An exergy–cost–energy–mass analysis of a hybrid copper–chlorine thermochemical cycle for hydrogen production

An exergy–cost–energy–mass analysis of a hybrid copper–chlorine thermochemical cycle for hydrogen production

international journal of hydrogen energy 35 (2010) 4831–4838 Available at journal homepage: An exe...

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international journal of hydrogen energy 35 (2010) 4831–4838

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An exergy–cost–energy–mass analysis of a hybrid copper–chlorine thermochemical cycle for hydrogen production Mehmet F. Orhan*, Ibrahim Dincer, Marc A. Rosen Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario, L1H 7K4, Canada

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Article history:

An exergoeconomic assessment using exergy–cost–energy–mass (EXCEM) analysis is

Received 15 June 2009

reported of a copper–chlorine (Cu–Cl) thermochemical water splitting cycle for hydrogen

Received in revised form

production. The quantitative relation is identified between capital costs and thermody-

17 August 2009

namic losses for devices in the cycle. A correlation detected in previous assessments,

Accepted 30 August 2009

suggesting that devices in energy systems are configured so as to achieve an overall

Available online 9 October 2009

optimal design by appropriately balancing thermodynamic (exergy-based) and economic characteristics of the overall system and its components, is observed to apply for the Cu–Cl


cycle. Exergetic cost allocations and various exergoeconomic performance parameters are


determined for the overall cycle and its components. The results are expected to assist


ongoing efforts to increase the economic viability and to reduce product costs of potential

Copper–chlorine cycle

commercial versions of this process. The impacts of these results are anticipated to be


significant since thermochemical water splitting with a copper–chlorine cycle is a prom-

Exergoeconomic analysis

ising process that could be linked with nuclear reactors to produce hydrogen with no

Thermochemical cycles

greenhouse gases emissions, and thereby help mitigate numerous energy and environ-

Hybrid cycles

ment concerns. ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.



The rapid growth in worldwide population, technology advancement and demand for energy resources, combined with increasing greenhouse gas emissions and diminishing fossil fuel reserves, has increased the need to improve the efficiency of energy utilization and to develop environmentally benign energy resources. One of the more promising alternative energy carriers for the transportation energy sector is hydrogen, which has the potential to reduce CO2 and other greenhouse gases emissions and the dependence on fossil fuels, and to prepare society for diminishing oil reserves.

Nuclear energy is a candidate to supply the energy needed for extracting the hydrogen from water or other molecules while avoiding concerns related to greenhouse gas emissions. Thermochemical water splitting with a copper–chlorine (Cu–Cl) cycle is a promising process that could be linked with nuclear reactors to decompose water into its constituents, oxygen and hydrogen, through intermediate copper and chlorine compounds. The cycle consists of five main steps, in each of which a reaction takes place. Heat is transferred between various endothermic and exothermic reactions in the Cu–Cl cycle, through heat exchangers that supply or recover heat from individual processes.

* Corresponding author. E-mail addresses: [email protected] (M.F. Orhan), [email protected] (I. Dincer), [email protected] (M.A. Rosen). 0360-3199/$ – see front matter ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2009.08.095


international journal of hydrogen energy 35 (2010) 4831–4838

Although technical studies of the Cu–Cl cycle have been reported, there is a need to understand the potential economics of the cycle, to facilitate eventual commercialisation. But such economic assessments are lacking, especially utilizing advanced tools like exergy. Exergy is defined as the maximum work that can be produced by a stream or system in a specified environment. Exergy is a quantitative measure of the ‘‘quality’’ or ‘‘usefulness’’ of an amount of energy. When energy quality decreases, exergy is destroyed. From the viewpoint of exergy, maximum efficiency is attained for a process in which exergy is conserved. Efficiencies determined using ratios of exergy provide a measure of ‘‘an approach to an ideal.’’ Efficiencies determined using energy are often misleading because, in general, they are not measures of an approach to an ideal. Exergy analysis accounts for energy quality and irreversibilities, and provides more meaningful and useful information than energy analysis about efficiency and losses. Exergy destruction can be used as the basis for the formulation of a theory of ‘‘cost’’ because it clearly relates the idea that to produce any output, some resources have to be ‘‘consumed.’’ Exergy is the ‘‘part’’ of energy that is useful to society and has economic value. In this paper, an exergoeconomic assessment of the copper–chlorine cycle using EXCEM (exergy, cost, energy and mass) analysis is described. Exergoeconomic analysis combines thermodynamic analysis based on the first and second laws with principles of economics, mostly cost accounting. The objective is to reduce product costs and to increase the economic viability of the process. In the study, the relations between exergy loss and capital cost and those between exergy and environmental impact are investigated. The relation between exergy and cost is demonstrated using plots of exergy loss as a function of cost generation. The applicability of a previously identified correlation, which suggests devices in energy systems are configured so as to achieve an overall optimal design, by appropriately balancing the thermodynamic (exergy-based) and economic characteristics of the overall system and its components, is investigated for the Cu–Cl cycle. Exergetic cost allocations and various exergoeconomic performance parameters are determined for the overall cycle and its components.


