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Strategic design of hydrogen infrastructure considering cost and safety using multiobjective optimization
international journal of hydrogen energy 33 (2008) 5887–5896
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Strategic design of hydrogen infrastructure considering cost and safety using multiobjective optimization Jiyong Kim, Il Moon* Department of Chemical Engineering, Yonsei University, 134 Shinchon-Dong Seodaemun-Gu, Seoul 120-749, Republic of Korea
article info
abstract
Article history:
This study presents a method for the design of a hydrogen infrastructure system including
Received 5 June 2008
production, storage and transportation of hydrogen. We developed a generic optimization-
Received in revised form
based model to support the decision-making process for the design of the hydrogen supply
8 July 2008
chain. The network design problem is formulated as a mixed integer linear programming
Accepted 9 July 2008
(MILP) problem to identify the optimal supply chain configurations from various alterna-
Available online 30 September 2008
tives. The objective is to consider not only cost efficiency, but also safety. Since there is a trade-off between these two objectives, formal multiobjective optimization techniques
Keywords:
are required to establish the optimal Pareto solutions that can then be used for decision-
Hydrogen infrastructure
making purposes. With the model, the effects of demand uncertainty can be also analyzed
Supply chain network design
by comparing the deterministic and the stochastic solutions. The features and capabilities
Mixed integer linear programming
of the model are illustrated through the application of future hydrogen infrastructure of
Multiobjective optimization
Korea. The optimal Pareto solutions utilize both cost-oriented and safety-oriented
Safety
strategies. ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
A number of questions still remain regarding the realization of the hydrogen economy. Nevertheless, the hydrogen economy is one of the most preferred candidates to succeed to the current carbon-based energy system. Hydrogen has the best potential to solve the problems of carbon-based fossil fuels such as carbon dioxide emissions and the dwindling supplies of petroleum. For example, using hydrogen in fuel cell vehicles (FCVs) has many advantages over current fuels. Despite the benefits of hydrogen, critical barriers prevent wide usage of hydrogen for fuel for FCVs. One barrier is the lack of hydrogen infrastructure [1]. FCV suppliers will not invest billions of dollars building FCV manufacturing facilities without a geographically dispersed, hydrogen refueling infrastructure. To overcome this barrier, the challenges for
developing sustainable hydrogen refueling infrastructure include the following: Cost efficiency In establishing a hydrogen infrastructure design strategy, the following two questions must be addressed [2,3]. (1) Which production option is more cost effective? Is centralized production (large-scale production at primary source suppliers) or decentralized production (small-scale production at local fueling stations or regional plants) more cost effective? (2) What are the most cost effective transportation modes and pathways to connect hydrogen demand with its supply?
* Corresponding author. Tel.: þ82 2 2123 2761; fax: þ82 2 312 6401. E-mail address: [email protected] (I. Moon). 0360-3199/$ – see front matter ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2008.07.028
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It is very important to design hydrogen infrastructure using the least expensive production, storage and transportation systems and using the optimal configuration for facilities, because building any new fueling infrastructure requires a significant investment cost and long-term commitment.
Production facility
Storage facility
Demand
Safety Vast quantities of hydrogen have been used as a chemical and a fuel in industries for decades. As a result, a relatively well-developed infrastructure has been developed. It has been shown that hydrogen can be safely utilized as a chemical and a fuel. But by introducing a large-scale hydrogen infrastructure, the hydrogen economy faces the following question:
: Transportation mode
Fig. 1 – Network representation of the hydrogen infrastructure.
(1) What is the safest method for production, storage and transportation of hydrogen? Hydrogen is actually no more dangerous than other flammable fuels such as gasoline and natural gas. Nevertheless, under specific conditions, hydrogen can behave dangerously. The burning or explosion of hydrogen causes most fatal accidents. Therefore, when hydrogen infrastructure design strategies are established, safety considerations are of paramount importance for the sustainable hydrogen economy. To answer questions related to cost efficiency, many researchers have attempted to evaluate the possibility of a hydrogen infrastructure and to apply their methods to real problems. For example, Thomas et al. [4] studied market scenarios for FCVs; Ogden [5] examined prospects for a hydrogen infrastructure; Ogden et al. [6] also compared usage of hydrogen with other fuels; Van den Heever and Grossmann [7] presented a mathematical model for a hydrogen supply chain; and recently Almansoori and Shah [8] proposed a mathematical model for various hydrogen activities. Yang and Ogden’s study focused on proper transportation modes [1]. On the other hand, studies about safety for hydrogen activities and infrastructure have gradually begun to receive increased attention [9–13]. Both the cost efficiency and the safety of a hydrogen infrastructure are essential decision-making factors in establishing investment strategies. A sustainable hydrogen economy is accomplished by solving a complex strategic problem requiring examination of the interaction between cost efficiency and safety.
2.
Problem statement
including production, storage and transportation systems. The model provides for minimization of two objectives (the total daily cost and the total relative risk) and takes into account decision-maker preferences. The decisions include the capacity and location of the plants and storage sites, the amount of hydrogen to be produced at each plant, the transportation modes for delivering hydrogen, the flow of hydrogen between each nodes and the total relative risk for each configuration. Several hydrogen activities were selected to effectively examine the proposed model. These are summarized in Table 1. In the absence of clear guidance as to how to estimate the relative risk of hydrogen infrastructure, many researchers and organizations have developed their own risk assessment approaches. These types of approaches suffer from limited data and the difficulty in applying the approaches to other systems. As a result, these types of risk assessments tend to be overly conservative and have the potential to misinform the public regarding the potential risk levels. Overstatement of risks can be of particular concern when risks of hydrogen infrastructure are compared to risks for other facilities where more straightforward risk assessment approaches exist, such as chemical processes. Therefore, this study introduces several variables and parameters that represent the total relative risk of hydrogen infrastructures as well as relative risks to individual components in the system. The relative risk of hydrogen activities is determined by risk ratings calculated
Table 1 – Hydrogen activities selected for case study Activity
A hydrogen infrastructure can be defined as the supply chain required to produce, store and deliver hydrogen [3]. Like any typical supply chain network, a hydrogen supply chain consists of several distinct components. The components include production plants and storage facilities as nodes in the networks and the arcs in the networks that represent connections between nodes as well as transportation modes (Fig. 1). This study proposes a new mathematical model that is capable of accounting for problems previously discussed. The proposed model helps design the hydrogen infrastructure
Type
Hydrogen production
Steam methane reforming (SMR) Electrolysis
Hydrogen storage
Liquid hydrogen (LH2) storage Compressed-gaseous hydrogen (CH2) storage
Hydrogen transportation
LH2 via tanker truck CH2 via tube trailer CH2 using pipeline
international journal of hydrogen energy 33 (2008) 5887–5896
based on a risk index method. A detailed explanation of the risk analysis method is presented in Section 4. Although simplification reduces the richness and realism of the model, the following assumptions are made in order to more easily apply the proposed model: (1) Although demand and supply are interrelated for the purposes of this model, the hydrogen network is assumed to be demand driven. (2) The delivery cost of raw materials to production plants are not considered in this study. Production site costs are determined just by the cost to meet hydrogen demands and safety requirements without referring to raw material and delivery costs. (3) The hydrogen network in this study is only a snapshot of the supply chain without considering a migration pathway from the existing carbon infrastructure [8]. (4) The relative risk of production plant, storage facilities and transportation modes are assumed not to change under the various demand scenarios. In order to efficiently solve the aforementioned optimization problem, the proposed model is formulated as a mixed integer linear programming (MILP) problem. The model is then applied to map out the future hydrogen infrastructure of Korea.
3.
Mathematical formulation
3.1.
Objective function
The production and distribution system whose model has been described previously must meet two target requirements: Minimize the total cost of the network Minimize the total relative risk of the network.
3.1.1.
Total daily cost
The stochastic model of Kim et al. is adopted as the benchmark formulation for representing the first objective function and constraints [2]. The first objective function is the total daily cost (TDC) of the hydrogen supply chain under the uncertain demand. TDC consists of the production capital cost (PCC), the storage capital cost (SCC), the transportation capital cost (TCC), the production operating cost (POC), the storage operating cost (SOC) and the transportation operating cost (TOC) as shown in the following equations; minimize TDC
(1)
TDC ¼ PCC þ SCC þ TCC þ POC þ SOC þ TOC
(2)
PCC ¼
XXX i
r
p
gr PCCpi NPpir
(3)
XXX
SCC ¼
r
i
TCC ¼
POC ¼
SOC ¼
gr SCCsi NSsir
XXX r
TOC ¼
r
UPCpi Ppir
(5)
(6)
p
XXXX i
(4)
s
TPIClrr0 Llrr0 if transportation mode is pipelines NTUil TMCil otherwise:
i
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p
USCsi STir
(7)
s
TPOCilrr0 Xilrr0 if transportation mode is pipelines FCþ LCþMCþGC otherwise
(8)
In the above formulation, the various indices are as follows: i (product physical forms), r (regions), p (plant types), s (storage facility types) and l (type of transportation modes). The various cost parameters are PCCpi (capital cost of plant), SCCsi (capital cost of storage site), TPIClrr0 (capital cost of pipeline installation), TPOCilrr0 (operating cost of pipelines), TMCil (cost of establishing transportation mode), UPCpi (unit production cost), USCsi (unit storage cost) and gr (weight factors of an establishment restraint rate). The variables are as follows: Ppir (production rate), NPpir (number of plants), NSsir (number of storage facilities), NTU (number of transport units), Llrr0 (distance), FC (fuel cost), LC (labor cost), MC (maintenance cost) and GC (general cost). These variables can be divided into two categories based on whether the corresponding tasks need to be carried out before or after demand realization [2]. The production and storage variables such as production costs and storage capital cost are considered in the first stage. Due to the significant lead times associated with these tasks, they are modeled as ‘here-andnow’ decisions, which need to be taken prior to demand realization. Post-production activities such as inventory management and supply of hydrogen, on the other hand, can be performed much faster. Consequently, these constitute supply chain variables, which can be fine-tuned in a ‘waitand-see’ setting after realization of the actual demand. Therefore, the objective function for this model becomes as follows;
TDC ¼
1 TCCx þ SOCx þ TOCx ðPCC þ SCCÞ þ POC þ Ex aCCF aCCF (9)
a is the network operating period (day/year) and CCF is the annual capital charge factordpayback period of capital investment (year). This classification of variables naturally extends to the constraints of the problem [2]. In this study, the scenario-based approach is employed to solve the stochastic mathematical model. The scenarios emerge from the assumption that the hydrogen demands are ‘above average’, ‘average’ or ‘below average’. Numerically, above average and below average scenarios are assumed as þ20% and 20% of the average values, respectively. The detailed explanations for
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the first objective and its constraints were described by Kim et al. [2].
