Expressions for the most common reaction mechanisms in solid-state reactions.

## Abstract

In this chapter, the kinetic behavior during the steam gasification of sawdust, plum, and olive pits was investigated by thermogravimetric analysis where the weight loss is measured with the temperature variation at different heating rates (5, 10, and 15 K/min). The weight loss and their derivative curves show that the gasification takes place in three visible stages. The kinetic study was carried out using Coats-Redfern methods. The Ginstling-Brounstein model showed better fit. The obtained activation energy values vary between 70 and 100 kJ/mol for the pyrolysis stage for all studied agro-industrial wastes. On the other hand, a thermodynamic model was proposed to predict the five waste gasification processes, considering the char and tar production. The proposed model allows it to perform a parametric study, analyzing the process variables’ effect on the exergetic efficiency. The higher temperatures favor the endothermic reactions as the H2 and CO formation reactions. Therefore, in the product, moles of H2 and CO increase and consequently the exergy efficiency of the process. Increasing the equivalence ratio value, H2, CO, and CH4 contents decrease; thus the calorific value of the produced gas and the exergetic efficiency decrease. In addition, the CO2 and H2O presences in the syngas composition diminish its calorific value and the exergetic efficiency. Considering the influence of supply steam/biomass ratio, the exergetic efficiency decreases with the growth of this parameter.

### Keywords

- gasification
- lignocellulosic wastes
- kinetic analysis
- thermodynamic analysis

## 1. Introduction

Energy demand has gradually become a critical factor for the international industrial sector. For this reason, technologies based on renewable-energy sources, such as biomass residues, have been developed and promoted. Biomass has the potential to become one of the main sources of energy worldwide; it is estimated that by 2050, its contribution to the global energy model could be between 100 and 400 EJ/year [1].

The biomass waste utilization, as a substitute for fossil biofuels, has the advantage to produce environmentally beneficial fuel, due to the energy production, and its sustainable use allows the emitted CO_{2} to be absorbed during the biomass growth. In short time periods, this cycle was fulfilled, which allows confirming that the energetic biomass uses under these conditions in neutral with respect to the CO_{2} emissions [2]. One of the main disadvantages for the biomass waste utilization is its low production per unit area, causing high costs related with the collection and the transport from the origin to the consumption place [3]. Due to this reason, the systems using biomass must have a high efficiency.

Recently, to develop the energy obtaining from waste biomass, several works have been carried out; particularly about pyrolysis and gasification because these thermal processes are effective and attractive methods [4, 5]. Considering the gasification, it converts biomass wastes into low heating value gas generally called syngas. This product is more suitably used to produce electricity through internal combustion engines or gas turbines [6].

Different operating variables have a high influence on the gasification behavior: biomass feedstocks, temperature (T), equivalence ratio (ER, supply air/stoichiometric air), and supply steam/biomass ratio (SBR) [7]. In order to evaluate the gasification performance, the exergy analysis can be employed (based on the second law of thermodynamic).

On the other hand, considering the kinetic behavior, the biomass waste gasification occurs in three stages: drying (evaporation of moisture contained in the solid), pyrolysis (thermal decomposition in the oxygen absence), and the last step associated with the reaction of the char by CO_{2} to produce CO. When the solid fuel is heated to temperatures between 473 and 648 K in the absence of an oxidant agent, it is pyrolyzed. The process products are a solid (char), condensable hydrocarbons (tar), and gases. Then, at higher temperatures, the condensable fraction and the gases form part of the volatile phase of the pyrolysis. The additional permanence of the solid and volatile phases in the reaction zone allows their conversion to a fraction of gases (gasification) [8].

The tar presence in the gas mixture is the main problem in the technological development of the gasification systems of biomass. The generated char during the pyrolysis stage can react with water vapor, CO_{2}, and oxygen. These reactions occur slower than that corresponding to the volatile phase; however, these contribute significantly to increase the amount and calorific value of the syngas.

Considering the gasification process description above, the involved reaction number, and their unknown mechanisms, simple kinetic models cannot describe the global reactions.

In this chapter, the kinetic characterization of different lignocellulosic waste gasification processes by thermogravimetric techniques using the Coats-Redfern method is presented [8]. The experimental data were fitted with several models, and each one was evaluated with different statistical parameters. Using the model with the best fit, the activation energy and pre-exponential factor were calculated, and their variation with the heating rate was evaluated [9]. On the other hand and in order to extend and improve the basic knowledge on composition and properties and to apply this knowledge for the most advanced and environmentally safe utilization, an exergy analysis of a gasification process is presented, taking into account different byproducts’ production.