Exergy-based economics

A design engineer often strives for high efficiency and low cost under prevailing conditions (technological, economic, legal, ethical, environmental, social, etc.). The merit of a system or process has conventionally been based on parameters like performance, efficiency, economics and safety. Concerns like environmental impact and resource scarcity have recently made the evaluation of merit more complex. Designing efficient and cost effective systems, which also meet environmental requirements, is a significant challenge for engineers. Given the world’s finite natural resources and growing energy demands, it is increasingly important to understand energy and resource degradation and to improve systems while reducing environmental impact.

The selection of energy sources for industrial and other uses is primarily governed by prices. Sometimes energy conversion systems are shown to be uneconomic over the long term and prices become inadequate for planning. For example, problems can occur when prices are set based on near-term political assessments or insufficient knowledge of the resource and the consequences of its use. It is therefore important to set prices using appropriate methods, and enhanced approaches have been sought. One alternative method, ‘‘thermoeconomics,’’ combines economic and thermodynamic methods. In this approach, efficiencies are calculated via exergy analysis, and ‘‘nonenergetic expenditures’’ (financial, labour and environmental remediation) are explicitly related to the technical and thermodynamic parameters of the process under consideration. Corresponding optimization activities determine the final design point and operating schedule that minimize the overall monetary costs under a proper set of financial, environmental, technical and other constraints. A comprehensive methodology for the analysis of systems and processes was developed by Rosen et al. [1]. The methodology is based on the quantities exergy, cost, energy and mass, and is referred to as EXCEM analysis. Excluding the zeroth and third laws of thermodynamics, thermodynamics can be defined from a broad perspective as the science of energy and exergy. These terms involve a number of concepts such as temperature, pressure, enthalpy, heat, work, energy and entropy. The first law of thermodynamics embodies energy analysis, which identifies only external energy wastes and losses. Potential improvements for the effective use of resources are not consistently evaluated with energy, e.g. for an adiabatic throttling process. However, the second law of thermodynamics, which can be formulated in terms of exergy, takes entropy into consideration and accounts for irreversibilities. Although exergy has received the least attention of the EXCEM components, it is often considered the most important. In combination with economics (both macro and micro), exergy provides a powerful tool for the systematic study and optimization of systems. Exergy is a useful tool for engineers and offers unique insights into the nature, cause and location of losses and possible improvements. Exergy has also been linked with environmental tools. For instance, exergy-based life cycle analysis has been proposed as more advantageous than conventional methods for improving environmental conditions. Exergy is also useful in economics. Exergy offers a means in macroeconomics to reduce resource depletion and environmental destruction, e.g. via an exergy tax. In microeconomics, exergy has been combined beneficially with costbenefit analysis to improve designs. By minimizing life cycle costs, the most beneficial system under given prevailing economic conditions is obtained by reducing exergy losses and environmental effects. Exergy is thus applicable not only to efficiency studies but also to cost accounting and economic assessments. Exergy provides a rational basis for evaluating fuels and resources, efficiencies, dissipations, value and costs. Costs should reflect value. Since value is not generally associated with energy but with exergy, costing based on energy can be inappropriate, often leading to difficulties. Exergy-based cost accounting can


