# Kinetic Study on the Pyrolysis of Medium Density Fiberboard: Effects of Secondary Charring Reactions

^{*}

## Abstract

**:**

## 1. Introduction

^{3}over the world in 2017. Specially, in China, the number was more than 59 million m

^{3}. A large amount of waste MDF was generated from the need for regular replacement of furniture due to aging, mechanical damage, fire burning, etc. [2]. At the beginning, most of the waste MDF was sent to burn for cooking or space heating, while a small portion was disposed in landfills [3]. With the rapid rising of MDF waste, land occupation and environmental problems are becoming more serious. From the perspective of protecting the natural environment and the sustainable use of resources, it is a good choice to recycle this large amount of waste as energy fuel. Pyrolysis has been proved to be a promising thermochemical conversion technology for resource and energy recovery [4]. On one hand, biomass can be converted into low molecular weight products during the pyrolysis process with low environmental damage. On the other hand, the products generated can be recycled as useful chemicals or gaseous fuels. Hence, it is important to investigate the pyrolysis behavior and pyrolysis kinetics of MDF.

## 2. Experimental and Kinetic Modeling

#### 2.1. Experimental

#### 2.1.1. MDF Sample

#### 2.1.2. TGA Tests

#### 2.2. Kinetic Modeling

#### 2.2.1. Kinetic Reaction Model

_{0}, m

_{t}, and m

_{∞}represent the initial, instantaneous, and the final solid mass of samples, respectively; the kinetic triplets A is the pre-exponential factor, E is the activation energy and n is the reaction order; R is the gas constant; for component i, W

_{i}is the instantaneous mass fraction, W

_{i,0}is the initial mass fraction, γ

_{i}, σ

_{i}, and φ

_{i}are the stoichiometry coefficient of tar and char, respectively.

**Model I**

_{tot}and the total solid mass fraction W

_{tot}can be calculated as:

**Model II**

_{1}and the solid mass fraction W

_{1}of step 1 can be calculated as:

_{tar,0}is the initial mass fraction of tar which is calculated from step 1:

_{tar}, A

_{tar}, E

_{tar}, n

_{tar}denote the instantaneous mass fraction the kinetic triplets for tar generated by step 1, respectively.

_{char}

_{,2}is calculated as:

#### 2.2.2. Optimization Method—Differential Evolution Algorithm

**Initialization**

**Variation**

**Crossover**

_{tot}and (dW/dt)

_{tot}are the calculated solid mass and mass loss rate in the pyrolysis process, respectively. exp means the corresponding experimental data. n

_{j}is the number of data points considered in each single heating rate and k is the number of heating rates. c is the weight coefficient, and c = 0.5 is set for equally weighted both mass and mass loss rate.

_{i}, A

_{i}, n

_{i}), initial mass fractions (W

_{i,0}), tar yields (γ

_{i}), and char yields (σ

_{i}, θ) for each component and tar. Since the initial mass fraction of the sum of the four components is equal to 1, the initial mass fraction of lignin can be calculated by W

_{l,0}= 1 − W

_{r,0}− W

_{h,0}− W

_{c,0}. Then the number of unknown variables is 27. So, there are 27 individuals in Model II and 19 in Model I. In order to obtain the optimal solution, appropriate algorithm parameters should be set. In this work, the population size, scaling factor, crossover probability and maximum iteration number of the optimization are set as 60, 0.5, 0.2, and 1000, respectively. The optimization process is implemented in MATLAB.

#### 2.2.3. Estimation of Initial Guesses of Model Parameters for DE

## 3. Results and Discussion

#### 3.1. Thermogravimetric Analysis

^{2}of fitting curves at different conversions are demonstrated. The values of E at each conversion determined by different model-free methods are almost the same. In addition, the values of E increase gradually at 0 ≤ α ≤ 0.1, followed by a sharp increase at 0.1 < α ≤ 0.2. Then E remains almost constant at 0.2 < α ≤ 0.8. Finally, a second sharp increase of E occurs at 0.8 < α ≤ 1.0. These ranges are coincidence with the position where the differences observed in Figure 4a–c. Therefore, four stages which related to four sub-reactions of four components can be divided in the pyrolysis process by α = 0.1, α = 0.2 and α = 0.8.

