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Liu, D., Ma, Y., Li, J., Teng, D., Qiu, S., Li, Y., Mao, X., and Wang, H. (2022). "Optimization of parameters associated with pellets made from biomass residue from anaerobic digestion using Box-Behnken design," BioResources 17(2), 2743-2767.


Fuel pellets were produced with biomass residue from anaerobic digestion. Single-factor experiment and Box-Behnken design were employed to investigate the effects of pellets-associated variables on the mechanical properties of pellets, and the optimal condition was determined. The results revealed that the pellets-associated variables, including particle size, moisture content, die temperature, and molding pressure had significant influences on the mechanical properties of pellets, such as compressive resistance (CR), durability (DU), and density (DE). The regression models were obtained with the R2 values of 0.9802, 0.9628, and 0.9610 for CR, DU, and DE, respectively, suggesting that the differences between the actual and predicted values could be explained by the regression models. The optimal values of pellets-associated variables were determined (particle size of 0.4 mm, moisture content of 8.4%, die temperature of 115 °C, and molding pressure of 150 MPa); the corresponding responses were 1470 N, 99.6%, and 1180 kg/m3 for CR, DU, and DE, respectively. The results of verification showed a good agreement between the predicted data and experimental outputs. In summary, a novel approach was presented for the preparation of pellet fuels made from biomass residue from anaerobic digestion, and a reliable reference was therefore provided for the comprehensive utilization of biomass materials.

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Optimization of Parameters Associated with Pellets Made from Biomass Residue from Anaerobic Digestion Using Box-Behnken Design

Dan Liu,a Yongcai Ma,b,* Jun Li,c Da Teng,b Shiting Qiu,b Yanlong Li,b Xin Mao,b and Hanyang Wang b

Fuel pellets were produced with biomass residue from anaerobic digestion. Single-factor experiment and Box-Behnken design were employed to investigate the effects of pellets-associated variables on the mechanical properties of pellets, and the optimal condition was determined. The results revealed that the pellets-associated variables, including particle size, moisture content, die temperature, and molding pressure had significant influences on the mechanical properties of pellets, such as compressive resistance (CR), durability (DU), and density (DE). The regression models were obtained with the R2 values of 0.9802, 0.9628, and 0.9610 for CR, DU, and DE, respectively, suggesting that the differences between the actual and predicted values could be explained by the regression models. The optimal values of pellets-associated variables were determined (particle size of 0.4 mm, moisture content of 8.4%, die temperature of 115 °C, and molding pressure of 150 MPa); the corresponding responses were 1470 N, 99.6%, and 1180 kg/m3 for CR, DU, and DE, respectively. The results of verification showed a good agreement between the predicted data and experimental outputs. In summary, a novel approach was presented for the preparation of pellet fuels made from biomass residue from anaerobic digestion, and a reliable reference was therefore provided for the comprehensive utilization of biomass materials.

DOI: 10.15376/biores.17.2.2743-2767

Keywords: Pellet; Biomass residue from anaerobic digestion; Optimization; Box-Behnken design

Contact information: a: College of Civil Engineering and Water Conservancy, Heilongjiang Bayi Agricultural University, Daqing 163319, China; b: College of Engineering, Heilongjiang Bayi Agricultural University, Daqing 163319, China; c: College of Food Science and Engineering, Henan University of Technology, Zhengzhou 450001, China; *Corresponding author:


The global consumption of natural energy is increasing due to the rapid industrial variations. However, the storage of natural energy is limited, especially with regard to fossil fuels. Some fossil fuels, such as crude oil, coal, and gas, may be exhausted in the next 50 years (Shafiee and Topal 2009). Therefore, it is essential to explore renewable resources of energy to globally alleviate the energy crisis and meet the energy demand in the future (Callegari et al. 2019). In addition to wind energy and solar energy, biofuel is recognized as one of the renewable, sustainable, and environmentally friendly resources of energy, and it can be an appropriate alternative for fossil fuels (Ramezanzade and Moghaddam 2018). Biofuels, including synthetic biofuels, bioethanol, biogas, biodiesel, and bio-hydrogen, are prepared from biomass or their residuals (Lin et al. 2014). Compared with the traditional resources of energy, biofuels possess several attractive properties, such as being cost-effective, low emission of greenhouse gases, broadly accessible, etc. (Li et al. 2015). Hence, further in-depth research on biofuels should be conducted.

