Thermochemical Properties for Valorization of Amazonian Biomass as Fuel

Abstract

The use of agroforestry residues for energy purposes has long been a reality in Brazil. About 84.8% of the produced electricity comes from renewable resources; vegetable biomass contributes 9.1% to this total. This percentage has the potential to increase if Amazon biomass residues are processed to be used as fuel. The major difficulty for this scenario is the lack of available information on energy properties, mainly the HHVs for Amazon agroforestry biomass types. Considering that there are important deviations in the equations for predicting the HHVs of Amazon biomass types in the literature, the main objective of this work was to propose equations to determine the HHVs of these biomass types using the proximate or ultimate analysis results as input. The methodology adopted to develop such equations was simple and multiple linear regression methods, using experimental results for HHVs and proximate and ultimate analyses for biomass types from the north region of Brazil. Four distinct equations were considered based on ranges from the proximate and ultimate analyses of the biomass types to deliver better results. The obtained equations were validated by application to 28 other biomass types from the same region. The proposed HHV equations presented good agreement between predicted and experimental values, with errors below 5% for equations based on proximate analysis and below 3% for equations based on ultimate analysis.

1. Introduction

Different to most countries worldwide where renewable resources typically produce, on average, 27% of consumed electricity, Brazilian renewable electricity amounts to 84.8%. In this total, vegetable biomass contributes 9.1%, the major source being sugarcane bagasse [1,2]. This percentage has the potential to increase if Amazon biomass residue is converted into fuel.

The Amazon region is a unique ecosystem in the world. In Brazil, the Amazon region has an approximate area of 5,000,000 km², which is about 58.9% of the national territory. The region has around 2500 species of large trees and 30,000 species of cataloged plants [3].

Amazon region agro-industrial activities have a significant amount of solid waste without a proper destination, resulting in an environmental liability [3]. The agents of this sector know that they could use agroforestry residues for energy production, since the conversion technologies are available, requiring adjustments depending upon biomass properties; however, they do not know which type of residue can be applied. Such a lack of knowledge is specifically associated with the lack of information on biomass thermochemical properties, which are essential in predicting the behavior of a fuel in equipment that involves combustion, gasification or pyrolysis processes, such as boilers and reactors [3]. The absence of technical information results in resistance to using locally available biomass residues for thermochemical process [4].

There is little published information on the thermochemical properties of these large amounts of biomass types; specifically, proximate and ultimate analyses and, in particular, the high heating value (HHV). This is related to the lack of experimental infrastructure that would make it possible carry out these studies in the Amazon region, as it is costly and, furthermore, the price of HHV determination in external laboratories is high. However, users can obtain good estimations of HHVs using analytical correlations [3,4,5] based on proximate analysis or ultimate analysis, which are less costly than the experimental determination of HHVs.

Currently, there are several correlations in the literature to determine HHVs [6,7,8]. Most existing HHV equations are obtained from proximate analysis, since the equipment and the procedure to obtain experimental data are more economical and simpler in comparison to ultimate analysis [9,10,11,12].

Table 1 shows that various authors have different approaches to obtain HHV equations. Some use the proximate results and others use the ultimate results. Using the proximate results [5,13,14,15,16,17,18], a combination of volatile and fixed carbon contents are applied [15,16,17,19], while a combination of volatile and ash contents are used elsewhere [5]. Concerning the statistical procedure, the function intercepting the axis at origin (zero interception) is used by some authors [13,16,17]. Elsewhere, the technique of correlating variables through division can be observed [7], and such an approach probably mitigates the effects of multicollinearity. An approach that combines all solutions in nonlinear regression is well-presented in [18]. It can be seen that equations based on ultimate analysis present correlations between the chemical elements with almost all compounds (C, H, O, N and S) [19,20,21,22] and, in a more simple and practical equation, only with the carbon dependence [19,23,24].

A variety of HHV equations for biomass from different types of residues can be founded in the open literature. A well-known characteristic of biomasses is their wide diversity of species and their susceptibility to the environmental conditions of origin (land, climate, etc.), which lead to chemical variations in their composition, even if the same species is grown in different locations [25]. Among the characterization methods available in the literature are ultimate analysis and proximate analysis. The HHV prediction equations can use carbon, hydrogen, nitrogen, sulfur and oxygen (from ultimate analysis) or volatiles, fixed carbon and ash (proximate analysis), or they may even combine the information from both analyses [26,27,28]. Therefore, the use of a wide range of data points and fuel types can provide a general equation, but it is not very accurate or applicable for other fuel types. Table 1 shows HHV equations for agricultural and wood biomass easily found in the open literature.

The local industrial sector in the Amazon region uses equations to determine HHVs that were developed from the thermochemical properties of European species or from other countries. This practice leads to inaccuracies in the HHVs that compromise the success of the thermal process. Thus, the gap in the scientific literature on HHV correlations for Amazonian biomass residues needs to be addressed.

Therefore, the main objective of this work was to propose equations to determine the HHVs of these biomasses types using proximate analysis or ultimate analysis results as input. Exclusive data from the proximate and ultimate analyses and the HHV for selected biomasses from the Amazon region are also presented. The methodology adopted to develop such equations involved simple and multiple linear regression methods using the experimental data from proximate or ultimate analyses and experimental HHV results for 55 biomass types from the northern region of Brazil.

Table 1. Equations to determine HHVs from proximate analysis (volatiles (V), fixed carbon (FC) and ash (A)) or elemental analysis (carbon (C), hydrogen (H), oxygen (O), nitrogen (N), sulfur (S) and ash (A)).

