# Kinetic Analysis of Digestate Slow Pyrolysis with the Application of the Master-Plots Method and Independent Parallel Reactions Scheme

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### The Importance of Digestate Slow-Pyrolysis Process

## 2. Results

#### 2.1. TG-DTG Curves

_{2}, and carbonaceous residues at low temperature; and (2) integration of bonds at high temperature with the formation of liquid product containing a wide range of organic compounds. After 400 °C, the third stage of pyrolysis began where the slow decomposition of lignin causes the typical long tail of TG-curves. Biochar yield at 800 °C was in the range of 35.08%–36.45%, which was higher than the char yield of other lignocellulosic biomass, such as rice straw (23.68%) and rice bran (25.17%) at 700 °C [24], and camel grass (30.46%) at 550 °C [25], while it was comparable with the char yield of empty fruit bunch (35.14%) at 500 °C [26], reflecting that the lignin content of biomass plays a significant role in biochar formation.

#### 2.2. Determination of Activation Energy

^{1.92}). The plots used for the determination of activation energy at different conversion rates are shown in Figure 2. In particular in the linear plot of ln(β/T

^{1.92}) versus 1/T the slopes obtained at different conversion rates are equal to -1.0008E/R. Figure 3 presents the values of E and the standard deviation, calculated using the data retrieved from 3 repetitions of the same experiment. The average value of the Activation Energy is about 204.1 kJ/mol, with a standard deviation of 25 kJ/mol, which is about 12% of the average value. The variation range of the Activation Energy is about 99 kJ/mol, which is a high value. This means that the average E value cannot be used to statistically represent the activation energy variation.

^{2}) are shown in Figure 4. As recommended by the ICTAC Committee [28], since this work was performed with three heating rates, the number of degrees of freedom (calculated as n-2) is only 1, so “in statistical terms, such a plot can be accepted as linear with 95% confidence only when its respective correlation coefficient, R is more than 0.997 (equal to R

^{2}of 0.994)”. In our case (see Figure 3), the first two points have a correlation coefficient that is lower than that 0.994. This happened also in the publication of de Carvalho et al. [18] and denotes high uncertainty of the measure activation energies (at least for conversion of 0.05 and 0.1).

#### 2.3. Identification of the Reaction Model

#### 2.4. Independent Parallel Reactions Scheme

^{2}) between the experimental data and the multi peak fitting result is higher than 0.992 for each of the three considered heating rates.

^{10}and 2.2 × 10

^{19}min

^{−1}[30]. In particular the work of Conesa et al. [30] reports a value of 3.0 × 10

^{17}min

^{−1}, which is quite similar to the one obtained in this study. Dealing with the order of reaction usually a first order reaction is assumed by Antal and Varheghyi [31], and also confirmed in Reference [32].

^{−1}. Both values are in agreement with this study. The reaction order is also in agreement with Reference [32].

_{d}denotes the total number of experimental points; Np denotes the total number of unknown parameters (3 in this case); ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{e}}$ and ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{c}}$ denote the values of experimental and calculated x, respectively.

^{2}) between calculated and experimental data is about 0.990. These values are higher with respect to those shown in the paper of Wang et al. [29]. However, it has to be considered that, compared to the methods used in literature, the one used in this work performs two fitting stages: The first one during peaks deconvolution and the second one when each peak is fitted to a curve finding optimal values of activation energies, pre-exponential factor and reaction order for each pseudo-component. For this reason the method followed in this work is more easy and quick to implement, but probably less accurate. This can also be seen from the correspondence of the blue line shown in Figure 6 with the purple line, there is still space for improving the correlation coefficient and also improve peak deconvolution.