In China, more than 3 billion tons of manures and 650 million tons of crop straws are generated annually, which are important raw materials that can be used to produce biological products (Awasthi et al. 2019). Although manure and crop straw are high-quality biomass resources, their huge outputs have caused some problems for the development of agriculture and breeding industries. Anaerobic digestion is currently regarded as one of the most environmentally friendly methods for treating various organic substances, including sewage sludge (Stefaniuk and Oleszczuk 2015). Due to its potential in producing renewable energy (i.e. methane content of biogas), anaerobic digestion has attracted attention (Baetge and Kaltschmitt 2018). With the rapid development of biogas industry, China’s biogas consumption is annually 19 billion cubic meter (m3). Correspondingly, a large amount of biomass residue from anaerobic digestion (BRAD), which are difficult to dispose and may easily lead to secondary pollution, are produced during anaerobic digestion (Meng et al. 2018). Generally, the most common method of utilizing BRAD is to use it as organic fertilizer in agriculture, as it possesses several merits of providing nutrients for plants, enhancing the moisture and buffering capacities of soil (Bai et al. 2020). However, the direct application of BRAD to soil may cause leaching of the nutrients from the soil and the deterioration of water, due to the mobility property of its water-soluble contents and an excessive content of heavy metals produced by the use of animal feed additives, resulting in serious environmental concerns (Govasmark et al. 2011). Therefore, it is highly essential to develop a novel and environmentally friendly approach for the resourceful utilization of BRAD.

Given the drawbacks of traditional treatment for BRAD, the conversion of BRAD into compressed solid biofuels may be an alternative technique for addressing this challenge. BRAD can be converted into pellets or briquettes using densification technology, including pelletization, briquetting, and extrusion (Liu et al. 2014). The purpose of densification is to agglomerate small particles into larger particles by a mechanical process combined with moisture, heat, and pressure (Gilvari et al. 2019). Densification increases the bulk density of the biomass materials while reducing the expenses of handling, transportation, and storage; it has been applied widely to the biomass industry in the developed countries (Prawisudha et al. 2012). A relevant study showed that the densification of the biofuel pellets could increase the density up to 1,000 to 1,200 kg/m3; the volume was reduced by 8 to 19 times compared with the raw biomass (Mostafa et al. 2019). In addition, biofuel pellets possess a large number of advantages, such as a low level of pollution, a high heating rate, and less emission of odors. Thus, they can be applied directly to residential heating stoves, power plants, and heating boilers (Chen et al. 2011). In summary, using BRAD to produce biofuel not only can provide an approach for the treatment of BRAD, but also they can be helpful to meet the large demand for energy in the future. Meanwhile, biofuel pellets from BRAD could improve the utilization value of BRAD. Hence, it is essential to investigate the effects of different parameters on physicochemical properties of pellets from BRAD, as well as the optimal conditions for producing pellets with BRAD.

The physical quality of a produced pellet is mainly affected by the properties of raw materials, including chemical composition, moisture content, particle size, and parameters associated with manufacturing processes, such as forming temperature, applied pressure, holding time, and die geometry (Lestander et al. 2012). Numerous researchers have explored the effects of associated parameters and properties of biomass materials on the physical and chemical properties of pellets made from single or mixture of different types of biomass materials under different conditions. Rhén et al. reported that the density and compression strength of the pellets from sawdust were elevated by increasing the pelletizing temperature and lowering the moisture content of raw materials (Rhén et al. 2005). Puig-Arnavat et al. (2016) found that the moisture content of 10 wt.% was optimal for 6 biomass feedstocks, in which the friction increased first and then declined with the increase of die temperature. Stasiak et al. (2017) revealed that the density of pellets made from a blend of pine sawdust, wheat straw, and rapeseed straw increased with the raised percentage of the two straws in the mixture and the compaction pressure.

