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Optimal design of a small-scale LNG supply chain combining sea and land transports Alice Bittante, Raine Jokinen, Jan Krooks, Frank Pettersson, and Henrik Saxen Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b01061 • Publication Date (Web): 07 Sep 2017 Downloaded from http://pubs.acs.org on September 16, 2017

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Industrial & Engineering Chemistry Research

Optimal design of a small-scale LNG supply chain combining sea and land transports Alice Bittante†*, Raine Jokinen‡, Jan Krooks§, Frank Pettersson† and Henrik Saxén†. †

Åbo Akademi University, Thermal and Flow Engineering Laboratory, 20500 Turku, Finland.

‡

Pöyry, 01620 Vantaa, Finland.

§

Wärtsilä-Energy Solutions, 65100 Vaasa, Finland.

KEYWORDS Energy Systems; MILP; Optimization; Small Scale LNG; Supply Chain.

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ABSTRACT

A mixed integer linear programming (MILP) model for optimal design of small-scale supply chains of liquefied natural gas (LNG) is presented. LNG is delivered from supply terminals to receiving (satellite) terminals by ship transportation, and by land-based truck transportation to customers on or off the coast. The objective is to minimize the overall cost, considering fuel price, investment and operational costs. Demands not satisfied by LNG are taken to be satisfied by an alternative fuel. The results of the optimization provide information about the location of the satellite terminals, their capacity, the optimal maritime and land-based fleets, the travelling routes, and the amount of LNG to be supplied to the demand sites. The model is illustrated by a case study in the region around the Gulf of Bothnia. The short computational time required to solve the optimal solution makes the model ideal for use in studies of potential future scenarios.


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1. INTRODUCTION Natural gas (NG) is the fastest growing energy source among the fossil fuels. Its global demand is growing at an average rate of 1.8 % per year, compared to 0.9 % for oil.1 According to the International Energy Agency (IEA), the natural gas consumption is expected to reach 5.4 trillion cubic meter in 2040, replacing coal and becoming the second largest fuel source after oil.2 Liquefied natural gas (LNG) is today playing a very important role in the supply chain of natural gas, since it can be used to supply energy to very remote or stranded sites, for which pipeline delivery is impossible or infeasible. Its share of the world energy demand is expected to grow from 10 % to reach 15 % in 2035, surpassing NG supplied by pipeline.1 LNG is produced by cooling natural gas below -162 °C (at atmospheric pressure), which reduces the volume to approximately one six-hundredth of the original one. NG in liquid form can be economically transported over long distances by specially designed vessels, which are able to keep the fuel in liquid state. Traditional LNG supply chains deliver large volumes over distances of thousands of kilometers with LNG cargo ranging between 125,000 m3 and 160,000 m3 in capacity.3 In recent years a new market segment of small-scale LNG logistic chains has become more important,3,4 supplying gas for more local demand. The increasing energy demand and the constraints imposed by environmental regulations have in many countries promoted the use of LNG for medium- and small-scale applications, where NG pipelines are absent or unpractical, e.g., for small and sparsely distributed demands. The recently introduced sulfur emission control areas of the International Maritime Organization (IMO) also serve to increase the popularity of LNG use as fuel in ships.5 The use of LNG for heavy vehicles (trucks, tractors, dumpers, etc.) is also gaining popularity due to low CO2, SOx and NOx emissions, as well as low maintenance costs. In a small-scale supply chain, LNG is shipped from larger supply terminals to customers through a network of satellite terminals with a combination of sea- and land-based transport. The design of such supply networks is a challenging task and the high costs of both infrastructure and operation 3 ACS Paragon Plus Environment


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make it a relevant problem for mathematical optimization. Both tactical and strategical aspects are involved in the design of such LNG logistic chains. Tactical planning addresses the vehicle routing problem (VRP), for both the maritime and land transports, while strategic planning deals with decisions regarding location of satellite terminals and size of the optimal fleet to solve the overall transportation problem. Vehicle routing problems are a well-established area of research with a rich literature tackling different aspects of the problem. A recent review on VRP6 classifies 277 papers published during the period 2009-2015, revealing a broad range of problems as variants of the classical VRP. The problem we study in this paper is inspired by real-life cases and it is therefore a special variant of a combination of the classical problems. The single tactical aspect of the problem is very similar to the so-called fleet size and mix vehicle routing problem (FSMVRP) while the addition of the strategic part makes it similar to the location routing problem (LRP). A review paper on both maritime and land transport for the FSMVRP was presented by Hoff et al.7 Most of the literature in this field is based on heuristic methods, as the one proposed by Salhi and Sari,8 which differs from our deterministic approach. Exact formulations have also been applied; Jokinen et al.9 proposed a mixed integer linear programming (MILP) model for an LNG transportation problem along a coastline, using a one-dimensional approximation of the spatial problem, while Baldacci et al.10 designed an MILP model to solve a similar two-dimensional problem, but each customer was associated with a single route. A paper by Koza et al.11 proposes a path-flow model to solve an infrastructure and fleet size problem in the liner shipping business. They focus on large-scale LNG supply and therefore exclude load split deliveries and satellite terminal locations, which are central features in our study. A very recent paper by Zhang et al.12 applied a hybrid method on an LNG supply problem along a river also including land transportation. The authors address uncertainty in demands and LNG price by stochastic programming.


