Renewable and Sustainable Energy Reviews

This paper presents a mathematical model for a multi-period hydrogen supply chain design problem considering several design features not addressed in other studies. The model is formulated as a mixed-integer program allowing the production and storage facilities to be extended over time. Pipeline and tube trailer transport modes are considered for carrying hydrogen. The model also allows finding the optimal pipeline routes and the number of transport units. The objective is to obtain an efficient supply chain design within a given time frame in a way that the demand and carbon dioxide emissions constraints are satisfied and the total cost is minimized. A computer program is developed to ease the problem-solving process. The computer program extracts the geographical information from Google Maps and solves the problem using an optimization solver. Finally, the applicability of the proposed model is demonstrated in a case study from Oman.


Introduction
H 2 has been regarded by governments and experts as a sustainable alternative to diversify the energy portfolio while ensuring supply safety since it can be easily converted into electricity whenever it is required.H 2 has a high energy density, and it is approximately 2.5 times more efficient than gasoline [1].The energy density of H 2 is about 33.6 kW h/kg, while for diesel, this value is about 12-14 kW h/kg.H 2 burns with oxygen, and the by-product is pure water.This property makes H 2 one of the cleanest fuels in terms of emissions of pollutants or greenhouse gases.H 2 can be used as fuel in vehicles or to generate electricity.It can also be used in manufacturing processes to produce chemicals, foods, and electronics.
Designing an H 2 fuel network from production to delivery is a complex supply chain problem.A Hydrogen Supply Chain (HSC) comprises several echelons with a high level of dependency among them.In recent years, numerous studies have used mathematical programming to model the HSC in different countries.Depending on the geographical location of the case study and its requirements, the developed models vary in various aspects.From the perspective of the planning horizon, the existing models can be categorized into static and multi-period Environment, Birmingham City University, B4 7XG, Birmingham, UK.
E-mail address: reza.kia@bcu.ac.uk (R. Kia).models [2].Static models can be used to determine the configuration of the HSC at a point in time.As a result, such models do not provide detailed information about how HSC needs to be evolved.To deal with this issue, some studies suggested the idea of using multi-period models to optimize the evolution of the HSC over a predefined time frame.To compensate for some of the shortcomings in the existing literature, in this paper a new model is presented for designing a Multiperiod Hydrogen Supply Chain (MHSC).The model is formulated as a mixed-integer program allowing the production and storage facilities to be extended over time.Pipeline and tube trailer transport modes are considered for carrying H 2 .The model also allows finding pipeline routes and the number of transport units.A maximal coverage strategy is applied within the model to satisfy H 2 demands.The performance of the model is evaluated in terms of total discounted costs and CO 2 emissions.A computer program is developed to ease the problemsolving process.The computer program uses APIs from Google Maps to extract the geographical information and solves the problem using CPLEX solver.The applicability of the proposed model is demonstrated in a case study from Oman.Finally, the best HSC configuration is determined through scenario comparisons and sensitivity analysis.In summary, the main contributions of this study can be listed as follows: https://doi.org/, where  0 is the number of periods at the design stage) • Pipe-line and Tube trailer are simultaneously considered as the transport modes in an MHSC model.• Salt cavern is considered as one of the storage options in this study.• The proposed model allows the expansion of production plants and storage facilities in different periods.• A maximal coverage strategy is applied to determine how the HSC should evolve.• A computer program is developed to simplify the data-entry and problem-solving process.• Both cost and CO 2 emissions criteria are used to evaluate the performance of the HSC.• The proposed model is applied to a case study from Oman.
Many experts agree that H 2 could play an important role in the future economy.This study can contribute to an efficient design of an HSC in those countries that are planing to increase the share of H 2 fuel in their economy while keeping the CO 2  This makes it possible to easily implement the proposed mathematical model in a case study or use it as a benchmark in future works.

Literature review
In this section, various design features considered in the current literature of the MHSC are discussed and several shortcomings in the existing models are identified.Table 1 gives an overview of the studies dedicated to the category of MHSC design problems, a detailed review of other types of HSC models can be found in [3].In the following sub-sections, these design features are discussed in detail.

H 2 production and storage
H 2 is not naturally found on Earth.Therefore, primary energy should be applied to extract H 2 from renewable sources such as water  Coal Gasification (CG), and Biomass Gasification (BG) are the production technologies that have been considered in the reviewed papers.The WE technology can produce less CO 2 emissions if the electricity used to produce H 2 originates from nuclear or renewable energies.Nevertheless, the other three production theologies release greenhouse gases into the atmosphere.Carbon Capture and Storage (CCS) systems can be used to reduce CO 2 emissions.As is seen in Table 1, Agnolucci et al. [8] and Murthy Konda et al. [6] are the only studies investigating different production technologies with the CCS.H 2 storage facilities play a critical role in an HSC.H 2 storage allows coping with the variability of renewable energy resources and fluctuations in H 2 demands [24].Compression in gaseous form is the most common method to achieve higher storage densities [25].However, high-pressure gas tanks require high investment costs.Salt cavern storage is another viable option, especially for large H 2 volumes [26].Although the storage of H 2 in salt cavern has been investigated in static HSC models, see for example [25,27], still no research work is done to consider this storage option in multi-period models.In an MHSC, it is important to know when and where to establish the production and storage facilities.Except for Murthy Konda et al. [6], the remaining studies assume that once a facility is established, no further changes can be made to increase its capacity.However, in practice, the construction of a facility can be completed gradually to meet the demand requirements while allowing a more distributed investment.

