Estimating the specific chemical exergy of municipal solid waste

Abstract

A new model for predicting the specific chemical exergy of municipal solid waste (MSW) is presented; the model is based on the content of carbon, hydrogen, oxygen, nitrogen, sulfur, and chlorine on a dry ash-free basis (daf). The proposed model was obtained from estimations of the higher heating value (HHV) and standard entropy of MSW using statistical analysis. The ultimate analysis of 56 different parts of MSW was used for the derivation of the HHV expression. In addition, 30 extra parts were used for validation. One hundred and seventeen relevant organic substances that represented the main constituents in MSW were used for derivation of the standard entropy of solid waste. The substances were divided into different waste fractions, and the standard entropies of each waste fraction and for the complete mixture were calculated. The specific chemical exergy of inorganic matter in the waste was also investigated by considering the inorganic compounds in the ash. However, as a result of the extremely low value calculated, the exergy of inorganic matter was ignored. The results obtained from the HHV model show a good correlation with the measured values and are comparable with other recent and previous models. The correlation of the standard entropy of the complete waste mixture is less accurate than the correlations of each individual waste fraction. However, the correlations give similar results for the specific chemical exergy, indicating that HHV has a greater impact when estimating the specific exergy of solid waste than entropy.

Introduction

The quantities of solid wastes increase as the population continues to grow throughout the world, whereas the available space for disposal decreases. If this waste is not properly treated and handled, it will pollute the air, land, ground water, and soil as well as has a negative impact on the hygienic conditions of the people [1]. A waste-to-energy (WTE) plant is one of the most robust and effective posttreatment options to decrease the volume of produced waste, reduce greenhouse gas emissions, and utilize the energy content in nonrecyclable waste for the production of electricity and heat, thereby reducing the dependence on fossil fuel.

For the efficient design of energy conversion processes, the chemical exergy and energy content of the fuel are basic properties to be considered to estimate the maximum available energy entering the system for performance analysis and optimization of the entire process. This can be done by detecting and evaluating quantitatively the thermodynamic imperfection (exergy loss) of the process under consideration, its main sources of loss and possible ways of improving such process can be indicated [2]. Estimating the chemical exergy of fuel is an important step when performing exergy analysis [3] in waste-to-energy plants. Exergy analysis is a method that uses the conservation of mass and energy together with the second law of thermodynamics. This analysis method is useful to achieve a more efficient energy-resource use because it enables the locations, types, and magnitudes of losses to be identified and to determine meaningful efficiencies [4].

However, because many solid fuels have unknown structures and chemical compositions, their exergy values cannot be calculated directly because of the lack of standard absolute entropy values [5]. Many models for the prediction and estimation of the chemical exergy of carbon-based fuels with complex bond interactions and unknown thermodynamics properties have been proposed based on the characteristics of the known homogeneous organic substances in the fuel. The first attempt was performed by Rant [6], involving the formulation of a semiempirical model to evaluate the availability (exergy) content of a structurally complicated material species. In that model, the chemical exergy of a fuel is evaluated from the computation of pure organic substances of known absolute entropies. Rant evaluated the ratios of the estimated chemical exergies and the higher heating values for seven gases and 12 liquid organic substances. Szargut and Styrylska [7] improved Rant′s correlation by considering the chemical composition of the fuels. They obtained correlation formulas to express the dependence between the ratio of the standard chemical exergy to the lower heating value using mass ratios of hydrogen, oxygen, nitrogen and sulfur to carbon that describe the chemical composition of the fuel. Due to lack of thermodynamic data, sulfur was not considered in their model for solid fuels, and their correlations were theoretically limited to Szargut′s reference environmental (R.E) model.

Using a model for estimating the thermodynamic properties of coal, char, tar, and ash, Eisermann et al. [8] approximated the standard entropy of coal by comparing the behavior of the standard entropies of a number of aliphatic and aromatic hydrocarbons as a function of several elemental ratios: H/(C + N), O/(C + N), N/(C + N) and S/(C + N). Shieh and Fan [9] estimated the specific chemical exergy of a structurally complicated material by adopting the concepts of the dead (or reference) state and the properties of the constituents in the material based on the first and second laws of thermodynamics. It was assumed that the entropy of a fuel is equal to the entropies of its constituent elements. This assumption is not accurate in many cases. Ikumi et al. [10] developed a method for estimating the entropies of coals based on the mole ratios of hydrogen, oxygen, nitrogen, and sulfur elements to the carbon element. Bilgen and Kaygusuz [11] used the entropy correlation proposed by Eisermann et al. [8] to improve the Shieh and Fan [9] model for the calculation of the chemical exergy of coals, and Stepanov [5] applied the entropy model developed by Ikumi et al. [10] to modify Shieh and Fan [9] to calculate the exergies of coke-oven gases of different metallurgical mills. These models are limited to coal fuels only because their constituent organic compounds have been derived from the standard entropies of the relevant organic substances of coals.

Song et al. [3] developed a model based on Shieh and Fan [9] to estimate the specific entropy of the organic matter in biomass used for the exergy calculations. Although their model showed a high accuracy and was simpler than the Szagut and Styrylskas correlation, it has a limited application, as it is only applicable to biomass. Song et al. [12] also proposed a model for estimating the entropy of solid fuels and then extended the Shieh and Fan [9] model using the major organic constituents of solid fuel for the prediction of the specific chemical exergy of solid fuels. However, they combined the higher heating value derived on a dry basis (db) with values of the standard entropy obtained based on a dry ash-free basis (daf) for the estimation of the chemical exergy. Furthermore, their model cannot be used for estimating the chemical exergy of substances containing elements other than C, H, O, N, and S and for combustible materials, such as certain categories of leather, plastic, and rubber, that are part of municipal solid waste. To the authors knowledge, no model has been found in the literature that is derived for predicting the chemical exergy of MSW.

The objective of this work is to propose a model for calculating the specific chemical exergy of MSW containing the C, H, O, N, S, and Cl from its elemental compositions on a dry ash-free basis.

Derivation of the Estimated Model

Municipal Solid Waste consists of a complex, heterogeneous mixture of organic and inorganic substances. The organic elements in MSW are mainly C, H, O, N, S, and Cl, which can be obtained from ultimate analysis, whereas the inorganics are commonly Si, Ca, K, P, Al, Mg, Fe, S, Na, Zn, Cu, Mn, and Cr, from which their oxides can be obtained from ash analysis data. Previous reports have shown that the influence of inorganic matters on the exergy value can be neglected in solid fuel as a result of their relatively small value [3, 12].

The standard chemical exergy of a substance that is not present in the environment can be evaluated by considering a reaction of the substance with other substances for which the chemical exergies are known [13]. The exact calculation of the chemical exergy of a material with complicated structures is difficult [14]; as a result, the standard chemical exergy of the substance in the environment is not readily available.

