Energy quality and energy grade: concepts, applications and prospects

Abstract

A more comprehensive view on the energy properties could contribute to the deepening of thermodynamic theories and efficient utilization of energy, which has both theoretical and practical significance. As derivative concepts of exergy, energy quality and energy grade, which characterize the quality of energy, have been fully applied in the field of engineering thermophysics during the past four decades. However, their concepts and calculations have not been fully clarified, and summaries of related applications are very rare in the literature. This has led to a considerable degree of ambiguity and confusion in the utilization of these concepts, which is not conducive to the application and promotion of the concepts, and would also hinder the process of the cognition for energy properties. Based on literature research, this paper explains the history of the energy quality and energy grade concepts and expands the calculations and related benchmark issues (environmental reference states) in detail. Moreover, in order to better understand the functions of energy quality and energy grade, analysis methods derived from the concepts and their applications are reviewed. Through summarizing existing research, future research needs on energy quality and energy grade is elaborated. This paper will help to clarify the physical meanings and calculations of energy quality and energy grade, as well as contribute to in-depth thinking on the energy quality and energy grade and other potential energy properties.

INTRODUCTION

The development of thermodynamic theories is accompanied by a deepening understanding of energy properties [1]. In the 1840s, with the establishment of the first law of thermodynamics, the concept of energy gradually became clear and became one of the core concepts in physics. The second law of thermodynamics stated that although the total amount of energy in the transfer and conversion remained the same, its ‘quality’ would degrade [2]. In the 1950s, the concept of exergy was formally proposed to measure the deviation of the system state from the environment [3]. As a product of the combination of the first and second laws, exergy could characterize the available energy of the energy contained in substance or the energy itself. Therefore, the concept of exergy and its analysis methods have been continued and gradually standardized in the oil crisis and were widely utilized in the evaluation and optimization of thermodynamic and thermoeconomic performances of thermal systems [4].

With the deepening of thinking and practice, people gradually realized that exergy can only quantify the available energy contained in the system but does not identify the quality of energy. Besides, exergy analysis cannot directly deal with the energy quality matching of energy donators and acceptors in the energy transfer and conversion. In the 1980s, scholars successively proposed the parameters that characterize the quality of energy, i.e. the energy quality factor and energy grade [5, 6]. As cognitive tools of energy properties, the energy quality factor and energy grade concepts have effectively guided the innovation and improvement of advanced thermal systems such as multi-energy complementary systems and polygeneration systems in recent decades and spawned a series of ideas and achievements [7]. Figure 1 illustrates the gradual deepening of the understanding on energy properties during the history of thermodynamics, among which the energy potential is beyond the scope of this paper and will not be considered.

Figure 1

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The cognitive process of energy properties

Although energy quality and energy grade have been developed for 40 years, their concepts and calculations have not been fully clarified, and the summary and induction of related applications are very rare in the literature. Since the concepts of energy quality and energy grade were proposed and developed in parallel almost at the same time, their physical meanings gradually converged in recent years. The partial overlap in physical meanings and tortuous historical development led to a certain confusion in the use of terms. In the long run, such situation is not conducive to the application and promotion of related concepts and would also hinder our cognition process of energy properties.

In view of the above problems, this paper will focus on the concepts of energy quality and energy grade and carry out a review based on the literature. The contents mainly include (i) review of the historical development of the concepts, (ii) clarification of the calculation methods and related benchmark issues and (iii) introduction of analysis methods derived from concepts and their applications. Finally, on the basis of summarizing the existing research, future research needs on energy quality and energy grade is prospected.

ENERGY QUALITY

Energy quality is a concept that exists in a wide range of disciplines, such as economics and ecology, but its quantitative calculation is related to technological level or value judgment with strong subjective flavor, so it is not the focus of this paper. In the field of engineering thermophysics, in 1985, Jensen [8] put forward the idea of describing energy quality with entropy, which started from the fact that the total amount of energy remained unchanged in during the energy transfer, storage and conversion processes, but entropy would change. However, he pointed out that the quality of energy can be characterized by the ease and value of conversion. Similarly, in 1994, Ohta [9] pointed out that energy quality is a measure and indicator of the relative ease with which one form of energy can be converted into another form, which was based on technical feasibility and conversion efficiency. From the judgment basis, the above two scholars’ understanding of energy quality has not been able to completely get rid of the category of value judgment, which is also not the concern of this paper.

Concept and calculation

The knowledge for energy quality in the existing literature mostly comes from the exergy method. Exergy characterizes the theoretical maximum work that can be obtained from its specified state to the state in equilibrium with the environment. The concept of exergy was coined by Rant [3] in 1956. Available energy (or availability) represents the same physical meaning as exergy. Exergy analysis has been continued and gradually standardized during the great development of the Japanese chemical industry and is widely used in engineering thermophysical analysis. On the basis of exergy analysis, the concept of energy quality and its application has been studied extensively.

] proposed the concept of the energy quality factor in his book, which was defined as

$$ \begin{equation} \alpha \left(T,p,x\right)=\frac{\varepsilon \left(T,p,x\right)}{H\left(T,p,x\right)}, \end{equation}$$

(1)

Energy quality is defined as the capacity to do work per unit of energy, which is an intensive quantity. In 1961, Rant proposed the concept of exergy ratio of energy, denoted as ε/E, in which ε and E are exergy and energy, respectively. This definition of energy quality is suitable for evaluating the difference in available energy of various substances such as chemical fuels and working fluids. In 1980, Zhu [ 5 ] proposed the concept of the energy quality factor in his book, which was defined aswhere T, P, x represents the temperature, pressure and composition of substance in a given state. The energy quality factor has the same physical meaning as the exergy ratio of energy and ‘energy’ in the exergy ratio of energy is specified as the enthalpy H, which makes the meaning clearer. On the basis of thermodynamic consistency, the energy quality factor is a state quantity, which can be used to evaluate the quality of energy contained in various substances.

) shows that the exergy and enthalpy of substance are required to calculate the energy quality factor. Note that the thermodynamic standard state refers to the physical state of pure substance under a pressure of 100 kPa and a specified temperature, as defined by the international union of pure and applied chemistry, but 1 atm (101.325 kPa) was often used as the standard pressure in earlier literature. In addition, the temperature T0 of the standard state is often specified as 298.15 K in practice. Based on the general principles of thermodynamics, the exergy of mixture can be written as

$$ \begin{align} \varepsilon \left(T,p,x\right)&=\sum {x}_i\left[{\varepsilon}_i\left(T,p\right)+R{T}_0\ln \frac{{\hat{f}}_i}{f_i^{\uptheta}}\right]\nonumber\\&\quad- RT\left(1-\frac{T_0}{T}\right)\sum {x}_i{\left(\frac{\partial }{\partial \ln T}\ln \frac{{\hat{f}}_i}{f_i^{\uptheta}}\right)}_{p,x}, \end{align}$$

(2)

|${\hat{f}}_i$|

and

|${f}_i^{\uptheta}$|

are the fugacity of pure substance i in a given state (T, p) and standard state (T0, pθ), respectively, and the exergy εi(T, p) of pure substance is calculated by

$$ \begin{equation} {\varepsilon}_i\left(T,p\right)={\varepsilon}_i^{\uptheta}\left({T}_0,{p}^{\uptheta}\right)+\Delta {\varepsilon}_i\left({T}_0,{p}^{\uptheta}\to T,p\right). \end{equation}$$

(3)

Equation ( 1 ) shows that the exergy and enthalpy of substance are required to calculate the energy quality factor. Note that the thermodynamic standard state refers to the physical state of pure substance under a pressure of 100 kPa and a specified temperature, as defined by the international union of pure and applied chemistry, but 1 atm (101.325 kPa) was often used as the standard pressure in earlier literature. In addition, the temperature Tof the standard state is often specified as 298.15 K in practice. Based on the general principles of thermodynamics, the exergy of mixture can be written aswhereandare the fugacity of pure substance i in a given state (T, p) and standard state (T, p), respectively, and the exergy ε(T, p) of pure substance is calculated by

The first item on the right side of (3) |${\varepsilon}_i^{\uptheta}$|(T0, pθ) is the standard exergy of pure substance i, involving the setting of the environmental reference state (environmental component), and the second item represents the exergy change of pure substance i from the given state (T, p) to the reference state (T0, pθ).

$$ \begin{equation} H\left(T,p,x\right)=\sum {x}_i{H}_i\left(T,p\right)-R{T}^2\sum {x}_i{\left(\frac{\partial }{\partial \ln T}\ln \frac{{\hat{f}}_i}{f_i^{\uptheta}}\right)}_{p,x}, \end{equation}$$

(4)

i(T, p) stands for the enthalpy of pure substance, which can be calculated by from the enthalpy change from the standard state (T0, pθ) to the given state (T, p):

$$ \begin{equation} {H}_i\left(T,p\right)={H}_i^{\uptheta}\left({T}_0,{p}^{\uptheta}\right)+\varDelta {H}_i\left({T}_0,{p}^{\uptheta}\to T,p\right), \end{equation}$$

(5)

|${H}_i^{\uptheta}$|

(T0, pθ) is the standard enthalpy of pure substance i in the environmental reference state. The standard exergy of a compound

|${\varepsilon}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}$|

can be calculated from its elemental composition, written as

$$ \begin{equation} {\varepsilon}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}={\Delta}_{\mathrm{f}}{G}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}+\mathrm{a}{\varepsilon}_{\mathrm{A}}^{\uptheta}+\mathrm{b}{\varepsilon}_{\mathrm{B}}^{\uptheta}, \end{equation}$$

(6)

f

|${G}_{\mathrm{AaBb}}^{\uptheta}$|

is the standard Gibbs free energy of formation of compound AaBb.

|${\varepsilon}_{\mathrm{A}}^{\uptheta}$|

and

|${\varepsilon}_{\mathrm{B}}^{\uptheta}$|

are the standard exergy of elements A and B, and a and b represent the number of elements in compound AaBb, respectively. Equation (

) only shows compounds composed of two elements, but it can be simply extrapolated to substances composed of any number of elements, which is universal. Similarly, the enthalpy of a compound can be expressed as

$$ \begin{equation} {H}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}\left({T}_0,{p}^{\uptheta}\right)={\Delta}_{\mathrm{f}}{H}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}+\mathrm{a}{H}_{\mathrm{A}}^{\uptheta}\left({T}_0,{p}^{\uptheta}\right)+\mathrm{b}{H}_{\mathrm{B}}^{\uptheta}\left({T}_0,{p}^{\uptheta}\right), \end{equation}$$

(7)

f

|${H}_{\mathrm{AaBb}}^{\uptheta}$|

is the standard enthalpy of formation of AaBb.

|${H}_{\mathrm{A}}^{\uptheta}$|

(T0, pθ) and

|${H}_{\mathrm{B}}^{\uptheta}$|

(T0, pθ) are the standard enthalpies of elements A and B.

Similarly, the enthalpy of mixture can be expressed aswhere H(T, p) stands for the enthalpy of pure substance, which can be calculated by from the enthalpy change from the standard state (T, p) to the given state (T, p):where(T, p) is the standard enthalpy of pure substance i in the environmental reference state. The standard exergy of a compoundcan be calculated from its elemental composition, written aswhere ∆is the standard Gibbs free energy of formation of compound Aandare the standard exergy of elements A and B, and a and b represent the number of elements in compound A, respectively. Equation ( 6 ) only shows compounds composed of two elements, but it can be simply extrapolated to substances composed of any number of elements, which is universal. Similarly, the enthalpy of a compound can be expressed aswhere ∆is the standard enthalpy of formation of A(T, p) and(T, p) are the standard enthalpies of elements A and B.

$$ \begin{equation} {\varepsilon}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}={\overline{\varepsilon}}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}-R{T}_0\ln {x}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}, \end{equation}$$

(8)

|${x}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}$|

is the molar fraction of substance AaBb in the environmental reference state,

|${\overline{\varepsilon}}_{\mathrm{AaBb}}^{\uptheta}$|

is the partial molar exergy of AaBb and RT0ln

|${x}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}$|

indicates the exergy derived from the difference in mole fraction from the environmental reference state (mixture). Therefore, the standard exergies of elements with simple reference substances can be inversely calculated by (

), i.e.

$$ \begin{equation} {\varepsilon}_{\mathrm{A}}^{\uptheta}=-\frac{1}{a}\left({\varDelta}_{\mathrm{f}}{G}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}+R{T}_0\ln {x}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}+b{\varepsilon}_{\mathrm{B}}^{\uptheta}\right). \end{equation}$$

(9)

Note that the substance in the environmental reference state has no ability to do work, i.e. its partial molar exergy is zero. Consider the relationship between the molar quantity of pure substance and its partial molar quantity in the ideal mixed solutionwhereis the molar fraction of substance Ain the environmental reference state,is the partial molar exergy of Aand RTlnindicates the exergy derived from the difference in mole fraction from the environmental reference state (mixture). Therefore, the standard exergies of elements with simple reference substances can be inversely calculated by ( 6 ), i.e.

$$ \begin{equation} {\overline{H}}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}={\overline{\varepsilon}}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}+{T}_0{\overline{S}}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}, \end{equation}$$

(10)

|${\overline{H}}_{\mathrm{AaBb}}^{\uptheta}$|

and

|${\overline{S}}_{\mathrm{AaBb}}^{\uptheta}$|

are the standard partial molar enthalpy and entropy of substance AaBb in the environmental reference state, respectively, then combined with the expression of partial molar entropy in ideal solution

$$ \begin{equation} {\overline{S}}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}={S}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}-R\ln {x}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}, \end{equation}$$

(11)

On this basis, standard exergies of elements with more complex reference substances can be solved; thereby, the system of standard exergies of elements can be established. For the calculation of the standard enthalpy, the environmental reference state of standard enthalpy and standard exergy should be consistent according to the principle of thermodynamic consistency. According to the relation of partial molar propertieswhereandare the standard partial molar enthalpy and entropy of substance Ain the environmental reference state, respectively, then combined with the expression of partial molar entropy in ideal solution

|${S}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}$|

is the entropy of pure substance AaBb, and since the partial molar enthalpy of substance in ideal solution is equal to the enthalpy of pure substance, the enthalpy of pure substance AaBb can be calculated by

$$ \begin{equation} {H}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}\left({T}_0,{p}^{\uptheta}\right)={\overline{H}}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}={T}_0\left({S}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}-R\ln {x}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}\right). \end{equation}$$

(12)

whereis the entropy of pure substance A, and since the partial molar enthalpy of substance in ideal solution is equal to the enthalpy of pure substance, the enthalpy of pure substance Acan be calculated by

$$ \begin{equation} {H}_{\mathrm{A}}^{\uptheta}=-\frac{1}{a}\left[{T}_0\left({S}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}-R\ln {x}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}\right)-{\Delta}_{\mathrm{f}}{H}_{{\mathrm{A}}_{\mathrm{a}}{\mathrm{B}}_{\mathrm{b}}}^{\uptheta}-\mathrm{b}{H}_{\mathrm{B}}^{\uptheta}\right]. \end{equation}$$

(13)

Therefore, the standard enthalpy of element A can be inversely calculated by

According to (1–13), theoretically, the energy quality factor of substance can be calculated based on its fugacity, standard enthalpy and Gibbs free energy of formation and composition. Therefore, in addition to obtaining accurate thermodynamic data, the core issue in obtaining the energy quality factor is to specify the environmental reference state. The main content of establishing the environmental reference state is to select proper reference substances for elements and determine their components in the reference state. Depending on the definition of exergy, the exergy of all substances in equilibrium with the environment is zero. However, the environment in which humans live is inherently in a non-equilibrium state, so the environmental reference state cannot be completely determined by the principle of thermodynamics, and there is a flexible space for its determination. In this regard, relevant scholars hold different views and put forward different environmental reference state models.