international journal of hydrogen energy 35 (2010) 4831–4838

help manage prices and profits. Exergy can also assist operating and design engineering decisions and optimization. Many exergy-based economic studies have been reported [2–26]. For example, Abusoglu et al. [2,3] have performed exergy and thermoeconomic analyses of diesel engine cogeneration systems. Formulations and procedures for the analysis have been provided along with the application. Exergy and exergoeconomic analyses of a combined heat and power system with a micro-gas turbine have been reported by Aras et al. [4]. Exergy and exergy cost balances for each component and the overall system are considered, and exergy consumption and cost generation within the system determined. An exergoeconomic analysis has been reported by Bakan et al. [5] of glycol cold thermal energy storage, which is an application of sensible heat storage where the temperature of a storage material changes in order to store cold, usually generated from electricity when its cost is low. Balli et al. [6] have presented an exergoeconomic analysis of a combined heat and power system. An exergy cost balance is presented for each component and the overall system, while exergy cost generation within the system is determined.

3. Description of the copper–chlorine thermochemical cycle Most thermochemical cycles require process heat at high temperatures, exceeding 850–900  C. However, existing nuclear power plants are typically water-cooled plants operating at 250–500  C. Recently, Atomic Energy of Canada and Argonne National Laboratory in the U.S. have been developing low-temperature cycles, designed to accommodate heat sources around 500  C. Such cycles can be more readily integrated with nuclear reactors. For this temperature range, the copper–chlorine (Cu–Cl) cycle is one of the most promising. Several Cu–Cl cycles have been examined in the laboratory and various alternative configurations identified. Proof-ofprinciple experiments that demonstrate the feasibility of the processes have been undertaken and a preliminary assessment of the cycle efficiency has demonstrated its potential. A conceptual layout of the Cu–Cl process is illustrated in Fig. 1. Thermochemical water decomposition, potentially driven by nuclear heat, occurs via intermediate copper and chlorine compounds. This cycle consists of three thermal reactions and one electrochemical reaction. The cycle involves five steps: (1) HCl(g) production using such equipment as a fluidized bed, (2) oxygen production, (3) copper (Cu) production, (4) drying, and (5) hydrogen production. A chemical reaction takes place in each step, except drying. The chemical reactions form a closed internal loop that re-cycles the copper–chlorine compounds on a continuous basis, without emitting any greenhouse gases to the atmosphere. As illustrated in Fig. 2, only water and nuclear-derived heat enter the cycle and at the end of the process only H2 and O2 are produced (with no greenhouse gas emissions). Liquid water at ambient temperature enters the cycle and passes through several heat exchangers where it evaporates and increases in temperature to 400  C. Heat for this process is obtained from cooling the hydrogen and oxygen gases before they exit the cycle. Steam at 400  C and solid copper chloride (CuCl2) at


1. Step


Cu2OCl2 CuCl 2


2. Step

5. Step

4. Step


CuCl H2O CuCl

CuCl2 + H2O Cu

3. Step

Fig. 1 – Conceptual thermochemical Cu–Cl hydrogen production cycle.

400  C from the dryer enter the fluidized bed, where a chemical reaction occurs. This reaction is endothermic and yields hydrochloric acid gas (HCl) and Cu2OCl2. Hydrochloric acid gas is compressed and Cu2OCl2 is transferred to another process step after its temperature is increased to the oxygen production reaction temperature of 500  C. In the second (oxygen production) step an endothermic chemical reaction takes place in which Cu2OCl2 is heated and O2 and copper monochloride (CuCl) are produced. Liquid copper monochloride is solidified by cooling it to 20  C, after which it enters the third (copper production) step together with the solid copper monochloride from the fifth step. In the third process step solid copper monochloride and water react endothermically at 20  C. However in this reaction water acts as a catalyst, and does not react with the other elements or compounds. Another specification for this third reaction that differentiates this step from others and makes it the most expensive, based on the price of electricity, is that electrolysis occurs. In this reaction, solid copper and a copper chloridewater solution are produced. A mixture of copper chloride and water is transferred to the dryer, and solid copper enters the fifth step after its temperature is increased to that step’s operating temperature. In the fifth (hydrogen production) step, hydrochloric gas and copper enter, and are converted to gaseous hydrogen (H2) and solid copper monochloride (CuCl). The reaction takes place at 450  C at steady state.