#### 3.2. Estimated Initial Guess of Model Parameters

^{−2})]/(−2) (183.88 kJ/mol) is closest to the value by the model-free methods (159.70 kJ/mol, as shown in Table 3). Thus, the 3rd-order reaction model may be the most appropriate model to express the pyrolysis process in the range of 0.2 < α ≤ 0.8.

^{2}, the E

_{α}obtained by FWO are used to determine the pre-exponential factor. The lnA

_{α}values evaluated by FWO with the 3rd-order reaction model are plotted in Figure 5. It can be seen that lnA

_{α}varies with E

_{α}, and a fitting line which shows the so-called kinetic compensation effect [41] can be obtained: $\mathrm{ln}{A}_{\alpha}=0.17058{E}_{\alpha}+11.797,\text{}{R}^{2}=0.993$. According to Yao et al. [42], if a compensation effect is observed, the choice of 3rd-order reaction model is appropriate. At the same time, the compensation effect parameters, a = 0.17058 and b = 11.797, can describe the whole pyrolysis process well for that they are not affected by experimental conditions [43]. Thus, the evaluations of lnA

_{α}based upon the compensation effect are listed in Table 3. The mean values of E and lnA of the four stages will be used as the initial guesses for the optimization process below.

#### 3.3. Model Parameter Optimization by DE

^{−1}, respectively. The initial values of reaction orders n are assumed to be 1. According to the manufacture and Munir et al. [44], the initial values of mass fractions of resin, hemicellulose and cellulose are assumed to be 0.1, 0.18, and 0.48, respectively. The initial values of φ, σ, γ, and θ are all assumed to be 0.5. The lower limit values of search range for parameters are set to 10% of the respective initial values. The upper limit values of search range for n

_{i}are set to 8 [19]. The upper limit values for other parameters are set to 200% of the respective initial values. In Equation (18), it may cost a lot of computational time when data from all heating rates are used. Since 20 °C/min is a typical heating rate for slow pyrolysis [15], the experimental data of 20 °C/min and 30 °C/min are selected to obtain optimized parameters by DE.

#### 3.4. Effects of Secondary Charring Reactions on the Components and Products

_{m}and w

_{exp}represent the char yield obtained from model and experiment, respectively. Table 7 lists the percentage differences in the char yields calculated by two models. The average error of char yield for Model I in four heating rates is 23.6% while the average error is 2% for Model II. Therefore, the components’ contents and products’ yields can be better estimated by Model II.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) FWO plots; (

**b**) KAS plots; (

**c**) Starink plots at the conversion of 0.1–0.9; and (

**d**) activation energy E and temperature at 10 °C/min versus conversion α.

**Figure 6.**Comparisons between experimental TG/DTG data and predictions based on optimized parameters: (

**a**) β = 10 °C/min; (

**b**) β = 20 °C/min; (

**c**) β = 30 °C/min; and (

**d**) β = 40 °C/min.

**Figure 7.**Experimental curves of |DDTG| and |DTG| of MDF at 10 °C/min with four components by: Model I is shown in dashed lines; Model II is shown in solid lines.

**Figure 8.**Comparisons of components mass between Model I and Model II at four heating rates: (

**a**) 10 °C/min; (

**b**) 20 °C/min; (

**c**) 30 °C/min; and (

**d**) 40 °C/min. Model I is shown in dashed lines, and Model II is shown in solid lines.

**Figure 9.**Comparisons of product yields between Model I and Model II at four heating rates: (

**a**) 10 °C/min; (

**b**) 20 °C/min; (

**c**) 30 °C/min; and (

**d**) 40 °C/min. Model I is shown in dashed lines, and Model II is shown in solid lines.

Feedstock | Proximate Analysis (wt %) | Ultimate Analysis (wt %) | |||||||
---|---|---|---|---|---|---|---|---|---|

MDF | Moisture | Ash | Volatiles | Fixed carbon | C | H | O ^{a} | N | S |

- | 8.28 | 4.69 | 81.2 | 5.83 | 44.96 | 6.26 | 44.87 | 3.35 | 0.56 |

^{a}By difference.