Environmental reference state

Generally speaking, there are two ways to determine the environmental reference state: one is to consider the thermodynamic equilibrium; the other is to consider the real natural environment. In 1980, Ahrendts [10] established an equilibrium reference state with 15 elements based on the atmosphere, ocean and crustal layer that can be utilized for technical processes. However, the limit of equilibrium made the standard pressure of the reference state change to 0.770 atm, and the substance composition of the reference state was obviously different from that of the natural environment. In 1982, Kameyama et al. [11] determined the reference substances of elements through thermodynamic stability and used saturated humid air as the reference component of gas, especially liquid water as the reference substance of hydrogen. For other elements, they calculated the standard exergies of 79 elements based on the corresponding pure reference substance. In theory, one element can only correspond to one reference substance, but there are two reference substances for hydrogen in Ahrendts’s model, namely water vapor in humid air and liquid water and the latter is used in calculation, which is not smooth enough in theory. In 1989, Szargut [12] pointed out that thermodynamic stability could not be taken as the sole determinant for the reference state because although some substances were stable in thermodynamics, their formation might be hindered in kinetics (such as nitrate), or the formation probability was very small due to the rarity of elements. Therefore, he comprehensively considered gaseous components in the atmosphere, dissolved substances in seawater and solid compounds on the earth’s surface and designated reference substances for 86 elements, thus establishing the environmental reference state. However, because the reference system is in a non-equilibrium state, the calculated exergy may be negative, which is contrary to the physical meaning of exergy ‘available energy’.

It can be seen that although both the environmental reference state models proposed by Ahrendts and Kameyama are not perfect, they have been developed and applied accordingly in the subsequent years. In 2002, Valero [3] changed the reference substances of some elements and revised the standard exergy of elements based on Szargut’s reference state model with more accurate thermodynamic data. In 2006, Rivero and Garfias [13] revised and updated the standard chemical exergy of elements proposed by Szargut, in which exergy values of nitrogen and aluminum changed significantly. It was noted that the standard pressure adopted in these literature was 1 atm instead of 100 kPa, which would affect the calculation accuracy of standard exergy of elements.

Based on the environmental reference state model proposed by Kameyama, Japan first formulated a national standard for exergy analysis in the world in 1980 and revised it in 1992. China also promulgated related standard in 1994, namely Technical Guides for Exergy Analysis in Energy System (GB/T 14909-94) [14]. In 2005, China revised the standard [15]. The revision of the reference state model was mainly reflected in (i) the standard pressure was changed to 100 kPa; (ii) based on the technical energy systems of ISO13600 (1997), the environmental reference state was not only established on the basis of thermodynamic stability but also combined the actual environment of the atmosphere, hydrosphere and lithosphere; and (iii) the standard atmosphere adopted the condition of the US standard atmosphere 1976, deleted the very small components of krypton, hydrogen and methane and adjusted it to saturated air. In 2020, China revised the standard for the second time, deleting the vapor in the atmosphere component of the 2005 revised edition and using dry air as the standard component of the atmosphere [16]. Table 1 integrates the settings of the elemental reference substances and components in the above environmental reference state models, and the US standard atmosphere 1976 is used for reference.

Table 1

Elements

. 

Reference substances

. 

Ahrendts [

10]
0.770 atm
mass fraction

. 

Kameyama [

11]
1 atm
mole fraction

. 

Szargut [

12]
1 atm
mole fraction

. 

GB/T 14909-94
1 atm
mole fraction

. 

GB/T 14909-2005
1 bar
mole fraction

. 

GB/T 14909-2021
1 bar
mole fraction

. 

US standard atmosphere (1976)
1 atm
mole fraction

. 

N N2 0.9524 0.7557 0.7578 0.7557 0.7561 0.78085 0.78084 O O2 3 × 10−7 0.2034 0.2039 0.2034 0.2028 0.209477 0.209476 Ar Ar 0.0166 0.00901 0.00906 0.0091 0.0091 0.00934 0.00934 C CO2 0.0052 0.0003 0.000335 0.0003 0.0003 0.000314 0.000314 Ne Ne  1.8 × 10−5 1.77 × 10−5 1.8 × 10–5 1.77 × 10−5 1.1818 × 10−5 1.818 × 10−5 He He  5.24 × 10−6 4.85 × 10−6 5.24 × 10−6 5.08 × 10−6 5.24 × 10−6 5.24 × 10−6 H H2O (vapor) 0.0258√ 0.0316 0.022√ 0.0316 0.03167    H2O (liquid)  √  √ √ √  Other elements Corresponding substances The actual environment of the atmosphere, hydrosphere and lithosphere Pure substances The actual environment of the atmosphere, hydrosphere and lithosphere Pure substances Pure substances Pure substances  Elements

. 

Reference substances

. 

Ahrendts [

10]
0.770 atm
mass fraction

. 

Kameyama [

11]
1 atm
mole fraction

. 

Szargut [

12]
1 atm
mole fraction

. 

GB/T 14909-94
1 atm
mole fraction

. 

GB/T 14909-2005
1 bar
mole fraction

. 

GB/T 14909-2021
1 bar
mole fraction

. 

US standard atmosphere (1976)
1 atm
mole fraction

. 

N N2 0.9524 0.7557 0.7578 0.7557 0.7561 0.78085 0.78084 O O2 3 × 10−7 0.2034 0.2039 0.2034 0.2028 0.209477 0.209476 Ar Ar 0.0166 0.00901 0.00906 0.0091 0.0091 0.00934 0.00934 C CO2 0.0052 0.0003 0.000335 0.0003 0.0003 0.000314 0.000314 Ne Ne  1.8 × 10−5 1.77 × 10−5 1.8 × 10–5 1.77 × 10−5 1.1818 × 10−5 1.818 × 10−5 He He  5.24 × 10−6 4.85 × 10−6 5.24 × 10−6 5.08 × 10−6 5.24 × 10−6 5.24 × 10−6 H H2O (vapor) 0.0258√ 0.0316 0.022√ 0.0316 0.03167    H2O (liquid)  √  √ √ √  Other elements Corresponding substances The actual environment of the atmosphere, hydrosphere and lithosphere Pure substances The actual environment of the atmosphere, hydrosphere and lithosphere Pure substances Pure substances Pure substances  
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Table 1

Elements

. 

Reference substances

. 

Ahrendts [

10]
0.770 atm
mass fraction

. 

Kameyama [

11]
1 atm
mole fraction

. 

Szargut [

12]
1 atm
mole fraction

. 

GB/T 14909-94
1 atm
mole fraction

. 

GB/T 14909-2005
1 bar
mole fraction

. 

GB/T 14909-2021
1 bar
mole fraction

. 

US standard atmosphere (1976)
1 atm
mole fraction

. 

N N2 0.9524 0.7557 0.7578 0.7557 0.7561 0.78085 0.78084 O O2 3 × 10−7 0.2034 0.2039 0.2034 0.2028 0.209477 0.209476 Ar Ar 0.0166 0.00901 0.00906 0.0091 0.0091 0.00934 0.00934 C CO2 0.0052 0.0003 0.000335 0.0003 0.0003 0.000314 0.000314 Ne Ne  1.8 × 10−5 1.77 × 10−5 1.8 × 10–5 1.77 × 10−5 1.1818 × 10−5 1.818 × 10−5 He He  5.24 × 10−6 4.85 × 10−6 5.24 × 10−6 5.08 × 10−6 5.24 × 10−6 5.24 × 10−6 H H2O (vapor) 0.0258√ 0.0316 0.022√ 0.0316 0.03167    H2O (liquid)  √  √ √ √  Other elements Corresponding substances The actual environment of the atmosphere, hydrosphere and lithosphere Pure substances The actual environment of the atmosphere, hydrosphere and lithosphere Pure substances Pure substances Pure substances  Elements

. 

Reference substances

. 

Ahrendts [

10]
0.770 atm
mass fraction

. 

Kameyama [

11]
1 atm
mole fraction

. 

Szargut [

12]
1 atm
mole fraction

. 

GB/T 14909-94
1 atm
mole fraction

. 

GB/T 14909-2005
1 bar
mole fraction

. 

GB/T 14909-2021
1 bar
mole fraction

. 

US standard atmosphere (1976)
1 atm
mole fraction

. 

N N2 0.9524 0.7557 0.7578 0.7557 0.7561 0.78085 0.78084 O O2 3 × 10−7 0.2034 0.2039 0.2034 0.2028 0.209477 0.209476 Ar Ar 0.0166 0.00901 0.00906 0.0091 0.0091 0.00934 0.00934 C CO2 0.0052 0.0003 0.000335 0.0003 0.0003 0.000314 0.000314 Ne Ne  1.8 × 10−5 1.77 × 10−5 1.8 × 10–5 1.77 × 10−5 1.1818 × 10−5 1.818 × 10−5 He He  5.24 × 10−6 4.85 × 10−6 5.24 × 10−6 5.08 × 10−6 5.24 × 10−6 5.24 × 10−6 H H2O (vapor) 0.0258√ 0.0316 0.022√ 0.0316 0.03167    H2O (liquid)  √  √ √ √  Other elements Corresponding substances The actual environment of the atmosphere, hydrosphere and lithosphere Pure substances The actual environment of the atmosphere, hydrosphere and lithosphere Pure substances Pure substances Pure substances  
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Correlation estimation models

In light of thermodynamics, the exergy, enthalpy and energy quality factor of any substance can be accurately calculated by combining thermodynamic properties of pure substances with the environmental reference state model. However, the chemical composition of actual substances (such as biomass fuels) is complex and difficult to accurately determine, which directly blocks the use of theoretical calculation methods. To this end, researchers have developed a variety of correlation models for estimating the thermodynamic properties of complex substances with measured thermodynamic data. It is considered that the acquisition of enthalpy of substance is easier than exergy, which can be characterized by directly measurable properties such as the combustion heat and lower heat value. Therefore, the review mainly focuses on the acquisition of exergy of substance. These estimation models for exergy can be roughly divided into three categories according to the required data, which are based on the heat values, elements composition and ash content and the integration of these aspects, respectively.

Based on heat values

For complex substances, the heat value was relatively easy to measure compared with entropy, enthalpy, et al., and therefore became a common parameter in estimation models. In 1961, Rant [17] first proposed three simple correlations for estimating chemical exergy of fuels based on lower heat values in terms of solid, liquid and gas phases. The model defined the correlations by fuel phase states, which could not distinguish the exergy ratio of energy of fuels in the same phase, but the idea of associating fuel exergy with heat value was continued and improved. In 2011, Song et al. [18] proposed a method for estimating chemical exergy of dry biomass based on elements and ash content, which was applied to varieties of biomass, and the result showed that the average ratio of specific chemical exergy to higher heat value of dry biomass was 1.047. In 2015, Zhang et al. [19] studied the higher and lower heat values and exergies of 64 woody biomasses and pointed out that the exergies had a linear relationship with heat value. In 2018, Huang et al. [22] calculated the chemical exergy of six typical plastic wastes and established the linear relationship between the chemical exergy of plastic wastes and its high calorific value. In 2020, Huang et al. [23] emphasized the importance of consistency of thermodynamic reference system. Based on the data of 194 typical fuels, the quadratic prediction model for standard enthalpy and exergy of fuel was proposed with the standard combustion heat (higher heat value) as the only variable.

Based on elements composition and ash content

The elements composition and ash content of substance could be obtained by elemental composition analysis and thus could be served as the basis for estimation models. In 1982, Shieh and Fan [20] estimated the enthalpy and exergy of complex substances by using the mass fraction of carbon, hydrogen, oxygen, halogen elements and ash in fuels, but the model’s estimation for standard entropy was not completely correct. In 1995, Stepanov [21] revised and compared several estimation models for chemical exergy available at that time and recommended the model proposed by Shieh and Fan to be used in practical applications. In 2012, Song et al. [22] presented a unified estimation correlation for chemical exergy of liquid and dry fuels on dry basis and pointed out that the contribution of inorganic matter and ash in fuels to chemical exergy can be ignored. In 2016, Huang et al. [23] established two chemical exergy prediction models for agricultural biomass, which were a general regression neural network model based on elements content and a linear model based on higher heat value, respectively, and the comparison showed that the former had higher prediction accuracy. In 2017, Qian et al. [24] established three prediction models for chemical exergy of biomass on dry basis using only elements composition and compared their accuracy. In 2020, Aghbashlo et al. [25] proposed a hybrid method combining partial least square method, adaptive network-based fuzzy inference system and particle swarm optimization algorithm to determine chemical exergy of biomass based on component analysis method.