Equation	Source	HHV Equation (MJ/kg) wt. %, Dry Basis	Biomass Data Origin	Type of Analysis
(1)	[23]	HHV = −1.6701 + 0.4373 × C	Wood from different countries	Ultimate
(2)	[21]	HHV = −0.763 + 0.301 × C + 0.525 × H + 0.064 × O	Field crop residues, orchard pruning, vineyard pruning, food and fiber processing wastes, forest residues and energy crops from California	Ultimate
(3)	[15]	HHV = −10.81408 + 0.3133 × (V + FC)	Agricultural residues from Spain	Proximate
(4)	[5]	HHV = 35.43 − 0.1835 × V − 0.3543 × A	Forest and agricultural wastes/chars from Spain and Cuba	Proximate
(5)	[16]	HHV = 0.1534 × V + 0.312 × FC	Turkey	Proximate
(6)	[19]	HHV = −1.3675 + 0.3237 × C + 0.7009 × H + 0.0318 × O	Various types from the open literature	Ultimate
(7)	[19]	HHV = 3.4597 + 0.3259 × C	Various types from the open literature	Ultimate
(8)	[19]	HHV = −3.0368 + 0.2218 × V + 0.26 × FC	Various types from the open literature	Proximate
(9)	[22]	HHV = 0.3491 × C + 1.1783 × H + 0.1005 × S − 0.1034 × O − 0.0151 × N − 0.0211 × A	Gases, liquids, solid fuels (coal/coke), wood, sawdust, refuse, MSW, animal waste from the open literature	Ultimate
(10)	[13]	HHV = 0.3536 × FC + 0.1559 × V − 0.0078 × A	Fuels such as coals/lignite/manufactured fuel/all kinds of biomass/industry waste from the open literature	Proximate
(11)	[20]	HHV = 0.3560 + 0.4328 × C − 0.2977 × H + 0.2874 × N	Straw from China	Ultimate
(12)	[17]	HHV = 0.1905 × V + 0.2521 × FC	Agricultural byproducts/wood from Argentina, Australia, Cuba, Greece, India, Morocco, the Netherlands, Spain, Turkey and the United States of America	Proximate
(13)	[17]	HHV = 0.2949 × C + 0.8250 × H	Agricultural byproducts/wood from Argentina, Australia, Cuba, Greece, India, Morocco, the Netherlands, Spain, Turkey and the United States of America	Ultimate
(14)	[26]	HHV = −3.393 + 0.507 × C − 0.341 × H + 0.067 × N	Crop species from Spain	Ultimate
(15)	[26]	HHV = −13.173 + 0.416 × V	Crop species from Spain	Proximate
(16)	[14]	HHV = 19.2880 − 0.2135 × (V/FC) − 1.9584 × (A/V) + 0.0234 × (FC/A)	Various types from the open literature	Proximate
(17)	[12]	HHV = 0.879 × C + 0.321 × H + 0.056 × O − 24.826	Oil palm fronds from Malaysia	Ultimate
(18)	[24]	HHV = 0.4373 × C − 1.6701	Agroforestry biomass from Russia	Ultimate
(19)	[27]	HHV = 0.2328 × C + 6.9703	Various types from the open literature	Ultimate
(20)	[18]	HHV = −0.0038 × (−19.9812 × FC1.2259) + (−1.0298 × 10−13 × V × 8.0664) + (0.1026 × A2.423) + (−1.2065 × 10−7 × FC × A4.6653 + 0.0228 × FC × V × A) + (−0.2511 × (V/A) − (0.0478 × (FC/V)) + 15.7199	Various types from the open literature	Proximate
(21)	[28]	HHV = 0.3826 × C − 0.3681 × H + 2.7882 × S − 0.0378 × O + 0.9262	Biomass/biochar from Malaysia	Ultimate

Table 1. Equations to determine HHVs from proximate analysis (volatiles (V), fixed carbon (FC) and ash (A)) or elemental analysis (carbon (C), hydrogen (H), oxygen (O), nitrogen (N), sulfur (S) and ash (A)).

Equation	Source	HHV Equation (MJ/kg) wt. %, Dry Basis	Biomass Data Origin	Type of Analysis
(1)	[23]	HHV = −1.6701 + 0.4373 × C	Wood from different countries	Ultimate
(2)	[21]	HHV = −0.763 + 0.301 × C + 0.525 × H + 0.064 × O	Field crop residues, orchard pruning, vineyard pruning, food and fiber processing wastes, forest residues and energy crops from California	Ultimate
(3)	[15]	HHV = −10.81408 + 0.3133 × (V + FC)	Agricultural residues from Spain	Proximate
(4)	[5]	HHV = 35.43 − 0.1835 × V − 0.3543 × A	Forest and agricultural wastes/chars from Spain and Cuba	Proximate
(5)	[16]	HHV = 0.1534 × V + 0.312 × FC	Turkey	Proximate
(6)	[19]	HHV = −1.3675 + 0.3237 × C + 0.7009 × H + 0.0318 × O	Various types from the open literature	Ultimate
(7)	[19]	HHV = 3.4597 + 0.3259 × C	Various types from the open literature	Ultimate
(8)	[19]	HHV = −3.0368 + 0.2218 × V + 0.26 × FC	Various types from the open literature	Proximate
(9)	[22]	HHV = 0.3491 × C + 1.1783 × H + 0.1005 × S − 0.1034 × O − 0.0151 × N − 0.0211 × A	Gases, liquids, solid fuels (coal/coke), wood, sawdust, refuse, MSW, animal waste from the open literature	Ultimate
(10)	[13]	HHV = 0.3536 × FC + 0.1559 × V − 0.0078 × A	Fuels such as coals/lignite/manufactured fuel/all kinds of biomass/industry waste from the open literature	Proximate
(11)	[20]	HHV = 0.3560 + 0.4328 × C − 0.2977 × H + 0.2874 × N	Straw from China	Ultimate
(12)	[17]	HHV = 0.1905 × V + 0.2521 × FC	Agricultural byproducts/wood from Argentina, Australia, Cuba, Greece, India, Morocco, the Netherlands, Spain, Turkey and the United States of America	Proximate
(13)	[17]	HHV = 0.2949 × C + 0.8250 × H	Agricultural byproducts/wood from Argentina, Australia, Cuba, Greece, India, Morocco, the Netherlands, Spain, Turkey and the United States of America	Ultimate
(14)	[26]	HHV = −3.393 + 0.507 × C − 0.341 × H + 0.067 × N	Crop species from Spain	Ultimate
(15)	[26]	HHV = −13.173 + 0.416 × V	Crop species from Spain	Proximate
(16)	[14]	HHV = 19.2880 − 0.2135 × (V/FC) − 1.9584 × (A/V) + 0.0234 × (FC/A)	Various types from the open literature	Proximate
(17)	[12]	HHV = 0.879 × C + 0.321 × H + 0.056 × O − 24.826	Oil palm fronds from Malaysia	Ultimate
(18)	[24]	HHV = 0.4373 × C − 1.6701	Agroforestry biomass from Russia	Ultimate
(19)	[27]	HHV = 0.2328 × C + 6.9703	Various types from the open literature	Ultimate
(20)	[18]	HHV = −0.0038 × (−19.9812 × FC1.2259) + (−1.0298 × 10−13 × V × 8.0664) + (0.1026 × A2.423) + (−1.2065 × 10−7 × FC × A4.6653 + 0.0228 × FC × V × A) + (−0.2511 × (V/A) − (0.0478 × (FC/V)) + 15.7199	Various types from the open literature	Proximate
(21)	[28]	HHV = 0.3826 × C − 0.3681 × H + 2.7882 × S − 0.0378 × O + 0.9262	Biomass/biochar from Malaysia	Ultimate

2. Materials and Methods

2.1. Biomass Characteristics

The database for biomass characteristics used in this study was provided by the Biomass Characterization Laboratory of the Federal University of Pará (Brazil), with characteristics chosen from among the most abundant residues in the region and obtained during the last five years. The samples were collected from local industrial plant waste disposal yards from several locations in Pará state. These samples were classified according to their type (seeds, husks and woody residues).