Demand coverage strategy
From the perspective of demand coverage, the existing studies can be classified into complete and maximal strategies [20].In the complete coverage strategy, the demands are known in advance, and the objective is to fulfill the demands completely.In the maximal coverage strategy, a lower limit is set on the total covered demands, and then the model decides how much H 2 should be transferred to each demand location.Such an approach could provide valuable information about how demand nodes should be prioritized for coverage as the HSC network evolves.Among the studied listed in Table 1, only Fazli-Khalaf et al. [20] and Güler et al. [21] have addressed the maximal strategy for the coverage of H 2 demands.Fig. 1.Small example illustrating how pipeline routing can reduce the overall pipeline length,  is the source node,  1 - 4 are the demand nodes, and the number on the edges shows the corresponding shipment amount.

H 2 transport modes
In an HSC, different transport modes can be utilized for carrying H 2 from one location to another.As is seen in Table 1, one of the common H 2 transport modes is tube trailer that has widely been considered in MHSC models.In studies such as [8,20] it is implicitly assumed that the tube trailers are already available, and the transportation cost is calculated by multiplying the distance by the transportation cost per unit distance.Although such an assumption may be valid in other supply chain design problems, in HSCs, it does not match reality.Tube trailers are special-purpose trucks that can safely carry H 2 under high pressure.As a result, it is crucial to determine how many transport units (tube trailers) are required in the network.
Tube trailers are generally feasible for carrying H 2 in smaller quantities; however, other alternatives such as pipeline might be more economical for higher quantities.Although pipeline transport mode has been well studied in static HSC models, see for example [27][28][29][30][31], a few studies have addressed this transport mode in multi-period models.The model presented by Murthy Konda et al. [6] was one of the first attempts considering both pipeline and tube-trailer transport modes.However, for the sake of simplicity, it was assumed that direct pipeline links should be established from source nodes to destination nodes to satisfy the demand in the destination node; this approach is illustrated in Fig. 1(a).In practice, the pipeline can originate from a source node and then extend to other nodes to satisfy their demands; this approach also shown in Fig. 1(b).By implementing this approach, H 2 can be distributed more efficiently in the HSC while using shorter pipeline links and investing less money.Among the studies listed in Table 1, only Agnolucci et al. [8] and Yoon et al. [23] implemented a similar idea in which the CO 2 produced at H 2 production plants is delivered to some storage reservoirs using pipelines.Adding the pipeline transport mode to an MHSC to find the pipeline routes is a computationally challenging problem; because a considerable number of binary decision variables are required to reflect these features in the mathematical model.The optimization problem becomes even more complex if tube trailer transport mode is also included.This might be one of the reasons for the lack of studies in this area.

Objective function
From Table 1, it is seen that monetary criteria such as total costs and net present value are the basis of optimization models in MHSC.Low CO 2 emissions as one of the main aspects of green economy is crucial against climate change and environmental issues.An HSC could be pollutive in terms of greenhouse gases such as CO 2 ; these emissions mainly steam from production, storage, and transport processes.As is seen in Table 1, since 2018, there have been continuous research works addressing CO 2 emissions in the MHSC models.These studies have treated this issue either by directly calculating the amount of CO 2 emissions, see [15][16][17]20], or indirectly by calculating the carbon tax, see [2,18,22].

Case studies
The models presented in the studies listed in Table 1 were all tested on case studies from different countries.Table 2 provides some important information regarding the specification of these case studies and the solution approach applied to solve the optimization problems.This table shows that most of the existing models have been used for longterm planning.Generally, the number of regions and the number of periods are two critical factors that affect the computational complexity of MHSC models.The case study conducted by Bae et al. [19] is one of the largest ones of its kind in the literature.Table 2 also shows that optimization solvers have widely been utilized to solve MHSC models, see also [3].According to Table 2, [18] is the only study applying a metaheuristic optimization method.

Problem statement and mathematical model
A two-stage supply chain framework shown in Fig. 2 is used in this study to formulate a mathematical model for the production and delivery of H 2 .In this framework, the first stage corresponds to the production and storage of H 2 , and the second stage corresponds to the distribution of H 2 to the demand points.In both stages, pipeline and tube trailer can be utilized for transferring H 2 .Notation  is defined to denote the set of all locations.H 2 is produced in production plants and then transferred to storage facilities for distribution to the customers.The set of potential locations where production plants and storage facilities can be established are denoted by  and , respectively ( and  ⊆ ).It is assumed that different production and storage technologies of different capacities can be utilized within the HSC.For each production and storage technology, the capital cost, operating cost, and CO 2 emissions factor are known.The planning horizon is divided into two main time intervals, starting from periods 1 to  0 , and  0 + 1 to  0 +  1 , respectively.Production plants and storage facilities are established in the first time interval to fulfill the H 2 demand.The second time interval is also used to represent the effective lifetime of the HSC.For each location, the potential H 2 demand is known in advance.A parameter called penetration rate is used within periods 1 to  0 to represent how much of the total potential H 2 demand needs to be fulfilled in the corresponding period.Production plants and storage facilities can be extended gradually over periods 1 to  0 , i.e., all facilities should reach their full capacity by the end of period  0 .This approach allows more uniform budget distribution throughout the periods while meeting the demand requirements.Tube trailer and pipeline are two transport modes in the proposed HSC.For each transport mode, parameters such as capacity, capital cost, and operating cost are known.To determine the required number of tube trailers, parameters such as load/unload time, average driving speed, and distances between locations are taken into consideration.The objective of the model is to minimize the total discounted costs of the HSC in a way that demand and CO 2 emissions requirements are met during different periods.Note that the total discounted costs is used to account for the time value of money [6].In this respect, costs for each period are discounted back to the present time (at a certain discount rate) and then summed [8].As mentioned earlier, the planning horizon was divided into time intervals . Since the construction phase of the HSC takes place within time interval [ 1,  0 ] , for the periods belonging to this time interval, both capital and operating costs are incurred.While, within time interval only operating costs are incurred.