Based on the integration of heat values, elements composition and ash content

The estimation models that comprehensively consider heat values, elements composition and ash content were expected to show better performance. In 1964, Szargut and Styrylska [26] used the mass fraction of elements in fuels to modify the chemical exergy of liquid and solid fuels in the Rant’s model and thus proposed the first chemical exergy estimation model that comprehensively considered the fuel’s heat value, elements composition and ash content. In 2000, Govin et al. [27] further considered the contribution of nitrogen and sulfur in elements composition to exergy and estimated the contribution of ideal solution mixing term and the non-ideality of the mixture to the chemical exergy and thus improved the Szargut model. In 2012, Bilgen et al. [28] showed that the chemical composition of organic fuels strongly affected the fuel’s heating value and chemical exergy and then proposed a chemical exergy prediction model that comprehensively considers the chemical composition and heating value of fuels. In 2016, Zhang et al. [29] presented two estimation correlations for exergy of woody biomass by combining elements composition and heat value with consideration of ash content and ash exergy.

Table 2 summarizes the three types of correlations for estimating chemical exergy of various substances. The first models actually ignore the effect of the specific entropy on exergy because the value of the specific entropy is much less than that of heat value. By comparison, the second and third models consider the effect of the specific entropy on exergy, while more information (elements composition and ash content) is required for estimation models.

Table 2

Methods

. 

Year

. 

Authors

. 

Correlations

. 

Unit

. 

Error

. 

Applications

. 

(1) 1961 Rant [

17] ε = 0.95LHV (gas phase)
ε = 0.975LHV (liquid phase)
ε = LHV-hm (solid phase) kJ/kg  Fuels  2011 Song et al. [

18] ε = 1.047HHV kJ/kg (−2%, 2%) Dry biomass  2015 Zhang et al. [

19] 

|$\varepsilon =342.50+1.04\mathrm{HHV}\ \Big(7560\le \mathrm{HHV}\le 23997\Big)$|

|$\varepsilon =2289.87+1.01\mathrm{LHV}$|

 kJ/kg (−4.80%, 4.80%)
(−2.78%, 1.98%) Woody biomass  2016 Huang et al. [

23] ε = 0.978HHV + 2124.118 kJ/kg (−2%, 2%) Agricultural biomass  2018 Huang et al. [

37] ε = 0.890HHV + 5151.097 kJ/kg 5% Plastic waste  2020 Huang et al. [

36] ε = −1.2983 × 10−6(ΔcHθ)2 + 1.0561ΔcHθ-9.4419 × 10−2 (gas phase))
ε = −2.5674 × 10−6(ΔcHθ)2 + 1.1270ΔcHθ-5.9389 × 10−2 (liquid phase)
ε = −2.2668 × 10−6(ΔcHθ)2 + 0.97864ΔcHθ + 1.3779 × 10−2 (solid phase) MJ/kg 1.18%
1.67%
1.20% Biomass fuels (2) 1982 Shiehand Fan [

20] 

|$\varepsilon =8177.79[\mathrm{C}]+5.25[\mathrm{N}]+27892.63[\mathrm{H}]+4364.33[\mathrm{S}]-3173.660$|

|$+5763.41[\mathrm{F}]+2810.57[\mathrm{Cl}]+1204.30[\mathrm{Br}]+692.50[\mathrm{I}]-298.15{[\mathrm{S}]}_{\mathrm{ash}}\mathrm{A}$|

|$+0.15[\mathrm{O}](7837.667[\mathrm{C}]+33888.889[\mathrm{H}]-4236.1[\mathrm{O}]+3828.75[\mathrm{S}]$|

|$+4447.37[\mathrm{F}]+1790.9[\mathrm{Cl}]+681.97[\mathrm{Br}]+334.86[\mathrm{I}])$|

 kcal/kg  Solid and liquid fuels, biomass, waste  1995 Stepanov et al. [

21] 

|$\varepsilon =32904.076[\mathrm{C}]+2040.24[\mathrm{N}]+117714.337[\mathrm{H}]+16341.556[\mathrm{S}]-13405.192[\mathrm{O}]$|

|$+8278.838[\mathrm{F}]+348.382[\mathrm{Cl}]+416.593[\mathrm{Br}]+128.567[\mathrm{I}]-298.15{[\mathrm{S}]}_{\mathrm{ash}}\mathrm{A}$|

|$+0.15[\mathrm{O}][32833.33[\mathrm{C}]+141865.08([\mathrm{H}]-0.125[\mathrm{O}])+19500[\mathrm{S}]+9789.47[\mathrm{F}]$|

|$+705.06[\mathrm{Cl}]+1226.29[\mathrm{Br}]+685.47[\mathrm{I}]]$|

 kJ/kg  Solid and liquid fuels  2011 Song et al. [

18] ε = 1812.5 + 295.606[C] + 587.354[H] + 17.506[O] + 17.735[N] + 95.615[S]-31.8A kJ/kg (−1.5%, 1.5%) Dry biomass  2012 Song et al. [

22] ε = 363.439[C] + 1075.633[H]-86.308[O] + 4.147[N] + 190.798[S]-21.1A kJ/kg 0.338% Solid and liquid fuels  2017 Qian et al. [

24] ε = 119.184(1/3[C] + [H]-1/8[O] + 1/8[S])
ε = 920.08(1/3[C] + [H] + 1/8[S])
ε = 920.72(1/3[C] + [H]) kJ/kg 2.882%
0.643%
0.634% Dry biomass  2020 Aghbashlo et al. [

25] – kJ/kg Ultimate analysis: 0.207%
Proximate analysis: 0.506% Biomass (3) 1964 Szargut and Styrylska [

26] 

|$\varepsilon =\beta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+9683[\mathrm{S}]+{\upvarepsilon}_{\mathrm{ash}}\mathrm{A}+{\upvarepsilon}_{\mathrm{w}}\mathrm{W}$|

|$\upbeta =(1.0412+0.2160[\mathrm{H}]/[\mathrm{C}]-0.2499[\mathrm{O}]/[\mathrm{C}](1+0.7884[\mathrm{H}]/[\mathrm{C}])+0.0450[\mathrm{N}]/[\mathrm{C}])$|

|$/(1-0.3035[\mathrm{O}]/[\mathrm{C}])$|

(woody)

|$\upbeta =1.0437+0.0140[\mathrm{H}]/[\mathrm{C}]+0.0968[\mathrm{O}]/[\mathrm{C}]+0.0467[\mathrm{N}]/[\mathrm{C}];[\mathrm{O}]/[\mathrm{C}]\le 0.5$|

|$\upbeta =(1.044+0.0160[\mathrm{H}]/[\mathrm{C}]-0.3493[\mathrm{O}]/[\mathrm{C}](1+0.0531[\mathrm{H}]/[\mathrm{C}])+0.0493[\mathrm{N}]/[\mathrm{C}])$|

|$/(1-0.4124[\mathrm{O}]/[\mathrm{C}]);[\mathrm{O}]/[\mathrm{C}]\le 2$|

(other biomass) kJ/kg  Biomass  2000 Govin et al. [

27] 

|$-\varepsilon /{\Delta}_{\mathrm{c}}{H}^0=1.02034-0.01381[\mathrm{H}]/[\mathrm{C}]+0.03374[\mathrm{O}]/[\mathrm{C}]+0.02593[\mathrm{N}]/[\mathrm{C}]$|

|$-0.08408[\mathrm{S}]/[\mathrm{C}]$|

 kJ/kg  Fuel mixtures  2012 Bilgen et al. [

28] 

|$\varepsilon =\upbeta \mathrm{LHV}$|

|$\upbeta =1.047+0.0154[\mathrm{H}]/[\mathrm{C}]+0.0562[\mathrm{O}]/[\mathrm{C}]+0.5904[\mathrm{N}]/[\mathrm{C}](1-0.175[\mathrm{H}]/[\mathrm{C}]);$|

|$[\mathrm{O}]/[\mathrm{C}]<1$|

 kJ/kg  Organic fuels  2016 Zhang et al. [

29] 

|$\upvarepsilon =\upbeta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+{\upvarepsilon}_{\mathrm{w}}\mathrm{W}+9683[\mathrm{S}]+1685.63\mathrm{A}\ (0.09\%\le \mathrm{A}\le 29.73\%)$|

|$\varepsilon =\upbeta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+{\varepsilon}_{\mathrm{w}}\mathrm{W}+9683[\mathrm{S}]+10.25\mathrm{A}+10.29\ (0.09\%\le \mathrm{A}\le 29.73\%)$|

 kJ/kg (−0.76%, 1.38%)
(−1.16%, 0.88%) Woody biomass Methods

. 

Year

. 

Authors

. 

Correlations

. 

Unit

. 

Error

. 

Applications

. 

(1) 1961 Rant [

17] ε = 0.95LHV (gas phase)
ε = 0.975LHV (liquid phase)
ε = LHV-hm (solid phase) kJ/kg  Fuels  2011 Song et al. [

18] ε = 1.047HHV kJ/kg (−2%, 2%) Dry biomass  2015 Zhang et al. [

19] 

|$\varepsilon =342.50+1.04\mathrm{HHV}\ \Big(7560\le \mathrm{HHV}\le 23997\Big)$|

|$\varepsilon =2289.87+1.01\mathrm{LHV}$|

 kJ/kg (−4.80%, 4.80%)
(−2.78%, 1.98%) Woody biomass  2016 Huang et al. [

23] ε = 0.978HHV + 2124.118 kJ/kg (−2%, 2%) Agricultural biomass  2018 Huang et al. [

37] ε = 0.890HHV + 5151.097 kJ/kg 5% Plastic waste  2020 Huang et al. [

36] ε = −1.2983 × 10−6(ΔcHθ)2 + 1.0561ΔcHθ-9.4419 × 10−2 (gas phase))
ε = −2.5674 × 10−6(ΔcHθ)2 + 1.1270ΔcHθ-5.9389 × 10−2 (liquid phase)
ε = −2.2668 × 10−6(ΔcHθ)2 + 0.97864ΔcHθ + 1.3779 × 10−2 (solid phase) MJ/kg 1.18%
1.67%
1.20% Biomass fuels (2) 1982 Shiehand Fan [

20] 

|$\varepsilon =8177.79[\mathrm{C}]+5.25[\mathrm{N}]+27892.63[\mathrm{H}]+4364.33[\mathrm{S}]-3173.660$|

|$+5763.41[\mathrm{F}]+2810.57[\mathrm{Cl}]+1204.30[\mathrm{Br}]+692.50[\mathrm{I}]-298.15{[\mathrm{S}]}_{\mathrm{ash}}\mathrm{A}$|

|$+0.15[\mathrm{O}](7837.667[\mathrm{C}]+33888.889[\mathrm{H}]-4236.1[\mathrm{O}]+3828.75[\mathrm{S}]$|

|$+4447.37[\mathrm{F}]+1790.9[\mathrm{Cl}]+681.97[\mathrm{Br}]+334.86[\mathrm{I}])$|

 kcal/kg  Solid and liquid fuels, biomass, waste  1995 Stepanov et al. [

21] 

|$\varepsilon =32904.076[\mathrm{C}]+2040.24[\mathrm{N}]+117714.337[\mathrm{H}]+16341.556[\mathrm{S}]-13405.192[\mathrm{O}]$|

|$+8278.838[\mathrm{F}]+348.382[\mathrm{Cl}]+416.593[\mathrm{Br}]+128.567[\mathrm{I}]-298.15{[\mathrm{S}]}_{\mathrm{ash}}\mathrm{A}$|

|$+0.15[\mathrm{O}][32833.33[\mathrm{C}]+141865.08([\mathrm{H}]-0.125[\mathrm{O}])+19500[\mathrm{S}]+9789.47[\mathrm{F}]$|

|$+705.06[\mathrm{Cl}]+1226.29[\mathrm{Br}]+685.47[\mathrm{I}]]$|

 kJ/kg  Solid and liquid fuels  2011 Song et al. [

18] ε = 1812.5 + 295.606[C] + 587.354[H] + 17.506[O] + 17.735[N] + 95.615[S]-31.8A kJ/kg (−1.5%, 1.5%) Dry biomass  2012 Song et al. [

22] ε = 363.439[C] + 1075.633[H]-86.308[O] + 4.147[N] + 190.798[S]-21.1A kJ/kg 0.338% Solid and liquid fuels  2017 Qian et al. [

24] ε = 119.184(1/3[C] + [H]-1/8[O] + 1/8[S])
ε = 920.08(1/3[C] + [H] + 1/8[S])
ε = 920.72(1/3[C] + [H]) kJ/kg 2.882%
0.643%
0.634% Dry biomass  2020 Aghbashlo et al. [

25] – kJ/kg Ultimate analysis: 0.207%
Proximate analysis: 0.506% Biomass (3) 1964 Szargut and Styrylska [