Standard chemical exergy of a substance

The chemical exergy of a substance is equal to the maximum amount of work that can be obtained from the substance by taking it to chemical equilibrium with the reference environment [15]. The standard exergy of a substance can be evaluated by considering an idealized reaction of the substance with other substances (generally reference substances) of known chemical exergies [16]. The known chemical exergies can be obtain from the table of standard chemical exergy based on Szarguts R.E model (Model II), as shown in Table 1. With consideration of the reversible reaction for chemical formation of a compound, Szargut et al. [2] expressed the standard chemical exergy of elements or compounds as

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): b_{ch}^o\quad =\quad \Delta G_f^o+{\sum }_in_ib_{chi}^o\quad \left(\mbox{kJ}/\mbox{mol}\right)

(1)

Table 1. Standard chemical exergy and standard entropies of various compounds
Substance	e⁰ (kJ/mol)	s⁰ (kJ/mol K)
l, liquid phase. Source: [3, 17, 18].
CO₂	19.87	0.214
H₂O_l	0.95	0.070
O₂	3.97	0.205
N₂	0.72	0.192
SO₂	310.93	0.248
SiO₂	1.636	0.041
HCl	85.5	0.187
CaO	129.881	0.038
K₂O	412.544	0.102
P₂O₅	377.155	0.117
Al₂O₅	4.479	0.051
MgO	62.417	0.027
Fe₂O₃	17.656	0.087
SO₃	242.003	0.257
Na₂O	296.32	0.075
MnO	122.390	0.060
ZnO	37.080	0.042
Cr	538.610	0.024
Pb	226.940	0.065
As	477.040	0.035
Cd	290.920	0.052
Cl	163.940	0.166

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle \Delta G_f^o} , n_i, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle b_{chi}^o}

represent the standard Gibbs energy of formation, the mole fraction of component i in the mixture, and the standard chemical exergy of the constituent element i, respectively.

Calculation of the specific chemical exergy of municipal solid waste

For simplicity, suppose 1 kg of MSW (daf), expressed as C_mH_nN_pO_qC_rS_t, undergoes complete combustion at a standard state for the steady condition to produce carbon dioxide, water, nitrogen, hydrogen chloride, and sulfur dioxide as follows:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{cl} & C_mH_nN_pO_q{\mbox{Cl}}_rS_t+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)O_2\\ & \rightarrow \quad \quad {\mbox{mCO}}_2+\left(\frac{n-r}{2}\right)H_2O+\frac{P}{2}N_2+r\mbox{HCl}+\mbox{tS}O_2 \end{array}

(2)

All substances are assumed to enter and exit at the reference temperature, T₀ = 298.15 K, and reference pressure, P₀ = 101.325 kPa. The subscripts m, n, p, q, r, and t are the numbers of atoms of C, H, N, O, Cl, and S, respectively, in kmol/kg MSW or the molal compositions per kg of MSW expressed as:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): m=\frac{0.01C}{12.011}\quad \mbox{kmol/kg}\quad \mbox{or}\quad \frac{10C}{12.011}\quad \mbox{mol/kg}

(3)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): n=\frac{0.01H}{1.008}\quad \mbox{kmol/kg}\quad \mbox{or}\quad \frac{10H}{1.008}\quad \mbox{mol/kg}

(4)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): p=\frac{0.01N}{14.007}\quad \mbox{kmol/kg}\quad \mbox{or}\quad \frac{10N}{14.007}\quad \mbox{mol/kg}

(5)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): q=\frac{0.01O}{15.999}\quad \mbox{kmol/kg}\quad \mbox{or}\quad \frac{10O}{15.999}\quad \mbox{mol/kg}

(6)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): r=\frac{0.01\mbox{Cl}}{35.45}\quad \mbox{kmol/kg}\quad \mbox{or}\quad \frac{10\mbox{Cl}}{35.45}\quad \mbox{mol/kg}

(7)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): t=\frac{0.01S}{32.066}\quad \mbox{kmol/kg}\quad \mbox{or}\quad \frac{10S}{32.066}\quad \mbox{mol/kg}

(8)

where the elements in Equations (3)-(8) are expressed in wt% (daf). For the steady state, under the standard condition, the energy balance of the reaction in Equation (2) is given by

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} W\quad =\quad & Q+h_{MSW}^0+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)h_{O_2}^0-mh_{{CO}_2}^0\\ & -\left(\frac{n-r}{2}\right)h_{H_2O}^0-\frac{p}{2}h_{N_2}^0-{rh}_{HCl}^0-th_{{SO}_2}^0 \end{array}

(9)

The entropy balance is expressed as

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} 0\quad =\quad & \frac{Q}{T_o}+s_{MSW}^0+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)s_{O_2}^0-ms_{{CO}_2}^0\\ & -\left(\frac{n-r}{2}\right)s_{H_2O}^0-\frac{p}{2}s_{N_2}^0-rs_{HCl}^0-ts_{{SO}_2}^0+S_{gen} \end{array}

(10)

where W and Q are the work and heat transfer, respectively. S_gen is the entropy generated by the irreversibility in the reaction, and s⁰ and h⁰ represent the standard entropy and enthalpy, respectively.

Eliminating the heat transfer Q between Equation (9) and (10) gives the following:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} W\quad =\quad & h_{MSW}^0,+,\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right),h_{O_2}^0,-,h,s_{{CO}_2}^0\\ & -\left(\frac{n-r}{2}\right)h_{H_2O}^0-\frac{p}{2}h_{N_2}^0-rh_{HCl}^0-th_{{SO}_2}^0\\ & -T_os_{MSW}^0+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)s_{O_2}^0\\ & -hs_{{CO}_2}^0-\left(\frac{n-r}{2}\right)s_{H_2O}^0-\frac{p}{2}s_{N_2}^0-rs_{HCl}^0-ts_{{SO}_2}^0-T_oS_{gen} \end{array}

(11)

The maximum work, W_max, will occur when there is no irreversibility in the system. Hence, Equation (11) can be expressed as

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} W_{max}\quad =\quad & h_{MSW}^0+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)h_{O_2}^0-mh_{{CO}_2}^0\\ & -\left(\frac{n-r}{2}\right)h_{H_2O}^0-\frac{p}{2}h_{N_2}^0-rh_{HCl}^0-th_{{SO}_2}^0\\ & -T_os_{MSW}^0+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)s_{O_2}^0-ms_{{CO}_2}^0\\ & -\left(\frac{n-r}{2}\right)s_{H_2O}^0-\frac{p}{2}s_{N_2}^0-rs_{HCl}^0-ts_{{SO}_2}^0 \end{array}

(12)

or

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} W_{max}\quad =\quad & -\Delta H_r^o-T_os_{MSW}^0+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)s_{O_2}^0\\ & -ms_{{CO}_2}^0-\left(\frac{n-r}{2}\right)s_{H_2O}^0-\frac{p}{2}s_{N_2}^0-rs_{HCl}^0-ts_{{SO}_2}^0 \end{array}

(13)

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle \Delta H_r^o}

represents the heat of reaction of the combustion process, which is equal to the negative higher heating value [9], that is

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \Delta H_r^o\quad =\quad -\mbox{HHV}

(14)

then

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} W_{max}\quad =\quad & \mbox{HHV}-T_os_{msw}+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)s_{O_2}^0-ms_{{CO}_2}^0\\ & -\left(\frac{n-r}{2}\right)s_{H_2O}^0-\frac{p}{2}s_{N_2}^0-rs_{HCl}^0-ts_{{SO}_2}^0 \end{array}

(15)

Assume that the reaction in Equation (2) at 298.15 K and 101.325 kPa is an adiabatic process with no irreversibility. The exergy balance equation, in absence of changes in the kinetic and potential energy for reacting systems, is given by

