individual capacity of each LNG bunker vessel (capacity understood as according to their technical parameters):

$${\sum }_{b\mathsf{ϵ}\mathrm{J}}{d}_{k,u}{\sum }_{b\mathsf{ϵ}\mathrm{J}}{\mathrm{x}}_{\mathrm{k},\mathrm{u}}\le v_u {\forall }_{\mathrm{u}\mathsf{ϵ}\mathrm{P}}.$$

(6)

With emission limits calculated as follows:

$${\mathrm{e}\mathrm{p}}_{\mathrm{c}} \le {\mathrm{E}}_{\mathrm{m}\mathrm{a}\mathrm{x}} {\forall }_{\mathrm{u}\mathsf{ϵ}\mathrm{P}}.$$

(7)

The applied methodology enabled the achievement of the best solution for LNG distribution while optimizing costs and revealing the real demand for the resource.

2.1. Study Area

Considering the availability of data on major traffic streams, the study area was limited to the southern coast of the Baltic Sea. The analysis was conducted for the Baltic Proper (Figure 3) using the data available on sea-going vessels that render services in major traffic streams and taking into consideration the fact that there is no bunkering infrastructure along the coast.

For possible locations of LNG storage facilities, 33 seaports situated along the southern Baltic coast were selected, namely Szczecin, Police, Stepnica, Trzebież, Nowe Warpno, Lubin, Wapnica, Przytór, Świnoujście-Karsibór, Świnoujście, Wolin, Sierosław, Kamień Pomorski, Dziwnów, Mrzeżyno, Dźwirzyno, Kołobrzeg, Darłowo, Ustka, Rowy, Łeba, Władysławowo, Hel, Jastarnia, Puck, Gdynia, Gdańsk, Krynica Morska, Kąty Rybackie, Elbląg, Tolkmicko, Frombork, and Nowa Pasłęka. All the seaports located along the analyzed area are listed. The following very small fishing ports were omitted: Mechelinki, Rewa, Kuźnica, Jastarnia Bor, and Chłapowo. An analysis of the ship traffic volume in the southern Baltic Sea (Figure 4) was carried out in IALA IWRAP Mk2 software. This software supports calculations of frequency with which specific types of sea-going ships pass through a certain sea area based on the characteristics of traffic volume.

2.2. LNG Fleet

Based on the global number of sea-going ships S_1–8, the shares of ships by type S_H were worked out (

Table 3. Global sea-going LNG-powered ships by type in 2021 [77].

Type of Ship	Number of Ships	SH [%]
Tankers	12,802	0.130
Bulk carriers	10,650	0.108
Container ships	5009	0.051
Specialized vessels	30,193	0.308
General cargo carriers	10,973	0.112
RO-RO/Passenger ships	2236	0.023
Cruise ships	5288	0.054
Other	21,021	0.214
Total	98,172	1

).

$${ NS}_K=\left({\displaystyle \frac{N{U}_H}{\sum {NU}_{1-8}}}\right)\left[\%\right],$$

(8)

where

NU_H—the number of ships of one type;

NU_1–8—the total number of ships by type.

The sea areas along the southern coast of the Baltic Sea are frequented by various types of sea-going ships, which can use the services of 17 Polish ports. The ports were selected on the basis of the number and size of marine units handled.

Detailed information on the status quo of the maritime economy for the area under analysis, represented by the number of ships calling at selected ports, is shown in Figure 5 below.

Since the Sulfur Directive came into force, the number of orders for LNG-powered sea-going ships has been on a continuous upward trend [23]. The growth can be especially observed in the SECAs. The number of newly built ships powered mainly with LNG has been increasing year-on-year.

Since 2011, a daily average of two thousand sea-going ships has rendered services in the Baltic Sea, and the number has been on a continuous upward trend compared to the period before 2021. The growth corresponds to the fact that transport services performed in the Baltic Sea account for 15% of the global trade. Slight drops are caused by the withdrawal of ships that have reached the end of operating life [79].

On the basis of the above, a conclusion can be drawn that port infrastructure capable of providing bunkering services to LNG-powered sea-going ships along the Polish coast is absolutely necessary. Investment in LNG distribution will open the door to the development of local LNG transport branches, especially for LNG bunkering services. Construction of facilities suited for LNG operations will contribute to the development of local ports and their cargo handling capacity.

