A Simulation-Based Planning Tool for Floating Storage and Regasification

logistics

Article A Simulation-Based Planning Tool for Floating Storage and Regasiﬁcation Units

Christos Papaleonidas * , Emmanouil Androulakis and Dimitrios V. Lyridis Laboratory for Maritime Transport, School of Naval Architecture and Marine Engineering, National Technical University of Athens, 15780 Athens, Greece; [email protected] (E.A.); [email protected] (D.V.L.) * Correspondence: [email protected]; Tel.: +30-210-772-1456

Received: 10 October 2020; Accepted: 26 October 2020; Published: 30 November 2020

Abstract: The objective of this paper was to propose a functional simulation model for the operation of floating storage and regasification units (FSRUs) used for the import of liquefied natural gas (LNG). The physical operation of an FSRU is decomposed for each critical component of the LNG carrier (LNGC) and the FSRU, in order to construct a realistic model in Simulink. LNG mass balance equations are used to perform flow calculations from the tanks of an LNG carrier to the tanks of the FSRU and from there to shore. The simulation model produces results for cases, when multiple LNG carriers discharge cargoes during a monthly time horizon. This produces an accurate operational profile for the FSRU with information about the volume of LNG inside each of the cargo tanks of the FSRU, LNG cargo discharging and gas send-out rate. Potential practitioners may exploit the proposed planning tool to explore the feasibility of alternative operation scenarios for an FSRU terminal. The simulations can check the system sensitivity to different parameters and support schedule regarding: (i) slots for LNG carrier calls, (ii) LNG inventory fluctuation, and (iii) impact of gas demand and send-out rate changes.

Keywords: LNG; FSRU; tactical planning; simulation; simulink

1. Introduction A floating storage regasification unit (FSRU) is a special type of ship, which is used for the storage and regasification of liquefied natural gas (LNG). Over the past two decades, they have been utilized to enable the import of LNG to remote markets lacking access to pipeline gas. An FSRU is a vital component of the LNG supply chain, required to convert natural gas back into its gaseous form and feed it into the gas network. FSRUs provide operators with much needed flexibility to address increasing gas demand, while allocating significantly fewer capital expenses than an onshore LNG import terminal. Currently, there are 34 FSRUs around the globe owned by specialized companies as shown in Figure1, while 12 more are under construction as of February 2020 [ 1]. Apart from the number of niche FSRU owners, operators have also grown in number, as the technology is now well proven and in many cases it is more advantageous financially to build, own and operate the unit [2]. The increasing number as well as the higher utilization rate of operational FSRUs create planning challenges for the terminal operators. As more and more LNG vessels become active in the market and perform ship-to-ship (STS) cargo transfers to meet the growing LNG demand, precise scheduling for the slots of an FSRU terminal is required. However, the number of vessels and availability of unloading slots is only one aspect. The vaporization of LNG from the FSRU and subsequent transfer to the gas network is the other, which is conducted constantly and sometimes simultaneously with the unloading of the cargo from an LNG vessel. The send-out of gas from the FSRU to the network might be affected by the fluctuation of the end user demand (power plants, industries, residential distribution networks, transport sector) throughout the year. Causes behind this phenomenon may include seasonality

Logistics 2020, 4, 31; doi:10.3390/logistics4040031 www.mdpi.com/journal/logistics Logistics 2020, 4, 31 2 of 16

patterns, general economic and market conditions, lower LNG price lower compared to other fuels or extraordinary events. As a result, the FSRU operator must be capable of adapting the schedule of the terminal to guarantee its constant operation and accommodate the discharging of all scheduled LNG vessels. This can be achieved proactively for diﬀerent operation scenarios, if the simulation of the Logistics 2020, 4, x FOR PEER REVIEW 2 of 14 FSRU terminal is practicable.

Figure 1. Active number of floating storage and regasification units (FSRUs) by owner [1]. Figure 1. Active number of floating storage and regasification units (FSRUs) by owner [1]. The aim of the present research is to propose a simulation-based tool, which enables the FSRU Theoperator increasing to meet thenumber aforementioned as well as requirement. the higher Theutilization simulation rate model of operational incorporates theFSRUs critical create planningcomponents challenges of the for FSRU the terminal and its interface operators. with theAs LNGmore vessels and more in a realisticLNG vessels manner. become It is constructed active in the marketto generateand perform volatile ship-to-ship scenario cases, (STS) providing cargo users transfers with ato reliable meet toolthe togrowing validate LNG their operationsdemand, andprecise schedulingcheck the for system’s the slots sensitivity of an toFSRU different terminal parameters. is required. However, the number of vessels and availabilityPrevious of unloading research relatedslots is to only operational one aspect. issues ofThe FSRUs vaporization is rather limited of LNG and from has dealt the with FSRU the and subsequentsubject fromtransfer different to the scopes. gas network Artana [3 ]is examined the other, the which strategic is issueconducted of optimum constantly location and selection sometimes for an FSRU based on quantitative (distance, current speed, water depth, tide, wave height, and wind simultaneously with the unloading of the cargo from an LNG vessel. The send-out of gas from the speed) and qualitative criteria (noise, emissions, waste water, nearby housing/industry/explosive FSRU to the network might be affected by the fluctuation of the end user demand (power plants, locations and sea traffic). To the authors’ knowledge, many research publications (indicatively [4–7]) industries,related residential to FSRUs focus distribution on technical networks, aspectssuch tran assport the simulationsector) throughout of chemical the and year. thermodynamic Causes behind this phenomenonprocesses related may to theinclude cargo seasonality tanks and the patterns, vaporizer general unit. economic and market conditions, lower LNG priceTo lower the best compared knowledge to ofother the authors,fuels or only extraordinary the work of events. Briano etAs al. a [ 8result,] studied the the FSRU subject operator of mustlogistical be capable planning of adapting for an FSRU the schedule terminal. of The the authors terminal developed to guarantee a simulation its constant model to operation verify the and accommodatefeasibility ofthe LNG discharging supply via of an FSRUall scheduled to a power LNG plant, vessels. under realistic This can operating be achieved conditions proactively and with for differentparticular operation technical scenarios, specifications if the simulation for the vessels of the unloading FSRU terminal the LNG. is The practicable. developed model had the Thecapacity aim toof simulate the present three research LNG vessel is to unloading propose scenariosa simulation-based (a dedicated tool, LNG which vessel, enables two dedicated the FSRU operatorvessels, to meet and an the emergency aforementioned spot ship). requirement. Regardless of The the scenario, simulation the shipsmodel imported incorporates LNG from the twocritical designated terminals and operated with a given constant load/discharge rate. However, the discharging components of the FSRU and its interface with the LNG vessels in a realistic manner. It is constructed of cargo depended on two conditions affected by the environment, light of day and marine weather. to generate volatile scenario cases, providing users with a reliable tool to validate their operations To address the limited operational window during adverse conditions, a safety stock level was set. and checkThe constant the system’s send-out sensitivity rate of the to FSRUdifferent changed parameters. for two scenarios based on the workload of the Previouspower plant research receiving related gas from to operational the terminal, issues albeit withof FSRUs no seasonality is rather patterns. limited Theand demand-drivenhas dealt with the subjectdeterministic from different model scopes. used power Artana plant [3] operating examined conditions the strategic as inputs issue to simulate of optimum scenarios location and identify selection for anthe FSRU ones based that minimize on quantitative the cost and (distance, secure LNG curre availability.nt speed, The water simulation depth, platformtide, wave was height, implemented and wind speed)in theand software qualitative Powersim criteria Studio (noise, 8TM Expert.emissions, waste water, nearby housing/industry/explosive locations Theandwork sea traffic). of Briano To et the al. [ 8authors’] and the knowledge, current research many share research similarities publications on the subject (indicatively of simulation, [4–7]) relatedwhich to FSRUs is the LNG focus unloading on technical from theaspects vessel such to the as FSRU the simulation and the loading of chemical of the FSRU and tank. thermodynamic However, processes related to the cargo tanks and the vaporizer unit. To the best knowledge of the authors, only the work of Briano et al. [8] studied the subject of logistical planning for an FSRU terminal. The authors developed a simulation model to verify the feasibility of LNG supply via an FSRU to a power plant, under realistic operating conditions and with particular technical specifications for the vessels unloading the LNG. The developed model had the capacity to simulate three LNG vessel unloading scenarios (a dedicated LNG vessel, two dedicated vessels, and an emergency spot ship). Regardless of the scenario, the ships imported LNG from two designated terminals and operated with a given constant load/discharge rate. However, the discharging of cargo depended on two conditions affected by the environment, light of day and marine weather. To address the limited operational window during adverse conditions, a safety stock level was set. The constant send-out rate of the FSRU changed for two scenarios based on the workload of the power plant receiving gas from the terminal, albeit with no seasonality patterns. The