Response surface methodology (RSM) is an effective method to optimize process conditions, and it can determine the influence of various factors and their interactions on the indexes under investigation (Alhajabdalla et al. 2021). Generally, it is used for mapping a response surface over a particular region of interest (ROI), optimizing the response, or for selecting operating conditions to achieve target specifications or a customer’s requirements (Cheng et al. 2021). In particular, RSM based on a Box-Behnken design (BBD) is advantageous for the analysis on the effects of various factors on the responses by simultaneously modulating the effective parameters, formulating second-order polynomial equations of multiple factors, and describing interactions among independent variables (Belgada et al. 2021). Compared with other response surface designs, BBD possesses attractive advantages in the necessity of performing a small number of experiments and a higher efficiency. To date, BBD has been successfully utilized in several engineering fields.

In the present study, BRAD were selected as raw materials to produce a type of solid biofuel pellet using heating molding process. This study explored the effects of parameters, such as particle size and moisture content of raw materials, die temperature, and molding pressure on the mechanical properties of the pellets produced using BRAD. The optimal values of the mentioned parameters under different conditions were determined.



Biomass residue from anaerobic digestion (BRAD), as used in the current study, mainly consisted of corn straw and cow manure. These components were obtained from the Biomass Energy Laboratory of Heilongjiang Bayi Agricultural University (Daqing, China) after the fermentation process, as shown in Fig. 1a. First, the collected residues were air-dried at room temperature for 10 days. The dried residues were ground using a hammer mill of YB-1000A (Yongkang Sufeng Gongmao Co., Ltd., Zhejiang, China) and then passed through a sieve with different screen sizes to obtain desired particle sizes (0.2, 0.4, 0.6, 0.8, 1.0, 1.2, and 1.4 mm) (Fig. 1b). The chemical compositions of BRAD and other biomass (wheat straw, corn stover, rice straw, Chinese fir sawdust and camphor sawdust) are presented in Table 1.

Before pelletizing, the grounds were dried in a convection oven at 40 °C until the weight of samples remained constant. The moisture content of the feedstocks was adjusted by addition of purified water (predetermined amount) to the grounds. They were subsequently calculated on a wet-weight basis. After that, the feedstocks were put into a plastic sealed container and stored at 4 ± 0.5 °C for 2 days for equilibration of the moisture (Zhang and Guo 2014).

Table 1. Chemical Compositions of Biomass Species

Fig. 1. Experimental materials of (a) initial BRAD and (b) ground BRAD

Pelletizing Apparatus and Procedures

A pelletizer used in the test was manufactured at Heilongjiang Bayi Agricultural University (Fig. 2). The single press consisted of a cylindrical die lagged with an electromagnetic heating unit, a spiral water-cooling unit, and a computer control system. The inside diameter and length of cylinder were 15 and 50 mm, respectively, and the diameter and length of piston were 15.3 and 70 mm, respectively. A thermocouple placed into a cylinder was used to ensure that the temperature reached the desired value. The die temperature can be detected and controlled by a computer system in the range of 0 to 400 °C.

(1) Frame; (2) Temperature sensor; (3) Molding unit; (4) Water cooling unit; (5) Temperature controller; (6) Controlling computer; (7) Thermocouple; (8) Heating unit; (9) Base; (10) Pellet; (11) Cooling unit; (12) Cylinder; (13) Piston

Fig. 2. Photo and schematic illustration of the single press unit

The preparation of the pellet was conducted as follows. Prior to each test, the heating system was run for 15 to 20 min for the desired die temperature. A total of 4 g of ground residues (dry basis) with a specific moisture content was placed in the die. The piston with a preset load applied by the universal testing machine began to compress the materials (loading speed, 5 mm per min). The loading force was controlled by the computer, which recorded the force and displacement curves. After the loading force preset was reached, the pressure was kept at a full pressure for twenty seconds. When 25 °C or below was reached for the die temperature, the cooling system was closed, and the pellet was pressed out from the mold. The produced sample was cooled at an ambient temperature for 10 min. The sample was stored in a plastic bag at 4 ± 0.5 °C.