Model I | Model II | ||
---|---|---|---|

1 *: | $\mathrm{resin}\to {\upsilon}_{r}\text{}gases+{\phi}_{r}\text{}char$ | 1 *: | $\mathrm{resin}\to {\gamma}_{r}\text{}tar+{\delta}_{r}\text{}gases+{\sigma}_{r}\text{}char$ |

$\mathrm{hemicellulose}\to {\upsilon}_{h}gases+{\phi}_{h}\text{}char$ | $\mathrm{hemicellulose}\to {\gamma}_{h}\text{}tar+{\delta}_{h}\text{}gases+{\sigma}_{h}\text{}char$ | ||

$\mathrm{cellulose}\to {\upsilon}_{c}\text{}gases+{\phi}_{c}\text{}char$ | $\mathrm{cellulose}\to {\gamma}_{c}\text{}tar+{\delta}_{c}\text{}gases+{\sigma}_{c}\text{}char$ | ||

$\mathrm{lignin}\to {\upsilon}_{l}\text{}gases+{\phi}_{l}\text{}char$ | $\mathrm{lignin}\to {\gamma}_{l}\text{}tar+{\delta}_{l}\text{}gases+{\sigma}_{l}\text{}char$ | ||

2 *: | $\mathrm{tar}\to \tau \text{}gases+\theta \text{}char$ |

α | FWO | KAS | Starink | Average Value | |||||
---|---|---|---|---|---|---|---|---|---|

E (kJ/mol) | R^{2} | E (kJ/mol) | R^{2} | E (kJ/mol) | R^{2} | E (kJ/mol) | lnA | R^{2} | |

0.05 | 65.94 | 0.96 | 63.89 | 0.95 | 64.06 | 0.95 | 64.63 | 22.82 | 0.95 |

0.1 | 80.66 | 0.90 | 70.06 | 0.86 | 71.19 | 0.86 | 76.30 | 24.81 | 0.87 |

0.2 | 152.10 | 0.99 | 150.86 | 0.99 | 151.10 | 0.99 | 151.36 | 37.62 | 0.99 |

0.3 | 145.11 | 0.99 | 143.06 | 0.99 | 143.33 | 0.99 | 143.84 | 36.33 | 0.99 |

0.4 | 154.83 | 0.99 | 152.97 | 0.99 | 153.24 | 0.99 | 153.68 | 38.01 | 0.99 |

0.5 | 165.71 | 0.99 | 164.15 | 0.99 | 164.43 | 0.99 | 164.77 | 39.90 | 0.99 |

0.6 | 168.79 | 0.99 | 167.17 | 0.99 | 167.45 | 0.99 | 167.80 | 40.42 | 0.99 |

0.7 | 170.73 | 0.99 | 169.04 | 0.99 | 169.32 | 0.99 | 169.70 | 40.74 | 0.99 |

0.8 | 170.30 | 0.99 | 168.38 | 0.99 | 168.68 | 0.99 | 169.12 | 40.65 | 0.99 |

0.9 | 280.67 | 0.97 | 283.51 | 0.96 | 283.75 | 0.96 | 282.64 | 60.01 | 0.96 |

Mean value (0.05–0.1) | 73.30 | 0.93 | 66.98 | 0.90 | 67.63 | 0.91 | 69.30 | 23.82 | 0.92 |

Mean value (0.1–0.2) | 116.38 | 0.95 | 110.46 | 0.93 | 111.15 | 0.93 | 112.66 | 31.21 | 0.94 |

Mean value (0.2–0.8) | 160.08 | 0.99 | 159.38 | 0.99 | 159.65 | 0.99 | 159.70 | 39.10 | 0.99 |

Mean value (0.8–0.9) | 225.49 | 0.98 | 225.95 | 0.98 | 226.22 | 0.98 | 225.88 | 50.33 | 0.98 |

Heating Rate (°C/min) | First Stage α/T (°C) | Second Stage α/T (°C) | Third Stage α/T (°C) | Forth Stage α/T (°C) |
---|---|---|---|---|

10 | 0–0.1/25–214 | 0.1–0.2/214–274 | 0.2–0.8/274–363 | 0.8–1.0/363–800 |

20 | 0–0.1/25–220 | 0.1–0.2/220–285 | 0.2–0.8/285–375 | 0.8–1.0/375–800 |

30 | 0–0.1/25–231 | 0.1–0.2/231–292 | 0.2–0.8/292–382 | 0.8–1.0/382–800 |

40 | 0–0.1/25–234 | 0.1–0.2/234–296 | 0.2–0.8/296–389 | 0.8–1.0/389–800 |

Reaction Model [29,41] | 10 °C/min | 20 °C/min | 30 °C/min | 40 °C/min | Mean Value | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