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The model proposed in the present paper tackles a two-dimensional spatial problem and allows for multiple visits at the customers by multiple vessels, as it has been developed on the basis of the MILP formulation presented by Bittante et al.13 The strategic part concerning the location of the satellite terminals is addressed in problems known as two-echelon location routing problem (2ELRP). An extensive review on recent papers in this specific field is included in a general survey of the classical LRP by Drexl and Schneider.14 Gonzalez-Feliu15 proposed a mixed integer programming (MIP) formulation for the generic NE-LRP based on set-partitioning problems and three sets of variables indicating the activation of the satellite terminal (binary), the activation of the route (binary) and the delivery associated to the route (floating point). The same sets of variables are also used in the formulation of the problem tackled here, but we substitute the route activation binary variable with an integer variable, thus allowing for multiple visits to the same satellite terminal or customer. The paper presents an MILP model where both the tactical and strategic aspects of designing a small-scale LNG supply chain are optimized simultaneously. The model is illustrated on the problem of delivering LNG to an emerging gas market in the northern part of the Baltic Sea region.

2. PROBLEM DESCRIPTION In this work we developed a mathematical model for solving a regional supply problem of LNG from a set of potential supply ports to inland end customers, through a set of potential satellite terminals. The LNG is transported from the supply terminals to satellite terminals by ship and from the supply or satellite terminals to the inland customers by truck. Potential satellite terminals and inland customers have given demands for the time horizon considered. The inland customers may represent center sites of clusters of consumers. If a satellite terminal is built, the total amount of LNG to be delivered from the supply ports to it is the sum of the satellite terminal’s demand and the demands of the customers associated to it in the optimized solution. Alternatively, demands can be 5 ACS Paragon Plus Environment


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fully or partially fulfilled by an alternative fuel, for which transportation cost is not considered. This fuel is merely used to allow the model to partly or fully exclude customers from the LNG supply chain. A heterogeneous fleet of rented vessels, each with a given capacity, cruising speed, fuel consumption and loading/unloading rate, performs the maritime transportation. Some types of vessels can perform split delivery. None of the ships are associated with a specific port and therefore they are not forced to return to the same supply port they departed from. On the other hand, some vessels can be restricted from visiting certain ports due to incompatibility with the port specifications (i.e., port depth). Restrictions regarding the maximum amount of LNG available at the supply ports are included in the formulation and can be parametrically activated. Land transportation is carried out by a homogeneous fleet of LNG tank trucks of given capacity and fuel consumption. Trucks are associated to a single supply or receiving terminal, have a maximum distance they can cover and are not allowed to perform split delivery. Customers are assumed to have large enough storage capacity to stock the full LNG demand for the time period. No tank investment costs are considered at this sites since the supply chain to be optimized is taken to end at the customers’ sites. By contrast, when a satellite terminal is activated, a storage tank must also be constructed and the associated size-dependent investment costs are imposed. This storage size is calculated as the problem is solved. Maritime distances between all ports and road distances between terminals and customers are given. The aim of the model is to solve the overall LNG distribution problem, selecting the most suitable ports, if any, where satellite terminals should be built and the size of the LNG storages, the optimal fleet and routing for the maritime transportation, the number of LNG tank trucks for each port, and the port-customer connections to satisfy the inland demand.


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3. MATHEMATICAL MODEL This section introduces the mathematical model designed to solve the fuel procurement problem described in the previous section. Subsection 3.1 defines the sets and variables, followed by a description of the objective function in subsection 3.2 and the constraints in subsection 3.3.

3.1. Sets and Variables In the mathematical formulation, let be the index set of ports , and denote the set of customers of given demand . Let ⊂ be the subset of satellite terminals which receive LNG from supply ports ∈ through a fleet of ship types ∈ . As is also subset of , the energy demand in the satellite terminal can also be satisfied by trucked LNG and/or by an amount of alternative fuel . Likewise, inland customers ∈ can be satisfied by LNG or alternative fuel. Ship routing is modelled with three sets of variables. Let integer variables ,, and denote the number of times a ship of type travels between ports and , and the number of ships of type needed, respectively. Let variables ,, indicate the number of LNG loads of ship of type that is transported between ports and . The land transport is also expressed by the use of three sets of variables. Let variables , indicate the total amount of LNG transported by truck from port to customer . Let integer variables denote the number of trucks allocated to port , and integer variables , give the total number of trips undertaken between and . Two sets of variables are introduced to handle the activation of satellite terminals. Binary variables specify the activation of the satellite terminal while variables give the corresponding size of the storage.

3.2. Objective Function The goal is to minimize the total combined cost associated with the fuel procurement min!" = "$ + "& + "' (,

(1) 7 ACS Paragon Plus Environment


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where the cost functions are expressed as "$ = ∑*∈1 ∑∈/ ∑∈. "*+ , *,, + ∑*∈1 ∑∈0 "*+ *, + ∑∈0 " ,

(2)

"& = 0 ∑(,)∈4 ∑∈. " ,, + ∑∈. 5"/ + ∑(,)∈4 ∑∈. "6 7, ,, + 2 ∑∈4 ∑∈0 " 6 7, , ,(3)

"' = 9: ∑;4 + ∑∈/( < + 1 )=.

