A Systematic Hierarchical Thermodynamic Analysis of Hydrogen

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Ind. Eng. Chem. Res. 2011, 50, 1278–1293

A Systematic Hierarchical Thermodynamic Analysis of Hydrogen Producing Iron-Chlorine Reaction Clusters Ryan J. Andress and Lealon L. Martin* Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180

Here, we apply our systematic methodology for thermochemical cycle evaluation to the well-studied Fe-Cl system. Using an integer linear program, thermochemical cycles are identified from species consisting of Fe, Cl, H, and O atoms and a corresponding nonlinear (in temperature) thermodynamic database. Using Aspen Plus simulation software and heat pinch analysis, maximum attainable cycle efficiencies of up to 51% are calculated, exceeding our base-level target of 35%. The most promising of these cycles is evaluated in more detail considering thermodynamic yields. A higher-level evaluation results in a significant reduction in cycle efficiency due to increased thermal requirements resulting from low-yield reactions and competing by-products. Results of this higher-level analysis and the base-level analysis are consistent with literature findings on Fe-Cl thermochemical cycles. Introduction The use of hydrogen as an energy carrier is an attractive alternative for overcoming global energy challenges. Through PEM fuel cells, hydrogen can be directly converted into electrical energy, achieving significantly higher efficiencies than traditional combustion engines without adverse emissions. However, large-scale production of carbon-free hydrogen is largely unrealized and poses distinct engineering challenges. Currently, 96% of all hydrogen demands are met through the conversion of fossil fuels.1 Although the steam reforming of natural gas is currently the most economical route to hydrogen production, it is not a permanent solution for alternative energy.2 Carbon emissions are an added cost that cannot be overlooked because of their significant environmental effects. With possible carbon taxes and limitations on emissions, the cost of hydrogen through steam reforming will increase significantly. If carbon sequestration methods ultimately fail, then hydrogen production through fossil fuel is not a viable long-term solution. Besides large quantities of carbon dioxide being released from fossil fuel based production methods, trace amounts of contaminants (e.g., CO, sulfur compounds) are present in the hydrogen product stream.3 These contaminants are damaging to PEM fuel cells because they can poison the catalyst. The cost of natural gas is also likely to increase.4 As the price of oil increases, due to its limited supply, the demand for natural gas will increase, causing a corresponding rise in price. Natural gas is also a limited resource and will eventually be depleted. The presented limitations to hydrogen production via fossil fuels provide motivation for processes involving alternative, sustainable energy sources. The splitting of water into hydrogen and oxygen through electrolysis, paired with an alternative energy source (e.g., nuclear, solar) is an attractive method for carbon-free production. This process however is very inefficient, with reported efficiencies between 20% and 32%,3,5 as it involves the conversion of heat into mechanical work through a bottoming cycle and mechanical work into electricity. Higher efficiencies can be achieved through the direct use of thermal energy in a thermochemical cycle. With * To whom correspondence should be addressed. E-mail: [email protected].

thermochemical cycles, a combination of reactions is sequenced to produce an overall reaction of water-splitting. The concept of thermochemical cycles was first posed in the early 1960s by Funk and Reinstrom,6 for the Energy Depot project, as a two-step alternative to the electrolysis of water. Further interest in thermochemical cycles was exhibited at the International Round Table on Direct Production of Hydrogen with Nuclear Heat in 1969, leading to investigations by the Joint Research Center, at Ispra.5 Key criteria identified for potential cycles include thermal efficiency; reaction completion; and the safety, cost, and abundance of the required species. A high operating temperature, achieved through high-temperature nuclear reactors or solar power, is often demanded for increased cycle efficiency.7 The thermodynamic feasibility of each reaction is also necessary for a viable thermochemical cycle.8 Extensive work has been conducted on identifying and evaluating thermochemical cycles.3,9,10 The Institute of Gas Technology reported that, of the 165 cycles studied (from the 4-6 million possible cycles with three and four reactions), only two-thirds of those are thermodynamically feasible, and less than 10% are experimentally workable.11 They determined four reaction metal oxide-metal chloride cycles to be among the most promising, with Fe-Cl cycles having reported maximum efficiencies of 47%. The Fe-Cl system of thermochemical cycles, identified in the 1970s,5 is a well studied system with potentially high reaction yields and thermal efficiencies.10 Here, we will re-evaluate the Fe-Cl system of thermochemical cycles in a more systematic manner. In our previous work,12,13 we developed a systems engineering method for accomplishing this task, in which feasible reaction clusters are generated through an automatic selection algorithm and evaluated for efficiency using process simulation software and heat integration. The cycle generation algorithm is first reformulated so that we can search a system of species more systematically; then the Fe-Cl system is evaluated in a case study of our methodology. Computational Methodology Effective screening for potentially economically viable thermochemical cycles begins with exhausting the reaction cluster search space of a given system. In our previous work,12 we developed an automatic selection algorithm to identify thermodynamically feasible reaction clusters8 from systems of candidate species and

10.1021/ie100398r  2011 American Chemical Society Published on Web 07/08/2010

Ind. Eng. Chem. Res., Vol. 50, No. 3, 2011

corresponding Gibbs energy data within a given temperature range. This algorithm was formulated as the following mixed integer nonlinear mathematical program (MINLP): min

δij,γij,Tj,βij,θij

∑ ∑ (d δ

i ij

Table 1. List of Parameters for Algorithm P2 Used in the Fe-Cl Case Study

(P1)

i∈I j∈J

subject to:

∑ (δ

ij

- γij) - νi ) 0; i ∈ I

(1)

- γij) ) 0; k ∈ K, j ∈ J

(2)

- γij) + zRTj e 0; j ∈ J

(3)

j∈J

∑ B (δ ki

ij

i∈I

∑ ∆G i∈I

iTj(δij

δij - δuijβij e 0; i ∈ I, j ∈ J

(4)

γij - γuijθij e 0; i ∈ I, j ∈ J

(5)

βij + θij - 1 e 0; i ∈ I, j ∈ J

(6)

∑β

ij

- sP e 0; j ∈ J

(7)

∑θ

ij

- sR e 0; j ∈ J

(8)

δlj e

∑δ

e δuj ; j ∈ J

(9)