Currently, LNG ship traffic is observed along the southern part of the Baltic Sea. However, it is not as intense compared to other parts of the world, such as the United States coast. The number of LNG vessels in the analyzed area is increasing due to the LNG terminal in Świnoujście and the potential further development of infrastructure. The importance of the region is also growing. The southern part of the Baltic Sea is one of the most important transport corridors. The regularity of ship traffic, which has been adapted to market needs, will increase along with the demand for LNG. Therefore, an increase in the number of ships can be expected in the future. The LNG terminal in Świnoujście is a key piece of infrastructure and the only distribution point in the region and the demand for LNG along the southern Baltic Sea is clearly visible and growing. It is essential to establish a distribution fleet and LNG infrastructure capable of meeting the demand for resources.

3. Results

For the purpose of specifying the best locations for LNG bunkering stations, 33 ports situated along the Polish coast were selected. For each port, 20 Nm, 30 Nm, and 50 Nm ranges of service were set (where 1 nautical mile (NM) is equal to 1852 m), within which LNG bunkering vessels would be able to meet demand for fuel from all LNG-powered vessels in the area.

For further analysis of the ranges of service, 17 ports rendering commercial services were selected, namely Gdańsk, Gdynia, Szczecin, Świnoujście, Police, Darłowo, Elbląg, Frombork, Hel, Kołobrzeg, Krynica Morska, Międzyzdroje, Sopot, Stepnica, Trzebież, Ustka, and Władysławowo (Figure 6). The task was completed using MATLAB R2019a–Mapping Toolbox software. The ports were also analyzed for the number of calling ships, by type: tankers, bulk carriers, container ships, specialized vessels, general cargo ships, dry cargo barges, RO-RO/passenger ships, and cruise ships. The fields that were not covered between individual ports were characterized by the small number and size of marine units served. Consequently, the number of LNG-powered vessels served by these ports will be small and the fuel requirements can be covered within the LNG bunker coverage area of the nearest LNG storage facility.

The analysis shows that, within the range of service of 20 Nm, the optimal locations of the LNG facilities would be in five ports along the southern coast of the Baltic Sea. To summarize, locations of LNG storage facilities or bunkering stations along the southern coast of the Baltic Sea were determined considering the following factors:

• The number of sea-going ships calling at the ports;
• The size of ships calling at the ports;
• The surface area of the overlapping ranges of service.

Further analysis covered five ports, namely the following:

• Świnoujście;
• Kołobrzeg;
• Darłowo;
• Gdynia;
• Krynica Morska.

The other ports were discarded due to the characteristics of the calling ships. Considering the small numbers and sizes of ships operating in those sea areas, it can be inferred that the number of LNG-powered ships calling at those ports was insignificant (as the demand for fuel can be met by the closest LNG storage facility in the area).

Based on the above, a yearly forecast of the ships that may use LNG as marine fuel was made (Figure 7).

For the purpose of the determination of the yearly demand for LNG, the average yearly LNG consumption by ship type (Figure 8) and the forecast number of LNG-powered ships that can be bunkered in the specified ports were used.

Further analysis, in the form of computer simulations, was carried out in MATLAB R2019a software. It is worth noting that the parameters for the simulations were based on real data, namely the following:

• Location of seaports;
• Technical parameters of the LNG-powered ships classified by type (tankers, bulk carriers, container ships, specialized vessels, general cargo carriers, RO-RO/passenger ships, cruise ships, and other) and fuel tank capacity.

Additionally, a service area was assigned to each port, which extended up to the port’s anchorage perimeter:

• Świnoujście—up to 11 Nm;
• Darłowo—up to 2 Nm;
• Kołobrzeg—up to 1.5 Nm;
• Gdynia—up to 2.5 Nm;
• Krynica Morska—up to 1 Nm.

For the purpose of the model, the LNG bunkering position was assumed to be within a radius of 0.5 Nm from the port under analysis. Fifty simulations, performed for each port separately, generated solutions for 365 days (

Table 4. Results of the simulations for Świnoujście for 10 days.