Assumptions
The main assumptions made in this study are given below.
• All parameters of the model are certain and known in advance.
• Only the gaseous form of H 2 is studied in this research.
• The logistics of energy sources before the production stage of H 2 is not taken into consideration.• The available budget is not limited at each period, and it would be available at the beginning of each period.• The repair/renewal cost of facilities is disregarded.
• All tube trailers are of the same type.
• All pipelines are of the same diameter.
• Only one pipeline link can be installed from location  to location .• Local H 2 distribution is not considered in this study.

Mathematical model
The problem is now formulated as the following mixed-integer program.
subject to: In the proposed mathematical model, objective function (1) minimizes the total discounted costs.Eq. ( 2) gives the total capital cost associated with the production plants, storage facilities, and pipelines, Eq. (3) corresponds to the total operating cost of the production plants, storage facilities, and pipelines.Eq. ( 4) is the total transportation cost associated with the pipeline and tube trailer transport modes.Constraint set (5) limits the total amount of CO 2 emitted by the production plants, storage facilities, and tube trailers at each period.Constraint sets ( 6) and ( 7) make sure that only one plant type or one storage type can be established at each potential location.Constraint sets ( 8) and ( 9) restrict the number of production plants and storage facilities in the HSC.Constraint sets (10) and (11) ensure that the production plants and storage facilities reach their full capacity by the end of period  0 ; in other words, these constraint sets allow the facilities to be extended gradually.
Constraint set (12) makes sure that the inflow to a location after producing H 2 is equal to the outflow from that location; in other words, this constraint set determines the amount of H 2 which is stored at each period in different locations.Fig. 3(a) illustrates the inflow/outflow of a node in the first stage of the proposed two-stage supply chain framework.Constraint set (13) states that the amount of H 2 shipped by tube trailers from a production plant cannot be greater than the corresponding production amount.Constraint set (14) states that the amount of H 2 shipped from location  via pipeline cannot exceed the amount of H 2 produced at location  plus the amount of H 2 sent by other pipelines to location ; in other words, this constraint set makes sure that pipelines carrying H 2 to the storage facilities are connected to a production plant or other pipelines.It should be noted that constraint sets ( 12)-( 14) are associated with the first stage of the proposed twostage supply chain framework shown in Fig. 2. Constraint set (15) makes sure that the inflow to a location after storing H 2 is equal to the outflow from that location; in other words, this constraint set guarantees that the demand requirements are met in different locations.Fig. 3(b) illustrates the inflow/outflow of a node in the second stage of the proposed two-stage supply chain framework.Constraint set (16) states that the amount of H 2 shipped by tube trailers from a storage facility cannot be greater than the corresponding storage amount.Constraint set (17) states that the amount of H 2 shipped from location  via pipeline cannot exceed the amount of H 2 stored at location  plus the amount of H 2 sent by other pipelines to location ; in other words, this constraint set makes sure that pipelines carrying H 2 to the customers are connected to a storage facility or other pipelines.It should be noted that constraint sets ( 15)-( 17) are associated with the second stage of the proposed two-stage supply chain framework shown in Fig. 2.
Constraint sets (18), (19), (20), and ( 21) are the capacity constraints for the production plants, storage facilities, and pipelines.Constraint sets (22) and (23) prevent installing more than one pipeline from one location to another.Constraint set (24) ensures the committed penetration rate for the H 2 demand is met at each period.Constraint sets (25) and (26) jointly determine the amount of H 2 transferred between locations  and  at period  via tube trailers.Constraint set (27) ensures that the number of tube trailers is enough for carrying H 2 in the HSC.Constraint sets ( 28)-( 30) prevent H 2 shipment in case the distance limit is exceeded.Finally, constraint sets (31)- (36) indicate the type of the decision variables.

Developed computer program
A user-friendly computer program is developed using RAD Studio 10.4.2 [32] programming software. 1The developed program is integrated with APIs from Google Maps to extract geographical information such as the potential locations and the corresponding distances.Once the required data for the HSC is entered, the program can quickly generate the optimization problem and solve it using IBM ILOG CPLEX 20.1.0[33] solver with just one click.As the mathematical model is already embedded in the program, the user is not required to have any mathematical modeling knowledge.This makes it possible to implement the proposed mathematical model in any other case study around the world.After solving the problem, the user can see a detailed solution report, as well as a graphical representation of the HSC on a map.The interface of the developed computer program is shown in Fig. 4. It should be mentioned that this program can also be used as a benchmark in future studies. 1 Developed computer program can be requested by contacting the authors.