E (kJ/mol) | R^{2} | E (kJ/mol) | R^{2} | E (kJ/mol) | R^{2} | E (kJ/mol) | R^{2} | E (kJ/mol) | R^{2} | ||

Reaction order | |||||||||||

0th-order | g(α) = α | 32.83 | 0.99 | 35.13 | 0.99 | 34.06 | 0.99 | 33.43 | 0.99 | 33.86 | 0.99 |

1st-order | g(α) = −ln(1 − α) | 66.67 | 0.99 | 70.92 | 0.99 | 69.01 | 0.99 | 68.20 | 0.99 | 68.7 | 0.99 |

2nd-order | g(α) = [1 − (1 − α)^{−1})]/( −1) | 115.9 | 0.98 | 122.96 | 0.98 | 119.8 | 0.97 | 118.81 | 0.98 | 119.37 | 0.98 |

3rd-order | g(α) = [1 − (1 − α)^{−2})]/( −2) | 178.58 | 0.97 | 189.23 | 0.97 | 184.49 | 0.96 | 183.24 | 0.98 | 183.88 | 0.97 |

4th-order | g(α) = [1 − (1 − α)^{−3})]/( −3) | 250.5 | 0.96 | 265.3 | 0.96 | 258.65 | 0.95 | 257.24 | 0.97 | 257.92 | 0.96 |

Diffusional | |||||||||||

1-D | g(α) = α^{2} | 75.91 | 0.99 | 80.73 | 0.99 | 78.73 | 0.99 | 77.57 | 0.99 | 78.23 | 0.99 |

2-D | g(α) = (1 − α)ln(1 − α)+α | 93.87 | 0.99 | 99.68 | 0.99 | 97.19 | 0.99 | 95.94 | 0.99 | 96.67 | 0.99 |

3-D (Jander) | g(α) = [1 − (1 − α)^{1/3}]^{2} | 117.64 | 0.99 | 124.71 | 0.99 | 121.8 | 0.99 | 120.47 | 0.99 | 121.16 | 0.99 |

GB | g(α) = 1 − 2/3α− (1 − α)^{2/3} | 101.6 | 0.99 | 107.92 | 0.99 | 105.34 | 0.99 | 104.01 | 0.99 | 104.71 | 0.99 |

Nucleation | |||||||||||

2/3-Power law | g(α) = α^{3/2} | 54.37 | 0.99 | 57.95 | 0.99 | 56.37 | 0.99 | 55.45 | 0.99 | 56.04 | 0.99 |

2-Power law | g(α) = α^{1/2} | 11.28 | 0.98 | 12.34 | 0.99 | 11.74 | 0.99 | 11.37 | 0.98 | 11.68 | 0.99 |

3-Power law | g(α) = α^{1/3} | 4.07 | 0.95 | 4.74 | 0.98 | 4.32 | 0.95 | 3.99 | 0.92 | 4.28 | 0.95 |

2-AE | g(α) = [−ln(1 − α)]^{1/2} | 28.18 | 0.99 | 30.26 | 0.99 | 29.18 | 0.98 | 28.77 | 0.99 | 29.10 | 0.99 |

3-AE | g(α) = [−ln(1 − α)]^{1/3} | 15.38 | 0.99 | 16.63 | 0.99 | 15.96 | 0.98 | 15.63 | 0.99 | 15.90 | 0.99 |

4-AE | g(α) = [−ln(1 − α)]^{1/4} | 8.97 | 0.98 | 9.89 | 0.99 | 9.31 | 0.96 | 9.03 | 0.99 | 9.30 | 0.98 |

Contracting geometry | |||||||||||

Area | g(α) = 1 − (1 − α)^{1/2} | 47.89 | 0.99 | 51.05 | 0.99 | 49.55 | 0.99 | 48.89 | 0.99 | 49.34 | 0.99 |