Port of Świnoujście
Day	Type of Ship *	Requested LNG Volume [m3]	Distance [Nm]	Type of Ship *	Requested LNG Volume [m3]	Distance [Nm]
1	0	0	0	0	0	0
2	0	0	0	0	0	0
3	4	399	6.5	0	0	0
4	8	24	7.5	1	0	0
5	1	1728	8.5	0	0	0
6	1	1728	7.5	0	0	0
7	2	130	9.5	0	0	0
8	2	130	7.0	5	125	8.0
9	0	0	0	0	0	0
10	2	200	9.5	1	619	7.5

* 1. Tankers, 2. Bulk carriers, 3. Container ships, 4. Specialized vessels, 5. General cargo carriers, 6. RO-RO/Passenger ships, 7. Cruise ships, 8. and Other.

):

• The number of LNG-powered ships and their types;
• The requested volume of LNG;
• The distance of LNG-powered ships from the LNG terminal (storage facility) under analysis.

For example, on the 10th day, two ships called at the port of Świnoujście with the following characteristics:

• A bulk carrier requesting 200 m³ of LNG at a distance of 9.5 Nm from the port;
• A tanker requesting 619 m³ of LNG at a distance of 7.5 Nm from the port.

As a result of the analysis, the yearly demand for LNG for each port was worked out (Figure 9).

A conclusion can be drawn that the considerable differences that can be observed in the demand for LNG in specific ports results from the port size, i.e., the number and size of LNG-powered ships calling in a year.

The simulations also permitted determining the bunkering lead time and the distance that an LNG bunkering vessel has to cover for 365 days for each port separately via taking into consideration the following parameters:

• The type of LNG-powered ship;
• The requested amount of LNG [m³];
• The loading rate [m³/h] (amount of fuel received in a time unit);
• The distance between facilities [Nm];
• The speed of the LNG bunkering ship [kn].

The bunkering lead time and the highest and lowest requested volume of LNG were determined for the LNG storage facilities located in the ports of Świnoujście (

Table 5. The lead time of the LNG bunkering service for the port of Świnoujście.

Type of Ship	Requested LNG Volume [m3]		Loading Rate [m3/h]		Speed of LNG Bunkering Ship [kn]		Bunkering Lead Time [h]
	MIN	MAX	MIN	MAX	MIN	MAX	MIN	MAX
Tankers	325	2000	500	1200	10	14	1.6	3.0
Bulk carriers	110	500	500	500	10	10	1.3	2.2
Container ships	490	18,600	500	1200	10	14	2.1	17.1
Specialized vessels	70	450	500	500	10	10	1.2	2.0
General cargo carriers	63	450	500	500	10	10	1.1	2.0
RO-RO/Passenger ships	25	500	500	500	10	10	1.1	2.0
Cruise ships	10	3400	500	1200	10	14	1.1	3.6
Other	25	800	500	1000	10	10	1.1	1.9

), Darłowo, Kołobrzeg, Gdynia, and Krynica Morska. The lead time was worked out for one LNG bunkering ship as a function of the loading rate and the volume of fuel received.

The simulations carried out for the specified ports permitted the specification of the capacities of the LNG storage facilities that are required to meet the demand for LNG in their respective areas (

Table 6. LNG infrastructure in specific ports.

Facility	Port	Bunkering	Size of LNG Storage Tanks
Small handling capacity	Darłowo Krynica Morska Kołobrzeg	Import terminals capable of bunkering <10,000 m3/year	1000 m3
Medium handling capacity	Świnoujście	Import terminals capable of bunkering 10,000–100,000 m3/year	25,000 m3
High handling capacity	Gdynia	Import terminals capable of bunkering >100,000 m3/year	3 × 25,000 m3

). The size and type of LNG infrastructure in a particular port depends on the services rendered.

These analyses covered the 35 sizes of LNG bunkering ships (

Table 7. Parameters of the LNG bunkering ships under analysis.