Case study
Oman is divided into eleven governorates, Musandam, Al Buraimi, Al Batinah North, Al Batinah South, Muscat, Ad Dhahirah, Ad Dakhiliya, Ash Sharqiyah North, Ash Sharqiyah South, Al Wusta, and Dhofar [34].The governorates are further subdivided into 61 provinces.According to National Center for Statistics and Information [35], in 2020, the population of the residents in these provinces was 4 481 042.There are three Governorates, Dhofar, Al Wusta, and Musandam, which are not taken into consideration in the case study.The Dhofar Governorate is located in Oman's far South, and the Al Wusta Governorate is mainly desert; the Musandam Governorate is also an exclave, separated from the rest of the country by the United Arab Emirates.There is also an island in Ash Sharqiyah South Governorate called Masirah Island, which is neglected in the case study.These reduce the H 2 demand locations to 42 provinces.The total number of residents in the selected provinces is 3 948 034, accounting for 88.11% of Oman's population.The name of the considered provinces, along with their geographical information, can be seen in Table 3 and Fig. 5.

Locations and H 2 demand
For each province, the H 2 demand is estimated based on 20% of the annual electric power consumption.According to The World Bank [36], Oman's annual electric power consumption is 6445.581kWh per capita.Assuming one kg H 2 generates 33.33 kWh of electric power and each year is 365 days, the equivalent amount of H 2 is estimated to be about 0.106 kg H 2 per capita.Now, by multiplying this number by the population of each province, the H 2 demand can be estimated.The estimated daily H 2 demands are given in Table 3.It should be noted that the estimated values are rounded to one decimal place.The number of potential locations for the establishment of H 2 facilities will have a significant impact on the computational complexity of the problem.Therefore, to be able to solve the resulting problem effectively within a given time limit, the potential locations of hydrogen storage and production facilities are limited to eleven provinces, Nizwa, Ibri, Sohar, Rustaq, Barka, Al Buraimi, Al Mudhaibi, Ibra, Sur, Al Seeb, and Muscat.These provinces, also shown in Fig. 5, are either the capital of their corresponding governorate or the province with the highest population in the governorate.

Penetration rate and CO 2 emissions criteria
A time period of ten years (each year as 365 days) is considered for the construction of the HSC network (i.e.,  0 = 10), and after finishing the construction phase, a lifetime of 15 years is assumed (i.e.,  1 = 15).The H 2 penetration rate at the first period is set to 0.1, and after that, it is incremented by 0.1 until it reaches one at the 10th year, that is,   = 0.1 × , for  = 1, 2, … , 10.It should be mentioned that later, in Section 6.3, two additional penetration profiles will be examined.The     of the project is evaluated at an interest rate of 4.0% [37].As a base case, the CO 2 emissions factor is set to 15 kg CO 2 /kg H 2 ; however, later in Section 6.2, some analyses are carried out to investigate the effect of this parameter on the HSC.

H 2 production facilities
In the case study, four representative technologies are considered for the production of H 2 ; these production technologies involve SMR, CG, WE, and BG.There are a maximum of three alternatives for the capacity of the H 2 production technologies; these capacity alternatives are represented in Small (S), Medium (M), and Large (L) sizes.The capacity and cost parameters of the H 2 production technologies are adopted from Bique et al. [38], and the corresponding CO 2 emissions factors are taken from Al-Qahtani et al. [39].H 2 production plants, especially the large SMR and CG plants, are the primary sources of CO 2 emissions [3].So, for the sake of CO 2 reduction, a CCS option is also considered with the SMR and CG technologies.Production of H 2 through the WE technology, however, emits a very low amount of CO 2 .Therefore, CCS is not required for the WE technology.The BG technology is highly CO 2 pollutive.However, for this production technology, capturing CO 2 using a CCS becomes very costly and inefficient [39].Therefore, in the case study, the CCS option is disregarded with BG technology.According to these explanations, three would be fifteen alternatives to be considered for the production of H 2 ; these alternatives are shown in Table 4.It should be mentioned that for the SMR and CG technologies coupled with the CCS option, there were no data for the capital and operating costs of the plants.Therefore, to estimate these parameters, the CCS cost is taken from Al-Qahtani et al. [39] and scaled based on the plant capacity.Then, the resulting cost is added to the costs given in [38].

H 2 storage facilities
For the storage of H 2 , two types of storage facilities are taken into account.The first storage option is an above-ground tank operating at 15-250 bar, and the second is a salt cavern operating at 60-150 bar [25].For the above-ground tank and salt cavern, respectively, five and six storage capacities are defined.Then, based on the capacity of each storage option, the information given in [25] is used to estimate the capital and operating costs.It also should be mentioned that according to Almansoori and Shah [7], the average storage time of H 2 is assumed to be ten days.The information available in [25] however does not include the CO 2 emissions data.Thus, this data is estimated based on the energy required for the compression of H 2 to the given operating pressures.According to Burheim [40], the amount of electric energy required to compress H 2 from one bar to 150 and bar is approximately 1.7 and 1.85 kWh, respectively.Also, according to International Energy Agency: IEA [41], in 2019, natural gas, with 97% share, and crude oil, with 3% share, were the primary sources of electricity generation in Oman [41].These electricity generation sources roughly produce 0.402 kg CO 2 /kWh.As a result, approximately 0.68 and 0.74 kg CO 2 /kg H 2 will be produced for the storage of H 2 in a salt cavern and above-ground tank, respectively.A summary of information for the proposed storage facilities are given in Table 5.