(4)

The first term, "$ , represents the fuel cost, given as the amount of LNG and/or alternative fuel used multiplied by the specific fuel price. The second term, the transportation cost "& , is the sum of costs of port calls, chartering of the ships, ship propulsion and truck fuel consumption. Finally, the third term, "' , is the investment, including purchase of the trucks and the construction of the satellite terminals. The latter is expressed by a fixed cost and a capacity dependent factor. The factor 9 rescales the total investment cost to the contribution for the time horizon 5 considered in the optimization, including interest rate, >, according to ?

D

9 = '@A B ∙ $E($FD)GH

(5)

where I is the project length of the investment expressed in years.

3.3. Constraints Constraints are needed to ensure that the demand is fulfilled at the satellite terminals and at the inland customers. At a satellite terminal that is activated, the net amount of LNG shipped to the port minus the LNG transported by truck from the port must at least equal the demand at the port. If, in turn, the satellite terminal is not activated the demand can be satisfied by alternative fuel or by LNG supplied by truck. This gives the condition ∑∈4 ∑∈. , ,, − ∑K∈/ ∑∈. , ,K, + ∑∈4 , − ∑∈0 , + ≥ 5 ∀ ∈ .

(6)

For inland customers, the demand is satisfied either by LNG from land transports or by alternative fuel 8 ACS Paragon Plus Environment

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∑∈4 ,O + O ≥ 5O ∀ ∈ .

(7)

The activation of the satellite terminal is defined by ∑∈4 ∑∈.:,, + ,, = ≤ Q ∀ ∈ ,

(8)

where Q is a big-M parameter. If the satellite terminal is activated ( = 1), the variable indicating the size of the tank storage is allowed to take values greater than zero, thus implying the existence of a storage, by the constraint

≤ Q SGWhW ∀ ∈ .

(9)

where the unit reported in brackets is multiplied for dimensional consistency. The size of the storage, , must be greater than the net LNG shipped to the port plus a storage heel (1 − X 1 ) ≥ ∑∈4 ∑∈. , ,, − ∑K∈/ ∑∈. , ,K, ∀ ∈ .

(10)

where the heel is expressed as a fraction, X 1 , of the total storage capacity. Land transportation is controlled by five sets of constraints. Land transportation of LNG from a non-activated satellite terminal is banned by the condition ∑∈0 , ≤ Q SGWhW ∀ ∈ .

(11)

The number of truck voyages from port to customer required to deliver the amount of LNG, , , is obtained from , ≥

YZ,[ \

∀ ∈ , ∈ .

(12)

as trucks are allowed to have partial loads. The number of trucks at each port must be sufficient to carry out the delivery of LNG within the available time horizon. An availability factor ] is applied to adjust the time horizon according to specific restrictions on the vehicles. The time needed to travel the port-to-customer distance including a fixed refilling time, ^ _ , has to satisfy the condition &

0 ]5 ≥ ∑∈0 `a 7, + ^ _ b , ∀ ∈ ,

(13)

where the average speed of the truck is c.



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Furthermore, two sets of constraints were introduced to limit the number of trucks and the number of truck voyages from port , based on the number of loading stations and loading time restrictions at the port, so ≤ de SdW ∀ ∈ .

(14)

A

∑∈0 , ≤ 5de ∀ ∈ .

(15)

g

where parameter de represents the maximum number of truck loads per day available at each port on the basis of loading stations and operation time. This is also taken as maximum number of trucks per port, in the case of every truck being loaded once a day (eq 14). In eq 15 the ratio 5/7 represents the number of working days per week, as we assume that the land transport is available only during weekdays. Ship routing is controlled by six sets of constraints. The integer variables ,, , indicating the number of voyages undertaken by a ship of type between ports and , are defined based on the variables ,, , connected to the amount of LNG transported on the same arc ,, ≥ ,, ∀ ∈ , ∈ , ∈ .

(16)

Route continuity is guaranteed by ∑∈4 ,, = ∑∈4 ,, ∀ ∈ , ∈ ,

(17)

while intermediate loading at the satellite terminals during multistep voyages is banned by ∑∈4 ,, ≥ ∑K∈/ ,K, ∀ ∈ , ∈ .

(18)

h , split delivery is technically infeasible and a minimum load is For a specific set of ship types, required for safety in operation. The set of constraints (19) bans multistep voyages while constraints (20) impose the minimum load, expressed as fraction, X, of the total capacity of the ship h, ∑(,K)∈/ ,K, = 0 ∀ ∈

(19)

h. *,, ≥ X*,, ∀ ∈ , ∈ , ∈

(20)


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Similarly to the constraints (13) for the land transportation, the number of ships of each type is determined based on the time usage expressed as the time spent on travelling the routes, summed with the time at the port for berthing operation and the loading and unloading processes, so ] 5 ≥

$

aj

∙ ∑(,)∈4 7, ,, + ∑∈4:^k ∑∈4 ,, = +

&

lj

∑*∈1 ∑∈/ , *,, ∀ ∈ , (21)

where c is the speed of ship type . Two extra sets of constraints are available to model possible terminal restrictions. Constraints (22) limit the amount of LNG available at supply port , while constraints (23) impose a limit (,e ) on the maximum ship size allowed to visit port . ∑∈/ ∑∈. , *,, + ∑∈0 *, ≤ 5,*e ∀ ∈ ,

(22)

, ,, ≤ ,e ,, ∀ ∈ , ∈ , ∈ .