All samples were collected and subjected to a pre-treatment of drying, grinding and sieving and then stored in a desiccator in accordance with CEN/TS 14778-1:2005. Fifty-five Amazonian biomass types were used in this research. All of them had HHVs and proximate analysis experimentally determined, while only 17 were also subject to ultimate analysis. HHV equations based on proximate analysis data were developed using 27 of the 55 biomass types, leaving the remaining 28 biomass types for validation. The group with 17 types with ultimate analysis was used to develop HHV equations based on ultimate analysis. To validate these latter equations, an external source was used [29,30,31,32,33], these data were compiled in

Table 2. Thermochemical data on Amazonian biomasses used for ultimate HHV equation validation.

ID *	Source	Biomass Residues	HHV 1	C 2	H 3	O 4	N 5	S 6
			(MJ/kg)	(wt. %, Ash-Free, Dry Basis)
1	[33]	Açaí seed Euterpe oleracea	18.60	47.60	6.40	45.12	0.78	-
2	[33]	Banana stem Musa spp.	16.13	39.00	5.44	54.84	0.82	-
3	[33]	Banana stalk Musa spp.	15.73	37.95	4.73	55.85	1.46	-
4	[33]	Bamboo Guadua sarcocarpa	18.33	43.34	5.55	48.93	0.91	-
5	[33]	Coconut Cocos nucifera	18.70	47.40	5.41	46.64	0.55	-
6	[32]	Babassu mesocarp Attalea speciosa	19.07	47.13	5.17	40.70	0.27	-
7	[30]	Babassu Attalea speciosa	21.95	56.90	5.20	36.90	-	-
8	[29]	Guarana seed Paullinia cupana	17.58	41.55	6.44	44.91	1.51	-
9	[31]	Maçaranduba Manilkara huberi	20.44	49.54	6.31	43.45	0.67	0.01

¹ High heating value; ² carbon; ³ hydrogen; ⁴ oxygen; ⁵ nitrogen; ⁶ sulfur; * Biomass identification.

. This procedure is explained in more detail in Section 2.2.

The proximate analysis of the biomass samples was carried following the CEN/TS standards (14774-1:2004 for moisture, 14775:2004 for ash and 15148:2005 for volatile matter). The proximate analysis provided the volatile, fixed carbon and ash contents in mass percentages. The ultimate analysis, following ASTM E775/E777/E778/E870 (with 0.01% uncertainty for the measured value), provided the elements of carbon, hydrogen, oxygen, nitrogen and sulfur in mass percentages. The analysis was performed using a 2400 Series II CHNS/O—Perkin Elmer elemental analyzer, with an uncertainty of 0.3% of the measured value. The oxygen (O) content was calculated by subtracting the sum of the percentages of C, H, N, S and ashes from 100%.

The analysis of the high heating values was performed with a model C 2000 Control—Ika Werke calorimetric pump following ASTM E711, with an average relative error of 0.2% and a deviation range of 0.4%.

2.2. Development of Regression Equations

To develop the HHV equations, a methodology was adopted combining linear regression methods and statistical analysis. There are several statistical tools with the capabilities to create a linear regression from a database [34]. Among the options, Python programming language was chosen to realize the calculation because it is an open code with several freely available packages. Among these packages, Statsmodels 0.14.0 stands out. This module is known for its excellent precision in statistical analysis [35] and contains a large library of models and statistical functions. A scheme of the methodology applied in the process for the analysis of the experimental data, the validation data and the proposed equations is presented in Figure 1.

The first step was to apply the experimental data and validation data in a Pearson’s correlation test. This test reveals the variables (chemical elements, in this case) that have the greatest correlation with HHVs and indicates which should be used in the linear regression. This procedure is shown with dotted lines in Figure 1.

In the second step, linear regression was performed using the experimental data from the proximate analysis or ultimate analysis, as presented in

Table 3. Thermochemical data fir proximate and ultimate analyses of the studied biomass residues.