Measure of Compressive Resistance

Compressive resistance, sometimes called crushing resistance or hardness, is defined as the maximum crushing force of a pellet or a briquette that can withstand before cracking or breaking (Kaliyan and Morey 2009). It is an essential property of densified pellets because of its effects on the mechanical strength and efficiency during the processes of handling, transportation, and storage. Compressive resistance can be measured using different measuring devices with the same working principle. There is currently no standard method to assess the compressive resistance of densified biomass pellets or briquette; however, the compressive resistance of the densified biomass materials can be evaluated by the maximum force that can withstand until failure or breakage (Kambo and Dutta 2014; Hu et al. 2016). In the present study, the compressive resistance of the pellets was measured using a WDW-200E Computerized Electronic Universal Testing Machine (Jinan Time Shijin Testing Machine Co., Ltd., Shandong, China). The sample was placed between two horizontal steel plates, and an axial force was applied to the sample at a constant rate of 10 mm per minute until failure and breakage. In the compression process, force-displacement curves were drawn by the computer, and the peak of the force was determined as the compressive resistance of the pellet.

Measure of Durability

Durability is a measure to assess the ability of densified biofuel pellets to withstand against destructive forces of compression, impact, and shear during handling and transportation processes (Gilvari et al. 2019), because breakage of pellets during processing and transportation has a negative effect on the supply chain. Previously, different devices of rotating drum, tumbling can, and Holmen and Ligno testers have been applied to measure the durability of the densified products. The tumbling can method simulates the mechanical handling of pellets and predicts the possible fines produced by collision of pellets against each other and against the walls of a defined rotating chamber. In the current report, the tumbling can method was employed to determine the durability of the densified pellets. Before each test, a known mass of 10 pellets was applied to the rotating chamber. The rotation speed was fixed to 50 ± 2 rpm, and the revolution lasted for 10 min. After stopping the test, pellets were sieved using a sieve with the screen size of 0.8 times a pellet’s diameter. Finally, the durability was calculated using Eq. 1,

DU = Me/Ma × 100       (1)

where DU refers to the durability of the densified pellets (%), Me refers to the initial mass of the tested pellets before the test (g), and Ma refers to the mass of the tested pellets after the test (g).

Measurement of Density

The density of densified pellets is mainly considered as an essential index related to management and transportation processes. It presents the ratio of the sample mass to its volume with inclusion of inner porosity. After 24 h of pelletizing, each pellet was weighed using an analytical balance with an accuracy of 0.001 g. The dimensions of the pellets, including diameter and length, were gauged with a Vernier caliper with a precision of 0.01 mm. The density of the densified pellet was calculated as the mass of the pellet divided by its volume. As reported previously, an optimal density of a single pellet is in the range of 1,000 to 1,400 kg/m3 (Emadi et al. 2016).

Table 2. Variables and Levels for Single-Factor Experiment

Experimental Design and Optimization

The particle size, moisture content, die temperature, and molding pressure were selected as variables, and were coded of x1, x2, x3, and x4, respectively. The compressive resistance, durability, and density, with the codes of y1, y2, and y3, respectively, were deemed as responses. Single-factor experiments were performed to determine the reasonable ranges of variables in the BBD experiment. Table 2 lists the variables and their values in the single-factor experiments. The principle of changing one factor, while other factors were fixed at a middle level was used during the single-factor experiments.

Based on the results of single-factor experiments, BBD was employed to assess the main, interaction, and quadratic effects of many variables on the responses, and the optimal condition in the pelleting process was determined. The variables and their values in the BBD experiment are listed in Table 3.

Table 3. Variables and Levels Used in BBD Experiment

For BBD, the required number of runs can be calculated by Eq. 2 (Rakhmania et al. 2021),

N = 2k0(k0-1)+C0         (2)

where k0 is the number of variables, and C0 is the number of center points, which is equal to 5 in this study.

