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Energy Quality Factor and a New ThermodynamicApproach to Evaluate Cascade Utilization of Fossil Fuels

Danxing Zheng, and Zhi HouEnergy Fuels, Article ASAP • DOI: 10.1021/ef8011307 • Publication Date (Web): 27 March 2009

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Energy Quality Factor and a New Thermodynamic Approach toEvaluate 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 thatis a basis of state evaluation and process analysis to effectively use fossil fuels. On base of the thermodynamicconsistency, the energy quality factor was defined as an index for the energy quality of a fluid. General methodsof calculating the enthalpy and the energy quality factor of fluid were established by means of defining standardenthalpy. The standard exergy, the standard enthalpy, and the standard energy quality factor of common purespecies related to combustion of fossil fuels were given. A graphic methodology on the energy factor andrelated functions, enthalpy and exergy, was proposed for investigating the state characteristics and processperformance. To validate and demonstrate the approaches, four routes of methane combustion have beeninvestigated in the R-H-ε diagram. The results show that preheating and endothermic reforming beforecombustion can result in the cascade utilization of methane, which appears as a gradual decrease in the energyquality factor. The results prove that the exergy regeneration through conversions of heat and substance isimportant for the effective use of fossil fuels.

1. Introduction

The requirement for sustainable development of humansociety makes people seriously research the reasonable andeffective use of energy and natural resources. Some innovationsabout effective use of fossil fuels have been proposing recentyears.1-3 In the course of these studies, people are aware thatthe second law of thermodynamics is becoming more and moreimportant.

Many methods of using fossil fuel maybe exist, even thoughthe aims are the same. It is advisable to evaluate the proposals,above all using the thermodynamic principles. It is especiallytrue both in optimum selections for many proposals and invalidity assessment for a proposal. However, novel proposalsand evaluating approaches of using fossil fuels have beendeveloping simultaneously.

Combustion is a common method of releasing energy of fossilfuels. Researchers thought about energy conversion of fossilfuels traditionally on the heat concept. The combustion tem-perature is regarded as the quality of heat. For example, theCarnot coefficient represents the ability of power generation ofa high-temperature heat source by combustion, relative to a low-temperature heat sink. On the recognitions, traditional researchhas concentrated primarily on the effective use of heat forthermal cycles. The overall thermal efficiency can be achievedto more than 50%4 in a combined cycle based on the principle

of cascade utilization of energy.5 Cogeneration systems can alsogreatly promote the efficient use of energy produced by fossilfuels.6

Furthermore, the exergy analysis based on the second law ofthermodynamics has promoted theoretical study about theconversion and utilization of energy. In 1961, Rant7 proposedthe concept of the exergy ratio of energy, which was defined asa ratio of exergy to energy and written as

where ε and E represent exergy and energy, respectively. Thevalues of the exergy ratio of energy are usually less than 1.0.Rant8 also appointed the values of the exergy ratio of energyfor gas fuel as 0.95 and for liquid fuel as 0.975.

According to Govin et al.,9 if the elemental composition offuel is known, the Szargut’s correlation formula can be applied:

where ∆cH0 and ε0 denote the enthalpy and the exergy ofcombustion at the reference state; [H]/[C] and [O]/[C] are atomicratios 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 ofenergy of fossil fuel for state evaluation, Ishida defined a newindex for analyzing a process composed of state change, thatis, the energy level, as a ratio of the exergy change to theenthalpy change.10 It is written as,

* To whom correspondence should be addressed. Telephone: +86 106441 6406. Fax: +86 10 6441 6406. E-mail: dxzh@mail.buct.edu.cn.

(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).

(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. Warmetechn. 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.

� ≡ ε/E (1)

-ε0/∆cH0 ) a + b[H]/[C] + c[O]/[C] + ... (2)

Energy & Fuels XXXX, xxx, A

10.1021/ef8011307 CCC: $40.75 XXXX American Chemical Society

where ∆ε and ∆H represent the exergy change and the enthalpychange, respectively. Other research, including that of Hebeckerand Bittrich,11 has involved similar studies.