According to Rosen et al. [1], the rationale underlying an EXCEM analysis is that an understanding of the performance of a system requires an examination of the flows of each of the quantities represented by EXCEM into, out of and at all points within a system. The EXCEM analysis concept is illustrated in Fig. 3. Of the quantities represented by EXCEM, only mass and energy are subject to conservation laws. Cost increases or


international journal of hydrogen energy 35 (2010) 4831–4838

OUTPUT H2 (20ºC ) 1

O 2 (20ºC )

H 2O


HE: Heat Exchanger S: Step

P1 2 3 5


HE1 7

P: Compressor

4 8

Steam (400ºC )






HCI(g) production, Fluidized bed 12 S1

CuCl2(s) 400ºC


31 14 Cu2OCl2(s) 400ºC





HCl (g) 400ºC



heat 15


430ºC -475ºC






Flash dryer


430ºC -475ºC

CuCl(s) 36 33


O2 production

18 CuCl(l) 500ºC Heat recovery 20 HE4 38 CuCl(s) 21 HE8 22 20ºC

Steam (150ºC ) 23

19 28


Water (20°C)

26 Cu(s)


24 CuCl2

S3 Cu production


Heat (Qin)

He at recov ery


CuCl2(s) 150ºC


H2 production 34



20ºC + Water



Fig. 2 – Conceptual layout of a thermochemical Cu–Cl hydrogen production cycle.

remains constant, while exergy decreases or remains constant. The application of EXCEM analysis requires that the appropriate balance be written for each EXCEM quantity. A general balance for a quantity in a system may be written as

The general balance equation may be written in integral form, where the terms are expressed as amounts, and in differential form, where the terms are expressed as rates, as follows: Amount input þ Amount generated  Amount output Amount consumed ¼ Amount accumulated


Input þ Generation  Output  Consumption ¼ Accumulation


where input and output refer, respectively, to quantities entering and exiting through system boundaries. Generation and consumption refer, respectively, to quantities produced and consumed within the system. Accumulation refers to change (either positive or negative) of the quantity within the system. The general balance applies to the EXCEM quantities. Exergy


Cost Energy

Cost Cu-Cl Cycle


Fig. 3 – Application of EXCEM analysis to a Cu–Cl thermochemical cycle (modified from [1]).

Energy Mass

Input rate þ Generation rate  Output rate Consumption rate ¼ Accumulation rate


The integral balance describes what happens in a system between two instants of time, and the differential balance describes what is occurring in a system at a given instant of time. Integral balances are usually applied to batch processes and differential balances to continuous processes. For steady state processes, the accumulation rate term is zero. Mass and energy, being subject to conservation laws (neglecting nuclear reactions), can be neither generated nor consumed. Consequently, the general balance for each of these quantities becomes: Mass input  Mass output ¼ Mass accumulation


Energy input  Energy output ¼ Energy accumulation



international journal of hydrogen energy 35 (2010) 4831–4838

Fig. 4 – Overall rate balance of mass in the Cu–Cl cycle.

Fig. 6 – Overall rate balance of exergy in the Cu–Cl cycle.

Exergy is consumed due to irreversibilities, and exergy consumption is proportional to entropy generation, which is also attributable to irreversibilities. By combining the conservation law for energy and non-conservation law for entropy, an exergy balance can be obtained. The general balances for entropy and exergy follow: Entropy input þ Entropy generation  Entropy output ¼ Entropy accumulation



Exergy input  Exergy output  Exergy consumption ¼ Exergy accumulation


The general balance for cost can be written as Cost input þ Cost generation  Cost output ¼ Cost accumulation

exergy are defined by scientific relationships. Cost input and generation are usually well defined, but cost outputs are allocated subjectively, depending on the type and purpose of the system and other economic considerations. Detailed energy, exergy [27–31] and cost [32,33] analyses of the Cu–Cl cycle have been reported elsewhere by the authors and further explanations are available there.


where cost input, output and accumulation represent, respectively, the cost associated with all inputs, outputs and accumulations for the system. Cost is an increasing quantity, and cost generation corresponds to the appropriate capital and other costs associated with the creation and maintenance of a system. The ‘‘cost generation rate’’ term in a differential cost balance represents the total cost generation levelized over the operating life of the system. The ‘‘amount of cost generated’’ term in an integral cost balance represents the portion of the total cost generation for a time interval. Note in the cost balance that the distribution of costs over outputs and accumulations is not defined, while values associated with all quantities in the balance equations for mass, energy and