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} 0\quad =\quad & -W_{max}+e_{MSW}+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)e_{O_2}^0-me_{{CO}_2}^0\\ & -\left(\frac{n-r}{2}\right)e_{H_2O}^0-\frac{p}{2}e_{N_2}^0-re_{HCl}^0-te_{{SO}_2}^0 \end{array}

(16)

where e represents the specific chemical exergy. Substituting Equation (15) into Equation (16), the specific chemical exergy of MSW (daf), e_MSW, is presented as

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} e_{MSW}\quad =\quad & \mbox{HHV}-T_os_{MSW}^0+\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)s_{O_2}^0-ms_{{CO}_2}^0\\ & -\left(\frac{n-r}{2}\right)s_{H_2O}^0-\frac{p}{2}s_{N_2}^0-rs_{HCl}^0-ts_{{SO}_2}^0+me_{{CO}_2}^0\\ & +\left(\frac{n-r}{2}\right)e_{H_2O}^0+\frac{p}{2}e_{N_2}^0+re_{HCl}^0\\ & +e_{{SO}_2}^0-\left(m,+,t,-,\frac{q}{2},+,\frac{n-r}{4}\right)e_{O_2}^0 \end{array}

(17)

or

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} e_{MSW}\quad =\quad & m\left(e_{{CO}_2}^0,+,T_o,s_{{CO}_2}^0\right)-\left(e_{O_2}^0,+,T_o,s_{O_2}^0\right)\\ & +\frac{n}{2}\left(e_{H_2O}^0,+,T_o,s_{H_2O}^0\right)-\frac{1}{2}\left(e_{O_2}^0,+,T_o,s_{O_2}^0\right)\\ & +\frac{q}{2}\left(e_{O_2}^0,+,T_o,s_{O_2}^0\right)+\frac{p}{2}\left(e_{N_2}^0,+,T_o,s_{N_2}^0\right)\\ & +t\left(e_{{SO}_2}^0,+,T_o,s_{{SO}_2}^0\right)-\left(e_{O_2}^0,+,T_o,s_{O_2}^0\right)\\ & -\frac{r}{2}\left(e_{H_2O}^0,+,T_o,s_{H_2O}^0\right)-\frac{1}{2}\left(e_{O_2}^0,+,T_o,s_{O_2}^0\right)\\ & -2\left(e_{HCl}^0,+,T_o,s_{HCl}^0\right)+{\mbox{HHV}}_{MSW}-T_os_{MSW}^0\quad \left(\mbox{kJ}/\mbox{kg}\right) \end{array}

(18)

where e⁰ is the standard exergy in kJ/mol and s⁰ is the standard entropy in kJ/mol K, as tabulated in Table 1. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle s_{MSW}^0}

is the standard entropy of municipal solid waste, in kJ/K kg (daf), and HHV_MSW is the higher heating value (HHV) of MSW, in kJ/kg (daf). The specific chemical exergy of MSW can be calculated once the standard chemical exergies of CO_2, H₂O(l), N₂, O₂, SO₂, and HCl; the higher heating value; and the absolute entropies are known.

Estimating the higher heating value of municipal solid waste

In the absence of a measured value, the HHV of fuel can be estimated from their elemental composition [19, 20]. In this study, the HHV estimate was performed by considering 56 data points and 30 data points of MSW samples for the derivation and validation of the correlation, respectively; in addition, the chemical composition and HHV of each sample was collected from the published literature and presented in Tables A1 and A2 (Appendix 1). These data cover six categories of combustible MSW fractions, namely, food, wood, paper, textiles, plastics, and rubber waste [21, 22]. For the selection of a suitable model, 9 assumed algebraic expressions from previous work based on the correlation of the HHV and ultimate analysis of solid fuel (daf) were used, as shown in Table 2. Using regression analysis based on the generalized method of least squares [19] on the 56 data points, the constant terms of these algebraic expressions were evaluated. The correlation that has the least error and highest coefficient of determination, as described in 'Selection of the best correlation', was selected. The newly estimated correlation was compared with the experimental values of HHV and the results of previous models collected from the open literature, for further validation.

Table 2. Assumed correlations used for the selection of the proposed model for HHV (daf)
S. No.	Assumed expression	Criteria for selection	Reference
where C, H, O, N, S, and Cl represents carbon, hydrogen, oxygen, nitrogen, sulfur, and chlorine, respectively, in % by mass on a dry ash free basis. a⁰, a, b, c, d, e, and f are constants of correlation.
1.	HHV = aC + bH + cO + dN + eS + fCl	Assuming fuel HHV to be a linear function of it constituents.	Current model
2.	HHV = aC + bH + cO + dN + eS	Based on Gumzs criteria	[19]
3.	HHV = a⁰ + bH + cO + dN + eS + fCl	Based on Changs criteria	[23]
4.	HHV = aC + b (H − O/8) + eS	Based on Dulongs criteria	[19]
5.	HHV = aC + bH + cO + eS	Based on modified version of Dulongs criteria	[19]
6.	HHV = a⁰ + aC + bH + cO²	Based on Seylers criteria	[19]
7.	HHV = a (C − (3/8) O) + b (3/8) O) + c (H − (1/6) O) + eS	Based on Steuers criteria	[19]
8.	HHV = a (C − 0.75 (O/2)) + b (H − 0.125 (O/2)) + eS	Based Sumegis criteria	[19]
9.	HHV = aC + bH + c ((N + O − 1)/8) + eS	Dulong-Berthelots criteria	[19]

Estimating the standard entropy of municipal solid waste

Municipal solid waste (MSW) contains mainly organic polymers in plastics, wood, paper, textile, rubber, and food waste. The entropies of these polymers in the organic waste are estimated or evaluated by the entropies of their organic monomers structures as there is no significant difference between the entropies of the solid organic monomers and their polymers [24]. The difference ranges from 0.1 to 12.5% (Table 3).

Table 3. Standard entropies of some solid organic polymers and monomers at 298.15 K
S. No.	Substance	S⁰ (J/mol K)
Source: [24].
1.	C₆H₁₁NO	173.21
1.	(C₆H₁₁NO)_n	173.0
2	C₄H₄O₄	157.2
2	(C₄H₄O₄)_n	151.4
3	C₁₅H₁₀N₂O₂	332.5
3	(C₁₅H₁₀N₂O₂)_n	294
4	C₁₃H₂₄O₂	401.9
4	(C₁₃H₂₄O₂)_n	351.6

The standard entropy of MSW was derived from organic substances with known standard entropies. In this work, 117 samples of organic compounds relevant to MSW were collected from the published literature [3, 8, 10, 12, 17, 24] and tabulated in Table A3 (Appendix 1). The data points where selected based on the molecular structures of the organic substances that are associated or linked with the formation of larger molecular structure network of municipal solid waste. The organic compounds were grouped into the six categories of waste fractions, as previously used for the higher heating value, namely: food, plastic, textile, rubber, wood, and paper. This was accomplished by considering the molecular structures of the organic substances that can be found in each of the molecular structures of the waste fractions. For wood, it contains three major chemical components: cellulose, hemicelluloses, and lignin [25]. Each of the chemical structure of the wood constituents [26, 27] was studied and organic compounds (monomers) that can be made or found from these structures are selected. In the food, the main structural elements identified are proteins, carbohydrate and lipids [28]. The molecular structures of these food components [29, 30] were also investigated and organic monomers that are linked with the structure are selected. The same method was carried on chemical structures of plastic [31], textile [32, 33], and rubber [34] materials with identifications of biologically important molecules which form the building structure of their polymers. Based on the absolute entropies and elemental compositions of the selected organic substances, a first-order polynomial correlation was derived statistically for the standard entropy of the waste fractions and the mixture.

