POTENTIAL ROLE OF EXERGY IN ANALYSIS OF HYDROGEN 

INFRASTRUCTURE 

A. A. Jalalzadeh-Azar1

Abstract 

The objective of this paper is to demonstrate the potential role of exergy (second-law) 

analysis, as a complementary tool for economic assessments of hydrogen infrastructures. 

Comprehensive thermodynamic analysis is particularly valuable for evaluating hydrogen 

production technologies that are energy intensive and represent a key infrastructural 

component. 

This study focuses on three selected distributed hydrogen production technologies: 

natural gas steam reforming, ethanol steam reforming, and electrolysis. The prospect of 

distributed systems for early market adoption in the absence of a well-developed 

hydrogen distribution network is a compelling reason for this selection. The 

thermodynamic performance of these systems are evaluated and discussed in conjunction 

with their energy costs as major contributors to the total hydrogen production costs. 

Analyses are also performed in the context of the source energy and feedstock. 

For these systems operating under prescribed conditions, the differences between the 

energetic and exergetic efficiencies are found to be rather insignificant. In light of the 

calculated unused/destroyed exergies, the limitations for potential hydrogen cost 

reduction via energy savings are discussed as well. 

1. Introduction 

The potential benefits of hydrogen as an alternative fuel and the prospects of a growing 

demand advocate development of viable hydrogen infrastructures [1 and 2]. As with any 

energy carriers, the key components for a hydrogen infrastructure are production, storage, 

and distribution/delivery, all of which pose technical and economic challenges to 

successful deployments. The production aspect is perhaps the most important of all as it 

encompasses issues, such as availability of source energy (feedstocks), fuel utilization 

efficiency, and environmental effects, among others. However, the ultimate contribution 

of this alternative fuel to the future energy market will depend on the overall performance 

of the nascent infrastructure, not just its constituents. 

Small-scale distributed hydrogen production technologies can be of particular interest to 

the industry and other stakeholders because of (1) their minimal dependency (if any at 

all) on the existence of distribution facilities and (2) an early investor perception of a 

more manageable risk associated with the technological maturity and the uncertainties 

 

1

 Ali A. Jalalzadeh-Azar is a Senior Engineer II at the National Renewable Energy Laboratory, Golden, 

CO. 

1 

NREL/CP-560-43064. 

Presented at the 2008 NHA Annual Hydrogen Conference 

March 30 – April 3, 2008, Sacramento, California 
with the future energy market. Drawing from these attributes, the analytical study 

presented in this paper focuses on three distributed (forecourt) production technologies 

without carbon sequestration: natural gas steam reforming, ethanol steam reforming, and 

electrolysis. The rationale for this selection is as follows: 

• The natural gas (methane) reforming technology is matured and a good candidate 

for early market adoption given the well-developed natural gas infrastructure. 

• For the case of ethanol reforming, the feedstock can be produced via a mix of 

fossil and renewable fuels, mitigating the demand for the fossil fuel. Furthermore, 

as a liquid, ethanol can be transported to hydrogen production sites without some 

of the drawbacks inherent in transporting gaseous fuels, especially hydrogen. 

• By producing hydrogen as a storage medium, electrolysis can help overcome the 

intermittency effects of wind and photovoltaic (PV) power generation by closing 

the temporal gap between the supply and demand for energy. 

The purpose of this paper is to explore the potential role of an exergetic analysis in 

economic assessment of hydrogen production systems that constitute a key infrastructural 

element. To accomplish this, the cost data were obtained from the available case studies 

facilitated by the U.S. Department of Energy (DOE) H2A Production Analysis tool [3] 

for the three aforementioned distributed (forecourt) technologies. H2A Production is a 

model developed for cost analysis of forecourt and central hydrogen production systems. 

The forecourt systems, which are the focus of this study, have a capacity of 100 to 1,500 

kg of hydrogen per day. The hydrogen produced at an elevated pressure is further 

compressed for storage and dispensing. Detailed information on the methodology, 

assumptions, and case studies of H2A are available in the cited reference [3]. 

