Energy & Fuels 2009, 23, 2613–2619
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Energy Quality Factor and a New Thermodynamic Approach to Evaluate Cascade Utilization of Fossil Fuels Danxing Zheng* and Zhi Hou Beijing UniVersity of Chemical Technology, P.O. Box 100, Beisanhuan Rd. E., Beijing 100029, China ReceiVed December 24, 2008. ReVised Manuscript ReceiVed February 13, 2009
This paper made an effort to establish a thermodynamic fundamental for evaluating the energy quality that is a basis of state evaluation and process analysis to effectively use fossil fuels. On base of the thermodynamic consistency, the energy quality factor was defined as an index for the energy quality of a fluid. General methods of calculating the enthalpy and the energy quality factor of fluid were established by means of defining standard enthalpy. The standard exergy, the standard enthalpy, and the standard energy quality factor of common pure species related to combustion of fossil fuels were given. A graphic methodology on the energy factor and related functions, enthalpy and exergy, was proposed for investigating the state characteristics and process performance. To validate and demonstrate the approaches, four routes of methane combustion have been investigated in the R-H-ε diagram. The results show that preheating and endothermic reforming before combustion can result in the cascade utilization of methane, which appears as a gradual decrease in the energy quality factor. The results prove that the exergy regeneration through conversions of heat and substance is important for the effective use of fossil fuels.
1. Introduction The requirement for sustainable development of human society makes people seriously research the reasonable and effective use of energy and natural resources. Some innovations about effective use of fossil fuels have been proposing recent years.1-3 In the course of these studies, people are aware that the second law of thermodynamics is becoming more and more important. Many methods of using fossil fuel maybe exist, even though the aims are the same. It is advisable to evaluate the proposals, above all using the thermodynamic principles. It is especially true both in optimum selections for many proposals and in validity assessment for a proposal. However, novel proposals and evaluating approaches of using fossil fuels have been developing simultaneously. Combustion is a common method of releasing energy of fossil fuels. Researchers thought about energy conversion of fossil fuels traditionally on the heat concept. The combustion temperature is regarded as the quality of heat. For example, the Carnot coefficient represents the ability of power generation of a high-temperature heat source by combustion, relative to a lowtemperature heat sink. On the recognitions, traditional research has concentrated primarily on the effective use of heat for thermal cycles. The overall thermal efficiency can be achieved to more than 50%4 in a combined cycle based on the principle * To whom correspondence should be addressed. Telephone: +86 10 6441 6406. Fax: +86 10 6441 6406. E-mail:
[email protected]. (1) Adelman, S. T.; Hoffman, M. A.; Baughn, J. W. J. Eng. Gas Turb. Power 1995, 117, 16–23. (2) Ishida, M.; Zheng, D.; Akehata, T. Energy 1987, 12, 147–154. (3) Abdallah, H.; Facchini, B.; Danes, F.; De Ruyck, J. Energy ConVers. Manage. 1999, 40, 1679–1686. (4) Wu, Z. Energy Cascade Utilization and Gas Turbine Total Energy System; Mechanical Press: Beijing, 1988; p 55. (in Chinese).
of cascade utilization of energy.5 Cogeneration systems can also greatly promote the efficient use of energy produced by fossil fuels.6 Furthermore, the exergy analysis based on the second law of thermodynamics has promoted theoretical study about the conversion and utilization of energy. In 1961, Rant7 proposed the concept of the exergy ratio of energy, which was defined as a ratio of exergy to energy and written as Ξ ≡ ε/E
(1)
where ε and E represent exergy and energy, respectively. The values of the exergy ratio of energy are usually less than 1.0. Rant8 also appointed the values of the exergy ratio of energy for gas fuel as 0.95 and for liquid fuel as 0.975. According to Govin et al.,9 if the elemental composition of fuel is known, the Szargut’s correlation formula can be applied: -ε0 /∆cH0 ) a + b[H]/[C] + c[O]/[C] + ...
(2)
where ∆cH0 and ε0 denote the enthalpy and the exergy of combustion at the reference state; [H]/[C] and [O]/[C] are atomic ratios of hydrogen to carbon and oxygen to carbon; and a, b, and c represent parameters related to the atomic ratios. Avoiding the problem in quantifying the exergy ratio of energy of fossil fuel for state evaluation, Ishida defined a new index for analyzing a process composed of state change, that is, the energy level, as a ratio of the exergy change to the enthalpy change.10 It is written as, (5) Najjar, Y. S. H. Appl. Therm. Eng. 2001, 21, 407–438. (6) Zaporowski, B.; Szczerbowski, R. Appl. Energy 2003, 75, 43–50. (7) Rant, Z. BWK 1961, 13, 496–500. (8) Rant, Z. Allgem. Wa¨rmetechn. 1961, 10, 172–176. (9) Govin, O. V.; Diky, V. V.; Kabo, G. J.; Blokhin, A. V. J. Therm. Anal. Calorim. 2000, 62, 123–133. (10) Ishida, M.; Kawamura, K. Ind. Eng. Chem. Process Des. DeV. 1982, 21, 690–695.
