Transportation Research Part E 46 (2010) 534–545

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Transportation Research Part E

journal homepage: www.elsevier .com/locate / t re

From waste to hydrogen: An optimal design of energy production anddistribution network

Nathan Parker, Yueyue Fan *, Joan OgdenInstitute of Transportation Studies, University of California, Davis, CA 95776, United States

a r t i c l e i n f o

Keywords:Renewable energyLogistics network designFacility locationHydrogen infrastructureFreight transport

1366-5545/$ - see front matter � 2009 Elsevier Ltddoi:10.1016/j.tre.2009.04.002

* Corresponding author. Tel.: +1 530 754 6408; faE-mail address: yyfan@ucdavis.edu (Y. Fan).

a b s t r a c t

This paper focuses on evaluating the economic potential and infrastructure requirementsof hydrogen production from agricultural residues, a representative green energy pathway.A mixed-integer nonlinear programming model is constructed for finding the most effi-cient and economical configuration of the whole pathway. Using northern California casestudies, we found that hydrogen from agricultural wastes can be delivered at costs similarto producing hydrogen from natural gas, a non-renewable energy source. The potentialimpact of this energy pathway on local freight transport is also discussed depending onthe choice of hydrogen delivery mode.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Existing energy supply and consumption face pressing issues on energy security and global climate change (IEA, 2006).Improving the sustainability of both the energy and transportation sectors will largely depend on the success of producingclean energy from renewable resources. It is clear that no single technology can provide a long-term solution to addressexisting energy problems. A large suite of alternative energy technologies will be needed to achieve a sustainable energyfuture (Pacala and Socolow, 2004). In this paper, we will explore the economic potential and the infrastructure requirementsof producing hydrogen from agricultural residues, which is a representative green energy pathway that has received muchattention for its clean energy carrier and renewable energy sources (National Research Council and National Academy ofEngineering, 2004).

A bioenergy pathway includes all the facilities and operations involved in the supply chain of bioenergy from the rawfeedstock supply to the end users. A simple example of bio-hydrogen pathway is illustrated in Fig. 1. The efficiency of theentire pathway depends on the geography of the feedstock resources, the layout and operation of the biorefineries, andthe cost of accessing the energy market. These factors are not independent of each other. The cost of hydrogen is stronglydependent on the cost of the feedstock and the size of the production facility (Hamelinck and Faaij, 2002; Lau, 2003; Spathet al., 2003;Larson et al., 2005). In addition, transportation costs constitute a significant portion of the total cost. The lowenergy density and the dispersed nature of agricultural residues lead to high feedstock delivery cost. Transporting hydrogenis also expensive because it is a low-density gaseous fuel. Therefore, in order to achieve the most efficient and economic pro-duction of hydrogen, individual components of bio-hydrogen pathway, the supplies, the production, and the delivery sys-tems, need to be designed simultaneously as an integrated supply chain system.

From a technology perspective, extensive research has been carried out to assess technological and economic feasibilityfor individual components of hydrogen production, including biomass feedstock availability and costs (ORNL, 2005), the

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x: +1 530 752 7872.

Fig. 1. A simple example of biohydrogen pathway.

N. Parker et al. / Transportation Research Part E 46 (2010) 534–545 535

costs of producing hydrogen from biomass (Katofsky, 1993; Hamelinck and Faaij, 2002; Simbeck and Chang, 2002; Lau, 2003;Spath et al., 2003; NAS, 2004; Larson et al., 2005; Spath et al., 2005), and hydrogen delivery cost (Simbeck and Chang, 2002;NAS, 2004; Yang and Ogden, 2007). However, to our knowledge, an integrated system analysis for the entire hydrogen path-way from biomass waste is still lacking in the literature.