26] 

|$\varepsilon =\beta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+9683[\mathrm{S}]+{\upvarepsilon}_{\mathrm{ash}}\mathrm{A}+{\upvarepsilon}_{\mathrm{w}}\mathrm{W}$|

|$\upbeta =(1.0412+0.2160[\mathrm{H}]/[\mathrm{C}]-0.2499[\mathrm{O}]/[\mathrm{C}](1+0.7884[\mathrm{H}]/[\mathrm{C}])+0.0450[\mathrm{N}]/[\mathrm{C}])$|

|$/(1-0.3035[\mathrm{O}]/[\mathrm{C}])$|

(woody)

|$\upbeta =1.0437+0.0140[\mathrm{H}]/[\mathrm{C}]+0.0968[\mathrm{O}]/[\mathrm{C}]+0.0467[\mathrm{N}]/[\mathrm{C}];[\mathrm{O}]/[\mathrm{C}]\le 0.5$|

|$\upbeta =(1.044+0.0160[\mathrm{H}]/[\mathrm{C}]-0.3493[\mathrm{O}]/[\mathrm{C}](1+0.0531[\mathrm{H}]/[\mathrm{C}])+0.0493[\mathrm{N}]/[\mathrm{C}])$|

|$/(1-0.4124[\mathrm{O}]/[\mathrm{C}]);[\mathrm{O}]/[\mathrm{C}]\le 2$|

(other biomass) kJ/kg  Biomass  2000 Govin et al. [

27] 

|$-\varepsilon /{\Delta}_{\mathrm{c}}{H}^0=1.02034-0.01381[\mathrm{H}]/[\mathrm{C}]+0.03374[\mathrm{O}]/[\mathrm{C}]+0.02593[\mathrm{N}]/[\mathrm{C}]$|

|$-0.08408[\mathrm{S}]/[\mathrm{C}]$|

 kJ/kg  Fuel mixtures  2012 Bilgen et al. [

28] 

|$\varepsilon =\upbeta \mathrm{LHV}$|

|$\upbeta =1.047+0.0154[\mathrm{H}]/[\mathrm{C}]+0.0562[\mathrm{O}]/[\mathrm{C}]+0.5904[\mathrm{N}]/[\mathrm{C}](1-0.175[\mathrm{H}]/[\mathrm{C}]);$|

|$[\mathrm{O}]/[\mathrm{C}]<1$|

 kJ/kg  Organic fuels  2016 Zhang et al. [

29] 

|$\upvarepsilon =\upbeta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+{\upvarepsilon}_{\mathrm{w}}\mathrm{W}+9683[\mathrm{S}]+1685.63\mathrm{A}\ (0.09\%\le \mathrm{A}\le 29.73\%)$|

|$\varepsilon =\upbeta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+{\varepsilon}_{\mathrm{w}}\mathrm{W}+9683[\mathrm{S}]+10.25\mathrm{A}+10.29\ (0.09\%\le \mathrm{A}\le 29.73\%)$|

 kJ/kg (−0.76%, 1.38%)
(−1.16%, 0.88%) Woody biomass 
Open in new tab

Table 2

Methods

. 

Year

. 

Authors

. 

Correlations

. 

Unit

. 

Error

. 

Applications

. 

(1) 1961 Rant [

17] ε = 0.95LHV (gas phase)
ε = 0.975LHV (liquid phase)
ε = LHV-hm (solid phase) kJ/kg  Fuels  2011 Song et al. [

18] ε = 1.047HHV kJ/kg (−2%, 2%) Dry biomass  2015 Zhang et al. [

19] 

|$\varepsilon =342.50+1.04\mathrm{HHV}\ \Big(7560\le \mathrm{HHV}\le 23997\Big)$|

|$\varepsilon =2289.87+1.01\mathrm{LHV}$|

 kJ/kg (−4.80%, 4.80%)
(−2.78%, 1.98%) Woody biomass  2016 Huang et al. [

23] ε = 0.978HHV + 2124.118 kJ/kg (−2%, 2%) Agricultural biomass  2018 Huang et al. [

37] ε = 0.890HHV + 5151.097 kJ/kg 5% Plastic waste  2020 Huang et al. [

36] ε = −1.2983 × 10−6(ΔcHθ)2 + 1.0561ΔcHθ-9.4419 × 10−2 (gas phase))
ε = −2.5674 × 10−6(ΔcHθ)2 + 1.1270ΔcHθ-5.9389 × 10−2 (liquid phase)
ε = −2.2668 × 10−6(ΔcHθ)2 + 0.97864ΔcHθ + 1.3779 × 10−2 (solid phase) MJ/kg 1.18%
1.67%
1.20% Biomass fuels (2) 1982 Shiehand Fan [

20] 

|$\varepsilon =8177.79[\mathrm{C}]+5.25[\mathrm{N}]+27892.63[\mathrm{H}]+4364.33[\mathrm{S}]-3173.660$|

|$+5763.41[\mathrm{F}]+2810.57[\mathrm{Cl}]+1204.30[\mathrm{Br}]+692.50[\mathrm{I}]-298.15{[\mathrm{S}]}_{\mathrm{ash}}\mathrm{A}$|

|$+0.15[\mathrm{O}](7837.667[\mathrm{C}]+33888.889[\mathrm{H}]-4236.1[\mathrm{O}]+3828.75[\mathrm{S}]$|

|$+4447.37[\mathrm{F}]+1790.9[\mathrm{Cl}]+681.97[\mathrm{Br}]+334.86[\mathrm{I}])$|

 kcal/kg  Solid and liquid fuels, biomass, waste  1995 Stepanov et al. [

21] 

|$\varepsilon =32904.076[\mathrm{C}]+2040.24[\mathrm{N}]+117714.337[\mathrm{H}]+16341.556[\mathrm{S}]-13405.192[\mathrm{O}]$|

|$+8278.838[\mathrm{F}]+348.382[\mathrm{Cl}]+416.593[\mathrm{Br}]+128.567[\mathrm{I}]-298.15{[\mathrm{S}]}_{\mathrm{ash}}\mathrm{A}$|

|$+0.15[\mathrm{O}][32833.33[\mathrm{C}]+141865.08([\mathrm{H}]-0.125[\mathrm{O}])+19500[\mathrm{S}]+9789.47[\mathrm{F}]$|

|$+705.06[\mathrm{Cl}]+1226.29[\mathrm{Br}]+685.47[\mathrm{I}]]$|

 kJ/kg  Solid and liquid fuels  2011 Song et al. [

18] ε = 1812.5 + 295.606[C] + 587.354[H] + 17.506[O] + 17.735[N] + 95.615[S]-31.8A kJ/kg (−1.5%, 1.5%) Dry biomass  2012 Song et al. [

22] ε = 363.439[C] + 1075.633[H]-86.308[O] + 4.147[N] + 190.798[S]-21.1A kJ/kg 0.338% Solid and liquid fuels  2017 Qian et al. [

24] ε = 119.184(1/3[C] + [H]-1/8[O] + 1/8[S])
ε = 920.08(1/3[C] + [H] + 1/8[S])
ε = 920.72(1/3[C] + [H]) kJ/kg 2.882%
0.643%
0.634% Dry biomass  2020 Aghbashlo et al. [

25] – kJ/kg Ultimate analysis: 0.207%
Proximate analysis: 0.506% Biomass (3) 1964 Szargut and Styrylska [

26] 

|$\varepsilon =\beta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+9683[\mathrm{S}]+{\upvarepsilon}_{\mathrm{ash}}\mathrm{A}+{\upvarepsilon}_{\mathrm{w}}\mathrm{W}$|

|$\upbeta =(1.0412+0.2160[\mathrm{H}]/[\mathrm{C}]-0.2499[\mathrm{O}]/[\mathrm{C}](1+0.7884[\mathrm{H}]/[\mathrm{C}])+0.0450[\mathrm{N}]/[\mathrm{C}])$|

|$/(1-0.3035[\mathrm{O}]/[\mathrm{C}])$|

(woody)

|$\upbeta =1.0437+0.0140[\mathrm{H}]/[\mathrm{C}]+0.0968[\mathrm{O}]/[\mathrm{C}]+0.0467[\mathrm{N}]/[\mathrm{C}];[\mathrm{O}]/[\mathrm{C}]\le 0.5$|

|$\upbeta =(1.044+0.0160[\mathrm{H}]/[\mathrm{C}]-0.3493[\mathrm{O}]/[\mathrm{C}](1+0.0531[\mathrm{H}]/[\mathrm{C}])+0.0493[\mathrm{N}]/[\mathrm{C}])$|

|$/(1-0.4124[\mathrm{O}]/[\mathrm{C}]);[\mathrm{O}]/[\mathrm{C}]\le 2$|

(other biomass) kJ/kg  Biomass  2000 Govin et al. [

27] 

|$-\varepsilon /{\Delta}_{\mathrm{c}}{H}^0=1.02034-0.01381[\mathrm{H}]/[\mathrm{C}]+0.03374[\mathrm{O}]/[\mathrm{C}]+0.02593[\mathrm{N}]/[\mathrm{C}]$|

|$-0.08408[\mathrm{S}]/[\mathrm{C}]$|

 kJ/kg  Fuel mixtures  2012 Bilgen et al. [

28] 

|$\varepsilon =\upbeta \mathrm{LHV}$|

|$\upbeta =1.047+0.0154[\mathrm{H}]/[\mathrm{C}]+0.0562[\mathrm{O}]/[\mathrm{C}]+0.5904[\mathrm{N}]/[\mathrm{C}](1-0.175[\mathrm{H}]/[\mathrm{C}]);$|

|$[\mathrm{O}]/[\mathrm{C}]<1$|

 kJ/kg  Organic fuels  2016 Zhang et al. [

29] 

|$\upvarepsilon =\upbeta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+{\upvarepsilon}_{\mathrm{w}}\mathrm{W}+9683[\mathrm{S}]+1685.63\mathrm{A}\ (0.09\%\le \mathrm{A}\le 29.73\%)$|

|$\varepsilon =\upbeta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+{\varepsilon}_{\mathrm{w}}\mathrm{W}+9683[\mathrm{S}]+10.25\mathrm{A}+10.29\ (0.09\%\le \mathrm{A}\le 29.73\%)$|

 kJ/kg (−0.76%, 1.38%)
(−1.16%, 0.88%) Woody biomass Methods

. 

Year

. 

Authors

. 

Correlations

. 

Unit

. 

Error

. 

Applications

. 

(1) 1961 Rant [

17] ε = 0.95LHV (gas phase)
ε = 0.975LHV (liquid phase)
ε = LHV-hm (solid phase) kJ/kg  Fuels  2011 Song et al. [

18] ε = 1.047HHV kJ/kg (−2%, 2%) Dry biomass  2015 Zhang et al. [

19] 

|$\varepsilon =342.50+1.04\mathrm{HHV}\ \Big(7560\le \mathrm{HHV}\le 23997\Big)$|

|$\varepsilon =2289.87+1.01\mathrm{LHV}$|

 kJ/kg (−4.80%, 4.80%)
(−2.78%, 1.98%) Woody biomass  2016 Huang et al. [

23] ε = 0.978HHV + 2124.118 kJ/kg (−2%, 2%) Agricultural biomass  2018 Huang et al. [

37] ε = 0.890HHV + 5151.097 kJ/kg 5% Plastic waste  2020 Huang et al. [

36] ε = −1.2983 × 10−6(ΔcHθ)2 + 1.0561ΔcHθ-9.4419 × 10−2 (gas phase))
ε = −2.5674 × 10−6(ΔcHθ)2 + 1.1270ΔcHθ-5.9389 × 10−2 (liquid phase)
ε = −2.2668 × 10−6(ΔcHθ)2 + 0.97864ΔcHθ + 1.3779 × 10−2 (solid phase) MJ/kg 1.18%
1.67%
1.20% Biomass fuels (2) 1982 Shiehand Fan [

20] 

|$\varepsilon =8177.79[\mathrm{C}]+5.25[\mathrm{N}]+27892.63[\mathrm{H}]+4364.33[\mathrm{S}]-3173.660$|

|$+5763.41[\mathrm{F}]+2810.57[\mathrm{Cl}]+1204.30[\mathrm{Br}]+692.50[\mathrm{I}]-298.15{[\mathrm{S}]}_{\mathrm{ash}}\mathrm{A}$|

|$+0.15[\mathrm{O}](7837.667[\mathrm{C}]+33888.889[\mathrm{H}]-4236.1[\mathrm{O}]+3828.75[\mathrm{S}]$|

|$+4447.37[\mathrm{F}]+1790.9[\mathrm{Cl}]+681.97[\mathrm{Br}]+334.86[\mathrm{I}])$|

 kcal/kg  Solid and liquid fuels, biomass, waste  1995 Stepanov et al. [

21] 

|$\varepsilon =32904.076[\mathrm{C}]+2040.24[\mathrm{N}]+117714.337[\mathrm{H}]+16341.556[\mathrm{S}]-13405.192[\mathrm{O}]$|

|$+8278.838[\mathrm{F}]+348.382[\mathrm{Cl}]+416.593[\mathrm{Br}]+128.567[\mathrm{I}]-298.15{[\mathrm{S}]}_{\mathrm{ash}}\mathrm{A}$|

|$+0.15[\mathrm{O}][32833.33[\mathrm{C}]+141865.08([\mathrm{H}]-0.125[\mathrm{O}])+19500[\mathrm{S}]+9789.47[\mathrm{F}]$|

|$+705.06[\mathrm{Cl}]+1226.29[\mathrm{Br}]+685.47[\mathrm{I}]]$|

 kJ/kg  Solid and liquid fuels  2011 Song et al. [

18] ε = 1812.5 + 295.606[C] + 587.354[H] + 17.506[O] + 17.735[N] + 95.615[S]-31.8A kJ/kg (−1.5%, 1.5%) Dry biomass  2012 Song et al. [

22] ε = 363.439[C] + 1075.633[H]-86.308[O] + 4.147[N] + 190.798[S]-21.1A kJ/kg 0.338% Solid and liquid fuels  2017 Qian et al. [

24] ε = 119.184(1/3[C] + [H]-1/8[O] + 1/8[S])
ε = 920.08(1/3[C] + [H] + 1/8[S])
ε = 920.72(1/3[C] + [H]) kJ/kg 2.882%
0.643%
0.634% Dry biomass  2020 Aghbashlo et al. [

25] – kJ/kg Ultimate analysis: 0.207%
Proximate analysis: 0.506% Biomass (3) 1964 Szargut and Styrylska [