∑γ

e γuj ; j ∈ J

(10)

i∈I

i∈I

ij

i∈I

γlj e

ij

i∈I

δij ∈ I [0, δuij]; i ∈ I, j ∈ J

(11)

γij ∈ I [0, γuij]; i ∈ I, j ∈ J

(12)

βij, θij ∈ I [0, 1]; i ∈ I, j ∈ J

(13)

Tj (K)

η

91

6HCl + 2Fe2O3 f 2FeCl3 + 2Fe(OH)3 H2 + 2Fe(OH)3 f 4H2O + O2 + 2Fe 3H2O + 2FeCl3 f 6HCl + Fe2O3 3H2O + 2Fe f 3H2 + Fe2O3 H2 + Fe3O4 f H2O + 3FeO 3H2O + 3FeCl2 f 6HCl + 3FeO Fe + 2Fe(OH)3 f 3H2 + O2 + Fe3O4 6HCl + 6FeO f 3FeCl2 + Fe + 2Fe(OH)3 6FeCl2 + 8H2O f 2Fe3O4 + 12HCl + 2H2 2Fe3O4 + 16HCl f 4FeCl3 + 2FeCl2 + 8H2O 4FeCl3 f 4FeCl2 + 2Cl2 2Cl2 + 2H2O f 4HCl + O2 Fe + 3Fe(OH)2 f 3H2 + O2 + 4FeO 6HCl + 6FeO f 2FeCl3 + Fe + 3Fe(OH)2 3H2O + 2FeCl3 f 6HCl + Fe2O3 H2 + Fe2O3 f H2O + 2FeO 6FeCl3 f 3Cl2 + 6FeCl2 3Cl2 + 2FeO f O2 + 2FeCl3 12HCl + 4FeO f 4H2O + 2H2 + 4FeCl3 6H2O + 6FeCl2 f 12HCl + 6FeO

300 1100 600 400 1000 1100 1100 300 1200 400 620 1200 1200 300 600 1100 600 300 300 1100

0.417

107

109

(15)

115

The above formulation generates thermodynamically feasible cycles, which are based on NS molecular species composed of NA desired atomic species, consisting of NR reactions subject to a desired overall reaction.

127

ij

i

f

4 14 4 10 I [300, 1200] K 1 5 5 1 1 1 2 6 3 3 3 3 3 3 2 1 -2 0 50000 kJ/mol 0.1 kJ/mol 16 3 2 1 20

reactions

I ≡ {1, ..., NS}; J ≡ {1, ..., NR}; K ≡ {1, ..., NA}

j∈J i∈I

N NS NR NT I [Ψ1, ΨNT] dH2O, cH2O dH2, cH2 dO2, cO2 dHCl, cHCl dCl2, cCl2 dFeCl2, cFeCl2 dFeCl3, cFeCl3 dFe2Cl6, cFe2Cl6 dFe3O4, cFe3O4 dFeO, cFeO dFe2O3, cFe2O3 dFe, cFe dFe(OH)2, cFe(OH)2 dFe(OH)3, cFe(OH)3 νH2 νO2 νH2O νi ∉{νH2, νO2, νH2O} M zRΨl δiju, γiju sP sR δjl, γjl δju, γju

obj.

(14)

∑ ∑γ Λ

value(s)

Table 2. Fe-Cl Thermochemical Cycles, with Reported Base Efficiencies, Generated Using Algorithm P2 with the Parameters from Table 1

Tj ∈ I [T , T ]; j ∈ J L

parameter(s) A

+ ciγij)

U

∑ ∑δ Λ ij

i

(16)

j∈J i∈I

where δij and γij represent product and reactant coefficients for species i in reaction j, respectively. Constraint 1 enforces the overall reaction (net water-splitting), with coefficients νi. Constraint 2 is the atomic balance for each atomic species k in each reaction j, where Bki is the number of atoms of k in molecular species i. The thermodynamic feasibility criterion is then imposed through constraint 3, where ∆GiTj is the Gibbs energy for molecular species i at reaction temperature Tj, R is the universal gas constant, and z is a positive, user-defined thermodynamic driving force. Constraints 4 and 5 define species i as a product or reactant in reaction j, respectively. Constraint 6 establishes that each

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0.356

0.513

0.397

0.217

species can participate only as a product or a reactant in a given reaction. Constraints 7 and 8 impose upper limits on the number of product and reacting species in a given reaction. Reaction stoichiometry is bounded through constraints 9 and 10. The decision variables are constrained to closed sets through bounds (11-14), where [a, b] and I [a, b] denote continuous and integer sets, respectively. P1 was shown to be solvable as an integer linear program (ILP) through a priori knowledge of the reaction temperatures.12 A full range of cycles, for a given system, can be identified through solving P1 multiple times for all possible sets of reaction temperatures. Although this solution procedure is a sound generation algorithm for complete sets of thermochemical cycles for a given system, it is not the most efficient procedure.

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Computationally, the ILP is easily solved; however, the same cycles are generated multiple times when exploiting each reaction temperature set. Ideally, one would prefer to solve P1 in a more systematic manner, i.e. without specifying reaction temperatures. This would allow for a precise solution procedure, where complete sets of cycles are generated in order of increasing objective function values with minimal probing of the reaction cluster search space. Such a solution procedure is presented here through the reformulation of P1, followed by our systems approach to thermochemical cycle evaluation. ILP Formulation for Identifying Thermochemical Cycles. The objective function and all of the constraints of P1, except for constraint 3, are integer and linear. As posed, constraint 3 presents a challenge because the decision variable Tj is an index of the variable ∆G and that overall constraint is nonlinear. To make the solution of P1 computationally tractable, we introduce new temperature variables, Ψl and ξlj, such that the following relationships hold:

Tj ≡

∑ξ Ψ; j ∈ J

(17)

∑ ξ ∆G

(18)

lj

l

l∈L

∆GiTj ≡

lj

l∈L

∑ξ

lj

iΨl ;

j∈J

) 1; j ∈ J

(19)

l∈L

Ψl ∈ I [TL, TU]; l ∈ L

(20)

ξlj ∈ I [0, 1]; l ∈ L, j ∈ J

(21)

L ≡ {1, 2, ..., NT}

(22)

where NT is the number of temperatures in the set I [TL, TU]. The first goal is to remove all of the decision variables from the indices found in the constraints of P1, specifically the index

Figure 1. Base-level Aspen Plus flowsheet of the Fe-Cl cycle, cycle B-1 in the Carty report. Information regarding the streams and unit operations can be found in Tables 3 and 4, respectively.