## 2. Kinetic analysis

Coats and Redfern [8] method has been widely applied to study the thermal decomposition kinetics of biomass. The reaction kinetic equation is

where k(T) is the rate constant, dα/dt is the process rate, T is the absolute temperature, t is the time, f(α) represents function commonly used for description of biomass thermal decomposition, and α is the degree of transformation; α can be calculated from the corresponding TG curve by the following equation:

where m is the mass of the sample at a given time t and m_{0} and m_{f} refer to values at the initial and final mass of samples. For non-isothermal conditions, when the temperature varies with time with a constant heating rate defined by

According to Arrhenius expression:

where A is the pre-exponential factor, E is the activation energy, and R is the universal gas constant.

After a combination of Eqs. (1) and (4) and integrating, the following expression is obtained:

Eq. (5) can be integrated when the right hand side is expanded into an asymptotic series and higher order terms are ignored:

The term 2RT/E can be neglected since it is much less than unity for the thermal decomposition of lignocellulosic materials. Plotting the left hand side of Eq. (6), which includes g(α)/T^{2} versus T, for the proposed models (Table 1), gives the E and A parameters. The least squares nonlinear regression was used by means of the Marquardt [10] and Levenvrg [11] algorithm using MATLAB software.

Reaction model | g(α) |
---|---|

Reaction order | |

Zero order | α |

First order | −ln (1 − α ) |

Nth order | (n − 1) − 1 (1 − α)1 − n |

Diffusional | |

One-dimensional diffusion | α2 |

Two-dimensional diffusion | (1 − α) ln (1 − α) + α |

Three-dimensional diffusion (Jander) | [1 − (1 − α)1/3]2 |

Three-dimensional diffusion (Ginstling-Brounstein) | (1 − 2α/3)−(1 − α)2/3 |

Nucleation | |

Power law | αn n = 3/2, 1, ½, 1/3, 1/4 |

Exponential law | α |

Avrami-Erofeev | [−ln (1 − α)](1/n), n = 1, 2, 3, 4 |

Contracting geometry | |

Contracting area | (1 − α)(1/n), n = 2 |

Contracting volume | (1 − α)(1/n), n = 3 |

Table 1 lists several reaction models (g(α)) used in this work to describe biomass thermal decomposition.

## 3. Thermodynamic model

The proposed model in this work is derived from the thermodynamic equilibrium applying the following assumptions:

The gasifier is considered as a system in stationary state, with homogeneous temperature and pressure.

The C content in the biomass is converted in gases due to the gasification and combustion processes, and it can remain in the fly and bottom ash like char. The considered gaseous products are CO, H

_{2}, CO_{2}, CH_{4}, H_{2}O, and N_{2}. The quantities of other produced hydrocarbons are considered negligible. The tar production is considered in this model.The ash contents in the studied biomass are considered inert during all the process reactions.

All gaseous products behave as ideal gases. This assumption error is not significant for the gasifiers operating at low pressure and high temperature.

The S, Cl, and N contents in the biomass are negligible because they are very low compared with the C, H, and O contents.

The biomass is represented by the general formula CH_{a}O_{b} obtained from elemental analysis. The gasification process of the regional wastes can be characterized by the following global reaction:

where w is the water mol/biomass mol; m is the air mol/biomass mol; x_{1}, x_{2}, x_{3}, x_{4}, and x_{5} are unknown moles of exit gas composition; and x_{6} and x_{tar} are char and tar exit moles, respectively.

Zainal et al. [12] presented a representative tar composition; this composition was used in this work. w and m are determined as function of the steam/biomass ratio (SBR, kg/kg) and ER (oxygen/biomass ratio, kmol/kmol). So, w and m expressions are

where w_{w} is the mass faction of moisture content in the biomass and M_{bm} is reactant biomass quantity expressed as kmol of dry biomass/h:

Taking into account global reaction (a), the balances for C, H, and O are

Zainal et al. [12] considered the following reactions:

Water-gas-shift reaction:

Methane reaction:

In these reactions, the oxygen is not involved directly, and the steam is implicated in a limited form (water-gas-shift reaction). So, the gasifying agent’s effect on the equilibrium reactions is not important. The equilibrium constants as partial pressure function are

where p and p_{0} are the total and reference pressures, respectively. They are equal to 101.3 kPa. x_{total} is the mol quantity of produced gas, excluding the inert gas.

The variation of Gibbs free energy at a determined temperature was used in order to know the K_{wgs} and K_{methan} values, according to the following equations:

where

The necessary thermodynamic data were obtained of Reid, Prausnitz, and Polling [13]. The equilibrium constants as temperature function can be expressed by

### 3.1. Nonequilibrium factors

The assumed thermodynamic equilibrium for these reactions is not valid for real process due to the reactions that are not complete and the mass transfer resistance, too [14]. The equilibrium constant is modified to consider the nonequilibrium behavior:

where f_{wgs} and f_{methan} are the nonequilibrium factors of the water-gas displacement and methanation reactions, respectively. Lim and Lee [14] obtained the values of these factors analyzing the T, ER, and SBR influences on them, considering several biomasses. Thereby, two empirical equations of f_{wgs} and f_{methan} are obtained:

f_{wgs} is smaller than 0.5, and this reaction is close by to equilibrium. Since the CO production during the gasification decreases when ER increases, f_{wgs} augments with this parameter in order to promote the water-gas displacement reaction. However, ER significantly affects f_{methan} varying between 20 and 33 approximately [14].