3.1.2.
Total relative risk
The other objective function is the total relative risk (ToRisk) of the hydrogen supply chain that consists of total relative risk of production sites (TPRisk), total relative risk of storage sites (TSRisk) and total relative risk of transportation (TTRisk).
3.1.2.1. Relative risk of production. The relative risk of production in this model is a function of production type, which is the population of the region in which a particular production facility is located. The relative risk of each plant is determined using the following relationship: PRpir ¼
NP X
RPnr Prnr
(10)
n¼1
where PRpir is the relative risk of plants, RPnr is the risk level of the type of production such as SMR and electrolysis and Prnr is the weight factor related to the population of the region in which a production plant or a storage site is located. Therefore, the total risk of production facilities is given by the following equation: XXX PRpir NPpir (11) TPRisk ¼ p
i
IRFrr0 ¼ Lrr0 ½TTrr0 ð1 þ DPÞ
where DP is the weight factor considering the risk from timeworn pipelines, if pipelines are old. Thus, the relative risk of each transportation arc is calculated as follows: TRilrr0 ¼ EIrr0 IRFrr0
i
SRpir ¼
NP X
ESnr Prnr
(12)
n¼1
where SRpir is the relative risk of storage facilities, ESnr is the risk level of storage type such as LH2 and CH2. Therefore, the total risk of storage facilities is given by the following equation: XXX SRsir NSsir (13) TSRisk ¼ s
i
r
where NSsir is the number of each type of storage facility in a region.
3.1.2.3. Relative risk of transportation. The relative risk of each transportation arc (TRilrr0 ) is associated with the external effect (EIrr0 ) and the internal risk factor (IRFrr0 ). The external effect refers to how much risk each transportation arc brings to the region that it passes through. N X An Pn (14) EIrr0 ¼ n¼1
where An is urban adjacency rate which is a function of adjacency level and the number of regions that it passes by while Pn is the population of adjacent regions. On the other hand, the internal risk factor (IRGrr0 ) is associated with the transportation mode (TTrr0 ) and the distance between regions by transportation mode (Llrr0 ) as indicated by
l
r
r0
By combining Eqs. (11), (13) and (17) derived earlier, we obtain the total relative risk of the hydrogen supply chain: ToRisk ¼ TPRisk þ TSRisk þ TTRisk
3.2.
(18)
Multiobjective problem
The supply chain design in this study is mathematically formulated as follows: minimize fTDC; ToRiskg x;y
Subject to:
hðx; yÞ ¼ 0 gðx; yÞ 0
3.1.2.2. Relative risk of storage. The relative risk associated with storage in this model is a function of storage type, amount of storage and population of a region in which a particular storage facility is located. The relative risk of each storage facility is given by the following relationship:
(16)
The total relative risk associated with transporting the hydrogen between regions r and r¢ is a function of the relative risk of each transportation arc (TRillrr0 ) and amount of transportation as follows: XXXX TRilrr0 Qilrr0 (17) TTRisk ¼
r
where NPpir is the number of each production type in each region.
(15)
8 9 Demand satisfaction > > > > > Overall mass balance > > > > > > > > > > Capacity limitations > < = Distribution network design > > > > > > > Site allocation > > > > > > > Cost correlations > > : ; Non-negativity constraints
(19)
m x˛Rn ; y˛Y ¼ f0; 1g ;
The objective of this formulation is to find values of the operational ðx˛Rn Þ and strategic ðy˛Y ¼ f0; 1gm Þ decision variables, subject to the set of equality ðhðx; yÞ ¼ 0Þ and inequality constraints ðgðx; yÞ 0Þ. In this model, the continuous operational variables indicate decisions concerned with production, storage and transportation rate, whereas the discrete strategic variables capture the investment decisions such as selection of activity types. On the other hand, we can expect that there will be a conflict between the two objectives (the total daily cost and the total relative risk) because the lowest-cost infrastructure is not also the one with the least risk. Because of this trade-off, there is no single solution to this type of problem. Instead, the solution consists of a set of Pareto optimal SC configurations. These are obtained by applying the 3-constraint method first introduced by Haimes et al. [14]. This method is based on the maximization of one objective function while considering the other objectives as constraints bounded by some allowable levels 3n. Then, the levels 3n may be altered to generate the entire Pareto optimal set. Therefore, the following single MILP optimization formulation is applied to obtain the Pareto solutions: minimizefTDC; ToRiskg Subject to: hðx; yÞ ¼ 0 gðx; yÞ 0 x˛Rn ; y˛Y ¼ f0; 1gm and ToRisk en ðn ¼ 0; 1; 2; .; NÞ
(20)
international journal of hydrogen energy 33 (2008) 5887–5896
Therefore, by changing the values of the bound levels 3n, a set of results can be obtained. Each of these results implies an SC configuration. The resulting Pareto solutions may be represented in a two-dimensional chart (TDC, ToRisk). The proposed strategy would lead to a final supply chain design representing the desired compromise among the different objectives from the decision-maker’s perspective.
4. Determining the relative risk of hydrogen activities For estimating the total relative risk of hydrogen infrastructure, a risk index method is adopted in this study. The risk method is an attempt to measure the chance that an accidental event may elicit harmful consequences. Therefore, this study proposes a novel relative risk index for hydrogen infrastructure using relative risks of individual components within the hydrogen infrastructure. The first step in this is that individual risks of hydrogen activities need to be assessed. The expected frequency of undesired events and the associated volume of damage are determined. The schematic representation of the procedure for risk assessment of hydrogen activities is shown in Fig. 2. STEP 1: Hazard identification First, hazard identification is performed using failure modes and effects analysis (FMEA). With the help of an FMEA, the safety plan identifies failure modes for equipments and processes and establishes the consequences of such failures. STEP 2: Consequence and frequency analysis Data for the consequences of hydrogen release accidents are handled as described by Rosyid et al. and in CEC’s report
[9,15]. With the lack of reliability data for components in hydrogen infrastructure, accident probability data were compiled from several safety papers [9,16–19]. The results are expressed as the expected frequencies for either puff or continuous releases of hydrogen. STEP 3: Risk evaluation To evaluate the risks for each scenario according to the key failure modes, a risk-binning matrix, as adopted from the CEC report [15] is used in this study. The ratings are factors determining the relative risk of potential failures as calculated in steps 1–2. The risk-binning matrix summarizes the consequence and frequency ratings for each scenario. Each hazard is plotted on a frequency vs. consequence matrix, which indicates its level of risk as high, moderate, low, or negligible. High risks are considered as the combinations of (MH), (HM) and (HH) ratings. Moderate risks are combinations of (LH), (HL) and (MM). Finally, low risks are combinations of (LM), (ML), (LL) and no safety hazard or negligible risk scenarios. STEP 4: Development of a relative risk index A novel relative risk index for the hydrogen infrastructure is developed using failure modes and ratings for each type of hydrogen activity such as production, storage and transportation. When a decision-maker installs hydrogen activities, this index provides safety guidelines comparing the risk of each type of hydrogen activity. This study estimates risk levels for various hydrogen activities using the previously described risk assessment methods. Hydrogen production activities including electrolysis and SMR, LH2 and CH2 storage options, LH2 via tanker truck and CH2 via tube trailer and pipeline are all considered. For brevity, all practical estimating processes will not be explained, but instead the emphasis will be on the fact that
Define scope of analysis : analysis object, aspects to include, restrictions HI (Hydrogen Infrastructure) RISK ANALYSYS HAZARD IDENTIFICATION FMEA Scenarios
System breakdown • Process • Activity
Failure modes
Event tree
Probability data (OREDA et al.,2002)
FREQUENCY ANALYSYS
• Exposed to risk Accident propagation scenarios CONCEQUENCE ANALYSYS
PHAST model (Rosyid, 2007)
Individual risk Failure mode (Frequency, Consequence) RISK EVALUATION RATING RISK
Risk-binning matrix
System integration RELATIVE RISK DETERMINATION Applications
RISK INDEX for HI
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Internal risk factor & External effect
Fig. 2 – The risk assessment model in this study.