Figures 1 and 2, respectively, illustrate the simplified schematics of the steam reformers 

and the electrolyzer analyzed in this study. In the interest of consistency, efforts were 

made to emulate the key features of the respective H2A systems, including the operating 

conditions, in the thermodynamic assessments. The hydrogen leaving the depicted 

systems corresponds to the product stream of the H2A model upstream of the dispensing/ 

delivery components (compressors and storage units), which are not addressed in this 

paper. Both energy (first-law) and exergy (second-law) efficiencies of the systems were 

evaluated and discussed for the designated control volumes (Figures 1 and 2). The energy 

efficiencies were evaluated based on (1) the delivered electrical energy and pure feed and 

(2) the source energy for the electricity and for processing the raw feedstock. The latter 

did not apply to natural gas. 

For the thermodynamic analyses, the following assumptions were made: 

• An overall efficiency of approximately 32% for electrical power generation and 

transmission. 

2 
• Reference environment temperature (To ) and pressure ( Po ) of 298 K (25o

C) and 1 

atm (101.325 kPa). 

• Treatment of natural gas, hydrogen, and carbon dioxide as ideal gases. 

• A net energy ratio of 1.5 for production of ethanol (i.e., producing 1.5 kJ ethanol 

per kJ of fossil fuel) – based on a literature review [4, 5, and 6]. 

• The reactants enter the system at the reference environment conditions ( PT oo , ), 

and the products leave at temperature To and pressure P ( > PP o ), which is taken 

as the operating pressure in the H2A model. 

Steam 

Reformer 

Shift 

Reactor 

Separator / 

Purifier 

Comp. / 

Pump 

Syngas H2 & CO2 Mix. 

H2 

Feedstock 

Water 

Fuel 

Flue Gas 

CO2 

Elect. Energy Heat Loss 

Air 

Burner CV 1 

CV 2 

Figure 1. Schematic of natural gas and ethanol reformers. 

Electrolyzer Comp. H2 

Elect. 

O2 

Heat Loss 

CV 

Water 

Figure 2. Schematic of electrolyzer. 

3 
2. Chemical Reactions 

The overall chemical reactions for natural gas and ethanol steam reforming are as 

follows: 

Natural Gas: 4 2 2 2 + ↔ 4)(2)( + COHlOHgCH (1) 

Ethanol: 52 + 2 ↔ 2 + 26)(3)( COHlOHlOHHC 2 (2) 

The combined reaction for each reformer consists of a strongly endothermic reforming 

process and a moderately exothermic water–gas shift reaction. The endothermic reaction 

takes place at a high temperature and pressure. The operating conditions used in the H2A 

case studies for reforming (850oC and 20 atm) are within the typical ranges [1, 7, and 8]. 

However, appropriate operating conditions for the reformer and shift reactor of a 

production plant are determined in part based on the catalyst type and volume. For 

example, studies have shown that relatively high yields of hydrogen can be obtained at 

significantly lower temperatures using special catalysts for ethanol reforming [9, 10, and 

8]. 

For reaction (1), a minimum heating amount of 253 MJ per kmol of methane (enthalpy of 

reaction, ) is required at the standard conditions: (298 K) and pressure (1atm). 

For the ethanol reforming, reaction (2), 348 MJ per kmol of ethanol is required. To meet 

these heating requirements, the necessary combustion fuel for the burner (CV 2 in Figure 

1) is 0.32 kmol/kmol of the feed for the natural gas reformer and 0.28 for the ethanol. 

These estimates are based on the lower heating value (LHV) of the combustion fuel and 

the assumption that the fuel is the same as the feed (i.e., natural gas or ethanol). (The 

theoretical combustion fuel requirement for the natural gas reformer is in good agreement 

with the estimate of 33% reported by Rosen [9]). The total hydrogen production rates 

derived from the H2A cases for the natural gas and ethanol reformers are, respectively, 

2.43 and 3.49 kmol per kmol of total fuel (feed and combustion fuel combined). The 

hydrogen yield per kmol of the feed is about 3.2 for the natural gas reformer and 4.47 for 

the ethanol. These estimates were derived from the reported H2A input and output energy 

fluxes in conjunction with the respective lower heating values. 