Logistics 2020, 4, 31 3 of 16 the proposed tool extends the modeling to represent the vaporization of LNG and send-out gas to the network, which affects the inventory level of each cargo tank in the FSRU. In addition, a monthly time horizon is deemed more appropriate than the 4 days used by Briano et al., due to the fact it allows the simulation of multiple LNG vessel berths and gives a more comprehensive representation of the FSRU operation profile. Another reason is that service slots for an FSRU are usually booked by the operator for a monthly period, to optimize the overall schedule for the terminal users. The simulation model proposed by the authors combines technical aspects to perform a realistic simulation of the STS transfer and FSRU send-out operations. LNG mass balance equations are used to perform flow calculations from the tanks of an LNG carrier to the tanks of the FSRU and from there to shore. The model is implemented using the Simulink software and produces an accurate operation profile for an FSRU, with information regarding the volume of LNG inside each of the cargo tanks of the FSRU, LNG cargo discharging and gas send-out rate. Potential practitioners may exploit the proposed planning tool to explore the feasibility of alternative operation scenarios and check how different parameters might affect: (i) slots for LNG Carrier (LNGC) calls, (ii) LNG inventory fluctuation, and (iii) the impact of gas demand and send-out rate changes. Initially, the paper analyses the technical information linked with FSRU operation in order to clarify the system FSRU as an LNG intermediate storage and host system. The LNG STS procedures from an LNG carrier to the FSRU are described. These procedures are illustrated by a diagram (flowsheet) highlighting key elements that play an important role during LNG STS transfer. The last part of the methodology focuses on how the model works and how each technical parameter (pumps, valves, etc.) is simulated in Simulink. Upon the completion of the model methodology, a structured case study was used to validate the proposed model. The case study consists of three scenarios. Each scenario is related to a different gas demand profile and a different set of transshipment technical parameters. The main target is to present the capability of the model to simulate the LNG in each of the FSRU cargo tanks in a period of one (1) month. The results are plotted in LNG-time charts. Following the results of the case study, discussion is made to understand the FSRU operations and draw preliminary conclusions on how the system can be optimized. The remainder of the paper is organized as follows. In Section2, the methodology used in the research is delineated. Section3 outlines the assumptions and parameters used in the case study and presents the results of the simulation. Finally, Section4 elaborates on the results and the conclusion of the research.