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detailed risk analyses for hydrogen activities were performed. Detailed data and parameter used in this study (i.e., failure modes and effects of them such as frequencies and consequences) are well described in previous studies [9,13,15,18,19]. These individual risks are estimated using many assumptions hence the results should not be interpreted quantitatively. Instead, the risks should be rated by comparing the relative risks of individual activities. Table 1 shows the riskbinning matrix for each individual risk and relative risk level according to its remark raking. The relative risk level in Table 2 is defined using a collection of matrices in order to measure the relative risk at system level and measure the effect on surroundings. The definition of the risk level used in Table 1 is determined based on the results of EIHP2 study [19]. In this report, there are five risk levels from Levels V to I according to harmfulness for people, the environment and facilities. All hydrogen activities considered in this study are marked as Levels II–IV. The acceptance criterion of Levels II–IV are as follows: Level II People: Medical treatment and lost time injury Environment: damage of short duration (<1 month) Facilities: Minor structural damage and minor influence on operations. Level III People: Permanent disability Environment: Time for restitution of ecological resource (<1 year) Facilities: Considerable structural damage and operation interrupted for weeks Level IV People: Several fatalities Environment: Time for restitution of ecological resource (1–3 years) Facilities: Loss of main part of system and operation interrupted for months.
5.
Case study
In order to illustrate the capabilities of the proposed model, the results of a hypothetical case study (the hydrogen
infrastructure of Korea in the future) are presented here. The problem consists of finding the optimal solutions in terms of cost and safety by combining these types and modes together. The problem specification for case studies is shown in Fig. 3. For convenience, this study divided Korea into 15 administrative districts of the Korea government. Fig. 1 shows the hydrogen demand of each region. The total hydrogen demand and each region’s demand were estimated by Kim et al. [2]. They estimated Korean hydrogen demand in 2044 using an energy and economy model based on various scenarios such as carbon tax, BTU tax and oil price. Additionally, Fig. 3 shows the total population and the population level of each region. This simplification is useful to easily calculate the relative risk of hydrogen activities (production, storage and transportation). When the population of a particular region is over 5 million, the region is considered to be Level I. Similarly, Level II regions have populations between 2 million and 5 million and Level III population is under 2 million. To use the model, upper/lower boundary capacity, capital cost and unit operation cost of each production plant or each storage facility is required. This study used data and parameters from the study of Kim et al. [2]. They collected data and parameters from previous studies and national reports, and applied a number of engineering-oriented methods such as the cost estimation. This study also assumed that the capital charge factors associated with the network investment of production and storage facilities, tube trailer and tube trailer and pipelines are 10, 5 and 20 years, respectively. To calculate the external effect of hydrogen activity, the regional population level in Fig. 3 is used. Table 3 shows relative risk matrix for production plants and storage facilities in each region. Regions 1 and 8 have the highest relative risk for both production and storage because they have the highest populations in Korea. For example, if an SMR plant that has the relative risk Level III is installed in region 1 where population level is I, the final weight factor of the SMR plant in region 1 is 25. However, transportation of hydrogen is not an activity that occurs in a specific region, but it rather extends through several regions. Therefore, the environmental impact of transportation is a function of distance from the centre of the region in which the path is located and a function of population levels of regions in which the path is located. This study assumes an impact range that is divided into two levels
Table 2 – Comparison of a relative risk level of hydrogen activities selected for examining the model Combined risk ¼ consequence frequency
Production plant Electrolysis plant SMR plant Storage facility LH2 storage CH2 storage Transportation mode tanker truck tube trailer Pipeline
Relative risk level
Low or negligible risk
Moderate risk
High risk
4 (2LM, 2LL) 2 (LM, LL)
5 (4LH, MM) 8 (LH, MM)
0 0
II III
2 (LM, ML) 4 (LM, 3ML)
2 (LH, MM) 2 (LM, MM)
2 (MH, HM) 0
III II
2 (LM, ML) 4 (LM, 3ML) 1 (LM)
2 (LH, MM) 2 (LM, MM) 3 (LH, 2MM)
2 (MH, HM) 0 2 (2HH)
III II IV
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Table 4 – Risk matrix for the effect of transportation into city from various distances Population level Region 4 (1.28E+06)
Region 9 (5.42E+05)
Region 1 (4.20E+06) Region 8 (6.26E+06)
Distance (km) Transiting (<1)
Close (1–10)
5 3 2
3 2 1
I (Big region) II (Medium region) III (Small region)
Region 10 (6.07E+05) Region 11 (8.88E+05) Region 6 (7.15E+05)
Region 14 (9.96E+05)
Region 12 (6.07E+05)
Region 5 (6.28E+05)
Region 3 (9.31E+05)
Region 15 (1.36E+06)
Region 7 (4.98E+05) Region 2 (1.30E+06)
Region 13 (6.07E+05) • Korea in the year 2044 Total H2demand : 2.17E+07 Kg/Day Total Population : 4.49E+07 persons • Population level Level 1 (over 5.0E+07) Level 2 (2.0E+07~5.0E+07) Level 3 (under 2.0E+07)
Fig. 3 – Problem specifications for the regional hydrogen demand and population level.
(transiting and close) according to the distance. Table 4 shows the transportation risk factor as a function of population level and distance. A detailed analysis for the risk factors of all transportation arcs was performed using geographic information system (GIS) of Korea. However, for the sake of brevity, only the procedure used to calculate the risk matrix for effect
Table 3 – Relative risk matrix for production and storage in various regions Region Production (weight factor) Storage (weight factor)
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15
SMR (5)
Electrolysis (3)
LH2 (5)
CH2 (3)
25 15 10 15 10 10 10 25 10 10 10 10 10 15 I5
15 9 6 9 6 6 6 15 6 6 6 6 6 9 9
25 15 10 15 10 10 10 25 10 10 10 10 10 15 I5
15 9 6 9 6 6 6 15 6 6 6 6 6 9 9
of transportation through cities from R1 is listed in Table 5; external factors for transportation arcs from region 1 to the other 14 regions were considered. For example, if hydrogen produced in region 1 is transported to region 2, this transportation arc has to penetrate four regions (R8, R14, R3 and R15) and pass by close to two regions (R9 and R10) (See Fig. 3). Therefore, the external effect factor of the transportation arc from region 1 to 2 is 12. Table 6 shows the total relative risk matrix for impact on city transportation between regions. These values include not only the value gained during transportation (i.e., 12 between regions 1 and 2) but also the weight factors for the start and terminal regions. The hydrogen transportation between regions 1 and 2 has the highest relative risk potential of 17. The highest risk line is the hydrogen transportation from region 1 (168) and the lowest risk line is the hydrogen transportation from regions 8 and 6 (87). If decision-makers design the hydrogen supply chain by considering only transportation safety, it is safer to completely avoid transportation from region 1.
6.
Result and discussions
The resulting mathematical formulations of both the deterministic and stochastic models are implemented in GAMS and solved using MILP solver of CPLEX 7.0 [20].
6.1.
The deterministic Pareto optimal solutions
First, the model is solved as a deterministic case, which means that there is no variation of hydrogen demand and that the
Table 5 – External effect factors gained during transportation from region 1 to other regions (excludes the values of start and terminal regions) Region 1 R1–R2 R1–R3 R1–R4 R1–R5 R1–R6 R1–R7 R1–R8 R1–R9 R1–R10 R1–R11 R1–R12 R1–R13 R1–R14 R1–R15
Transiting (<1) 4 2 0 2 1 3 0 0 1 1 2 3 1 3
(R8, R14, R3, R15) (R8, R1) (R8, R11) (R8) (R8, R14, R3)
(R8) (R8) (R8, R11) (R8, R11, R12) (R8) (R8, R14, R3)
Close (1–10) 2 1 1 1 2 2 0 1 1 0 0 0 3 2
(R9, R10) (R14) (R8) (R12) (R10, R11) (R9, R10) (R8) (R11)
(R9, R10) (R9, R10)
Total 12 12 3 8 7 12 0 3 6 5 7 9 7 12
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Table 6 – Relative risk matrix for the effect of transportation between various regions (including the values of start and terminal regions) Region
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
3 17 16 8 12 11 16 6 7 10 9 11 13 12 17
17 2 8 15 7 10 6 14 12 11 15 6 5 9 4
16 8 1 12 6 5 4 9 6 6 7 8 9 3 3
8 9 12 2 13 12 14 5 11 9 8 10 12 11 15
12 8 6 13 1 6 9 9 15 8 5 3 2 10 4
11 10 5 12 6 1 7 7 7 2 2 3 5 4 5
16 6 4 14 9 7 1 10 8 8 9 10 7 5 5
6 14 8 5 9 7 10 3 9 6 4 6 8 7 11
7 12 6 11 15 7 8 9 1 7 9 12 12 4 9
10 11 6 9 8 2 8 6 7 2 1 5 7 3 7
9 15 7 8 5 2 9 4 9 2 2 5 4 6 6
11 6 8 10 3 3 10 6 12 5 5 2 6 3 3
13 5 9 12 2 5 7 8 12 7 4 2 2 10 3
12 9 3 11 10 4 5 7 5 3 6 7 10 2 6
17 4 3 15 4 5 5 11 9 7 6 3 3 6 2
168
141
103
151
111
87
119
113
129
92
93
93
101
100
100
Total
demand value is known as in Fig. 3. The deterministic case includes all hydrogen activities (two production types, two storage types and three transportation modes). When the deterministic case is solved without constraining the value of the total relative risk of hydrogen infrastructure (ToRisk), the result of the model leads to a solution with ToRisk ¼ 61, i.e., the best economic performance is reached satisfying demand. Above this demand satisfaction level, some trade-off exists between the objectives and below it the solution is the same as that of the model without constraining the total relative risk. Therefore, this study assumes that the safety level ¼ 100%, when ToRisk is 61, and the safety level ¼ 0% when the total network cost is minimized (ToRisk ¼ 61). The Pareto deterministic optimal curve is then obtained by minimizing the total network cost and progressively constraining the ToRisk. Therefore, each point of this Pareto curve implies an infrastructure design operating under a total relative risk level represented by the target 31 imposed to the optimization problem.