Tj for ∆G in constraint 3. With the new variables, constraint 3 is rewritten as

∑ ∑ ξ ∆G lj

i∈I l∈L

iΨl(δij

- γij) + zR

l

e 0; j ∈ J (23) T (K)

l∈L

This new inequality is more accessible; however there are bilinear terms which are difficult to solve due to their nonconvex nature.14,15 To make constraint 23 less computationally taxing, it is desirable to remove these bilinear terms. This is achieved through the introduction of parameter M.

∑ ∆G i∈I

iΨl(δij

- γij) + zRΨl e M(1 - ξlj); l ∈ L, j ∈ J (24) M . 0

(25)

M is sufficiently large such that constraints 23 and 24 are equivalent under all possible circumstances. P1 is now rewritten as the following equivalent ILP through a change of variables and the replacement of constraint 3 with 24: min

δij,γij,ξlj,βij,θij

Table 3. Stream Temperatures, Flow Rates, and Compositions for the Process Shown in Figure 1, for Producing 2 mol/s of Hydrogen flow (mol/s)

∑ξ Ψ lj

∑ ∑ (d δ

i ij

1281

+ ciγij)

(P2)

i∈I j∈J

subject to: 1, 2, 4-13, 19, 21, and 24. This new minimization problem can be solved with any ILP solver. P2 has 4NSNR + NTNR decision variables with 4NSNR + NTNR - NANR - NS - NR degrees of freedom, as compared to 4NSNR decision variables and 4NSNR - NANR - NS degrees of freedom for each linear subproblem of P1 (created by assuming reaction temperatures). Despite the added computational effort, P2 allows for a more direct evaluation of a given system for feasible thermochemical cycles. P1 must be solved combinatorially, through different linear subproblems, in order to obtain complete sets of reaction clusters for a given system. As an ILP, globally optimal solutions of P2 can be obtained15 without a priori knowledge of reaction temperatures, significantly reducing the total number of times the problem is solved. Cycle Evaluation and Optimization. A systematic method must also be employed in the construction and analysis of identified thermochemical cycles. Two levels of evaluation, loosely based on the Argonne National Laboratory (ANL) thermochemical cycle evaluation procedure,16-18 are conducted, base-level and higher-order analyses, each using a simulation engine and heat pinch analysis19 to determine cycle performance. Identified cycles are screened promptly using a base-level analysis, and promising cycles are further evaluated with a higher-order analysis. Base-level analysis begins with the assumption that the desired reactions go to completion and that there are no competing products. This allows for a prompt evaluation of all generated thermochemical cycles, serving as a screening mechanism to identify those cycles which should be considered in greater detail. Ideal, isothermal reactors, which are sequenced appropriately, are simulated with 100% conversion rates at temperatures that fall within the feasible ranges as determined from the thermodynamic database. Combinations of heat exchangers and ideal reactors are used to model temperature changes and phase transitions. The details of flow separation and work of pumping are not considered in any stage of the base-level analysis, as to expedite the screening process.

S-1

298

S-2

1200

S-3

1200

S-4

1200

S-5

1200

S-6

298

S-7

400

S-8

400

S-9

400

S-10

400

S-11

400

S-12

1200

S-13

1200

S-14

620

S-15

1200

S-16

620

S-17

1200

S-18

1200

S-19

620

S-20

620

S-21

298

S-22

400

S-23

1200

S-24

1200

H2O(l, g) FeCl3(s,g)

H2(g) Fe3O4(s)

2 (l) 0 2 (g) 0 0 0 0 0 0 0 0 0 0 0 8 (g) 4 (s) 0 0 8 (g) 0 0 4 (s) 0 0 8 (g) 0 0 4 (g) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 0 0 2 0 0 0 0 2 0 0 2 0 0 0 0

O2(g)

Cl2(g)

HCl(g)

FeCl2(s, l)

0

0

0

0

0

0

0

0

1

0

4

0

1

0

0

0

0

0

4

0

1

0

0

0

0

0

4

0

0

0

0

2 (s)

0

0

0

2 (s)

0

0

0

0

0

0

0

0

0

0

0

2 (l)

0

0

0

0

0

0

0

0

0

0

12

0

0

2

0

4 (s)

0

0

0

0

0

0

12

0

0

2

0

0

0

0

0

4 (s)

0

0

0

0

0

0

12

0

0

2

0

0

0

0

0

4 (l)

Once a given cycle has been constructed, the latent, sensible, and reaction heats from the simulated flowsheet are used to construct a pinch diagram. Temperature intervals, which break at phase transitions and reaction temperatures, are determined for the hot (i.e., require cooling) and cold (i.e., require heating) process streams. Overall heating and cooling requirements are determined for each temperature interval, and a composite heating curve is constructed. The two curves can be shifted horizontally in enthalpy so that a minimum approach temperature is maintained. The areas where the curves overlap is where heat can be integrated. The remaining heat must be provided by hot and cold utilities. The total amount of utility needed is the heat duty (Q) of the cycle. The standard performance measure for thermochemical cycles, as prescribed by ANL,16 is cycle efficiency (η). The efficiency considers the cycle heat duty (Q) and required work (W) against the standard heat of formation of water (∆HH°2O, 298K). This is a performance measure equal to the ratio of the energy output, the combustion enthalpy of hydrogen, and the energy introduced into

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Table 4. Temperature and Heat Duty of Each Unit Operation Shown in Figure 1, for Producing 2 mol/s of Hydrogen unit

unit type

inlet T (K)

outlet T (K)

heat duty (kW)

R-1 R-2 R-3 R-4 PHASE-1

RXN RXN RXN RXN HEX PHASE HEX HEX PHASE HEX HEX PHASE HEX HEX PHASE HEX HEX HEX HEX HEX HEX HEX

1200 400 620 1200 298 373 373 400 950 950 400 589 589 620 950 950 1200 1200 400 1200 1200 620