2. Methodology

2.1. Technical Description of the FSRU Operation Technical fundamentals for FSRUs have been presented in various studies. Indicatively, the evolution of technology can be traced through the work of Leet et al. [9] and Songhurst [2,10]. In the referenced studies, the reader can find an extensive review of the technical solutions adopted by FSRU projects depending on the project site, specific commercial requirements, etc. Further technical analysis of the FSRU operation in the form of standard procedures is described in specific documents. The documents issued by the shipyard, submitted to the FSRU owner and approved by a classification organization are three (3), namely the “cargo operation manual”, “operating manual for regasification” and “machinery operating manual”. Certainly, the terminal operation must be consistent with existing international and national rules and regulations, implemented by the flag state/port state of the terminal. Industry recommendations from organizations such as Oil Companies International Marine Forum (OCIMF), Society of International Gas Tanker and Terminal Operators (SIGTTO) and International Group of Liquefied Natural Gas Importers (GIIGNL) were also taken into consideration. Logistics 2020, 4, x FOR PEER REVIEW 4 of 14 organizations such as Oil Companies International Marine Forum (OCIMF), Society of International Gas Tanker and Terminal Operators (SIGTTO) and International Group of Liquefied Natural Gas Importers (GIIGNL) were also taken into consideration. LogisticsBefore2020 ,the4, 31 loading of the FSRU initiates, certain preparatory procedures must be followed4 of 16 thoroughly, including works as well as the proper exchange of information and security measures. These stepsBefore are the required loading to of ensure the FSRU that initiates,the tanks certain of the preparatoryFSRU are clear procedures of water must and vapors, be followed before thethoroughly, cooling of includingthe piping works system. as wellDuring as thethis proper step, the exchange FSRU starts of information pumping and LNG security from the measures. vessel at a slowThese rate steps for are approximately required to ensure 15 thatmin, the in tanks order of to the avoid FSRU arehigh clear stress of water on the and pipes, vapors, minimize before the the likelihoodcooling of of the leaks piping through system. the During joints thisor other step, theparts FSRU of the starts piping pumping system LNG and from prevent the vessel the atformation a slow of rateBOG for (boil-off approximately gas) as the 15 min,LNG in flows order through. to avoid high stress on the pipes, minimize the likelihood of leaksFollowing through the jointscompletion or other of parts the preparatory of the piping work systems, the and discharging prevent the formationof the cargo of BOG from (boil-o the LNGff vesselgas) and as the the LNG loading flows of through. the FSRU takes place. LNG is pumped using submersible pumps located at the bottomFollowing of each the tank. completion The usual of theprocedure preparatory is to start works, two the recirculation discharging pumps of the cargo in one from tank the and LNG then startvessel discharging. and the loading A similar of the procedure FSRU takes is place. then LNG applied is pumped to the usingother submersible tanks with pumps a short located period interveningat the bottom for ofeach each tank. tank. Since The usualall pumps procedure start isoperating to start two at a recirculation 60% load, it pumps slowly in increases one tank andto the maximum.then start As discharging. the pressure A similardrops on procedure the tank, is the then BOG applied created to thein the other FSRU tanks tanks with is asent short back period to the dischargingintervening tank for of each the tank. LNGC, Since which all pumps maintains start the operating tank pressure at a 60% for load, the itvessel slowly at increasesan agreed to level. the maximum.The cargo As is the transferred pressure drops with ongreat the care tank, due the BOGto the created movement in the FSRUof the tanksLNGC is sentin relation back to to the the FSRUdischarging (roll, sway, tank heave, of the etc.). LNGC, In whichparallel, maintains the air tr theapped tank inside pressure the for piping the vessel of the at cargo an agreed transfer level. system The cargo is transferred with great care due to the movement of the LNGC in relation to the FSRU is removed, with Nitrogen gas (N2) injected and compressed to about 4 to 6 bars. After the (roll, sway, heave, etc.). In parallel, the air trapped inside the piping of the cargo transfer system is compression, the vent valve opens to release the N2 gas into the atmosphere. This procedure is removed, with Nitrogen gas (N ) injected and compressed to about 4 to 6 bars. After the compression, repeated and a pipeline leak test2 with soap is performed simultaneously. The purification of the the vent valve opens to release the N2 gas into the atmosphere. This procedure is repeated and a pipeline gas ends when the oxygen (O2) content of the released gas from the pipes system drops pipeline leak test with soap is performed simultaneously. The purification of the pipeline gas ends below 2%. when the oxygen (O2) content of the released gas from the pipes system drops below 2%. WithWith the the release release of of the remaining liquids liquids and and vapor, vapor, the the pipes pipes must must be cleaned be cleaned after theafter cargo the hascargo hasbeen been fully fully unloaded. unloaded. After After the the cleaning cleaning is complete, is complete, a final a final tonnage tonnage measurement measurement is performed is performed and andthen then the the cargo cargo transfer transfer system system is disconnected. is disconnected. InIn terms terms of of information information exchange, exchange, immediately immediately after thethe departuredeparture of of the the LNG LNG vessel vessel from from the the portport of oforigin origin to to the the FSRU, FSRU, a adocument document containing containing all all relevant relevant information aboutabout the the quantity, quantity, quality, quality, compositioncomposition of of the the cargo, cargo, ship ship configuration configuration and thethe conditionsconditions under under which which she she operates operates must must be be sentsent to tothe the FSRU FSRU operator. operator. In In addition, addition, this this notice notice must must include anyany otherother request request for for the the STS STS transfer, transfer, as aswell well as as any any information information aaffectingffecting thethe LNG. LNG. A A more more detailed detailed scope scope of the of LNGthe LNG discharging discharging from thefrom thevessel vessel to to the the FSRU FSRU is illustratedis illustrated inFigure in Figure2. 2.

Berthing Initial gauging Final gauging

Ship/Shore pre- Return BOG vapours Purge liquid from transfer preparation to shore arm/hose

Arms/hoses cool Disconnect cargo Start water curtain down transfer arms/hoses

Connect cargo Start cargo transfer Stop water curtain transfer arms/hoses

Ship/shore final Start water curtain Finish cargo transfer communications

O2 purging / Leak Drain the liquid from Unberthing test arm/hose

Figure 2. LNG to FSRU transfer processes (authors’ illustration based on relevant technical manuals). Figure 2. LNG to FSRU transfer processes (authors’ illustration based on relevant technical manuals).

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A schematic representation of the LNGC and the FSRU developed in AutoCAD is presented in AppendixA, illustrating the main technical elements and parameters of the LNG transfer system. The schematic enables the distinction amongst several ﬂows (LNG, BOG, etc.) and processes for the loading of FSRU and regasiﬁcation of LNG is performed. The assumed layout and processes are the basis for the proposed simulation model. Finally, some critical elements are controlled and monitored by the FSRU cargo control room constantly during operations. The most important elements are:

LNGC and FSRU cargo tank levels; • LNGC and FSRU cargo tank pressure; • FSRU pump load and discharging pressure; • Draft and trim of the LNGC. • Most of the aforementioned characteristics are incorporated in the proposed model described in the following section.

2.2. Description of the FSRU Simulation Model The aim of the computational model was to simulate the operation of an FSRU in the context of tactical planning. With the loading and discharging parameters being known for the LNG vessel and the FSRU, the simulation model was able to calculate the time required to accomplish each process. In addition, the model produces results regarding the FSRU cargo tank level (or LNG inventory) and the send out rate of the natural gas from the FSRU to the gas network. The simulation model consists of two basic subsystems, the LNG vessel and FSRU. The basis of the model is the cargo flows between the LNGC–FSRU subsystems. To encapsulate the flows in an accurate manner, specific input data parameters are required, namely technical characteristics for each LNG ship and the FSRU, as well as the estimated arrival time of each ship to the FSRU. The input parameters are presented in Table1. Storage capacity is used in connection with the tank level to simulate the LNG cargo inside each cargo tank of the LNGC and the FSRU. The commencement and ceasing of STS operations is triggered by those parameters. Other input parameters are the flow rate used to simulate the LNG flows from each cargo tank to the vaporizer unit. “NG send out rate” refers to the gas end out rate to the shore network.

Table 1. Parameters used in the simulation tool.

