# Numerical Study of Cylindrical Tropical Woods Pyrolysis Using Python Tool

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- a
- Assumptions

- The studied sample is of cylindrical geometry, of infinite length, heated through its surface by convection and radiation;
- Samples are directly exposed to the heat fixed numerically, thus the heating rates are neglected.
- Pyrolysis does not generate any change in the volume of the sample and the latter is considered isotropic;
- For simplicity, heat is assumed to be transmitted inside the solid particle by conduction only;
- The heat and mass transfer of the volatile products and the vapor inside the solid are ignored;
- The volatile products and the vapor leave the solid as soon as they are produced. They are in thermal equilibrium with the solid matrix and therefore the rate of solid mass loss is taken as the mass flux of the volatiles;
- Secondary reactions of the volatile products are not taken into account;
- The chemical reactions of pyrolysis are described by the Arrhenius law of first order.

- b
- Setting in equation of the pyrolysis of wood

- Heat balance

- Mass balance

- Heat balance

^{2}/s]. It is calculated as follows:

- Mass balances of wood, charcoal, gas, liquid and steam:

- Initial and boundary conditions

- -
- At $t=0$,

- -
- Due to the cylindrical symmetry, the condition at the center gives:

- -
- At the surface of the sample, in r = R, we have:

- c
- Numerical values of the model constants

## 3. Results and Discussion

#### Validation of the Model

^{3}. Figure 1 presents the wood temperature evolutions at the surface (r = 25 mm), at 5 mm, and 15 mm to the axis of the cylindrical wood. In general, temperature increases from the surface to the center because parts near the surface are more heated than parts far from the surface. Model 1 (one-reactional model) gives acceptable results that are more satisfactory than model 2 (multi-reactional model).

^{5}s

^{−1}and 127.4 kJ/kg, experimental and theoretical curves of the wood’s relative density are close to each other. A space step of 0.05 s has been used. In effect, Di-Blasi et al. [23] show that pyrolysis reaction heat depends on the produced char and the type of studied materials. Using a cylindrical temperate sample of 3 cm diameter, Preau [24] found that temperatures of all parts of the sample increase until they reach the value of the oven (400 °C), this value is reached after 1000 s. At 1.5 cm diameter, the oven temperature (420 °C) is obtained after 400 s [25]. Influences of the heating rates experimentally considered can also increase this distance, as revealed in literature reviews [25,26].

_{f}= 673.15 K. At 973.15 K, cylindrical wood is totally transformed after 40 min. The conversion should vary from 0 at the beginning of the pyrolysis to 1 at the end. As the sample is considered dry, no latency period, which would be due to moisture evaporation, is to be noted in both cases. However, at low heating temperatures, the conversion increases slowly due to the fact that the temperature of the sample has not reached the temperature of the beginning of pyrolysis; during this time, the sample is only heated but no degradation takes place.

_{f}= 973.15 K. When the mass of wood increases, temperature takes time to heat all of the product. After 1000 s, all cylindrical wood of 15 mm radius is totally transformed, 2500 s are needed to totally transform a cylindrical wood with 25 mm of radius, while after 3000 s cylindrical wood with a radius higher than 35 mm is not totally transformed. The temperature increases more rapidly with small diameter samples as observed by Preau [24] in his experiments on the pyrolysis of solid wood samples.

_{f}= 973.15 K, R = 25 mm, RH = 0.3. When the wood is in non-hygroscopic domain (moisture content higher than 30%), free water is rapidly dried on the surface and evolutions of temperature at the surface of the cylindrical wood are almost the same. In hygroscopic domain (moisture content lower than 30%), the surface of the wood heated rapidly. However, after 400 s all curves align because the effects of the initial moisture content have been cancelled. Figure 13 shows that average moisture content in the cylindrical wood decreases exponentially and all curves align after 400 s. The samples are totally dried after 800 s. Figure 14 shows the distribution of temperature during the process at five positions of the cylindrical wood using Model 2. It is clear that wood samples will degrade progressively from the surface to the center because temperature takes time to heat internal parts of the cylindrical wood. After 500 s, the temperature of the surface is near the temperature of the source (973.15 K) but the temperature at the center has not changed. After 3500 s, the temperature of the position located at 10 mm to the axis of the cylindrical wood is equal to 750 K. Literature also shows similar experimental results [24].

