Estimating the higher heating value of biomass fuels from basic analysis data

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Biomass and Bioenergy 28 (2005) 499–507 www.elsevier.com/locate/biombioe

Estimating the higher heating value of biomass fuels from basic analysis data Changdong Sheng1, J.L.T. Azevedo Mechanical Engineering Department, Instituto Superior Te´cnico, Pavilha˜o de Meca˜nica I, 21 Andar, Av. Rovisco Pais, 1049-001 Lisbon, Portugal Received 20 January 2003; received in revised form 13 October 2004; accepted 17 November 2004

Abstract The heating value is one of the most important properties of biomass fuels for design calculations or numerical simulations of thermal conversion systems for biomass. There are a number of formulae proposed in the literature to estimate the higher heating value (HHV) of biomass fuels from the basic analysis data, i.e. proximate, ultimate and chemical analysis composition. In the present paper, these correlations were evaluated statistically based on a larger database of biomass samples collected from the open literature. It was found that the correlations based on ultimate analysis are the most accurate. The correlations based on the proximate data have low accuracy because the proximate analysis provides only an empirical composition of the biomass. The correlations based on the bio-chemical composition are not reliable because of the variation of the components properties. The low accuracy of previous correlations is mainly due to the limitation of samples used for deriving them. To achieve a higher accuracy, new correlations were proposed to estimate the HHV from the proximate and ultimate analyses based on the current database. The new correlation between the HHV and dry ash content of biomass (in weight percent, wt%) (i.e. HHV (MJ/kg) ¼ 19.914–0.2324 Ash) could be conveniently used to estimate the HHV from proximate analysis. The new formula, based on the composition of main elements (in wt%) C, H, and O (i.e. HHV ðMJ=kgÞ ¼ 1:3675 þ 0:3137 C þ 0:7009 H þ 0:0318 O ), is the most accurate one, with more than 90% predictions in the range of 5% error. r 2005 Elsevier Ltd. All rights reserved. Keywords: Biomass; Higher heating value; Correlations

Corresponding author. Tel.: +351 218 417 993;

fax: +351 218 475 545. E-mail address: [email protected] (J.L.T. Azevedo). 1 Present address: Department of Power Engineering, Southeast University, Nanjing 210096, PR China.

1. Introduction Environmental and economic concerns of reducing greenhouse gas CO2 emissions and of increasing fuel flexibility have been motivating

0961-9534/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.biombioe.2004.11.008

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using biomass fuels to substitute fossil fuels for heat and electricity generation. Among the various conversion technologies, combustion is the most common and developed way of converting biomass fuels to energy [1–3]. The design and operation of biomass combustion systems significantly relies on biomass characteristics such as the heating value, moisture content, elemental composition, ash properties, etc. [4]. The heating value, also called calorific value or heat of combustion, defines the energy content of a biomass fuel and is one of the most important characteristic parameters for design calculations and numerical simulations of thermal systems no matter how biomass is used, direct combustion [1] or co-firing with other fuels (e.g. coals) [1–3]. Generally, the heating value of a fuel may be reported on two bases, the higher heating value or gross calorific value and the lower heating value or net calorific value. The higher heating value (HHV) refers to the heat released from the fuel combustion with the original and generated water in a condensed state, while the lower heating value (LHV) is based on gaseous water as the product. The heating value of a biomass fuel can be determined experimentally by employing an adiabatic bomb calorimeter, which measures the enthalpy change between reactants and products. However, the measurement is a complicated and time-consuming process that requires the set-up, measurement and calculation procedures. In contrast, the conventional analysis, i.e. proximate and ultimate analyses, is a basic fuel characterisation and can be carried out more easily, quickly, and cheaply by using common or modern laboratory equipments. Therefore, many attempts have been made to estimate the HHV based on correlating the heating value of biomass with the data of proximate analysis [5–7] and ultimate analysis [7–13]. Additionally, chemical analysis, dividing biomass organic matter into four bio-chemical components (i.e. cellulose, hemicellulose, lignin and extractives) and determining their contents, is sometimes conducted to characterise a biomass. Therefore, a few formulae were also proposed to correlate the HHV with biomass chemical composition [5,8,14,15].