ID *	Biomass Residues	HHV 1	V 2	FC 3	A 4	C 5	H 6	O 7	N 8	S 9
		(MJ/kg)	(wt. %, Dry Basis) ª
1	Açaí berry (seed) Euterpe oleracea	19.23	78.88	19.91	1.21	46.16	6.01	47.26	0.43	0.13
2	Tucumã (seed) Astrocaryum aculeatum	22.18	78.56	17.02	4.42	51.35	6.50	41.52	0.52	0.11
3	Açaí tree bark (husk) Euterpe oleracea	16.73	74.70	17.99	7.31	-	-	-	-	-
4	Coconut shell (husk) Cocos nucifera	19.33	73.78	23.46	2.76	51.14	5.70	42.57	0.51	0.00
5	Palm oil kernel shell (PKS) (husk) Elaeis guineensis	21.22	77.92	19.55	2.53	49.55	5.96	42.92	0.60	0.96
6	Angelim pedra (woody) Hymenolobium modestum	19.42	80.60	17.85	1.55	49.15	6.26	43.34	0.39	0.86
7	Angelim vermelho (woody) Dinizia excelsa	20.10	82.90	14.86	2.24	48.44	6.22	43.99	0.45	0.9
8	Bamboo with stripes (woody) Bambusa vulgaris vulgaris	18.83	80.14	18.47	1.39	46.93	5.92	45.82	0.43	0.13
9	Imperial bamboo (woody) Bambusa vulgaris vittata	18.76	81.64	16.97	1.39	47.48	6.14	45.21	0.35	0.82
10	Giant bamboo (woody) Dendrocalamus giganteus	19.56	79.73	19.09	1.18	47.82	6.15	44.83	0.37	0.83
11	Bamboo (woody) Guadua sarcocarpa	18.80	78.63	17.96	3.41	44.96	5.90	47.99	0.39	0.77
12	Cedro (woody) Cedrela fissilis	19.83	82.60	16.54	0.86	50.10	6.34	42.37	0.37	0.82
13	Cupiuba (woody) Goupia glabra	19.37	83.44	16.20	0.36	49,09	7.83	42.52	0.19	-
14	Ipê amarelo (woody) Handroanthus albus	21.43	80.50	19.27	0.23	52.24	6.08	40.45	0.55	0.69
15	Jatobá (woody) Hymenaea courbaril	20.32	79.06	20.57	0.37	50.17	5.77	42.89	0.50	0.67
16	Louro (woody) Ocotea spp.	20.90	81.39	18.31	0.30	48.42	6.13	44.23	0.42	0.79
17	Marupá (woody) Simarouba amara	19.66	87.42	12.38	0.20	48.53	6.28	44.05	0.41	0.73
18	Muiracatiara (woody) Astronium ulei	20.34	80.89	18.91	0.20	-	-	-	-	-
19	Pacapeua (woody) Swartzia Racemosa	18.68	81.49	15.02	3.49	-	-	-	-	-
20	Tatajuba (woody) Maclura tinctoria	19.62	78.50	21.20	0.30	49.50	6.06	43.32	0.33	0.79
21	Timborana (woody) Piptadenia suaveolens	19.77	80.36	18.17	1.47	49.52	6.30	42.88	0.55	0.75
22	Casca de amêndoa (husk) Prunus dulcis	22.21	77.73	20.66	1.61	-	-	-	-	-
23	Talo de uncária (husk) Uncaria tomentosa	19.51	74.81	22.32	2.87	-	-	-	-	-
24	Tanimbuca (woody) Buchenavia capitata	19.58	78.01	19.80	2.26	-	-	-	-	-
25	Tauari (woody) Couratari tauari	19.86	82.56	16.75	0.69	-	-	-	-	-
26	Pau-preto (woody) Dalbergia melanoxylon	22.21	79.36	20.02	0.62	-	-	-	-	-
27	Uncária (husk) Uncaria tomentosa	20.77	70.10	21.49	8.41	-	-	-	-	-
	Sample mean	19.74	79.66	27.60	1.79	48.19	6.25	43.79	0.43	0.77
	Standart deviation	1.23	3.06	2.43	1.82	1.89	0.46	1.90	0.12	0.37

¹ High heating value; ² volatiles; ³ fixed carbon; ⁴ ashes; ⁵ carbon; ⁶ hydrogen; ⁷ oxygen; ⁸ nitrogen; ⁹ sulfur; - denotes that ultimate analysis is not available; * biomass identification; ª proximate and ultimate analyses were on a wt. % dry biomass basis.

. Based on Pearson’s test, several equations were obtained using various combinations of the variables (FC, V and A for proximate analysis and C, H, O, N and S for ultimate analysis).

The third step consisted in applying statistical tests, such as adjusted R², p-value, F-test and MAPE, to the equations resulting from second step.

After statistical evaluation, in step four, the remaining equations were subjected to an error test using the concepts of the mean absolute error (MAE), the mean absolute percentage of error (MAPE) and the square root of mean error (SRME). The experimental data used for this validation are provided in

Table 4. Thermochemical data of proximate analysis for the studied biomass residues used for validation.

ID *	Biomass Residues	HHV 1	V 2	FC 3	A 4
		(MJ/kg)	(wt. %, Dry Basis) ª
28	Angelim (woody) Andira fraxinifolia	17.50	70.01	15.13	14.86
29	Breu (woody) Protium heptaphyllum	19.90	85.62	14.19	0.19
30	Buchas trituradas de dendê (husk) Elaeis guineensis	17.33	72.86	15.23	9.91
31	Cacho seco de amêndoa (husk) Prunus dulcis	19.34	80.55	16.60	2.85
32	Brazil nut shells (husk) Bertholletia excelsa	20.27	71.04	27.07	1.88
33	Walnut shell (husk) Juglans regia L.	21.08	75.86	22.49	1.65
34	Copaíba (woody) Copaifera langsdorffii	19.90	90.87	9.05	0.08
35	Cumaru (woody) Dipteryx odorata	20.13	86.65	13.29	0.07
36	Falso Pau-Brasil (woody) Biancaea sappan	22.00	78.39	21.42	0.19
37	Fibra de coco (husk) Cocos nucifera	18.65	70.60	24.67	4.73
38	Garapa (woody) Apuleia leiocarpa	18.67	78.51	18.33	3.17
39	Louro-Faia (woody) Roupala montana	19.71	82.04	17.75	0.21
40	Maçaranduba (woody) Manilkara bidentata	20.10	82.43	17.36	0.20
41	Mandioqueira (woody) Manihot esculenta	19.69	83.23	16.04	0.73
42	Melancieiro (woody) Alexa grandiflora	19.96	93.87	5.36	0.77
43	Mogno (woody) Swietenia macrophylla	19.83	78.43	19.72	1.84
44	Pau-marfim (woody) Balfourodendron riedelianum	19.29	84.07	15.25	0.69
45	Pequiá (woody) Caryocar brasiliense	19.87	82.63	15.60	1.77
46	Pracuuba (woody) Dimorphandra paraensis Ducke	20.48	80.92	18.17	0.91
47	Quaruba (woody) Vochysia maxima	18.91	81.96	17.06	0.97
48	Coconut shell (husk) Cocus nucifera	20.54	79.74	19.30	0.95
49	Resíduo de Favadanta (husk) Dimorphandra mollis Benth	19.98	76.86	19.08	4.06
50	Roxinho (woody) Peltogyne angustiflora	19.83	80.08	19.59	0.33
51	Sucupira (woody) Pterodon emarginatus	20.18	82.76	16.70	1.69
52	Acapu (woody) Vouacapoua americana	20.69	78.72	20.91	0.37
53	Casca de palmito (husk) Bactris gasipaes	16.17	76.14	18.00	5.86
54	Palm fruit fibre (husk) Elaeis guineensis	16.54	76.21	19.59	4.20
55	Pupunha bark (husk) Bactris gasipaes	16.64	76.24	17.63	6.13
56	Empty palm fruit bunch (EFB) Elaeis guineensis	18.27	84.32	15.68	2.32
	Sample mean	19.65	80.06	17.77	2.17
	Standard deviation	1.32	5.19	3.87	3.00

¹ High heating value; ² volatiles; ³ fixed carbon; ⁴ ashes. * Biomass identification; ª proximate analyses were on a wt. % dry biomass basis.