(23)

It should be noted that when > 1, constraint (21) gives an approximation of the number of ship types needed to solve the routing problem, as it lumps together the time usages of all the ships of the same type. As an alternative, an exact formulation is obtained by converting to a binary variable and introducing multiple ships of the same type in the set . However, this results in more and variables, making the optimization problem larger and its solution more time consuming. Therefore, the approximate equation was used first and, if > 1, a run with the exact formulation was performed to ensure the feasibility of the solution.

4. CASE STUDY This section presents a case study where the model is applied to optimize the energy supply to a region. Subsection 4.1. describes the problem and presents the parameters used in the model equations, followed by a report of the model’s results for a base case in subsection 4.2. A sensitivity analysis of the results is presented in subsection 4.3, where the effect of key parameters is analyzed.

4.1 Problem Formulation and Model Parameters



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During the last few years LNG has attracted large attention in the region around the Baltic Sea as a more environment-friendly fuel for both ship propulsion and heat and power generation. Several projects for construction of receiving terminals for LNG are under discussion and their location and associated supply chain routing is a relevant question, which makes this area an interesting case for computational studies. Two terminals are (being) built in Finland (at the cities of Pori and Tornio) and the possibility of connecting the European and Finnish natural gas networks by a pipeline between Paldiski in Estonia and Inkoo in Finland is being debated. To analyze this emerging gas supply system, the model presented in the previous section was applied in a case study of the LNG supply chain in the Gulf of Bothnia, i.e., the northern part of the Baltic Sea. The study considers three possible supply terminals (Inkoo, Tornio, Stockholm) and seven potential satellite terminals (Turku, Pori, Vaasa, Raahe, Luleå, Umeå, Sundsvall) on the coasts of Finland and Sweden. The maritime distances were obtained from an online tool for calculation of distances between sea ports.16 These are reported in kilometres in Table S1 in the Supporting Information. As inland customers, twenty-three clusters distributed in Finland and Sweden were identified. The region and the locations considered in the case study are shown in Figure 1. Remote locations far away from the closest (potential) LNG terminal were not considered, as a maximum feasible distance for land transportation of 350 km was imposed. The road distances, reported in Table S2 in the Supporting Information, were collected from a web mapping service.17 Demands were assigned on the basis of the population, extent of industrial activity and time horizon considered. It should be stressed that these are gross estimates used for the mere purpose of illustration, and they are not claimed to represent the true demands in these locations. Furthermore, these do not represent single consumer demands but the joint demand of multiple potential consumers clustered together. The average daily demands used in the computational study of this work are listed on the last row of Table S2. 12 ACS Paragon Plus Environment

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FINLAND SWEDEN

Figure 1. Location of the demands (•) in the case study, potential satellite terminals (●) and supply ports (■) on a map of Finland and Sweden. Table 1. Parameters for the potential ships in the fleet: Capacity, loading/unloading rate, propulsion speed and costs, and monthly renting costs (inspired by values reported on small-scale LNG carrier design18). ,

n

c

"6

"/

MWh (m3)

MWh (m3/h)

km/h

€/km

€/day

Type 1

29,167 (5,000)

4667 (800)

23

5

14,448

Type 2

37,917 (6,500)

4667 (800)

24

5

17,361

Type 3

58,333 (10,000)

4667 (800)

26

6

23,471

Type 4

70,000 (12,000)

4667 (800)

27

7

26,667

Type 5

116,666 (20,000)

4667 (800)

28

9

38,129

Ship

Vessel parameters used in the study were estimated based on a report on small-scale LNG carrier design18. Five ship types, with capacities of 5,000 m3, 6,500 m3, 10,000 m3, 12,000 m3 and 20,000 13 ACS Paragon Plus Environment