Component of the Input Parameter Subsystem Units Subsystem Storage capacity LNGC/FSRU Each cargo tank m3 Tank level LNGC/FSRU Each cargo tank m3 LNG ﬂow rate from the LNGC Pump in each cargo tank m3/h LNG Carrier (LNGC) NG send out rate FSRU LNG vaporizer m3/h

The simulation tool was developed using MathWorks software tools, MATLAB and Simulink. Initially, a MATLAB code is used to request input for all the technical elements presented in Table1. This code makes the simulation modeling straightforward for the user, enabling them to insert data according to the speciﬁcations of the system under study. The features are not only able to meet the computational requirements, but also provide the user with a practical graphic interface of the Simulink processes. As a result, the user can produce a more intricate model for the FSRU operation by expanding the systems included in the initial model. Apart from the items in the Simulink library, developers can create their own functional blocks, either by designing them in Simulink or by coding them using the MATLAB platform. Logistics 2020, 4, 31 6 of 16

The basic principle of the model is the proper representation of LNG flows during the STS and LogisticsFSRU 2020 operation., 4, x FOR PEER To achieve REVIEW this, Simulink signals and blocks are used to model the LNGC and FSRU6 of 14 pipelines, pumps and valves. The underlying principle of the block arrangement is the mass balance 6 principle.principle. The Theplanning planning horizon horizon isis 2.5 2.5 × 10106 ss (or (or approximately 29 29 days), days), which which is considered is considered as a as a × sufficientsufficient time time period period to tosimulate simulate the the operation operation of an FSRUFSRU and and draw draw reasonable reasonable conclusions conclusions in terms in terms of tacticalof tactical planning planning [11]. [11 The]. The tool tool has has the the capacity capacity to to simulate multiple multiple consecutive consecutiv discharges,e discharges, limited limited onlyonly by the by thetime time horizon. horizon. Figure Figure 33 shows shows a a conceptu conceptualal representation representation of theof the model model with with an indicative an indicative numbernumber of five of five (5) (5)LNG LNG ships ships and and the the FSRU FSRU unit.

SUM OF FLOW TANK 1

time LNGC1 (for t=(t1,t2) Clock To Workspace

SUM OF FLOW TANK 2

LNGC2 (for t=(t3,t4)

SUM OF FLOW TANK 3 LNG total flow Vollume(t) of Tanks

LNGC3 (for t=(t5,t6) 29 days operation FSRU

FSRU

SUM OF FLOW TANK 4

LNGC4 (for t=(t7,t8)

SUM OF FLOW TANK 5

LNGC5 (for t=(t9,t10) FigureFigure 3. 3.ConceptualConceptual representation representation of of the the simulation simulation model. model. The general principle of the simulation is the calculation of the LNG flows during an STS transfer, accordingThe general to the principle formula: of the simulation is the calculation of the LNG flows during an STS transfer, according to the formula: Z tend V(t) = Q(t)dt tstart 𝑉(𝑡) = 𝑄(𝑡)𝑑𝑡 where V is the volume of LNG as a function of time, and Q is the flow of LNG. To ensure a realistic simulation approach, each LNG ship is further analyzed as a unique subsystem, whereshown V is inthe Figure volume4. A of block LNG is assignedas a function to each of of time, the cargo and Q tanks is the (i =flow1, ... of,n), LNG. which sets a signal for theTo maximumensure a valuerealistic of the simulation pump flow. approach, By selecting each each LNG block, ship the useris further can enter analyzed a parameter as a that unique subsystem,remains shown constant in over Figure time 4. (“constant A block value”).is assigned Then, to the each signal of the enters cargo the “use-valvetanks (i = 1, over ... n), time” which block sets a signalin whichfor the the maximum flow is represented value of as the a function pump of flow. time. TheBy selecting time sequence each is completedblock, the by user multiplying can enter a parameterthe flow that signal remains by a new constant time-signal over time that the(“constant user creates value”). based Then, on the the chosen signal scenario. enters Thethe “use-valve blocks over“time” time” and block “% ofin usage”which are the an flow f(t) signal is represente function thatd as takes a function the form of the time. user decidesThe time by insertingsequence is completedtwo variables by multiplying (time and %). the flow signal by a new time-signal that the user creates based on the chosen scenario. The blocks “time” and “% of usage” are an f(t) signal function that takes the form the user decides by inserting two variables (time and %).

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0.3 0

Gain Constant17

1 > 1 > PF11 constant flow flow(t) s s Integrator Integrator4 MAX Pump Flow of Tank 1 AntiTurbulance Full tank use of valve 1 over time Switch 1 Switch 1 0.3 0

Gain5 Constant8

1 > 1 > PF12 constant flow flow(t) s s Integrator5 Integrator1 MAX Pump Flow of Tank 2 AntiTurbulance Full tank use of valve 2 over time Switch 2 Switch 2 SUM OF FLOW 0.3 0 1

Gain6 Constant9

1 > 1 > PF13 constant flow flow(t) s s Integrator6 Integrator2 MAX Pump Flow of Tank 3 use of valve 3 over time AntiTurbulance Full tank Switch 3 Switch 3 0.3 0

Gain7 Constant10

1 > 1 > PF14 constant flow flow(t) s s Integrator7 Integrator3 MAX Pump Flow of Tank 4 AntiTurbulance Full tank use of valve 4 over time Switch 4 Switch 4 Figure 4. LNGC subsystem modeled in Simulink.