Volume | g(α) = 1 − (1 − α)^{1/3} | 53.71 | 0.99 | 57.20 | 0.99 | 55.62 | 0.99 | 54.87 | 0.99 | 55.35 | 0.99 |

Component | Parameter | Initial Guess | Range | Model I Optimized Value | Model II Optimized Value |
---|---|---|---|---|---|

Resin | lnA_{r} (ln s^{−1}) | 23.82 | (2.4, 47.6) | 8 | 16.87 |

E_{r} (kJ/mol) | 69.30 | (6.9, 138.6) | 133.81 | 138.49 | |

n_{r} | 1 | (0.1, 8) | 2.75 | 3.00 | |

W_{r}_{,o} (%) | 10 | (1, 20) | 13.83 | 9.70 | |

φ_{r}/σ_{r} (%) | 50 | (5, 95) | 23.84 | 54.88 | |

γ_{r} (%) | 50 | (5, 95) | − | 7.83 | |

Hemicellulose | lnA_{h} (ln s^{−1}) | 31.21 | (3.1, 62.4) | 16.08 | 15.77 |

E_{h} (kJ/mol) | 112.66 | (11.3, 225.3) | 188.22 | 177.86 | |

n_{h} | 1 | (0.1, 8) | 2.68 | 1.12 | |

W_{h}_{,o} (%) | 18 | (1.8, 36) | 28.67 | 20.04 | |

φ_{h}/σ_{h} (%) | 50 | (5, 95) | 20.91 | 11.51 | |

γ_{h} (%) | 50 | (5, 95) | − | 45.02 | |

Cellulose | lnA_{c} (ln s^{−1}) | 39.10 | (3.9, 78.2) | 18.49 | 19.00 |

E_{c} (kJ/mol) | 159.70 | (16, 319.4) | 170.24 | 169.65 | |

n_{c} | 1 | (0.1, 8) | 1.75 | 1.85 | |

W_{c}_{,o} (%) | 48 | (4.8, 96) | 33.88 | 43.48 | |

φ_{c}/σ_{c} (%) | 50 | (5, 95) | 31.73 | 13.87 | |

γ_{c} (%) | 50 | (5, 95) | − | 40.26 | |

Lignin | lnA_{l} (ln s^{−1}) | 50.33 | (5, 100.7) | 17.15 | 12.99 |

E_{l} (kJ/mol) | 225.88 | (22.6, 451.8) | 221.25 | 222.25 | |

n_{l} | 1 | (0.1, 8) | 3.96 | 2.80 | |

W_{l}_{,o} (%) | − | 23.62 | 26.78 | ||

φ_{l} /σ_{l} (%) | 50 | (5, 95) | 22.71 | 5.95 | |

γ_{l} (%) | 50 | (5, 95) | − | 76.20 | |

Tar | lnA_{t} (ln s^{−1}) | 17.9 | (1.8, 35.8) | − | 33.24 |

E_{t} (kJ/mol) | 124 | (12.4, 248) | − | 110.25 | |

n_{t} | 1 | (0.1, 8) | − | 4.02 | |

θ (%) | 50 | (5, 95) | − | 14.42 |

Model | 10 °C/min | 20 °C/min | 30 °C/min | 40 °C/min | Mean Value |
---|---|---|---|---|---|

Model I | 22.9% | 26.6% | 24.2% | 20.7% | 23.6% |

Model II | 1.1% | 4.3% | 2.5% | 0.3% | 2% |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pan, L.; Jiang, Y.; Wang, L.; Xu, W. Kinetic Study on the Pyrolysis of Medium Density Fiberboard: Effects of Secondary Charring Reactions. *Energies* **2018**, *11*, 2481.
https://doi.org/10.3390/en11092481

**AMA Style**

Pan L, Jiang Y, Wang L, Xu W. Kinetic Study on the Pyrolysis of Medium Density Fiberboard: Effects of Secondary Charring Reactions. *Energies*. 2018; 11(9):2481.
https://doi.org/10.3390/en11092481

**Chicago/Turabian Style**

Pan, Longwei, Yong Jiang, Lei Wang, and Wu Xu. 2018. "Kinetic Study on the Pyrolysis of Medium Density Fiberboard: Effects of Secondary Charring Reactions" *Energies* 11, no. 9: 2481.
https://doi.org/10.3390/en11092481