Elsevier

Thermochimica Acta

Volume 497, Issues 1–2, 10 January 2010, Pages 60-66
Thermochimica Acta

Exergoeconomic analysis of a thermochemical copper–chlorine cycle for hydrogen production using specific exergy cost (SPECO) method

https://doi.org/10.1016/j.tca.2009.08.008Get rights and content

Abstract

The manner is investigated in which exergy-related parameters can be used to minimize the cost of a copper–chlorine (Cu–Cl) thermochemical cycle for hydrogen production. The iterative optimization technique presented requires a minimum of available data and provides effective assistance in optimizing thermal systems, particularly in dealing with complex systems and/or cases where conventional optimization techniques cannot be applied. The principles of thermoeconomics, as embodied in the specific exergy cost (SPECO) method, are used here to determine changes in the design parameters of the cycle that improve the cost effectiveness of the overall system. The methodology provides a reasonable approach for improving the cost effectiveness of the Cu–Cl cycle, despite the fact that it is still in development. It is found that the cost rate of exergy destruction varies between $1 and $15 per kilogram of hydrogen and the exergoeconomic factor between 0.5 and 0.02 as the cost of hydrogen rises from $20 to $140 per GJ of hydrogen energy. The hydrogen cost is inversely related to the exergoeconomic factor, plant capacity and exergy efficiency. The results are expected to assist ongoing efforts to increase the economic viability and to reduce product costs of potential commercial versions of this process. The impact of the results are anticipated to be significant since thermochemical water splitting with a copper–chlorine cycle is a promising process that could be linked with nuclear reactors to produce hydrogen with no greenhouse gases emissions, and thereby help mitigate numerous energy and environment concerns.

Introduction

Increasing demand for energy, combined with diminishing fossil-fuel resources and concerns about greenhouse gas emissions, have increased the interest in the efficient and cost effective generation and use of hydrogen. Interest has also increased on the development of fossil-fuel-fired “zero-emission” power plants [1].

The design of thermal systems requires the explicit consideration of engineering economics, as cost is always an important consideration. Thermoeconomics (also known as exergoeconomics) is the branch of engineering that combines exergy analysis and economic principles to provide information useful for designing a system and optimizing its operation and cost effectiveness, but not available through conventional energy analysis and economic evaluation. A plant owner wants to know the true cost at which each of the utilities is generated; these costs are then charged to the appropriate final products according to the type and amount of each utility used to generate each final product. Accordingly, the objectives of thermoeconomic analysis include one or more of the following: (a) to calculate separately the costs of each product generated by a system having more than one product, (b) to understand the cost formation process and the flow of costs in the system, (c) to optimize specific variables in a single component, and (d) to optimize the overall system [2], [3].

Another important aspect of thermoeconomics is the use of exergy for allocating costs to the products of a thermal system. This involves assigning to each product the total cost to produce it, namely the cost of fuel and other inputs plus the cost of owning and operating the system (e.g., capital, operating and maintenance costs). Such costing is a common problem in plants where utilities such as electrical power, chilled water, compressed air and steam are generated in one department and used in others. The plant operator needs to know the cost of generating each utility to ensure that the other departments are charged properly according to the type and amount of each utility used. Common to all such considerations are fundamentals from engineering economics, including procedures for annualizing costs, appropriate means for allocating costs and reliable cost data [4].

The total cost is the sum of the capital cost and the fuel and other operating costs. A simple example of optimizing design variables is shown in Fig. 1, where the total cost curve exhibits a minimum at the point labelled a. Note that the curve is relatively flat in the neighbourhood of the minimum, so there is a range of design variables that could be considered nearly optimal from the standpoint of minimum total cost. If reducing the fuel cost were deemed more important than minimizing the capital cost, we might choose a design that would operate at point a′. Point a″ would be a more desirable operating point if capital cost were of greater concern. Such trade-offs are common in design situations [4].

The actual design process can differ significantly from the simple case considered above. For instance, costs cannot be determined as precisely as implied by the curves in Fig. 1. Fuel prices may vary widely over time, and equipment costs may be difficult to predict as they often depend on a bidding procedure. Equipment is manufactured in discrete sizes, so the cost also does not vary continuously as shown in the figure. Furthermore, thermal systems usually consist of several components that interact. Optimization of components individually usually does not guarantee an optimum for the overall system. Finally, a general system involves numerous design variables must be considered and optimized simultaneously [4].

The development and application of exergoeconomics has provided a theoretical basis for designing efficient and cost effective energy systems. Since the 1950s, exergoeconomics has been described in various studies and applied to numerous technologies and processes [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. For example, Hua et al. [8] presented a new exergoeconomic approach to optimize energy systems in which, after tracing the energy evolution and degradation within a system, a binary subsystem model was proposed and optimization strategies introduced.