First, the subsystem subsystem “use “use of of valve valve i iover over time” time” was was used used to to formulate formulate the the signal signal as asa function a function of oftime. time. The The actual actual LNG LNG flow flow is continuous is continuous and andhas hasbeen been set as set a asfunction a function of time. of time. Its signal Its signal will pass will passthrough through the switch the switch blocks. blocks. The role The of role the of“anti-turb the “anti-turbulenceulence switch” switch” and “full and tank “full switch” tank switch” is to reduce is to reducethe pump the flow pump for flow safety for and safety functional and functional reasons, reasons, when the when LNGC the LNGC cargo tank cargo reaches tank reaches a certain a certain limit. limit.In every In case, every the case, user the sets user the sets percentage the percentage by whic byh the which LNG the flow LNG will flow be willreduced be reduced to. In the to. current In the currentresearch, research, the LNG the flow LNG decrease flow decrease is represented is represented by the by 0.3 the (or 0.3 30%) (or 30%) gain gainvalue. value. Furthermore, Furthermore, the theswitches switches are areintended intended to stop to stop the the flow flow completely, completely, when when the the LNGC LNGC tank tank has has reached reached its its preset preset limit. limit. The two switches have an input which is the volu volumeme of LNG that has passed from the pump. Volume Volume is calculated by integrating the flowflow of LNG over time,time, via the use of a pair of “integrator” blocks for each cargo tank. It is observed that when the full tank switch commutes between positions, the gas flowflow changes steeply without aaffectingffecting the simulation result, because the valve placement is rapid in comparison with the time horizon of the simulation. Each Each switch switch block block has has three three input, input, one one threshold, threshold, and one output values. values. The The two two inputs inputs are are the the signal signalss which which the the block block will will process process and and select select one one as asthe the output, output, while while the thethird third input input is the is thereference reference value value that thatthe block the block usesuses to make to make the decision. the decision. The Thethreshold threshold is selected is selected by the by theuser user for foreach each LNGC LNGC an andd the the FSRU. FSRU. In In the the end, end, the the signals signals from from the four tanks are combined to create the overalloverall flowflow to simulate the unloading of each LNGC in its entirety. The modeling of the FSRU subsystem, as displayeddisplayed in Figure 55,, enablesenables thethe simulationsimulation ofof thethe loading process andand thethe subsequent LNGLNG vaporizationvaporization overover time.time. The blocks for the FSRU cargo tanks are built in a similarsimilar fashion to thethe LNGCLNGC blocks.blocks. Indicatively, there are four tanks in the selected FSRU, as this is the usual case, and each one of themthem hashas itsits ownown blockblock series.series. The LNG flow from the LNGC to the FSRU is represented as a separate subsystem. The signal of the FSRU cargo tanks is processed to ensure that when a tank is filled up to its given limit, the LNG flow is directed to the next empty tank. With the loading rate known (LNG rate from LNGC to FSRU), the flow signal is an input for the FSRU tank valve component, which simulates the flows according to a user-defined function. The simulation time for the FSRU is not limited to the discharging process of one LNGC, but includes all the operations taking place during the time horizon of the tool (29 days).

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Constant13 4 1 Constant12 Constant2 0

% of usage 1 Flow before valve 1 Tot al L NG 1 Flow after valve 1 LNG IN 1 control valve 1 gas 1 FSRU TANK VALVE 1 FSRU TANK 1 U counter1 TFF1

Constant14 Constant 1 Constant1 Chart 1 Product8

% of usage 2 Flow before valve 2 control valve 2 Tot al LNG 2 U counter2 Flow after valve 2 LNG IN 2 TFF2 gas 2 Switch5 FSRU TANK VALVE 2 Constant9 0 ~= FSRU TANK 2 Chart1 Saturation Constant15 1

1 Saturation1 Vollume(t) of Tanks 1 % of usage 3 Flow before valve 3 LNG total flow Tot al LNG 3 U counter3 Flow after valve 3 control valve 3 LNG IN 3 TFF3 gas 3 Saturation2 FSRU TANK VALVE 3 Constant10 FSRU TANK 3 Chart2 Constant16 Saturation3 1

% of usage 4 Flow before valve 4 Tot al L NG 4 U counter4 Flow after valve 4 LNG IN 4 TFF4 control valve 4 gas 4 FSRU TANK VALVE 4 Constant11 FSRU TANK 4 Chart3

Figure 5. Figure 5. TheThe FSRU FSRU subsystem subsystem modeled in in Simulink. Simulink. FSRU loading must satisfy the mass balance principle and is assumed to comply with the respective rulesThe LNG and regulations flow from to the ensure LNGC its stability to the andFSRU safe is operation. represented According as a separate to the mass subsystem. balance principle The signal of thethe FSRU total cargo mass accumulationtanks is processed in a system to ensure without that bu whenffer must a tank be equalis filled to zero.up to Inits order given to limit, satisfy the the LNG flow principleis directed in theto the system, next aempty feedback tank. signal With is the added, loading which rate will known re-introduce (LNG the rate excess from LNG LNGC resulting to FSRU), the flowfrom signal the valve is an block input to for the the system, FSRU when tank a tankvalve fills component, up. The Simulink which simulates component the performing flows according the to a user-definedabove procedure function. is shown The in simulation Figure5. time for the FSRU is not limited to the discharging process of one LNGC,The signal but ofincludes the FSRU all tank the subsystemoperations accounts taking forplace the LNGduring flow the into time the tankhorizon and theof the outflow tool (29 days).of gas (vaporized LNG) sent out over time. The technical characteristics for the vaporizer are set by the userFSRU and loading its flow must time sequence satisfy the generates mass thebalance LNG flowprinciple rate heading and is for assumed gasification. to comply By comparing with the the total volume within the tank, to the tank filling limits the model which computes the LNG flow respective rules and regulations to ensure its stability and safe operation. According to the mass into the tank over time. The LNG flow is then converted to a volume signal, which is directed through balance principle the total mass accumulation in a system without buffer must be equal to zero. In a switch comparing the volume with the filling limit of the tank to avoid exceeding it. It is worth ordernoting to satisfy that thethe LNG principle balance in within the system, the FSRU a feedback can be negative, signal inis caseadded, there which is only will LNG re-introduce outflow for the excessgasification LNG resulting without anfrom LNGC the discharging.valve block to the system, when a tank fills up. The Simulink componentIn Sectionperforming3, the validity the above of the procedure proposed simulationis shown in model Figure is checked 5. through di fferent structured scenariosThe signal for of the the operation FSRU tank of an subsystem FSRU. The accounts simulation for assumes the LNG basic flow technical into the characteristics tank and the for outflow the of gasLNGC (vaporized and FSRU. LNG) In addition sent out to over validation, time. theThe case technical study results charac willteristics be used for to the discuss vaporizer implication are inset by the usermanagement and its issuesflow regardingtime sequence FSRU terminal generates operations. the LNG flow rate heading for gasification. By comparing the total volume within the tank, to the tank filling limits the model which computes the 3. Case Study LNG flow into the tank over time. The LNG flow is then converted to a volume signal, which is directed throughIn this section, a switch we presentcomparing the results the volume of the four with numerical the filling examples. limit of Inthe the tank first to set avoid of scenarios, exceeding it. It iswe worth conducted noting a comparison that the LNG between balance the twowithin diff erentthe FSRU demand can scenarios be negative, to see in how case this there factor is aonlyffects LNG the inventory management of the FSRU, when five (5) identical vessels discharge their cargo during outflow for gasification without an LNGC discharging. a monthly period. In the second set of scenarios, we repeat the simulations, albeit with five (5) In Section 3, the validity of the proposed simulation model is checked through different different vessels. structuredFirst, scenarios the assumptions for the andop inputeration parameters of an FSRU. are presented, The simula followedtion by assumes the presentation basic oftechnical the characteristicsresults. The for simulations the LNGC were and implemented FSRU. In addition in Simulink to onvalidation, a personal the computer case study with anresults AMD will Ryzen be 5used to discuss3500U implication with Vega Mobile in management Gfx 2.10 GHz issues and 6 regarding GB RAM. FSRU terminal operations.