Area 3
Total network cost ($/day)
6.46E+07 6.42E+07 Area 2
6.38E+07 6.34E+07 6.30E+07
Applying the deterministic multiobjective optimization approach to the case study results in the set of trade-off solutions presented in Fig. 4. At the one extreme of the curve lies the minimum TDC solution, whereas at the other extreme the minimum ToRisk solution. All design strategies of the hydrogen infrastructure captured within the optimal trade-off curve result in less relative risk than the business-as-usual case. Moving along the trade-off front from one extreme to the other extreme involves a series of different infrastructures. Noting that each solution within the set represents an alternative infrastructure design and investment strategy, the extent of the compromise between the solutions achieving maximum return on the investment and minimum relative risks can be explicitly quantified. The optimal trade-off is broken into design strategies based on different production, storage and transportation options that are consistent over the decision-making area of the curve (Fig. 4). Table 7 shows the supply chain features corresponding to these design strategies. In area 1 (from starting at the minimum TDC to safety level 30%), the investment cost is less although the total risk is higher than other design strategies. In contrast, in area 3 (from safety level of 80% to the maximum safety level), the hydrogen supply chain can be designed more safely. The detailed supply chain component descriptions of these areas are represented in Table 8. This includes three configurations (locations, the number of plants and hydrogen quantities imported from other regions) that correspond to different points on the curve (safety level ¼ 0%, 30%, 60%, 90% and 100%). It is interesting to note how the number of plants as well as location of plants changes as relative risk level is
6.26E+07 6.22E+07 Area 1
Table 7 – Design strategies of the decision-making area in the trade-off front
6.18E+07 6.14E+07
0
10
20
30
40
50
60
70
80
90
100
Safety level (%) Fig. 4 – Optimal Pareto solutions of deterministic model and design strategies.
Area
Design strategic
Supply chain feature
Area 1 Cost-oriented strategy Centralized and Distribution type Area 2 Moderate strategy Nearly centralized type Area 3 Safety-oriented strategy Local production type
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international journal of hydrogen energy 33 (2008) 5887–5896
Table 8 – Deterministic Pareto design Safety level ¼ 0% Safety level ¼ 30% Safety level ¼ 60% Safety level ¼ 90% Safety level ¼ 100% Total network cost (million$/day) The number of SMR plant The number of electrolysis plant The number of transportation The amount of transported H2 (ton/day)
61.4
61.6
63.4
64.4
64.5
45
46
50
52
54
2
0
6
9
0
14
13
6
2
0
6490
5100
4200
1800
0
varied. For instance, the solution with a ToRisk ¼ 30% implies the set-up of a new SMR plants while five and seven new SMR plants are established when a ToRisk is forced to be higher than 60% and 80%, respectively. The number of regions that imported hydrogen from other regions and the transported quantities of hydrogen are substantially decreased. At the point on the curve where the safety level ¼ 100%, there is only one transportation mode between regions and the required demand of hydrogen in each region is fulfilled almost entirely by local production. Some hydrogen activities are not chosen in the Pareto optimal solution as shown in Table 8. The multiobjective optimization framework not only identifies the most promising candidates, but also assists in the elimination of inferior solutions [3]. The reason for this phenomenon is that the hydrogen activities that are not chosen in the optimal tradeoff front do not offer either financial benefits or the safety guarantees. However, the superiority may shift from current activities to other activities as technologies develop or as the relative risk of each hydrogen activity is changed by different methods.
6.2.
The stochastic Pareto optimal solutions
The same case study including eight hydrogen activities taking into account the demand uncertainty is solved here. The number of binary variables in this case is the same as that in the deterministic formulation, since first-stage decisions (the number of production facilities) are not dependant on the uncertain demand. Fig. 5 shows the Pareto curve obtained for Deterministic pareto curve Stochastic pareto curve +20% hydrogen demand -20% hydrogen demand
Total network cost ($/day)
6.45E+07 6.41E+07 6.37E+07
the stochastic problem. As in the deterministic case, satisfying demand is profitable up to a ToRisk ¼ 61 level. Similar to the deterministic case, this study assumes that the safety level ¼ 100% when ToRisk is 61, and the safety level ¼ 0% when the total network cost is minimized (ToRisk ¼ 61). Above this level, there is a trade-off between both objectives, since a decrement in the value of ToRisk implies an increase in the associated total network cost as shown in Fig. 5. At higher safety levels, additional plants are established to fulfill the required hydrogen demand because the transportation of hydrogen increases the value of ToRisk (Table 8). The difference between the deterministic and the stochastic solutions should be discussed. At solution area starting at the minimum TDC to safety level 30%, the result of stochastic model is different from the deterministic result. This difference decreases progressively as one moves toward the maximum safety level. This is explained by the effect of demand uncertainty. For the stochastic model, the first-stage decision variable is the number of production and storage facilities before any variations in hydrogen demand, and the second-stage decision variables include the transported quantities and storage quantities. The second-stage decision variables affect the facility operating cost, the transportation capital cost and the transportation operating cost [2]. This means that at a solution area near the maximum safety level, the supply chain of the stochastic model is scarcely affected by variation of demand, because optimal solutions near the maximum safety level do not include decision variables within the degree of uncertainty. Therefore, in the area between safety level 0% and 30%, the difference of the Pareto curve of the stochastic and the deterministic model is rather wide (approximately 0.2–0.5%). However, as more ToRisk levels are considered, the total network costs are nearly equal to those achieved by their corresponding stochastic counterparts.
6.33E+07 6.29E+07
7.
Conclusion
6.25E+07 6.21E+07 6.17E+07 6.13E+07
0
10
20
30
40
50
60
70
80
90
Safety level (%) Fig. 5 – Deterministic vs. stochastic Pareto solutions.
100
Hydrogen economy is the preferred alternative to succeed to the existing carbon-based energy system. Investment strategies for designing a sustainable hydrogen economy are established based on careful analysis that takes into account critical issues such as cost efficiency and safety. To support strategic decision-making, this article proposes a generic model for design of hydrogen supply chain under demand
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uncertainty. This model employs a specific technique to address a multiobjective optimization technique that results from considering cost efficiency and safety simultaneously. The model was then applied to the problem of building the future hydrogen supply chain of Korea. The results of this case study reveal that the model can identify the optimal hydrogen supply chain including the types, the amounts and the locations of hydrogen activities, and the total relative risks involved. Through analysis of production plants and the transportation modes, it was determined that changing the type of plant or mode does not offer additional financial benefits or safety guarantees. We also studied the effect of demand uncertainty by comparing the deterministic and the stochastic solutions. In particular, the optimal Pareto solutions for cost efficiency and safety established several design strategies including the cost-oriented strategy and safetyoriented strategy. As such, model proposed in this study provides a useful guideline for designing the hydrogen infrastructure with improved cost efficiency and safety.
Acknowledgements This work was supported by the Ministry of Education (MOE) of Korea by its BK21 Program.
references
[1] Yang C, Ogden JM. Determining the lowest-cost hydrogen delivery mode. Int J Hydrogen Energy 2007;32:268–86. [2] Kim J, Lee Y, Moon I. Optimization of a hydrogen supply chain under demand uncertainty. Int J Hydrogen Energy 2008;33:4715–29. doi:10.1016/j.ijhydene.2008.06.007. [3] Hugo A, Rutter P, Pistikopoulos S, Amorelli A, Zoia G. Hydrogen infrastructure strategic planning using multi-objective optimization. Int J Hydrogen Energy 2005;30:1523–34. [4] Thomas C, James B, Lomax F. Market penetration scenarios for fuel cell vehicles. Int J Hydrogen Energy 1998;23:949–66. [5] Ogden JM. Prospects for building a hydrogen energy infrastructure. Annu Rev Energy Environ 1999;23:227–79.