1200 400 620 1200 373 373 1200 950 950 1200 589 589 620 950 950 1200 298 400 1200 298 400 1200

-297.6 -497.4 -330.9 118.9 11.3 81.5 48.8 92.3 157.6 51.1 85.6 551.0 10.1 112.6 315.2 51.1 -29.8 -98.0 248.0 -53.6 -637.6 43.3

PHASE-2 PHASE-3 PHASE-4 H-1 H-2 H-3 H-4 H-5 H-6

the system, in the form of hot and cold utilities, chemical, electrical, and mechanical work. η)

-∆H°298K(H2O) W Q+ 0.5

(26)

For a base-level analysis, if no electrochemical reactions occur, only the work required to separate the product streams is considered in the evaluation. This work is equal in magnitude to the Gibbs energy of mixing, defined below, where R is the universal gas constant, T is the absolute temperature, n is the molar output, and y is the mole fraction. ∆Gsep ) -RT

∑ n ln y i

i

i

(27)

Table 5. Calculated Base-Level Efficiency of the Fe-Cl Cycle (Cycle B-1 in the Carty Report) and the Values for That Calculation, Based on a Production of 2 mols of Hydrogen parameter

value

hot utility cold utility ∆Gsep,O2 ∆Gsep,H2 ∆H °298K (H2O) Q W η

520.1 kJ 430.6 kJ 25.0 kJ 57.3 kJ -571.7 kJ 950.7 kJ 82.3 kJ 0.513

Equation 26 assumes an efficiency of 50% for the thermal equivalent of the required work, which is acceptable for this paper where the work is only chemical separations. The efficiency is calculated for the higher heating value (HHV, i.e. all inlet and outlet streams are at ambient temperature), which is more conservative and accurate, accounting for all the necessary heating and cooling requirements. If the efficiency calculated at the initial screening stage exceeds a threshold value of 35%, the cycle is evaluated with a higher-level analysis. The first step in a higher-order analysis is performing sensitivity analyses on different process conditions. Each reaction in a given cycle is first simulated separately, considering thermodynamics. The known expected reactants are supplied, and all likely products (desired and competing) are specified. Temperature, pressure, and feed ratio sensitivity analyses are then carried out using a simulation engine to predict the thermodynamically favored product composition and determine the most favorable operating conditions and maximum attainable yield. An entire cycle is then simulated, with the optimal reaction conditions from above, using reactors driven by thermodynamics. The cycle heat duty is determined as before using heat pinch analysis, and a cycle efficiency is calculated using eq 26. In a higher-level analysis, all necessary separation work is considered and is calculated using eq 27 or a more rigorous manner. A first approximation of a higher-level analysis assumes all separation steps are ideal (i.e., determined by Gibbs energy of mixing) with no pumping and pressurizing cost considerations. A successful

Figure 2. Base-level pinch diagram of the Fe-Cl cycle shown in Figure 1 (cycle B-1 in the Carty report) for a production of 2 mols of hydrogen. Each area of latent heat (horizontal components of the process streams) is labeled with the corresponding unit(s) from Figure 1.


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Figure 3. Temperature sensitivity analysis for reaction 1 (reaction 28) of the Fe-Cl cycle (cycle B-1 in the Carty report). Based on the results of supplying the reactants, at the stoichiometric ratio, to an Aspen Plus Gibbs reactor at multiple temperatures and a pressure of 1 bar.


cycle has a final efficiency greater than 30%, as to be competitive with the total efficiency of obtaining hydrogen from water through a combined bottoming cycle-electrolysis process. If a higher-level calculated efficiency exceeds this value, for a given cycle, then more complexity is added (e.g., kinetics, pumping costs, pressure drops) to the evaluation process and another higher-level analysis is executed.

species involved in the cycle are Fe, Cl, H, and O, selected for factors such as economics, environmental concerns, and reaction potential. From these species, a list of 14 molecular species is generated to be included in the cluster synthesis search:

Results and Discussion: Systematic Evaluation of Fe-Cl Cycles

FeCl2, FeCl3, Fe3O4, H2O, HCl, Cl2, H2, O2, Fe, FeO, Fe2O3, Fe(OH)2, Fe(OH)3, Fe2Cl6

The proposed methodology is now applied in a case study to assess the performance of iron-chlorine-based thermochemical cycles for hydrogen production.11,20 The atomic

The algorithm P2 is solved using an AMPL based mixed integer linear program solver, FEASPUMP, available through the NEOS Server at ANL. Cycles are identified using the

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parameters in Table 1 and Gibbs energy data from Aspen Properties V7.0, which is calculated using the SOLIDS thermodynamic base method for the above species at 100 K Table 6. Pertinent Phase Transitions for Fe-Cl Thermochemical Cycles species

phase transition

temperature (K)

H2O FeCl3 FeCl2 FeCl2

vaporization sublimation fusion vaporization

373 589 950 1296

temperature intervals between 300 K and 1200 K. The value of zRΨl is chosen to be constant, at 0.1 kJ/mol ∀l ∈ L, as to allow for the largest possible set of cycles while avoiding null reaction sets within a cluster. The first five thermodynamically feasible Fe-Cl cycles and their calculated base efficiencies are shown in Table 2. Reaction temperatures are chosen to minimize the Gibbs energy of reaction while maintaining a maximum temperature of 1100 K (unless a maximum temperature of 1200 K is necessary for the system to be feasible). One cycle identified, shown in Table 2 with an objective value of 109, is


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Figure 7. Sensitivity analysis on reaction stoichiometry for reaction 1 (reaction 28) of the Fe-Cl cycle (cycle B-1 in the Carty report). Based on an Aspen Plus Gibbs reactor at a temperature of 950 K and a pressure of 1 bar.