o ΔHr To Po

For the electrolyzer, the chemical reaction is 

2 2 2 +↔ 21)( OHlOH (3) 

3. Exergy Analysis 

Applying the second law of thermodynamics to the hydrogen production system (CV 1) 

in Figure 1 yields the following steady-state exergy balance: 

− )/1( . 2 2 2 . ≥=−−++++ 0 ∫ bo elec Fsep OH H CO cons δ xxcxbxaxxxqTT (4) 

4 
In this equation, F x , OHx 2 , H 2 x , and CO2 x are the flow exergies of the fluids crossing the 

system boundary on molar basis, expressed in terms of kJ per kmol of entering fuel 

(feed). Neglecting the kinetic and potential energy effects, the flow exergy on a molar 

basis is the sum of chemical exergy, chx , and thermo-mechanical exergy, thmx , [11]: 

)()( ooo

ch thm ch −−−+=+= ssThhxxxx (5) 

The coefficients in Equation (4) respectively correspond to the molar 

quantities of water, hydrogen, and carbon dioxide in the actual chemical reactions. The 

first term on the left of Equation (4) represents the algebraic sum of exergy flows 

accompanying the heat transfer crossing the system boundary: 

,, candba

[ ] [ ] System Cooling bo Endothermic bo bo qTTqTT qTT ∫ ∫ ∫ − δ −= )/1()/1( δ −+ )/1( δ (6) 

In this equation, the second term on the right has a negative value and denotes the unused 

thermal exergy that leaves the system via active and passive cooling. The minimum 

exergy required for separating CO2 from the CO2/H2 mixture is approximated by the 

following expression [12]: 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ = +

2

2

2

ln ln 2

.

CO

m

m

CO

H

m

m

H

sep o n

n

n

n

n

n

n

n TRx (7) 

The parameters 2 , 2 , and denote, respectively, the number of moles of 

hydrogen, carbon dioxide, and the mixture in the separator, neglecting other impurities. 

For both natural gas and ethanol steam reforming systems, the minimum separation 

exergy translates into less than 1% of the chemical energy of the feed (0.75% and 0.82% 

for the separators in the natural gas and ethanol systems, respectively). The exergy input 

for separation may be viewed as the thermo-mechanical exergy of the steam applied for 

regeneration of the material (e.g., alkaline solution) used to separate the carbon dioxide 

constituent. 

nH nCO nm

The exergetic efficiency used in this study is defined as 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

F

H

x

x

b 2 ε (8) 

The energy efficiency is defined as 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = F

H

LHV

LHV b 2

η (9) 

5 
In Equations (8) and (9), the coefficient b is the number of moles of hydrogen product 

per mole of the feed, and LHV is the lower heating value in kJ per kmole of the 

substance. As will be seen later, the exergy efficiency is fairly close to the energy 

efficiency. This agreement is also demonstrated by another study [13]. 

Upon rearrangement, Equation (4) can be expressed as 

[ ]

[ ] )/1( 0

)/1(

2 .

. 2 2

−− >++

− =−++++

∫

∫

CO cons System Cooling bo

elec Fsep OH H Endothermic bo

qTT xxc

qTT xbxaxxx

δ

δ

 (10) 

The underlined term in this equation represents the unused exergy. Considering that the 

exergy consumed (also referred to as exergy destroyed or irreversibility) within the 

control volume (CV 1in Figure 1), , is always positive, examination of Equation (9) 

leads to the following observations: 

cons. x

A lower reformer operating temperature can help reduce the exergy transfer 

accompanying the heat input and, consequently, reduce the total irrevesibilty and unused 

exergy. However, depending on the catalyst type and volume, lowering the operating 

temperature can also reduce the hydrogen yield and consequently negate the efficiency 

gains. The concentration of hydrogen in the gaseous mixture leaving the reformer 

(upstream of the shift reactor) is theoretically influenced by the following second-law 

based equilibrium criterion. 