[6] Ogden JM, Steinbulger M, Kreutz T. A comparison of hydrogen, methanol and gasoline as fuels for fuel cell vehicles: implications for vehicle design and infrastructure development. J Power Sources 1999;79:143–68. [7] Van den Heever S, Grossmann I. A strategy for the integration of production planning and reactive scheduling in the optimization of a hydrogen supply chain network. Comput Chem Eng 2003;27:1813–39. [8] Almansoori A, Shah N. Design and operation of a future hydrogen supply chain-Snapshot model. Chem Eng Res Des 2006;84:423–38. [9] Rosyid OA, Jablonski D, Hauptmanns U. Risk analysis for the infrastructure of a hydrogen economy. Int J Hydrogen Energy 2007;32:3194–200. [10] Jo JK. Risk assessment for the energetic use of hydrogen, master thesis. Abteilung Anlagentechnik und Anlagensicherheit, Otto-von-Guericke-University of Magdeburg, Germany, 2001. [11] Dorofeev S. Evaluation of safety distances related to unconfined hydrogen explosions. Int J Hydrogen Energy 2007; 32:2118–24. [12] Maclntyre I, Tchouvelev A, Wong J, Grant J, Benard P. Canadian hydrogen safety program. Int J Hydrogen Energy 2007;32:2134–43. [13] Janssen H, Bringmann J, Emonts B, Schroeder V. Safetyrelated studies on hydrogen production in high pressure electrolyzers. Int J Hydrogen Energy 2004;29: 759–70. [14] Haimes Y, Lasdon L, Wismer D. On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans Systems Man Cybernet 1971;1:296–7. [15] California Energy Commission (CEC). Failure modes and effects analysis for hydrogen fueling options. US Contract: 600-01-095. 2004. [16] OREDA 2002-offshore reliability data, Det Norske Veritas (DNV), Hovik, Norway, 2002. [17] Hauptmanns U. A procedure for analyzing the flight of missiles from explosions of cylindrical vessels. J Loss Prevention Process Ind 2001;14:395–402. [18] Hauptmanns U. Reliability data for process plants. Germany. Report No. IAUT-AS. 2003. [19] European Integrated Hydrogen Project (EIHP2). Methodology for rapid risk rating of hydrogen refueling station concepts. EU. Contract: ENK6-CT2000-00442. 2002. [20] Brooke A, Kendrick A, Meeraus D, Raman R, Rosenthal R. GAMS: a user’s guide. Washington: Scientific Press; 1998.
Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Strategic design of hydrogen infrastructure considering cost and safety using multiobjective optimization Jiyong Kim, Il Moon* Department of Chemical Engineering, Yonsei University, 134 Shinchon-Dong Seodaemun-Gu, Seoul 120-749, Republic of Korea
article info
abstract
Article history:
This study presents a method for the design of a hydrogen infrastructure system including
Received 5 June 2008
production, storage and transportation of hydrogen. We developed a generic optimization-
Received in revised form
based model to support the decision-making process for the design of the hydrogen supply
8 July 2008
chain. The network design problem is formulated as a mixed integer linear programming
Accepted 9 July 2008
(MILP) problem to identify the optimal supply chain configurations from various alterna-
Available online 30 September 2008
tives. The objective is to consider not only cost efficiency, but also safety. Since there is a trade-off between these two objectives, formal multiobjective optimization techniques
Keywords:
are required to establish the optimal Pareto solutions that can then be used for decision-
Hydrogen infrastructure
making purposes. With the model, the effects of demand uncertainty can be also analyzed
Supply chain network design
by comparing the deterministic and the stochastic solutions. The features and capabilities
Mixed integer linear programming
of the model are illustrated through the application of future hydrogen infrastructure of
Multiobjective optimization
Korea. The optimal Pareto solutions utilize both cost-oriented and safety-oriented
Safety
strategies. ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
A number of questions still remain regarding the realization of the hydrogen economy. Nevertheless, the hydrogen economy is one of the most preferred candidates to succeed to the current carbon-based energy system. Hydrogen has the best potential to solve the problems of carbon-based fossil fuels such as carbon dioxide emissions and the dwindling supplies of petroleum. For example, using hydrogen in fuel cell vehicles (FCVs) has many advantages over current fuels. Despite the benefits of hydrogen, critical barriers prevent wide usage of hydrogen for fuel for FCVs. One barrier is the lack of hydrogen infrastructure [1]. FCV suppliers will not invest billions of dollars building FCV manufacturing facilities without a geographically dispersed, hydrogen refueling infrastructure. To overcome this barrier, the challenges for
developing sustainable hydrogen refueling infrastructure include the following: Cost efficiency In establishing a hydrogen infrastructure design strategy, the following two questions must be addressed [2,3]. (1) Which production option is more cost effective? Is centralized production (large-scale production at primary source suppliers) or decentralized production (small-scale production at local fueling stations or regional plants) more cost effective? (2) What are the most cost effective transportation modes and pathways to connect hydrogen demand with its supply?
* Corresponding author. Tel.: þ82 2 2123 2761; fax: þ82 2 312 6401. E-mail address: [email protected] (I. Moon). 0360-3199/$ – see front matter ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2008.07.028
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It is very important to design hydrogen infrastructure using the least expensive production, storage and transportation systems and using the optimal configuration for facilities, because building any new fueling infrastructure requires a significant investment cost and long-term commitment.
Production facility
Storage facility
Demand
Safety Vast quantities of hydrogen have been used as a chemical and a fuel in industries for decades. As a result, a relatively well-developed infrastructure has been developed. It has been shown that hydrogen can be safely utilized as a chemical and a fuel. But by introducing a large-scale hydrogen infrastructure, the hydrogen economy faces the following question:
: Transportation mode
Fig. 1 – Network representation of the hydrogen infrastructure.
(1) What is the safest method for production, storage and transportation of hydrogen? Hydrogen is actually no more dangerous than other flammable fuels such as gasoline and natural gas. Nevertheless, under specific conditions, hydrogen can behave dangerously. The burning or explosion of hydrogen causes most fatal accidents. Therefore, when hydrogen infrastructure design strategies are established, safety considerations are of paramount importance for the sustainable hydrogen economy. To answer questions related to cost efficiency, many researchers have attempted to evaluate the possibility of a hydrogen infrastructure and to apply their methods to real problems. For example, Thomas et al. [4] studied market scenarios for FCVs; Ogden [5] examined prospects for a hydrogen infrastructure; Ogden et al. [6] also compared usage of hydrogen with other fuels; Van den Heever and Grossmann [7] presented a mathematical model for a hydrogen supply chain; and recently Almansoori and Shah [8] proposed a mathematical model for various hydrogen activities. Yang and Ogden’s study focused on proper transportation modes [1]. On the other hand, studies about safety for hydrogen activities and infrastructure have gradually begun to receive increased attention [9–13]. Both the cost efficiency and the safety of a hydrogen infrastructure are essential decision-making factors in establishing investment strategies. A sustainable hydrogen economy is accomplished by solving a complex strategic problem requiring examination of the interaction between cost efficiency and safety.
2.
Problem statement
including production, storage and transportation systems. The model provides for minimization of two objectives (the total daily cost and the total relative risk) and takes into account decision-maker preferences. The decisions include the capacity and location of the plants and storage sites, the amount of hydrogen to be produced at each plant, the transportation modes for delivering hydrogen, the flow of hydrogen between each nodes and the total relative risk for each configuration. Several hydrogen activities were selected to effectively examine the proposed model. These are summarized in Table 1. In the absence of clear guidance as to how to estimate the relative risk of hydrogen infrastructure, many researchers and organizations have developed their own risk assessment approaches. These types of approaches suffer from limited data and the difficulty in applying the approaches to other systems. As a result, these types of risk assessments tend to be overly conservative and have the potential to misinform the public regarding the potential risk levels. Overstatement of risks can be of particular concern when risks of hydrogen infrastructure are compared to risks for other facilities where more straightforward risk assessment approaches exist, such as chemical processes. Therefore, this study introduces several variables and parameters that represent the total relative risk of hydrogen infrastructures as well as relative risks to individual components in the system. The relative risk of hydrogen activities is determined by risk ratings calculated
Table 1 – Hydrogen activities selected for case study Activity
A hydrogen infrastructure can be defined as the supply chain required to produce, store and deliver hydrogen [3]. Like any typical supply chain network, a hydrogen supply chain consists of several distinct components. The components include production plants and storage facilities as nodes in the networks and the arcs in the networks that represent connections between nodes as well as transportation modes (Fig. 1). This study proposes a new mathematical model that is capable of accounting for problems previously discussed. The proposed model helps design the hydrogen infrastructure
Type
Hydrogen production
Steam methane reforming (SMR) Electrolysis
Hydrogen storage
Liquid hydrogen (LH2) storage Compressed-gaseous hydrogen (CH2) storage
Hydrogen transportation
LH2 via tanker truck CH2 via tube trailer CH2 using pipeline
international journal of hydrogen energy 33 (2008) 5887–5896
based on a risk index method. A detailed explanation of the risk analysis method is presented in Section 4. Although simplification reduces the richness and realism of the model, the following assumptions are made in order to more easily apply the proposed model: (1) Although demand and supply are interrelated for the purposes of this model, the hydrogen network is assumed to be demand driven. (2) The delivery cost of raw materials to production plants are not considered in this study. Production site costs are determined just by the cost to meet hydrogen demands and safety requirements without referring to raw material and delivery costs. (3) The hydrogen network in this study is only a snapshot of the supply chain without considering a migration pathway from the existing carbon infrastructure [8]. (4) The relative risk of production plant, storage facilities and transportation modes are assumed not to change under the various demand scenarios. In order to efficiently solve the aforementioned optimization problem, the proposed model is formulated as a mixed integer linear programming (MILP) problem. The model is then applied to map out the future hydrogen infrastructure of Korea.
3.
Mathematical formulation
3.1.
Objective function
The production and distribution system whose model has been described previously must meet two target requirements: Minimize the total cost of the network Minimize the total relative risk of the network.
3.1.1.