Selection of the best correlation

Three statistical parameters were used as evaluating parameters for both HHV and the standard entropy of MSW, which are computed as follows:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \mbox{Average absolute error (AAE)}\quad =\quad \frac{1}{n}\sum_{i=1}^n\left|\frac{Z_{est}-Z_{exp}}{Z_{exp}}\right|\times 100\%

(19)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \mbox{Average bias error (ABE)}\quad =\quad \frac{1}{n}\sum_{i=1}^n\frac{Z_{est}-Z_{exp}}{Z_{exp}}\times 100\%

(20)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \mbox{Coefficient of determination}\quad \left(R^2\right)\quad =

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \quad 1-\sum_{i=1}^n\frac{{\left(Z_{est},-,Z_{exp}\right)}^2}{{\left(Z_{exp},-,\quad ,{\overline{Z}}_{exp}\right)}^2}

(21)

where Z_est and Z_exp denote the estimated and experimental values, respectively. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle {\overline{Z}}_{exp}}

is the experimental average value. AAE is the average error of a correlation. A smaller error of correlation will occur when AAE is low, which indicates higher accuracy. ABE denotes the average bias error of correlation. A positive value of ABE indicates an overall overestimation, whereas a negative value implies an overall underestimation. The smaller the absolute value of ABE, the smaller the bias of correlation. R² is used as a comprehensive parameter to measure the accuracy of the model. A higher R² value means a better estimation and fitting [20]. These three parameters are the important statistical criteria and are primarily employed to assess correlations [3, 12, 19].

Specific chemical exergy of inorganic matter in municipal solid waste

Inorganic substances of waste materials are contained in the ash and obtained from complete combustion of solid fuel; ash is mainly contained in various metallic oxides and has a high thermal stability [35, 36]. The specific chemical exergy of inorganic matter in kJ/kg MSW was calculated from the major ash compositions data in Table 4 from a stoker-type incinerator [37] as follows [3, 12, 36]:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): e_{ioc}\quad =\quad 0.01A\left(\sum ,n_i,x_i,e_{ioc}^0,+\right.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \left. ,R,T_o,\sum ,n_i,x_i,\mbox{ln},x_i\right)\quad \left(\mbox{kJ/kg}\right)

(22)

Table 4. Chemical composition of MSW ashes
Component	Bottom ash, BA (wt%)	Fly ash, FA (wt%)
Source: [37].
SiO₂	37.8	2.47
CaO	20.79	44.5
K₂O	0.85	3.01
P₂O₅	3.63	0.26
Al₂O₃	13.4	0.55
MgO	2.91	0.57
Fe₂O₃	7.46	0.32
SO₃	1.01	1.61
Na₂O	5.38	4.39
ZnO	0.52	2.25
CuO	0.51	0.096
MnO	0.17	0.04
Cr	0.63	0.008
Pb	0.22	0.51
As	0.021	0.062
Cd	0.0003	0.003
Cl	3.51	35.15

where n_i represents number of moles of the component in inorganic matter, in mol/kg. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle e_{ioc}^0}

and x_i are the standard chemical exergy and mole fraction of components i in inorganic matter, respectively. R is the universal gas constant, 0.0083145 kJ/mol K, and A is the ash content of MSW in wt%.

Results and Discussion

Correlation based on the higher heating value

For the higher heating value of MSW, the correlation derived that showed the minimum error with a higher accuracy among the nine assumed correlations used in Table 2 was expressed as

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} \mbox{HHV}\quad =\quad & 0.364C+0.863H-0.075O\\ & +0.028N-1.633S+0.062\mbox{Cl}\quad (\mbox{MJ}/\mbox{kg}) \end{array}

(23)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} 35.8\% & \leq C\leq 86.1\%,4.1\%\leq H\leq 13.9\%,0.0\%\\ & \quad \leq O\leq 54.9\%,0.0\%\leq N\leq 20.3\%,0.0\%\\ & \quad \leq S\leq 2.7\%,0.0\%\leq Cl\leq 56.4\%,\quad \\ & \quad 13.0\quad MJ/kg\leq HHV\leq 43.2\quad MJ/kg. \end{array}

The results of the validation of the derived model and the comparison with published correlations using the experimental values of 30 samples of MSW in the different categories of food, wood, plastic, textile, rubber, and paper waste are shown in Table 5 and represented in Figures 1-5. Figures 1, 2, and 4 show the best correlation with experimental data (highest coefficient of determination), representing the model developed in this work, model by Channiwala and Parikh [19] and Dulongs correlation. However, the proposed model shows significantly better estimations when considering the errors (AAE and ABE) compared to the other models. This is not surprising, as these models have been derived from mixed solid fuel and coal. Figure 3 shows a correlation proposed by Sheng and Azevedo [20]. Although the correlation has a good coefficient of determination (R² = 0.92), it has a higher error and underestimated the HHV. In addition, the correlation is limited to biomass. The correlation proposed by Chang (Table 5 and Fig. 5) has a considerable accuracy, with a coefficient of determination of R² = 0.93. Although this correlation was derived from MSW, it overestimated the correlation and has a higher error value when compared with the present model.

Table 5. Derived correlation compared with previous models
S No.	Name	Correlation (MJ/kg)	Application	AAE (%)	ABE (%)	R²	Reference
(*) shows the correlations obtained in % by mass on a dry basis, whereas the others are on dry ash-free basis.
1.	Proposed Model	HHV = 0.364C + 0.863H − 0.075O + 0.028N − 1.633S + 0.062Cl	MSW	5.738	0.032	0.95	Current model
2.	Channiwala and Parikh	HHV* = 0.3491C* + 1.1783H* + 0.1005S− 0.1034O− 0.0151N* − 0.0211A*	Mixed waste	6.456	2.254	0.95	[19]
3.	Sheng and Azevedo	HHV* = −1.3675 + 0.3137C* + 0.7009H* + 0.0318 (100 − C* − H* − A*)	Biomass	9.657	−3.650	0.92	[20]
4.	Dulong	HHV = 0.3383C + 1.443 (H − (O/8)) + 0.0942S	Coal	11.822	−4.832	0.95	[19]
5.	Chang	HHV = 35.8368 + 0.7523H − 0.2674S − 0.4654O − 0.3814Cl − 0.2802N	MSW	7.234	3.067	0.93	[19]

Figure 1.

Comparison between the experimental and the estimated HHV by the developed correlation.

Figure 2.

Comparison between the experimental and the estimated HHV by the Channiwala and Parikh [19] correlation.

Figure 3.

Comparison between the experimental and the estimated HHV by the Sheng and Azevedo [20] correlation.

Figure 4.

Comparison between the experimental and the estimated HHV by Dulongs correlation.

Figure 5.

Comparison between the experimental and the estimated HHV by Changs correlation.