, for the proximate analysis, and Table 2, for the ultimate analysis. The best equations were selected from the results of this step.

Finally, a comparison of the proposed HHV equations with equations from the open literature was carried out to analyze their performance.

2.2.1. Pearson’s Correlation

Pearson’s coefficient measures the statistical relationship between two variables. The values range from −1 to +1, where values close to zero indicate that there is weak relationship between the variables. Values smaller than zero indicate an inversely proportional correlation. When greater than zero, the correlation is directly proportional. Thus, this test is useful to identify the best variables that can be used in linear regression.

2.2.2. Linear Regression Methods

Multiple linear regression is a multivariate statistical technique that aims to look for relationships between a single dependent variable and a set of independent variables. Such a technique is applied in problems that require a predictive and explanatory model. The regression is represented in Equation (22):

$$Y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\cdots +{\beta }_n{x}_n+ϵ$$

(22)

where Y is the dependent variable, ${\beta }_0$ is the intercept point, ${\beta }_n$ is the nth coefficient of the regression model, $x_n$ is the nth independent variable and ϵ indicates the regression error.

The regression technique has several methods to find ${\beta }_n$. The method used in this work was the least squares method (LSM), expressed in Equation (23) [36]. It is an optimization technique that seeks to adjust the generated data by minimizing the sum of the squares of the differences between the estimated value and the actual value:

$${\beta }_n=\frac{{{\displaystyle \sum }}_{i=1}^n{y}_i{x}_i-\frac{\left({{\displaystyle \sum }}_{i=1}^n{y}_i\right) \left({{\displaystyle \sum }}_{i=1}^n{x}_i\right)}{n}}{{{\displaystyle \sum }}_{i=1}^n{x}_i^2\frac{{\left({{\displaystyle \sum }}_{i=1}^n{x}_i\right)}^2}{n}}$$

(23)

Equation (23) has similar parameters as Equation (22), with the addition of $y_i$, which is the nth dependent variable, and n, which equals the sample size.

The choice of multiple linear regression was due to the fact that the variables with the greatest impact on the prediction of HHV show clearly linear behavior, so multiple regression was considered suitable for the biomasses under analysis, and it is still widely used in the scientific environment, as can be seen in previous work [24,27]. The quadratic model can lead to the phenomenon of overfitting, where the model becomes too complex and can lead to random errors that have no correlation with the variables; this problem is aggravated in situations where there is little training data and many independent variables [37], besides being more suitable for models that work with machine learning, which was not the objective of this study.

2.2.3. Statistical Analysis

To assess the quality of the equations generated by the linear regression model, certain variable parameters associated with the statistical analysis were been taken into account. These parameters allow the identification of the most important terms in the HHV equation. They are presented in the following sections.

R² and R²-Adjusted

The determination coefficient, R², is an indicator of how good the regression fits with the data. An R² close to 1 indicates that the equation explains the case well. However, this value can be overestimated in cases of multiple regression due the addition of data. Therefore, R²-adjusted should be taken into account. This tends to be more realistic because it corrects the problem of increasing polynomial coefficients.

F-Test and p-Value

The F-test is used when comparing statistical models that have been fitted to a dataset in order to identify the model that best fits the population from which the data were sampled. The p-value indicates the probability of rejecting the null hypothesis (when no correlation between the dependent and non-dependent variables exists); this hypothesis suggests that there are no statistical relationships between two or more sets of variables [38]. The null hypothesis is true if the p-value is above 0.05, and it is false if the p-value has a result below 0.05.

Error Analysis

From the selected equations, a comparison was made between the estimated values and experimental HHVs. The differences between them produced residues that were treated by the following error analyses:

• Mean absolute error (MAE);
• Mean absolute percentage of error (MAPE);
• Square root of mean error (SRME).

The MAE is used to avoid underestimation (Equation (24)). This metric provides the mean distance from the experimental value to the estimated value:

$$\mathrm{MAE}=\frac{1}{n}{\displaystyle \sum }_{i=1}^n\left|y_i-\widehat{y_i}\right|$$

(24)

where n is the total number of observations worked on, $y_i$ is the real value of the response variable and $\widehat{y_i}$ is the estimated value of the response variable.

MAPE (Equation (25)) is very similar to MAE but adds $y_i$ to the division, thus indicating how many percentage points the prediction differs from the experimental value:

$$\mathrm{MAPE}=\frac{1}{n}{\displaystyle \sum }_{i=1}^n\frac{\left|y_i-\widehat{y_i}\right|}{y_i}\times 100\%$$

(25)

The SRME (Equation (26)) works on the same principle as the MAE, but it squares the difference and applies a square root, so that the final value is on the original scale. It penalizes values that are very different between the predicted and the experimental HHVs. Therefore, the higher the SRME value is, the worse the model performs.

$$\mathrm{SRME}=\sqrt{{\displaystyle \sum }_{i=1}^n\frac{{\left(\widehat{y_i}-y_i\right)}^2}{n}}$$

(26)

2.3. Validation Databank

For the validation of the proximate analysis equations, there was no need for an external database, since the laboratory had enough data for a split between the creation and validation steps, as shown in Table 3 and Table 4.

The HHV equations obtained from ultimate analysis were validated with experimental results (Table 2) collected from the literature [29,30,31,32,33] that contained information on various local biomass types, thus allowing for an excellent test of the proposed regressions.

2.4. HHV Equations from the Literature: Models Used for Comparison

In order to evaluate the accuracy of HHV equations using Amazon species data available from the literature, several equations were selected from Table 1. The main criterion for the selection was the suitability for the biomass types studied in this work; for example, woody biomass. For the proximate analysis, eight known equations were chosen (Equations (3)–(5), (8), (10), (12), (16) and (20)), and a further eight equations were chosen for the ultimate analysis (Equations (1), (2), (6), (7), (9), (13), (18) and (19)).

3. Results and Discussion

This section presents the results for the characterization of the biomass types selected and the regression equations developed to predict the HHVs based on the proximate analysis and ultimate analysis of the biomass.