3. Case Study In this section, we present the results of the four numerical examples. In the first set of scenarios, we conducted a comparison between the two different demand scenarios to see how this factor affects the inventory management of the FSRU, when five (5) identical vessels discharge their cargo during a monthly period. In the second set of scenarios, we repeat the simulations, albeit with five (5) different vessels.

Logistics 2020, 4, 31 9 of 16

3.1. Assumptions The structured case study examines six (6) scenarios corresponding to a realistic FSRU operational profile, whilst adopting assumptions common to all scenarios. For the purpose of the study, five (5) vessels are calling the FSRU terminal, with the main parameters presented in Tables2 and3. Each LNGC is assumed to arrive loaded to the terminal with the contracted cargo and without calculating part of the cargo consumed as fuel. In the beginning of the simulation, the FSRU is considered to be empty of cargo. Each LNGC and the FSRU consist of four (4) cargo tanks, with the nominal capacity of each of them set by the user prior to the simulation. The piping system and consequently the flow rate are considered to be identical for all the LNGCs as presented in Section 2.2.

Table 2. Parameters for scenarios 1, 2 and 3.

Input Parameter Value Units LNGC 1 LNGC 2 LNGC 3 LNGC 4 LNGC 5 FSRU Tank 1 storage capacity 20,000 35,000 35,000 35,000 35,000 20,000 Tank 2 storage capacity 40,000 42,182 42,182 42,182 42,182 40,000 Tank 3 storage capacity 40,000 42,182 42,182 42,182 42,182 40,000 m3 Tank 4 storage capacity 32,000 37,096 37,096 37,096 37,096 32,000 Tank level 2000 LNG ﬂow rate from the LNGC 0.94 - m3/s

Table 3. Parameters for scenarios 4, 5 and 6.

Input Parameter Value Units LNGC 1 LNGC 2 LNGC 3 LNGC 4 LNGC 5 FSRU Tank 1 storage capacity 18,750 10,200 21,000 11,250 16,500 20,000 Tank 2 storage capacity 37,500 20,400 42,000 22,500 33,000 40,000 Tank 3 storage capacity 37,500 20,400 42,000 22,500 33,000 40,000 m3 Tank 4 storage capacity 31,250 17,000 35,000 18,700 27,500 32,000 Tank level 2000 LNG ﬂow rate from the LNGC 0.94 - m3/s

The parameter “storage capacity” is an input for both the vessels and the FSRU. For each LNGC it accounts for the cargo delivered, whereas for the FSRU it quantifies the storage capacity available. This parameter is identical for each vessel in scenarios 1, 2 and 3, but it is given a different value in scenarios 4, 5 and 6, in order to check how it affects the planning process. The filling level for each cargo tank in the LNGCs and the FSRU are set in advance by the user to enable the start/stop of the LNG flow. Except for the above, a dedicated FSRU parameter, “NG send out rate”, is set to represent the onshore gas demand. This is an input parameter that relates to the replenishment of the LNG inventory and the gasification of LNG. The demand is presented in the form of a Figure displaying the time evolution of gas demand that the FSRU must meet, thus adjusting the operational capacity of its vaporizer unit. Figure6 illustrates the onshore gas demand for the scenarios under study.

3.2. Results In this section, the simulation results for the scenarios in regards to the monthly operation of an FSRU terminal are addressed. The operation includes the: (a) LNG STS transfer from the LNGCs to the FSRU, (b) the LNG inventory level in the FSRU and, (c) the gas send-out rate to the onshore network. The results obtained by the proposed simulation model are shown in Figures7–9. Logistics 2020, 4, 31 10 of 16

(a) Demand for scenario 1. (b) Demand for scenarios 2 and 3.

Figure 6. Natural gas demand for diﬀerent operation scenarios presented in the form of send out rate from the FSRU. Logistics 2020, 4, 31 11 of 16

(a) Scenario 1: 5 identical LNGCs discharging. Low gas demand. (b) Scenario 2: 5 identical LNGCs discharging. High gas demand. (c) Scenario 3: 5 identical LNGCs discharging. Alternate management for high gas demand.

(d) Scenario 4: 5 different LNGCs discharging. Low gas demand. (e) Scenario 5: 5 different LNGCs discharging. High gas demand. (f) Scenario 6: 5 different LNGCs discharging. Alternate management for high gas demand.

Figure 7. LNG pumped to the vaporizer of the FSRU for diﬀerent operation scenarios. Logistics 2020, 4, 31 12 of 16

Figure 8. LNG stored in each cargo tank of the FSRUs for diﬀerent operation scenarios. Logistics 2020, 4, 31 13 of 16

Figure 9. LNG inventory held in the FSRU for diﬀerent operation scenarios. Logistics 2020, 4, 31 14 of 16

Figure7 shows the time evolution of the LNG sent from each cargo of the FSRU to the vaporizer unit. The difference of the LNG flow between low (a,d) and high (b,c,e,f) gas demand scenarios is evident. In all cases, it is adjusted to meet the required rate of gas send out to the onshore network. Figures8 and9 summarize the time evolution of the LNG volume inside the FSRU. The versatility of the proposed tool enables the user to simulate the LNG inventory in each tank independently, as well as monitor the total volume to enable holistic inventory management. As a result, the user has a complete picture of the volume of LNG within the FSRU tanks over the defined time period (29 days). The user can check the scenarios for operational feasibility. This is proved by the fact that the simulation results in Figure8b,e and Figure9b,e show a defect in the preliminary vessel arrival schedule. Before the arrival of each LNGC, the LNG inventory stops decreasing, which is an indication that no further LNG is pumped for vaporization. Consequently, the FSRU does not send gas for a short time period before the arrival of each vessel. In the aforementioned scenarios, the terminal would not operate as planned and consequently the gas demand onshore would not be satisfied. To resolve this issue, a different arrival time for each LNGC was used as input to the model. The results of the simulation with the new arrival time are those of scenarios 3 and 6. From Figure8c,f and Figure9c,f, it can be deduced that the new schedule for LNGC berths to the FSRU deals with the requirement for uninterruptible gas send out. The schedule of arrivals for each LNGC is presented in Table4.