Name	Gas Tank Capacity [m3]	Speed [kn]	Loading Rate [m3/h]
DALIAN 1 G8500-1	8330	10.00	1200
BUNKER BREEZE	7800	10.00	1200
HYUNDAI MIPO 8250	7521	13.50	1200
KAIROS	7521	13.50	1200
SM JEJU LNG1	7501	13.00	1200
KEPPEL SINGMARINE H410	7500	14.00	1200
CORAL METHANE	7401	14.00	1200
KEPPEL SINGMARINE H400	7350	14.00	1000
KEPPEL SINGMARINE H401	7350	14.00	1000
NANTONG CIMC SINOPACIFIC S1049	7350	14.00	1200
NANTONG CIMC SINOPACIFIC S1050	7350	14.00	1200
SAMSUNG 2234	7350	14.00	1200
SM JEJU LNG2	7350	14.00	1200
CARDISSA	6469	10.00	1200
CORAL ANTHELIA	6443	15.50	1200
DAMEN GORINCHEM 559014	6000	13.40	1000
ELENGER	6000	13.40	500
ESTI GASS	6000	13.40	1000
KEPPEL SINGMARINE H414	5800	12.00	1000
CORALIUS	5781	13.50	1000
ENGIE ZEEBRUGGE	5000	10.50	1000
AKEBONO MARU	3515	13.00	500
KAGUYA	3500	12.00	500
KAWASAKI SAKAIDE 1744 (EX-2020)	3500	12.00	500
LNG LONDON	3000	10.70	500
JMU ARIAKE	2500	14.00	1200
KAKUYU MARU	2488	14.90	500
SHINJU MARU 1	2487	12.70	500
SHINJU MARU 2	2485	13.00	500
NORTH PIONEER	2462	13.30	500
CLEAN JACKSONVILLE	2200	8.00	500
PIONEER KNUTSEN	1078	14.00	500
OIZMENDI	600	9.30	500
FJALIR	167	12.50	500
LNG SE-601	3000	10.00	1000

).

Based on the resultant characteristics of the LNG infrastructure, the number of LNG bunkering ships and their sizes were determined for each port under analysis required to meet the total demand for LNG in its respective service area (

Table 8. Characteristics of the LNG bunkering ships.

Port	LNG Bunkering Ship’s Capacity
Świnoujście	Less than 3000 m3
Gdynia	5500–8000 m3
Darłowo	Less than 3000 m3
Kołobrzeg	1000–8000 m3
Krynica Morska	1000–3000 m3

).

The above figures permit a specification of the number of LNG bunkering ships required to meet the total demand for LNG from ships operating in the southern Baltic Sea (

Table 9. The number of LNG bunkering ships by port.

Port	LNG Bunkering Ships
Gdynia	3 × > 5500–8000 m3
Świnoujście	3 × ≤ 1000 m3 2 × 1000–3000 m3
Darłowo	2 × ≤ 1000 m3 1 × 1000–3000 m3
Krynica Morska	1 × 1000–3000 m3
Kołobrzeg	1 × 1000–3000 m3 1 × 3500–4000 m3 2 × 5500–8000 m3

).

Each simulation generated a graph of the objective function values (Figure 10). The initial values varied because they were generated randomly. The achievement of the best solutions was indicated by a decrease in the objective function value. Any increases suggest the presence of a random factor that does not enhance the solution quality. Consistent and repeating values of the objective function suggest that the best solution has been reached. This means that additional simulations are unlikely to produce substantial improvements in the final result. The optimal solution was identified as suitable and acceptable according to all established criteria.

The correctness of the task solution was determined, categorized by days, based on the distribution of the number of ships entering various ports from 2018 to 2022. The distribution of the port entry frequencies was a normal distribution, indicating that the sample size criterion (N < 100) was met. A Shapiro–Wilk test, with a significance level of α = 0.05, was used to examine the distribution (

Table 10. The Shapiro–Wilk test for the selected port.

Parameter	2018	2019	2020	2021	2022
Test value	0.968	0.969	0.969	0.9389	0.9391
Critical value	0.953	0.958	0.959	0.959	0.961
	Normal distribution

).

A normal distribution was subsequently fitted to the frequency of the port entries in Świnoujście. It was shown that the expected value and standard deviation could be determined (Figure 11).

Conducting the distribution study was very important for the correctness of the model. This study demonstrated that it is a normal distribution and that it is possible to create a task that will provide solutions for the optimization algorithm. This means that, with knowledge of the distribution of LNG-powered ships entering various ports around the expected value, it is possible to present a solution for the real situation.