10.1021/ef8011307 CCC: $40.75 2009 American Chemical Society Published on Web 03/27/2009
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A ≡ ∆ε/∆H
Zheng and Hou
(3)
where ∆ε and ∆H represent the exergy change and the enthalpy change, respectively. Other research, including that of Hebecker and Bittrich,11 has involved similar studies. The quest to understand the energy quality has prompted a break from the traditional knowledge of heat conversion, and to look at new methods, for example, through substance conversion, to effective use of fossil fuels. One typical new method is the chemical recuperation for gas turbine cycle,1,3 which is particularly concerned with substituting clean synthetic fuels for conventional fossil fuels. Another one is chemical looping combustion,2 which decomposes traditional combustion into two reactions with a solid looping reactant: reduction of metal oxide by fuel and oxidation of the resulting metal by air. To reveal the thermodynamic principle of the new method, some new approaches and explanations were proposed. For example, the energy utilization diagram, which consists of the energy lever and the enthalpy change, has been used to explain why less exergy loss hss occurred and why more work can be obtained in the chemical looping combustion than in direct combustion.2 Okazaki et al.12 studied the exergy regeneration in hydrogen production processes. They concluded that the exergy ratio of low quality thermal energy can be enhanced through the reforming process from hydrocarbon fuel to hydrogen. Cao and Zheng13 defined the exergy regeneration ratio as a ratio of the exergy value of the acceptor to that of the donor, and they investigated the exergy regeneration performance of chemical recuperation with CO2-natural gas reforming. Although the importance of the quality assessment of fossil fuels has been known, its quantification has lain in a situation where only some values can be estimated. Furthermore, both the variation of energy quality in different methods and the impacts of conversion conditions need to be studied, when investigating the mechanisms of cascade utilization of fossil fuels. However, an appropriate method is absent at present. This paper focuses on quantifying the energy quality of multispecies fluids and then quests for new approaches of thermodynamics on the concept of the energy quality of fossil fuels. 2. Energy Quality Factor 2.1. Definition. The energy quality factor was defined as a ratio of exergy to enthalpy of a multispecies fluid by eq 4,14,15 R(T, p, _x) ) ε(T, p, _x)/H(T, p, _x)
(4)
where the term (T, p, x) represents the specified state at temperate, pressure, and composition. The energy quality factor is an intensive property, because both enthalpy and exergy are extensive prosperities of fluid. From the viewpoint of the ability of power generation of a fluid, the R value is an index of the fluid’s energy quality. The higher the value of R is, the more the power generation of unit energy. (11) Hebecker, D.; Bittrich, P. Int. J. Therm. Sci. 2001, 40, 316–328. (12) Okazaki, K.; Kishida, T.; Ogawa, K.; Nozaki, T. Energy ConVers. Manage. 2002, 43, 1459–1468. (13) Cao, W.; Zheng, D. Energy ConVers. Manage. 2006, 47, 3019– 3030. (14) Zhu, M. S. Exergy Analysis of Energy Systems; Tsinghua University Press: Beijing, 1988; p 6, in Chinese. (15) Zheng, D.; Deng, W.; Jin, H.; Ji, J. Appl. Therm. Eng. 2007, 27, 1771–1778.