3.1. Biomass Characteristics

Thermochemical properties for the set of experimental data used in the development of the HHV equations obtained through proximate and ultimate analyses, as well as the HHVs of Amazonian biomasses, are presented in Table 3. Generally, woody species have higher HHVs, higher volatiles content and lower ash content. The exception is the açaí seed, which despite being a seed, performs like a woody species. For all fifty-five biomass types (Table 3 and Table 4), it was observed that the HHVs ranged from 16.17 to 22.21 MJ/kg, volatile matter ranged from 70.01 to 93.87 wt. % and fixed carbon ranged from 5.36 to 27.07 wt. %.

In this section, an extensive discussion of the biomass properties is not provided, because the goal was to use those thermochemical properties to develop regression equations for HHV instead.

The experimental results obtained from the proximate analysis of the 27 types of Amazonian biomasses shown in Table 3 are presented from a graphical perspective in Figure 2, allowing the identification of the ranges of the parameters of fixed carbon, volatiles and ash (in wt. %) for each biomass type, as well as a comparison between them.

Concerning the ultimate analysis, the experimental results for the 17 types of biomasses presented in Table 1 are shown in Figure 3, allowing the identification of the ranges of the chemical elements (C, H, O, N and S on a wt. % dry basis) for the biomass types, as well as a comparison between them.

The second set of experimental results for Amazonian biomasses used to validate the HHV equations obtained from the proximate analysis are presented in Table 4. The same trend as observed in Table 3 can also be noticed here: woody species had higher HHVs, higher volatile matter content and lower ash content (wt. %). The exception was the Angelin woody species, which was similar to husks, with low HHVs, low volatile matter content and high ash content (14.86 wt. %).

Experimental results from the proximate analysis for all 55 Amazonian biomasses are presented in Table 3 and Table 4. The Table 4 dataset is shown in Figure 4, allowing the identification of the composition ranges (fixed carbon, volatiles and ash) for each biomass type, as well as a comparison between them.

3.2. Development of the Models for the HHV

Several tests were required to find the relevant equations and achieve the purpose of this study. The proximate analysis brought a greater challenge to the regression, as the literature showed that the proximate analysis parameters could be correlated in several different ways, producing many more equations for evaluation.

The proximate analysis data from Table 3 and Table 4 were organized and tested using Pearson’s method to find a correlation with the HHVs by identifying the most influential parameter or independent variable. The results in

Table 5. Pearson’s test for experimental results from the proximate analysis.

	HHV 1	V 2	FC 3	A 4	V/FC	FC/V	V/A	FC/A	A/V	A/FC	FC + V	FC + A	V + A
HHV 1	1.000
V 2	0.132	1.000
FC 3	0.218	−0.795	1.000
A 4	−0.520	0.073	−0.660	1.000
V/FC	0.004	−0.859	0.755	−0.180	1.000
FC/V	0.063	0.985	−0.870	0.215	−0.823	1.000
V/A	0.072	−0.342	0.374	−0.196	0.308	−0.342	1.000
FC/A	0.128	−0.283	0.365	−0.256	0.256	−0.297	0.974	1.000
A/V	−0.507	0.079	−0.664	0.999	−0.182	0.222	−0.186	−0.243	1.000
A/FC	−0.520	−0.050	−0.560	0.983	−0.071	0.089	−0.180	−0.238	0.982	1.000
FC + V	0.523	−0.064	0.656	−0.995	0.174	−0.206	0.190	0.248	−0.994	−0.983	1.000
FC + A	−0.206	0.808	−0.998	0.647	−0.763	0.880	−0.377	−0.367	0.650	0.543	−0.637	1.000
V + A	−0.113	−0.996	0.814	−0.102	0.861	−0.986	0.344	0.285	−0.108	0.019	0.100	−0.822	1.000

¹ High heating value; ² volatiles; ³ fixed carbon; ⁴ ash.

show weak correlations between volatiles and fixed carbon with the HHV at 0.132 and 0.218, respectively, indicating the amount of the total HHV that was obtained, proportionally, from volatiles and fixed carbon. Despite the apparently low correlation, it is known that carbon has a high correlation with calorific value. The authors of [39] state that, on average, for every 1% of carbon in woody biomass samples, there is an increase of 0.39 MJ/kg. A strong and inverse correlation was indicated for ash at −0.520, indicating that increasing ash fraction reduced the HHV. As a reminder, results close to zero indicate weak correlation and results close to 1 or −1 indicate a strong correlation.

When the variable relationship methodology was used, it was possible to notice a strong influence from the association FC + V at 0.523. This was expected since this association can explain the biomass combustion process, with the volatiles helping at the beginning of the combustion process in the ignition and the fixed carbon, which had the greatest energy relevance, being consumed afterwards, so it is undeniable that the parameters were directly linked to each other [39]. There were influences from the divisions A/V, at 0.507, and A/FC, at −0.520 [14,15]. However, the last two relationships did not produce a physical meaning in determining the high heating value.

In addition to the Pearson’s test analysis, the behaviors of the proximate analysis components with the HHV were graphically evaluated. The graphs presented in Figure 5 show the HHVs as functions of each independent variable from the proximate analysis results. It is possible to observe the influence of each independent variable through its angular coefficient. If the angular coefficient value is positive, the heating value increases; this can be observed in Figure 5a,b,d. If negative, the opposite occurs (Figure 5c). The higher the angular coefficient was, the higher the Pearson’s number tended to be, as observed in Figure 5c,d. For example, in Figure 5d, with FC + V vs. HHV, the angular coefficient was 0.2487, and in the Pearson’s test, the factor was 0.523, as seen in Table 5.

In the second step, traditional linear regression was performed. The hypothesis of the null intercept was used in the proximate analysis equations. This hypothesis states that the intercept variable ${\beta }_0$ will be equal to zero, as seen in Equations (27) and (28), if all species in the analysis results are present in the equation. If not, an intercept different from the origin must be used.

$$Y={\beta }_0+{\beta }_n{x}_n+ϵ$$

(27)

where ${\beta }_0=0$, so:

$$Y={\beta }_n{x}_n+ϵ$$

(28)

Adopting a similar methodology as [14], several regressions were performed combining the chemical species in different ways. Thus, several equations were obtained as a result. These equations were submitted to the third step presented in the diagram in Figure 1, where statistical tests and error tests were performed in order to determine the best equation. At the end, two HHV prediction equations based on proximate analysis were proposed.

Table 6. Summary of the obtained HHV equations from proximate analysis, AI-1 and AI-2.