Thus, in the current research, a total of 29 runs were carried out with the purpose of minimizing the effect of unexplained variabilities on the response observed. The BBD method has the potential to analyze several factors with the minimum experimental trials compared with other response surface methods. Based on analysis of variance (ANOVA) of the experimental data of selected points, the model of objective function on the variables was obtained, and the response surface was plotted. Finally, optimal conditions could be calculated from the final model and verified by an actual experiment (Le et al. 2019).

Statistical Analysis

Origin 8.5 software (OriginLab Corporation, Northampton, MA, USA) was used for graph-based analysis. Using Design Expert 8.0.6 software (Stat-Ease Inc., Minneapolis, MN, USA), ANOVA was performed and the 3D response surface was plotted. Duncan’s multiple range test was used to calculate the least significant difference (P<0.05). All experiments were repeated three times.


Single Factor Experiment

The effects of particle size, moisture content, die temperature, and molding pressure on the mechanical properties of CR, DU, and DE of the pellets are shown in Fig. 3.

Fig. 3. The effects of independent variables on CR, DU and DE. (a) – (c) Particle size, (d) – (f) Moisture content, (g) – (i) Die temperature, and (j) – (l) Molding pressure. (CR: compressive resistance, DU: durability, DE: density)

Effect of particle size on compressive resistance, durability, and density

The effects of particle size on mechanical properties of the pellets are depicted in Fig. 3a-c. The experiment was conducted at a moisture content of 10%, die temperature of 120 °C, and molding pressure of 140 MPa. The relationships between CR, DU, and DE and particle size were negative. Furthermore, the association between particle size and the three responses was statistically significant (P<0.05) according to the one-way ANOVA of the experimental data. This result confirmed that particle size is an important factor influencing the mechanical properties of the pellets. When particle size increased from 0.2 to 1.4 mm, CR, DU, and DE decreased by 658.8 N, 16.9%, and 531 kg/m3, respectively. Several reasons can be used for interpreting the variation. First, finely ground biomass can greatly increase the inter-particle contact area and decrease the inter-particle distance, contributing to the development of the solid bridge between adjacent particles at the points of contact. Common inter-molecular attractive forces, including hydrogen bonds, van der Waals forces, and magnetic forces, were produced during the densification process. The inter-molecular forces can cause particles to adhere to each other and generate strong interlocking bonds between adjacent particles, which are advantageous for improving the quality of the pellets. A previous study demonstrated that van der Waals forces can be strongly affected by the particle size of the biomass materials (Stelte et al. 2011). Generally, the finer the grind, the higher the quality of pellet. Fine particles usually accept more moisture than large particles and, therefore, undergo a higher degree of conditioning. Also, large particles are fissure points that cause cracks and fractures in pellets (Kaliyan and Morey 2009). Second, reducing the particle size can enhance the mobility of the feedstock in the cylinder during the pelletizing, causing flow of smaller particles into the void fractions of biomass particles, thereby resulting in an increase in strength and density of the pellets. Moreover, decreasing the particle size could provide a greater surface area, promoting absorption of moisture and heat, which is highly significant for activating the binding properties of some natural binders (e.g., lignin, starch, cellulose, protein, and hemicellulose) (Carone et al. 2011). A previous study recommended a particle size of 0.5 to 0.8 mm to produce pellets with a promising quality (Kaliyan and Morey 2009). Though fine particles produce high-quality biomass pellets with higher hardness, durability, and density, fine grinding is undesirable due to the raised production cost. Therefore, in the present study, the particle size of the BRAD used for the BBD experiment was determined to be in the range of 0.4 to 1 mm.