Transport modes
Two types of transport modes are considered in the case study.The first transport mode is tube trailer, and the second one is pipeline.In the following sub-sections, these two transport modes are discussed in detail.

Tube trailer
Two types of tube trailers are considered for the transportation of H 2 .The first type is a conventional tube trailer which has been considered in many case studies such as [28,29,42,43].This type of tube trailer is built from steel and operates at 162 bar [28].Although the capital cost of conventional tube trailers is relatively cheap, their capacity is not high.According to Yang and Ogden [28], a conventional tube trailer costing $300000 can provide a capacity of 300 kg H 2 .The second type of tube trailer considered in the case study is a modern one made from composite materials and can reach a capacity of up to kg H 2 at 500 bar.However, due to the expensive material used in their  The average storage time is assumed to be 10 days [7].a CO 2 emissions data is estimated based on the energy required for the compression of H 2 at the given operating pressures [40,41].
structure, the capital cost of these tube trailers is much higher than conventional tube trailers.Such a tube trailer costs about $1360, $150 for the cab and undercarriage [28], and $1210 for the container [44].Table 6 includes the capacity and capital cost of tube trailers, along with the other necessary information.In this table, the shipping cost comprises the maintenance cost plus the fuel cost of driving in Oman.According to Yang and Ogden [28], 1% of the capital cost is considered as the maintenance cost.So, assuming that the average driving speed is 55 km/h and the tube trailers are available 365 × 18 hours a year, the maintenance cost of conventional and modern tube trailers are calculated as 8.302 × 10 −3 and 3.764 × 10 −2 $/km.The fuel cost for a tube trailer operating in Oman is about 2.803×10 −3 $/km [28,45].Thus, the shipping cost of conventional and modern tube trailers is estimated to be 2.886 × 10 −4 and 3.179 × 10 −4 k$/km, respectively.The general expenses of tube trailers are calculated based on 5% of the capital cost of the corresponding tube trailer.It should be mentioned that the driver wage is estimated based on the average salary of an experienced truck driver in Oman, assuming each month is 22 working days and each day is eight hours [46].Also, the driving distance limit is based on the distance that a driver can travel in eight hours at an average speed of 55 km/h.

Pipeline
The second transport mode considered in the case study is a pipeline.According to Johnson and Ogden [30], a pipeline with a diameter of 20.32 centimeters costs about 285000 $/km, and can transfer up to 120 t H 2 /d.Table 7 gives the required information on this transport mode.
In the proposed mathematical model, a significant portion of the binary variables is associated with the consideration of pipeline transport mode.Since the number of demand points in the case study is relatively large, obtaining a good solution in a reasonable computational time becomes challenging.To deal with this issue, the potential pipeline links in the HSC network can be restricted.So, for each location, only five of the shortest links connecting that location to the other locations are maintained.The selected potential pipeline links are displayed in Fig. 5.As seen in this figure, the minimum number of links originating from each location is five.

Proposed scenarios
Eight main scenarios are defined considering different options introduced for the H 2 transport modes and storage facilities.Table 8 lists the options considered in each scenario.The purpose of defining these scenarios is to compare and evaluate different alternatives for the storage and distribution of H 2 in the case study.As is seen in Table 8, the basic configuration is given in Scenario 1, which only allows the use of conventional tube trailers and above-ground tanks in the HSC.Scenario 8 is the most comprehensive one allowing the simultaneous use of pipelines, tube trailers, above-ground tanks, and salt caverns.

Computational results
Although in Sections 5.1 and 5.5.2 some restrictions were made to reduce the number of binary variables, it might still be difficult to a The shipping cost comprises the maintenance and fuel costs.b The General expenses are based on 5% of the tube trailer's capital cost.c The driver wage is estimated based on the average salary of an experienced truck driver in Oman, assuming each month is 176 working hours.d The driving distance limit is based on the distance that a driver can travel in eight hours at an average speed of 55 km/h.
optimally solve the resulting optimization problems in a limited time frame, especially if the pipeline transport mode is included.Therefore, the solver is interrupted if the solving time exceeds seven hours (25 200 s) or the optimality gap obtained by the solver reaches below 0.2% after two hours (7200 s).It also should be noted that the resulting optimization problems are solved using the developed software, on a Windows 10 operating system with an Intel(R) Core(TM) i7-4510U CPU (operating at the base clock speed of 2.6.GHz) and 8 GB of RAM.A summary of computational results, along with the number of variables and constraints for each scenario, is given in Table 9.For Scenarios 1-4, the optimization problems were optimally solved by CPLEX.For Scenarios 5-7, CPLEX could not solve the optimization problem with a guaranteed optimality proof in the time limit of seven hours; this is due to the inclusion of pipeline transport mode, which has significantly increased the number of constraints and binary variables.However, as is seen in Table 9, in the worst case, the relative optimality gap is 2.17%, meaning that the obtained solutions might be either optimal or near-optimal.Also, for Scenario 8, the solver was interrupted since the optimality gap reached below 0.2% after two hours of solving.