26] 

|$\varepsilon =\beta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+9683[\mathrm{S}]+{\upvarepsilon}_{\mathrm{ash}}\mathrm{A}+{\upvarepsilon}_{\mathrm{w}}\mathrm{W}$|

|$\upbeta =(1.0412+0.2160[\mathrm{H}]/[\mathrm{C}]-0.2499[\mathrm{O}]/[\mathrm{C}](1+0.7884[\mathrm{H}]/[\mathrm{C}])+0.0450[\mathrm{N}]/[\mathrm{C}])$|

|$/(1-0.3035[\mathrm{O}]/[\mathrm{C}])$|

(woody)

|$\upbeta =1.0437+0.0140[\mathrm{H}]/[\mathrm{C}]+0.0968[\mathrm{O}]/[\mathrm{C}]+0.0467[\mathrm{N}]/[\mathrm{C}];[\mathrm{O}]/[\mathrm{C}]\le 0.5$|

|$\upbeta =(1.044+0.0160[\mathrm{H}]/[\mathrm{C}]-0.3493[\mathrm{O}]/[\mathrm{C}](1+0.0531[\mathrm{H}]/[\mathrm{C}])+0.0493[\mathrm{N}]/[\mathrm{C}])$|

|$/(1-0.4124[\mathrm{O}]/[\mathrm{C}]);[\mathrm{O}]/[\mathrm{C}]\le 2$|

(other biomass) kJ/kg  Biomass  2000 Govin et al. [

27] 

|$-\varepsilon /{\Delta}_{\mathrm{c}}{H}^0=1.02034-0.01381[\mathrm{H}]/[\mathrm{C}]+0.03374[\mathrm{O}]/[\mathrm{C}]+0.02593[\mathrm{N}]/[\mathrm{C}]$|

|$-0.08408[\mathrm{S}]/[\mathrm{C}]$|

 kJ/kg  Fuel mixtures  2012 Bilgen et al. [

28] 

|$\varepsilon =\upbeta \mathrm{LHV}$|

|$\upbeta =1.047+0.0154[\mathrm{H}]/[\mathrm{C}]+0.0562[\mathrm{O}]/[\mathrm{C}]+0.5904[\mathrm{N}]/[\mathrm{C}](1-0.175[\mathrm{H}]/[\mathrm{C}]);$|

|$[\mathrm{O}]/[\mathrm{C}]<1$|

 kJ/kg  Organic fuels  2016 Zhang et al. [

29] 

|$\upvarepsilon =\upbeta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+{\upvarepsilon}_{\mathrm{w}}\mathrm{W}+9683[\mathrm{S}]+1685.63\mathrm{A}\ (0.09\%\le \mathrm{A}\le 29.73\%)$|

|$\varepsilon =\upbeta (\mathrm{LHV}+\mathrm{W}{\mathrm{h}}_{\mathrm{w}})+{\varepsilon}_{\mathrm{w}}\mathrm{W}+9683[\mathrm{S}]+10.25\mathrm{A}+10.29\ (0.09\%\le \mathrm{A}\le 29.73\%)$|

 kJ/kg (−0.76%, 1.38%)
(−1.16%, 0.88%) Woody biomass 
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Intelligent prediction models

Except for correlation estimation models, intelligent prediction models were also developed for the prediction of chemical exergy of substance, especially organic substances. Generally speaking, the input parameters of these models can be divided into two categories: one is molecular weight, atomic polarizability and number of atoms [30, 31]; the other is the number of occurrences of chemical substructures [32, 33]. In addition, there were also intelligent models using molecular formula and standard boiling point [34], or element composition [35] as input parameters. Table 3 presents the key information of these models.

Table 3

Year

. 

Authors

. 

Input parameters

. 

Methods

. 

Error/accuracy

. 

Applications

. 

2007 Gharagheizi et al. [

30] Molecular weight, atomic polarizability and number of atoms Genetic algorithm R2 = 0.9977 134 organic substances 2014 Gharagheizi et al. [

32] Number of occurrences of chemical substructures Group contribution method 1.6% 133 organic substances 2017 Wu et al. [

31] Molecular weight, atomic polarizability and number of atoms Genetic algorithm and support vector machine 1.8351% 134 organic substances 2018 He et al. [

38] Molecular weight, atomic polarizability and number of atoms Neural network and radial basis function 2.21% 135 organic substances 2018 Gharagheizi et al. [

33] Number of occurrences of chemical substructures Group contribution method 0.3% 3148 organic substances 2020 Haghbakhsh and Raeissi [

34] Molecular formula and standard boiling point Atomic contribution method 0.64% 4129 organic substances 2020 Petković et al. [

35] Element composition Adaptive neuro fuzzy inference system R2 = 0.919 Agricultural biomass Year

. 

Authors

. 

Input parameters

. 

Methods

. 

Error/accuracy

. 

Applications

. 

2007 Gharagheizi et al. [

30] Molecular weight, atomic polarizability and number of atoms Genetic algorithm R2 = 0.9977 134 organic substances 2014 Gharagheizi et al. [

32] Number of occurrences of chemical substructures Group contribution method 1.6% 133 organic substances 2017 Wu et al. [

31] Molecular weight, atomic polarizability and number of atoms Genetic algorithm and support vector machine 1.8351% 134 organic substances 2018 He et al. [

38] Molecular weight, atomic polarizability and number of atoms Neural network and radial basis function 2.21% 135 organic substances 2018 Gharagheizi et al. [

33] Number of occurrences of chemical substructures Group contribution method 0.3% 3148 organic substances 2020 Haghbakhsh and Raeissi [

34] Molecular formula and standard boiling point Atomic contribution method 0.64% 4129 organic substances 2020 Petković et al. [

35] Element composition Adaptive neuro fuzzy inference system R2 = 0.919 Agricultural biomass 
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Table 3

Year

. 

Authors

. 

Input parameters

. 

Methods

. 

Error/accuracy

. 

Applications

. 

2007 Gharagheizi et al. [

30] Molecular weight, atomic polarizability and number of atoms Genetic algorithm R2 = 0.9977 134 organic substances 2014 Gharagheizi et al. [

32] Number of occurrences of chemical substructures Group contribution method 1.6% 133 organic substances 2017 Wu et al. [

31] Molecular weight, atomic polarizability and number of atoms Genetic algorithm and support vector machine 1.8351% 134 organic substances 2018 He et al. [

38] Molecular weight, atomic polarizability and number of atoms Neural network and radial basis function 2.21% 135 organic substances 2018 Gharagheizi et al. [

33] Number of occurrences of chemical substructures Group contribution method 0.3% 3148 organic substances 2020 Haghbakhsh and Raeissi [

34] Molecular formula and standard boiling point Atomic contribution method 0.64% 4129 organic substances 2020 Petković et al. [

35] Element composition Adaptive neuro fuzzy inference system R2 = 0.919 Agricultural biomass Year

. 

Authors

. 

Input parameters

. 

Methods

. 

Error/accuracy

. 

Applications

. 

2007 Gharagheizi et al. [

30] Molecular weight, atomic polarizability and number of atoms Genetic algorithm R2 = 0.9977 134 organic substances 2014 Gharagheizi et al. [

32] Number of occurrences of chemical substructures Group contribution method 1.6% 133 organic substances 2017 Wu et al. [

31] Molecular weight, atomic polarizability and number of atoms Genetic algorithm and support vector machine 1.8351% 134 organic substances 2018 He et al. [

38] Molecular weight, atomic polarizability and number of atoms Neural network and radial basis function 2.21% 135 organic substances 2018 Gharagheizi et al. [

33] Number of occurrences of chemical substructures Group contribution method 0.3% 3148 organic substances 2020 Haghbakhsh and Raeissi [

34] Molecular formula and standard boiling point Atomic contribution method 0.64% 4129 organic substances 2020 Petković et al. [

35] Element composition Adaptive neuro fuzzy inference system R2 = 0.919 Agricultural biomass 
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It is worth noting that, except for the estimation models given by Huang et al. [36] and Shieh and Fan [20], the above literature tended to focus only on exergy calculation instead of enthalpy calculation at the same time, which may not meet the thermodynamic consistency in subsequent calculation for energy quality. Only when exergy and enthalpy are calculated based on the consistent thermodynamic standard state and environmental reference state can the energy quality factor of substance be accurately evaluated.

Graphical analysis method and its application

The applications of energy quality concerned in this paper refer exclusively to analysis methods and applications developed on the basis of (1), excluding studies only related to energy quality in the background. On the basis of accurate definition and calculation of energy factor quality, Zheng et al. developed a graphic analysis method. In 2005, they proposed a new thermodynamic analysis method by taking the energy quality factor α as the evaluation criterion and utilizing the α-h diagram as a graphical tool [39]. The case study on generator absorber heat exchange cycle showed that the α-h diagram can clearly express the energy quality levels at various state points in complex cycles, as well as the energy quality level changes and energy loads during thermodynamic process, which was helpful to observe the specific principles of energy cascade utilization. Similar studies were also found in subsequent paper [40]. In 2009, they added a coordinate exergy ε to the α-H diagram, making it a 3D α-h-ε diagram for thermodynamic process analysis [41]. The graphical analysis method was validated and demonstrated by four routes of methane combustion (direct combustion, preheating combustion, steam reforming combustion and CO2 reforming combustion). In 2017, they applied this analysis method to evaluate four routes of CO2 hydrogenation (the products were CO, methanol, methane and dimethyl ether, respectively), and the results showed that the methanol route is a promising option [42]. Here, the methanol route of CO2 hydrogenation could be taken as an example to demonstrate the principle of the α-h-ε diagram. As shown in Fig. 2, the reactants involved in the reaction were CO2 and hydrogen with a molar ratio of 1:3, and the products were methanol and water. The substances before and after the reaction each determined a state point on the α-h-ε diagram. The connection between state points represented the reaction process. Combined with the projection of the process line on three planes, the changes of parameters α, h and ε in the process can be clearly seen, and then the performance of the process in terms of thermodynamics can be judged.

Figure 2

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α-H-ε diagram of the methanol route of CO2 hydrogenation

For complex systems, they took the unit process as the horizontal axis and the energy quality factor α as the vertical axis to form the distribution diagram of energy quality factor α. The values of exergy and enthalpy before and after the processes were marked in the diagram to indicate the changes of energy, exergy and energy quality factor in each process of the system. The distribution diagram of energy quality factor was applied to their studies on the low-rank coal based process system [43], absorption power and cooling cogeneration cycle [44, 45] and chemical cascade coproduction system [46]. In 2017, Jing et al. [47] also analyzed a polygeneration system coproducing semicoke, coal gas, tar and power with the α-H-ε diagram and the distribution diagram of energy quality factor. They pointed out that the difference in the energy quality factor was the main reason for the exergy loss of the system. In 2020, Zhang et al. [48] studied exergy flow and efficiency of the integrated system of coal gasification and Chemical-looping hydrogen generation with the distribution diagram of energy quality factor, and the results showed that the high efficiency of the integrated system attributed to a reasonable energy matching relationship.

Summarizing the existing studies on energy quality, it can be concluded that the energy quality factor is a dimensionless state quantity with a clear definition and calculation method. Its calculation requires defining the environmental reference state. Due to the non-equilibrium nature of the human environment, different researchers have put forward different views on the definition of the environmental reference state. In general, equilibrium and proximity to the real environment are not compatible and the definition of the reference state should consider both of two aspects. In addition, the above studies focused on the calculation of the exergy and enthalpy of substance, especially fuels and biomass. Although this was the basis of the energy quality factor, its application has not received sufficient attention. In terms of energy forms, the existing studies on energy quality were mostly limited to the physical energy and chemical energy contained in substances, but for other forms of energy, such as radiant energy, there were few related discussions [49].

ENERGY GRADE

Energy grade is not a concept independent of energy quality. The national standard of China GB/T 14909-2021 [16] pointed out that energy grade can be divided into energy grade of substance and energy grade of the process (energy level), among which energy grade of substance can be described as the energy quality factor, which has been recognized by scholars [42, 50]. This shows that the energy quality factor and energy grade can communicate with each other in certain scenarios, but energy grade can also characterize the property of thermodynamic processes, which is a function that the energy quality factor does not possess. It can be considered that the energy quality and energy grade gradually intersect in independent development. In order to clarify the relationship and difference between the two, it is necessary to review the concepts related to energy grade.

Difference and connection with energy quality

] proposed the concept of availability factor, defined as

$$ \begin{align} A=\frac{\varDelta \varepsilon \left(T,p,x\right)}{\varDelta H\left(T,p,x\right)}, \end{align}$$

(14)

]. Obviously, energy grade A here is a process variable related to the path, thus avoiding the obstacle to the evaluation for energy quality caused by the definition of the reference state.

In 1982, Japanese scholars Ishida and Kawamura [ 6 ] proposed the concept of availability factor, defined aswhich was used to characterize energy grade of a thermodynamic process, also recorded as energy level. The same definition appeared in other studies but may be called different names, such as the normalized exergy proposed by Hebecker and Bittrich [ 51 ]. Obviously, energy grade A here is a process variable related to the path, thus avoiding the obstacle to the evaluation for energy quality caused by the definition of the reference state.

In 2017, Zheng et al. [42] decomposed the concept of energy grade into energy grades of the process and substance, in which energy grade of the process followed the definition of (14), and energy grade of substance was described by the emery quality factor. In the same year, Shi et al. made a similar argument on energy grade [50]. This view was adopted by the national standard of China (GB/T 14909-2021). Thus, the concept of energy quality has been incorporated into the physical meaning of energy grade. It can be seen that the concepts of energy grade and energy quality factor were proposed in the same period, and later with the development and application of these two concepts, they gradually crossed in the physical meaning.

Principle of graphical analysis method

Since energy grade of the process is a process variable related to the path, it avoids the obstacle to calculation caused by the definition of the reference state. In addition, the calculation of energy grade of substance (energy quality factor) has been presented in detail in Section 2.1. Therefore, the focus here is directly on the application of the concept of energy grade.