So many correlations are available in the literature and each was reported with a high accuracy applied to the investigator’s own database. An extrapolation to various biomass species, however, leads to considerable differences between the calculated results of the correlations (e.g. [10,12]). As a result, it would be very confusing for engineers to make their own selection. In the present paper, the correlations proposed and applied for the estimation of biomass HHV in the literature are reviewed. The accuracy of these correlations is statistically evaluated based on a database of a large quantity of biomass samples collected from the open literature. The objective of the present work is to provide quantitative evidences for the correlation selection in engineering applications. Moreover, a couple of new correlations are also proposed with improved accuracy.

2. Methodology Fifteen correlations proposed and/or applied for estimating the biomass HHV were collected from the literature, which are summarised in Table 1. The correlations are combined into three groups according to the approaches used, i.e. estimating the HHV based on the proximate, ultimate and chemical analysis, including four correlations based on the proximate data (Eqs. (1), (3–5)), seven based on the ultimate analysis (Eqs. (7), (9–14)) and four based on the chemical composition (Eqs. (16–19)). It can be seen in Table 1 that the coefficients of the formulae in the same groups are considerably different. Therefore, it is not surprising that the resulting predictions might also be very different and the accuracy of a correlation must be evaluated to make a proper selection. Generally, the inaccuracy of a formula is most probably attributed to the limited biomass samples used for its derivation although the analysis methods used in the biomass characterisation as well as the method of deriving the formulae also have influence. In the present work, a large quantity of biomass samples together with their HHVs and the basic analysis data were collected from the open literature, mainly [3–8,11,12,16–22],

Table 1 HHV correlations and their evaluationsa Number Name of author

Correlation (HHV, MJ/kg)

AAE (%) ABE (%) Coefficient, R2

HHV ¼ 10:81408 þ 0:3133 ðVM þ FCÞ HHV ¼ 19:914  0:2324 Ash HHV ¼ 0:196 FC þ 14:119 HHV ¼ 0:312 FC þ 0:1534 VM HHV ¼ 0:3543 FC þ 0:1708 VM HHV ¼ 3:0368 þ 0:2218VM þ 0:2601FC

4.43 3.78 8.85 7.69 5.68 3.65

1.16 0.30 5.60 6.97 4.23 0.26

0.533 0.625 0.647 0.306 0.247 0.617

(7) (8) (9) (10) (11) (12) (13) (14) (15)

Based on ultimate analysis Tillman [8] Current authors Boie [11] IGT [9] Graboski and Bain [10] Channiwala and Parikh [12] Demirbas [7] Jenkins [13] Current authors

HHV ¼ 0:4373 C  1:6701 3.73 HHV ¼ 0:3259 C þ 3:4597 3.16 HHV ¼ 0:3516 C þ 1:16225 H  0:1109 O þ 0:0628 N þ 0:10465 S 3.51 HHV ¼ 0:341 C þ 1:322 H  0:12 O  0:12 N þ 0:0686 S  0:0153 Ash 3.55 HHV ¼ 0:328 C þ 1:4306 H  0:0237 N þ 0:0929 S  ð1  Ash=100Þð40:11 H=CÞ + 0.3466 4.26 HHV ¼ 0:3491 C þ 1:1783 H þ 0:1005 S  0:1034 O  0:0151 N  0:0211 Ash 3.47 HHV ¼ 0:335 C þ 1:423 H  0:154 O  0:145 N 6.73 HHV ¼ 0:763 þ 0:301 C þ 0:525 H þ 0:064 O 2.95 HHV ¼ 1:3675 þ 0:3137 C þ 0:7009 H þ 0:0318 O b 2.59

0.49 0.19 0.59 1.18 2.85 0.11 1.67 1.78 0.07

0.666 0.758 0.720 0.695 0.647 0.733 0.081 0.792 0.834

(16) (17) (18) (19)

Based on chemical compositionc Shafizadeh and Degroot [15] Jimennez and Gonzalez [5] Tillmand [8] Demirbase [14]