From a system modeling viewpoint, bioenergy system design falls within the general category of supply chain manage-ment problems. Strategic supply chain management aims at finding the best supply chain configuration, including locationsetup, procurement, production, storage, and distribution, to support efficient operations of the whole supply chain (Cordeauet al., 2006). As shown in Fig. 1, a bioenergy pathway represents a typical supply chain. Therefore, the bioenergy system de-sign problem considered in this research fits in the category of multi-location-layer supply chain management problems.Publications in supply chain management have been fast growing in recent years (see recent review article by Melo et al.(2007)). Advanced stochastic models (for example, Geoffrion and Powers, 1995; ReVelle and Laporte, 1996; Daskin et al.,2002; Snyder, 2006; Lieckens and Vandaele, 2007) and dynamic models (for example, Van Roy and Erlenkotter, 1982; Chard-aire et al., 1996; Dias et al., 2007) have been proposed.

Modeling energy pathways for the future involves significant uncertainties in demand, supply, and technology. Theemphasis of the work presented herein is, however, on the development of a deterministic model that bridges operationsresearch with sophisticated domain knowledge in bio-hydrogen industry. A carefully constructed and validated determinis-tic model can serve as the basis for more advanced stochastic models. For example, sensitivity analyses of the deterministicmodel can help identify important model parameters that may need stochastic treatment explicitly. Moreover, the determin-istic model is equivalent to a scenario sub problem in the corresponding stochastic problem. Solutions to scenario sub prob-lems may be effectively aggregated using progressive hedging method (Mulvey and Vladimirou, 1991;Rockafellar and Wets,1991) to arrive at the solution to its stochastic counterpart.

The rest of the paper is organized as follows. In Section 2, we will provide the mathematical model for optimizing theproduction and distribution of bio-hydrogen. A case study based on northern California geographic setting will be designedin Section 3, which will be followed by discussions and potential research extensions in Section 4.

2. Methods

An integrated model based on geographic information systems (GIS) and mathematical programming is developed toevaluate the economic potential and the infrastructure requirements of biohydrogen production from agricultural residues.This model will be used to answer the following questions: (1) Is biohydrogen production economically sustainable? (2) Howshould we plan the production and delivery infrastructure systems involved in the biohydrogen supply chain and allocateavailable biomass resources to achieve the best economic performance?

There are three important layers in the supply chain: the procurement and transport of feedstock from fields to produc-tion plants, the production of hydrogen the plants, and the delivery of hydrogen from plants to demand sites. Standard truck-ing is considered for biomass transportation. Three delivery technologies are considered for hydrogen delivery: pipelinesprovide low cost delivery of large volumes of hydrogen; compressed gas tube trailers are relatively cheap to operate for smallquantities of hydrogen transported over short distances; cryogenic or liquid tanker trucks have low marginal costs of deliv-ery but require the liquefaction of hydrogen, which is expensive in both cost and energy. The abstract representation of thissupply chain is given in Fig. 2.

2.1. Model assumptions and notations

A mixed integer non-linear programming (MINLP) model with real world GIS data is developed. See Table 1 for the def-initions of notations used in the model. This model describes the optimal behavior of an industry to supply vehicular hydro-

Fig. 2. Network representation of biohydrogen pathway.

Table 1Notation table.

Indices:Subscript ’i’ refers to different fieldsSubscript ’j’ refers to different potential conversion sitesSubscript ’k’ refers to different demand clustersSubscript ’m’ refers to different modes of hydrogen deliver

Model inputs:Feedstockyield i � feedstock available at field ‘i’Pk � selling price of at demand cluster ‘k’(given)dailydemand k � demand at cluster ‘k’aq � scaling factor for various technologiesf2H � factor converting yearly feedstock deliveries into daily hydrogen capacityfloss � loss factor accounting for feedstock losses in storage and transporttm

loss � loss factor accounting for hydrogen losses at a terminal of mode ‘m’dm

loss � loss factor for hydrogen losses in the distribution system of mode ‘m’CF � capacity factor indicating the fraction of a year the facility is operating

