Application of the Simplex-Centroid Mixture Design to Biomass Charcoal Powder Formulation Ratio for Biomass Charcoal Briquettes

Abstract

This study aims to increase the quality and value of raw materials with a low higher heating value, HHV (secondary ingredients), but which is abundantly available throughout the year by mixing it with high HHV materials (main ingredients) to obtain quality and standardized charcoal products in accordance with the industrial product standards as approved for commercial use. As for the ingredients, charcoal A is Eucalyptus bark coal (EuBC) with an average HHV of 3779.98 cal/g, charcoal B is rice husk coal (RHC) with an average HHV of 4863.29 cal/g, and charcoal C is charcoal from a biomass power plant (CBPP) with an average HHV of 5991.18 cal/g. The results from the simplex-centroid mixture design method allowed increased quality and value of the biomass charcoal powder (raw material) that has a low heating value but is sufficiently available throughout the year due to the mixing of secondary ingredients with raw materials that have a high heating value (main ingredient). The charcoal briquettes production must be qualified and meet the industrial product standards, and be approved for commercial use.

1. Introduction

Rapid increasing of global energy demand is a cause leading to an energy crisis [1] Due to expansion of population and industrial section, global warming situation, environmental pollution, and loss of forest resources. Forest areas are a source of raw materials for firewood and charcoal, from human encroachment to use as farmland, the lumber industry, and improper use as a fuel. Thailand has seen a forest reduction rate of 0.02% per year in the past few years. The forest area is reduced to only 25.6% of the total land area [2,3,4]. In regard to the fact that liquid petroleum gas (LPG) is generally used as a household cooking fuel [5], it still requires substantial subsidies of importation because Thailand is unable to produce LPG sufficiently for domestic usage. Moreover, natural gas is not a renewable resource [6]. However, the demand for charcoal and firewood is considered the primary source of fuel for household cooking in developing countries [7,8,9]. Nevertheless, affecting forest resources can cause environmental pollution, and smoke inhalation also contributes to premature death [10]. In the grilled food culture, there are grilled food and barbecue business demands for large amounts of charcoal. The usage of charcoal is more favorable due to fewer smoke problems during cooking [11]. Firewood has a calorific value or higher heating value (HHV) of 4539–4778 kcal/kg with 70% volatile content, 28% fixed carbon content, and 2% ash content [12]. After being heated in the absence of air and processed to remove the volatile compounds but left fixed carbon content, firewood turns into charcoal with an HHV of about 7167 kcal/kg and 15–20% volatile content. Currently, the developed countries mostly use biomass charcoal briquettes in households [13] because of wood charcoal depletion [3]. Biomass is green, and renewable energy sources have become more favorable and the global trend as a replacement of fossil fuel [14,15]. Currently, biomass energy sources are prioritized fourth, after petroleum, gas, and coal [16]. It accounts for 14% of the world’s energy consumption. Biomass is a sustainable energy source that can be found anywhere in the world [17]. It is a source commonly derived from agricultural crops and residue, plantation products, and animal waste [18]. The source can be restored to its original form and can multiply in quantity. There are several methods for converting biomass into energy [19,20,21], such as direct combustion, gasification or pyrolysis (gas biofuel), anaerobic digestion, hydrolysis, hydrogenation or fermentation (liquid biofuel or biogas, e.g., bioethanol, biodiesel, biomethane, etc.), and briquetting (solid biofuel), where the latter is preferable for household use for direct combustion.

For this reason, the utilization of biomass is an urgent need. Thailand has a wide variety of agricultural products and is one of the world’s top exporters of agricultural and food products [4]. Thus, a variety of biomass resources are available to produce biomass fuel, especially by-products or wastes from harvesting and processing of agricultural products such as coconut shell, palm shell, corn cob, rice husk, rice straw, cassava stems and rhizomes, bagasse and sugarcane leaves, rubberwood chips, etc. The energy generated by these biomass materials each year is equivalent to 54 million tons of lignite coal [22]. The energy from biomass is a sustainable supply and provides an opportunity to replace fossil fuels in the future. Nonetheless, a crucial part is to find a process to enhance the heating value/weight unit of biomass [23]. HHV is an important factor leading to an increase in biomass energy utilization in the energy industry. Biomass utilization is not only meeting the energy demand but also helps people to protect forest resources and maintain the ecological balance in an environment-friendly concept because it contains low N and S in its composition. This material would be able to reduce the greenhouse effect by releasing an estimate of zero CO₂ emissions [24] and lower acidic gas emissions compared to fossil fuels [25].