HHV ¼ 0:1739 Ce þ 0:2663 L þ 0:3219 E HHV ¼ ½1  Ash=ð100  AshÞ ð0:1739 Ce þ 0:2663 L þ 0:3219 EÞ HHV ¼ 0:1739 Ce þ 0:2663ð1  Ce0 Þ HHV ¼ 0:0889 L þ 16:8218

6.90 1.92 4.10 8.50

0.503 0.451 1.068 0.875

7.62 7.41 9.24 10.96

a

Biomass composition, VM, FC, Ash, C, H, O, N, S are weight percent on dry biomass basis. Here O is the sum of the contents of oxygen and other elements (including S, N, Cl, etc.) in the organic matter, i.e. O ¼ 100  C  H  Ash: c Ce, L, E are weight percent of cellulose (including cellulose and hemicellulose), lignin and extractives on dry biomass basis, respectively. d Ce0 is cellulose (cellulose and hemicellulose) on dry extractable-free basis. e HHV and L in this equation are on dry ash free and extractable-free bases. b

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Based on proximate analysis Jimennez and Gonzalez [5] Current authors Demirbas [7] Demirbas [7] Cordero et al. [6] Current authors

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(1) (2) (3) (4) (5) (6)

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to form a database for the valuation. The characteristic data includes the measured HHV and at least one set of the three analysis data. The database includes 209 biomass samples having HHVs and proximate data [3–8,12,16–22], 191 biomass samples having HHVs and ultimate data [4,6,7,11,12,16–22] and 49 biomass samples with HHVs and chemical composition data [5–8,14,16,17]. There are a few public databases of biomass characteristics, such as ECN’s Phyllis [23] and IEA Task 32 database [24], available on the Internet, with information from more samples but the data are grouped and sometimes when isolated are not complete. The present study includes most of the data used for deriving previous correlations, so that the capacity of these correlations extended to cover more biomass samples can be accessed. Moreover, in the current database, not only the number of biomass species and samples, having both the HHVs and the analysis data, is large but also the properties cover the whole range of the biomass fuels, therefore the biomass materials and the related analysis data are comprehensive. For the sake of comparison, the reported heating values are all converted into the higher heating values on dry biomass basis, MJ/ kg, and the proximate, ultimate and chemical composition data are presented as weight percent on dry basis. The estimations are compared with the measured HHVs to evaluate the correlations. Three statistical parameters are employed as evaluating parameters, which are defined as follows: Average absolute error ðAAEÞ  n   1X HHV E  HHV M   100%, ¼   n HHV i¼1

M

Average bias error ðABEÞ n 1X HHV E  HHV M ¼  100%, n i¼1 HHV M Correlation coefficient ðR2 Þ n X ðHHV E  HHV M Þ2 = ¼1 i¼1

ðHHV M  HHV M Þ2 ,

where subscribes E and M denote the estimated and measured values, respectively, HHV M is the measured average HHV of all samples and n is the number of samples. AAE indicates the average error of a correlation. A lower AAE value means a smaller error of the correlation. ABE presents the average bias error of the correlation. A positive ABE value implies an overall overestimation while a negative one means an overall underestimation. The smaller the absolute value of the ABE is, the smaller the bias of the correlation. R2 ; used widely in statistical and regression analyses, is employed as a comprehensive parameter to quantify the accuracy of the correlation. A correlation with a higher R2 value makes a better estimation (A perfect correlation has a R2 of 1). The above three parameters are fundamental statistical criteria widely used in the error analysis, and also have been used to assess the fuel heating value correlations (e.g. [12]). Therefore they are adopted here as the evaluation parameters. The values of the three parameters for all the correlations are calculated and also listed in Table 1. The evaluations are performed on the three groups of the correlations respectively to establish the accuracy based on different analysis data so that the users can select a better formula for the HHV estimation whatever the analysis data of biomass available, e.g. estimating the HHV with proximate analysis data. Moreover, all the correlations are compared together to present a whole picture of the correlations.

3. Results and discussion 3.1. Correlation based on proximate analysis Proximate analysis presents the weight percent of the moisture, volatile matter (VM), fixed carbon (FC) and ash in a biomass material. It is the easiest and most widely used method to characterise a biomass fuel. Therefore, correlating the heating value with the proximate analysis data are always attractive to fuel researchers and engineers. Four such correlations have been recently reported in the literature, i.e. Eqs. (1) [5], (3) and (4) [7] and (5) [6].