4. Discussion

The created model has a universal character. Due to the constantly increasing number of the LNG fleet, it is necessary to forecast the number of LNG ships. The formula for calculating the forecasted number of LNG ships can be based on several variables, including historical growth trends, plans for new ship orders, the rate of decommissioning old ships, and various market and regulatory factors. One of the simpler models that also can be applied is the exponential growth model [80]. Among other things, the exponential growth model is characterized by its ease of implementation. It incorporates a minimum number of variables, which enables predictions to be made quickly. Exponential growth is used to describe situations in which a phenomenon grows at a rate proportional to its current size. This means that, in the case of the number of LNG vessels, if the market is growing rapidly due to increasing demand for LNG, exponential growth may be an appropriate model. As shown above, this formula is useful when forecasting the development of new markets or technologies, where growth in the development phase can be very fast and then stabilizes, which may be the case for LNG infrastructure development, where rapid growth can be expected in the early years.

Simple means that there are no complicated assumptions on variables and a small number of parameters as the formula uses basic variables (initial value, constant growth rate, and time). Above that, its universality is worth noting (phenomena in nature and processes in economics show exponential growth, at least in the initial phases). The exponential growth model is widely used in many fields (biology, accounting, etc.), which demonstrates its adaptability [81,82,83].

$$F\left(t\right)=F_0{e}^{st}$$

(9)

where

F(t)—the forecasted number of LNG-powered ships at the time t;

F₀—the present number of LNG-powered ships;

s—the growth rate of the number of LNG-powered ships;

t—the time (number of years from the starting point);

e—the base of the natural logarithm (approximately 2.71828).

Based on the above formula, it was concluded that the number of LNG-powered ships in the Baltic Sea will increase eightfold within 10 years. Therefore, the construction of appropriate LNG infrastructure in the southern part of the Baltic Sea is essential.

In this study, the LNG distribution model was constructed using MILP, which enabled the identification of a supply chain structure that minimizes economic aspects. The mathematical model is applicable to similar problems, such as the following:

• The supply chain in the Caribbean [84];
• The coast of Finland (69 receivers across Finland and 9 ports along the Finnish coastline of the Baltic Sea) [85].

By employing the MILP model (which is adaptable), the LNG supply chain in the Baltic Sea can define decision variables (such as LNG demand, the number of LNG bunker vessel routes, and storage periods) and continuous variables (such as transportation costs, distribution operation time, and the volume of stored material) with constraints like storage capacity or maximum LNG demand. MILP helps determine the efficiency and reliability of the LNG supply chain, which is the basis for a stable and cost-effective resource delivery in the southern part of the Baltic Sea.

The area of the Baltic Sea under analysis shows great development potential regarding the LNG industry. The requirement of diversification of natural gas supplies is met owing to the LNG terminal in Świnoujście, which receives LNG supplies from various parts of the world. In view of establishing an LNG infrastructure along the southern Baltic coast (the research problem), the authors propose a solution using computer implementation of a model built in MATLAB R2019a software. The solution to the research problem is a task that can be classified and presented as an NP-Hard problem with multiple possible solutions. LNG distribution facilities must be situated in locations that ensure that LNG bunkering ships can meet demand for fuel while covering the shortest possible distance within the shortest possible time. Five seaports along the southern coast of the Baltic Sea were selected as the best locations for the LNG infrastructure:

• Gdynia;
• Świnoujście;
• Darłowo;
• Krynica Morska;
• Kołobrzeg.

LNG storage facilities in the ports have been located with a view to meeting the total demand for LNG within their respective service areas. The number of LNG-powered ships and demand for LNG were determined, and each of the ports were assigned a specific number of LNG bunkering ships to cover the total demand for LNG. The real locations of LNG storage facilities are specified taking into consideration the number of LNG-powered ships that render services in the respective areas. The distance which the LNG bunkering vessels have to cover from an LNG storage facility to the position of an LNG-powered ship are specified based on radially set routes.

The conclusions comprise calculations that were made based on statistical, as well as forecast, data. Additionally, the solution to the problem includes the shortest bunkering lead time based on data on the capacity of the LNG-powered ship and its distance to the LNG facility.

Precise figures have been provided for the following:

• The number of LNG bunkering ships used;
• The demand for LNG as shipping fuel;
• The distance covered by an LNG bunkering ship;
• The LNG bunkering lead time.