The quest to understand the energy quality has prompted abreak from the traditional knowledge of heat conversion, andto look at new methods, for example, through substanceconversion, to effective use of fossil fuels.

One typical new method is the chemical recuperation for gasturbine cycle,1,3 which is particularly concerned with substitutingclean synthetic fuels for conventional fossil fuels. Another oneis chemical looping combustion,2 which decomposes traditionalcombustion into two reactions with a solid looping reactant:reduction of metal oxide by fuel and oxidation of the resultingmetal by air.

To reveal the thermodynamic principle of the new method,some new approaches and explanations were proposed. Forexample, the energy utilization diagram, which consists of theenergy lever and the enthalpy change, has been used to explainwhy less exergy loss hss occurred and why more work can beobtained in the chemical looping combustion than in directcombustion.2 Okazaki et al.12 studied the exergy regenerationin hydrogen production processes. They concluded that theexergy ratio of low quality thermal energy can be enhancedthrough the reforming process from hydrocarbon fuel tohydrogen. Cao and Zheng13 defined the exergy regeneration ratioas a ratio of the exergy value of the acceptor to that of the donor,and they investigated the exergy regeneration performance ofchemical recuperation with CO2-natural gas reforming.

Although the importance of the quality assessment of fossilfuels has been known, its quantification has lain in a situationwhere only some values can be estimated. Furthermore, boththe variation of energy quality in different methods and theimpacts of conversion conditions need to be studied, wheninvestigating the mechanisms of cascade utilization of fossilfuels. However, an appropriate method is absent at present.

This paper focuses on quantifying the energy quality ofmultispecies fluids and then quests for new approaches ofthermodynamics on the concept of the energy quality of fossilfuels.

2. Energy Quality Factor

2.1. Definition. The energy quality factor was defined as aratio of exergy to enthalpy of a multispecies fluid by eq 4,14,15

where the term (T, p, x) represents the specified state attemperate, pressure, and composition. The energy quality factoris an intensive property, because both enthalpy and exergy areextensive prosperities of fluid.

From the viewpoint of the ability of power generation of afluid, the R value is an index of the fluid’s energy quality. Thehigher the value of R is, the more the power generation of unitenergy.

2.2. Calculation Method of Exergy. Adopting an appropri-ate equation of state to estimate the fugacity of every speciesin the fluid, the exergy of the multispecies fluid can be calculatedby16

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 calculatedby

where, ∆εi(T0, pθf T, p) represents the exergy change of purespecies i from the environmental reference state (T0, pθ) at theenvironment temperature and the standard pressure to the spe-cified state (T, p). εi

θ(T0, pθ) is the standard exergy of purespecies i. It is a basis for exergy calculation and deals with aspecial thermodynamics state, called the environmental referencestate, which has many specifications.17-25

Kameyama et al.17 proposed a model of the environmentalreference state in which the published thermodynamic data canbe conveniently used. That is composed of a series of referencesubstances corresponding to elements at 298.15 K and 100 kPa.The Japanese National Standard (JIS Z9204-1980)18 and theChinese National Standard (GB/T 14909-2005)19 adoptedKameyama’s model.

The exergy values of the reference substances at theenvironmental reference state are zero. Generally, the standardexergy of a common pure species AaBb can be calculated by17

where, ∆ fGAaθ

Bb is the standard Gibbs energy change offormation. εA

θ and εBθ represent the standard exergy of elements

A and B, respectively. The cited literature19 has given thestandard exergy of elements based on the thermodynamics datain handbooks,26,27 as shown in Support information Table S1.

2.3. Definition of Standard Enthalpy and CalculationMethod of Enthalpy. The enthalpy of multispecies fluid canbe represented by28

(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.

(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. ChineseIndustrial 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 Com-pounds; Wiley-VCH: Weinheim, 2002; pp 14-807.