Table 4. Arrival schedule for each LNGC.

Scenario LNGC1 LNGC2 LNGC3 LNGC4 LNGC5 Units 1, 2, 4, 5 0 500,000 1,000,000 1,500,000 2,000,000 3 0 450,000 940,000 1,402,400 1,850,000 s 6 0 415,000 850,000 1,252,800 1,600,000

4. Conclusions and Discussion The paper presents a novel simulation tool for FSRUs, as more and more such units have been operating in recent years worldwide. The underlying simulation model incorporates all the technical features of the LNGC and the FSRU involved in LNG STS (pumps, valves, tanks). Using a user defined gas demand, the model produces a simulation for the LNG discharged inside the FSRU, a volume stored there and the evolution of the LNG regasified and fed in the onshore network with a monthly frequency. The simulations can check the system sensitivity to different parameters. A support schedule regarding: (i) slots for LNG carrier calls, (ii) LNG inventory fluctuation, and (iii) the impact of gas demand and send-out rate changes. The MATLAB and Simulink programming environment was used to implement the proposed tool. Simulink, through its simplicity as a graphical interface and its ability to handle a multitude of options (libraries, blocks, etc.) proves to be a suitable environment. Different scenarios are selected to validate the proposed planning tool, while modifying various parameters. The tool was checked against variations in regard to the LNGC cargo size delivered to the FSRU. Another parameter was the LNG flow to the vaporizer as per gas demand onshore. By examining two gas demand profiles, the versatility of the tool is illustrated in terms of planning the LNGC arrivals and adjusting the flow rate to the FSRU vaporizer. In conclusion, the simulation of an FSRU unit as shown by the results achieves the goals set initially. The model developed can support the preliminary tactical planning of FSRU operations. The interpretation of the aforementioned figures validate the capacity of the simulation model to create various scenarios, thus providing the user with a complete and comprehensive picture of the system’s sensitivity to natural gas consumption fluctuations, possible arrival delays for the LNGCs, maintenance operations, etc. Logistics 2020, 4, 31 15 of 16

Several other interesting extensions of the problem studied can be considered in future work. Developing further the simulation of FSRU operations may include some technical aspects such as the management of BOG in the cargo tanks, which is part of the LNG cargo inside the FSRU. The presence of BOG in the model will affect the LNG flows which in turn will affect STS transfer time. Another suggestion for future study is to add parameters related to weather. Wind and wave conditions affect the LNGC berthing to the FSRU terminal and the operation of the FSRU itself. The inclusion of such parameters could limit the operational window of the FSRU and provide a more accurate profile for locations and months with adverse weather. Finally, a non-constant over time gas demand profile can be examined, i.e., with hourly peaks, daily peaks. Such changes might derive from the process of time-series for existing FSRUs in operation and will lead to several useful insights regarding tactical planning.

Author Contributions: Conceptualization, C.P.; methodology, C.P., E.A. and D.V.L.; software, E.A.; validation, E.A.; formal analysis, C.P. and E.A.; investigation, E.A.; resources, C.P.; data curation, E.A.; writing—original draft preparation, C.P. and E.A.; writing—review and editing, C.P. and E.A.; visualization, E.A.; supervision, D.V.L.; project administration, C.P. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest. Logistics 2020, 4, x FOR PEER REVIEW 13 of 14 Appendix A Appendix A

VALVE

VM1 VM2 VMB1 VM3 VM4 PUMP VC11 VC12 VC10 VS1 VS2 VS3 VS4 COMPRESSOR HIGH HD COMPRESSOR DUTY/LOW DUTY VC8 VC9 VC7

VB6 HD COMPRESSOR LNG STRIPPING/SPRAY CROSSOVER VC5 VC6 VC4 ΒΟG VAPOUR CROSSOVER LD COMPRESSOR Strip Line VC2 LIQUID CROSSOVER VC3 VC1

VS5 VB4 LD COMPRESSOR VB5 STRIPPING/SPRAY HEADER VAPOUR HEADER LIQUID HEADER

VL44 VL34 VL24 VL14 VB41 VB31 VB21 VB11 VS41 VS31 VS21 VS11

VL41 VS44 VS42 VS43 VL31 VS34 VS32 VS33 VL21 VS24 VS22 VS23 VL11 VS14 VS12 VS13 VL42 VL32 VL22 VL12 VL43 VL33 VL23 VL13

CARGO CARGO CARGO CARGO TANK 4 TANK 3 TANK 2 TANK 1 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 Figure A1. AA schematicschematic of of the the LNGC LNGC components components used used during during discharging discharging (authors’ (authors’ illustration illustration based basedon relevant on relevant technical technical manuals). manuals).

VALVE

VM1 VM2 VMB1 VM3 VM4 PUMP VC11 VC12 VC10 VS1 VS2 VS3 VS4 COMPRESSOR HIGH HD COMPRESSOR DUTY/LOW DUTY VC8 VC9 VC7

VB6 HD COMPRESSOR LNG STRIPPING/SPRAY CROSSOVER VC5 VC6 VC4 ΒΟG VAPOUR CROSSOVER LD COMPRESSOR Strip Line VC2 LIQUID CROSSOVER VC3 VC1

VS5 VB4 LD COMPRESSOR VB5 STRIPPING/SPRAY HEADER VAPOUR HEADER LIQUID HEADER

VL44 VL34 VL24 VL14 VB41 VB31 VB21 VB11 VS41 VS31 VS21 VS11

VL41 VS44 VS42 VS43 VL31 VS34 VS32 VS33 VL21 VS24 VS22 VS23 VL11 VS14 VS12 VS13 VL42 VL32 VL22 VL12 VL43 VL33 VL23 VL13

CARGO CARGO CARGO CARGO TANK 4 TANK 3 TANK 2 TANK 1 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 Figure A2. A schematic of the FSRU components used during discharging (authors’ illustration based on relevant technical manuals).

References

1. IGU. 2020 World LNG Report—IGU; IGU: Barcelona, Spain, 2020; p. 68. 2. Songhurst, B. Floating LNG Update-Liquefaction and Import Terminals; Oxford Institute for Energy Studies: Oxford, UK, 2019. 3. Artana, K.B. Multiple Criteria Decision Making (MCDM) Process in Selecting Location for Floating Storage and Regasification Unit (FSRU): A Case Study of Bali Island Project. In Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, HI, USA, 31 May–5 June 2009; pp. 393–400. 4. Lee, S.; Choi, B.C. Thermodynamic assessment of integrated heat recovery system combining exhaust-gas heat and cold energy for LNG regasification process in FSRU vessel. J. Mech. Sci. Technol. 2016, 30, 1389– 1398.