Decision variable:Fij � yearly quantity of feedstock delivered from supply node to conversion site ‘j’Cj � capacity of conversion facility at site ‘j’tm

j � capacity of hydrogen terminal of mode‘m’at site ‘j’Hm

jk � capacity of hydrogen delivery link by mode from site ‘j’ to demand cluster ‘k’Hbjk � binary variable for the existence of pipeline link between site ‘j’ and cluster ‘k’Ik1 k2

� capacity of pipeline link between demand cluster ‘k1’and‘k2’Ibk1 k2

� binary variable for the existence of pipeline link between cluster ‘k1’andcluster ‘k2’Sm

k � hydrogen supply capacity for demand cluster ‘k’ by mode ‘m’

Intermediate variables:FCij � cost of feedstock delivered from field ‘i’ to site ‘j’CCj � conversion cost at site ‘j’TCm

j � terminal cost at site ‘j’ for hydrogen delivery mode‘m’DCm

jk � delivery costs from site ‘j’ to cluster ‘k’ by mode‘m’ICk1k2

� intercity pipeline delivery costs between cluster ‘k1’ and ‘k2’LCm

k � local delivery cost within cluster ‘k’ by mode ‘m’RCm

k � refueling station costs for cluster ‘k’ for stations receiving hydrogen by mode ‘m’Xk � yearly quantity of hydrogen sold at demand cluster ‘k’

536 N. Parker et al. / Transportation Research Part E 46 (2010) 534–545

gen from agricultural residues in a steady-state system of hydrogen demand, selling price, and feedstock supply. If hydrogenfrom agricultural residues can be delivered to the refueling stations for less than the given selling price then it is profitablefor the industry to supply that hydrogen and the infrastructure is built to reap that profit. It is assumed that:

(1) The optimality is measured by the annualized profit from hydrogen production. Most supply chain model choosesminimizing total cost as the objective. The advantages of choosing profit maximization lie in that it reflects theprofit-driven industrial operation, and it allows infrastructure design to respond to price differentials betweendemand centers.

N. Parker et al. / Transportation Research Part E 46 (2010) 534–545 537

(2) Hydrogen is produced from rice straw via a gasification process with co-production of a small amount of electricity.The technologies for rice straw harvest and delivery remain unchanged from current practice. Hydrogen is delivered torefueling stations using one of three modes, gaseous truck, liquid truck or via pipeline. The refueling stations dispensehydrogen to vehicles with 5000 psi onboard storage tanks.

(3) Hydrogen demand will be concentrated in areas of high population density and will be evenly distributed in thoseareas.

(4) Model parameters remain constant in the one-year study period. Note that the emphasis of this study is to evaluatethe economic feasibility of biohydrogen production in the long run when demand, supply, and technology are stabi-lized. If the focus is on system transition behavior from fossil fuel to biohydrogen, then a dynamic model is more suit-able to reflect the changes of the system over time (an example of such dynamic model is available in Lin et al., 2008).

The inputs to the model include GIS-based data describing biomass feedstock availability, geographic distribution andprojection for future hydrogen demand, and engineering economic sub models for computing the production and transpor-tation costs under different technology assumptions. Using this model, one can obtain:

(1) the maximum profit generated from biohydrogen production;(2) the optimal locations and sizes of biohydrogen production plants;(3) the optimal allocation of biomass resources to production plants; and(4) the optimal transportation infrastructure configuration and operation for biomass and produced hydrogen.

2.2. Model formulation

2.2.1. Objective functionThe objective is to build an industry that will maximize profit with given demands, supplies, and hydrogen market price.

The annualized profit function is given as

Maximizep ¼X

k

Pk � Xk � annualized cos t

annualized cos t ¼X

i;j

FCijðFij;dijÞ þX

j

CCjðCjÞ þX

m;j

TCmj ðT

mj Þ þ

X

j;k;m

DCmjkðH

mjk ;djkÞ þ

X

k1k2

ICk1k2ðIk1k2

;dk1k2Þ

þX

m;k

LCmk ðS

mk Þ þ

X

k

RCmk ðS

mk Þ ð1Þ

The annualized cost given in Eq. (1) is a nonlinear function, which depends on the capacities of the infrastructure built aswell as the quantities delivered or produced at each node and along each link. Eqs. (2)–(8) describe the details of each costterm in Eq. (1), including the feedstock costs, the conversion costs, the terminal costs, the truck delivery costs, the pipelinedelivery cost between terminal and demand sites, the intercity pipeline delivery costs, the intra-city delivery costs, and therefueling station costs.