One of the methods to convert biomass into energy is to increase density by compression, turning raw material into briquette or a bar product for convenient usage and storage. It also helps to reduce transportation costs and to increase the heating value property and combustion period as well [26,27,28]. Charcoal briquette production from biomass is a process to increase the density, and proper management can reduce transportation costs, storage space, and the problem of charcoal dust [29] whilst increasing the heating value and combustion period. As for the process of charcoal briquette production, the first step is turning raw material into charcoal by combustion and then reducing the size of the charcoal. The charcoal powder and binder are mixed before being compressed into charcoal briquettes by a charcoal briquette machine using the principle of cold compression. The final products are left for sun drying, then packaged for distribution. Charcoal compression by screw-press machine is capable of continuous production. The machine is composed of few parts, enabling a lower production cost than hydraulics compression [30,31]. Raw material, binder, and briquette machinery are the three main factors related to the production cost.

Factors related to raw materials are material type, the particle size of raw material powder, the type and quantity of the binder, and the amount of mixing water [32,33]. Qualified biomass material used as raw material should be sufficiently available [34]. According to a relevant literature review, the briquette production from a wide variety of biomass materials that are agricultural scraps could be delayed by a material shortage or seasonal-cultivation material. Some materials are abundantly available in the area but provide poor quality of heating property, for example, rice husk coal has an average HHV of 4384.043 cal/g. However, the HHV can be maximized by mixing with wood charcoal [35]. Most charcoal briquettes available in the domestic and oversea market are made of coconut shell coal, but the coconut shell cost has increased steadily due to raw material scarceness nowadays. Thus, other materials and local agricultural biomass scraps have been studied and used to produce charcoal briquette instead of coconut shell, such as rice husk [32,35,36,37,38,39], corn cob [37,38,39,40,41], Eucalyptus [26,42,43,44,45,46,47], cassava rhizome [25,41,47,48], etc. In the industrial production of charcoal briquettes, the product from the charcoal powder material must meet the Thai Community Product Standard for charcoal briquettes (TCPS 238/2004) [49]. In case of continuous production and to diminish raw material shortage problems, the use of several biomass types as raw materials is needed. However, these charcoal products must also meet the Thai Community Product Standard of bionic charcoal briquettes (TCPS 946/2005) [50].

Mixture design is a combination of mathematical and statistical techniques for modeling and analyzing the effects of individual components to find an optimal ingredient formula [51]. This method helps researchers to improve and develop product ingredients. The mixture design concept was developed by Scheffe in 1958 [52,53] and has been frequently adopted in the study of food and agriculture technology and engineering. The mixture must be composed of at least two substances which are called components. The response and characteristics of the resulting product depend on the proportion of the mixture, not the overall quantity of the components.

Therefore, in order to increase the quality and value of raw material that has a low heating value (secondary ingredients) but is sufficiently available throughout the year, the mixing of secondary ingredients with raw materials having a high heating value (main ingredients), the charcoal briquette production must be qualified and meet the industrial product standards and approved for commercial use. Therefore, it is necessary to have the starting charcoal ratio and the charcoal ratio be blended or formulated to produce charcoal briquettes from biomass charcoal. For this reason, the mixture design by the simplex-centroid experimental method was applied in this study.

2. Materials and Methods

2.1. Preparation of Biomass Charcoal Powder

For charcoal powder preparation, biomass material was collected from plantations and production sites in Nakhon Phanom Province, the northeast region of Thailand. The Eucalyptus barks were obtained from the Eucalyptus wood chips factory and stored to reduce moisture content to less than 20% (wet basis) before carbonizing into charcoal in a 200-L tank carbonizer. Rice husk was collected from a community rice mill in the production of coal by igniting heaps around traditional chimneys. Charcoal from a biomass power plant (CBPP) was a by-product of the gasification biomass power plant. The obtained charcoals were not suitable for direct use. They had to be ground to reduce in size by using a hammer mill machine with sieve size of 6 mm, speed of 1000 rpm, and a three-horsepower electric motor. The charcoal powder was tested for moisture content and dehumidified to a humidity level of <10% (wet basis), chemical composition (

Table 1. Chemical composition of charcoal powder (dry basis).