Logistics 2020, 4, x FOR PEER REVIEW 13 of 14

Appendix A

VALVE

VM1 VM2 VMB1 VM3 VM4 PUMP VC11 VC12 VC10 VS1 VS2 VS3 VS4 COMPRESSOR HIGH HD COMPRESSOR DUTY/LOW DUTY VC8 VC9 VC7

VB6 HD COMPRESSOR LNG STRIPPING/SPRAY CROSSOVER VC5 VC6 VC4 ΒΟG VAPOUR CROSSOVER LD COMPRESSOR Strip Line VC2 LIQUID CROSSOVER VC3 VC1

VS5 VB4 LD COMPRESSOR VB5 STRIPPING/SPRAY HEADER VAPOUR HEADER LIQUID HEADER

VL44 VL34 VL24 VL14 VB41 VB31 VB21 VB11 VS41 VS31 VS21 VS11

VL41 VS44 VS42 VS43 VL31 VS34 VS32 VS33 VL21 VS24 VS22 VS23 VL11 VS14 VS12 VS13 VL42 VL32 VL22 VL12 VL43 VL33 VL23 VL13

CARGO CARGO CARGO CARGO TANK 4 TANK 3 TANK 2 TANK 1 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2

LogisticsFigure2020 , A1.4, 31 A schematic of the LNGC components used during discharging (authors’ illustration16 of 16 based on relevant technical manuals).

VALVE

VM1 VM2 VMB1 VM3 VM4 PUMP VC11 VC12 VC10 VS1 VS2 VS3 VS4 COMPRESSOR HIGH HD COMPRESSOR DUTY/LOW DUTY VC8 VC9 VC7

VB6 HD COMPRESSOR LNG STRIPPING/SPRAY CROSSOVER VC5 VC6 VC4 ΒΟG VAPOUR CROSSOVER LD COMPRESSOR Strip Line VC2 LIQUID CROSSOVER VC3 VC1

VS5 VB4 LD COMPRESSOR VB5 STRIPPING/SPRAY HEADER VAPOUR HEADER LIQUID HEADER

VL44 VL34 VL24 VL14 VB41 VB31 VB21 VB11 VS41 VS31 VS21 VS11

VL41 VS44 VS42 VS43 VL31 VS34 VS32 VS33 VL21 VS24 VS22 VS23 VL11 VS14 VS12 VS13 VL42 VL32 VL22 VL12 VL43 VL33 VL23 VL13

CARGO CARGO CARGO CARGO TANK 4 TANK 3 TANK 2 TANK 1 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 LNG PUMP 1 AND 2 FigureFigure A2. A2. AA schematic schematic of of the the FSRU FSRU components components used used during during discharging discharging (authors’ (authors’ illustration illustration based based onon relevant relevant technical technical manuals). manuals).

ReferencesReferences

1.1. IGU.IGU. 20202020 World World LNG LNG Report—IGU Report—IGU;; IGU: IGU: Barcelona, Barcelona, Spain, Spain, 2020; 2020; p. 68. 68. 2.2. Songhurst,Songhurst, B. B. FloatingFloating LNG LNG Update-Liquefa Update-Liquefactionction and and Import Import Terminals Terminals; ;Oxford Oxford Institute Institute for for Energy Energy Studies: Studies: Oxford,Oxford, UK, UK, 2019. 2019. 3.3. Artana,Artana, K.B. K.B. Multiple Multiple Criteria Criteria Decision Decision Making Making (MCDM) (MCDM) Process Process in in Selecting Selecting Location Location for for Floating Floating Storage Storage andand Regasification Regasification Unit Unit (FSRU): (FSRU): A A Case Case Study Study of of Bali Bali Island Island Project. Project. In In Proceedings Proceedings of of the the ASME ASME 2009 2009 28th 28th InternationalInternational Conference Conference on on Ocean, Ocean, Offshore Offshore and and Ar Arcticctic Engineering, Engineering, Honolulu, Honolulu, HI, HI, USA, USA, 31 31 May–5 May–5 June June 2009;2009; pp. pp. 393–400. 393–400. 4.4. Lee,Lee, S.; Choi,B.C. B.C. Thermodynamic Thermodynamic assessment assessment of integrated of integrated heat recoveryheat recovery system system combining combining exhaust-gas exhaust-gas heat and heatcold and energy cold for energy LNG regasification for LNG regasification process in FSRU process vessel. in FSRUJ. Mech. vessel. Sci. Technol. J. Mech.2016 Sci., 30 Technol., 1389–1398. 2016, [ CrossRef30, 1389–] 5. 1398.Bisen, V.S.; Karimi, I.A.; Farooq, S. Dynamic Simulation of a LNG Regasification Terminal and Management of Boil-off Gas; Elsevier Masson SAS: Paris, France, 2018; Volume 44. 6. Yoonho, L. LNG-FSRU cold energy recovery regasification using a zeotropic mixture of ethane and propane. Energy 2019, 173, 857–869. [CrossRef] 7. Zhang, G.; Li, B.; Zhang, X.; Wang, Q. Design and Simulation Analysis of Cold Energy Utilization System of LNG Floating Storage Regasification Unit. IOP Conf. Ser. Earth Environ. Sci. 2019, 300, 022117. [CrossRef] 8. Briano, E.; Caballini, C.; Modula, D.; Revetria, R.; Testa, A. A System Dynamics Approach for Managing the LNG Procurement for an Offshore Platform Feeding a Power Plant. In Proceedings of the 9th WSEAS International Conference on System Science and Simulation in Engineering (ICOSSSE’10). World Scientific and Engineering Academy and Society (WSEAS), Stevens Point, WI, USA, 4–6 October 2010; pp. 259–269. 9. Lee, D.H.; Ha, M.K.; Kim, S.Y.; Shin, S.C. Research of design challenges and new technologies for floating LNG. Int. J. Nav. Archit. Ocean. Eng. 2014, 6, 307–322. [CrossRef] 10. Songhurst, B. The Outlook for Floating Storage and Regasification Units (FSRUs); Oxford Institute for Energy Studies: Oxford, UK, 2017. 11. Christiansen, M.; Fagerholt, K.; Nygreen, B.; Ronen, D. Chapter 4 Maritime Transportation. Handb. Oper. Res. Manag. Sci. 2007, 14, 189–284.

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