In 1986, Ishida and Zheng proposed a graphic exergy analysis method [expressed as energy utilization diagram (EUD), i.e. A-∆H diagram] based on energy grade A. This analysis method was utilized to analyze exergy destruction during the process of energy donation and acceptance, so as to reveal the thermodynamic principles of exergy destruction during the process of energy transfer and conversion [52]. The basic principle of EUD can be illustrated in Fig. 3.

Figure 3

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Schematic diagram of the principle of EUD

), exergy destruction during a thermodynamic process can be written as

$$ \begin{equation} E{x}_{\mathrm{D}}=\int \left({A}_{\mathrm{ed}}-{A}_{\mathrm{ea}}\right)\mathrm{d}H, \end{equation}$$

(15)

, where Aed and Aea stand for energy grades of energy donator and acceptor, respectively. Based on this principle, each process of thermodynamic systems can be expressed on the EUD, so as to obtain abundant information about the change and matching of energy grade and exergy destruction during the process of energy transfer and conversion, thus guiding the design and optimization of the system. In 2000, Ishida [

] condensed his research methodology and pointed out that thermodynamics can be developed hierarchically: the thermodynamics for substances, processes and process systems, where the EUD could measure the energy utilization potential of the system and indicate the potential for the improvement of energy utilization.

In the process of energy transfer or conversion, there are always energy donators and energy acceptors. According to the conservation of energy, the amount of energy in the process of energy donation and acceptance (abscissa ∆H) remains unchanged, but energy grade (ordinate A) will be reduced due to the irreversible loss. According to the definition of energy grade ( 14 ), exergy destruction during a thermodynamic process can be written aswhich can be indicated as the shadowing area in Fig. 3 , where Aand Astand for energy grades of energy donator and acceptor, respectively. Based on this principle, each process of thermodynamic systems can be expressed on the EUD, so as to obtain abundant information about the change and matching of energy grade and exergy destruction during the process of energy transfer and conversion, thus guiding the design and optimization of the system. In 2000, Ishida [ 7 ] condensed his research methodology and pointed out that thermodynamics can be developed hierarchically: the thermodynamics for substances, processes and process systems, where the EUD could measure the energy utilization potential of the system and indicate the potential for the improvement of energy utilization.

Applications of the graphic exergy analysis method

As an exergy analysis tool, the graphic exergy analysis method can be widely applied in the analysis of thermodynamic systems and components in various scenarios, especially the complex processes accompanying the substance conversion (chemical reactions).

Power cycle systems

In the field of power cycle systems, Ishida et al. [53] firstly applied the EUD to perform the energy and exergy analysis of the coal gasification-combined power cycle in 1986. On the EUD, the energy balance, exergy destruction and the strength of the driving force of each process were revealed graphically, which demonstrated the effectiveness of the graphic exergy analysis method. Since then, the EUD has been widely used in the design and optimization of power cycle systems. Later (1986–2001), they also extended the analysis method to liquefied natural gas power-generation systems [54], chemical-looping combustion power-generation system systems [55–57], humid air gas turbine cycles [58, 59] and supercritical steam turbine and combined cycles [60–62]. In 2011, Zhao and Yue [63] analyzed humid air turbine cycle with solar energy for methanol decomposition by means of EUD, and the results showed that low-grade solar energy could be converted into high-grade chemical energy through methanol reforming process. Although the grade of decomposed syngas after reforming was reduced, energy grade matching of the whole system was more reasonable, and the energy cascade utilization was enhanced; thereby, the exergy efficiency of the system could be improved.

In 2018, Ma et al. [64] adopted EUD to investigate the performance improvement potentials of the intercooling between compressor stages in supercritical Brayton cycle. Xu et al. [65] studied a solar-lignite hybrid power generation process by means of EUD, which effectively improved the performance of the hybrid energy conversion system. Also, they analyzed exergy destruction of a supercritical coal-fired power generation system incorporating a supplementary supercritical CO2 cycle. The results proved the economic and practical feasibility of integrating the supercritical CO2 cycle existing supercritical power plants [66]. In 2020, Ji et al. [67] carried out an exergy analysis on a solid oxide fuel cell turbine-less jet engines with traditional exergy analysis and advanced exergy analysis (EUD). The conclusions for improvement priority of system components suggested by two exergy analyses were different: combustors, SOFCs and heat exchangers for traditional exergy analysis, while nozzle, compressor, heat exchanger and motor for EUD. In 2021, Zhang et al. [68] conducted an exergy analysis on a novel system integrating chemical-looping hydrogen generation and solid oxide fuel cell with the aid of EUD, and results showed that the cascade utilization of waste heat and the high-efficiency hydrogen production were the main reasons for the high performance of the system.

Production and utilization of secondary fuels

In the field of the production and utilization of secondary fuels (such as methanol/hydrogen), Okazaki et al. [69] studied the exergy regeneration of direct conversion of methane into methanol by combining the concept of energy grade in 2002 and pointed out that the grade of low temperature heat energy could be improved in the reforming process of methanol to hydrogen. In 2006, Cao and Zheng [70] investigated the exergy regeneration of O2/CO2 power cycle with chemical recuperation by CO2 reforming of methane by the aid of EUD and revealed the thermodynamic principle of energy integration. In 2010, Bian et al. [71] developed the ethane recovery process from natural gas with liquefied natural gas cryogenic energy and optimized it by the aid of graphic exergy analysis method, then they applied this method to the study of natural gas liquids recovery process from oil field associated gas [72]. In 2016, Yan et al. [73, 74] applied EUD to analyze the energy cascade release for coal oxidation in the air and supercritical water and pointed out that supercritical water oxidation reduced energy grade of coal, thus narrowing the grade difference between chemical energy and thermal energy, and exergy destruction was reduced.

In 2017, Wu et al. [75] studied the exergy destruction mechanism of coal gasification by means of EUD and revealed the role of each reaction in coal gasification. In 2019, Chen et al. [76] adopted the graphic exergy analysis method to analyze and compare coal gasification with supercritical water and O2-H2O. The results showed that supercritical water coal gasification was superior to O2-H2O coal gasification, and the heating of water in both gasification technologies leaded to the maximum exergy destruction (40.21% and 53.57%, respectively). Also in 2019, Yan et al. [77] carried out an exergy analysis on indirect coal combustion such as supercritical water gasification re-combustion, steam reforming re-combustion and chemical-looping combustion by means of EUD. It was pointed out that indirect combustion changed the release pathways of chemical exergy, and reduced energy grade difference between chemical exergy of fuel and thermal energy in combustion; thus, exergy destruction was reduced. In 2020, Ruya et al. [78] adopted EUD to study hydrogen production from empty fruit bunch and palm oil mill effluent through supercritical water gasification and disclosed ~72–87% of exergy destruction was attributed to feed preheating.

Polygeneration systems

In the field of polygeneration systems, Li et al. [79] investigated a coal-based methanol and power polygeneration system with partial gasification in 2014. EUD analysis showed that exergy destruction in methanol synthesis could be greatly reduced by recovering unreacted gas. In 2016, Wang and Fu [80] proposed a cogeneration system by combining solar energy and methane chemical-looping combustion. By comparing EUD of the proposed system with that of the reference system, they explained the performance improvement mechanism of the proposed system. Similar analysis was conducted on the polygeneration system integrating chemical-looping combustion and methane reforming with CO2 [81]. In 2019, they proposed three paths for comprehensive utilization of cold-end energy in coal-fired power plants, namely reboiler condensate recirculation, absorption heat transformer and multi-stage air heating. EUD analysis disclosed the energy-saving mechanism of these three pathways [82].

Refrigeration and heat pump systems

The applications of EUD in field of refrigeration and heat pump systems were promoted by Ishida’s group. They analyzed the absorption heat pumps and heat transformers by EUD earlier than 2000 [83–86], and the results provided detailed information on internal phenomena such as the driving forces and the distribution of the exergy loss in each subsystem. Liu et al. [87] analyzed the energy-saving potential of heat pump heating system for coal-fired power plants by means of EUD and proposed a new system serial-parallel coupled with two type I lithium bromide absorption heat pumps in 2016. In 2019, Seki et al. [88] investigated two absorption heat pumps based on EUD, including an absorber heat exchanger and solution heat exchanger. The results proved that EUD could comprehensively display exergy destruction and improvement margin of components as well as operational properties of working fluids.

Distillation and wastewater treatment

The applications of EUD in distillation were also promoted by Ishida’s group. Based on EUD, they analyzed the energy transformation and exergy losses in the distillation column earlier than 2000 [89–91] and decomposed the exergy losses into losses caused by premixing in liquid phase and those caused by premixing in vapor phase. Since then, no relevant research appeared for a long time, until recently. In 2021, Cao et al. [92] adopted EUD to investigate multi-effect distillation-distillation-thermal vapor compression systems, and the results showed that thermal vapor compression could solve energy grade mismatch and improve energy utilization. Zhang et al. [93] studied a supercritical water oxidation system containing a hydrothermal flame by means of EUD, and the results showed that the introduction of evaporation module could greatly reduce the exergy input.

Cascade utilization principle of high-grade energy

Jin’s group made a great contribution to the research on the graphic exergy analysis method. It is especially worth mentioning that they applied it to the broader intersection field of thermal physics and chemistry. Their characteristic research objects include combined cycles by coupling solar energy and chemical-looping combustion [94–100], polygeneration systems for power and various fuels (coke [101], methanol [102, 103], hydrogen [104–110]). These studies involved a variety of systems in which the energy sources included natural gas, coal, solar energy and middle-low temperature waste heat. In the long-term research, they developed the energy cascade utilization principle of fossil fuel, which can be illustrated in Fig. 4.

Figure 4

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Schematic diagram of high-grade energy cascade utilization principle

The grade of low-grade energy (such as solar thermal energy and waste heat) AL is lower than that of thermal energy required in thermodynamic cycles Ath, so it cannot be utilized as the heat source in conventional cycles. The grade of low-grade energy can be improved (AL → AH2) by rationally designing the grade reduction process (AH1 → AH2) of high-grade energy (such as chemical energy).

Although exergy destruction of this process is inescapable, because the system receives low-grade energy (the value of received exergy could be indicated as the area of rectangular hijk), the exergy input the system could increase from the area of rectangular ablj area to that of eflk. Meanwhile, the decrease of the grade of high-grade energy could reduce the grade difference with the thermal energy required in cycles(∆(AH1-Ath) → ∆(AH2-Ath)), so that exergy destruction of converting high-grade energy into required thermal energy decreases from the area of rectangular abcd to that of efcg. In this way, energy grade matching of the whole system is more reasonable, i.e. the cascade utilization of high-grade energy is enhanced. In addition, low-grade energy is recovered. As a result, the overall performance of the system could be improved. This conclusion was reflected in detail in the cascade utilization principle of chemical energy and physical energy of fossil fuel [111].

Based on the concept and theory of energy grade, the conclusions of the above studies present considerable forward-looking, which also show the applicability and vitality of energy grade in a wide range of fields, especially in the multi-energy complementary cogeneration systems integrating substance conversion (chemical reaction) processes. However, it can be observed from the literature distribution that the applications of energy grade concentrate on the elucidation of energy grade of the process, which may be attributed to the unit role of processes in thermodynamic systems. Benefiting from this advantage, exergy analysis method based on energy grade A and processes as the core (EUD) was more widely applied, compared with the analysis method based on energy quality factor α and states as the core (α-h-ε diagram). Nonetheless, the applications of energy grade A are still limited to the utilization of thermal energy and chemical energy and have not yet been involved in other broader forms of energy.

COMPARISON OF ENERGY QUALITY AND ENERGY GRADE: A SIMPLE CASE

2 and hydrogen to generate methane is taken as an example to illustrate the calculation and analysis methods of energy quality factor α (energy grade of substance) and energy grade of the process A. The reaction is

$$ \begin{equation} {\mathrm{CO}}_2+{4\mathrm{H}}_2\to {\mathrm{CH}}_4+{2\mathrm{H}}_2\mathrm{O}. \end{equation}$$

(16)

In order to visually show the difference in definition and function of energy quality and energy grade, the reaction of COand hydrogen to generate methane is taken as an example to illustrate the calculation and analysis methods of energy quality factor α (energy grade of substance) and energy grade of the process A. The reaction is

Exergy, enthalpy and energy quality factors of the reactants and products can be determined by the calculation method in Section 2.1, as shown in Table 4.

Table 4

Parameters

. 

CO2

. 

H2

. 

CH4

. 

H2O

. 

ε (kJ/mol) 19.999 235.190 830.393 0 H (kJ/mol) 83.772 274.158 885.960 20.871 α 0.239 0.858 0.937 0 Parameters

. 

CO2

. 

H2

. 

CH4

. 

H2O

. 

ε (kJ/mol) 19.999 235.190 830.393 0 H (kJ/mol) 83.772 274.158 885.960 20.871 α 0.239 0.858 0.937 0 
Open in new tab

Table 4

Parameters

. 

CO2

. 

H2

. 

CH4

. 

H2O

. 

ε (kJ/mol) 19.999 235.190 830.393 0 H (kJ/mol) 83.772 274.158 885.960 20.871 α 0.239 0.858 0.937 0 Parameters

. 

CO2

. 

H2

. 

CH4

. 

H2O

. 

ε (kJ/mol) 19.999 235.190 830.393 0 H (kJ/mol) 83.772 274.158 885.960 20.871 α 0.239 0.858 0.937 0 
Open in new tab

Accordingly, the EUD corresponding to the reaction process can be presented as Fig. 5. The enthalpy change ΔrH and exergy change Δrε of the reaction are −252.702 and −130.366 kJ/mol, respectively. The enthalpy change ΔrH is negative, indicating that the reaction releases heat to the environment, and acts as an energy donor in the energy transfer, while the environment is the energy acceptor. Energy grade of the reaction process Aed = Δrε/ΔrH = 0.516. As the heat in the environment does not contain exergy, its energy grade Aea is zero. The grade difference between Aed and Aea leads to exergy destruction, whose value could be indicated as the shadow area in Fig. 5.