2.2. Calculation Method of Exergy. Adopting an appropriate equation of state to estimate the fugacity of every species in the fluid, the exergy of the multispecies fluid can be calculated by16 ε(T, p, _x) )
∑ x ε (T, p) + RT ∑ x ln( f /f ) RT(1 - T /T) ∑ x [∂ ln(fˆ /f )/∂ ln T ] θ
i i
0
i
i i
θ
0
i
i i
p,x
(5)
where fiθ denotes the fugacity of pure species i in the standard state. εi(T, p) is the exergy of pure species i and can be calculated by εi(T, p) ) εθi (T0, pθ) + ∆εi(T0, pθ f T, p)
(6)
where, ∆εi(T0, pθ f T, p) represents the exergy change of pure species i from the environmental reference state (T0, pθ) at the environment temperature and the standard pressure to the specified state (T, p). εθi (T0, pθ) is the standard exergy of pure species i. It is a basis for exergy calculation and deals with a special thermodynamics state, called the environmental reference state, which has many specifications.17-25 Kameyama et al.17 proposed a model of the environmental reference state in which the published thermodynamic data can be conveniently used. That is composed of a series of reference substances corresponding to elements at 298.15 K and 100 kPa. The Japanese National Standard (JIS Z9204-1980)18 and the Chinese National Standard (GB/T 14909-2005)19 adopted Kameyama’s model. The exergy values of the reference substances at the environmental reference state are zero. Generally, the standard exergy of a common pure species AaBb can be calculated by17 εAθ aBb ) ∆fGAθ aBb + aεAθ + bεθB
(7)
where, ∆ fGAθ aBb is the standard Gibbs energy change of formation. εAθ and εθB represent the standard exergy of elements A and B, respectively. The cited literature19 has given the standard exergy of elements based on the thermodynamics data in handbooks,26,27 as shown in Support information Table S1. 2.3. Definition of Standard Enthalpy and Calculation Method of Enthalpy. The enthalpy of multispecies fluid can be represented by28 (16) Riekert, L. Chem. Eng. Sci. 1974, 29, 1613–1620. (17) Kameyama, H.; Yoshida, K.; Yamauchi, S.; Fueki, K. Appl. Energy 1982, 11, 69–83. (18) Yamauchi, S. Guide of Available Energy Evaluation Method. Japanese Industrial Standard JIS Z 9204–1980; 1980. (in Japanese). (19) Zheng, D.; Wu, X.; Song, Z.; Chen, M.; Yu, Y.; Ren, X.; Zheng, Z. Technical Guides for Exergy Analysis in Energy System. Chinese Industrial Standard GB/T 14909–2005; 2005. (in Chinese). (20) Szargut, J. Energy 1980, 5, 709–718. (21) Kotas, T. J. Int. J. Heat Fluid Fl. 1980, 2, 105–114. (22) Riekert, L. Chem. Eng. Sci. 1974, 29, 1613–1620. (23) Gaggioli, R. A.; Petit, P. J. Chem. Tech. 1977, 7, 496–506. (24) Ahrendts, J. Energy 1980, 5, 667–677. (25) Shiehr, J. H.; Fan, L. T. Energy and exergy estimation using the group contribution method. In Efficiency and Costing; Gaggioli, R. A. Eds.; ACS Symposium Series 235; American Chemical Society: Washington DC, 1983; pp 351-371. (26) Binnewies, M. Thermodynamical Data of Elements and Compounds; Wiley-VCH: Weinheim, 2002; pp 14-807. (27) Barin, I. Thermodynamical Data of Pure Substances, 3rd ed.; WileyVCH: Weinheim, 1995; pp 695-1606. (28) Smith, J. M.; Van Ness, H. C.; Abbott, M. M. Introduction to Chemical Engineering Thermodynamics, 6th ed.; McGraw-Hill: New York, 2001; pp 406, 407, 436.
EValuating the Cascade Utilization of Fossil Fuels
H(T, p, _x) )
∑ x H (T, p) - RT ∑ x [∂ ln(fˆ /f 2
i
i
i
i
θ i )/∂T ]p,x
Energy & Fuels, Vol. 23, 2009 2615
(8)
where Hi(T, p) is the enthalpy of the pure species i, which can be obtained from the enthalpy change in a process from state (T0, pθ) to state (T, p) Hi(T, p) ) Hθi (T0, pθ) + ∆Hi(T0, pθ f T, p)
(9)
where Hθi (T0, pθ) denotes the enthalpy of pure species i at the environmental reference state, which is the same as in eq 6. Here, on the thermodynamic consistency and Levine’s work about the specification of the enthalpy value at the standard state,29 for eqs 5 and 6, Hθi (T0, pθ) is defined as the standard enthalpy of pure species i and can be calculated by following method. For pure species AaBb, the expression is HAθ aBb(T0, pθ) ) ∆fHAθ aBb + aHAθ (T0, pθ) + bHθB(T0, pθ) (10) where ∆ fHAθ aBb is the standard enthalpy of formation of species AaBb. HAθ and HθB represent the standard enthalpies of elements A and B, respectively. It should be noted that HOθ represents θ and not the standard enthalpy of atomic O. The same 1/2 HO2 notation is adopted for N, H, F, Cl, and Br. This is according with the standard exergies of elements.17,19 Taking a system of reference substances the same as that of exergy,19 the value of the standard enthalpy of reference substances can be obtained by Hθi (T0, pθ) ) εθi (T0, pθ) + T0Sθi (T0, pθ)
(11)
Combining eqs 10 and 11, the values of the standard enthalpy of elements can be calculated by a sequential method19 the same as that of the standard exergy of elements, which are listed in the Supporting Information Table S1. Therefore, the energy quality factor of the multispecies fluid is quantified by eq 4 after the values of exergy and enthalpy are yielded by eqs 5 and 8, respectively. 2.4. Standard Energy Quality Factor. Particularly, the ratio of the standard exergy to the standard enthalpy for a pure species i at the environmental reference state is defined as the standard energy quality factor Rθi (T0, pθ) ) εθi (T0, pθ)/Hθi (T0, pθ)
(12)
The thermodynamic data,30,31 the standard exergy,17,19 the standard enthalpy, and the standard energy quality factor of 40 kinds of common pure species related to the combustion of fossil fuels have been given in Supporting Information Table S2. In Figure 1, the standard energy quality factors of oxygen, nitrogen, and methane etc., versus their standard enthalpies are plotted separately. The figure is called the R-H diagram.15 Oxygen, nitrogen, carbon dioxide, and water are close to the origin of coordinate, but carbon, methanol, methane, hydrogen, and carbon oxide are far away. The standard energy quality factor of carbon reaches 0.927. Carbon has the highest value, indicating its highest energy quality among these species. The standard enthalpy of methane is 947.0 kJ · mol-1, which indicates that methane can release the largest energy when it is (29) Levine, I. N. Physical Chemistry, 2nd ed.; McGraw-Hill: New York, 1983; Ch 5. (30) Lide, D. R. CRC Handbook of Chemistry and Physics, 87th ed.; CRC Press: Boca Raton, FL, 2006; pp 5.4-5.42. (31) Yaws, C. L. Chemical Properties Handbook; McGraw-Hill: New York, 1999; pp 267, 269, 270.