ID *	Equation	$\overline{\mathit{R}2}$	F.	p-Value	MAPE
AI-1	HHV = 0.196 × V + 0.221 × FC	0.94	0.00	0.02	4.19%
AI-2	HHV = 0.204 × (V + FC) − 0.128 A	0.95	0.00	0.31	4.35%

* ID: equation identification. Concerning the equations with variables related through division (A/FC and A/V) [7], they were evaluated but did not provide good statistical quality indices, so they were not considered further in this work.

shows information about the HHV equations obtained in this work. Equations AI-1 and AI-2 apply the results of the proximate analysis presented in Table 3. The MAPE tests for both equations using data from Table 3 had errors below 5%. Equation AI-1 adopted the zero-interception concept and V and FC as independent variable combinations [16,17]. Table 3 and Table 4 show that the majority of the biomasses had ash content less than 3%. In these cases, neglecting the ash component would not have a significant impact on the accuracy of the HHV calculation, since ash does not contribute substantially to the overall heat released by combustion [39]. The AI-2 equation was developed based on the methodology with the sum of two chemical elements [15]. The independent variable combination V + FC and A were adopted due to the results in the Pearson’s test and the results shown in Figure 5d. The obtained R²-adjusted value was 0.95, the F-test result was less than 0.05 and the coefficient had a high p-value due to the ashes.

For the development of the HHV equations based on the ultimate analysis results, the same methodology for the Pearson’s test used in the development of the HHV equations from proximate analysis was adopted but with data from Table 2 and Table 3 for validation.

Table 7. Pearson’s test for experimental results from the ultimate analysis.

	HHV	C	H	N	S	O
HHV	1.000
C	0.899	1.000
H	0.502	0.447	1.000
N	−0.612	−0.736	−0.122	1.000
S	0.499	0.481	0.345	−0.544	1.000
O	−0.808	−0.848	−0.573	0.477	−0.366	1.000

summarizes the most important results for the Pearson’s test. All chemical elements showed strong correlations with HHV. Oxygen, carbon and nitrogen showed strong correlations with HHV, with Pearson´s values of −0.808, 0.899 and −0.612, respectively. Hydrogen and sulfur showed weaker influences on the HHV, with Pearson´s values of 0.502 and 0.499, respectively. These results show the influence of each chemical element on HHV, with the order C > O > N > H > S. Sulfur was the variable with the weakest correlation with HHV, and the experimental data in Table 3 indicate that the sulfur content was less than 1% wt., indicating a small effect on HHV calculation, and thus it could be disregarded without major consequence.

Pearson evaluation showed that there was multicollinearity between carbon and oxygen: the variables were related with the value of −0.848 in the Pearson’s test (Table 7). This can be explained by the fact that oxygen was the second most abundant element in the biomasses after carbon, as well as being of the same order of magnitude, and was related to the molecular composition of the carbohydrates that composed the biomasses.

Figure 6 presents the behavior of each chemical element resulting from the ultimate analysis (Table 3), except sulfur, for the reason explained above. It could be observed from the Pearson’s test that, as carbon, nitrogen and hydrogen increased (wt. %) (Figure 6a–c), the HHV increased. On the other hand, oxygen showed behavior inversely proportional to the calorific value, as shown in Figure 6d. High levels of oxygen are responsible for reduced HHVs, and they result from the lignocellulosic structure of plant tissues [40].

The linear regression processed with the ultimate analysis results from Table 3 provided several equations. These equations were submitted to the third step shown in the flow chart in Figure 1, where statistical tests and error tests were performed to determine the best equation. During steps 3 and 4 from the flowchart in Figure 1, it was noted that nitrogen and oxygen presented considerable statistical errors, especially for the p-value and F-test for nitrogen and the MAE and MAPE tests for oxygen, so these elements were not used in the final equations. Concerning hydrogen, as well as the strong correlation with HHVs, hydrogen presented a strong correlation in the Pearson´s test when combined with carbon. Despite its p-value being around 0.21, this value ended up not interfering in the HHV prediction, probably due to these chemical elements (carbon and hydrogen) being the most important parameters physically during the combustion process [24].

Table 8. Summary of the HHV equations, AE-1 and AE-2, obtained from ultimate analysis.

ID *	Equation a	$\overline{\mathit{R}2}$	F.	p-Value	MAPE
AE-1	HHV = 2.957 + 0.335 × C + 1.064 × H	0.49	0.01	0.26	2.98%
AE-2	HHV = 2.765 + 0.351 × C	0.57	0.00	0.00	2.84%

^a C, N, O—wt. %, dry basis. * ID: equation identification.

contains the statistical results from the selected regression models, equations AE-1 and AE-2, using ultimate experimental data. The statistical results from the AE-1 equation show an R2-adjusted factor with a relatively low value of 0.49, the F-test was low and the p-value was above the limit due to the combination with hydrogen. Nevertheless, the equation presented a MAPE of 2.98%, below the limit imposed in this work, when data from Table 3 were applied, so it was considered for selection. The greater influences of carbon and hydrogen were already expected be correlated with the HHVs, since they are chemical elements responsible for energy release when oxidized, whereas ashes have an inverse correlation with HHV because they do not generate an energy output during the combustion process and instead consume energy.

The AE-2 equation used only carbon as an independent variable influencing the HHV prediction. The adoption of a single chemical element can also be seen in other work [19,23]. The R²-adjusted value was 0.57. The F-test and the p-value test showed excellent results and could be considered zero. The MAPE of 2.84% was a considered value, since the acceptable limit adopted in this study was a MAPE below 5%.

At the end of the procedure to obtain the HHV equations, two prediction equations based on proximate analysis data and two equations based on ultimate analysis data were obtained. These equations were validated in the next step with the data from Table 2 and Table 4.

3.3. Validation of the Proposed HHV Equations

The HHV equations originating from proximate analysis (Table 3) were validated using the second part of the experimental results presented in Table 4.

Table 9. Proposed equations, AI-1 and AI-2, based on proximate analysis.

ID	This Work 1	MAE	MAPE	SRME
AI-1	HHV = 0.196 × V + 0.221 × FC	0.70	3.79%	1.04
AI-2	HHV = 0.204 × (V + FC) − 0.128 A	0.75	4.04%	1.04

¹ C, H—wt. %, dry basis.

shows the performance of the proposed equations in the error analysis using the experimental data from Table 4. The equations showed good results, with a mean absolute percentage error (MAPE) of 3.79%, which was below 5%.

Equations AI-1 and AI-2 presented quite good and similar performances for SRME and MAE results. Taking the example of equation AI-1, in the MAE test, the predicted HHV has a mean error of 0.78 MJ/kg for the experimental HHV, while, for the SRME, which adopts a different criterion, the mean values were 1.15 MJ/kg off.