TK )(ln TR

Go

= Δ − (11) 

where is the change in Gibbs function for the reaction and o ΔG K is the equilibrium 

constant at a given reaction temperature. However, the hydrogen concentration 

determined by Equation (11) is more favorable than what is expected in real-world 

applications, where the product mixture does not quite reach equilibrium at a given 

reactor temperature. 

The unused exergy departing the system due to the cooling process vanishes as the 

cooling occurs at a temperature approaching that of the reference environment. It should 

be noted that a low-temperature cooling would be advantageous only if it is achieved as a 

result of exhausting all available options for heat recovery, with the lowest possible 

temperature difference between the heat source and the target media. Otherwise, internal 

exergy destruction may occur even if the exergy loss associated with the cooling is 

insignificant. 

To improve the hydrogen yield, it is a common practice to supply a higher steam-to-fuel 

ratio to the reformer than the amount prescribed by the stoichiometric reactions [9, 10, 

and 11]. Therefore, introducing any excess steam will not only require a higher influx of 

6 
energy/exergy for heating but will likely exhibit a higher amount of unused exergy due to 

the discharge of the excess steam (not shown in Figure 1) – unless it receives a credit for 

an external use. 

For the type of electrolyzer used in this study, the exergy balance (Equation 10) reduces 

to the following. 

2. −+ ′ 2 [ −−= )/1( ] + ′ 2 . >+ 0 ∫ O cons System Cooling elec OH H bo xbxx δ qTT xxc (12) 

 

In this equation, elec. x represents the total exergy input, including the electrical exergy 

(energy) use for the ancillary equipment and sep x . The coefficients and denote the 

number of moles of hydrogen and oxygen, respectively, in the actual reaction. As before, 

the underlined term is the unused exergy. 

b′ c′

4. Results and Discussion 

Figure 3 presents the energy and exergy efficiencies of the three H2A distributed 

hydrogen production cases: natural gas steam reformer, ethanol steam reformer, and 

electrolyzer. As seen in this figure, when the efficiencies are determined based on the 

delivered energy, the energy efficiencies are within about 60% - 70%, with the natural 

gas reformer being the most efficient. The exergetic efficiencies of the natural gas 

reformer and electrolyzer are approximately the same as the corresponding energy 

efficiencies. This congruity can be attributed to: 

1. Relatively small thermo-mechanical exergy contribution relative to the chemical 

exergy of the stream. 

2. Closeness of the heating value to chemical exergy of the energy carriers. 

For the case of the ethanol reformer, a noticeable, but not significant, difference between 

the two efficiencies is noted primarily due to a greater difference between the LHV and 

chemical exergy of liquid ethanol. Close agreements between the two thermodynamic 

performance indices for other hydrogen technologies have been also demonstrated by 

Rosen [13]. 

When the energy efficiency values are determined based on the source energy input, the 

superiority of the ethanol reformer stands out (Figure 3). This favorable outcome is based 

on a hydrogen-to-fossil energy ratio of 1.5. Even significantly higher performance can be 

expected with ethanol produced in state-of-the-art facilities that emphasize use of 

renewable energy. The electrolysis system using grid electricity is shown to be the least 

attractive system from the standpoints of fossil fuel consumption and emissions. Even if 

50% of the grid electricity were to be supplied by renewable technologies (e.g., wind and 

PV) on average, the energy efficiency value that only accounts for the fossil energy input 

would merely increase to about 40%. 

7 
0

20

40

60

80

100

120

NG Steam Reformer Eth. Steam Reformer Electrolyzer

Efficiency, %

 H2A Case, Energy Eff.

 H2A Case, Exergy Eff.

 H2A Case, Energy Eff. (Source Fossil Energy)

With Fossil Fuel-Powered 

Electric Grid

Figure 3. Energy and Exergy Efficiencies. 

Table 1 compares the efficiency results of this study (based on the delivered energy not 

the source energy) with those of the studies selected from the literature. This table 

reflects a noticeable scatter among the reported data, which can be attributed to the 

differences in (1) the operating conditions, (2) the methodologies and assumptions, 

and/or (3) the technological characteristics of the investigated systems. 