Effect of moisture content on compressive resistance, durability, and density

The effects of moisture content on the mechanical properties of CR, DU, and DE are displayed in Fig. 3d-f. The data could be obtained from the tests carried out at a particle size of 0.8 mm, die temperature of 120 °C, and molding pressure of 140 MPa. The values of CR, DU, and DE increased first and then decreased with the raising of moisture content from 4% to 16%. As moisture content increased from 4% to 10%, the CR, DU, and, DE, increased from 764.3 to 108.4 N, 83.7% to 91.5%, and 705.3 to 947.2 kg/m3, respectively. With a further increase in the moisture content, CR, DU, and DE decreased by 262.6 N, 12.9%, and 222.6 kg/m3, respectively. This result was consistent with that reported previously, which demonstrated that the peak values of CR, DU, and DE were observed at an optimum moisture content of 10%, whereas higher values of moisture content negatively influenced the densification quality of the pellets as it exceeded the reasonable range (Kanliyan and Morey 2009; Zainuddin et al. 2011). Based on the one-way ANOVA of the data, the moisture content had an extremely significant effect (P<0.01) on CR and a significant effect (P<0.05) on DE; however, its effect on DU was not statistically significant (P>0.05). The moisture content, which is generally regarded as the most important factor affecting the mechanical properties of the pellets, acts as a lubricant and a binder in the pelleting process (Li et al. 2015). A thin film of water around the particles would exhibit bonds via capillary sorption between particles. In addition, the increase of water content is conducive to the briquetting process, as some water-soluble compounds (e.g., starch, sugar, soda ash, sodium phosphate, potassium salt, calcium chloride, etc.) are present in the feed. Once the protein and carbohydrate were squeezed out from the materials, they flowed into the gaps between particles with water in response to capillary pressure, which increased the inter-particle bonding forces, leading to the improvement of the pellet quality. After pelletizing, many chemical and physical changes, e.g., crystallization of some ingredients, chemical reactions, hardening of binders, and solidification of melted components are induced. However, the mechanical properties of the pellets decreased as the moisture content of the feed exceeded the optimum value. The decrease of CR, Du, and DE at a higher content of moisture may be attributed to the fact that excessive water molecules within the particles may generate a thick water layer on the surface of the particles because of the incompressibility of water, preventing the release of natural binder from the particles and resulting in less creation of the hydrogen bonds between polymers of particles. Additionally, the water layer caused an extra particle-to-particle sliding, thereby weakening the adhesion and cohesion forces from one particle to another, which may help to explain the decrease of quality under high moisture content conditions. Therefore, the optimum moisture content of the materials needs to be determined to achieve high-quality pellets. In the present research, the value of moisture content applied to the BBD experiment was finally identified as 8%-12% to maximize the responses.

Effect of die temperature on compressive resistance, durability, and density

The quality of pellets with respect to the die temperature at a particle size of 0.8 mm, a moisture content of 10%, and a molding pressure of 140 MPa was compared, and the results are shown in Fig. 3g-i. The CR and DU first increased when die temperature raised from 80 to 140 °C, and then reduced with the raised die temperature. Moreover, the peak values of CR (1021.6 N), DU (91.4%), and DE (938.7 kg/m3) were observed at a die temperature of 120 °C in the current research. A similar result has been reported previously, which revealed that the quality of pellets increased with the elevation of die temperature from 30 to 110 °C (Li et al. 2014). Contrary to this conclusion, the negative effects of die temperature on the quality of pellets were demonstrated in some previous studies (Ishii et al. 2014; Said et al. 2015). The effects of die temperature may be due to the differences in the pellets-associated parameters, type of materials, and test conditions. The positive effect of die temperature may be attributed to its induced function on some chemical ingredients, such as lignin, cellulose, hemicellulose, starch, and protein, which are considered as natural binders. In general, the synergistic effects of lignin softening and protein denaturation, contributing to the formation of a solid bridge between and within particles, are the principal binding mechanisms in the pelletization process. Under a lower die temperature, the binding role of the natural binders contained in the materials was limited; consequently, the bonding forces related to the pellets are mainly short-range forces, including van der Waals forces, hydrogen bonds, and mechanical interlocking. Nevertheless, when die temperature reached the glass transition, which has been reported at a temperature of 75 to 150 °C for a variety of biomass materials, the lignin and hemicellulose inside the materials were softened and squeezed out, and filled in the gaps of particles under the interaction of elevated temperature and pressure.