Exergonomics mirrors ordinary economics, using exergy expenditures instead of monetary ones. Some examples of optimization by a simple relation of invested exergy and current exergy expenditures, including heat transfer through a wall, an electrical conductor and a thermal insulating wall, have been recommended for educational purposes by Yantovski [9]. The progress of a systematic exergoeconomic methodology for analysis and optimization of process systems has been described by Zhang et al. [10]. Based on a three-link-model, by applying a reversed exergy costing method to process systems, a hierarchical exergoeconomic model has been developed and the decomposing-coordinating optimization strategy has been introduced to analyze and optimize the total process or system. A retrofit of an aromatic separation system has been used to illustrate this method [10].

A combination of exergy and economic analysis for complex energy systems has been proposed by Kim et al. [11]. A general cost-balance which can be applied to any component of a thermal system has been derived. In the study, the exergy of material streams is decomposed into thermal, mechanical and chemical exergy flows and an entropy-production flow. A unit exergy cost is assigned to each disaggregated exergy in the streams at any state. The methodology results in a set of equations for the unit costs of various exergies by applying the cost-balance to each component of the system and to each junction. The monetary evaluations of various exergy costs (thermal, mechanical, etc.), as well as the production cost of electricity for the thermal system, have been obtained by solving the set of equations. The lost costs of each system component can also be obtained by this method. The proposed exergy costing method has been applied to a 1000-kW gas turbine cogeneration system [11].

Tsatsaronis and Moran [12] have studied exergy-aided cost minimization, which shows how exergy-related variables can be used to minimize the cost of a thermal system. These variables include the exergy efficiency, the rates of exergy destruction and exergy loss, an exergy destruction ratio, the cost rates associated with exergy destruction, capital investment and operating and maintenance, a relative cost difference of unit costs and an exergoeconomic factor. A simple cogeneration system is used as an example to demonstrate the application of an iterative exergy-aided cost minimization method [12].

A comprehensive methodology for the analysis of systems and processes, based on the quantities exergy, cost, energy and mass, and referred to as EXCEM analysis, was developed by Rosen and Dincer [13]. 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. Economics, which are also important, are incorporated in EXCEM analysis through costs.

An EXCEM analysis of a copper–chlorine (Cu–Cl) thermochemical cycle for hydrogen production has been reported [20]. The current study continues that work by discussing how exergy-related parameters can be used to minimize the cost of a thermal system in general and the Cu–Cl cycle in particular. In this paper, principles of thermoeconomics, as embodied in the specific exergy cost (SPECO) method, are used to determine changes in the design parameters of the cycle that result in an improvement of the cost effectiveness of the overall system. We also present an exergy analysis of the Cu–Cl cycle and its production costs as a function of the amount and quality of the energy used for hydrogen production, as well as the costs of the exergy losses and the exergoeconomic improvement potential of all equipment in the process. The methodology used provides an exploratory approach for improving the cost effectiveness of the Cu–Cl cycle, which is reasonable since the process is still in development.

Section snippets

The copper–chlorine (Cu–Cl) cycle

A conceptual layout of a Cu–Cl plant for thermochemical water decomposition is illustrated in Fig. 2. The cycle, potentially driven by nuclear heat, splits water into hydrogen and oxygen through intermediate copper and chlorine compounds. This cycle includes three thermochemical reactions and one electrochemical reaction.

The cycle involves five steps (Table 1):

  • 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

Analysis

A comprehensive exergoeconomic analysis of the Cu–Cl cycle consists of (a) an exergy analysis [21], [22], [23], [24], [25], (b) an economic analysis [26], [27], (c) exergy costing, and (d) an exergoeconomic evaluation [20]. In the exergy analysis, we evaluate the exergy of all streams in the cycle as well as the rate of exergy destruction, E˙xdest, and the exergy (second law) efficiency ηex for each plant component.

In an economic analysis of thermal systems, the annual values of carrying

Results and discussion

Exergoeconomic analyses consider the quality of energy, as measured by exergy, in allocating the costs of a process to its products. It is important to determine the critical points in the unit from the exergy viewpoint and to properly allocate the total cost to the product streams, to determine the monetary flows through the cycle, and to state the relevance in economic terms of the exergy losses of each component.

The variation of the unit cost of hydrogen with respect to the exergy efficiency

Conclusions

Results are presented of the thermodynamic simulation, economic and exergoeconomic analyses of the copper–chlorine (Cu–Cl) thermochemical cycle for hydrogen production, including estimates of product costs. The exergoeconomic analysis identifies and evaluates the actual energy losses and the real cost sources in the Cu–Cl cycle. This analysis is a useful tool in evaluating the potential for improving the cycle efficiency and cost effectiveness. With the aid of this analysis, cost parameters can

Acknowledgement

The authors gratefully acknowledge the financial support provided by the Ontario Research Excellence Fund.

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