The feedstock cost (FC) has fixed costs of harvest, storage, and truck loading/unloading of feedstock that is dependent onthe amount of feedstock (Fij) and a variable cost that is linearly dependent on the delivery distance dij from filed i to plant j

FCijðFij; dijÞ ¼ ðharvest cos ti þ storage cos ti þ delivery cos tijðdijÞÞ � Fij ð2Þ

The conversion cost (CC) represents the capital and operating costs of the conversion facility. The capital cost is a nonlinearfunction dependent on the capacity. The yearly charge paid on the capital is the capital recovery factor (CRF in the equation)multiplied by the total installed cost of capital. Fixed operating cost is a multiplier (O&M in Eq. (3)) multiplying the capitalcost. The rest of the operating costs are linear functions of the quantity produced which equals the capacity multiplied by thecapacity factor (CF)

CCjðCjÞ ¼ ðCRF þ O&MÞ � cap cos t � ðCjÞa þX

q

variable cos tq � Cj � CF ð3Þ

The cost of preparing produced hydrogen for transport to the refueling stations is the terminal cost (TC). This cost appears atthe conversion facility is counted toward the total cost of the supply chain. TC includes nonlinear components in capacityrepresenting the capital and fixed operating cost for the terminal equipment and linear components for the variable costsuch as electricity. Each facility has three possible types of terminals and any combination is allowed to coexist at the samefacility

TCmj ðT

mj Þ ¼

X

q

ðCRFq þ O&MqÞ � cap cos tq � ðTmj Þ

aq þX

q

variable cos tq � Tmj � CF ð4Þ

The delivery costs are broken into truck and pipeline delivery cost as the two have different forms to their cost equations.Truck transmission costs have the form shown in Eq. (5). The two truck modes follow a linear function of capital and oper-

538 N. Parker et al. / Transportation Research Part E 46 (2010) 534–545

ating cost associated with the number of truck cabs (#cabs), trailers (#trailers), and driver salary. There are also distance-dependent costs associated with fuel, maintenance, and insurance

DCm¼gas;liqjk ðHm

jk ; djkÞ ¼ ðCRFcab þ O&McabÞ � cap cos tcab � ð#cabsðHmjkÞÞ þ driver salaryð#cabsðHm

jkÞÞþ ðCRFtr þ O&MtrÞ � cap cos tm

tr � ð#trailersÞ þ per milem � Hmjk � djk ð5Þ

The pipeline costs have the form shown in Eq. (6). These costs include capital and fixed operating and maintenance cost thatare distance-dependent. Note that compression cost is included in the terminal cost. For the size of pipes considered in mosthydrogen scenarios there is no significant difference between pipe sizes in the per mile installed cost (Parker, 2004). For thisreason the pipeline costs are treated with binary variables of whether a pipeline is installed on a link or not (Hbjk). Intercityand intracity pipelines are differentiated in costs with the intracity pipelines costing 1.5 times more than the intercitypipelines

DCm¼pipejk ðHbjk; djkÞ ¼ ðCRF þ O&MÞ � cap cos t � Hbjk � djk ð6Þ

For pipelines, there are also deliveries taking place between cities. These intercity delivery costs are represented by Eq. (7).The delivery costs follow the same form as Eq. (6), where dk1k2 is the distance between the two cities

ICk1k2ðIbk1k2

;dk1k2Þ ¼ ðCRF þ O&MÞ � cap cos t � Ibk1k2

� dk1k2ð7Þ

Refueling station costs (RC) are different for each hydrogen delivery mode. RC is a function of the station capacity, includingthe nonlinear capital and operations & maintenance costs, and linear variable costs