(27) Barin, I. Thermodynamical Data of Pure Substances, 3rd ed.; Wiley-VCH: Weinheim, 1995; pp 695-1606.

(28) Smith, J. M.; Van Ness, H. C.; Abbott, M. M. Introduction toChemical Engineering Thermodynamics, 6th ed.; McGraw-Hill: New York,2001; pp 406, 407, 436.

A ≡ ∆ε/∆H (3)

R(T, p, x_) ) ε(T, p, x_)/H(T, p, x_) (4)

ε(T, p, x_) ) ∑ xiεi(T, p) + RT0 ∑ xi ln( fi/fiθ) -

RT(1 - T0/T) ∑ xi[∂ ln(fi/fiθ)/∂ ln T ]p,x (5)

εi(T, p) ) εiθ(T0, pθ) + ∆εi(T0, pθ f T, p) (6)

εAaBb

θ ) ∆fGAaBb

θ + aεAθ + bεB

θ (7)

B Energy & Fuels, Vol. xxx, XXXX Zheng and Hou

where Hi(T, p) is the enthalpy of the pure species i, which canbe obtained from the enthalpy change in a process from state(T0, pθ) to state (T, p)

where Hiθ(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 standardstate,29 for eqs 5 and 6, Hi

θ(T0, pθ) is defined as the standardenthalpy of pure species i and can be calculated by followingmethod.

For pure species AaBb, the expression is

where ∆ fHAaθ

Bb is the standard enthalpy of formation of speciesAaBb. HA

θ and HBθ represent the standard enthalpies of elements

A and B, respectively. It should be noted that HOθ represents

1/2 HO2θ and not the standard enthalpy of atomic O. The same

notation is adopted for N, H, F, Cl, and Br. This is accordingwith the standard exergies of elements.17,19

Taking a system of reference substances the same as that ofexergy,19 the value of the standard enthalpy of referencesubstances can be obtained by

Combining eqs 10 and 11, the values of the standard enthalpyof elements can be calculated by a sequential method19 the sameas that of the standard exergy of elements, which are listed inthe Supporting Information Table S1.

Therefore, the energy quality factor of the multispecies fluidis quantified by eq 4 after the values of exergy and enthalpyare yielded by eqs 5 and 8, respectively.

2.4. Standard Energy Quality Factor. Particularly, the ratioof the standard exergy to the standard enthalpy for a pure speciesi at the environmental reference state is defined as the standardenergy quality factor

The thermodynamic data,30,31 the standard exergy,17,19 thestandard enthalpy, and the standard energy quality factor of 40kinds of common pure species related to the combustion of fossilfuels 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 areplotted separately. The figure is called the R-H diagram.15

Oxygen, nitrogen, carbon dioxide, and water are close to theorigin of coordinate, but carbon, methanol, methane, hydrogen,and carbon oxide are far away. The standard energy qualityfactor 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, whichindicates that methane can release the largest energy when it is

brought into equilibrium with the environmental reference state.Methane and methanol have more enthalpies and exergies andhigher energy quality factors, comparing with those of hydrogenand carbon oxide.

3. Methodologies of r-H Diagram and r-H-ε Diagram

3.1. Graphic Expression for Thermodynamic Characteris-tics of Fluids. As shown in Figure 1, the R-H diagram canrepresent the energy characters of a system when its energyquality factor is associated with its enthalpy. Through combiningthe energy quality factor with enthalpy and exergy and usingthe energy quality factor, enthalpy, and exergy as the vertical,abscissa, and ordinate axes, respectively, a new three-dimen-sional diagram can be obtained, called an R-H-ε diagram. It isa convenient thermodynamic tool for investigating the statecharacteristics and the process performance.

Projecting the three-dimensional diagram along the coordinateaxes directions results in three planar diagrams, named the ε-Hdiagram, the R-H diagram,15 and the R-ε diagram, respectively.