Figure 7 shows the behavior of the proposed equations with the validation data for the biomasses, where the predicted HHVs were compared to the experimental HHVs; the hatched lines indicate the upper and lower limits of the 5% error adopted in this work.

Both equations, AI-1 (Figure 7a) and AI-2 (Figure 7b), showed good results, predicting HHVs below the 5% error range for a large part of the validation database. However, eight biomass types resulted in HHVs with errors greater than 5%. They were the biomasses with IDs 22, 27, 33, 36, 45, 53, 54 and 55, these species can be found in Table 2 and Table 3.

The validation tests for the proposed HHV equations from the ultimate analysis were carried out with the experimental external data presented in Table 2, which contains ultimate data compiled by authors from the literature who have worked with Amazonian biomass.

Table 10. Proposed equations, AE-1 and AE-2, based on ultimate analysis.

ID	This Work 1	MAE	MAPE	SRME
AE-1	HHV = 2.957 + 0.335 × C + 1.064 × H	0.42	2.85%	0.64
AE-2	HHV = 2.765 + 0.351 × C	0.20	2.20%	0.45

¹ C, H—wt. %, dry basis.

shows the performances of the proposed equations in the error analysis using the validation data. The equations showed good results, with a mean absolute percentage of error (MAPE) below 3%. Both equations, AE-1 and AE-2, presented good results for the MAPE, SRME and MAE, with the second equation showing error analysis results slightly lower than the first one. In the AE-1 equation, the carbon and hydrogen combination made the equation more stable when dealing with external data and increased its versatility.

Both equations, AE-1 (Figure 8a) and AE-2 (Figure 8b), showed good results in predicting HHV. Equation AE-1 provided predictions for most of the database below the 5% error range; the only sample that was above, with an error of 5%, was the açaí seed. Equation AE-2 could predict all validation data with errors below 5%.

3.4. Results of the Comparison between the Proposed and Literature Equations

Table 11. Error table for equations based on proximate analysis.

Equation	Source	MAE	MAPE	SRME
3	[15]	0.79	4.29%	1.08
5	[16]	1.89	9.59%	4.21
4	[5]	0.94	5.12%	1.72
10	[13]	1.28	6.62%	2.16
8	[19]	0.72	3.86%	1.00
12	[17]	0.71	3.90%	1.10
16	[14]	1.15	5.97%	2.14
20	[18]	0.78	4.09%	0.97
AI-1	This work	0.70	3.79%	1.04
AI-2	This work	0.75	4.04%	1.04

shows the predictions of the HHVs using equations chosen from the literature with the proximate analysis results as along with the equations proposed in this work, using data from Table 4. The literature equations presented MAPE values above those of 5% obtained in this work, except Equations (3), (8), (12) and (20). Consequently, these equations were considered not suitable for predicting HHVs for Amazonian biomasses. In this comparison, the proposed equations and Equation (8) presented similar MAPE values.

The likely reason for the failure of the equations from the literature in correctly predicting HHVs for Amazonian biomass was that such samples have very low ash content and, thus, equations that depend on this parameter had worse performance in this study. All the data shown in Table 11 are shown from a graphical perspective in Figure 9.

The performance of the equations from the literature in predicting the HHVs of Amazonian biomasses with data from Table 4 are shown in Figure 10. The trend line indicates a perfect result, while the dashed lines indicate the upper and lower limits of the 5% error. It was observed that the equation proposed in [17,19] had similar results to the equations proposed in this work and had difficulties in predicting HHVs with errors less than 5% for the same biomasses described in Figure 7. The equations that had more points outside the limit of error were the equations proposed in [13,14,16].

The analysis of the equations for predicting HHVs based on ultimate analysis data was undertaken with the values from Table 2. The equations from the literature presented MAPE errors below 5%, except for the equation proposed in [41], with a MAPE of 5.67%. Equations (6) and (7) [19] had errors of 2.68% and 2.23%, respectively. Equation (13) [17] had an error of 2.60%. These equations used the chemical elements carbon, oxygen and hydrogen as independent variables. It was noted that many of the ultimate analysis equations in the literature met the 95% reliability criteria; a special highlight was Equation (7) [19], which had results very close to the AE-2 equation. All the data cited in

Table 12. Error table for equations based on ultimate analysis.

Equation	Source	MAE	MAPE	SRME
1	[23]	0.59	3.94%	0.77
2	[21]	0.53	3.46%	0.73
6	[19]	0.36	2.68%	0.6
7	[19]	0.24	2.23%	0.49
9	[22]	1.65	5.67%	1.28
13	[17]	0.35	2.60%	0.59
18	[24]	0.59	3.94%	0.77
19	[27]	1.02	4.51%	1.10
AE-1	This work	0.42	2.85%	0.65
AE-2	This work	0.20	2.21%	0.45

are shown from a graphical perspective in Figure 11.

Figure 12 shows the performances of the literature equations in predicting the HHVs of Amazonian biomasses with data from Table 2. The dashed lines indicate the upper and lower limits of the 5% error. The equation where more predicted HHV results seemed to be out of the ±5% margin error was Equation (9) [22].

4. Conclusions

Four equations for the prediction of Amazonian biomass HHVs were proposed: two based on proximate analysis and two based on ultimate analysis. The proposed equations and those from the literature were tested against a set of experimental data for the high heating value, proximate analysis and ultimate analysis of Amazonian biomasses, which was undertaken here for the first time.

It can be concluded that few of the equations from the literature can be used to predict the HHVs of Amazonian biomasses with errors below 5%; special notice should be given to Equation (8) from the proximate analysis and Equation (7) from the ultimate analysis. The MAPE errors presented by these equations were similar to those of the equations proposed in this work, indicating their suitability in predicting HHVs for Amazonian biomasses.

The equations developed in this work using proximate and ultimate analysis experimental results performed better than the equations obtained from the literature, with MAPE results in the range of 2.21% to 4.04%. Equation AI-1 was preferential for proximate data, with the best results in the test of errors. AI-2 also obtained excellent results and stood out for its versatility. For the ultimate data, equation AE-2 was preferred due to its practicality.

With these HHV equations using proximate and ultimate analysis data developed and validated for Amazon biomass types, they can provide researchers and companies with a safe and fast HHV prediction tool. Further, the experimental thermochemical properties provided in this work can be used in modeling and other studies involving the use of Amazonian agroforestry residues as fuel.