Results and discussion

The relation between exergy and cost is demonstrated using plots of exergy loss as a function of cost generation. Both internal exergy losses (i.e., consumptions) and total exergy losses (i.e., consumptions plus waste emissions) can be considered. The intensive properties of the reference environment need to be completely specified when total exergy losses are considered. Only the temperature of the reference environment needs to be specified when internal exergy losses are considered. The costs associated with inputs need not be specified. An overall rate balance for mass for the Cu–Cl cycle is shown in Fig. 4, with the main inlet and outlet streams highlighted. Water enters the cycle and is decomposed into hydrogen and oxygen. As seen in the figure, mass is conserved and, on the product side, oxygen account for 89% of total mass flow rate and hydrogen 11%. The copper and chlorine compounds form are contained in an internal closed loop. An overall rate balance for energy in the Cu–Cl cycle is given in Fig. 5, where energy is seen to be conserved. The Cu–

Table 1 – Cost of hydrogen production for Cu–Cl thermochemical plants of varying hydrogen production capacities (modified from [32,33]). H2 production capacity of Cu–Cl plant (tons/day)

Fig. 5 – Overall rate balance of energy in the Cu–Cl cycle.

Capital cost of plant ($/GJ) Capital cost of storage ($/GJ) Energy cost ($/GJ) Distribution cost ($/GJ) Total ($/GJ) Total ($/kg)





13.2 0.5 6.3 4.6 24.6 3.49

7.7 0.5 6.3 4.6 19.1 2.71

4.4 0.5 6.3 4.6 15.8 2.24

2.7 0.5 6.3 4.6 14.1 2.00


international journal of hydrogen energy 35 (2010) 4831–4838

Fig. 7 – Variation of hydrogen cost with hydrogen production capacity of a Cu–Cl thermochemical plant.

Cl cycle is a hybrid cycle, in which heat and electricity enter. The inlet energy can be broken down as 44% electricity and 56% heat since in the third step (Cu production step) of the cycle electrolysis occurs which accounts for 44% of total inlet energy to the cycle [29]. During the process, 30% of the inlet energy is lost via waste emissions. Hydrogen is observed to be produced with 43% energy efficiency, while the rest of the energy exits with the oxygen [34]. The exergy of the oxygen is mainly physical, and is relatively large because the oxygen exits the cycle at high temperature (500  C). Exergy flow rates are shown in Fig. 6 for the Cu–Cl cycle. Exergy is clearly not conserved in the system, as the exergy of the inlet heat and electricity significantly exceeds the exergy of the hydrogen and oxygen products. It also can be seen that the exergy content of oxygen is very small in comparison to that of hydrogen because of the differences in their chemical exergy values. The molar chemical exergy of hydrogen is 236,090 kJ/kmol [30], whereas for oxygen it is 3970 kJ/kmol [27]. The blackened area in Fig. 6 represents the exergy destruction during the process as well as waste exergy emissions from the cycle. The exergy flow rate values are explained in greater detail in Fig. 9. Costs associated with hydrogen production based on the Cu–Cl cycle, using values reported elsewhere [32,33], are shown in Table 1. There, it can be observed that production becomes more economic at larger capacities of hydrogen production (a result that can also be seen in Fig. 7). Based on costs in Table 1, Fig. 8 provides an overall rate balance for cost in the Cu–Cl cycle. The cost of the input energy (heat and

Fig. 8 – Overall rate balance for cost in the Cu–Cl cycle.

Fig. 9 – Flow rates of several of the EXCEM quantities for hydrogen production with the Cu–Cl thermochemical cycle.

electricity) combined with the capital and processing cost of the plant yields the total cost of hydrogen production. The blackened area in the figure represents the cost creation rate of the cycle for hydrogen production. In contrast to exergy, which is destroyed (see Fig. 6), cost is created during the process (see Fig. 8). Efficiency improvement measures for a thermal plant cost generally require financial resources since system efficiency can usually only be improved and thermodynamic losses reduced with more expensive equipment. At the design stage, system efficiency improvements typically require less capital cost (investment). The use of more expensive equipment or more advanced technology, normally results in higher

Fig. 10 – Variation of exergy loss and destruction rates with cost creation rate for the Cu–Cl cycle.