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m3 were considered, which were all assumed be able to carry out split deliveries (given their small capacity). The loading/unloading rate of the ships is identical (800 m3/h) but the travelling speed is different, as reported in Table 1. The optimization was performed for a time horizon of 5 = 30 d, which is long enough to allow complex ship routing. The availability of vessels and trucks is a portion of the total time horizon in order to allow for some extra time. An availability of 95 % was used for the ships (] = 0.95 in eq 21) while the corresponding number for trucks was 29.8 % (] = 0.298 in eq 13); the latter factor also considers a rescaling of the total time to ten-hour work days, in a five-day work week. The maximum supply of LNG from each of the supply ports was set to ,*e = 40 GWh/d (corresponding to roughly 7,000 m3) and a heel of 10 % (X t = 0.1) was required for the satellite terminals. As all the potential satellite terminal locations have relatively deep ports, the upper limit of the ship capacity was set to ,e = 100 GWh , so any of the ships in the potential fleet (cf. Table 1) could enter the ports. Considering the characteristics of the ports and the small size of the ships, the berthing time was set to ^k = 5 h for all ports. The truck capacity was 55 m3 which in terms of energy corresponds to , ≈ 321 MWh19, and the average travelling speed was c = 50 km/h. The maximum number of truck loads per day (de in eq 14 and eq 15) was estimated on economic grounds: there are five loading stations at the supply terminals and three loading stations at the receiving terminals, the loading operation takes two hours (^ _ = 2 h), and there is a ten-hour service at each port: This gave de = 25 for the supply terminals de = 15 for the satellite terminals. As for cost parameters, the investment costs of the satellite terminals were estimated on the basis of public reports in news media on the terminals being under construction in Finland. In the linear expression of eq 4 a fixed cost of < = 20 M€ and a slope of 1 = 200 €/MWh were used, while for a truck the investment of z = 2 M€ and a fuel cost of " 6 = 1

€

{|

were applied. The annuity of

the investment was determined by assuming a 15-year life length (I = 15), using an interest rate of 14 ACS Paragon Plus Environment

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15 % (> = 0.15), which yielded the factor 9 = 0.0141 in eq 4. The ship rental costs were estimated from a capacity-dependent expression / "/ = "}~ `

\j

\

b

.g

(22)

/ with a reference cost and capacity of "}~ = 800,000 €/month and ,}~ = 12,000 m' ,

respectively. This gave the monthly renting costs reported in Table 1, where the propulsion costs have also been reported. The port call fee was set to " = 5000 € for the supply ports, while no fee was imposed for satellite ports. The price of LNG was varied in the analysis and will be reported in the forthcoming subsections. The MILP model was implemented in AIMMS 4.8 − a software platform for systems optimization and scheduling problems − using the IBM ILOG CPLEX Optimizer.20 The problem of the case study results in 772 integer variables and 472 continuous variables. The solution time of one case was usually less than two minutes on a computer with a 3.5 GHz Intel Core i7 processor and 16 GB of RAM.

4.2 Base Case Results are first presented from a computational experiment termed Base Case, where the model parameters of the previous subsection are applied. The price of LNG at the three supply ports is identical, C*+ = 30 €/MWh (≈ 9.3 $/MMBtu at the current exchange rate 1 $ = 0.94 €), and the price of alternative fuel at the consumers is " = 40 €/MWh (≈ 12.3 $/MMBtu). Figure 2 illustrates the optimal maritime routing (indicated by curved arrowed arcs), active port locations (indicated by name) and port-to-customer truck connections (indicated by straight arrowed lines). Detailed numerical results of the optimization are reported in Tables 2 and 3.



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Figure 2. Optimal satellite terminal locations and LNG distribution from ports for the Base Case. Straight arrows indicate land transport by truck while arrowed arcs indicate maritime routing. Activated satellite terminals are indicated by name. The results show that almost all the customers are served partially or entirely with LNG. Only one demand (12.5 GWh in Kiruna, the northernmost point) is completely satisfied by alternative fuel. Four other customers are partially supplied with alternative fuel, while a total of twenty customers are entirely supplied by LNG by truck. The total amount of alternative fuel is 53 GWh, representing the 4.6 % of the energy demand, while 694.5 GWh (60.2 %) of LNG was transported by truck in a total of 2167 trips. Five of the seven possible satellite terminals are activated. Their storages vary from 12,000 m3 in Vaasa to 38,000 m3 in Raahe. Sundsvall, Umeå and Pori are assigned similar capacities of about 20,000 m3. The number of trucks per port is indicated in Table 2, ranging from 1 in Vaasa to 25 (the maximum) in Inkoo. Supply ports have the highest number of trucks as they serve the majority of the land customers reached. Among the satellite terminals, Raahe has the largest number of connections for truck transport, and therefore a high number of allocated trucks. 16 ACS Paragon Plus Environment

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It should also be mentioned that no satellite terminal is built in Luleå or Turku, but their demands are satisfied by truck transportation from Tornio and Inkoo, respectively. Furthermore, a satellite terminal in Pori is activated to satisfy only the local demand, where no trucks are assigned. Table 2. Number of trucks per port and storage size for active satellite terminals in the Base Case. Port

, -

, GWh

Inkoo

25

-

Tornio

22

-

Stockholm

20

-

Raahe

13

221.1

Sundsvall

8

117.8

Umeå

2

129.6

Vaasa

1

67.3

Pori

0

111.1

The maritime distribution of LNG is carried out with a single ship of Type 3 (10,000 m3 of capacity). The ship performs a few split deliveries on the routes Stockholm-Pori-Raahe-Tornio, Tornio-Vaasa-Raahe-Tornio and Tornio-Vaasa-Sundsvall-Stockholm. The optimal routes are indicated by arcs in Figure 2, while the number of voyages on the different routes is reported by variable y in Table 3. In the specific case, Inkoo supplies partially Pori, Stockholm serves partially Sundsvall, Pori and Raahe, while Tornio is the only supply port for both Umeå and Vaasa, and partially for all the other satellite ports. The total amount of LNG delivered to customers from the three supply terminals corresponds to about 230 GWh for Inkoo, 290 GWh for Stockholm and about 580 GWh for Tornio. Assuming a storage tank of 50,000 m3 (corresponding to a capacity of approximately 300 GWh) at the supply ports, the Base Case solution would suggest a minimum of two refills per month in Tornio and one refill in Inkoo and Stockholm, which is a reasonable frequency. Examining the objective function, the cost of fuel purchase was found to account for 17 ACS Paragon Plus Environment