Figure 8. Sensitivity analysis on reaction stoichiometry for reaction 4 (reaction 31) of the Fe-Cl cycle (cycle B-1 in the Carty report). Based on an Aspen Plus Gibbs reactor at a temperature of 1500 K and a pressure of 1 bar.

well documented in the literature as cycle B-1 in the Carty report.21 6FeCl2(s,l) + 8H2O(g) f 2Fe3O4(s) + 12HCl(g) + 2H2(g)

(28)

2Fe3O4(s) + 16HCl(g) f 4FeCl3(s,g) + 2FeCl2(s) + 8H2O(g) (29)

4FeCl3(s,g) f 4FeCl2(s) + 2Cl2(g)

(30)

2Cl2(g) + 2H2O(g) f 4HCl(g) + O2(g)

(31)

The evaluation of this Fe-Cl thermochemical cycle using our systems engineering methodology is now presented.

Initial Evaluation. The cycle is first constructed in Aspen Plus V7.0 (Figure 1), with the SOLIDS base method and MIXCISLD stream class, using reaction temperatures that are consistent with the literature20 while falling within the thermodynamically feasible range found from the data. Although the feasible reaction temperatures exceed the 1123 K limit imposed by the presumed hot utility temperature, the cycle is evaluated because of its historical significance. Hot utility temperatures exceeding 1200 K can be achieved with very high-temperature reactors or concentrating solar power (CSP) technologies.7,22 There are four unit operations, ideal isothermal reactors (RXN),

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Figure 9. Temperature sensitivity analysis for reaction 3 (reaction 30) of the Fe-Cl cycle (cycle B-1 in the Carty report), allowing for the formation of the dimer Fe2Cl6. Based on an Aspen Plus Gibbs reactor at a pressure of 1 bar.

Figure 10. Higher-level Aspen Plus flowsheet of the Fe-Cl thermochemical cycle (cycle B-1 in the Carty report). Information regarding the reaction blocks, streams, and unit operations can be found in Figures 11-14 and Tables 7 and 8.

heat exchangers (HEX), ideal flow splitters (SEP), and phase transitions (PHASE), in the Aspen flowsheet. The phase transitions take place within hierarchical blocks, which consist of PHASE and HEX units to discriminate between sensible and latent heat. The flowsheet is constructed at a pressure of 1 bar for a production rate of 2 mol/s of hydrogen, and each stream that enters and exits the system is at a temperature of 298 K.

Phase changes take place for H2O at 373 K (PHASE-1), FeCl2 at 950 K (PHASE-2, PHASE-4), and FeCl3 at 589 K (PHASE3). The stream temperatures, compositions, and flow rates can be found in Table 3. Table 4 gives the heat duty of each unit operation (the SEP units are treated separately in the analysis). Using the data contained within Table 4, a pinch diagram, Figure 2, is constructed as part of a heat pinch analysis. The


pinch point occurs at an enthalpy of 525.3 kJ (cold stream temperature of 400 K) with a minimum approach temperature of 20 K. Integrating the heat of the overlapping areas results in a total utility cost reduction of 61%, as compared to meeting all process stream demands with utilities. Table 5 gives the required utility and cycle heat duty (Q) for producing 2 mols of hydrogen. The work of the cycle, for a base-level analysis, is the separation energy needed to obtain the hydrogen and oxygen, as determined by eq 27. Calculating the work for units SEP-1 and SEP-3 gives the work required for separating oxygen and hydrogen, respectively (found in Table 5). The base-level (or maximum attainable) efficiency is calculated, using the values in Table 5 and eq 26, to be 51.3%, which exceeds the threshold efficiency of 35%. With such a high base-level efficiency, a higher-level analysis is conducted on this Fe-Cl thermochemical cycle. Higher-Level Evaluation Based on Thermodynamic Yield. For a second-level analysis, likely competing products and thermodynamically favored product compositions are considered. Evaluation begins with a sensitivity analysis on product yield for each reaction. Using Aspen Plus Gibbs reactors (reactors which predict the final products based on a minimization of Gibbs energy), with the SOLIDS base method and MIXCISLD stream class, changes in reaction temperature and the reactant stoichiometric ratio are carried out. For this level of evaluation, reaction temperatures up to 1500 K will be considered (if necessary), which are achievable with CSP.22 Figures 3-6 show the temperature sensitivity analyses for each reaction (product yield (Y) vs temperature). Y)

initial amount of limiting reactant - final amount of limiting reactant initial amount of limiting reactant

(32)

Figure 11. Detailed flowsheet of block RXN-1 from Figure 10.

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As can be seen from Figures 3-6, the thermodynamics of the Fe-Cl cycle are nonlinear in nature with phase changes occurring at multiple temperatures (Table 6). Reaction temperatures that maximize product yield are chosen. Reaction 28 is favorable at a temperature of 950 K, above the melting point of FeCl2. Reaction 29 has its highest yield at 298 K. At 589 K, in the gaseous phase of FeCl3, reaction 30 is most favorable. The highest yield for reaction 31 is at the imposed upper bound of 1500 K. Using the above reaction temperatures, a sensitivity analysis is conducted on reaction stoichiometry through manipulating the stoichiometric ratio (S) of the reactants. Since 29 achieves a near 100% yield at 298 K, an analysis on stoichiometry is not conducted for this reaction. This analysis is also not conducted on

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reaction 30 because it has only one reactant. The results of these studies are shown in Figure 7 and Figure 8. Si )

actual amount of species i stoichiometric amount of species i

(33)

Reaction 28 has a yield of 100% when SH2O ) 3. On the basis of Figure 8, and further analysis, reaction 31 nears, but never reaches, 100% yield as one reactant is an excess. Reaction 31 will be operated with SH2O ) 5. With possible optimal reaction conditions determined, competing products are considered.