The ε-H diagram can be used to investigate the conservationof the energy quantity and the depletion of energy quality fora process, in which the accepted energy and donated energy isthe same in quantity, however the exergy loss inevitably existsif the change of the energy quality factor has occurred. Theimpacts of the enthalpy change and the exergy change on theenergy quality factor can be investigated using the R-H and R-εdiagrams, respectively.

In Figure 2, the position expressing the state of a fluid, aswell as the values of energy quality factor, depends on the valuesof enthalpy and exergy. Furthermore, the variation in the energyquality factor in a process depends on the values of the enthalpychange and the exergy change. Therefore, the magnitude of thevector expressing a state change also depends on them.

3.2. r-H Diagram Use for Process Analysis. In the R-Hdiagram, the process composed of state change of the fluid isrepresented by a vector from the start point to the end point, asshown in Figure 2.

A classification result as summarized in Table 1 can beobtained by investigating the donating and accepting of enthalpyand exergy. According to the positive or negative values of ∆H,∆ε, ∆S, and ∆R, all possible processes are classified as eightkinds, and several examples are presented.

Correspondingly, a visual expression is described by Figure3. The heat-donating processes are divided into type A and typeB by the dot-line ∆R ) 0, as well as the heat-acceptingprocesses. The curves ∆S ) 0 and ∆ε ) 0 both depend on thethermodynamic character of the original point.

To validate and demonstrate proposed approaches in thispaper, the analysis on a heat exchange process and four routesof methane combustion are presented as follows.

(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: NewYork, 1999; pp 267, 269, 270.

H(T, p, x_) ) ∑ xiHi(T, p) - RT2 ∑ xi[∂ ln(fi/f iθ)/∂T ]p,x (8)

Hi(T, p) ) Hiθ(T0, pθ) + ∆Hi(T0, pθ f T, p) (9)

HAaBb

θ (T0, pθ) ) ∆fHAaBb

θ + aHAθ (T0, pθ) + bHB

θ(T0, pθ) (10)

Hiθ(T0, pθ) ) εi

θ(T0, pθ) + T0Siθ(T0, pθ) (11)

Riθ(T0, pθ) ) εi

θ(T0, pθ)/Hiθ(T0, pθ) (12)

Figure 1. Common pure substances in R-H diagram.

EValuating the Cascade Utilization of Fossil Fuels Energy & Fuels, Vol. xxx, XXXX C

3.3. r-H-ε Diagram Use for Process Analysis. In the heatexchange process, the flow rates of methanol (298 K) and hotwater (363 K) are 1.0 mol · s-1. Aspen Plus process simulationsoftware was used to calculate thermodynamic values in thiswork, and the necessary data was calculated by the aboveequations.

As shown as Figure 4, when the temperature of hot water isdecreased from 363 to 329 K, the enthalpy and exergy arereduced by 2.82 and 0.39 kJ · s-1, respectively. The energyquality factor decreases from 0.021 to 0.006.

Methanol accepts low quality heat and the temperatureincreases from 298 to 323 K. And the enthalpy and exergy areincreased by 2.82 and 0.11 kJ · s-1, respectively. The energyquality factor is decreased from 0.896 to 0.893.

In the H-axis, the enthalpy change of methanol is the sameas that of hot water. In the ε-axis, the exergy change of hotwater is more than that of methanol because of the irreversibility,and this results in a 0.28 kJ · s-1 exergy loss.

Therefore, the R-H-ε diagram not only expresses the variationof the energy quality, but also is convenient to perform theanalysis on the first and the second law of thermodynamicssimultaneously. As seen above, the analysis on a heat exchangeprocess has been given to validate and demonstrate proposedapproaches in this paper. Furthermore, analysis on four combus-tion routes of methane will be presented in the following section.

4. Analysis of Methane Combustion

4.1. Combustion Routes of Methane. The energy releasingmethods of methane can be simply represented by the followingchemical equations.