Figure 5

Open in new tabDownload slide

EUD of the reaction of CO2 hydrogenation to methane

It can be observed from Table 4 and Fig. 5 that the energy quality factor focuses on describing the state properties of substance, while energy grade focuses on describing the process properties of energy conversion and transfer, which is the most important difference between the two. Specifically, the energy quality factor could describe the proportion of exergy in the energy contained in substances and is adopted to evaluate the potential of different chemical substances in energy utilization. Energy grade characterizes the relative relationship between exergy change and enthalpy change in the process of energy conversion and transfer and is highly related to the pathway of energy utilization. Combined the law of energy conservation and the principle of energy dissipation, energy grade could provide guidance for the cascade utilization of energy.

CONCLUSIONS AND PROSPECTS

Summarizing the existing literature, it can be concluded that the research on energy quality mostly focus on the calculation of the energy quality factor, while the research on energy grade mostly focuses on the application of the graphic exergy analysis method based on the concept of energy grade. However, little attention has been paid to the more fundamental thermodynamic issues hidden behind the concepts. It is noted that the energy forms covered by the existing research system for energy quality and grade system are still limited to thermal energy and chemical energy, while other forms of energy, such as radiant energy, sound energy and magnetic energy, are out of reach. The root cause of this dilemma may be explained by the principles of thermodynamics. On one hand, the first and second laws of thermodynamics state that the quantity of energy remains the same during the conversion and transfer processes, but its quality degrades, which is the origin of the concepts of energy quality and energy grade. One the other hand, energy quality and energy grade can be regarded as sub-concepts of exergy, while exergy is a thermodynamic property highly dependent on the environmental reference state. Therefore, under the specified thermodynamic temperature scale, the concepts of energy quality and energy grade must rely on a third-party perspective, i.e. the earth environment in which human beings live. However, this environment is not universal in the context of thermodynamics. As a result, the concepts of energy quality and energy grade established on this basis inevitably have a strong engineering flavor, which lack the generality and universality that thermodynamic concepts should have, so they are difficult to generalize to the universal forms of energy.

In view of this, it is recommended that future research should focus on the following points.

(1) Normalization of the use of terms: historical evidence shows that the energy quality factor and energy grade were proposed and developed independently. With the development and application of these two concepts, the concept of energy grade gradually reached the physical meaning what the energy quality factor refers to, namely the energy grade of substance. Therefore, the use of correlated terms should be more normative, in particular, with regard to the energy grade, and it should be noted whether the object is substance or a process.

(2) Extension of the concepts of energy quality and energy grade: one should move deeper into the thermodynamic essence behind the two concepts so that they could be applied to more general forms of energy, not just limited to thermal and chemical energy.

(3) Completeness of parameters describing energy properties: one should consider if additional parameters are needed to describe undiscovered properties of energy in addition to energy quality and grade. In fact, some scholars have put forward the concepts of energy and energy potential in this regard [112, 113], even if their full physical meanings remain to be better determined. Besides, while accurately describing all aspects of energy properties, it is also necessary to avoid confusion between the concepts.

SUPPLEMENTARY DATA

Supplementary data are available at Oxford Open Energy online.

ACKNOWLEDGEMENTS

Study Funding

The work is supported by the National Natural Science Foundation of China (52176017) and the China Postdoctoral Science Foundation (2021TQ0237).

APC Funding

There is no Article Processing Charge for this paper.

CONFLICT OF INTEREST

None declared.

AUTHORS’ CONTRIBUTIONS

R.C.: conceptualization, data curation, writing (original draft), review and editing;

W.X. and R.Z.: validation, writing, review and editing;

S.D.: methodology, supervision;

L.Z.: methodology, funding acquisition, project administration;

W.Y., L.J. and Z.L.: investigation.

DATA AVAILABILITY

The data underlying this article will be shared on reasonable request to the corresponding author.

References

[1]

Reistad

GM

.

Available energy conversion and utilization in the United States

.

J Eng Power

.

1975

;

97

:

429

–

34

[2]

Moran

MJ

,

Shapiro

HN

,

Boettner

DD

et al. 

Fundamentals of Engineering Thermodynamics

, 9th edn.

New Jersey

:

John Wiley & Sons

,

2018

, 9th edn.

[3]

Valero

ABE

.

Exergetic evaluation of natural mineral capital (2) application of the methodology to current world reserves

.

ECOS

.

2002

;

2

:

63

–

78

[4]

Rosen

MA

.

Using exergy to assess regional and national energy utilization: a comparative review

.

Arab J Sci Eng

.

2013

;

38

:

251

–

61

[5]

Zhu

M

Exergy Analysis of Energy Systems

.

Beijing

:

Tsinghua University Press

,

1986

[6]

Ishida

M

,

Kawamura

K

.

Energy and exergy analysis of a chemical process system with distributed parameters based on the enthalpy-direction factor diagram

.

Ind Eng Chem Process Design Dev

.

1982

;

21

:

690

–

5

[7]

Ishida

M

.

Hierarchical structure of thermodynamics

.

Appl Energy

.

2000

;

67

:

221

–

30

[8]

Jensen

J

Energy Storage. In:

Sequeira

CAC

,

Hooper

A

, (eds.),

Solid State Batteries

.

Dordrecht, Netherlands

:

Springer

,

1985

,

377

–

86

[9]

Ohta

T

Energy Technology: Sources, Systems and Frontier Conversion

.

Amsterdam

:

Newnes

,

2012

[10]

Ahrendts

J

.

Reference states

.

Energy

.

1980

;

5

:

666

–

77

[11]

Kameyama

H

,

Yoshida

K

,

Yamauchi

S

et al. 

Evaluation of reference exergies for the elements

.

Appl Energy

.

1982

;

11

:

69

–

83

[12]

Szargut

J

.

Chemical exergies of the elements

.

Appl Energy

.

1989

;

32

:

269

–

86

[13]

Rivero

R

,

Garfias

M

.

Standard chemical exergy of elements updated

.

Energy

.

2006

;

31

:

3310

–

26

[14]

Zheng

D

,

Chen

M

,

Song

Z

et al. 

GB/T 14909-1994. Technical Guides for Exergy Analysis

.

Beijing

:

State Administration of Technical Supervision of China

,

1994

[15]

Zheng

D

,

Wu

X

,

Song

Z

et al. 

GB/T 14909-2005. Technical Guides for Exergy Analysis in Energy System

.

Beijing

:

General Administration of Quality Supervision, Inspection and Quarantine of China, Standardization Administration of China

,

2005

[16]

Zheng

D

,

Shi

L

,

Zhang

N

et al. 

GB/T 14909-2021. Technical Guidelines for Exergy Analysis in Energy Systems

.

Beijing

:

State Administration for Market Regulation of China, Standardization Administration of China

,

2021

[17]

Rant

Z

.

Towards the estimation of specific exergy of fuels

.

Germanica

.

1961

;

10

:

172

–

6

[18]

Song

GH

,

Shen

LH

,

Xiao

J

.

Estimating specific chemical exergy of biomass from basic analysis data

.

Ind Eng Chem Res

.

2011

;

50

:

9758

–

66

[19]

Zhang

YN

,

Gao

XY

,

Li

BX

et al. 

An expeditious methodology for estimating the exergy of woody biomass by means of heating values

.

Fuel

.

2015

;

159

:

712

–

9

[20]

Shieh

JH

,

Fan

LT

.

Estimation of energy (enthalpy) and exergy (availability) contents in structurally complicated materials

.

Energy Sources

.

2010

;

6

:

1

–

46

[21]

Stepanov

V

.

Chemical energies and exergies of fuels

.

Energy

.

1995

;

20

:

235

–

42

[22]

Song

GH

,

Xiao

J

,

Zhao

H

et al. 

A unified correlation for estimating specific chemical exergy of solid and liquid fuels

.

Energy

.

2012

;

40

:

164

–

73

[23]

Huang

YW

,

Chen

MQ

,

Li

Y

et al. 

Modeling of chemical exergy of agricultural biomass using improved general regression neural network

.

Energy

.

2016

;

114

:

1164

–

75

[24]

Qian

HL

,

Zhu

WW

,

Fan

SD

et al. 

Prediction models for chemical exergy of biomass on dry basis from ultimate analysis using available electron concepts

.

Energy

.

2017

;

131

:

251

–

8

[25]

Aghbashlo

M

,

Tabatabaei

M

,

Nadian

MH

et al. 

Determining biomass chemical exergy using a novel hybrid intelligent approach to promote biomass-based biorefineries

.

J Clean Prod

.

2020

;

277

:

124089

[26]

Szargut

J

,

Styrylska

T

.

Approximate evaluation of the exergy of fuels

.

Brennstoff-Waerme-Kraft

.

1964

;

16

:

589

–

96

[27]

Govin

OV

,

Diky

VV

,

Kabo

GJ

et al. 

Evaluation of the chemical exergy of fuels and petroleum fractions

.

J Therm Anal Calorim

.

2000

;

62

:

123

–

33

[28]

Bilgen

S

,

Keles

S

,

Kaygusuz

K

.

Calculation of higher and lower heating values and chemical exergy values of liquid products obtained from pyrolysis of hazelnut cupulae

.

Energy

.

2012

;

41

:

380

–

5

[29]

Zhang

YN

,

Zhao

WK

,

Li

BX

et al. 

Two equations for estimating the exergy of woody biomass based on the exergy of ash

.

Energy

.

2016

;

106

:

400

–

7

[30]

Gharagheizi

F

,

Mehrpooya

M

.

Prediction of standard chemical exergy by a three descriptors QSPR model

.

Energy Convers Manag

.

2007

;

48

:

2453

–

60

[31]

Wu

H

,

Yu

YM

,

Fu

HL

et al. 

On the prediction of chemical exergy of organic substances using least square support vector machine

.

Energy Sources A

.

2017

;

39

:

2210

–

5

[32]

Gharagheizi

F

,

Ilani-Kashkouli

P

,

Mohammadi

AH

et al. 

A group contribution method for determination of the standard molar chemical exergy of organic compounds

.

Energy

.

2014

;

70

:

288

–

97

[33]

Gharagheizi

F

,

Ilani-Kashkouli

P

,

Hedden

RC

.

Standard molar chemical exergy: a new accurate model

.

Energy

.

2018

;

158

:

924

–

35

[34]

Haghbakhsh

R

,

Raeissi

S

.

A novel atomic contribution model for the standard chemical exergies of organic compounds

.

Fluid Phase Equilib

.

2020

;

507

:

112397

[35]

Petković

B

,

Petković

D

,

Kuzman

B

.

Adaptive neuro fuzzy predictive models of agricultural biomass standard entropy and chemical exergy based on principal component analysis

.

Biomass Convers Biorefinery

.

2020

. https://link.springer.com/article/10.1007/s13399-020-00767-1

[36]

Huang

W

,

Zheng

D

,

Chen

X

et al. 

Standard thermodynamic properties for the energy grade evaluation of fossil fuels and renewable fuels

.

Renew Energy

.

2020

;

147

:

2160

–

70

[37]

Huang

YW

,

Chen

MQ

,

Li

QH

et al. 

A critical evaluation on chemical exergy and its correlation with high heating value for single and multi-component typical plastic wastes

.

Energy

.

2018

;

156

:

548

–

54

[38]

He

XS

,

Zhang

LG

,

Jiang

YQ

.

Application of neural network for the prediction of chemical exergy: application in exergy and economic analyses

.

Energy Sources A

.

2018

;

40

:

2423

–

31

[39]

Zheng

D

,

Deng

W

,

Jin

H

.

Thermodynamic analysis of GAX cycle by α-h diagram

.

J Eng Thermophys

.

2005

;

3

:

369

–

72

[40]

Zheng

D

,

Deng

W

,

Jin

H

et al. 

α–h diagram and principle of exergy coupling of GAX cycle

.

Appl Therm Eng

.

2007

;

27

:

1771

–

8

[41]

Zheng

DX

,

Hou

Z

.

Energy quality factor and a new thermodynamic approach to evaluate cascade utilization of fossil fuels

.

Energy Fuel

.

2009

;

23

:

2613

–

9

[42]

Zheng

DX

,

Wu

ZH

,

Huang

WJ

et al. 

Energy quality factor of materials conversion and energy quality reference system

.

Appl Energy

.

2017

;

185

:

768

–

78

[43]

Chen

X

,

Zheng

D

,

Guo

J

et al. 

Energy analysis for low-rank coal based process system to co-produce semicoke, syngas and light oil

.

Energy

.

2013

;

52

:

279

–

88

[44]

Zheng

D

,

Jing

X

.

Chemical amplifier and energy utilization principles of heat conversion cycle systems

.

Energy

.

2013

;

63

:

180

–

8

[45]

Jing

X

,

Zheng

D

.

Effect of cycle coupling-configuration on energy cascade utilization for a new power and cooling cogeneration cycle

.

Energy Convers Manag

.

2014

;

78

:

58

–

64

[46]

Chen

X

,

Zheng

D

,

Yi

X

et al. 

Optimal design of process configuration for a cascade coproduction system to produce furnace off-gas-based clean fuels and chemicals

.

Chem Eng Res Des

.

2016

;

109

:

780

–

90

[47]

Jing

X

,

Zhu

Z

,

Dong

P

et al. 

Energy quality factor and exergy destruction processes analysis for a proposed polygeneration system coproducing semicoke, coal gas, tar and power

.

Energy Convers Manag

.

2017

;

149

:

52

–

60

[48]

Zhang

F

,

Zhu

L

,

Wang

Y

et al. 

Energy quality factor and exergy destruction processes analysis for chemical looping hydrogen generation by coal

.

Int J Energy Res

.

2021

;

45

:

5527

–

43

[49]

Chu

SX

,

Liu

LH

.

Analysis of terrestrial solar radiation exergy

.

Sol Energy

.

2009

;

83

:

1390

–

404

[50]

Jiang

XZ

,

Wang

XY

,

Feng

LJ

et al. 

Adapted computational method of energy level and energy quality evolution for combined cooling, heating and power systems with energy storage units

.