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Table 7. Stream Temperatures, Flow Rates, and Compositions for the Process Shown in Figures 10-14, for Producing 2 mol/s of Hydrogen flow (mol/s)

flow (mol/s)

H2O(l,g)

H2(g)

O2(g)

T (K)

FeCl3(s,g)

Fe3O4(s)

Fe2Cl6(g)

Cl2(g)

HCl(g)

S-I

298

0

0

0

S-III

950

0

S-IV

589

S-V

298

S-VI

950

S-VII

950

S-1A

950

S-1B

950

S-1C

950

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0

1500

0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 2 0

0

S-II

2 (l) 0 2 (g) 0 8 (g) 0 0 4 (s) 0 0 0 0 0 0 16 (g) 0 0 0 16 (g) 0

H2O(l,g)

H2(g)

O2(g)

T (K)

FeCl3(s,g)

Fe3O4(s)

Fe2Cl6(g)

Cl2(g)

HCl(g)

FeCl2(s,l,g)

S-2A

298

0 0 0

0

2 (s)

298

0 0 0 0

0

S-2B

8 (l) 4 (s) 8 (l) 0

0

0

0

H2O(l,g)

H2(g)

O2(g)

T (K)

FeCl3(s,g)

Fe3O4(s)

Fe2Cl6(g)

Cl2(g)

HCl(g)

FeCl2(s,l,g)

S-3A

589

2.17 (s)

0

0

S-3C

589

0.08

S-3D

1500

0 1.92 0 0 0 1.92 0 1.92

0

589

0 0 0 0 0 0 0 0

0.08

S-3B

0 0 0 0 0 0 0 0

0.08

H2O(l,g)

H2(g)

O2(g)

T (K)

FeCl3(s,g)

Fe3O4(s)

Fe2Cl6(g)

Cl2(g)

S-1D

298

0

298

0

0.28

0

0

0

S-1F

298

0

11.72

0

0

0

2 (s)

S-1G

298

0

0.28

0

0

0

0

S-1H

298

0

0

0

0

0

2.17 (s)

S-1I

298

0

0

0

0

0

3.83 (s)

S-1J

298

0

11.72

0

0

12

0

S-1K

298

0

0

0

0

0

0

S-1 L

950

0

0

0

0

12

0

S-1M

950

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

12

S-1E

2 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0

0

0

16 (l, g) 0 15.56 (l) 0 0.44 (g) 0 0 0 15.56 (l) 0 0 0 0 0 0.44 (g) 0 15.56 (g) 0 0.44 (g) 0

0

0

0

H2O(l,g)

H2(g)

O2(g)

T (K)

FeCl3(s,g)

Fe3O4(s)

Fe2Cl6(g)

Cl2(g)

HCl(g)

FeCl2(s,l,g)

298

0 4 (s)

0 0

0

0

0

2 (s)

H2O(l,g)

H2(g)

O2(g)

T (K)

FeCl3(s,g)

Fe3O4(s)

Fe2Cl6(g)

Cl2(g)

HCl(g)

FeCl2(s,l,g)

S-3E

1500

3.83 (g)

1500

2

0

0

0

0

S-3G

1500

0

0

3.83 (g)

0

0

S-3H

1500

0 0 0 0 0 0 0 0

0

S-3F

0 0 0 0 0 0 0 0

2

2.17 (s)

0 5.47 (g) 0 0 0 0 0 5.47 (g)

0

0

0

FeCl2(s,l,g)

flow (mol/s)

HCl(g)

FeCl2(s,l,g)

flow (mol/s)

S-2C

flow (mol/s)

flow (mol/s)

flow (mol/s)

flow (mol/s)

H2O(l,g)

H2(g)

O2(g)

T (K)

FeCl3(s,g)

Fe3O4(s)

Fe2Cl6(g)

Cl2(g)

S-4A

1500

0

0.03

4

S-4C

298

0.03

S-4D

298

S-4E

298

S-4F

298

1 0 1 0 0 0 0 0 1 0 0 0

4

298

0 0 0 0 0 0 0 0 0 0 0 0

0.03

S-4B

8 (g) 0 8 (l, g) 0 0.16 (g) 0 7.84 (l) 0 0 0 0 0

H2O(l,g)

H2(g)

O2(g)

T (K)

FeCl3(s,g)

Fe3O4(s)

Fe2Cl6(g)

Cl2(g)

S-4G

298

0

298

0

0

0

3.87

0

S-4I

298

0

0

0

0

0.13

0

S-4J

298

0

0.13

0

0

0

0

S-4K

1500

0.03

0

0

0

3.87

0

S-4L

1500

0 0 0 0 0 0 0 0 0 0 0 0

0

S-4H

0 0 0 0 0 0 0 0 0 0 0 0

0.03

0

0 0 0.16 (l) 0 7.48 (l) 0 0 0 0 0 8 (g) 0

0

0

0

HCl(g)

FeCl2(s,l,g)

Noted competing products for reaction 28 include FeOCl and FeO,11,20 neither of which form at the optimal conditions of 950 K, 1 bar, and SH2O ) 3. FeOCl was not included in the list of candidate species for cycle generation because of its slow formation kinetics.23 Reaction 29 has possible competing products of Fe2Cl6 and FeOCl,11 which according to the simulation do not form at 298 K, 1 bar, and stoichiometric conditions. Reaction 31, the well documented reverse Deacon reaction,20,24 has no competing products. The greatest difficulty

HCl(g)

FeCl2(s,l,g)

with the proposed Fe-Cl cycle is the formation of the dimer Fe2Cl6 as a competing product in reaction 30.20 Figure 9 shows the resulting product composition, for reaction 30, when allowing the formation of dimer Fe2Cl6. From the previous analysis, FeCl3 only reacts when it is in the gaseous phase, with the phase transition temperature of 589 K being the most favorable condition. However, at low temperatures within the gaseous phase, as seen from Figure 9, conversion to the dimer is favorable. At higher temperatures, the dimer

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Table 8. Temperature and Heat Duty of Each Unit Operation Shown in Figures 10-14, for Producing 2 mol/s of Hydrogen unit

unit type

inlet T (K)

outlet T (K)

heat duty (kW)

R-1 R-2 R-3A R-3B R-4 PHASE-1

RXN RXN RXN RXN RXN HEX PHASE HEX HEX PHASE HEX HEX PHASE HEX PHASE HEX PHASE HEX HEX PHASE HEX HEX HEX HEX HEX HEX HEX HEX HEX

950 298 589 1500 1500 298 373 373 298 373 373 1500 1296 1296 950 298 373 373 298 373 373 298 950 589 950 298 589 1500 298

950 298 589 1500 1500 373 373 1500 373 373 950 1296 1296 950 950 373 373 950 373 373 1500 589 298 950 298 950 1500 298 1500

671.5 -501.1 263.8 666.6 119.8 11.3 100.8 71.9 45.3 403.3 94.1 -49.7 -359.3 -135.4 -301.9 86.9 635.6 332.7 44.9 327.5 365.4 173.6 -275.7 66.7 -1339.7 29.9 320.0 -924.1 0.8