Standard entropy of municipal solid fuel

For the prediction of the standard entropy of the organic substance in MSW, a correlation in the form of the first-order polynomial was used. The five correlations derived for estimating the standard entropy of waste fractions and the mixture of waste were expressed as follows:

For Plastic waste

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} s_{pl}^0\quad =\quad & 0.0087C+0.0753H+0.0134O\\ & +0.0077N+0.0084\mbox{Cl}\quad (\mbox{kJ}/K\quad \mbox{kg}) \end{array}

(24)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} 10.3\% & \leq C\leq 94.7\%,0.0\%\leq H\leq 14.3\%,0.0\%\leq O\leq 54.2\%,\\ & \quad 0.0\%\leq N\leq 66.7\%. \end{array}

With ABE, AAE, and R² of 0.722, 7.314, and 0.7674, respectively.

For Textile/Rubber waste

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} s_{tr}^0\quad =\quad & 0.0097C+0.0635H+0.0128O+0.0136N\\ & +0.0165S\quad (\mbox{kJ}/K\quad \mbox{kg}) \end{array}

(25)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} 15.8\%\leq & C\leq 95.1\%,3.0\%\leq H\leq 9.7\%,0.0\%\leq O\leq 55.2\%,\\ & 0.0\%\leq N\leq 66.7\%,0.0\%\leq S\leq 42.1\% \end{array}

With ABE, AAE, and R² of 0.714, 6.476, and 0.5457, respectively.

For Wood/Paper waste

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): s_{wp}^0\quad =\quad 0.0162C+0.0116H+0.0081O+0.00691\mbox{Cl}\quad \left(\mbox{kJ}/K\quad \mbox{kg}\right)

(26)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} 26.7\% & \leq C\leq 77.8\%,0.4\%\leq H\leq 7.7\%,5.1\%\leq O\leq 71.1\%,\\ 0.0\% & \leq \mbox{Cl}\leq 66.3\% \end{array}

With ABE, AAE, and R² of 0.329, 5.215, and 0.728, respectively.

For Food waste

(27)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} 19.2\%\leq C & \leq 92.3\%,1.4\%\leq H\leq 14.1\%,0.0\%\leq O\\ & \leq 59.7\%,0.0\%\leq N\leq 51.9\%,0.0\%\leq S\leq 34.0\% \end{array}

With ABE, AAE, and R² of 0.414, 5.886, and 0.6922, respectively.

For Mixed waste

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} s_{msw}^0\quad =\quad & 0.0101C+0.0630H+0.0106O+0.0108N\\ & +0.0155S+0.0084\mbox{Cl}\quad (\mbox{kJ}/K\quad \mbox{kg}) \end{array}

(28)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} 10.3\%\leq & C\leq 95.1\%,0.00\%\leq H\leq 14.3\%,0.0\%\leq O\leq 71.1\%,0.0\%\\ & \leq N\leq 66.7\%,0.0\%\leq S\leq 42.1\%,0.0\%\leq \mbox{Cl}\leq 89.7\%, \end{array}

with ABE, AAE, and R² of 1.118, 8.293, and 0.5414, respectively.

Comparing the five equations obtained, the results show that the standard entropy correlations for each waste fraction in MSW are more accurate than the standard entropy correlation for the waste mixture. This is as a result of complicated mixture, heterogeneous molecule structure and variation in municipal solid waste chemical compositions and properties. Nevertheless, because the standard entropy of plastic, textile/Rubber, wood/paper, food, and waste mixture gave similar average values for the specific exergy of the MSW estimation of 24,359, 24,364, 24,426, 24,393, and 24,387 (kJ/kg), respectively, the correlation of the standard entropy of the waste mixture can be used for the derivation of exergy.

Specific chemical exergy of municipal solid fuel (daf) and specific chemical exergy of ash

By substituting Equation (3)–(8), (23), and (24)–(28) into Equation (18), along with the standard chemical exergy data from Table 1, the specific chemical exergy of solid waste on a dry ash-free basis can be expressed as follows:

For Plastic waste:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} e_P\quad =\quad & 376.879C+787.351H-58.654O+46.398N\\ & -1533.261S+100.981\mbox{Cl}\quad (\mbox{kJ}/\mbox{kg}) \end{array}

(29)

For Textile/Rubber waste:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} e_{TR}\quad =\quad & 376.580C+790.869H-58.475O+44.639N\\ & -1538.180S+98.566\mbox{Cl}\quad (\mbox{kJ}/\mbox{kg}) \end{array}

(30)

For Wood/Paper waste

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} e_{WP}\quad =\quad & 374.642C+806.343H-57.074O+48.693N\\ & -1533.261S+101.425\mbox{Cl}\quad (\mbox{kJ}/\mbox{kg}) \end{array}

(31)

For Food waste

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} \mbox{Food}\quad e_F\quad =\quad & 377.535C+785.711H-58.446O+45.682N\\ & -1536.242S+103.486\mbox{Cl}\quad (\mbox{kJ}/\mbox{kg}) \end{array}

(32)

For mixed waste

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} e_{msw}\quad =\quad & 376.461C+791.018H-57.819O+45.473N\\ & -1536.242S+100.981\mbox{Cl}\quad (\mbox{kJ}/\mbox{kg}) \end{array}

(33)

The minimum, maximum, and average specific exergy values of municipal solid waste calculated were 17,602, 43,396, and 24,387 in (kJ/kg), respectively. Although Equation (33) slightly underestimated the specific chemical exergy calculated by Equations (29) and (30), that is, an ABE of −0.139 and −0.113, respectively, and slightly overestimated the exergy estimated by Equations (31) and (32), that is, an ABE of 0.179 and 0.009, respectively, when compared, the coefficient of determination shows that Equations (29)-(32) are similar to Equation (33) (i.e., a value of 1 was achieved in all cases). This result indicates that Equation (33) can be used to estimate the specific exergy of municipal solid waste, that is, the HHV has more impact on the exergy.

The overall average ratio of the specific exergy of MSW developed with the higher heating value was obtained as 1.036, showing that the value of exergy is slightly higher than the HHV. The ratio of exergies to heating values obtained in this work is similarly when compared with Szargut and Styrylska [7] model with ratio of 1.047. As their methods were commonly used for evaluating the chemical exergy of solid fuels. This result indicates that the present model is reliable and accurate. However, the slight variation in the ratios is due to different types of fuel used.

The specific exergies of inorganic matter in MSW calculated from Equation (22) using the chemical ash composition data in Table 4 are 0.86 and 1.79 kJ/kg for bottom ash and fly ash, respectively. These values are very small when compared with the average specific chemical exergy values, 24,387 kJ/kg of MSW (daf) estimated, demonstrating that the specific chemical exergy of inorganic matter can be neglected.

Conclusions

Following the evaluations of the previous equations for estimating the specific chemical exergy of solid fuels, the present proposed models in this study were found to be more accurate when using municipal solid waste as a fuel. All other methods have either ignored the inclusion of chlorine from the elemental compositions of waste or have used other solid fuels with a limited amount of MSW. In this work, a simple method for estimating the specific exergy of municipal solid waste on (daf) from their ultimate analysis based on HHV, standard entropy, and exergy equation of reaction was proposed.