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The HHV is firstly plotted as a function of the ash, VM, and FC contents in Fig. 1 to qualitatively show the correlation between the HHV and proximate analysis data. A clear trend can be seen in Fig. 1a that the HHV decreases with the

HHV, MJ/kg on dry basis

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20

15

10

5

Measured Equation 1 Equation 2 0

5

10

(a)

15

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25

Ash, wt% on dry basis

HHV, MJ/kg on dry basis

25

20

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10

5 50

60

70

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90

VM, wt% on dry basis

(b)

HHV, MJ/kg on dry basis

25

20

15

10

5

(c)

5

10

15

20

25

30

35

FC, wt% on dry basis

Fig. 1. HHV is correlated with proximate contents of biomass fuels (a) ash, (b) volatile matter (VM), and (c) fixed carbon (FC).

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increase of ash content in biomass materials, which was also observed by Jenkins et al. [4]. For the current database, there is a significant correlation between the HHV and the dry ash content ðR2 ¼ 0:625Þ: In contrast, only a trend exist between the HHV and the volatile matter ðR2 ¼ 0:307Þ while there is no correlation with fixed carbon ðR2 ¼ 0:042Þ as can be seen in Fig. 1b and 1c. Obviously, the good correlation between the HHV and the biomass ash content may be applied for estimating the HHV. Jimenez and Gonzalez [5] proposed an equation to correlate the HHV against the sum of VM and FC contents, i.e. Eq. (1) in Table 1. Considering Ash ¼ 100  ðVM þ FCÞ; it can be converted to the correlation between the HHV and the ash content. It was reported that the equation estimated the heating value with errors o10% for the materials they studied [5]. Evaluated with the current database, however, it is found that the correlation coefficient is quite low ðR2 ¼ 0:524Þ and a high positive ABE means its overall overestimation of the HHV. The prediction of this correlation, plotted in Fig. 1a with the dashed line, shows that it overestimates the HHV at low ash contents and underestimates at high ash contents. Therefore, a new correlation is proposed with the least-square regression method, which is also assessed in Table 1 (Eq. (2)) and its prediction is plotted with solid line in Fig. 1a for comparison. Both the evaluation parameters and the plot clearly show the improvement. Nevertheless, the accuracy is still not high (R2 is only increased to 0.625). The reason is that the ash does not make a contribution to the heat release of the biomass combustion. Actually, the HHV in our database varies in the range of about 14.0–22.5 MJ/kg. Converted to the HHV on dry ash free basis, the range is only a bit narrowed to 16.0–23.0 MJ/kg, still a wide variation. Due to the lack of correlation between the HHV and VM, FC (Fig. 1b and c), it is futile to establish a formula for estimating the HHV from only VM or FC. Table 1 indicates very poor quality of such kind of correlations, e.g. Eq. (3), although it was reported well done as applied to the samples to derive it [7].

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The other two correlations based on the proximate analysis of the biomass, i.e. Eqs. (4) [7] and (5) [6], have also low quality (see Table 1). Eq. (4) significantly underestimates the HHV ðABE ¼ 6:97%Þ; while Eq. (5) significantly overestimates HHV ðABE ¼ þ4:23%Þ: Since the measurement data containing the HHV and the proximate analysis are widely available in the literature while the current correlations are very inaccurate, we proposed here a more accurate correlation based on the present database (see Eq. (6) in Table 1). Eq. (6) was obtained simply by the least-squares regression. It can be found in Table 1 that the improvement is significant with lower errors and the correlation coefficient increases a lot to R2 ¼ 0:617: The average relative error is 3.65%, therefore, it may be acceptable for engineering estimations. Nevertheless, the accuracy of this equation (say R2 ) is still not high, similar to that of Eq. (2), i.e. the correlation between the HHV and dry ash. The only reason is that the proximate data VM and FC may not be enough for representing the variation of biomass composition and its effect on the HHV.