_{f}= 673.15 K, the axial part of the wood had 0.175 kg/kg moisture content after 600 s duration (Figure 15a). After 1200 s, the axial part of the wood was equal to 0.015 kg/kg (Figure 15b). It is clear from these curves that high heating temperatures accelerate the drying process. Figure 16 shows that after 600 s, the temperature of parts located at 10 mm of the axis have the same temperature as at the start of the process. Thus, variation of moisture content near the axis presented in Figure 15 is not explained by an increase in the temperature. However, as found by Di Blasi et al. [22], the presence of moisture slows down the pyrolysis process to the point that near the center, the temperature remains constant at its initial value during the evaporation of moisture. Once the drying process is over, in which case the region near the center has reached the equilibrium moisture content, this temperature increases. Indeed, a significant amount of energy is used for the evaporation of the water contained in the wood and only a small amount is transferred to the virgin wood. When the temperature at the surface of the sample reaches about 500 K, the pyrolysis reaction starts and a layer of charcoal forms near the surface, while the temperature in the center remains constant at its initial value. It can therefore be concluded that drying and pyrolysis take place successively, at high heating temperatures, at the same positions along the radius of the pyrolyzed solid wood sample.

_{f}. Figure 18 shows that the density of wood decreases progressively. When the temperature of the source is equal to 673.15 K, wood density starts to decrease after 10 min. When T

_{f}= 973.15 K, the density of the wood decreases after the first seconds of the process. In effect, Figure 16 shows that after 10 min of the process at T

_{f}= 673.15 K, some millimeters of the wood’s surface reaches a temperature equal to 500 K, the temperature from which charcoal is produced [22]. When T

_{f}= 973.15 K, a part of the sample reaches 500 K at 150 s, thus charcoal is produced rapidly. Figure 19 and Figure 20 show that when the wood density decreases, charcoal and gas are directly produced. Figure 19a,b show that during slow pyrolysis (Figure 19a), the density of charcoal obtained is lower than that obtained during the fast pyrolysis (Figure 19b). Values of densities found are not far from those obtained by Teixeira et al. [28] using wood pellets and wood chips at 700 °C. Figure 20 shows that the gas obtained has a density greater than 10 kg/m

^{3}after the first minutes of the process. Thus, it is possible to have some gas in a liquid state in order to justify the great value of gas density obtained. As showed in the literature, gas produced by the wood pyrolysis process is a mixture of many known gases such as CO, CH

_{4}, C, CO

_{2}, H

_{2}, H

_{2}O and O

_{2}[28]. In the liquid state, it is possible that these gases give a high density value. In addition, it has been shown that fast and slow pyrolysis give 13% and 35% of gas, respectively, near the solid products ratio given by the process [29]. Commandré et al. [30] confirm this ratio of gas density obtained during pyrolysis process and show experimentally that this ratio can reach up to 40%.

^{3}.s) and oscillates near this value. When T

_{f}= 973.15 K, a great variation is presented during the first 10 min of the process before reaching a stability near 0.1 kg/(m

^{3}.s). These two variations are also seen during production of gas and water vapor. At a given temperature, water vapor is more rapidly produced than charcoal, and charcoal more rapidly produced than gas (Figure 24, Figure 25 and Figure 26).

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Parameters | Units | Descriptions |

Latin letters | ||

$\mathrm{A}$ | $1/\mathrm{s}$ | Frequency factor |

${\mathrm{C}}_{\mathrm{p}}$ | $\mathrm{J}/\left(\mathrm{kg}.\mathrm{K}\right)$ | Specific heat |

$\mathrm{D}$ | ${\mathrm{m}}^{2}/\mathrm{s}$ | Mass diffusivity |

$\mathrm{E}$ | $\mathrm{kJ}/\mathrm{mol}$ | Activation energy |

$\mathrm{h}$ | $\mathrm{W}/\left({\mathrm{m}}^{2}.\mathrm{K}\right)$ | Convective exchange coefficient |

$\mathrm{H}$ | $\mathrm{kg}/\mathrm{kg}$ | Moisture content |

$\Delta \mathrm{h}$ | $\mathrm{kJ}/\mathrm{kg}$ | Enthalpy of the reaction |

$\mathrm{k}$ | $1/\mathrm{s}$ | Rate constant |

$\mathrm{Q}$ | $\mathrm{kJ}/\mathrm{kg}$ | Heat of pyrolysis |

${\mathrm{Q}}_{\mathrm{r}}^{\u201d}$ | $\mathrm{kW}/{\mathrm{m}}^{3}$ | Heat source |

$\mathrm{RH}$ | $\%/100$ | Relative humidity |

${\mathrm{R}}_{\mathrm{g}}$ | $\mathrm{J}/\mathrm{mol}$ | Perfect gas constant |

$\mathrm{T}$ | $\mathrm{K}$ | Temperature |

Greek letters | ||

$\mathsf{\epsilon}$ | Emissivity | |

$\mathsf{\eta}$ | Conversion | |

$\mathsf{\kappa}$ | ${\mathrm{m}}^{2}/\mathrm{s}$ | Thermal diffusivity |

$\mathsf{\lambda}$ | $\mathrm{W}/\left(\mathrm{m}.\mathrm{K}\right)$ | Thermal conductivity |