Effects of transport modes and storage facilities
For the proposed scenarios, the   of the HSC network (calculated based on 25 years) can be seen in Table 9.As mentioned in Section 3.2, the   consists of capital and operating costs.For each scenario, a detailed composition of these costs is shown in Fig. 6.The results show that the best configuration of the HSC can be achieved under Scenario 8, which is a combination of pipelines, modern tube trailers, and salt cavern storage.For the last four scenarios, which involve pipeline transport mode, the obtained HSC network is shown in Figs.A.1-A.4 in Appendix; in these figures, the number on the edges shows amount of H 2 which is transported between two locations (the unit is t H 2 /d).In the following sub-sections, further discussions are made regarding the effects of the proposed transport modes and storage types on the HSC.

Conventional tube trailer vs. modern tube trailer
As mentioned in Section 5.5.1, at the expense of higher capital costs, a modern tube trailer can provide a higher capacity than a conventional tube trailer.According to the scenarios defined in Table 8, four cases are associated with comparing these two types of tube trailers.These four cases are presented in Table 10.As is seen in this table, in all the cases, replacing conventional tube trailers with modern tube trailers reduces the  .This result justifies purchasing a modern tube trailer rather than a conventional one despite its higher capital cost.According to this table, this improvement reaches 11.048% in the best case.The number of tube trailers obtained under each scenario is also plotted in Fig. 7. Comparing Scenario 1 versus Scenario 2 and Scenario 3 versus Scenario 4 show that the number of tube trailers has been reduced significantly.Note that in these scenarios, pipeline transport mode has been neglected, and only tube trailers are allowed in the H 2 distribution network.Fig. 7 shows that in Scenario 6 less number of tube trailers are required in comparison with Scenario 5.However, a comparison between Figs.A.1 and A.2 shows that in Scenario 6, due to the higher capacity of modern tube trailers, a higher volume of H 2 is transferred using tube trailers.Unlike the previous cases, in Scenario 8, the required number of tube trailers is more than that in Scenario 7. Nevertheless, when comparing    8.
tube trailers are used for transferring H 2 .So, it can be concluded that if modern tube trailers are taken into consideration, installing many pipeline links is not economically justifiable.

Effect of considering pipeline
To examine the effect of pipeline transport mode on the HSC, four additional scenarios (Scenarios 5-8) were defined in Table 8 by adding the pipeline transport mode to Scenarios 1-4.As a result, there are four different cases to compare.The comparison results are reported in Table 10.From this table, it is seen that in all the cases, adding pipeline transport mode has improved the  ; the highest improvement percentage in the   is about 10.323% which corresponds to the comparison between Scenario 3 versus Scenario 7.These results conclude that pipelines combined with modern tube trailers are the best options for transferring H 2 , and conventional tube trailers are not recommended to be used in Oman's future HSC network.One of the main contributions of this study is the consideration of tube trailer and pipeline transport modes in an MHSC model, which allows for determining the pipeline routes and the number of transport units.The solutions depicted in Figs.A.1-A.4 demonstrate how the HSC can benefit from such a feature by simultaneously employing tube trailers and pipelines in the H 2 distribution network.The supply chain network could have benefited further from the pipeline transport mode if a broader range of potential pipeline links had been considered.However, the excess computational complexity of the resulting problem was  8. a barrier to consider more potential pipeline links.Another restricting assumption made in the proposed model is that only one pipeline link can be installed from a location to another, while in practice, it can be more than one.Also, it is more realistic to extend the model to include different pipeline diameters.These issues, along with the development of a more efficient solution method are the important topics that remain to be addressed in future works.4 show, such a large-scale storage facility makes the operations much more centralized.Although the results suggest that the storage of H 2 in the salt cavern is very promising, further technical and analytical investigations are required before implementing the salt cavern storage in Oman's HSC.Another important issue that needs to be highlighted is that this study only focused on the gaseous form of H 2 , while in practice, H 2 can also be stored and transferred in liquid form.This product form will require some additional facilities in the production, storage, and distribution stages of the HSC.Therefore, in future works, the proposed model can be extended to decide the product form of H 2 as well.