Chemical Composition	Eucalyptus Bark Coal (EuBC)	Rice Husk Coal (RHC)	Charcoal from a Biomass Power Plant (CBPP)
Ash (%)	38.7	31.3	10.0
Volatile matter (%)	27.2	21.2	12.9
Fixed Carbon (%)	34.6	47.6	77.1
Carbon; C (%)	48.036	52.823	84.238
Hydrogen; H (%)	1.609	2.661	-
Nitrogen; N (%)	0.264	0.617	0.059
Sulfur; S (%)	-	-	-
Oxygen; O (%)	17.001	11.081	-

), then stored in a sealed plastic container.

2.2. HHV Evaluation of Charcoal Powder

HHV is an indicator for energy content of biomass material. The heating value is the amount of energy stored in a unit of a biomass sample. In general, the heating value is measured from the combustion, which is gross energy released as heat from complete combustion with oxygen under standard conditions [54,55,56]. The result was shown as HHV using bomb calorimeter Model No. 1341 by PARR instrument company in accordance with ASTM D5865 under as-determined basis (adm); ASTM D 3180-89 referred to a value calculated from the sample under as-determined basis with the same remaining moisture as occurring during the testing. The heating value was measured before and after the mixing of charcoal powder according to the mixture design by simplex-centroid experimental method.

2.3. Determination of the Mixture Ratio of Biomass Powder to Produce Charcoal Briquette by the Mixture Design

In order to achieve the objectives of the ingredient proportion analysis and equations for biomass briquette in accordance with Thai Community Product Standards for charcoal briquette (TCPS 238/2004), HHV > 5000 cal/g and Thai Community Product Standards for bionic charcoal (TCPS 946/2005), HHV > 4000 cal/g; three charcoal powder types were studied, as shown in

Table 2. HHV Properties of charcoal powder in the study, Compared with Thai community product standards.

No.	Charcoal Powder Type	HHV(Average); (cal/g)
1	A, Eucalyptus Bark Coal, (EuBC)	3616.09–3873.91 (3779.98)
2	B, Rice husk Coal, (RHC)	4631.01–5038.64 (4863.29)
3	C, Charcoal from a Biomass Power Plant, (CBPP)	5815.29–6307.80 (5991.18)
TISI; Charcoal Briquettes (TCPS No. 238/2004)		≥5000
TISI; Bionic Charcoal Briquettes (TCPS No. 946/2005)		≥4000

. Eucalyptus bark coal (EuBC) provided lower heating value than the standard’s value. This material could not be used to produce charcoal briquettes unless mixed with other charcoal types.

An experimental mixture design required two or more ingredients to produce new compound in order to indicate the influence of each ingredient (components, q) on the variables and to obtain the optimal mixing ratio [51]. This was based on the mixing principle using the summed quantity(x_i) of the mixing components (q) = 1, as shown in Equations (1) and (2).

$$0\le x_i\le 1,i=1,2,\cdots ,q$$

(1)

$${{\displaystyle \sum }}_{i=1}^q{x}_i=x_1+x_2+\cdots +x_q=1$$

(2)

In this study, the mixture design experimental model of the simplex-centroid design was used for the analysis. The coordinate equals 2^q−1, consisted of 3 pure components (X₁, X₂, X₃; J, K, L), 3 binary mixtures (X₁ = X₂, X₁ = X₃, X₂ = X₃; M, N, O) and 3 ternary mixtures (X₁ = X₂ = X₃, P) as shown in Figure 1.

The condition of mixture formula and proportion of charcoal powder in this experiment was such that each mixture contained 3 types of charcoal powder with no binder in mixture, as shown in

Table 3. Mixture proportions in simplex-centroid, A:B:C.