(a)

3.2. Correlations based on ultimate analysis

(b)

HHV, MJ/kg on dry basis

25

20

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10

Measured Equation 7 Equation 8

5 30

35

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45

50

55

60

Carbon, wt% on dry basis

HHV, MJ/kg on dry basis

25

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15

10

5

4

5

6

7

8

9

Hydrogen, wt% on dry basis

HHV, MJ/kg on dry basis

25

Biomass is composed of elements C, H, O, N, S, and Cl, where the former three are the major, representing up to 97–99% of the biomass organic mass. Ultimate analysis gives the weight percent of the elements. In Fig. 2, the HHV is plotted against the contents of the three main elements. It can be seen in Fig. 2 that the HHV increases with the increase of C and H contents, consistent with commonsense that higher C and H contents mean a higher energy content of a biomass. On the other hand, no trend is shown between the HHV and the oxygen content (see Fig. 2c) although it is generally considered that oxygen is not a reactive element and increasing the O content leads to a decrease of the HHV. Due to the high correlation between the HHV and C, Tillman proposed a very simple equation (Eq. (7) in Table 1) to calculate the HHV from the biomass carbon content [8]. The evaluation (Table 1) indicates that such a simple equation gives a pretty good correlation ðR2 ¼ 0:67Þ: The estimation using this equation,

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5 30

(c)

35

40

45

50

Oxygen, wt% on dry basis

Fig. 2. HHV is plotted against the contents of main elements in biomass (a) carbon, (b) hydrogen, and (c) oxygen.

presented as the dashed line in Fig. 2a, yields a nice prediction. Nevertheless, the positive ABE (0.49%) in Table 1 implies a bit overestimation for the HHV mainly because Tillman’s equation was derived based on a limited amount of biomass

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expected, the new correlation is more accurate than all the above equations. The predictions of the three best equations based on the elemental composition (i.e. Eqs. (8), (12) and (15)) are compared with the measurements in Fig. 3. Just as indicated by the evaluation 24

Equation 8

HHV estimated

22

20

18

16

14

12 12

14

16

(a)

18

20

22

24

20

22

24

20

22

24

HHV measured 24

Equation 12

HHV estimated

22

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16

14

12 12

14

16

18

HHV measured

(b) 24

Equation 15 22

HHV estimated

species. In the present work, a new correlation was attempted by the least-squares regression (Eq. (8) in Table 1), which provides a much higher accuracy ðR2 ¼ 0:76Þ: The prediction is also shown, plotted as the solid line in Fig. 2a. In the literature, many sorts of empirical correlations have been established to estimate the HHV from the elemental composition particularly for coals and for other hydrocarbon fuels (e.g. biomass, char, oil) as well. Most of these formulae are the modifications of the famous Dulong’s equation. Considering biomass constituted of similar elements as coal, some correlations for estimating the coal heating value have been extended to biomass, such as Boie’s equation (Eq. (9)) suggested by Annamalai et al. [11], IGT equation [9] (Eq. (10)) and Eq. (12) proposed by Channiwala and Parikh [12]. Additionally, several correlations have been proposed especially for biomass, e.g. Eqs. (11), (13) and (14). The calculated evaluation parameters of these correlations, presented in Table 1, indicate that, except Eq. (13), all these correlations are more accurate than those based on the proximate data, because ultimate analysis quantifies the elemental contents providing more detailed chemical composition information on biomass. Among the equations based on the contents of all elements, Eq. (11) is the poorest since it was empirically derived from the formation energy, while the other three (namely Eqs. (9), (10), (12)) have a very similar accuracy. The most recent formula, i.e. Eq. (12) [12], has the highest accuracy, while both Eqs. (9) and (10) underestimate the HHV. Surprisingly, the correlation proposed by Jenkins (Eq. (14)) has the highest correlation efficient ðR2 ¼ 0:792Þ among all previous correlations although it only considers the three main elements i.e. C, H, and O. Nevertheless, it has a considerably high ABE (+1.78%), i.e. overestimating HHV. Therefore, a further attempt was made for the improvement. Considering C, H, O composing of up to 97–99% of the organic mass, and the other elements are minor, difficult to measure and actually not measured in most cases, therefore, the content of these minor elements are lumped into that of O to establish a new equation (Eq. (15)). The evaluation in Table 1 shows that, just as

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20

18

16

14

12 12

(c)

14

16

18

HHV measured

Fig. 3. Comparison of measured and estimated HHVs. (a) Eq. (8), (b) Eq. (12), and (c) Eq. (15). The solid lines indicate the estimation equals to the measured value, while the dashed lines denote 5% relative errors.