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84.3 % of the total costs, while the cost of transportation and the investment cost contribute by 3.8 % and 11.9 %, respectively. Table 3. Routing results for the Base Case. Integers y indicate the number of voyages undertaken and x the number of LNG loads for the given distances. Route

,,

,,

Inkoo – Pori

1

1.00

Stockholm – Sundsvall

1

1.00

Stockholm – Pori

1

1.00

Tornio – Raahe

3

2.89

Tornio – Umeå

2

2.00

Tornio – Vaasa

2

2.00

Pori – Raahe

1

0.29

Vaasa – Raahe

1

0.14

Vaasa – Sundsvall

1

0.82

Pori – Inkoo

1

Sundsvall – Stockholm

2

Raahe – Tornio

5

Umeå – Tornio

2

4.3 Effect of Fuel Price In order to make it economically feasible to build the supply chain of LNG, its price must obviously be sufficiently lower than the price of the alternative fuel. With the aim of studying the sensitivity of the solution to this margin, optimization runs were performed with different values of the alternative fuel price, keeping the LNG price at the supply terminals constant. The role played by the LNG price in the different supply ports was also studied.


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4.3.1 Price of Alternative Fuel The alternative fuel price was expressed as " = " + + ∆", where " + is the LNG price at the supply terminals, which was kept as in the Base Case (C*+ = 30 €/MWh). Some summarizing results for the cases with ∆" = 0 to 24 €/MWh (0 to 7.5 $/MMBtu) are presented in Figure 3, where the shares of the total energy supply are presented for the optimal solutions. 100 90

Share of Totaal Energy (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


LNG from satellite terminals by truck

80 70

Alternative fuel

60

LNG by ship and not further trucked

50 40 30

LNG from supply ports by truck

20 10 0 0

2

4

6

8

10

12

14

16

18

∆C (€/MWh) Figure 3. Share of total energy supply with respect to fuel and type of delivery.


20

22

24


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Page 20 of 33

(a)

(b)

(c)

(d)

Figure 4. Optimal satellite terminal locations and LNG distribution from supply ports for a) Case 1, b) Case 2, c) Case 3 and d) Case 4 where the price of alternative fuel exceeds the price of LNG by ∆" = 8, 9, 10 and 21 €/MWh. Case 3 corresponds to the Base Case of subsection 4.2. The quantity of alternative fuel used has been reported in GWh next to the locations. The total share of energy covered by LNG is seen to grow from 0 % to almost 100 % along with the increase in the price of alternative fuel, but the changes occur stepwise. Initially, at low values of ∆" the whole demand is satisfied by the alternative fuel. From ∆" = 2 €/MWh (0.6 $/MMBtu) onward, LNG starts being delivered to an increasing number of consumers by land transportation from the three supply ports. At ∆" = 8 €/MWh (2.5 $/MMBtu), called Case 1, the share of LNG increases strongly to exceed 80 %, where about 35 % of the energy demand is satisfied by LNG 20 ACS Paragon Plus Environment

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shipped to and through the satellite terminals, while 44 % is directly trucked from the supply ports. This is close to the maximum share of LNG directly trucked from the supply ports, where all the available truck loads (1607 in the 30-day horizon) are delivered. The LNG transportation routes of this solution are presented in Figure 4a, where the quantity of alternative fuel has been reported in GWh next to the locations on the maps. Already here, almost all the customers are served partially or entirely with LNG: One ship of Type 1 (5,000 m3) is needed for the whole LNG maritime transportation. Thirteen customers’ demands are entirely satisfied by trucked LNG, while only five demands (Mora, Sundsvall, Östersund, Kiruna and Kuopio, cf. Figure 1) are satisfied by alternative fuel only. Three of the seven possible satellite terminals are activated, but no satellite terminals are built in Sundsvall, Luleå, Vaasa and Turku; their demands are satisfied by alternative fuel or truck transportation of LNG from Tornio, Pori and Inkoo, respectively. The main remaining changes in the optimal solutions occur at ∆" = 9, 10 and 21 €/MWh (2.8, 3.1 and 6.5 $/MMBtu), after which no changes are seen. These points are called Cases 2-4 in the forthcoming analysis. Interestingly, for these solutions the share of LNG directly trucked from the supply ports is nearly constant (≈ 44.7 %), while the LNG delivered by ship is clearly higher for the latter two cases (cf. Figure 3). The solution for Case 2 (Figure 4b) is similar to that of Case 1 but presents the activation of a satellite terminal in Sundsvall. There are maritime LNG deliveries from all three supply ports carried out by one ship of Type 2 (6,500 m3). For Case 3, which is identical to the Base Case outlined in subsection 4.2, the share of LNG delivered by ship at the satellite terminals and not further trucked increases from about 30 % to 35 %, while the share of LNG trucked from the satellite terminals to land customers reaches almost 16 %, from being 12 % in Case 2. Figure 4c shows a more extensive maritime supply on the Finnish coastline, with a new satellite terminal in Vaasa and two more inland customers supplied by LNG (Kuopio and Mora). The higher maritime supply is realized by a larger ship (Type 3, 10,000 m3). As the alternative fuel price exceeds the price of LNG by ∆" = 21 €/MWh, the satellite terminal in Vaasa is suppressed 21 ACS Paragon Plus Environment