No.	Coordinate (Figure 1)	Mixture Proportions			Mixture Proportions by Weight (g)
		X1	X2	X3	X1	X2	X3
		EuBC; A	RHC; B	CBPP; C	EuBC; A	RHC; B	CBPP; C
1	J	1	0	0	200	0	0
2	K	0	1	0	0	200	0
3	L	0	0	1	0	0	200
4	M	1/2	1/2	0	100	100	0
5	N	1/2	0	1/2	100	0	100
6	O	0	1/2	1/2	0	100	100
7	P	1/3	1/3	1/3	66.67	66.67	66.67

. The total weight of mixture was 200 g/sample. Charcoal powder was weighed as of specified portion and mixed using an electric mixer. Mixed charcoal powder was stored in plastic zipper bags for heating value analysis by bomb calorimeter.

2.4. Evaluation and Validation of Predictive Equation of HHV

The relationship between predicted mixture and heating value of such mixture was applicable when the error of derived equation was within the acceptable range between the predicted value and experimental results. The testing parameters consisted of Mean Absolute Error (MAE), Equation (3) [57,58] Average Absolute Error (AAE), Equation (4) [57,58,59,60,61] being the error of prediction compared to the experimental result, and the Average Bias Error (ABE), Equation (5) [57,58,59,60,61,62,63,64].

$$MAE={{\displaystyle \sum }}_{i=1}^N \left|{\mathrm{HHV}}_P-{\mathrm{HHV}}_{\exp }\right|/N$$

(3)

$$AAE=\left({{\displaystyle \sum }}_{i=1}^N \left|{\mathrm{HHV}}_P-{\mathrm{HHV}}_{\exp }\right|/{\mathrm{HHV}}_{\exp }\right)/N$$

(4)

$$ABE=\left({{\displaystyle \sum }}_{i=1}^N\left({\mathrm{HHV}}_P-{\mathrm{HHV}}_{\exp }\right)/{\mathrm{HHV}}_{\exp }\right)/N$$

(5)

where ${\mathrm{HHV}}_P$ = HHV_predicted

$$HH{V}_{\exp }=\mathrm{HHV}{ }_{\mathrm{experimental}}$$

2.5. Data Analysis

This research used the simplex-centroid mixture design. The targets of HHV were more than 4500 cal/g and 5500 cal/g, respectively. The study assessed the quadratic correlation of the response variables (higher heating value) and factors with more than 2 variables. The MINITAB^®19 software was used for data analysis. The analysis consisted of (1) the suitable regression model for experimental design, (2) the Analysis of Variance (ANOVA) of regression model, (3) examination of the adequacy of the regression model, and 4) the suitable mixture proportion of charcoal powder giving the HHV that conformed to the standard of charcoal briquettes, by using contour plot, evaluation, and validation of the predictive equation HHV and the response optimization plot.

3. Results and Discussion

3.1. The Result of Simplex-Centroid Mixture Design of charcoal mixture A:B:C

The mixture of charcoal A (Eucalyptus bark coal: EuBC), charcoal B (rice husk coal: RHC), and charcoal C (charcoal from a biomass power plant: CBPP) was used to obtain the HHV that followed that standard of bionic charcoal briquettes (TCPS No. 946/2005; HHV more than 4000 cal/g) and the standard of charcoal briquettes (TCPS No. 238/2004; HHV more than 5000 cal/g), as shown in

Table 4. HHV From Mixture Design, A:B:C.

Trial No.	Treatment	Mixture Formula by Weight (g)			HHV (cal/g)
		A	B	C	R1	R2	R3	Average
1	T1	200	0	0	3748.43	3791.27	3870.20	3803.30
2	T2	0	200	0	4945.84	4813.26	4887.72	4882.27
3	T3	0	0	200	6034.07	5955.42	5843.30	5944.26
4	T4	100	100	0	4392.36	4187.09	4206.75	4262.07
5	T5	100	0	100	5108.87	5031.17	5350.42	5163.49
6	T6	0	100	100	5539.63	5159.47	5149.04	5282.71
7	T7	66.67	66.67	66.67	4766.26	4695.43	4962.33	4808.01

.

3.2. The Analysis of Suitable Regression Model for Experimental Design and Analysis of Variance (ANOVA) of the Regression Model

The influence of each mixture was analyzed using ANOVA with a significance level of 0.05. The analysis was completed by using a statistical software package, as shown in

Table 5. (a). Regression analysis of HHV in charcoal powder mixture A: B: C. Backward Elimination of Terms; Candidate terms: A, B, C, A × B, A × C, B × C. (b). Estimated Regression Coefficients for HHV (cal/g) (component proportions). (c) Model Summary. (d). Analysis of Variance for HHV (cal/g) (component proportions).