Total daily cost
The stochastic model of Kim et al. is adopted as the benchmark formulation for representing the first objective function and constraints [2]. The first objective function is the total daily cost (TDC) of the hydrogen supply chain under the uncertain demand. TDC consists of the production capital cost (PCC), the storage capital cost (SCC), the transportation capital cost (TCC), the production operating cost (POC), the storage operating cost (SOC) and the transportation operating cost (TOC) as shown in the following equations; minimize TDC
(1)
TDC ¼ PCC þ SCC þ TCC þ POC þ SOC þ TOC
(2)
PCC ¼
XXX i
r
p
gr PCCpi NPpir
(3)
XXX
SCC ¼
r
i
TCC ¼
POC ¼
SOC ¼
gr SCCsi NSsir
XXX r
TOC ¼
r
UPCpi Ppir
(5)
(6)
p
XXXX i
(4)
s
TPIClrr0 Llrr0 if transportation mode is pipelines NTUil TMCil otherwise:
i
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p
USCsi STir
(7)
s
TPOCilrr0 Xilrr0 if transportation mode is pipelines FCþ LCþMCþGC otherwise
(8)
In the above formulation, the various indices are as follows: i (product physical forms), r (regions), p (plant types), s (storage facility types) and l (type of transportation modes). The various cost parameters are PCCpi (capital cost of plant), SCCsi (capital cost of storage site), TPIClrr0 (capital cost of pipeline installation), TPOCilrr0 (operating cost of pipelines), TMCil (cost of establishing transportation mode), UPCpi (unit production cost), USCsi (unit storage cost) and gr (weight factors of an establishment restraint rate). The variables are as follows: Ppir (production rate), NPpir (number of plants), NSsir (number of storage facilities), NTU (number of transport units), Llrr0 (distance), FC (fuel cost), LC (labor cost), MC (maintenance cost) and GC (general cost). These variables can be divided into two categories based on whether the corresponding tasks need to be carried out before or after demand realization [2]. The production and storage variables such as production costs and storage capital cost are considered in the first stage. Due to the significant lead times associated with these tasks, they are modeled as ‘here-andnow’ decisions, which need to be taken prior to demand realization. Post-production activities such as inventory management and supply of hydrogen, on the other hand, can be performed much faster. Consequently, these constitute supply chain variables, which can be fine-tuned in a ‘waitand-see’ setting after realization of the actual demand. Therefore, the objective function for this model becomes as follows;
TDC ¼
1 TCCx þ SOCx þ TOCx ðPCC þ SCCÞ þ POC þ Ex aCCF aCCF (9)
a is the network operating period (day/year) and CCF is the annual capital charge factordpayback period of capital investment (year). This classification of variables naturally extends to the constraints of the problem [2]. In this study, the scenario-based approach is employed to solve the stochastic mathematical model. The scenarios emerge from the assumption that the hydrogen demands are ‘above average’, ‘average’ or ‘below average’. Numerically, above average and below average scenarios are assumed as þ20% and 20% of the average values, respectively. The detailed explanations for
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the first objective and its constraints were described by Kim et al. [2].
3.1.2.
Total relative risk
The other objective function is the total relative risk (ToRisk) of the hydrogen supply chain that consists of total relative risk of production sites (TPRisk), total relative risk of storage sites (TSRisk) and total relative risk of transportation (TTRisk).
3.1.2.1. Relative risk of production. The relative risk of production in this model is a function of production type, which is the population of the region in which a particular production facility is located. The relative risk of each plant is determined using the following relationship: PRpir ¼
NP X
RPnr Prnr
(10)
n¼1
where PRpir is the relative risk of plants, RPnr is the risk level of the type of production such as SMR and electrolysis and Prnr is the weight factor related to the population of the region in which a production plant or a storage site is located. Therefore, the total risk of production facilities is given by the following equation: XXX PRpir NPpir (11) TPRisk ¼ p
i
IRFrr0 ¼ Lrr0 ½TTrr0 ð1 þ DPÞ
where DP is the weight factor considering the risk from timeworn pipelines, if pipelines are old. Thus, the relative risk of each transportation arc is calculated as follows: TRilrr0 ¼ EIrr0 IRFrr0
i
SRpir ¼
NP X
ESnr Prnr
(12)
n¼1
where SRpir is the relative risk of storage facilities, ESnr is the risk level of storage type such as LH2 and CH2. Therefore, the total risk of storage facilities is given by the following equation: XXX SRsir NSsir (13) TSRisk ¼ s
i
r
where NSsir is the number of each type of storage facility in a region.
3.1.2.3. Relative risk of transportation. The relative risk of each transportation arc (TRilrr0 ) is associated with the external effect (EIrr0 ) and the internal risk factor (IRFrr0 ). The external effect refers to how much risk each transportation arc brings to the region that it passes through. N X An Pn (14) EIrr0 ¼ n¼1
where An is urban adjacency rate which is a function of adjacency level and the number of regions that it passes by while Pn is the population of adjacent regions. On the other hand, the internal risk factor (IRGrr0 ) is associated with the transportation mode (TTrr0 ) and the distance between regions by transportation mode (Llrr0 ) as indicated by
l
r
r0
By combining Eqs. (11), (13) and (17) derived earlier, we obtain the total relative risk of the hydrogen supply chain: ToRisk ¼ TPRisk þ TSRisk þ TTRisk
3.2.
(18)
Multiobjective problem
The supply chain design in this study is mathematically formulated as follows: minimize fTDC; ToRiskg x;y
Subject to:
hðx; yÞ ¼ 0 gðx; yÞ 0
3.1.2.2. Relative risk of storage. The relative risk associated with storage in this model is a function of storage type, amount of storage and population of a region in which a particular storage facility is located. The relative risk of each storage facility is given by the following relationship:
(16)
The total relative risk associated with transporting the hydrogen between regions r and r¢ is a function of the relative risk of each transportation arc (TRillrr0 ) and amount of transportation as follows: XXXX TRilrr0 Qilrr0 (17) TTRisk ¼
r
where NPpir is the number of each production type in each region.
(15)
8 9 Demand satisfaction > > > > > Overall mass balance > > > > > > > > > > Capacity limitations > < = Distribution network design > > > > > > > Site allocation > > > > > > > Cost correlations > > : ; Non-negativity constraints
(19)
m x˛Rn ; y˛Y ¼ f0; 1g ;
The objective of this formulation is to find values of the operational ðx˛Rn Þ and strategic ðy˛Y ¼ f0; 1gm Þ decision variables, subject to the set of equality ðhðx; yÞ ¼ 0Þ and inequality constraints ðgðx; yÞ 0Þ. In this model, the continuous operational variables indicate decisions concerned with production, storage and transportation rate, whereas the discrete strategic variables capture the investment decisions such as selection of activity types. On the other hand, we can expect that there will be a conflict between the two objectives (the total daily cost and the total relative risk) because the lowest-cost infrastructure is not also the one with the least risk. Because of this trade-off, there is no single solution to this type of problem. Instead, the solution consists of a set of Pareto optimal SC configurations. These are obtained by applying the 3-constraint method first introduced by Haimes et al. [14]. This method is based on the maximization of one objective function while considering the other objectives as constraints bounded by some allowable levels 3n. Then, the levels 3n may be altered to generate the entire Pareto optimal set. Therefore, the following single MILP optimization formulation is applied to obtain the Pareto solutions: minimizefTDC; ToRiskg Subject to: hðx; yÞ ¼ 0 gðx; yÞ 0 x˛Rn ; y˛Y ¼ f0; 1gm and ToRisk en ðn ¼ 0; 1; 2; .; NÞ
(20)
international journal of hydrogen energy 33 (2008) 5887–5896
Therefore, by changing the values of the bound levels 3n, a set of results can be obtained. Each of these results implies an SC configuration. The resulting Pareto solutions may be represented in a two-dimensional chart (TDC, ToRisk). The proposed strategy would lead to a final supply chain design representing the desired compromise among the different objectives from the decision-maker’s perspective.