$\mathsf{\rho}$ | $\mathrm{kg}/{\mathrm{m}}^{3}$ | Density |

$\mathsf{\sigma}$ | $\mathrm{W}/\left({\mathrm{m}}^{2}.{\mathrm{K}}^{4}\right)$ | Stefan-Boltzmann constant |

${\chi}_{\mathrm{eq}}$ | $\mathrm{kg}/\mathrm{kg}$ | Equilibrium moisture content |

Indices | ||

$0$ | Initial | |

$\mathrm{a}$ | Air | |

$\mathrm{b}$ | Wood | |

$\mathrm{c}$ | Charcoal | |

$\mathrm{g}$ | Gas | |

$\mathrm{h}$ | Wet | |

$\mathrm{i}$ | Component | |

$\mathrm{t}$ | Tar | |

moy | average |

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**Figure 1.**Wood temperature evolutions versus time of process for a cylindrical wood sample and validation using model 1, model 2 and experimental data taken from Larfeldt et al. [21].

**Figure 2.**Wood density evolutions versus time of process of a sample of cylindrical wood and validation using Model 1, Model 2 and experimental data taken from Larfeldt et al. [21].

**Figure 3.**Wood temperature evolutions versus time of process of a sample of cylindrical wood and validation using Model 1, Model 2 and experimental data taken from Larfeldt et al. [21]. A = 1 × 10

^{5}s

^{−1}, A

_{1}= 36.9 × 10

^{5}s

^{−1}, A

_{2}= 7.2 × 10

^{4}s

^{−1}, A

_{3}= 5.13 × 10

^{6}s

^{−1}, E = 127.4 kJ/kg, E

_{1}= 88.75 kJ/kg, E

_{2}= 73.83 kJ/kg, E

_{3}= 88 kJ/kg.

**Figure 4.**Wood relative density evolutions versus time of process of a sample of cylindrical wood and validation using Model 1 and experimental data taken from Larfeldt et al. [21]. A = 1 × 10

^{5}s

^{−1}, E = 127.4 kJ/kg.

**Figure 6.**Evolution of average temperature versus the time of process using Model 1 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**).

**Figure 7.**Wood relative density gradient using Model 1 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**).

**Figure 9.**Evolution of the velocity of degradation using Model 1 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**).

**Figure 10.**Wood conversion rate versus the duration of the process using Model 1 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**).

**Figure 11.**Influences of the wood size on wood temperature (

**a**) and wood conversion rate (

**b**) evolutions versus the duration using Model 1 at T

_{f}= 973.15 K.

**Figure 12.**Evolutions of the surface temperature versus the duration using Model 2, influence of initial moisture content at T

_{f}= 973.15 K and RH = 0.3%/100.

**Figure 13.**Influence of initial moisture content on the evolution of the average moisture content using Model 2 at T

_{f}= 973.15 K, RH = 0.3%/100 and R = 25 mm.

**Figure 14.**Evolutions of temperature in five positions versus duration of the process using Model 2 at T

_{f}= 973.15 K, RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 15.**Evolution of the wood’s average humidity gradient using Model 2 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**). RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 16.**Evolutions of the wood’s temperature gradient using Model 2 at 673.15 K (

**a**) and 973.15 K (

**b**) RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 17.**Evolutions of the wood’s average temperature using Model 2 at 673.15 K (

**a**) and 973.15 K (

**b**). RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 18.**Wood average density versus duration using Model 2 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**). RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 19.**Charcoal average density versus duration using Model 2 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**). RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 20.**Gas average density versus duration using Model 2 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**). RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 21.**Liquid average density versus duration using Model 2 at T

_{f}= 673.15 K (

**a**) and T

_{if}= 973. 15 K (

**b**). RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 22.**Vapor average density versus duration using Model 2 at T

_{f}= 673.15 K (

**a**) and T

_{if}= 973. 15 K (

**b**). RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 23.**Wood conversion rate versus duration using Model 2 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**) RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 24.**Average velocity of charcoal production versus duration using Model 2 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**). RH = 0.3%/100, R = 25mm and H

_{o}= 20%.