For each port under analysis, a set of LNG bunkering ships and LNG-powered ships were determined. Significant discrepancies could be observed in the yearly demand for LNG as shipping fuel in the ports under analysis. For example, the port of Świnoujście was on one end of the scale and showed double the demand for the port on the other end of the scale. The discrepancies can be explained by the fact that various sizes and types of ships are provided services within a period of 365 days. A port supplying LNG to large sea-going ships will show the greatest demand.

Last but not least, it is worth noting why ports as tiny as Darłowo and Krynica were not excluded from the analysis. The offshore wind farm investment project, implemented in the Baltic Sea, will certainly intensify vessel traffic in the area and attract new investors from the energy and oil and gas (pipelines) sectors. Construction of offshore wind farms will drive the development of the coastal regions and the entire country on many planes. In the shipping sector, a niche will be created for services such as maintenance, construction, and modernization of the infrastructure [86].

A detailed analysis of the results showed that demand for LNG in the port of Krynica Morska fell between 0.132–0.292 thousand m3, which accounts for 0.37% to 1.21% of the demand for LNG in the port of Gdynia. It was concluded that moving the service of LNG distribution from Krynica Morska to Gdynia will have no impact on the distribution network in the latter port. What is more, the distance between the two ports is only 32.9 Nm, i.e., Gdynia and Krynica Morska provide services in the same sea area. This paper proposes a solution for an optimal LNG distribution network. Therefore, it would be economically justified to discard the port of Krynica Morska from the project.

The problem was solved in terms of the following constraints:

• Temporal;
• Individual LNG bunkers, which are assigned a specific LNG bunker;
• Each LNG-fueled unit, which are assigned to exactly one LNG bunker;
• The existence of only one start and end point;
• The capacity of individual LNG bunkering units cannot be exceeded.

Considering the above, the optimal LNG bunkering infrastructure along the southern coast of the Baltic Sea would include the following ports:

• Gdynia;
• Świnoujście;
• Darłowo;
• Kołobrzeg.

Discarding the port of Krynica Morska as an LNG distribution station is further justified by the fact that a floating storage regasification unit (FSRU) is planned to be constructed in the vicinity of Gdańsk, which will support LNG operations, such as discharge, storage, and regasification. The demand for LNG from the port of Krynica Morska will be fully covered by the port of Gdynia, where, in a future investment project, specialized infrastructure will be built to receive additional supplies of LNG by sea [87].

5. Conclusions

The important role of LNG as an alternative fuel can be explained by, inter alia, its contribution to reducing harmful emissions and ensuring compliance with strict environmental regulations. LNG is an eco-friendly fuel, and its market price has been on a downward trend.

Vehicles designed to be powered by LNG, such as buses or tractor units, are growing in number. LNG is also used as marine fuel, with the LNG fleet expanding and driving the demand for LNG. However, sea-going fleets that use new technologies face the problem of unavailability of LNG at sea and a lack of LNG bunkering infrastructure. Expansion of the LNG-powered fleet is bound to drive the development of LNG handling, storage, and bunkering infrastructure.

The research topics were approached due to the following:

• LNG distribution issues in the southern part of the Baltic Sea;
• The projected size of the LNG fleet in the Baltic Sea;
• The lack of research results determining the real demand for LNG as bunker fuel in the Baltic Sea;
• The lack of LNG infrastructure in the southern part of the Baltic Sea.

Therefore, this paper proposes the size of the distribution of LNG as a marine fuel using the example of the southern Baltic Sea. This paper presents the distribution network for LNG as a marine fuel in the southern Baltic Sea. An analysis of ship traffic intensity was presented and the demand for LNG as a bunker fuel was determined. As a result, LNG storage locations were identified (Gdynia, Świnoujście, Darłowo, Kołobrzeg, and Krynica Morska) that will be able to supply marine vessels with fuel. Five ports were indicated for which LNG infrastructure should be developed to meet the demand for the resource, along with the adjustment of an appropriate LNG bunkering fleet. LNG is increasing in popularity owing to the safety of its carriage compared to oil products (in the event of a leakage, LNG, being lighter than air, evaporates, whereas conventional fuel fumes sink and may create explosive mixtures). However, it is important to remember that LNG is currently a popular choice in the maritime sector due to its lower emissions compared to traditional fuels and the availability of technology and infrastructure. However, with increasing decarbonization requirements, LNG is considered a temporary solution that will be replaced in the future by more sustainable fuels and technologies.