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while the one in Luleå is activated (Figure 4d) and all the customers are supplied, partially or entirely, by LNG. A characteristic of the solutions for ∆" > 8 €/MWh is split deliveries of LNG to the satellite terminals. The results of the sensitivity analysis clearly illustrate that the high investment cost of satellite terminals makes their construction feasible only in cases where the energy demand in the region is sufficient. The extent of the region covered by a satellite terminal increases with the price difference ∆". This feature makes the combinatorial problem challenging.

4.3.2 Price of LNG in the Supply Ports The price of LNG in the supply port naturally affects the optimal solution, since this cost represents a major share of the overall costs in the objective function that is minimized. A brief study of this was undertaken by changing the LNG price by ±2 €/MWh (0.6 $/MMBtu) in every supply port, and optimizing the energy supply for the system keeping the alternative fuel price as in the Base Case. Some results for the 27 points are condensed in Table 4. The optimal supply chain changes significantly with the variation of the LNG price in the different supply ports. This is expected as the points around which the perturbation of the price were made are in the transition region of the solution (cf. Figure 3). Nonetheless, it is interesting to notice that the solution evolves logically, generally increasing the energy share from alternative fuel when the LNG price rises. However, for the first eleven points the share is almost constant and can be traced to solutions where one inland customer (Kiruna) is not supplied by LNG and a number of other distant customers are only partially supplied. It can also be observed that the energy shares are almost identical in Points 6 and 10 (the latter corresponding to Base Case of section 4.2) where the LNG price at the three ports is the same. This no longer holds true for Point 27 where the LNG price is the same in all supply ports but so high that the competition with the alternative fuel price becomes pronounced: here the alternative fuel share has increased to 20 %. The solution (in terms 22 ACS Paragon Plus Environment

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of satellite terminals, ship routes, truck connections and energy shares) in this particular point is the same as Case 1 of subsection 4.3.1 since the difference between alternative fuel and LNG price is 8 €/MWh.

Table 4. Results of the sensitivity analysis of the solutions to changes in the parameter "*+ by ±2 €/MWh from the values in the Base Case. The points have been arranged in ascending order with respect to the share of alternative fuel. LNG price in (€/MWh)

Energy share, α (%)