(a). Regression analysis of HHV in charcoal powder mixture A: B: C. Backward Elimination of Terms; Candidate terms: A, B, C, A × B, A × C, B × C.
	-----Step 1----		-----Step 2----		-----Step 3----
	Coef	p	Coef	p	Coef	p
A	3806.9		3772.1		3778.6
B	4885.9		4851.1		4802.6
C	5947.9		5950.7		5899.6
A × B	−395	0.260
A × C	1087	0.006	1105	0.005	1131	0.006
B × C	−594	0.098	−576	0.110
S		127.407		128.886		135.761
R-sq		97.29%		97.04%		96.51%
R-sq (adj)		96.39%		96.30%		95.90%
R-sq (pred)		94.69%		94.67%		94.87%
Mallows’ Cp		6.00		5.37		6.30
(b). Estimated Regression Coefficients for HHV (cal/g) (component proportions).
Term	Coef	SE Coef		T-Value	p-Value	VIF
A	3778.6	71.3				1.33
B	4802.6	64.7				1.10
C	5899.6	71.3				1.33
A × C	1131	358		3.16	0.006	1.56
(c) Model Summary.
	S	R-sq		R-sq (adj)	PRESS	R-sq (pred)
	135.761	96.51%		95.90%	461052	94.87%
(d). Analysis of Variance for HHV (cal/g) (component proportions).
Source	DF	Seq SS	Adj SS	Adj MS	F-Value	p-Value
Regression	3	8,674,807	8,674,807	2,891,602	156.89	0.000
Linear	2	8,491,167	8,438,031	4,219,015	228.91	0.000
Quadratic	1	183,641	183,641	183,641	9.96	0.006
A × C	1	183,641	183,641	183,641	9.96	0.006
Residual Error	17	313,326	313,326	18,431
Lack-of-Fit	3	74,952	74,952	24,984	1.47	0.266
Pure Error	14	238,374	238,374	17,027
Total	20	8,988,133

α to remove = 0.1.

(a)–(d). It was found that charcoal powder A, B, and C, including the mixture proportion of A and C, had a significant effect on HHV (indicated by symbol*and (p-value < 0.05). While the mixture proportion of A and B, B and C had no significant effect on HHV (p-value > 0.05). The variables were analyzed in regression analysis using the Backward Elimination Technique and Quadratic model. It was found that the variables of the charcoal mixture could be statistically calculated using regression equations since the p-value was less than 0.05 and the decision coefficients: R-sq, R-sq(adj), and R-sq(predicted) were 96.51%, 95.90%, and 94.87%, respectively. Therefore, this indicated the suitability of the regression equation. The equation could describe the data variance at 96.51% of the total variance. The p-value of the lack-of-fit test was higher than 0.05, indicating that the model was sufficient to predict the HHV of charcoal powder. The quadratic model was displayed as in the following Equation (6).

HHV (cal/g) = 3778.6A + 4802.6B + 5899.6C + 1131A × C

(6)

where HHV (cal/g) = Higher Heating Value of charcoal powder.

in mixture (Cal/g)

A = Eucalyptus Bark Coal (EuBC)

B = Rice husk Coal (RHC)

C = Charcoal from a Biomass Power Plant (CBPP)

The total sum of charcoal mixture proportion A:B:C was 100%.

3.3. The Model Adequacy Checking of Regression Equation or Model Validation

The model adequacy checking was performed using the normality test, variance stability test, and independence test, as shown in Figure 2. The normality test: plots presented in the normal probability plot were linearly distributed, and the histogram of residuals had a normal distribution. Therefore, the residual was normally distributed.

The variance stability test: From the versus fits graph, the data distribution was random with no pattern. The distribution of residual above and below the zero line was similar. It could indicate that the data had stability (constant residual variance).

The independence test: The mean and residual variance were tested. The hypothesis of mean and residual variance was that the mean of residual equaled zero and had constant variance. It showed that the data were independent. The residual was not related to the order of the experiment, as shown in the versus order graph.