PHASE-2 PHASE-3

PHASE-I PHASE-IV H-I H-II H-III H-1A H-1B H-3 H-4A H-4B

becomes less favorable; however, the conversion rate of FeCl3 is much lower. It is not until temperatures above 1200 K are reached that the conversion of FeCl3 and the favorability of FeCl2 begin to increase. In the cycle, reaction 30 is divided into two reactions, the first being the low temperature (589 K) conversion into the dimer and the second one a high temperature (1500 K) conversion into FeCl2. Figure 10 shows the constructed Aspen Plus flowsheet for the higher-level analysis. The entire process is at a pressure of 1 bar. The details of the hierarchical reaction blocks are shown

Table 9. Calculated Higher-Level Efficiency of the Fe-Cl Thermochemical Cycle (Cycle B-1 in the Carty Report) and the Values for That Calculation, Based on a Production of 2 mols of Hydrogen parameter

value

hot utility cold utility ∆H°298K (H2O) Q W η

1088.4 kJ 643.2 kJ -571.7 kJ 1731.6 kJ 266.6 kJ 0.252

in Figures 11-14. Gibbs reactors are used in the flowsheet, along with heaters, flash separations (FLASH), and component separation blocks. Stoichiometric reactors are used for phase changes. Blocks marked as SOLID are ideal component separators to separate the solids from the fluid flow. Details regarding the flowsheet are in Tables 7 and 8. Using the data compiled in Table 8, a pinch diagram (Figure 15) is constructed for a production basis of 2 mols of hydrogen. The pinch point occurs at an enthalpy position of 890 kJ with cold and hot stream temperatures of 373 and 393 K, respectively. Through the pinch analysis, 3744 kJ of heat is integrated from each stream, resulting in hot and cold utility requirements of 1088 and 643 kJ, respectively. Cycle work requirements are calculated for each SEP unit on Figures 10-14, using eq 27. Using eq 26 and the parameters in Table 9, the higher-level cycle efficiency is calculated to be 25%. This does not meet the threshold requirement of 30%, for higher-level anlayses, so cycle B-1 from the Carty report is not considered further. Discussion. The literature reported maximum attainable HHV efficiency of around 50%11,21 for the Fe-Cl cycle shown in the above case study is confirmed with our evaluation procedure. However, thermal efficiency is grossly reduced with added complexities, as suggested by van Velzen and Langenkamp.20 The failure of the presented cycle can be linked to high thermal and temperature requirements. Large amounts of heat are exhausted for phase transitions, due primarily to the large

Figure 15. Higher-level pinch diagram of the Fe-Cl thermochemical cycle shown in Figure 10 (cycle B-1 in the Carty report) for a production of 2 mols of hydrogen. Each area of latent heat (horizontal components of the process streams) is labeled with the corresponding unit(s) from Figures 10-14.


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Figure 16. Higher-level pinch diagram of the Fe-Cl thermochemical cycle showing the hot utility stream with a supply temperature of 1773 K.

volume recycle streams needed to achieve a closed cycle. Excess water is required in reactions 28 and 31 to maintain high product yields. The formation of the dimer Fe2Cl6 and the difficulties encountered with the reverse Deacon reaction, 31, result in an upper temperature limit of 1500 K. Higher cycle efficiency might be achievable if reactor-catalyst schemes are used that inhibit dimer formation. Another key point is that there are significant changes in reactor heat duty with varying temperature and added assumptions about possible products. In the base-level calculation, reactions 28 and 30 had cooling requirements, where in the second level analysis they both have significant heating requirements. For the first reaction, this is likely due to the temperature difference between the two levels of analysis. This temperature change is to avoid the formation of competing products. For the third reaction, major differences exist because of the consideration of dimer formation. The changes in reactor heating demands result in a 100% increase in the hot utility requirement. However, despite the higher temperature of reaction 31, there is no real increase in energy demand between the two levels of analysis. Assumptions about the reactors and hot utility supply are somewhat optimistic. In both levels of analysis, the reactors are assumed to operate isothermally. This is a valid assumption for determining the maximum reaction yields and minimum heating requirements; however isothermal conditions at the upper temperature limit might not lie within the attainable region of the reactor. Supplying large amounts of heat at a constant temperature without a significant drop in the utility temperature is impractical and potentially infeasible. For a nuclear heat source, the helium utility is supplied back to the nuclear reactor at a temperature that is nearly 400 K less than the maximum hot utility temperature.25 If the reaction cluster uses the utility with a smaller temperature drop, then there is residual heat that can be used for power generation. Of course, if the required temperature drop is too small, the hot utility might not be capable of meeting that load. In our higher-level analysis pinch diagram (Figure 15), reactors R-3B and R-4 require a constant temperature of 1500

K. This temperature cannot be met with a nuclear reactor; however solar dish engine systems can achieve temperatures up to 1773 K and capacities up to 1000 MW.22,26 Assuming an upper utility temperature of 1773 K and a minimum approach temperature of 20 K, the heating requirements can be met with a 350 K drop, as shown in Figure 16. If our maximum temperature falls within the range of a very hightemperature nuclear reactor, then modifications to the pinch diagram or reactor assumptions can be made to achieve a significant utility temperature drop. However, a higher-level analysis conducted with a maximum temperature of only 1273 K results in a very low efficiency of 18.5%, confirming the importance of a high upper temperature limit for this cycle. The higher-level analysis also yields a lower efficiency due to the increased separation costs. The needed flashes to induce component separation add additional strain to the utility requirements. The cycle work requirements are also a considerable factor in the efficiency calculation, due to the 50% thermal efficiency assumption. The work of separation will likely increase when calculated using nonideal models. Additional work is also needed for pumping costs. Given the analysis, it is unlikely that this Fe-Cl thermochemical cycle will be cost competitive with other hydrogen production methodologies, which is consistent with literature findings.20 With this cycle achieving a 26% reduction in efficiency when a higher-level analysis was performed, it is also unlikely that the other cycles in Table 2 are economically competitve. Large amounts of heat are exhausted in the presented Fe-Cl cycle due to multiple phase changes, which are indicative of the Fe-Cl system. Given the high temperature, acutely endothermic demands of the iron(III) chloride decomposition reaction, reaction 30, it seems unlikely that any cluster with that reaction would be thermodynamically attractive. However the shortcomings of the Fe-Cl system do not detract from the strength of the methodology. Our thermochemical cycle identification, screening, and evaluation procedure can