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parameters in Table 1, while Eqs. (8) and (12) have a very similar accuracy, the new equation (Eq. (15)) is the most accurate, with 91% samples located within 5% errors, therefore it is acceptable for engineering use.

analysis data including both the HHV and the chemical analysis data are not widely available, no attempt was made for a more accurate correlation.

4. Conclusions 3.3. Correlations based on chemical analysis Chemically, biomass is made up of similar components, i.e. cellulose, hemicellulose, lignin and a small portion of solvent extractives. Chemical analysis is sometimes conducted to characterise biomass materials. As a result, a few equations were proposed to correlate the HHV with the chemical composition. Four such equations proposed in the literature (Eq. (16–19)) are listed in Table 1 and evaluated on a database of 49 biomass materials collected from Refs. [5–8,14,16,17]. Table 1 indicates that all these correlations are of very poor quality although good correlations were reported for the materials they were derived from. Theoretically, only cellulose has a uniform chemical formula, therefore has an almost constant HHV (nearly 18.6 MJ/kg). Hemicellulose is said to have a similar chemical structure as cellulose, however, its chemical composition depends on the biomass species and analysis procedure [10]. It is well known that lignin has various chemical structures too, therefore values of HHV from 23.3–25.6 MJ/kg. As to the extractives, its chemical structure also depends on biomass species and the extractive solvents used. In a word, the chemical components of biomass, except cellulose, have different chemical structure and composition, consequently, the heating values of these components may vary a lot among different biomass species. Moreover, the chemical composition of biomass not only varies with biomass materials but also with the analysis procedure. Therefore, it is not surprising that the accuracy of the correlations based on the biomass chemical composition is not good. Even only on dry, ash and extractive free basis, there is still lack of correlation between the HHV and the chemical composition (not shown here). Since the chemical analysis is not conventional to characterise biomass as a fuel in engineering practice and the

In the literature, there are many empirical formulae for estimating the higher heating value of biomass fuels from the basic analysis data, i.e. proximate, ultimate and chemical analyses. In the present paper, the accuracy of these formulae was statistically evaluated based on a large database of biomass samples collected from the literature. Mainly due to the limitation of samples as deriving these correlations, the accuracies are generally not high. Therefore, new correlations were proposed based on the proximate and ultimate data of the current database. The following conclusions were obtained from the present work: 1. The accuracy of the correlations based on the proximate analysis data are very low because the analysis provides only the empirical composition of biomass. A new formula correlating the HHV with the ash content on dry biomass basis (i.e. HHV ðMJ=kgÞ ¼ 19:914–0.2324 Ash) was proposed, which has the highest accuracy compared to its counterparts and may be used for convenience to estimate the biomass HHV. 2. The formulae based on the ultimate analysis are generally more accurate than those based on proximate analysis. The newly proposed correlation estimating the HHV from the composition of main elements C, H, and O (i.e. HHV ðMJ=kgÞ ¼ 1:3675 þ 0:3137 C þ 0:7009 H þ 0:0318 O Þ is the most accurate one, with more than 90% predictions in the range of 5% error. 3. The quality of the correlations based on chemical analysis was found to be very poor because of the variation of the biomass components properties as well as the biomass chemical composition. 4. The correlation coefficients of all the correlations, including the proposed, are less than 0.85. This shows the effect of variations in the

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biomass components. Nevertheless, the best correlations (e.g. Eq. (15)) may be acceptable in engineering applications for estimating the biomass heating value.

Acknowledgements Support from PRAXIS XXI/BPD/20160/99 of FCT (Fundaca˜o para a Cieˆncia e a Tecnologia) of the Ministry of Science and Technology of Portugal to Dr. C.-D. Sheng is appreciated.

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