3.4. The Use of Contour Plot and Response Optimization Plot to Analyze the Suitability of Mixture Proportion That Produced the Standard HHV of Charcoal Briquettes Production

Contour plot: After confirming that the quadratic model was applicable, the suitable proportion of charcoal mixture was investigated to obtain the HHV that followed the two standards of charcoal briquettes, HHV standard of bionic charcoal briquettes (TCPS No. 946/2005; HHV more than 4000 cal/g [50] and the standard of charcoal briquettes (TCPS No. 238/2004; HHV more than 5000 cal/g) [49]. However, a binder that was necessary for the charcoal powder to produce charcoal briquettes was not added to the mixture. Therefore, the target response value of HHV was determined for the charcoal powder to produce bionic charcoal briquettes (TCPS No. 946/2005) and charcoal briquettes (TCPS No. 238/2004) at 4500 cal/g and 5500 cal/g, respectively. From the contour plot shown in Figure 3a, there were points that HHV (response value) was greater than 4500 cal/g, which was the target value for producing bionic charcoal briquettes (TCPS No. 946/2005). The white area in Figure 3b was the mixture proportion of charcoal A:B:C that the HHV was greater than 4500 cal/g.

The contour plot in Figure 4a showed points where the HHV (response value) was greater than 5500 cal/g, which was the target value of this study for charcoal briquettes production (TCPS No. 238/2004). The white area in Figure 4b was the mixture proportion of charcoal A: B: C that the HHV was greater than 5500 cal/g, which contained the mixture of charcoal C (charcoal from a biomass power plant; CBPP) more than charcoals A and B.

3.5. Evaluation and Validation of the Prediction Equation for HHV

The experimental results to verify the equation are shown in

Table 6. The experimental results to evaluation and validation of the prediction equation for HHV in charcoal powder mixture.

No.	Mixture Proportions			Mixture Proportions by Weigh (g)			HHVexperimental (cal/g)	HHVpredicted (cal/g)	Basic Error	Absolute Error
	EuBC	RHC	CBPP	EuBC	RHC	CBPP
1	0.2	0.4	0.4	40	80	80	4691.04	5127.08	−436.04	436.04
							4875.50	5127.08	−251.58	251.58
							4937.45	5127.08	−189.63	189.63
2	0.6	0.2	0.2	120	40	40	4120.84	4543.32	−422.48	422.48
							4724.97	4543.32	181.65	181.65
							4201.86	4543.32	−341.46	341.46
3	0.8	0.1	0.1	160	20	20	3834.23	4183.58	−349.35	349.35
							3664.36	4183.58	−519.22	519.22
							4096.65	4183.58	−86.93	86.93
4	0.4	0.2	0.4	80	40	80	4339.32	5012.76	−673.44	673.44
							4551.34	5012.76	−461.42	461.42
							4644.83	5012.76	−367.93	367.93
5	0.2	0.6	0.2	40	120	40	4540.51	4862.44	−321.93	321.93
							4412.36	4862.44	−450.08	450.08
							4351.76	4862.44	−510.68	510.68
6	0.1	0.8	0.1	20	160	20	4459.45	4821.21	−361.76	361.76
							4501.43	4821.21	−319.78	319.78
							4219.91	4821.21	−601.30	601.30
7	0.4	0.4	0.2	80	80	40	5850.86	5668.28	182.58	182.58
							5033.56	5668.28	−634.72	634.72
							5413.04	5668.28	−255.24	255.24
8	0.2	0.2	0.6	40	40	120	5035.60	5391.72	−356.12	356.12
							5089.10	5391.72	−302.62	302.62
							4988.97	5391.72	−402.75	402.75
9	0.1	0.1	0.8	20	20	160	4647.74	4702.88	−55.14	55.14
							4540.28	4702.88	−162.60	162.60
							4557.83	4702.88	−145.05	145.05
Mean Absolute Error (MAE) 346.06 cal/g
Average Absolute Error (AAE)									0.08	7.68%
Average Bias Error (ABE)									0.07	7.17%