Energy

.

2017

;

120

:

209

–

16

[51]

Hebecker

D

,

Bittrich

P

.

Energy and materials conversion with the help of regeneration and energy transformation

.

Int J Therm Sci

.

2001

;

40

:

316

–

28

[52]

Ishida

M

,

Zheng

D

.

Graphic exergy analysis of chemical process systems by a graphic simulator

.

Comput Chem Eng

.

1986

;

10

:

525

–

32

[53]

Zheng

D

,

Moritsuka

H

,

Ishida

M

.

Graphic exergy analysis for coal gasification-combined power cycle based on the energy utilization diagram

.

Fuel Process Technol

.

1986

;

13

:

125

–

38

[54]

Zheng

D

,

Uchiyama

Y

,

Ishida

M

.

Energy-utilization diagrams for two types of LNG power-generation systems

.

Energy

.

1986

;

11

:

631

–

9

[55]

Ishida

M

,

Zheng

D

,

Akehata

T

.

Evaluation of a chemical-looping-combustion power-generation system by graphic exergy analysis

.

Energy

.

1987

;

12

:

147

–

54

[56]

Ishida

M

,

Jin

H

.

A new advanced power-generation system using chemical-looping combustion

.

Energy

.

1994

;

19

:

415

–

22

[57]

Jin

H

,

Ishida

M

.

Novel gas turbine cycle with hydrogen-fueled chemical-looping combustion

.

Int J Hydrog Energy

.

2000

;

25

:

1209

–

15

[58]

Jin

H

,

Ishida

M

.

Graphical exergy analysis of a new type of advanced cycle with saturated air

.

Heat Recovery Syst CHP

.

1994

;

14

:

105

–

16

[59]

Ishida

M

,

Ji

J

.

Proposal of humid air turbine cycle incorporated with absorption heat transformer

.

Int J Energy Res

.

2000

;

24

:

977

–

87

[60]

Jin

H

,

Ishida

M

,

Kobayashi

M

et al. 

Exergy evaluation of two current advanced power plants: supercritical steam turbine and combined cycle

.

ASME Adv Energy Syst Div Publ AES

.

1996

;

36

:

493

–

500

[61]

In

H

,

Shida

M

,

Kobayashi

M

et al. 

Exergy evaluation of two current advanced power plants: supercritical steam turbine and combined cycle

.

J Energy Resour Technol

.

1997

;

119

:

250

–

6

[62]

Srinophakun

T

,

Laowithayangkul

S

,

Ishida

M

.

Simulation of power cycle with energy utilization diagram

.

Energy Convers Manag

.

2001

;

42

:

1437

–

56

[63]

Zhao

H

,

Yue

P

.

Performance analysis of humid air turbine cycle with solar energy for methanol decomposition

.

Energy

.

2011

;

36

:

2372

–

80

[64]

Ma

YG

,

Liu

M

,

Yan

JJ

et al. 

Optimization of recompression supercritical Brayton cycle for high temperature concentrated solar power application

.

Kung Cheng Je Wu Li Hsueh Pao

.

2018

;

39

:

1649

–

55

[65]

Xu

C

,

Li

X

,

Xu

G

et al. 

Energy, exergy and economic analyses of a novel solar-lignite hybrid power generation process using lignite pre-drying

.

Energy Convers Manag

.

2018

;

170

:

19

–

33

[66]

Xu

C

,

Zhang

Q

,

Yang

Z

et al. 

An improved supercritical coal-fired power generation system incorporating a supplementary supercritical CO2 cycle

.

Appl Energy

.

2018

;

231

:

1319

–

29

[67]

Ji

Z

,

Qin

J

,

Cheng

K

et al. 

Advanced exergy and graphical exergy analyses for solid oxide fuel cell turbine-less jet engines

.

J Power Sources

.

2020

;

456

:

227979

[68]

Zhang

Q

,

Zhang

X

,

Deng

M

.

A novel system integrating chemical-looping hydrogen generation and solid oxide fuel cell

.

Proc Chin Soc Electr Eng

.

2021

;

41

:

1804

–

10

[69]

Okazaki

K

,

Kishida

T

,

Ogawa

K

et al. 

Direct conversion from methane to methanol for high efficiency energy system with exergy regeneration

.

Energy Convers Manag

.

2002

;

43

:

1459

–

68

[70]

Cao

W

,

Zheng

D

.

Exergy regeneration in an O2/CO2 gas turbine cycle with chemical recuperation by CO2 reforming of methane

.

Energy Convers Manag

.

2006

;

47

:

3019

–

30

[71]

Bian

HJ

,

Xu

WD

,

Li

XX

et al. 

Description and analysis of ethane recovery process from natural gas with LNG cryogenic energy

.

Modern Chem Ind

.

2010

;

30

:

58

–

61

[72]

Bian

H

,

Xu

W

,

Li

X

et al. 

A novel process for natural gas liquids recovery from oil field associated gas with liquefied natural gas cryogenic energy utilization

.

Chin J Chem Eng

.

2011

;

19

:

452

–

61

[73]

Yan

Q

,

Hou

Y

,

Luo

J

et al. 

Energy cascade release of coal in different oxidation environment

.

Huagong Xuebao

.

2016

;

67

:

5305

–

10

[74]

Yan

Q

,

Hou

Y

,

Luo

J

et al. 

The exergy release mechanism and exergy analysis for coal oxidation in supercritical water atmosphere and a power generation system based on the new technology

.

Energy Convers Manag

.

2016

;

129

:

122

–

30

[75]

Wu

H

,

Li

S

,

Gao

L

.

Exergy destruction mechanism of coal gasification by combining the kinetic method and the energy utilization diagram

.

J Energy Resour Technol

.

2017

;

139

:

62201

[76]

Chen

Z

,

Gao

L

,

Han

W

et al. 

Energy and exergy analyses of coal gasification with supercritical water and O2-H2O

.

Appl Therm Eng

.

2019

;

148

:

57

–

63

[77]

Yan

Q

,

Lu

T

,

Luo

J

et al. 

Exergy cascade release pathways and exergy efficiency analysis for typical indirect coal combustion processes

.

Combust Theory Model

.

2019

;

23

:

1134

–

49

[78]

Ruya

PM

,

Lim

SS

,

Purwadi

R

et al. 

Sustainable hydrogen production from oil palm derived wastes through autothermal operation of supercritical water gasification system

.

Energy

.

2020

;

208

:

118280

[79]

Li

Y

,

Zhang

G

,

Yang

Y

et al. 

Thermodynamic analysis of a coal-based polygeneration system with partial gasification

.

Energy

.

2014

;

72

:

201

–

14

[80]

Wang

J

,

Fu

C

.

Solar-hybrid combined cooling heating and power system integrated with methane chemical looping combustion

.

Proc Chin Soc Electr Eng

.

2016

;

36

:

3263

–

9

[81]

Wang

J

,

Fu

C

.

A solar assisted polygeneration system integrating methane reforming and chemical looping combustion with zero carbon emission

.

J Therm Sci Technol

.

2017

;

12

:

JTST0007

[82]

Xu

C

,

Gao

Y

,

Xu

G

et al. 

A thermodynamic analysis and economic evaluation of an integrated cold-end energy utilization system in a de-carbonization coal-fired power plant

.

Energy Convers Manag

.

2019

;

180

:

218

–

30

[83]

Chuang

CC

,

Ishida

M

.

Exergy study of the reverse cycles of absorption heat pumps by use of energy-utilization diagrams

.

J Chem Eng Japan

.

1990

;

23

:

755

–

60

[84]

Ishida

M

,

Ji

J

.

Energy level concept and its application to improvement of absorption heat transformer

.

ASME Adv Energy Syst Div Publ AES

.

1998

;

38

:

13

–

8

[85]

Ishida

M

,

Ji

J

.

Graphical exergy study on single stage absorption heat transformer

.

Appl Therm Eng

.

1999

;

19

:

1191

–

206

[86]

Ji

J

,

Ishida

M

.

Behavior of a two-stage absorption heat transformer combining latent and sensible heat exchange modes

.

Appl Energy

.

1999

;

62

:

267

–

81

[87]

Liu

Y

,

Sui

J

,

Liu

H

.

Research on heating system of serial-parallel coupling absorption heat pump for coal fired power plants

.

Proc Chin Soc Electr Eng

.

2016

;

36

:

6148

–

55

[88]

Seki

K

,

Hattori

H

,

Amano

Y

.

Optimal design method for absorption heat pump cycles based on energy-utilization diagram

.

Int J Thermodyn

.

2019

;

22

:

9

–

17

[89]

Ishida

M

,

Taprap

R

.

Application of energy-utilization diagram for graphic exergy analysis of multicomponent distillation columns

.

J Chem Eng Japan

.

1992

;

25

:

396

–

402

[90]

Taprap

R

,

Ishida

M

.

Graphic exergy analysis of processes in distillation column by energy-utilization diagrams

.

AICHE J

.

1996

;

42

:

1633

–

41

[91]

Budiman

A

,

Ishida

M

.

Optimal side heating and cooling in a distillation column

.

Energy

.

1998

;

23

:

365

–

72

[92]

Cao

C

,

Xie

L

,

Xu

S

et al. 

Exergy analysis and optimization of MED–TVC system with different effect group divisions

.

Desalination

.

2021

;

500

:

114891

[93]

Zhang

F

,

Li

Y

,

Jia

C

et al. 

Effect of evaporation on the energy conversion of a supercritical water oxidation system containing a hydrothermal flame

.

Energy

.

2021

;

226

:

120406

[94]

Hong

H

,

Jin

H

,

Liu

B

.

A novel solar-hybrid gas turbine combined cycle with inherent CO 2 separation using chemical-looping combustion by solar heat source

.

J Sol Energy Eng

.

2006

;

128

:

275

–

84

[95]

Hong

H

,

Jin

HG

,

Yang

S

.

Recovery combining chemical-looping combustion with low-temperature solar thermal energy

.

J Eng Thermophys

.

2006

;

27

:

729

–

32

[96]

Hong

H

,

Han

T

,

Jin

H

.

A low temperature solar thermochemical power plant with CO2 recovery using methanol-fueled chemical looping combustion

.

J Sol Energy Eng

.

2010

;

132

:

310021

–

8

[97]

Pan

Y

,

Han

T

,

Hong

H

et al. 

A solar-hybrid power plant integrated with ethanol chemical-looping combustion

.

J Eng Thermophys

.

2011

;

32

:

1461

–

5

[98]

Zhang

X

,

Li

S

,

Hong

H

et al. 

A hydrogen and oxygen combined cycle with chemical-looping combustion

.

Energy Convers Manag

.

2014

;

85

:

701

–

8

[99]

Li

S

,

Jin

H

,

Mumford

KA

et al. 

IGCC precombustion CO2 capture using K2CO3 solvent and utilizing the intercooling heat recovered from CO2 compressors for CO2 regeneration

.

J Energy Resour Technol

.

2015

;

137

:

42002

[100]

Wang

D

,

Li

S

,

Gao

L

et al. 

Novel coal-steam gasification with a thermochemical regenerative process for power generation

.

J Energy Resour Technol

.

2018

;

140

:

92203

[101]

Jin

HG

,

Sun

SE

,

Lin

RM

et al. 

Proposal of novel polygeneration system for producing coke and power

.

J Eng Thermophys

.

2007

;

28

:

901

–

4

[102]

Gao

L

,

Li

H

,

Chen

B

et al. 

Proposal of a natural gas-based polygeneration system for power and methanol production

.

Energy

.

2008

;

33

:

206

–

12

[103]

Lin

H

,

Jin

H

,

Gao

L

et al. 

A polygeneration system for methanol and power production based on coke oven gas and coal gas with CO2 recovery

.

Energy

.

2014

;

74

:

174

–

80

[104]

Jin

H

,

Han

W

,

Gao

L

.

A novel multifunctional energy system (MES) for CO2 removal with zero energy penalty

.

J Eng Gas Turbines Power

.

2008

;

130

:

21401

[105]

Jin

H

,

Xu

Y

,

Lin

R

et al. 

A proposal for a novel multi-functional energy system for the production of hydrogen and power

.

Int J Hydrog Energy

.

2008

;

33

:

9

–

19

[106]

Liao

TF

,

Hong

H

,

Liu

BQ

.

A hydrogen-power cogeneration system set up by combining medium-and-low temperature waste heat with methanol refining

.

Reneng Dongli Gongcheng

.

2009

;

24

:

670

–

5

[107]

Jin

H

,

Sun

S

,

Han

W

et al. 

Proposal of a novel multifunctional energy system for cogeneration of coke, hydrogen, and power

.

J Eng Gas Turbines Power

.

2009

;

131

:

052001

[108]

Sun

S

,

Jin

H

,

Gao

L

et al. 

Study on a multifunctional energy system producing coking heat, methanol and electricity

.

Fuel

.

2010

;

89

:

1353

–

60

[109]

Sun

SE

,

Lin

RM

,

Jin

HG

et al. 

Integration mechanism and characteristic of polygeneration system with mutual combination of coke oven gas and coal gas

.

J Eng Thermophys

.

2010

;

31

:

1081

–

4

[110]

Han

W

,

Jin

H

,

Lin

R

.

A novel multifunctional energy system for CO2 removal by solar reforming of natural gas

.

J Sol Energy Eng

.

2011

;

133

:

041004

[111]

Jin

H

,

Hong

H

,

Wang

B

et al. 

Integrated cascade utilization principle of chemical energy and physical energy

.

Sci Sin Technol

.

2005

;

35

:

299

–

313

[112]

Liu

W

,

Jia

H

,

Liu

ZC

et al. 

The approach of minimum heat consumption and its applications in convective heat transfer optimization

.

Int J Heat Mass Transf

.

2013

;

57

:

389

–

96

[113]

Liu

W

,

Bao

Y

,

Xie

P

et al. 

Energy level of residual heat resources and its matching property with ORC working medium

.

Chin Sci Bull

.

2016

;

61

:

1889

–

96

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