Effect of CO 2 emissions intensity on the HSC
In all the scenarios discussed so far, it was assumed that the CO 2 emissions intensity is not allowed to exceed 15 kg CO 2 /kg H 2 in each period, i.e.,   = 15 for  ∈  .In this sub-section, further analysis is carried out to investigate the effect of this parameter on the HSC.Among the eight scenarios considered in the case study, Scenario 8 was the best-case scenario in terms of the  .So, this scenario is selected as the basis of sensitivity analysis.For the solution obtained under Scenario 8, the CO 2 emissions intensity was about 11.125 kg CO 2 /kg H 2 .Now, considering the assumptions made under Scenario 8, the problem is optimized for different CO 2 emissions intensities ranging from   = 12 to   = 2 (kg CO 2 /kg H 2 ) for  ∈  .Fig. 8 shows the resulting Pareto frontier for the production cost and CO 2 emissions intensity.This figure also shows how the production cost of H 2 increases by reducing CO 2 emissions intensity.The amount of CO 2 produced by plants, storage facilities, and tube trailers under different levels of CO 2 emissions intensities is shown in Fig. 9. From this figure, it is seen that even under the lowest level of CO 2 emissions intensity, plants are the primary sources of CO 2 emissions.The interesting finding from this figure is that even though tube trailers burn fossil flue for carrying H 2 , their role in CO 2 emissions is neglectable compared to plant and storage facilities.As a result, if CO 2 emissions reduction is a goal, production plants and storage facilities are the main priorities to focus on.
In this study, the definitions provided by Ewing et al. [48] are applied as a reference for evaluating the CO 2 emissions of the HSC.From the perspective of CO 2 emissions, Ewing et al. [48] classified H 2 into three main types: green, blue, and gray.In this classification, the CO 2 emissions intensity for the green, blue and gray H 2 should lie within the following intervals [0-0.6],[2.3-4.1], and [11.3-12.1]kg CO 2 /kg H 2 , respectively.For each type of H 2 , these intervals are also highlighted in Fig. 8.As seen in this figure, in the worst situations, the CO 2 emissions intensity is about 11.125 kg CO 2 /kg H 2 , almost falling into the gray H 2 category.In this case, the production cost is about 1.679 $/kg H 2 .Two solutions fall into the blue H 2 requirements.Also one solution falls between the green and blue H 2 requirements.This figure shows that CO 2 emissions intensity can be reduced from 11.125 to 4 kg CO 2 /kg H 2 .However, this would increase the production cost from 1.679 to 2.265 $/kg H 2 by 34.87%.For this case, the evolution of the HSC for the even periods, i.e., periods 2, 4, 6, 8, and 10, are illustrated in Figs.A.5-A.9 in Appendix.Comparing Fig. A.9 with Fig. A.4 shows that to achieve blue H 2 , the production plant located in Al-Seeb province needs to be equipped with the CCS.Also, an additional SMR plant with a capacity of 150 t H 2 /d, as well as a salt cavern storage with a capacity of 1000 t, is required to be installed in Nizwa province.It should be noted that it is not required to equip the new production plant with the CCS, as the current configuration meets the CO 2 emissions intensity of 4 kg CO 2 /kg H 2 .
To avoid further complications in the resulting optimization problem, the logistics of energy sources were neglected in this study.Although the results from the case study show that using CCS in the production plants can lead to blue H 2 production, still it is not possible to produce green H 2 .To achieve this goal, one possibility could be utilizing green energy sources, such as solar and wind, for generating the electricity used in different parts of HSC.H 2 could play an important role in large-scale electricity storage.Surplus electricity produced during off-peak periods can be used to power up electrolysis plants and produce H 2 .The H 2 produced from this process can be stored and converted back to electricity at peak times, thus providing power balance for the grid.Therefore, further research can be done in future studies to address these issues.

Effect of different penetration profiles on the HSC
To determine the shape of H 2 demand over different time periods, a market penetration analysis needs to be carried out.In Section 5.2, it was assumed that the penetration rate of the H 2 demand increases linearly.In this section, two additional penetration profiles, S-shape [4,21] and piecewise linear [7,17] are taken into consideration to examine the effect of penetration rate on the HSC.Fig. 10 shows the trajectory of the penetration rate for each profile.Under the S-shaped penetration profile, the potential H 2 demand is expected to have an S-shape trajectory, where in early periods, the potential demand is expected to be limited.However, the potential demand increases sharply during the mid-periods, and eventually, it levels off in the last periods.Under the piecewise penetration profile, the potential H 2 demand is expected to increase linearly in a piecewise manner.According to these explanations, two additional optimization problem were solved using the CPLEX solver.It was determined that for the S-shape and piecewise penetration profiles, the   is about $2981M and $2875M, respectively, thus reducing the   by 5.24% and 8.36% compared to the base case, i.e., linear penetration profile.Despite having a considerable difference in the resulting  , the final HSC configuration is still the same for all three penetration profiles.However, the way that HSC evolves throughout the periods is different.Designing an HSC is a long-term process that takes place in a highly uncertain environment.Besides the uncertainty of environment, parameter estimation error is another factor that can significantly affect the optimization results.In supply chain design problems, essentially,  a wide variety of parameters are involved.Therefore, a significant amount of the work should be spend on reliable data collection and analyzing the effects of the parameters on the final design.Although techniques such as sensitivity analysis can provide some insights into the effects of such uncertainties on the final design of the HSC, employing more specific techniques, such as stochastic and robust optimization, could be more suitable and reliable for decision-making.

Conclusion
This paper presented a mathematical model for designing a multiperiod Hydrogen Supply Chain (HSC) considering pipeline and tube trailer transport modes.The model was formulated as a mixed-integer program allowing the production and storage facilities to be extended over time.The model also allows finding pipeline routes and the  number of transport units.The objective was to obtain an efficient plan for designing an HSC in a way that the demand and CO 2 emissions constraints are satisfied and the total cost is minimized.A computer program was developed to ease the problem-solving process.As the mathematical model is embedded in the developed computer program, the user is not required to have any mathematical modeling knowledge.This makes it possible to easily implement the proposed mathematical model in a case study or use it as a benchmark in future works.This study can contribute to an efficient design of an HSC in those countries that are planing to increase the share of H 2 fuel in their economy while keeping the CO 2 emissions low.To demonstrate this, a case study is provided from Oman.Different production and storage technologies, along with the CCS option, were examined in the case study.The option of using conventional tube trailers (built from steel) was compared against modern tube trailers (made from composite materials).The results of this comparison showed that although modern tube trailers are much   more expensive than conventional ones, their higher capacity makes it possible to reduce the total costs considerably, in some cases up to 11.048%.A comparison was also made to evaluate the effectiveness of pipeline transport on the HSC.It was shown that pipelines combined with modern tube trailers are the best options for transferring H 2 in Oman's future HSC.Next, two storage options were compared: aboveground tanks and underground salt caverns.The optimization results showed that storage of H 2 in salt caverns can reduce the total costs by up to 43%, as salt caverns can offer much higher capacity with much less capital cost.Finally, sensitivity analysis was carried out to estimate the CO 2 emissions of the HSC.The results revealed that even with the CCS, production plants are the primary source of CO 2 emissions.The results also indicated that even though tube trailers burn fossil flue for carrying H 2 , their role in CO 2 emissions is neglectable compared to plant and storage facilities.Lastly, it was shown that the HSC could achieve blue hydrogen requirements by employing the CCS.By doing

Fig. 3 .
Fig. 3. Inflows and outflows corresponding to a node in the HSC network.