Figure 1. Common pure substances in R-H diagram.
brought into equilibrium with the environmental reference state. Methane and methanol have more enthalpies and exergies and higher energy quality factors, comparing with those of hydrogen and carbon oxide. 3. Methodologies of r-H Diagram and r-H-ε Diagram 3.1. Graphic Expression for Thermodynamic Characteristics of Fluids. As shown in Figure 1, the R-H diagram can represent the energy characters of a system when its energy quality factor is associated with its enthalpy. Through combining the energy quality factor with enthalpy and exergy and using the energy quality factor, enthalpy, and exergy as the vertical, abscissa, and ordinate axes, respectively, a new three-dimensional diagram can be obtained, called an R-H-ε diagram. It is a convenient thermodynamic tool for investigating the state characteristics and the process performance. Projecting the three-dimensional diagram along the coordinate axes directions results in three planar diagrams, named the ε-H diagram, the R-H diagram,15 and the R-ε diagram, respectively. The ε-H diagram can be used to investigate the conservation of the energy quantity and the depletion of energy quality for a process, in which the accepted energy and donated energy is the same in quantity, however the exergy loss inevitably exists if the change of the energy quality factor has occurred. The impacts of the enthalpy change and the exergy change on the energy quality factor can be investigated using the R-H and R-ε diagrams, respectively. In Figure 2, the position expressing the state of a fluid, as well as the values of energy quality factor, depends on the values of enthalpy and exergy. Furthermore, the variation in the energy quality factor in a process depends on the values of the enthalpy change and the exergy change. Therefore, the magnitude of the vector expressing a state change also depends on them. 3.2. r-H Diagram Use for Process Analysis. In the R-H diagram, the process composed of state change of the fluid is represented by a vector from the start point to the end point, as shown in Figure 2. A classification result as summarized in Table 1 can be obtained by investigating the donating and accepting of enthalpy and exergy. According to the positive or negative values of ∆H, ∆ε, ∆S, and ∆R, all possible processes are classified as eight kinds, and several examples are presented. Correspondingly, a visual expression is described by Figure 3. The heat-donating processes are divided into type A and type B by the dot-line ∆R ) 0, as well as the heat-accepting processes. The curves ∆S ) 0 and ∆ε ) 0 both depend on the thermodynamic character of the original point. To validate and demonstrate proposed approaches in this paper, the analysis on a heat exchange process and four routes of methane combustion are presented as follows.
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Figure 2. Process in R-H-ε diagram.
Therefore, the R-H-ε diagram not only expresses the variation of the energy quality, but also is convenient to perform the analysis on the first and the second law of thermodynamics simultaneously. As seen above, the analysis on a heat exchange process has been given to validate and demonstrate proposed approaches in this paper. Furthermore, analysis on four combustion routes of methane will be presented in the following section. 4. Analysis of Methane Combustion 4.1. Combustion Routes of Methane. The energy releasing methods of methane can be simply represented by the following chemical equations. The direct combustion of methane is represented as
Figure 3. Process classification in R-H diagram. Table 1. Classification of Processes Based on Thermodynamic Characteristics
CH4 + 2O2 f CO2 + 2H2O, ∆rHθ ) 802.1 kJ · mol-1 (13)
region
∆H
∆ε
∆S
∆R
example
separation type heat-accepting type A heat-accepting type B chill-donating mixing type heat-donating type B heat-donating type A chill-accepting type
>0 >0 >0 >0