. MAE was 346.06 cal/g, AAE was 0.08 or 7.7%, and ABE was 0.07 or 7.2%. The positive value indicated that the predicted HHV was greater than the experimental HHV. The value of AAE and ABE are parameters commonly used as indicators comparing the residual or error between the actual measurements and the value obtained from the prediction model. While the MAE was not used for error indication of the predictive model, it showed the trend or direction of the data set. Lower MAE indicated the accuracy of HHV estimation [57] with consideration of measurement units such as J/g or cal/g. The AAE indicated the accuracy between the predicted value and the experimental value to confirm the predictability of the model. The value of ABE indicated the residual or error between the predicted value and the experimental results [57,60]. The low absolute AAE meant the low bias of ABE [65], and low ABE meant the predictive model had a low bias. The negative value of ABE meant the average HHV from the experiment was higher than that from the prediction model.

The AAE and ABE values close to zero indicated the suitability of such a prediction equation with high accuracy [60]. However, Kieseler et al. [61] reported some prediction equations that produced % AAE and % ABE ranging from 0.1 to 51.3. The study of Qian et al. [60] found that % AAE ranged between 5.98–10.36. The report of Nhuchhen and Abdul Salam [57] indicated that the developed equation for heating value prediction showed % AAE to be 9.43 and 5.88 and % ABE to be 1.68 and 0.80. The results were compared with other published data and prediction equations. It was found that % AAE was 11.47 and 11.99. The report of Hasan et al. [66] on the model development for C, H, and HHV prediction found that % ABE was between −12.1 and −11.9.

Figure 5 shows the relationship between the experimental HHV and the predicted HHV. The solid diagonal indicated the relationship between the predicted HHV to be equal to the experimental HHV. Values that were close to the solid diagonal line indicated the accuracy of prediction. From the error testing of this prediction equation, it was found that most of the experimental values were less than the prediction values, as most of the data points were above the solid line. In this experiment, although values of AAE and ABE were greater than five, which seemed to be inaccurate predictions, they did not exceed 10, usually considered to be within the acceptable criteria. Many prediction models from other publications reported values higher than 10. However, Hasan et al. [66] reported that such an error value was acceptable for engineering applications.

3.6. Response Optimization Plot

Response optimization analysis was conducted to investigate the suitability of mixture proportion for bionic charcoal briquettes production (TCPS No. 946/2005). The mixture proportion of charcoal A (Eucalyptus bark charcoal, EuBC) was determined to be more than 50% of the mixture. It was found that mixture proportion of charcoal A = 50%, charcoal B = 37.4% and charcoal C = 12.6% resulted in the HHV of 4500 cal/g, at desirability value = 1 (Figure 6).

Similarly, response optimization analysis to investigate the suitability of mixture proportion for charcoal briquettes production (TCPS No. 238/2004). The mixture proportion of charcoal A (Eucalyptus bark charcoal, EuBC) was determined to be the highest possible in the mixture. It was found that mixture proportion of charcoal A = 29.21%, charcoal B = 0.98% and charcoal C = 69.82% resulted in the HHV of 5500 cal/g, at desirability value = 1 (Figure 7).

4. Conclusions

Charcoal A is Eucalyptus bark coal (EuBC) with an average HHV of 3779.98 cal/g, charcoal B is rice husk coal (RHC) with an average HHV of 4863.29 cal/g, and charcoal C is charcoal from a biomass power plant (CBPP) with an average HHV of 5991.18 cal/g. The results from the simplex-centroid mixture design method reveal that the mixture proportion of charcoal A, 50%, B, 37.4% and C, 12.6% provides the HHV of 4500 cal/g, which is in accordance with the Thai Community Product Standards for bionic charcoal briquettes (TCPS 946/2005). The mixture proportion of charcoal A, 29.21%, B, 0.98%, and C, 69.82% provides the HHV of 5500 cal/g, which is in accordance with the Thai Community Product Standards for charcoal briquettes (TCPS 238/2004).

A quadratic equation of backward elimination of the regression analysis formulates a prediction equation for HHV of the charcoal mixture as: HHV (cal/g) = 3778.6A + 4802.6B + 5899.6C + 1131A × C; R² = 96.51%, when determining the sum percentage of charcoal A:B:C mixture as 100%. The evaluation and validation of the prediction equation reveal 7.7% of Average Absolute Error (AAE) and 7.2% of Average Bias Error (ABE).