4. Determining the relative risk of hydrogen activities For estimating the total relative risk of hydrogen infrastructure, a risk index method is adopted in this study. The risk method is an attempt to measure the chance that an accidental event may elicit harmful consequences. Therefore, this study proposes a novel relative risk index for hydrogen infrastructure using relative risks of individual components within the hydrogen infrastructure. The first step in this is that individual risks of hydrogen activities need to be assessed. The expected frequency of undesired events and the associated volume of damage are determined. The schematic representation of the procedure for risk assessment of hydrogen activities is shown in Fig. 2. STEP 1: Hazard identification First, hazard identification is performed using failure modes and effects analysis (FMEA). With the help of an FMEA, the safety plan identifies failure modes for equipments and processes and establishes the consequences of such failures. STEP 2: Consequence and frequency analysis Data for the consequences of hydrogen release accidents are handled as described by Rosyid et al. and in CEC’s report
[9,15]. With the lack of reliability data for components in hydrogen infrastructure, accident probability data were compiled from several safety papers [9,16–19]. The results are expressed as the expected frequencies for either puff or continuous releases of hydrogen. STEP 3: Risk evaluation To evaluate the risks for each scenario according to the key failure modes, a risk-binning matrix, as adopted from the CEC report [15] is used in this study. The ratings are factors determining the relative risk of potential failures as calculated in steps 1–2. The risk-binning matrix summarizes the consequence and frequency ratings for each scenario. Each hazard is plotted on a frequency vs. consequence matrix, which indicates its level of risk as high, moderate, low, or negligible. High risks are considered as the combinations of (MH), (HM) and (HH) ratings. Moderate risks are combinations of (LH), (HL) and (MM). Finally, low risks are combinations of (LM), (ML), (LL) and no safety hazard or negligible risk scenarios. STEP 4: Development of a relative risk index A novel relative risk index for the hydrogen infrastructure is developed using failure modes and ratings for each type of hydrogen activity such as production, storage and transportation. When a decision-maker installs hydrogen activities, this index provides safety guidelines comparing the risk of each type of hydrogen activity. This study estimates risk levels for various hydrogen activities using the previously described risk assessment methods. Hydrogen production activities including electrolysis and SMR, LH2 and CH2 storage options, LH2 via tanker truck and CH2 via tube trailer and pipeline are all considered. For brevity, all practical estimating processes will not be explained, but instead the emphasis will be on the fact that
Define scope of analysis : analysis object, aspects to include, restrictions HI (Hydrogen Infrastructure) RISK ANALYSYS HAZARD IDENTIFICATION FMEA Scenarios
System breakdown • Process • Activity
Failure modes
Event tree
Probability data (OREDA et al.,2002)
FREQUENCY ANALYSYS
• Exposed to risk Accident propagation scenarios CONCEQUENCE ANALYSYS
PHAST model (Rosyid, 2007)
Individual risk Failure mode (Frequency, Consequence) RISK EVALUATION RATING RISK
Risk-binning matrix
System integration RELATIVE RISK DETERMINATION Applications
RISK INDEX for HI
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Internal risk factor & External effect
Fig. 2 – The risk assessment model in this study.
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international journal of hydrogen energy 33 (2008) 5887–5896
detailed risk analyses for hydrogen activities were performed. Detailed data and parameter used in this study (i.e., failure modes and effects of them such as frequencies and consequences) are well described in previous studies [9,13,15,18,19]. These individual risks are estimated using many assumptions hence the results should not be interpreted quantitatively. Instead, the risks should be rated by comparing the relative risks of individual activities. Table 1 shows the riskbinning matrix for each individual risk and relative risk level according to its remark raking. The relative risk level in Table 2 is defined using a collection of matrices in order to measure the relative risk at system level and measure the effect on surroundings. The definition of the risk level used in Table 1 is determined based on the results of EIHP2 study [19]. In this report, there are five risk levels from Levels V to I according to harmfulness for people, the environment and facilities. All hydrogen activities considered in this study are marked as Levels II–IV. The acceptance criterion of Levels II–IV are as follows: Level II People: Medical treatment and lost time injury Environment: damage of short duration (<1 month) Facilities: Minor structural damage and minor influence on operations. Level III People: Permanent disability Environment: Time for restitution of ecological resource (<1 year) Facilities: Considerable structural damage and operation interrupted for weeks Level IV People: Several fatalities Environment: Time for restitution of ecological resource (1–3 years) Facilities: Loss of main part of system and operation interrupted for months.
5.
Case study
In order to illustrate the capabilities of the proposed model, the results of a hypothetical case study (the hydrogen
infrastructure of Korea in the future) are presented here. The problem consists of finding the optimal solutions in terms of cost and safety by combining these types and modes together. The problem specification for case studies is shown in Fig. 3. For convenience, this study divided Korea into 15 administrative districts of the Korea government. Fig. 1 shows the hydrogen demand of each region. The total hydrogen demand and each region’s demand were estimated by Kim et al. [2]. They estimated Korean hydrogen demand in 2044 using an energy and economy model based on various scenarios such as carbon tax, BTU tax and oil price. Additionally, Fig. 3 shows the total population and the population level of each region. This simplification is useful to easily calculate the relative risk of hydrogen activities (production, storage and transportation). When the population of a particular region is over 5 million, the region is considered to be Level I. Similarly, Level II regions have populations between 2 million and 5 million and Level III population is under 2 million. To use the model, upper/lower boundary capacity, capital cost and unit operation cost of each production plant or each storage facility is required. This study used data and parameters from the study of Kim et al. [2]. They collected data and parameters from previous studies and national reports, and applied a number of engineering-oriented methods such as the cost estimation. This study also assumed that the capital charge factors associated with the network investment of production and storage facilities, tube trailer and tube trailer and pipelines are 10, 5 and 20 years, respectively. To calculate the external effect of hydrogen activity, the regional population level in Fig. 3 is used. Table 3 shows relative risk matrix for production plants and storage facilities in each region. Regions 1 and 8 have the highest relative risk for both production and storage because they have the highest populations in Korea. For example, if an SMR plant that has the relative risk Level III is installed in region 1 where population level is I, the final weight factor of the SMR plant in region 1 is 25. However, transportation of hydrogen is not an activity that occurs in a specific region, but it rather extends through several regions. Therefore, the environmental impact of transportation is a function of distance from the centre of the region in which the path is located and a function of population levels of regions in which the path is located. This study assumes an impact range that is divided into two levels
Table 2 – Comparison of a relative risk level of hydrogen activities selected for examining the model Combined risk ¼ consequence frequency
Production plant Electrolysis plant SMR plant Storage facility LH2 storage CH2 storage Transportation mode tanker truck tube trailer Pipeline
Relative risk level
Low or negligible risk
Moderate risk
High risk
4 (2LM, 2LL) 2 (LM, LL)
5 (4LH, MM) 8 (LH, MM)
0 0
II III
2 (LM, ML) 4 (LM, 3ML)
2 (LH, MM) 2 (LM, MM)
2 (MH, HM) 0
III II
2 (LM, ML) 4 (LM, 3ML) 1 (LM)
2 (LH, MM) 2 (LM, MM) 3 (LH, 2MM)
2 (MH, HM) 0 2 (2HH)
III II IV
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Table 4 – Risk matrix for the effect of transportation into city from various distances Population level Region 4 (1.28E+06)
Region 9 (5.42E+05)
Region 1 (4.20E+06) Region 8 (6.26E+06)
Distance (km) Transiting (<1)
Close (1–10)
5 3 2
3 2 1
I (Big region) II (Medium region) III (Small region)
Region 10 (6.07E+05) Region 11 (8.88E+05) Region 6 (7.15E+05)
Region 14 (9.96E+05)
Region 12 (6.07E+05)
Region 5 (6.28E+05)
Region 3 (9.31E+05)
Region 15 (1.36E+06)
Region 7 (4.98E+05) Region 2 (1.30E+06)
Region 13 (6.07E+05) • Korea in the year 2044 Total H2demand : 2.17E+07 Kg/Day Total Population : 4.49E+07 persons • Population level Level 1 (over 5.0E+07) Level 2 (2.0E+07~5.0E+07) Level 3 (under 2.0E+07)
Fig. 3 – Problem specifications for the regional hydrogen demand and population level.
(transiting and close) according to the distance. Table 4 shows the transportation risk factor as a function of population level and distance. A detailed analysis for the risk factors of all transportation arcs was performed using geographic information system (GIS) of Korea. However, for the sake of brevity, only the procedure used to calculate the risk matrix for effect
Table 3 – Relative risk matrix for production and storage in various regions Region Production (weight factor) Storage (weight factor)
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15
SMR (5)
Electrolysis (3)
LH2 (5)
CH2 (3)
25 15 10 15 10 10 10 25 10 10 10 10 10 15 I5
15 9 6 9 6 6 6 15 6 6 6 6 6 9 9
25 15 10 15 10 10 10 25 10 10 10 10 10 15 I5
15 9 6 9 6 6 6 15 6 6 6 6 6 9 9
of transportation through cities from R1 is listed in Table 5; external factors for transportation arcs from region 1 to the other 14 regions were considered. For example, if hydrogen produced in region 1 is transported to region 2, this transportation arc has to penetrate four regions (R8, R14, R3 and R15) and pass by close to two regions (R9 and R10) (See Fig. 3). Therefore, the external effect factor of the transportation arc from region 1 to 2 is 12. Table 6 shows the total relative risk matrix for impact on city transportation between regions. These values include not only the value gained during transportation (i.e., 12 between regions 1 and 2) but also the weight factors for the start and terminal regions. The hydrogen transportation between regions 1 and 2 has the highest relative risk potential of 17. The highest risk line is the hydrogen transportation from region 1 (168) and the lowest risk line is the hydrogen transportation from regions 8 and 6 (87). If decision-makers design the hydrogen supply chain by considering only transportation safety, it is safer to completely avoid transportation from region 1.
6.
Result and discussions
The resulting mathematical formulations of both the deterministic and stochastic models are implemented in GAMS and solved using MILP solver of CPLEX 7.0 [20].
6.1.