Using the approach discussed above, a more detailed exergy analysis of the H2A cases 

was performed for the three distributed hydrogen production technologies. The results are 

illustrated in Figure 4. The stacked columns in this figure depict the exergy values of the 

energy flows entering and leaving the systems (Figures 1 and 2) in terms of MJ per kg of 

hydrogen produced. The total unused/destroyed exergies within the entire system (CV 1 

and CV2 combined) and the burners of the two reformers (CV 2) are also shown. 

For the natural gas and ethanol reformers, the relative magnitudes of the flow exergy 

accompanying the by-product CO2 and the electrical exergy input are either very small or 

even negligible (Figure 4). Therefore, inclusion or exclusion of either exergy component 

in the calculation of the exergetic efficiency will make no significant difference. The 

exergy value of the heat transfer to the reformer (the first term on the right side of 

Equation (6) is estimated using a constant operating temperature of 850o

C (applied in the 

H2A model) as the boundary temperature. The amount of heat is determined based on the 

fraction of the total fuel input (feed plus combustion fuel) required for the burner, as 

previously discussed – 0.32 for the natural gas reformer and 0.28 for the ethanol. For the 

steam reformers, the unused/destroyed exergy equals the difference between the heat 

8 
transfer exergy and the chemical exergy of the combustion fuel. The variation of the 

unused/destroyed exergies with the technology type is consistent with the exergetic 

efficiency trend depicted in Figure 3. 

Table 1. Comparison of efficiency results with selected data from the literature. 

Natural Gas 

Steam Reformer 

Ethanol Steam 

Reformer Electrolyzer Source 

η (%) ε (%) η (%) ε (%) η (%) ε (%) 

Current Study(1) 71 70 67 62 62 63 

Ref. [14](2) 73-75 --- --- --- 64-70 --- 

Ref. [13] 86 78 --- --- 30-49 26-41 

Ref. [15] --- --- --- --- 59 --- 

Ref. [12](3) --- 60-67 --- --- --- --- 

1. Determined using the results of the latest H2A Production case models based on the current state-ofthe-art technologies. 

2. Includes the net output of by-product (e.g., steam). The ranges are provided based on literature review. 

3. The reported range is for reformed product temperatures of 1100 K and higher. 

0

100

200

300

400

500

NG Steam Reformer Eth. Steam Reformer Electrolyzer

Exergy, MJ/kg of H2

 Feed (H2O for Electrolyzer) Heat Input to Reformer

 Electricity CO2 (O2 for Electrolyzer)

 H2 Total Unused / Destroyed

 Combustion Unused / Dest.

Figure 4. Exergy balance for hydrogen production systems. 

For the electrolyzer, the total electrical exergy (energy) input is the equivalent of the 

combined exergy (energy) of the feed, combustion fuel, and electricity used in the 

reformers. Given the second-law constraint on the fossil-to-electricity efficiency, the 

overall exergetic performance of the electrolyzer (fossil fuel to hydrogen conversion) is 

significantly less attractive unless renewable sources of energy are major contributors to 

9 
the electrical grid. When fully integrated with an on-site renewable power generator (e.g., 

wind energy or PV), the need for fossil-source energy diminishes for the electrolyzer. 

Regardless of the system, steam reformer or electrolizer, any reduction in the fossil fuel 

consumption proportionately reduces the greenhouse gas (GHG) emissions. 

Figure 5 provides the cost data for hydrogen production using the selected H2A cases. 

The stacked columns demonstrate the relative contributions of the main cost categories: 

energy (feed and combustion fuel), capital, and operating and maintenance. The total 

hydrogen cost represented by the solid line (Figure 5) is normalized based on the unit 

cost of hydrogen produced by the natural gas reformer. Clearly, the total cost of energy is 

dominant: 62% for the natural gas reformer, 77% for the ethanol reformer, and 58% for 

the electrolyzer. It should be pointed out that the higher energy cost of the ethanol 

reformer partly stems from the capital cost associated with the ethanol production. The 

capital cost is the second in significance – less than 30%. In contrast, the data complied 

by a European study [14] on various hydrogen production technologies, which did not 

include ethanol reforming, suggest a different cost composition for small-scale natural 

gas reformers and electrolyzers. In that study, the operations and maintenance (O&M) 

cost has a considerably greater share of the total cost. Figure 5 indicates that hydrogen 

production by the electrolyzer is the most expensive system, followed by the ethanol 

reformer. 