The direct combustion of methane is represented as

And the indirect combustion of methane after steam reformingis

In another way, the indirect combustion of methane after CO2

reforming provide equations

In addition, considering the impact of preheating, four routesof methane combustion are investigated. They are methane (1)mixing with oxygen f combustion; (2) mixing with oxygenf preheating f combustion; (3) mixing with steam freformingfmixing with oxygenf combustion; and (4) mixingwith carbon dioxide f reforming f mixing with oxygen fcombustion.

Figure 2. Process in R-H-ε diagram.

Figure 3. Process classification in R-H diagram.

Table 1. Classification of Processes Based on ThermodynamicCharacteristics

region ∆H ∆ε ∆S ∆R example

separation type >0 >0 <0 >0 separationheat-accepting type A >0 >0 >0 >0 water heatingheat-accepting type B >0 >0 >0 <0 methanol decompositionchill-donating >0 <0 >0 <0 refrigerationmixing type <0 <0 >0 <0 mixingheat-donating type B <0 <0 <0 <0 combustion reactionsheat-donating type A <0 <0 <0 >0 hot water coolingchill-accepting type <0 >0 <0 >0 cooling medium

CH4 + 2O2 f CO2 + 2H2O, ∆rHθ ) 802.1 kJ · mol-1

(13)

CH4 + H2O f 3H2 + CO, ∆rHθ ) -206.3 kJ · mol-1

(14)

3H2 + CO + 2O2 f CO2 + 3H2O,

∆rHθ ) 1008.4 kJ · mol-1 (15)

CH4 + 3CO2 f 2H2O + 4CO, ∆rHθ ) -329.9 kJ · mol-1

(16)

2H2O + 4CO + 2O2 f 4CO2 + 2H2O,

∆rHθ ) 1132.0 kJ · mol-1 (17)

D Energy & Fuels, Vol. xxx, XXXX Zheng and Hou

To present the R-H-ε diagrams conveniently, followingassumptions are given based on some literature data andidealized specifications.

(1) The minimum temperature difference of heat transfer is30 K.

(2) The combustion is carried out at 1573 K.13

(3) The reaction temperature of steam reforming of methaneis 858 K.32 For the reforming of methane, the temperature isrelatively lower. However, it is an appropriate condition for agas turbine cycle with chemical recuperation using steamreforming of methane, in which steam in feedstock is usuallysuperfluous.

(4) The CO2 reforming of methane occurred under 1273 K.13

(5) The pressures for all of fluids are 100 kPa. It is anidealized specification.

(6) The ratios of raw materials in the above reactions accordto their stoichiometric coefficient as eqs 13-17, and feed stocksreact totally. This assumption is also adopted for analysis ofthe steam reforming of methane for simplifying the methodologypresentation.

The flow rates of methane in four routes were specified as 1mol · s-1. The PR equation of state was used in the processsimulations. The values of the exergy, enthalpy, and the energyquality factor of fluids are obtained by the above equations.

4.2. r-H-ε Diagram Illustration. The states and processesin these four routes are illustrated in Figures 5-8, respectively.In the figures, the different dots express the initial state,intermediate states, and final state, and the sequential vectorsexpress the passed-through processes.

Figure 5 shows the direct combustion of methane. First, 1mol · s-1 of methane mixes with 2 mol · s-1 of oxygen. Then,the mixture combusts at 1573.2 K. The enthalpy change andthe exergy change in the combustion reaction are 629.4 and

693.1 kJ · s-1, respectively. The energy quality factor of theoriginal methane is 0.877. It decreases to 0.820 after mixingwith oxygen and then to 0.363 after combustion. In the end,629.4 kJ · s-1 combustion heat and 510.1 kJ · s-1 heat exergyare obtained.

Figure 6 illustrates the direct combustion of methane afterpreheating. First, 1 mol · s-1 of methane mixes with 2 mol · s-1

of oxygen. The mixture is preheated to 1073 K by exhaust gas.So the enthalpy and exergy values of the mixture increase 94.5and 50.1 kJ · s-1, respectively, and the energy quality factor ofthe mixture decreases from 0.820 to 0.796 after preheating. Themixture then combusts at 1573.2 K, and its energy quality factordecreases again to 0.363. The enthalpy and exergy of the mixturereduce 723.8 and 743.2 kJ · s-1, respectively, in the combustionreaction. In the end, 723.8 kJ · s-1 combustion heat and 586.6kJ · s-1 heat exergy are obtained.