RCmk ðS

mk Þ ¼

X

q

ðCRFq þ O&MqÞ � cap cos tq � ðSmk Þ

aq þX

q

variable cos tq � Smk � CF ð8Þ

2.2.2. ConstraintsThree types of constraints are considered, including capacity constraints, flow conservation constraints, and non-negativ-

ity constraints. The capacity constraints restrict quantities not to exceed the maximum allowed by the built or given capac-ities. Flow conservation constraints require that at each node the quantities going in must equal the quantities going out plus(or minus) the quantities supplied (or consumed) at the node. Non-negativity constraints require that all physical quantitiesbe positive as they cannot be negative.

2.2.2.1. Capacity constraints.

X

j

Fij � feedstock yieldi ð9Þ

which guarantees that the feedstock extracted from a field must be less than the feedstock yield of that field

X

i

f loss � Fij � f 2H � 365 � CF � Cj ð10Þ

indicating that the yearly capacity of a conversion facility (Cj) must be greater than the hydrogen production potential of thefeedstock coming into the conversion facility (Fij). The f2H multiplier converts feedstock quantity into equivalent hydrogenproduction capacity. The floss multiplier accounts for feedstock loss in storage and transport

X

m

Tmj ¼ Cj ð11Þ

indicating that the capacity of the terminals ðTmj Þ at a conversion facility needs to equal the capacity of the conversion facility

(Cj)

X

k

Hmjk � t lossm � Tm

j ð12Þ

restricting the capacity of the terminal of a mode at a conversion facility ðTmj Þ to be greater than the hydrogen leaving the

conversion facility by that mode ðHmjkÞ

X

j

d lossgas;liquid � Hgas;liquidjk � Sgas;liquid

k ð13Þ

indicating that the capacity of the gas truck or liquid truck local distribution and refueling infrastructure ðSgas; liquidk Þmust be at

least as large as the quantity of hydrogen coming into a demand center by gas truck or liquid truck

X

j

d losspipe � Hpipejk þ

X

k2

Ikk2�X

k2

Ikk2� Spipe

k ð14Þ

N. Parker et al. / Transportation Research Part E 46 (2010) 534–545 539

indicating that the capacity of the local pipeline distribution and refueling infrastructure ðSpipek Þmust be greater than the net

hydrogen coming into the demand center

Xk �X

m

365 � CF � Smk ð15Þ

indicating that capacity of the local distribution and refueling infrastructure at a demand center must be greater than theannual quantity of hydrogen sold at the demand center (Xk)

Xk � daily demandk � 365 ð16Þ

indicating that the amount of hydrogen sold at a demand center cannot be more than the hydrogen demanded at that center.

2.2.2.2. Flow constraints.

X

i

f loss � Fij � f 2H ¼X

k

Hgasjk =t lossgas þ

X

k

Hliquidjk =t lossliquid þ

X

k

Hbjk � Hpipejk =t losspipe ð17Þ

limiting that the hydrogen produced from the feedstock going into the conversion facility must equal the hydrogen comingout of the conversion facility

X

j

d lossgas � Hgasjk þ

X

j

d lossliquid � Hliquidjk þ

X

j

d losspipe � Hbjk � Hpipejk þ

X

k2

Ibk2k � Ik2k �X

k2

Ibkk2 � Ikk2 ¼ Xk ð18Þ

indicating that the net hydrogen delivered to a demand center must be consumed.

2.2.2.3. Non-negativity constraints.

Xk; Fij;Cj; Tmj ;H

mjk ; Ik1k2 ; S

mk � 0 ð19Þ

which restricts that all capacities and delivered quantities must have zero or positive values.Combining the constraints and the objective function gives a mixed-integer, non-linear program. Due to non-convexity,

solving this problem is computational expensive as more of the solution space must be searched to ensure a global optimalsolution.