Ship

Point

Inkoo

Stockholm

Tornio

Inkoo

Stockholm

Tornio

Alt. fuel

type

1

32

32

28

7.1

14.8

73.8

4.3

4

2

30

30

28

12.9

14.9

67.7

4.5

3

3

30

32

28

12.9

14.9

67.7

4.5

3

4

32

28

30

1.5

79.4

14.5

4.6

5

5

30

28

28

10.5

29.3

55.6

4.6

3

6

28

28

28

19.9

25.0

50.5

4.6

3

7

28

30

28

24.9

14.9

55.5

4.6

3

8

28

32

28

24.9

14.9

55.5

4.6

3

9

30

32

30

24.9

14.9

55.5

4.6

3

10

30

30

30

19.9

25.1

50.4

4.6

3

11

32

30

28

7.1

14.9

73.3

4.6

4

12

32

28

32

2.2

79.3

13.6

4.9

5

13

32

32

30

11.7

14.9

68.1

5.2

3

14

32

28

28

8.6

34.9

50.5

6.0

3

15

32

30

30

8.7

34.8

50.5

6.0

3

16

30

28

30

14.8

57.6

21.1

6.5

4

17

28

30

30

57.5

14.9

21.1

6.5

4

18

28

32

30

57.5

14.9

21.1

6.5

4



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Page 24 of 33

19

30

28

32

14.8

62.2

14.5

8.4

4

20

28

28

30

55.4

21.0

14.9

8.7

4

21

28

30

32

61.6

14.9

14.7

8.8

4

22

28

32

32

61.6

14.9

14.7

8.8

4

23

28

28

32

55.4

21.0

14.6

9.0

4

24

30

30

32

48.9

26.8

15.0

9.3

4

25

30

32

32

60.6

14.9

14.9

9.6

4

26

32

30

32

11.1

63.3

14.8

10.8

4

27

32

32

32

24.7

14.9

40.4

20.0

1

In order to facilitate the interpretation, the results have also been depicted in Figure 5, which shows the shares, , of the total demand delivered from the different supply ports. It can be observed that a price increase in Tornio (moving downwards along the panels) causes a more drastic change in the LNG distribution than a price increase in the other supply ports. This can be seen in Figure 5 and by comparing Points 9, 15 and 24 in Table 4 to the Base Case (Point 10). In the first two points, where the LNG price is increased in Stockholm and Inkoo, the energy shares vary moderately from their corresponding values in the Base Case. By contrast, in Point 24 the energy shares from Tornio and Inkoo change dramatically. This is due to the geographical location of the demands, making them more easily reachable from Tornio, so the solution evolves in a clearly coherent way. From Figure 5, top panel row, it can also be seen that a low LNG price in Tornio (28 €/MWh) makes the optimal solution rather insensitive to the price in the other supply ports. A final remark can be made concerning the optimal composition of the fleet, which for all points consist of a single ship. As the bigger ships have higher average speed (cf. Table 1), the solutions where the LNG supply is lower from Tornio and higher from the other two ports will promote the selection of a bigger ship (Type 4 or 5, cf. last column of Table 4). This makes it possible to deliver the LNG longer distances (to the farther satellite terminals in Luleå, Umeå, Raahe and Vaasa) within the time horizon, so the solutions are governed by speed requirements rather than capacity requirements. 24 ACS Paragon Plus Environment

αt{| (%)

α{ (%)

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α} (%)

Page 25 of 33

+ "t{| (€/MWh)

+ "{ (€/MWh)

+ "t{ | (€/MWh)

+ "{ (€/MWh)

+ "t{| (€/MWh)

+ "{ (€/MWh)

Figure. 5. Share of energy delivered as LNG from Tornio (left panel column), Inkoo (middle column) and Stockholm (right column) for the cases optimized with an LNG price in Tornio of + "} = 28 €/MWh (top row), 30 €/MWh (middle row) and 32 €/MWh (bottom row). The LNG

price in the other two supply ports is reported on the axes of the figures. The alternative fuel price is fixed at " = 40 €/MWh.

5. CONCLUSIONS AND FUTURE WORK This paper has presented an MILP model for the optimal design of a small-scale LNG supply chain. The objective function that is minimized expresses the total combined cost associated with fuel procurement. The resulting solution provides information about the optimal locations of satellite terminals, fleet configuration, number of tank trucks and the associated distribution network. The model makes it possible to evaluate the feasibility of small-scale LNG supply chains and to study the robustness of the solution to changes in the conditions. It can, for instance, be used in initial studies of the economic feasibility of LNG supply in potential or emerging markets for



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customers in coastal regions or islands. This makes it a valuable tool for decision makers and analysts. A case study has illustrated the features of the model and its coherent performance upon parameter perturbations. The proposed model has proven to be a flexible framework which can be easily applied to other similar supply chain optimization problems. The present model can be extended to a multi-period formulation with the aim to address variation of the demands and to be able to estimate the optimal storage inventory at the satellite terminals21. The new formulation would also allow for a more detailed study of the effect of the time horizon and possibly optimize it together with the storage size. This requires new sets of constraints to control the tank storage mass balance and sizing.

ASSOCIATED CONTENT Supporting Information Sea distances between the ports (Table S1), ports-customers road distances and customers’ daily demands (Table S2) (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] ACKNOWLEDGMENT This work was carried out in the Efficient Energy Use (EFEU) research program coordinated by CLIC Innovation Ltd. with funding from the Finnish Funding Agency for Technology and Innovation (Tekes) and participating companies. The financial support is gratefully acknowledged.


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NOMENCLATURE Sets

Set of inland customers

Set of ship types

h

Set of ship types which cannot perform split delivery

Set of customers

Set of ports

Set of satellite terminals

Set of supply ports

Indices

Inland customers

Ship types

,

Customers (, )

Ports

,

Satellite terminals ( , )

Supply ports

Variables

Continuous variable indicating the amount of energy from alternative fuel, MWh

,

Continuous variable indicating the amount of energy from LNG trucked, MWh

Continuous variable indicating the size of the tank storage, MWh

Integer variable indicating number of trucks at port , -

,

Integer variable indicating number of truck trips between and , -

ACS Paragon Plus Environment

27


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Page 28 of 33

Binary variable, = 1 if satellite terminal is activated, -

,,

Continuous variable indicating ship load transported, -

,,

Integer variable indicating number of times the route between and is

travelled,

Integer variable indicating number of ship type , -

Parameters

Energy share, %

]

Truck availability, -

]

Ship availability, -

"

Price of alternative fuel, €/MWh

"*+

Price of LNG in supply port , €/MWh

"

Port call cost, €

"6

Truck fuel consumption cost, €/km

"6

Ship propulsion cost, €/km

"/

Ship renting cost, €/d

7,

Maritime distance, km

0 7,

Road distance, km

Energy demand, MWh/d

>

Interest rate, -

X

Fraction of the total capacity of the ship, -

Xt

Fraction of storage capacity for LNG heel, -

n

Loading/unloading rate, MW

5

Time horizon, d

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z

Truck investment cost, €

1

Tank storage investment cost, €/MWh

Optimal Design of a Small-Scale LNG Supply ... - ACS Publications

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