In the preheating process, the temperature of the exhaust gas(CO2 and H2O) decreases from 1103 to 473 K, and conse-quently, its energy quality factor from 0.272 to 0.159. The valuesof the enthalpy and the exergy reduce 94.5 kJ · s-1 and 57.2kJ · s-1, respectively.

Figure 7 shows the indirect combustion of methane aftersteam reforming. First, 1 mol · s-1 of methane mixes with 1mol · s-1 of water. In the following steam reforming reaction,the values of the enthalpy and the exergy of the mixture increase316.2 kJ · s-1 and 174.0 kJ · s-1, respectively, and the energyquality factor decreases from 0.858 to 0.782. In the finalcombustion reaction, the enthalpy and the exergy of CO andH2, decrease 848.0 kJ · s-1 and 815.8 kJ · s-1, respectively, andthe energy quality factor decrease to 0.359. In the end, 848.0kJ · s-1 combustion heat and 687.3 kJ · s-1 heat exergy areobtained.

In the steam reforming reaction, the temperature of theexhaust gas (CO2 and H2O) decreases from 1103 to 473 K, andconsequently, its energy quality factor from 0.272 to 0.159. And

(32) Harvery, S.; Kane, N. Energy ConVers. Manage. 1997, 38, 1671–1679.

Figure 4. Heat exchange process in R-H-ε diagram.

Figure 5. Direct combustion of methane.

Figure 6. Direct combustion of methane after preheating.

Figure 7. Indirect combustion of methane after steam reforming.

EValuating the Cascade Utilization of Fossil Fuels Energy & Fuels, Vol. xxx, XXXX E

its enthalpy and exergy reduce 316.2 kJ · s-1 and 191.4 kJ · s-1,respectively.

Figure 8 shows the indirect combustion of methane after CO2

reforming. One mol · s-1 of methane first mixes with 3 mol · s-1

of CO2. In the following CO2 reforming reaction, the enthalpyand exergy values of the mixture increase 532.6 and 338.1kJ · s-1, respectively, and the energy quality factor decreasesfrom 0.738 to 0.707. In the final combustion reaction, theenthalpy and exergy of CO and H2 decrease 963.8 kJ · s-1 and887.1 kJ · s-1, respectively, and the energy quality factordecreases to 0.384. In the end, 963.8 kJ · s-1 combustion heatand 781.2 kJ · s-1 heat exergy are obtained.

In the steam reforming reaction, the temperature of theexhaust gas (CO2 and H2O) decreases from 1303 to 473 K, andconsequently, its energy quality factor reduces from 0.312 to0.159. Its enthalpy and exergy reduce 532.6 and 342.9 kJ · s-1,respectively.

4.3. Discussion. Methane first accepts energy from theexhaust gas, whose energy quality factor is lower, throughpreheating, CO2 reforming, and steam reforming. Then, theaccepted energy is released during combustion at highertemperature. Hence, more combustion heat is obtained in theindirect combustion than that in the direct combustion.

The exergy loss in the combustion processes in the later threeroutes are 156.6, 128.5 and 106.0 kJ · s-1, respectively. Theyare smaller than that in the first route, where the exergy loss is183.0 kJ · s-1. The values of exergy loss in preheating, steamreforming, and CO2 reforming are 7.1, 17.4, and 4.8 kJ · s-1,respectively.

The changes in the energy quality factor of combustionprocess in the later three routes are 0.432, 0.378, and 0.287,respectively. They are smaller than that in the first route, wherethe change in the energy quality factor is 0.457. This is becausethe energy quality factor of methane first decreased during thepreheating and reforming processes to upgrading the energyfrom a fluid with lower energy quality factor.