Once exiting the pelletizer, the pellets were left to cool down, lignin was hardened, and protein was re-associated, significantly enhancing the strength, durability, and density of pellets. In addition, as the molding temperature was in an appropriate range, the increase in die temperature led to the plasticization of lignocellulosic fibers, resulting in the reduction of the modulus of elasticity of biomass particles, which made the material more flexible. Consequently, it caused the reduction of empty spaces within and between particles, which contributed to improvement of the pellets’ quality. In contrast, when die temperature exceeded glass transition or even more, the higher temperature decreased the quality of pellets. This may be due to that an elevated temperature, nearly all of the moisture inside the materials would be evaporated, which negatively influenced the quality of pellets. A further increase in die temperature would cause brittle protein after excessive denaturation, which may be detrimental to the pelletization. Consequently, aiming to obtain high-quality pellets, the rational values of die temperature used in the BBD were set within the range of 100 to 140 °C.

Effect of molding pressure on compressive resistance, durability, and density

The effects of molding pressure on CR, DU, and DE of the pellets are illustrated in Fig. 3j-l. During the densification process, the molding pressure applied in this study was 80, 100, 120, 140, 160, 180, and 200 MPa when particle size, moisture content, and die temperature were kept at 0.8 mm, 10%, and 120 °C, respectively. The maximum values of CR, DU, and DE were 1314.4 N, 93.4%, and 1072 kg/m3, respectively. Significant correlations between molding pressure and CR and DE were observed by one-way ANOVA. Additionally, molding pressure showed to play an extremely significant role in DU. It has been reported that applied pressure positively influences the quality of pellets during the pelletization process, as it can activate different binding mechanisms within the feed particles (Carone et al. 2011; Poddar et al. 2014; Said et al. 2015; Guo et al. 2016). At a low pressure, the particles rearranged and maintained their original physical properties, reducing the volume of the raw materials to a certain extent; however, these changes had slight effects on CR and DU, because there was no effective molecular binding force between particles, which may be the possible reason for the lower mechanical properties of the pellets under a low pressure. Nevertheless, at a high pressure, elastic and plastic deformation of the particles occurred, which caused flow of the smaller particles into the empty spaces between particles. When particles were close together, the inter-particle bonding was formed. Moreover, the softened natural binding components in the materials, e.g., lignin, water soluble carbohydrate, cellulose, protein, and starch, were pressed out and diffused from one particle to another at the points of contact to act as a binder. These features facilitate formation of van der Waals forces and electrostatic forces and hydrogen bonds. Subsequently, the higher molding pressure applied, the higher pellet quality obtained. To date, it has been a common industrial technique to improve adhesion by increasing pressure to enhance molecular contact between adjacent molecules. Several studies have suggested that the expected pressure in a pellet mill should be in the range of 100 to 150 MPa, as well as 100-200 MPa in a roll press (Thomas et al. 1997; Dec et al. 2003). Considering that the molding pressure is associated with the production cost, the final values of the molding pressure used in BBD were in the range of 120 to 160 MPa.

Box-Behnken Design Experiment

The BBD experimental results are listed in Table 4.

Fitting of data to the models and statistical analysis

The data were fitted individually to multiple polynomial mathematical models, which are shown in Table 5. Based on the four selected factors, the possible model could be linear, 2FI, quadratic, or cubic. Results showed the P-value (0.2878) for cubic versus quadratic model was more than 0.05, the P-value for quadratic versus 2FI was less than 0.0001, and the P-value (0.9648) for 2FI versus linear was more than 0.05. Generally, a low order model is chosen if the comparison of low order and high order model is not statistically significant, otherwise a higher order model is chosen. Therefore, the quadratic model was chosen in the work.

Table 4. Values of Compressive Resistance, Durability, and Density in the BBD Experiment

Table 5. Model Summary Statistics

ANOVA was performed to identify the significance and accuracy of the chosen model. The results are shown in Tables 6 through 8. These results would be used to examine the significance of the model and the independent variables on the response based on the F-value and P-value. Important variables are commonly rated using the F-value or P-value at a 95% confidence interval. The larger the F-value and the smaller the P-value obtained, the more significant the corresponding coefficient achieved (Ashraf et al. 2021).

Table 6. ANOVA Results of the Regression Models for Compressive Resistance

Table 7. ANOVA Results of the Regression Models for Durability