62% 77% 58%

28%

17%

29%

10% 6% 13%

0%

20%

40%

60%

80%

100%

120%

NG Steam Reformer Eth. Steam Reformer Electrolyzer

Constituent Costs of H2 Production

0

1

2

3

4

5

6

Norm. Total Cost of H2 Production

 Energy Cost Capital Cost

 O&M Cost Norm. Total Cost

Figure 5. Costs of hydrogen production. 

10 
The confluence of the thermodynamic and economic results (Figures 4 and 5) has 

important implications. On the one hand, Figure 5 suggests that there may be an 

opportunity for a substantial reduction in the hydrogen cost by curtailing the dominant 

energy (feed, fuel, and electricity) share of the total cost. On the other hand, the 

unused/destroyed portion of the total exergy input (Figure 4) limits this perceived 

opportunity. For example, for the natural gas reformer, assuming that the capital and 

O&M costs remain intact, the maximum theoretically possible reduction in energy use 

translates into a hydrogen cost reduction of about 20%. However, in real-world 

applications, the energy-related savings cannot be this high because of insurmountable 

challenges in eliminating the exergy destruction and in recovering low-grade heat loss. 

Similar analyses, in concert with inputs from real-world experiences, are imperative for 

realistically predicting the cost-reduction potentials for the future infrastructural systems. 

5. Conclusions 

In this paper, economic and thermodynamic analyses were conducted for three distributed 

hydrogen production systems – a natural gas steam reformer, an ethanol steam reformer, 

and an electrolyzer. The economic evaluation was based on the cost data obtained from 

the H2A Production case studies. For the thermodynamic analysis, the attention was 

devoted to both energetic and exergetic performance of the selected systems. The impact 

of the intermediate process that occurs between the source and the point of delivery was 

addressed from the thermodynamic standpoint for the required inputs of energy and 

feedstock. The relative contributions of the key cost and exergy constituents were 

elaborated. 

The first- and second-law efficiencies for the gas reformers were either virtually equal or 

slightly different, owing to the slight difference between the corresponding heating values 

and chemical exergies of the feed (natural gas) and hydrogen. For the ethanol reformer, 

the difference between the two performance indices was noticeable, but not very 

significant. Roughly equal energy and exergy efficiencies were also observed with the 

electrolyzer. Overall, the results from the energy and exergy analyses were rather similar. 

The only major difference between the two approaches pertains to the thermal interaction 

between the burner and the reforming process, as the exergy accompanying the heat 

transfer is influenced by the operating reactor temperature. However, this exergy 

component has a limited role in the overall system performance. 

For the investigated cases, the energy cost has a greater share than the sum of capital and 

non-energy operating costs, particularly for the case of the ethanol reformer. However, 

any predictive analyses attempting to project energy cost reduction through efficiency 

improvements are subject to the ineluctable laws of thermodynamics, as demonstrated in 

this study. 

11 
6. Nomenclature 

,, cba Molar coefficients of substances in chemical reaction, kmol / kmol of fuel 

h Specific enthalpy, kJ/kmol of fuel 

HHV Higher heating value, kJ/kmol of fuel 

K Equilibrium constatn 

LHV Lower heating value, kJ/kmol of fuel 

P Pressure, kPa 

δ q Differential heat transfer, kJ/kmol of fuel

R Universal gas constant, 8.314 kJ/kmol.K 

s Specific entropy, kJ/kmol.K 

T Temperature, K 

x Flow exergy, kJ/kmol 

o ΔG Change in Gibbs function, kJ/kmol 

ε Exergetic (second-law) efficiency 

η Energetic (first-law) efficiency 

Subscripts 

b Boundary 

F Fuel / feed 

m Mixture 

o Reference environment 

sep. Associated with separation of mixed gases 

Superscripts 

ch Chemical 

thm Thermo-mechanical 

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