The higher heating values of the estimated MSW showed a good correlation and a higher accuracy compared with previous models. It is calculated as

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} \mbox{HHV}=\quad & 0.364C+0.863H-0.075O+0.028N\\ & -1.633S+0.062\mbox{Cl}\quad (\mbox{MJ}/\mbox{kg}) \end{array}

The standard entropy of the estimated waste mixture has a rather low accuracy when compared with the waste fractions. However, the standard entropy can be used for the estimation of the specific chemical exergy of a solid, as it showed a similar result with the standard entropy of waste fractions; the standard entropy is expressed as

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} s_{msw}^0\quad =\quad & 0.0101C+0.0630H+0.0106O+0.0108N\\ & +0.0155S+0.0084\mbox{Cl}\quad (\mbox{kJ}/K\quad \mbox{kg}). \end{array}

This result indicates that a higher heating value has more impact on the derivation of the specific chemical exergy of solid waste than entropy. In other words, the specific exergy of MSW mainly depends on the values of HHV.

Due to very low calculated values of specific chemical exergy of inorganic matter in MSW, the specific chemical exergy developed in this work is equal to the specific chemical exergy of the organic matter in MSW and is presented as

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): \begin{array}{rl} E_{msw}\quad =\quad & 376.461C+791.018H-57.819O\\ & +45.473N-1536.242S+100.981\mbox{Cl}\quad (\mbox{kJ}/\mbox{kg}). \end{array}

The results obtained demonstrate that the specific chemical exergy is always slightly higher than the highest heating value, indicating the validity and accuracy of the model.

The present correlation can be accepted for estimating the specific chemical exergy of MSW using the elemental compositions of the fuel within the range specified based on a dry ash-free basis. The model is applicable for the efficient modeling of a combustion system in a waste-to-energy plant.

Acknowledgments

The authors acknowledge the Nigerian Government and Michael Okpara University of Agriculture Umudike, Abia State, Nigeria, for supporting this work through TETfund Academic Staff Training and Development.

Conflict of Interest

None declared.

Nomenclature

AAE

average absolute error

A

ash content in the waste (%)

ABE

average bias error

E

chemical exergy (kJ)

e

specific chemical exergy (kJ/kg) or (kJ/mol)

FC

fixed carbon (%)

G

Gibbs energy (kJ/kg) or (kJ/mol)

H

enthalpy (kJ/kg)

HHV

higher heating value (kJ/kg)

MSW

municipal solid waste

P

pressure (kpa)

R²

coefficient of determination

S

entropy (kJ/K)

S_gen

entropy generated

s

specific entropy (kJ/kg K) or (kJ/mol K)

T

Temperature (K)

V

volatile matter (%)

Subscripts

ba

bottom ash

daf

dry ash-free basis

est

estimate

exp

experiment

fa

fly ash

f

formation

fo

food

ioc

inorganic compound

max

maximum

msw

municipal solid waste or mixed solid waste

o

standard state

pl

plastic

R

reaction

tr

textile/rubber

wp

wood/paper

Superscripts

0

reference state

Greek Symbols

∆

change

∑

summation

Appendix

Table A1. Chemical characteristics of MSW (daf) used for derivation
MSW groups, Subgroup and variety	Proximate analysis (wt %)			Ultimate analysis (wt %)						HHV (MJ/kg)	Reference
MSW groups, Subgroup and variety	A	V	FC	C	H	O	N	S	Cl	HHV (MJ/kg)	Reference
All the proximate, ultimate analysis data and HHV on dry basis are converted to dry ash-free basis. Also all HHV are converted to MJ/kg.
Food waste
1. Flour	–	–	–	42.78	6.19	48.39	2.48	0.15	–	18.157	[21]
2. Rice	0.40	84.42	15.18	45.97	6.35	45.74	1.67	0.25	–	18.213	[22]
3. Peanut shell	–	–	–	53.6	6.70	38.3	1.20	0.20	–	20.598	[21]
4. Pea	–	–	–	42.13	5.88	48.62	3.14	0.22	–	16.533	[21]
5. Scallion	–	–	–	48.12	6.27	41.74	3.09	0.78	–	18.042	[21]
6. Potato	3.15	79.52	17.33	44.41	5.33	47.82	1.81	0.64	–	17.656	[22]
7. Spinach	15.97	65.26	18.77	47.58	6.48	43.93	1.57	0.43	–	20.326	[22]
8. Celery	14.58	65.36	20.06	38.46	6.16	54.52	0.21	0.65	–	15.886	[22]
9. Pakchoi	18.44	63.97	17.59	43.37	5.93	48.64	1.25	0.81	–	23.173	[22]
10. Tangerine peel	2.91	76.49	20.6	48.74	5.92	43.83	1.43	0.08	–	19.024	[22]
11. Banana peel	10.85	64.38	24.77	35.8	4.79	54.93	4.37	0.10	–	18.385	[22]
12. Orange peel	2.44	76.27	21.29	43.93	5.64	48.93	1.34	0.07	0.08	18.550	[21]
13. Rib	–	–	–	52.92	8.83	25.63	2.29	0.32	–	17.277	[21]
14. Fish bone	39.82	56.25	3.93	63.87	8.01	19.08	8.39	0.64	–	26.245	[21]
15. Food waste	6.1	82.11	18.00	51.54	7.14	37.06	3.13	0.21	0.92	21.619	[38]
Wood waste
16. Poplar wood	7.54	73.85	18.61	51.36	5.86	41.00	1.52	0.22	–	20.009	[22]
17. Poplar leaf	15.69	68.74	15.57	49.54	5.24	43.30	1.32	0.59	–	19.986	[22]
18. Chinar leaf	9.23	69.74	21.03	52.95	4.88	40.51	1.01	0.65	–	21.064	[22]
19. Gingko leaf	11.62	73.19	15.19	41.35	5.54	50.88	1.36	0.87	–	17.289	[22]
20. Pine wood	0.95	83.5	15.54	50.51	5.95	43.39	0.11	0.03	–	19.834	[21]
21. Sawdust	0.42	81	18.58	49.42	7.26	42.92	0.39	0.01	–	21.267	[21]
22. Wood	1.00	81.62	18.38	50.10	6.16	43.47	0.17	0.02	0.07	19.697	[38]
23. Wood chips	1.95	82.66	15.4	49.54	6.21	44.06	0.12	0.04	0.03	19.544	[21]
24. Bamboo	0.69	81.03	18.27	50.46	6.32	42.73	0.22	0.1	0.16	19.716	[21]
25. Leaves	8.92	73.7	17.38	47.25	5.57	46.26	0.19	0.73	–	18.882	[21]
26. Pine needles	–	–	–	52.57	6.3	40.44	0.54	0.16	–	20.843	[21]
27. King grass	7.44	74.12	18.43	46.91	5.89	46.3	0.7	0.21	–	19.428	[21]
Paper waste
28. Blank printing paper	10.69	79.33	9.98	45.12	5.31	48.91	0.38	0.28	–	15.127	[22]
29. Tissue paper	0.52	90.47	9.01	45.18	6.13	48.32	0.25	0.11	–	17.340	[22]
30. Newspaper	8.07	79.54	12.39	48.01	5.71	45.86	0.33	0.09	–	18.666	[22]
31. Magazine	29.49	62.44	8.07	41.04	8.99	49.15	0.42	0.4	–	16.771	[21]
32. Writing paper	–	–	–	43.66	5.84	50.16	0.16	0.18	–	13.69	[21]
33. Cardboard	5.27	81.75	12.97	46.09	5.36	48.02	0.32	0.21	–	18.239	[21]
34. Carton	7.22	83.95	8.82	48.97	6.14	44.52	0.21	0.16	–	18.430	[21]
35. Printing paper	9.70	82.83	17.17	47.51	5.98	46.25	0.14	0.03	0.09	18.051	[38]
36. Packaging paper	12.2	85.88	14.12	46.92	5.92	46.74	0.22	0.09	0.10	17.654	[38]
Textile
37. Absorbent cotton gauze	0.14	94.85	5.01	46.74	5.69	47.23	0.27	0.08	–	14.664	[22]
38. Cotton cloth	3.09	78.71	18.21	56.49	5.87	33.3	3.52	0.18	0.65	14.664	[21]
39. Wool	1.24	84.76	14.00	60.07	4.24	31.48	2.65	1.55	–	21.183	[21]
40. Acrylic fiber	0.14	75.25	24.61	66.78	5.2	7.31	20.26	0.45	–	29.812	[21]
41. Chemical fiber	–	–	–	48.09	7.16	34.06	9.43	1.26	–	21.959	[21]
42. Polyester taffeta	0.44	90.63	8.93	60.1	4.5	35.11	0.28	0.01	–	22.178	[21]
43. Terylene	0.49	88.6	10.91	62.16	4.14	33.12	0.29	0.28	–	20.963	[22]
44. Textiles	1.40	82.86	17.14	52.54	6.19	39.26	1.76	0.20	1.42	21.197	[38]
Plastics waste
45. PS	0.04	99.57	0.39	86.06	6.27	1.93	5.73	–	–	38.946	[22]
46. LDPE	–	99.98	0.02	85.98	11.20	2.61	0.21	–	–	46.480	[22]
47. HDPE	0.18	99.57	0.25	85.35	12.70	1.90	0.05	0.14	–	46.444	[22]
48. PVC	–	94.93	5.07	38.34	4.47	–	0.23	0.61	56.35	20.830	[22]
49. PET	0.09	90.44	9.47	63.01	4.27	32.69	0.04	–	–	23.111	[22]
50. PE	0.15	99.85	–	85.45	14.32	–	0.16	0.07	–	46.388	[21]
51. PP	0.02	99.97	0.01	85.41	12.51	1.85	0.23	–	–	46.248	[21]
52. Packaging plastic	3.90	95.21	4.79	75.75	9.78	12.00	0.35	0.03	2.08	26.951	[38]
53. Other plastic	1.30	99.09	0.91	84.90	9.63	0.97	3.35	0.03	1.11	41.135	[38]
Rubber waste
54. Rubber	8.36	84.77	6.86	77.72	10.12	7.42	0	2.66	2.08	25.474	[21]
55. Tire	25.70	68.05	6.25	79.19	8.45	11.38	0.69	0.28	–	35.654	[21]
Other combustibles
56. Other combustibles	20.40	90.83	9.17	70.48	8.79	17.53	1.63	0.83	0.74	32.161	[38]