**Figure 25.**Average velocity of gas production versus duration using Model 2 at T

_{f}= 673.15 K (

**a**) and T

_{f}= 973.15 K (

**b**). RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

**Figure 26.**Average velocity of water vapor production versus duration using Model 2 at T

_{if}= 673. 15 K (

**a**) and T

_{f}= 973.15 K (

**b**). RH = 0.3%/100, R = 25 mm and H

_{o}= 20%.

Parameters | Numerical Values | Reference | ||
---|---|---|---|---|

Uni-Reactionary Approach | ||||

$\mathsf{\lambda}$ (W.m^{−1}.K^{−1} ) | $10.5\times {10}^{-5}$ | [19] | ||

$\mathsf{\epsilon}$ | 0.8 | [12] | ||

${\mathsf{\omega}}_{0}$ (kg.m^{−3}) | 650 | [19] | ||

${\mathrm{C}}_{\mathrm{b}}$ (J.kg^{−1}.K^{−1}) | 1.46 | [19] | ||

${\mathrm{h}}_{\mathrm{c}}$ (W.m^{−2}.K^{−1}) | 20 | [13] | ||

$\mathrm{Q}$ (kJ.kg^{−1}) | −418 | [20] | ||

$\mathrm{A}$ (s^{−1}) | $1.0\times {10}^{8}$ | [9] | ||

$\mathrm{E}$ (kJ.mol^{−1}) | $125.4$ | [9] | ||

Multi-reaction approach | ||||

Pyrolysis reaction | Drying reaction | |||

${\mathrm{k}}_{1}$(s^{−1}) | ${\mathrm{k}}_{2}$(s^{−1}) | ${\mathrm{k}}_{3}$(s^{−1}) | ||

${\mathrm{A}}_{\mathrm{i}}$ (s^{−1}) | $1.38\times {10}^{5}$ | $1.44\times {10}^{4}$ | $5.13\times {10}^{6}$ | [12,20] |

${\mathrm{E}}_{\mathrm{i}}$ (kJ.mol^{−1}) | 106.5 | 88.6 | 88 | [12,20] |

$\Delta {\mathrm{h}}_{\mathrm{i}}^{0}$ (kJ.kg^{−1}) | −420 | −420 | −2440 | [12] |

${\mathrm{C}}_{\mathrm{p}}$ (J.kg^{−1}.K^{−1}) | ${\mathrm{C}}_{\mathrm{b}}=1950$ ${\mathrm{C}}_{\mathrm{c}}=1390$ ${\mathrm{C}}_{\mathrm{g}}=2400$ ${\mathrm{C}}_{\mathrm{l}}=4180$ ${\mathrm{C}}_{\mathrm{v}}=1580$ | [12] | ||

${\mathsf{\kappa}}_{\mathrm{a}}$ (m^{2}.s^{−1}) | $2.77\times {10}^{-5}$ | In this work | ||

${\mathsf{\lambda}}_{\mathrm{c}}$ (W.m^{−1}.K^{−1} ) | 0.105 | |||

${\mathsf{\lambda}}_{\mathrm{a}}$ (W.m^{−1}.K^{−1} ) | $0.024$ | |||

${\mathrm{D}}_{\mathrm{a}}$ (m^{2}.s^{−1}) | $2.55\times {10}^{-5}$ | |||

${\mathrm{H}}_{0}$ (kg.kg^{−1}) | 0.2 | |||

$\mathrm{RH}$ (%⁄100) | $0.3$ |

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## Share and Cite

**MDPI and ACS Style**

Assoumani, N.; Simo-Tagne, M.; Kifani-Sahban, F.; Tagne Tagne, A.; El Marouani, M.; Obounou Akong, M.B.; Rogaume, Y.; Girods, P.; Zoulalian, A.
Numerical Study of Cylindrical Tropical Woods Pyrolysis Using Python Tool. *Sustainability* **2021**, *13*, 13892.
https://doi.org/10.3390/su132413892

**AMA Style**

Assoumani N, Simo-Tagne M, Kifani-Sahban F, Tagne Tagne A, El Marouani M, Obounou Akong MB, Rogaume Y, Girods P, Zoulalian A.
Numerical Study of Cylindrical Tropical Woods Pyrolysis Using Python Tool. *Sustainability*. 2021; 13(24):13892.
https://doi.org/10.3390/su132413892

**Chicago/Turabian Style**

Assoumani, Nidhoim, Merlin Simo-Tagne, Fatima Kifani-Sahban, Ablain Tagne Tagne, Maryam El Marouani, Marcel Brice Obounou Akong, Yann Rogaume, Pierre Girods, and André Zoulalian.
2021. "Numerical Study of Cylindrical Tropical Woods Pyrolysis Using Python Tool" *Sustainability* 13, no. 24: 13892.
https://doi.org/10.3390/su132413892