The deterministic Pareto optimal solutions
First, the model is solved as a deterministic case, which means that there is no variation of hydrogen demand and that the
Table 5 – External effect factors gained during transportation from region 1 to other regions (excludes the values of start and terminal regions) Region 1 R1–R2 R1–R3 R1–R4 R1–R5 R1–R6 R1–R7 R1–R8 R1–R9 R1–R10 R1–R11 R1–R12 R1–R13 R1–R14 R1–R15
Transiting (<1) 4 2 0 2 1 3 0 0 1 1 2 3 1 3
(R8, R14, R3, R15) (R8, R1) (R8, R11) (R8) (R8, R14, R3)
(R8) (R8) (R8, R11) (R8, R11, R12) (R8) (R8, R14, R3)
Close (1–10) 2 1 1 1 2 2 0 1 1 0 0 0 3 2
(R9, R10) (R14) (R8) (R12) (R10, R11) (R9, R10) (R8) (R11)
(R9, R10) (R9, R10)
Total 12 12 3 8 7 12 0 3 6 5 7 9 7 12
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Table 6 – Relative risk matrix for the effect of transportation between various regions (including the values of start and terminal regions) Region
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
3 17 16 8 12 11 16 6 7 10 9 11 13 12 17
17 2 8 15 7 10 6 14 12 11 15 6 5 9 4
16 8 1 12 6 5 4 9 6 6 7 8 9 3 3
8 9 12 2 13 12 14 5 11 9 8 10 12 11 15
12 8 6 13 1 6 9 9 15 8 5 3 2 10 4
11 10 5 12 6 1 7 7 7 2 2 3 5 4 5
16 6 4 14 9 7 1 10 8 8 9 10 7 5 5
6 14 8 5 9 7 10 3 9 6 4 6 8 7 11
7 12 6 11 15 7 8 9 1 7 9 12 12 4 9
10 11 6 9 8 2 8 6 7 2 1 5 7 3 7
9 15 7 8 5 2 9 4 9 2 2 5 4 6 6
11 6 8 10 3 3 10 6 12 5 5 2 6 3 3
13 5 9 12 2 5 7 8 12 7 4 2 2 10 3
12 9 3 11 10 4 5 7 5 3 6 7 10 2 6
17 4 3 15 4 5 5 11 9 7 6 3 3 6 2
168
141
103
151
111
87
119
113
129
92
93
93
101
100
100
Total
demand value is known as in Fig. 3. The deterministic case includes all hydrogen activities (two production types, two storage types and three transportation modes). When the deterministic case is solved without constraining the value of the total relative risk of hydrogen infrastructure (ToRisk), the result of the model leads to a solution with ToRisk ¼ 61, i.e., the best economic performance is reached satisfying demand. Above this demand satisfaction level, some trade-off exists between the objectives and below it the solution is the same as that of the model without constraining the total relative risk. Therefore, this study assumes that the safety level ¼ 100%, when ToRisk is 61, and the safety level ¼ 0% when the total network cost is minimized (ToRisk ¼ 61). The Pareto deterministic optimal curve is then obtained by minimizing the total network cost and progressively constraining the ToRisk. Therefore, each point of this Pareto curve implies an infrastructure design operating under a total relative risk level represented by the target 31 imposed to the optimization problem.
Area 3
Total network cost ($/day)
6.46E+07 6.42E+07 Area 2
6.38E+07 6.34E+07 6.30E+07
Applying the deterministic multiobjective optimization approach to the case study results in the set of trade-off solutions presented in Fig. 4. At the one extreme of the curve lies the minimum TDC solution, whereas at the other extreme the minimum ToRisk solution. All design strategies of the hydrogen infrastructure captured within the optimal trade-off curve result in less relative risk than the business-as-usual case. Moving along the trade-off front from one extreme to the other extreme involves a series of different infrastructures. Noting that each solution within the set represents an alternative infrastructure design and investment strategy, the extent of the compromise between the solutions achieving maximum return on the investment and minimum relative risks can be explicitly quantified. The optimal trade-off is broken into design strategies based on different production, storage and transportation options that are consistent over the decision-making area of the curve (Fig. 4). Table 7 shows the supply chain features corresponding to these design strategies. In area 1 (from starting at the minimum TDC to safety level 30%), the investment cost is less although the total risk is higher than other design strategies. In contrast, in area 3 (from safety level of 80% to the maximum safety level), the hydrogen supply chain can be designed more safely. The detailed supply chain component descriptions of these areas are represented in Table 8. This includes three configurations (locations, the number of plants and hydrogen quantities imported from other regions) that correspond to different points on the curve (safety level ¼ 0%, 30%, 60%, 90% and 100%). It is interesting to note how the number of plants as well as location of plants changes as relative risk level is
6.26E+07 6.22E+07 Area 1
Table 7 – Design strategies of the decision-making area in the trade-off front
6.18E+07 6.14E+07
0
10
20
30
40
50
60
70
80
90
100
Safety level (%) Fig. 4 – Optimal Pareto solutions of deterministic model and design strategies.
Area
Design strategic
Supply chain feature
Area 1 Cost-oriented strategy Centralized and Distribution type Area 2 Moderate strategy Nearly centralized type Area 3 Safety-oriented strategy Local production type
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Table 8 – Deterministic Pareto design Safety level ¼ 0% Safety level ¼ 30% Safety level ¼ 60% Safety level ¼ 90% Safety level ¼ 100% Total network cost (million$/day) The number of SMR plant The number of electrolysis plant The number of transportation The amount of transported H2 (ton/day)
61.4
61.6
63.4
64.4
64.5
45
46
50
52
54
2
0
6
9
0
14
13
6
2
0
6490
5100
4200
1800
0
varied. For instance, the solution with a ToRisk ¼ 30% implies the set-up of a new SMR plants while five and seven new SMR plants are established when a ToRisk is forced to be higher than 60% and 80%, respectively. The number of regions that imported hydrogen from other regions and the transported quantities of hydrogen are substantially decreased. At the point on the curve where the safety level ¼ 100%, there is only one transportation mode between regions and the required demand of hydrogen in each region is fulfilled almost entirely by local production. Some hydrogen activities are not chosen in the Pareto optimal solution as shown in Table 8. The multiobjective optimization framework not only identifies the most promising candidates, but also assists in the elimination of inferior solutions [3]. The reason for this phenomenon is that the hydrogen activities that are not chosen in the optimal tradeoff front do not offer either financial benefits or the safety guarantees. However, the superiority may shift from current activities to other activities as technologies develop or as the relative risk of each hydrogen activity is changed by different methods.
6.2.
The stochastic Pareto optimal solutions
The same case study including eight hydrogen activities taking into account the demand uncertainty is solved here. The number of binary variables in this case is the same as that in the deterministic formulation, since first-stage decisions (the number of production facilities) are not dependant on the uncertain demand. Fig. 5 shows the Pareto curve obtained for Deterministic pareto curve Stochastic pareto curve +20% hydrogen demand -20% hydrogen demand
Total network cost ($/day)
6.45E+07 6.41E+07 6.37E+07
the stochastic problem. As in the deterministic case, satisfying demand is profitable up to a ToRisk ¼ 61 level. Similar to the deterministic case, this study assumes that the safety level ¼ 100% when ToRisk is 61, and the safety level ¼ 0% when the total network cost is minimized (ToRisk ¼ 61). Above this level, there is a trade-off between both objectives, since a decrement in the value of ToRisk implies an increase in the associated total network cost as shown in Fig. 5. At higher safety levels, additional plants are established to fulfill the required hydrogen demand because the transportation of hydrogen increases the value of ToRisk (Table 8). The difference between the deterministic and the stochastic solutions should be discussed. At solution area starting at the minimum TDC to safety level 30%, the result of stochastic model is different from the deterministic result. This difference decreases progressively as one moves toward the maximum safety level. This is explained by the effect of demand uncertainty. For the stochastic model, the first-stage decision variable is the number of production and storage facilities before any variations in hydrogen demand, and the second-stage decision variables include the transported quantities and storage quantities. The second-stage decision variables affect the facility operating cost, the transportation capital cost and the transportation operating cost [2]. This means that at a solution area near the maximum safety level, the supply chain of the stochastic model is scarcely affected by variation of demand, because optimal solutions near the maximum safety level do not include decision variables within the degree of uncertainty. Therefore, in the area between safety level 0% and 30%, the difference of the Pareto curve of the stochastic and the deterministic model is rather wide (approximately 0.2–0.5%). However, as more ToRisk levels are considered, the total network costs are nearly equal to those achieved by their corresponding stochastic counterparts.
6.33E+07 6.29E+07
7.
Conclusion
6.25E+07 6.21E+07 6.17E+07 6.13E+07
0
10
20
30
40
50
60
70
80
90
Safety level (%) Fig. 5 – Deterministic vs. stochastic Pareto solutions.
100
Hydrogen economy is the preferred alternative to succeed to the existing carbon-based energy system. Investment strategies for designing a sustainable hydrogen economy are established based on careful analysis that takes into account critical issues such as cost efficiency and safety. To support strategic decision-making, this article proposes a generic model for design of hydrogen supply chain under demand
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uncertainty. This model employs a specific technique to address a multiobjective optimization technique that results from considering cost efficiency and safety simultaneously. The model was then applied to the problem of building the future hydrogen supply chain of Korea. The results of this case study reveal that the model can identify the optimal hydrogen supply chain including the types, the amounts and the locations of hydrogen activities, and the total relative risks involved. Through analysis of production plants and the transportation modes, it was determined that changing the type of plant or mode does not offer additional financial benefits or safety guarantees. We also studied the effect of demand uncertainty by comparing the deterministic and the stochastic solutions. In particular, the optimal Pareto solutions for cost efficiency and safety established several design strategies including the cost-oriented strategy and safetyoriented strategy. As such, model proposed in this study provides a useful guideline for designing the hydrogen infrastructure with improved cost efficiency and safety.
Acknowledgements This work was supported by the Ministry of Education (MOE) of Korea by its BK21 Program.
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