Table A2. Chemical characteristics of MSW (daf) used for validation
MSW groups, Subgroup and variety	Proximate analysis (wt %)			Ultimate analysis (wt %)						HHV (MJ/kg)	Reference
MSW groups, Subgroup and variety	A	V	FC	C	H	O	N	S	Cl	HHV (MJ/kg)	Reference
All the proximate, ultimate analysis data and HHV on dry basis are converted to dry ash-free basis. Also all HHV are converted to MJ/kg.
Food waste
1. Rice	0.42	87.74	11.84	44.2	5.73	48.75	1.20	0.1	0.02	18.048	[21]
2. Potato	–	–	–	42.09	6.5	49.06	2.12	0.23	–	16.912	[21]
3. Orange peel	2.91	76.49	20.6	48.74	5.92	43.72	1.43	0.19	–	19.024	[21]
4. Rib	38.22	61.56	0.23	51.61	6.38	31.91	9.48	0.69	–	22.716	[21]
Wood waste
5. Wood	0.82	81.64	17.54	48.35	6.62	44.7	0.04	0.29	–	20.868	[21]
6. Wood chips	3.45	81.5	15.05	49.03	5.69	44.98	0.22	0.07	–	19.255	[21]
7. Wooden chopsticks	2.18	83.45	14.37	48.79	5.16	45.7	0.3	0.04	–	19.355	[39]
8. Bamboo	1.79	81.36	16.84	51.42	6.01	41.92	0.36	0.29	–	19.974	[40]
9. Leaves	9.43	74.32	16.25	47.18	5.61	46.35	0.18	0.68	–	20.278	[21]
10. King grass	–	–	–	48.37	6.30	44.58	0.49	0.25	–	22.127	[21]
Paper waste
11. Newspaper	5.43	85.04	9.53	45.24	7.17	47.1	0.25	0.23	–	17.204	[21]
12. Printing paper	12.3	87.65	0.04	44.93	4.55	50.43	0.09	–	–	16.233	[21]
13. Cardboard	–	–	–	46.71	5.31	47.35	0.32	0.32	–	18.367	[21]
14. Toilet paper	0.52	90.47	9.01	45.18	6.13	48.32	0.25	0.11	–	17.337	[21]
15. Paper food cartons	6.93	–	–	48.07	6.55	45.04	0.16	0.17	–	18.137	[41]
16. Magazine stock	29.26	–	–	46.55	6.56	46.44	0.16	0.30	–	17.967	[41]
17. Plastic-coated paper	2.77	–	–	44.53	6.35	46.80	0.19	0.08	–	17.556	[41]
Textile
18. Cotton cloth	1.52	84.53	13.95	46.51	5.8	46.98	0.43	0.28	–	17.699	[22]
19. Cotton	1.45	86.7	11.85	46.19	6.12	47.07	0.54	0.08	–	17.500	[21]
20. Wool	–	–	–	58.53	6.48	18.23	15.12	1.65	–	23.632	[22]
21. Shoe heel and sole	30.09	–	–	76.13	10.14	11.10	0.72	1.92	–	36.676	[41]
22. leather	10.1	–	–	66.74	8.90	12.79	11.12	0.44	–	22.892	[41]
23. Upholstery	2.80	–	–	48.46	6.28	44.86	0.31	0.10	–	17.891	[41]
Plastics waste
24. PE	0.15	99.85	–	85.45	14.32	–	0.16	0.07	–	46.388	[42]
25. PP	0.16	99.84	–	84.3	14.44	1.05	0.18	0.03	–	45.842	[21]
26. PVC	0.04	95.16	4.8	38.75	5.21	–	0.22	–	55.82	22.575	[21]
27. Polyurethane	4.38	87.29	8.32	66.17	6.55	18.46	6.26	0.02	2.53	27.300	[41]
28. Plastic film	6.72	–	–	72.05	10.42	16.96	0.49	0.08	–	34.519	[41]
Rubber waste
29. Rubber	15.38	65.26	19.36	89.18	8.54	–	1.23	1.05	–	39.473	[21]
30. Tire	19.27	63.11	17.61	88.56	8.52	0.88	0.75	1.29	–	37.364	[21]