3. Case studies

This section gives a case study using rice straw in California’s Sacramento Valley for the production of hydrogen for use asa transportation fuel. Four separate rice straw availability scenarios (5%, 25%, 50% and 75% of gross rice straw yield) arematched with four different hydrogen demand scenarios (1%, 10%, 25%, and 50% of total light duty vehicle fleet in the urbanareas using hydrogen) to produce 16 scenarios. In each of the 16 scenarios, the model runs were performed over a range ofhydrogen selling prices to identify the lowest price point that biohydrogen would be produced in significant volume. Wecompared this selling price to the cost of hydrogen produced at each refueling station using distributed steam methanereformers (SMR) at the same volume of sales for reference.

3.1. Case study description

3.1.1. Choice of gasification sitesPotential sites were selected from an earlier analysis that used simplified engineering-economic models for single facility

cost curves at each field and major population center (Parker, 2006). For large facilities (hydrogen capacity >80,000 kg/day), asite at the eastern edge of the San Francisco Bay Area was favorable. Smaller facilities (<60,000 kg/day) favored a site on theNorthern edge of Sacramento. Finally for moderately-sized facilities (60,000–80,000 kg/day), a site located to minimize strawcollection costs was most attractive (labeled ‘‘Field site”). Two other sites were added out of curiosity. One near Vacaville wasadded as a compromise between the Sacramento and Richmond sites. Another was added near Modesto as a potential smallfacility utilizing local straw for a small local demand. Fig. 3 shows these sites with respect to the rice fields and the demandcenters for the 10% demand scenario.

3.1.2. Road network dataThe road network used in this analysis is the ‘‘California base” network from California Department of Transportation as

shown in Fig. 4. This network consists of all interstates, major highways and major urban arterial roads.

3.1.3. Cost dataEach component of the production system, rice straw harvest, storage, transport, hydrogen production, hydrogen termi-

nals, hydrogen distribution, and refueling stations, has a cost function depending on a number of design parameters. The cost

Fig. 3. Potential facility location.

Fig. 4. Road network.

540 N. Parker et al. / Transportation Research Part E 46 (2010) 534–545

Table 2Model sizes.

Number of demand centers Number of variables Number of non-linear variables Number of binary variables Number of equations

1% demand 13 534 116 24 19210% demand 34 911 240 55 33925% demand 23 783 224 51 28350% demand 29 834 236 54 304

N. Parker et al. / Transportation Research Part E 46 (2010) 534–545 541

data used for this analysis comes from three main sources, (Jenkins et al., 2000) for all costs related to rice straw, (Larson etal., 2005) for the costs associated with the hydrogen production facility, and the Department of Energy’s H2A Analysisspreadsheets for all costs involved in the distribution of hydrogen to the end-users (DOE, 2006). Due to page limit, the costparameters and engineering economics sub models are not included in this paper. For those interested reproducing the re-sults reported in this paper, the values of all cost parameters can be found in (Parker, 2007), also available online at http://www.cee.engr.ucdavis.edu/faculty/fan/Journal%20Publications.html/Parker_sub.pdf.

3.1.4. Complexity reductionThe size of the problem resulted from each of the four hydrogen demand cases is summarized in Table 2. The binary vari-

ables represent potential pipeline links. Ideally we should have binary variables associated with all possible pipeline connec-tions between plant–city and city–city pairs. However, having too many integer variables significantly increases thecomputational complexity of the problem. We then reduced the potential pipeline links to only those that are likely to bein an optimal solution. These potential links include those from the minimal spanning tree connecting the demand centers,the additional links connecting the tree and the plant sites, and those providing missing connectivity. The number of binaryvariables reported in Table 2 is a result from this complexity reduction.

3.2. Results

The model was solved using BARON1 (Sahinidis and Tawarmalani, 2005) on the NEOS2 server (Dolan, 2001). The 16 basecase scenarios lead to a variety of optimal configurations. As an example, the layout of the optimal system configuration forthe case of 10% demand/50% rice straw availability is illustrated in Fig. 5.