international journal of hydrogen energy 35 (2010) 4831–4838


Fig. 12 – Relation between exergy and cost flow rates of Cu–Cl cycle. Fig. 11 – Variation of energy loss rates with cost creation rate for the Cu–Cl cycle.

efficiency. Thus, efficiency improvements cause initial cost creation. The total exergy input is wasted if no investment is made, i.e., Total exergy loss / Total exergy input as capital cost generation / 0 The performance approaches the ideal if a very large investment is made, i.e., Total exergy loss / 0 as capital cost generation / infinity Efficiency improvements decrease energy or exergy losses from the system and exergy destruction within the system. Also, decreases in losses lead a decrease in inlet energy for fixed production. This often leads to a decrease in cost creation for a unit production. Therefore, an efficiency improvement (or decrease in losses) causes an increase in the capital cost creation rate but a decrease in the energy cost creation rate. Thus if reducing the energy cost were deemed more important than minimizing the capital cost, we might choose a design that would operate at the highest possible efficiency. A design with a lower efficiency would be more desirable if capital cost were of greater concern. This balance is generally evaluated by considering the total cost generation rate, which is the accumulation of capital and energy cost rates. Flow rates in the Cu–Cl cycle for hydrogen production of the EXCEM quantities are shown in Fig. 9, where costs are in Canadian dollars. These costs are evaluated based on a plant with an assumed capacity of 50 tons/day. Details on the costs and their evaluation are given elsewhere [32,33]. The exergy loss rate and exergy destruction rate for the Cu–Cl cycle are plotted as a function of total cost creation rates for the plant in Fig. 10. Plots of the type in Fig. 10 demonstrate that exergy and cost are the only EXCEM quantities subject to non-conservation laws. Since for any device, the associated values of cost creation and exergy loss are positive, the lines in these plots always rise to the right. The variation of exergy loss and destruction rates with cost creation rate shown in Fig. 10 illustrates the trade-off between cost and efficiency. Exergy destruction represents the exergy that is destroyed within the cycle while exergy loss refers to exergy that escapes to the environment or is transferred with oxygen.

The variation of energy loss from the cycle with heat and oxygen (which is a potential by-product) with cost creation rate is presented in Fig. 11. The analogous curve in Fig. 11 to the exergy destruction rate curve in Fig. 10 is a straight line along the horizontal axis (because energy is conserved). The idea that costing should be based on exergy rather than energy because exergy often is a consistent measure of value (i.e., a large quantity of exergy is often associated with a valuable commodity), while energy is only sometimes a consistent measure of value, is supported by these results. A more general version of Fig. 10, in which the flow rates of exergy and cost at different points in the cycle are plotted, is shown in Fig. 12. The intensive properties of the reference environment must be completely specified, and the costs associated with all inputs must be known to construct Fig. 12. A monotonically decreasing composite line is again traced. However, the line does not necessarily begin at the origin of the plot. The properties of the reference environment and the costs associated with inputs determine the origin of the composite line. Fig. 12 is obtained used data given in Fig. 9. As can be seen from both figures, the cost flow rate at the inlet of the cycle is 0.893 $/kg while it is 2.24 $/kg at the outlet of the cycle, since 1.347 $/kg is generated within the cycle. The situation is reversed for exergy. Exergy enters at the inlet at the rate of 0.151 GW and exit at the rate of 0.068 GW; the remaining exergy is destroyed in the cycle and/or lost to the environment.



The Cu–Cl thermochemical cycle for hydrogen production has been analysed with the EXCEM methodology, which is based on four quantities: exergy, cost, energy and mass. We conclude that the insights gained with the EXCEM analysis are informative, because efficiencies are determined which are measures of an approach to an ideal, the causes of losses in efficiency are accurately pinpointed, and the relations between economics and thermodynamics are explained. The results of the EXCEM analysis reported here can assist in the design, improvement and optimization of the Cu–Cl cycle. More generally, the results support the notion that EXCEM


international journal of hydrogen energy 35 (2010) 4831–4838

analysis can assist in the formulation of energy, economic and environmental policies.

Acknowledgment The authors acknowledge the support provided by the Ontario Research Excellence Fund and the Natural Sciences and Engineering Research Council of Canada.


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