## 3. Materials and Methods

#### 3.1. Sample Preparation

^{3}/d), olive pomace (19 t/d), maize silage (19.6 t/d), sorghum silage (36.4 t/d), and onion scraps (1 t/d). The feedstock is mainly constituted by lignocellulosic biomasses. The set-up of the biogas plant consisted of two anaerobic digesters in parallel (operating at a temperature of 43–44 °C), followed by a post fermenter (operating at a temperature of 37 °C). The solid fraction was obtained by mechanical separation with a screw press separator fed with raw digestate. The sample has been air-dried for 24 h and then oven-dried in a muffle furnace at 105 °C for 8 h. The dried digestate has been ground using an ultracentrifugal mill (mod. ZM200, Retsch) and sieved to obtain a particle size lower than 500 μm. This was done in particular to ensure a heat transfer rate within the kinetic regime of decomposition. The chemical composition of the solid digestate is reported in Table 3.

#### 3.2. Experimental Setup

^{−1}. According to ICTAC recommendations [28], kinetic experiments should be performed using three to five different heating rates (less than 20 °C min

^{−1}); therefore, solid digestate was tested at three heating rates of 5, 10, and 20 °C min

^{−1}. Thermogravimetric (TG) and differential thermogravimetric (DTG) curves were obtained as a function of temperature during each test. Blank tests have been carried out without sample for TG baseline correction in order to avoid any buoyancy effects. All the thermal analyses were repeated for three times to decrease the test error, and the reproducibility was good. The standard deviation on the TG residues is always lower than 0.5 wt%. The experimental thermogravimetric analysis data have been treated, as recommended in Reference [34].

#### 3.3. Kinetic Analysis through Iso-Conversional Methods

_{t}is the mass of the sample at temperature T, m

_{f}is the final mass of the sample.

^{−1}) is the activation energy, A (s

^{−1}) is the pre-exponential coefficient and R (J mol

^{−1}K

^{−1}) is the universal gas constant. Then, under non-isothermal conditions at a constant heating rate, β = dT/dt, Equation (3) is transformed into Equation (6):

^{1.92}) vs. 1/T for the Starink method.

#### 3.3.1. Master-Plots Method

_{0.5}= E/RT

_{0.5}, T

_{0.5}is the temperature at α=0.5 and g(0.5) is the integral form of the reaction model at α = 0.5.

_{0.5}), master plots are plotted as a function of the conversion rate. In particular, for a single step decomposition process with a constant g(α) expression, the master-plots method allows to obtain the proper kinetic model with a high degree of certainty [37]. Table 4 shows the most common kinetic functions f(α) and their integral forms g(α).

#### 3.3.2. Independent Parallel Reactions Scheme

_{0}is the maximum position.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Thermogravimetric (

**a**) and Differential thermogravimetric (

**b**) curves generated during solid digestate pyrolysis at different heating rates.

**Figure 2.**Linear plots in the 0.05–0.95 conversion range for determining activation energy of solid digestate, calculated according to the Starink method.

**Figure 5.**Theoretical and experimental master plots functions from (

**a**) 0.2–0.5 and (

**b**) 0.5–0.8 of conversion.

**Figure 7.**Comparison between experimental DTG data and the combined kinetics of the three-parallel-reaction model (Heating Rate 5 °C/min).

Heating Rate (°C/min) | Temperature * | DTGmax * | ||
---|---|---|---|---|

Ti (°C) | Tf (°C) | Tm (°C) | ||

5 | 184 (1) | 377 (3) | 319 (1) | 2.9 (0.5) |

10 | 188 (1) | 382 (2) | 329 (1) | 4.5 (0.7) |

20 | 190 (1) | 392 (3) | 346 (2) | 9.5 (0.9) |

Pseudo-Component | Activation Energy | Pre-Exponential Factor | Reaction Order | |||
---|---|---|---|---|---|---|

Value | SD | Value | SD | Value | SD | |

Cellulose | 189 kJ/mol | 15 kJ/mol | 4.7 × 10^{17} min^{−1} | 1.5 × 10^{16} min^{−1} | 1.0 | 0.1 |

Hemicellulose | 151 kJ/mol | 21 kJ/mol | 4.4 × 10^{14} min^{−1} | 5.0 × 10^{12} min^{−1} | 1.1 | 0.2 |