When the hydrogen demand is relatively low (1% and 10%), compressed gas trucks were chosen to be the optimal deliverymode in most of the cases. As the hydrogen demand increases (25% and 50%), pipeline delivery becomes more economicallyefficient.

In all scenarios, only one conversion facility is recommended. Sacramento is the optimal location for the conversion facil-ity in most cases. Vacaville appears to be optimal when hydrogen demand is low (1%). The Richmond site (near large BayArea demand) is favored for the 25% demand scenarios with 50% and 75% rice straw availability.

The optimal levelized costs of delivered hydrogen range from $2.85 to $6.04 per kilogram as the total production in-creases due to economy of scale. These costs compare favorably with hydrogen produced at the refueling station from nat-ural gas, whose costs are estimated to range between $2.71 and $5.58 per kilogram depending on production scale andtechnological maturity over the same range.3 Fig. 6 shows how each component contributes to the levelized cost of deliveredhydrogen. In most of the cases, transportation cost shares a significant portion of the total cost of delivered hydrogen usingpipeline or compressed gas trucks, except for the case of 10% demand/75% rice straw availability, in which liquid trucks arechosen for the delivery of hydrogen and the terminal cost is dominating. In addition to the direct transportation cost imposedto the hydrogen industry, the transport of feedstock and hydrogen will also impact the local freight transport. For example, at10% demand level and 50% rice straw availability, the bio-fuel production adds an extra of 45 million ton miles of biomassand 4 million ton miles of hydrogen freight movement to the local area. While the majority of the biomass freight will travelover rural roads and highways, most hydrogen freight transportation will occur in urban areas or on major connections be-tween urban areas.

Compared to the gasoline distribution system replaced, hydrogen distribution will either significantly increase or reducethe number of fuel delivery trucks on urban roads. Delivery of hydrogen by compressed gas trucks requires 28.6 truck trips todeliver the same quantity of energy as one gasoline delivery truck. Liquid trucks perform better, requiring a little more thantwo truck trips for every gasoline truck trip. With hydrogen, the quantity of energy required at the refueling station will belower due to efficiency improvements provided by fuel cell vehicles. Therefore hydrogen delivered by liquid trucks is notlikely to increase the number of truck-trips required to fuel a vehicle fleet but delivered by compressed gas trucks the num-ber of truck-trips would increase more than 10-fold. On the other hand, delivering hydrogen via pipeline will take all fueldelivery trucks off the road.

1 BARON is a global solver for a certain type of (continuous, purely integer and mixed indexed) nonlinear programming problems.2 NEOS server provides web access to a cluster of optimization solvers.3 Assuming a natural gas price of $6.50/mmBtu and onsite steam methane reformer performance estimated in (NAS).

Fig. 5. Optimal system configuration for 10% demand/50% rice straw scenario.

542 N. Parker et al. / Transportation Research Part E 46 (2010) 534–545

3.2.1. Sensitivity analysisSensitivity analysis was performed on parameters that are expected to have significant effect on not only the cost of deliv-

ered hydrogen but also the configuration of the entire system. These parameters and their values of the lower bound, basecase, and upper bound are given in Table 3.

Sensitivity analysis is performed on the 10% and 25% hydrogen demand scenarios with 50% rice straw availability. Thesetwo scenarios were chosen because they represent the gaseous truck delivery and pipeline delivery paradigms respectively.They are also closer to breakpoints where the delivery mode is switched than the 5% and 50% demand scenarios.

A tornado plot of the sensitivity results for the 10% demand scenario is given in Fig. 7. The tornado chart depicts the var-iation from the base case levelized cost (denoted by the center line) for each uncertain parameter. The parameter valueresulting in a lower value is shown in gray with the larger value in black. This analysis compares the lowest cost system

$0.00

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

$7.00

75%

50%

25% 5% 75%

50%

25% 5% 75%

50%

25% 5% 75%

50%

25% 5%

Lev

eliz

ed C

ost

($/k

g)

StationDistributionTerminalConversionFeedstock

Feedstock Availability

Hydrogen Demand

50%25%10%5%

Fig. 6. Breakdown of levelized costs in base case scenarios.