Table A3. Standard entropies at 298.15K of organic compounds relevant to MSW
Name	Formula	S⁰ (kJ/kg K)
Source: [3, 8, 10, 12, 17, 24].
Food
1. Allantoin	C₄H₆N₄O₃	1.233
2. Alloxan	C₄H₂N₂O₄	1.314
3. Arginine	C₆H₁₄N₄O₂	1.439
4. Asparagine	C₄H₈N₂O₃	1.322
5. Aspartic acid	C₄H₇NO₄	1.279
6. Citric acid	C₆H₈O₇	1.312
7. Creatine	C₄H₉N₃O₂	1.445
8. Cystine	C₆H₁₂N₂O₄S₂	1.347
9. d-Glutamic acid	C₅H₉NO₄	1.230
10. l-Lactic acid	C₃H₆O₃	1.579
11. l-Phenylalanine	C₉H₁₁NO₂	1.293
12. l-Proline	C₅H₉NO₂	1.425
13. Maleic acid	C₄H₄O₄	1.373
14. Malic acid	C₄H₆O₅	1.199
15. Methionine	C₅H₁₁NO₂S	1.552
16. Phenanthrene	C₁₄H₁₄	1.207
17. Trytophan	C₁₁H₁₂N₂O₂	1.229
18. Tyrosine	C₉H₁₁NO₃	1.181
19. Uric acid	C₅H₄N₄O₃	1.030
20. Valine	C₅H₁₁NO₂	1.527
21. Xanthine	C₅H₄N₄O₂	1.059
22. Stearic acid	C₁₈H₃₆O₂	1.531
23. Taurine	C₂H₇NO₃S	1.231
24. Urea	CH₄N₂O	1.742
25. Hexadecanoic acid	C₁₆H₃₂O₂	1.764
26. Adenine	C₅H₅N₅	1.118
27. Creatinine	C₄H₇ON₃	1.483
28. l-Serine	C₃H₇O₃N	1.419
29. l-Glutamine	C₅H₁₀O₃N₂	1.335
30. dl-Alanyl glycine	C₅H₁₀O₃N₂	1.460
31. Glycylglycine	C₄H₈N₂O₃	1.438
32. Alanine	C₃H₇NO₂	1.450
33. Cysteine	C₃H₇NO₂S	1.402
34. Dimethyl sulfone	C₂H₆O₂S	1.509
35. d-Lactic acid	C₃H₆O₃	1.593
36. Fumaric acid	C₄H₄O₄	1.447
37. Guanine	C₅H₅N₅O	1.061
38. Gycine	C₂H₅NO₂	1.379
39. Isoleucine	C₆H₁₃NO₂	1.586
40. Leucine	C₆H₁₃NO₂	1.586
41. l-Glutamic acid	C₅H₉NO₄	1.279
42. 1-Hexadecanol	C₁₆H₃₄O	1.864
43. Hypoxanthine	C₅H₄ON₄	1.070
44. Glycolide	C₄H₄O₄	1.354
Plastic
45. 1,3,5-Trioxane	C₃H₆O₃	1.476
46. Benzophenone	C₁₃H₁₀O	1.346
47. Biphenyl	C₁₂H₁₀	1.358
1.002	48. Hexachloroethane	C₂Cl₆
49. Diphenyl carbonate	C₁₃H₁₀O₃	1.300
50. Diphenyl ether	C₁₂H₁₀O	1.372
51. Diphenylcarbinol	C₁₃H₁₂O	1.330
52. Polypropylene, isotatic	(C₃H₆)_n	1.662
53. Polypropylene, syndiotic	(C₃H₆)_n	1.798
54. Pyromellitic dianhydride	C₁₀H₂O₆	1.087
55. Naphthalene	C₁₀H₈	1.306
56. Succinic acidic	C₄H₆O₄	1.417
57. Cyanuric acid	C₃H₃N₃O₃	1.947
58. Acetamide	C₂H₅NO	1.840
59. Durene	C₁₀H₁₄	1.166
60. Hexamethlenetetramine	C₆H₁₂N₄	1.116
61. Triphenylene	C₁₈H₁₂	1.273
62. Hydroquinone	C₆H₆0₂	1.182
63. Melamine	C₃H₆N₆	1.251
64. Phthalic acid	C₈H₆O₄	1.215
65. Phathalic anhydide	C₈H₄O₃	1.405
66. Triethylenediamine	C₆H₁₂N₂	1.947
67. 4,4′-diphenylmethane diisocyanate	C₁₅H₁₀N₂O₂	1.329
68. Polyisocyanurate	(C₁₅H₁₀N₂O₂)_n	1.175
69. Tridecanolactone	C₁₃H₂₄O₂	1.893
70. Polytridecanolactone	(C₁₃H₂₄O₂)_n	1.656
71. Polyvinylidene chloride	(C₂H₂Cl₂)_n	0.894
72. Polyvinyl chloride	(C₂H₃Cl)_n	1.042
73. poly(1-butene), isotactic	(C₄H₈)_n	1.836
74. Polystyrene	(C₈H₈)_n	1.294
Textile
75. 3-Nitrobenzoic acid	C₇H₅NO₄	1.227
76. 1,2-Diphenylethene	C₁₄H₁₂	1.39
77. Adipic acid	C₆H₁₀O₄	1.504
78. 2-Methlnaphthalene	C₁₁H₁₀	1.547
79. Acenaphthene	C₁₂H₁₀	1.225
80. Anthracene	C₁₄H₁₀	1.164
81. 1,4-Benzoquinone	C₆H₄O₂	1.506
82. Diphenylamine	C₁₂H₁₁N	1.666
83. Pyrene	C₁₆H₁₀	1.112
84. Thiourea	CH₄N₂S	1.523
85. Ammonium thiocyanate	CH₄N₂S	1.842
86. 3-Nitroaniline	C₆H₆N₂O₂	1.276
87. Resorcinol	C₆H₆O₂	1.341
88. Triphenylmethane	C₁₉H₁₆	1.277
89. Triphenylmethanol	C₁₉H₁₆O	1.265
90. Isoquinoline	C₉H₇N	1.324
91. Acridine	C₁₃H₉N	1.161
92. 2-Nitrobenzoic acid	C₇H₅O₄N	1.247
93. 1,3-Phenylenediamine	C₆H₈N₂	1.429
94. Dicyanodiamide	C₂H₄N₄	1.538
95. ε-Caprolactam	C₆H₁₁NO	1.531
96. Poly-ε-Caprolactam	(C₆H₁₁NO)_n	1.529
97. Polyglycolide	(C₄H₄O₄)_n	1.304
Wood
98. l-Sorbose	C₆H₁₂O₆	1.226
99. o-Cresol	C₇H₈O	1.530
100. Oxalic acid	C₂H₂O₄	1.220
101. p-Cresol	C₇H₈O	1.547
102. Sucrose	C₁₂H₂₂O₁₁	1.052
103. d-Mannitol	C₆H₁₄O₆	1.309
104. Pentachlorophenol	C₆HCl₅O	0.946
105. Galactose	C₆H₁₂O₆	1.14
106. Phenol	C₆H₆O	1.53
107. 2-Hydroxybenzoic acid	C₇H₆O₃	1.29
108. Glucose	C₆H₁₂O₆	1.161
109. Xylose	C₅H₁₀O₅	0.956
110. 3-Hydroxybenzoic acid	C₇H₆O₃	1.281
111. 4-Hydroxybenzoic acid	C₇H₆O₃	1.272
112. Benzoic acid	C₇H₆O₂	1.372
113. Catechol	C₆H₆O₂	1.364
114. Lactose	C₁₂H₂₂O₁₁	1.128
115. o-Hydroxybenzoic acid	C₇H₆O₃	1.29
116. o-Hydroxybenzoic acid	C₇H₆O₃	1.281
117. o-Hydroxybenzoic acid	C₇H₆O₃	1.272

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