Lignin | 64 k/mol | 7 kJ/mol | 6.3 × 10^{3} min^{−1} | 1.2 × 10^{3} min^{−1} | 1.6 | 1.1 |

**Table 3.**Characterization of the digestate sample [33].

Solid Digestate | |
---|---|

Proximate analysis (wt.%, dry basis) | |

Ash | 12.38 |

Volatile Matter | 67.07 |

Fixed Carbon | 20.55 |

VM/FC | 3.29 |

Ultimate analysis (wt.%, dry basis) | |

C | 42.52 |

H | 5.94 |

N | 1.79 |

O | 49.75 |

Compositional analysis (wt.%, dry basis) | |

Cellulose | 21.64 |

Hemicellulose | 15.08 |

Lignin | 40.88 |

Extractives | 10.02 |

Calorific value (MJ/kg, dry basis) | |

Higher Heating Value | 19.74 |

**Table 4.**Most frequently used mechanism functions and their integral forms [38].

Mechanism | Symbol | f (α) | g (α) * |
---|---|---|---|

Order of reaction | |||

First-order | F_{1} | 1 − α | −ln(1 − α) |

Second-order | F_{2} | (1 − α)^{2} | (1 − α)^{−1} − 1 |

Third-order | F_{3} | (1 − α)^{3} | [(1 − α)^{−2} − 1]/2 |

Diffusion | |||

One-way transport | D_{1} | 0.5α | α^{2} |

Two-way transport | D_{2} | [−ln(1 − α)]^{−1} | (1 − α)ln(1 − α) + α |

Three-way transport | D_{3} | 1.5(1 − α)^{2/3}[1 − (1 − α)^{1/3}]^{−1} | [1 − (1 − α)^{1/3}]^{2} |

Ginstling-Brounshtein equation | D_{4} | 1.5[(1 − α)^{–1/3}]^{−1} | (1 − 2α/3) − (1 − α)^{2/3} |

Limiting surface reaction between both phases | |||

One dimension | R_{1} | 1 | α |

Two dimensions | R_{2} | 2(1 − α)^{1/2} | 1 − (1 − α)^{1/2} |

Three dimensions | R_{3} | 3(1 − α)^{2/3} | 1 − (1 − α)^{1/3} |

Random nucleation and nuclei growth | |||

Two-dimensional | A_{2} | 2(1 − α)[−ln(1 − α)]^{1/2} | [−ln(1 − α)]^{1/2} |

Three-dimensional | A_{3} | 3(1 − x)[−ln(1 − x)]^{2/3} | [−ln(1 − x)]^{1/3} |

Exponential nucleation | |||

Power law, n =1/2 | P_{2} | 2α^{1/2} | α^{1/2} |

Power law, n = 1/3 | P_{3} | 3α^{2/3} | α^{1/3} |

Power law, n = 1/4 | P_{4} | 4α^{3/4} | α^{1/4} |

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**MDPI and ACS Style**

Bartocci, P.; Tschentscher, R.; Stensrød, R.E.; Barbanera, M.; Fantozzi, F.
Kinetic Analysis of Digestate Slow Pyrolysis with the Application of the Master-Plots Method and Independent Parallel Reactions Scheme. *Molecules* **2019**, *24*, 1657.
https://doi.org/10.3390/molecules24091657

**AMA Style**

Bartocci P, Tschentscher R, Stensrød RE, Barbanera M, Fantozzi F.
Kinetic Analysis of Digestate Slow Pyrolysis with the Application of the Master-Plots Method and Independent Parallel Reactions Scheme. *Molecules*. 2019; 24(9):1657.
https://doi.org/10.3390/molecules24091657

**Chicago/Turabian Style**

Bartocci, Pietro, Roman Tschentscher, Ruth Elisabeth Stensrød, Marco Barbanera, and Francesco Fantozzi.
2019. "Kinetic Analysis of Digestate Slow Pyrolysis with the Application of the Master-Plots Method and Independent Parallel Reactions Scheme" *Molecules* 24, no. 9: 1657.
https://doi.org/10.3390/molecules24091657