Table 3Sensitivity analysis parameter values.

Parameter High value Base case Low value

Feedstock harvest cost +90% $20.14 wet tonne�1 �40%Gasifier capital cost +30% $185 million for 100,000 kg day�1 �30%Pipeline capital cost ($ mile�1) $1,230,680 $615,340 $461,505

$1,846,020 $923,010 $692,258Gasifier efficiency (%) 65 63 51Electricity price $0.11 kWh�1 $0.09 kWh�1 $0.055 kWh�1

Diesel price $3.50 gal�1 $2.50 gal�1 $1.50 gal�1

Internal rate of return (%) 15 10 5Gasifier capacity factor 0.95 0.9 0.8

$3.50 $3.75 $4.00 $4.25 $4.50 $4.75

Feedstock Harvest Cost

Gasifier Capital Cost

Pipeline Capital Cost

Efficiency

Electricity Price

Diesel Price

Internal Rate of Return

Gasifier Capacity Factor

Indicates change inquantity of hydrogen produced.

Indicates change in optimal facility location or delivery mode.

Fig. 7. Tornado plot for 10% demand sensitivity analysis.

N. Parker et al. / Transportation Research Part E 46 (2010) 534–545 543

configuration for each value of the parameters which in some cases results in different hydrogen quantities delivered and bydifferent modes. The white stars denote a significant change in the optimal quantity of straw consumed by the system. Blackstars point out where the system configuration is altered in facility location and/or hydrogen delivery mode.

Through scenario and sensitivity analysis, we are able to identify the parameters that may have large impact on the de-sign of the production and distribution facilities. The two most important factors are hydrogen demand and feedstock sup-ply. The cost of hydrogen pipelines has a major impact on supply chain design and is highly uncertain even at the initial

544 N. Parker et al. / Transportation Research Part E 46 (2010) 534–545

design phase. The price of electricity is especially important for the viability of liquid hydrogen delivery. While the desiredrate of return on capital has a major impact on the cost of producing hydrogen, it is not likely to be uncertain at the time ofdesign by industry. These findings will inform the selection of most important and representative random scenarios in ourfuture research of extending the model to stochastic version.

4. Discussion

Through integration of knowledge in mathematical modeling, hydrogen technology and economics, and geographic infor-mation system, we have developed a tool for evaluating the economic feasibility and infrastructure requirements for hydro-gen production from agricultural wastes. Using northern California case study, we found that hydrogen from agriculturalwastes can be delivered at costs similar to producing hydrogen from natural gas, a non-renewable energy source. Hydrogenfrom agricultural wastes would occur significant costs through transportation of both feedstock and hydrogen. The on-roadfreight requirements for feedstock delivery will be significantly greater than current petroleum-based fuels. Delivery ofhydrogen may significantly increase fuel delivery traffic within urban areas especially at low hydrogen demands where gas-eous truck delivery is the preferred over pipelines.

One of the immediate extensions is to address the stochastic nature of the problem. As shown in the sensitivity and sce-nario analysis, different values of model parameters may result in completely different system configuration. A method thatcan incorporate many possible future scenarios and hedges well against uncertainty is needed. We are exploring this areawith options of stochastic programming and decomposition methods such as progressive hedging. In addition, we shall alsoconsider multiple resources of biomass feedstock in the study region and other regions. Different feedstock and different re-gions will have different geographic characteristics, which will influence the final design of the production and distributionsystem. Our assessment of the economic feasibility of biohydrogen production is based on the case study of northern Cali-fornia. It should be noted that this assessment is regional specific: other geographic areas may result in different costs andinfrastructure needs. In studying a wide variety of real-world cases, we are striving to develop broadly applicable measuresof biomass hydrogen production costs for given supply and demand densities. Efforts on improving these limitations are cur-rently undergoing.

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