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be applied to numerous systems of candidate species (e.g., Ca-Br, Ce-Cl, Cu-Cl, V-Cl). Conclusions In this paper, we successfully modified our thermochemical cycle identification algorithm to generate thermodynamically feasible cycles without assuming the reaction temperatures, allowing for a more systematic approach to reaction cluster screening. The original formulation was inherently nonlinear (MINLP) and required a combinatorial approach to cluster synthesis. In the new formulation, no such combinatorial step is required. Following this reformulation, two levels of cycle evaluation were demonstrated through an assessment of the Fe-Cl system of thermochemical cycles. The first four Fe-Cl cycles identified had promising base-level efficiencies ranging from 36% to 51%, exceeding our threshold value of 35%. A higher-level evaluation, based on thermodynamically favored product yields, was then conducted on a well studied cycle identified by our search algorithm. The result of our systematic analysis on this Fe-Cl thermochemical cycle was consistent with literature findings, validating our methodology and eliminating this cycle, due to its high temperature demands and low higher-level efficiency of 25%, as a future candidate for cost competitive hydrogen production. Acknowledgment Financial support from Argonne National Laboratory, through Grant No. W-31-109-ENG38, and from the IGERT fellowship, through NSF Grant No. DGE-0504361, is gratefully acknowledged. We also acknowledge Prof. Vasilios Manousiouthakis of UCLA and Prof. Kristin Bennett of RPI for fruitful discussions. Nomenclature Bki ) number of atoms of k in a molecule of species i (atom/ molecule) ci ) computational weight on reactant coefficients for species i di ) computational weight on product coefficients for species i ∆G ) Gibbs energy of formation (kJ/mol) ∆Gsep ) ideal separation work (kJ/mol) ∆H° ) standard heat of formation (kJ/mol) M ) Large, positive parameter used for linearizing the cycle identification algorithm (kJ/mol) n ) molar output (mol) NA ) number of atomic species in a cycle NR ) number of reactions in a cycle NS ) number of molecular species in a cycle NT ) number of temperatures in the set I [TL,TU] Q ) cycle heat duty (kJ/mol) R ) universal gas constant (kJ/mol · K) Si ) stoichiometric ratio of reactant i sP ) upper bound on the total number of molecular species that participate as products in a reaction sR ) upper bound on the total number of molecular species that participate as reactants in a reaction Tj ) temperature of reaction j (K) TL ) lower bound on the reaction temperatures in a cycle (K) TU ) upper bound on the reaction temperatures in a cycle (K) W ) required work for a given cycle (kJ/mol) Y ) product yield yi ) mole fraction of species i z ) thermodynamic driving force for reaction

[a, b] ) continuous set of the bound inclusive interval from a to b I [a, b] ) integer set of the bound inclusive interval from a to b Greek βij ) flag variable that indicates species i as a product in reaction j γij ) reactant coefficient for molecular species i in reaction j γiju ) upper limit on the reactant coefficient for species i in reaction j γjl ) lower bound on the sum of the reactant coefficients for reaction j γju ) upper bound on the sum of the reactant coefficients for reaction j δij ) product coefficient for molecular species i in reaction j δiju ) upper limit on the product coefficient for species i in reaction j δjl ) lower bound on the sum of the product coefficients for reaction j δju ) upper bound on the sum of the product coefficients for reaction j η ) cycle efficiency θij ) flag variable that indicates species i as a reactant in reaction j Λi ) molecular species i νi ) coefficient of species i in the overall reaction for a cycle ξlj ) flag variable that indicates if reaction j occurs at temperature index l Ψl ) temperature corresponding to temperature index l (K) Indices i ) molecular species I ) set of allowable i indicies j ) reaction J ) set of allowable j indicies k ) atomic species K ) set of allowable k indicies l ) temperature L ) set of allowable l indicies

Literature Cited (1) Balat, M. Potential importance of hydrogen as a future solution to environmental and transportation problem. Int. J. Hydrogen Energy 2008, 33, 4013–4029. (2) Berry, G. D.; Aceves, S. M. The case for hydrogen in a carbon constrained world. J. Energy Res. Technol. 2005, 127, 89–94. (3) Abanades, S.; Charvin, P.; Flamant, G.; Neveu, P. Screening of watersplitting thermochemical cycles potentially attractive for hydrogen production by concentrated solar energy. Energy 2006, 31, 2805–2822. (4) Gorensek, M. B.; Forsberg, C. W. Relative economic incentives for hydrogen from nuclear, renewable, and fossil energy sources. Int. J. Hydrogen Energy 2009, 34, 4237–4242. (5) Beghi, G. E. A decade of research on thermochemical hydrogen at the Joint Research Centre, Ispra. Int. J. Hydrogen Energy 1986, 11, 767– 771. (6) Funk, J. E.; Reinstrom, R. M. Energy requirements in the production of hydrogen from water. Ind. Eng. Chem. Proc. Res. DeV. 1966, 5, 336– 342. (7) Yildiz, B.; Kazimi, M. S. Efficiency of hydrogen production systems using alternative nuclear energy technologies. Int. J. Hydrogen Energy 2006, 31, 77–92. (8) Holiastos, K.; Manousiouthakis, V. Automatic synthesis of thermodynamically feasible reaction clusters. AIChE J. 1998, 44, 64–73. (9) Brown, L. C.; Funk, J. F.; Showalter S. K. Initial screening of thermochemical water-splitting cycles for high efficiency generation of hydrogen fuels using nuclear power. General Atomics 2000, GA-A23373. (10) Knoche, K. F.; Cremer, H.; Steinborn, G. A thermochemical process for hydrogen production. Int. J. Hydrogen Energy 1976, 1, 23–32.

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ReceiVed for reView February 22, 2010 ReVised manuscript receiVed April 8, 2010 Accepted May 11, 2010 IE100398R

A Systematic Hierarchical Thermodynamic Analysis of Hydrogen

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