Fig. 4 .
Fig. 4. Interface of the developed computer program for designing an HSC.

Fig. 5 .
Fig. 5. Map of Oman showing the provinces along with the potential pipeline links and potential locations for the placement of H 2 storage and production facilities.
Fig. A.3 related to Scenario 7 against Fig. A.4 related to Scenario 8, it is seen that many pipeline links installed in Scenario 7 are not used in Scenario 8. Instead, modern

Fig. 6 .
Fig. 6.Composition of cost components in the solutions obtained under the scenarios defined in Table8.

Fig. 7 .
Fig. 7. Number of tube trailers obtained for the HSC considering the scenarios defined in Table8.

Fig. 8 .
Fig. 8. Pareto frontier obtained based on Scenario 8, where green, blue, and gray regions are defined according to Ewing et al. [48].

Fig. 11 .
Fig. 11.Evolution of the HSC under Scenario 8 considering penetration profiles shown in Fig. 10.
Figs. 11(a) and 11(b) show how the demand requirement under each penetration profile can be met by gradually completing the construction of the production plants

Fig. A. 1 .
Fig. A.1.HSC network obtained based on Scenario 5, where above-ground tank is used for the storage of H 2 and a combination of pipeline and conventional tube trailer is used as the transport modes.

Fig. A. 2 .
Fig. A.2. HSC network obtained based on Scenario 6, where above-ground tank is used for the storage of H 2 and a combination of pipeline and modern tube trailer is used as the transport modes.

Fig. A. 3 .
Fig. A.3.HSC network obtained based on Scenario 7, where salt cavern is used for the storage of H 2 and a combination of pipeline and conventional tube trailer is used as the transport modes.

Fig. A. 4 .
Fig. A.4. HSC network obtained based on Scenario 8, where salt cavern is used for the storage of H 2 and a combination of pipeline and modern tube trailer is used as the transport modes.

Fig. A. 5 .
Fig. A.5. HSC network obtained based on Scenario 8 (for the 2nd period) meeting the blue H 2 requirements with a CO 2 emissions intensity of 4 kg CO 2 /kg H 2 .

Fig. A. 6 .
Fig. A.6.HSC network obtained based on Scenario 8 (for the 4th period) meeting the blue H 2 requirements with a CO 2 emissions intensity of 4 kg CO 2 /kg H 2 .

K
.Forghani et al.

Fig. A. 7 .
Fig. A.7. HSC network obtained based on Scenario 8 (for the 6th period) meeting the blue H 2 requirements with a CO 2 emissions intensity of 4 kg CO 2 /kg H 2 .

Fig. A. 8 .
Fig. A.8. HSC network obtained based on Scenario 8 (for the 8th period) meeting the blue H 2 requirements with a CO 2 emissions intensity of 4 kg CO 2 /kg H 2 .
emissions low.As the Distance limit for transferring H 2 via tube trailer (km)  Number of days in each period  Average storage time of H 2 in a storage facility (d)  Maximum number of production plants allowed to be established in the Hydrogen Supply Chain (HSC)  Maximum number of storage facilities allowed to be established in the Hydrogen Supply Chain (HSC)   Fixed operating cost of pipeline (k$/km)  Capacity of a tube trailer per each trip (t H 2 )  Average speed of a tube trailer (km/h) mathematical model is embedded in the developed computer program, the user is not required to have any mathematical modeling knowledge.

Table 1
Summary of the design features considered in the MHSC studies.

Table 2
Specification of the case studies in the reviewed papers.
a OS: optimization software; GA: genetic algorithm.

Table 3
Locations and estimated H 2 demand for Oman.
a Capital province.

Table 6
Parameters of the tube trailer transport mode.

Table 7
Parameters of the pipeline transport mode.

Table 8
Main scenarios investigated in the case study.

Table 9
Summary of the results obtained for the scenarios introduced in Table8.

Table 10
Comparison results between different components of the HSC.
6.1.3.Above-ground tank vs. salt cavern Four cases are involved in comparing storage options.The corresponding scenarios, as well as the resulting improvement percentage in the  , are shown in Table 10.The comparison results show a significant improvement in the   if the salt cavern is added to the storage options.According to the results, the improvement percentage in the   varies from 38.292% to 42.967%.Referring to the solutions depicted in Figs.A.1-A.4, under Scenarios 5 and 6, the storage of H 2 requires seven above-ground storage tanks of different sizes.While under Scenarios 7 and 8, a large-scale salt cavern with a capacity of 5000 t H 2 is enough for the storage of H 2 in the whole supply chain.As Figs.A.3 and A.