The energy quality factor of exhaust at 1303 K or lowertemperatures is relatively lower. So the exhaust energy is notconveniently converted to power. Preheating and reformingprocesses enable the cascade utilization of methane. The processof cascade utilization is expressed by the gradual decrease ofthe energy quality factor.

The energy upgrading from a fluid with lower energy qualityfactor to higher level through process coupling is an exergyenrichment process, which is called exergy regeneration.12 Theexergy regeneration can be achieved through substance conver-sion by thermochemical reactions or heat conversion by heat-driving heat pumps.33 The exergy enrichment abilities aredifferent for every road, 50.1, 174.0, and 338.1 kJ · s-1 forpreheating, steam reforming, and CO2 reforming, respectively.

5. Conclusion

Thermodynamic approach studies of effective use of fossilfuels were carried out, and the subsequent conclusions can bedrawn.

It was emphasized and redefined that the energy quality factorprovides a reasonable index of the fluid’s energy quality. Onbase of the environmental reference state and the thermodynamicconsistency, taking a system of reference substances the sameas that of exergy, the standard enthalpy of a pure species i wasdefined, and the general method proposed in this work can beused to quantify the energy quality factor of multispecies fluids.

Then, the standard exergy, the standard enthalpy, and thestandard energy quality factor of common pure substancesrelated to combustion of fossil fuels were given.

The graphic methodologies of R-H diagram and R-H-εdiagram can visually express the variation of the energy qualityfactor in the state evaluation and the process analysis. Tovalidate and demonstrate the approaches, in the R-H-ε diagram,four routes of methane combustion have been investigated.

The changes in the energy quality factor of combustionprocess in the latter three routes are 0.432, 0.378, and 0.287,respectively. They are smaller than that in the first route,where the change in the energy quality factor is 0.457. Thisis because the energy quality factor of methane first decreasedduring the preheating and reforming processes to upgradethe energy from a fluid with lower energy quality factor. Inthe latter three routes, the exergy regeneration process isdriven by another coupling process in which the energyquality factor of fluid is decreased.

The results show that preheating and endothermic reformingbefore combustion can result in the cascade utilization ofmethane, which appears as a gradual decrease in the energyquality factor. The results prove that the exergy regenerationthrough conversions of heat and substance is important for theeffective use of fossil fuels.

Acknowledgment. The support provided by National NaturalScience Foundation of China (No.s 50576001 and 50890184) forthe completion of the present work is gratefully acknowledged.

Appendixa,b, c ) parameters in eq 2A ) energy levelE ) energy, kJ ·mol-1

fi ) fugacity of species i, kPafiθ ) standard fugacity of species i, kPa

G ) Gibbs free energy, kJ ·mol-1

H ) enthalpy, kJ ·mol-1 or kJ · s-1

p ) pressure, kPaR ) gas constant, J ·mol-1 ·K-1

S ) entropy, J ·mol-1 ·K-1

T ) temperature, Kx ) mole fraction

Greek Letters

R ) energy quality factorε ) exergy, kJ ·mol-1 or kJ · s-1

∆ ) change� ) exergy ratio of energy

Superscripts

θ ) standard state(33) Ziegler, F.; Alefeld, G. Int. J. Refrig 1987, 10, 285–295.

Figure 8. Indirect combustion of methane after CO2 reforming.

F Energy & Fuels, Vol. xxx, XXXX Zheng and Hou

Subscripts

0 ) reference state and environmental statea,b ) numbers of elements A and BA,B ) elements A and BAaBb ) species AaBb

c ) combustionf ) formationi ) species i

Supporting Information Available: The standard exergy andthe standard enthalpy of elements are supported in the SupportingInformation Table S1, and the thermodynamic data, the standardexergy, the standard enthalpy, and the standard energy qualityfactor of 40 kinds of common compounds related to combustionsare given in the Table S2. This material is available free ofcharge via the Internet at http://pubs.acs.org.

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EValuating the Cascade Utilization of Fossil Fuels Energy & Fuels, Vol. xxx, XXXX G