### 3.2. C conversion fraction

C is partially converted into gas under substoichiometric conditions, and it is related with O concentration in the atmosphere and the gasification temperature. C conversion fraction (f_{c}) is defined as the ratio between the mol total number in the gas composition and the C concentration present in the biomass. The non-converted C will be [14]

The empirical parameters of these correlations were determined considering the experimental results obtained during the biomass gasification using air/steam mixture as gasifier agent [14].

### 3.3. Tar formation

Abuadala [15] defined the tar yield as a percentage by weight of the total gasification products:

The total weight of gasification products is obtained applying a global mass balance. The tar mass is obtained by

where M_{bm} and w_{w} are the fed biomass mass flow and moisture fraction of fed biomass (dry basis), respectively. The tar moles can be calculated by

where PM_{tar} is the tar molecular weight. In this case, the considered tar chemical formula is CH_{1.003}O_{0.33} proposed by Allesina et al. [16]. Considering Eqs. (5)–(7), (13)–(15), (17), and (21), the syngas composition can be obtained as operative variable function, T, ER, and SBR.

### 3.4. Process performance condition

The performance condition used in this work is the exergetic efficiency (η_{ex}). It is defined as the ratio between the profitable exergy outputs flow from the gasifier and the necessary exergy input flow to the gasifier [18]:

where

where

The exergy depends on the biomass composition (chemical exergy), temperature, and pression (physical exergy). The chemical exergy (

where xi and

where H and S are the enthalpy and entropy of a species when the gasifier operates at determined T and pression and H° and S° are the enthalpy and entropy when the reactor works under standard conditions (T° = 298 K and p° = 1 atm). The total exergy is

In order to carry out the analysis of the first and second thermodynamic laws, the entropy and enthalpy values are necessary. The specific heat capacity of tar (kJ/kgtar·K) from biomass gasification process is [20]

The tar enthalpy and the entropy are calculated with the following expression [21]:

where x_{i} and H°_{i} are the molar fraction and the standard formation enthalpy of i species, respectively. The tar entropy is

where

where C, H, N, O, and S are the weight fraction of carbon, hydrogen, nitrogen, oxygen, and sulfur present in the biomass, respectively. Usually, the gasifier losses at the environment are negligible comparing with the incoming and leaving energy of the gasifier. Several researchers consider that these losses are between 1 and 2% [22]. On the other hand, it is assumed that the char is pure carbon. Its specific heat capacity (kJ/kmol·K) is

The char chemical exergy is equal to 410 kJ/kmol, according to Moran and Shapiro [19]. Cengel [23] listed the values of standard enthalpy, entropy, and chemical exergy for the gaseous components. The biomass wastes are fed at environment temperature; its physical exergy is negligible. Ptasinski [24] calculated the biomass chemical exergy according to the expression present:

β factor is calculated by the following Eq. (24):

Similarly, the tar chemical exergy is calculated using the liquid combustible correlation [25]:

To evaluate the biomass high heating value (HHV,MJ/kg), the correlations presented by Sheng and Azevedo [26] were used, Eq. (1). The biomass low heating value (MJ/kg) is calculated with the following expression:

2 MJ/kg is the latent heat of water vaporization at 298 K. In order to calculate the tar HHV, the following correlation is applied [27]

According to Richard and Thunman [28], the tar mass fraction of C, H, and O fractions of the tar are 0.545, 0.065, and 0.39, respectively.

## 4. Kinetic model application to biomass gasification

### 4.1. Experimental weight loss

The experiments were carried out in a tubular reactor of 5 cm of internal diameter and 100 cm of height. It is heated by electrical resistance and is coupled to an analytical balance. This equipment is connected to a control system, through which it is possible to vary the heating rate and to register time, mass data, and temperature in a computer.

Experiments were carried out under air/steam atmosphere; the steam flow rate was 0.17 ml/min, guarantying the steam/biomass ratio equal to 2.5 [7, 17]. The temperature increased from ambient temperature (approximately 300 K) to 1173 K. This final temperature ensures the highest decomposition. Three heating rates, 5, 10, and 15 K/min, were used. In order to minimize heat transfer and mass phenomena, 5 g of sample with size between 0.212 and 0.250 mm was used. Figures 1–3 show these experiments.

### 4.2. Kinetic parameter determination

To determinate of kinetic parameters for the two stages, such as E and A, the weight loss curves have been used. Eq. (6) was applied to the experimental data, and a plot of g(α)/T^{2} versus T for each biomass was obtained. Figures 4–6 show the comparison of experimental data and the predicted values at different heating rates for the pyrolysis stage. The coefficient of correlation (R^{2}) for all cases is higher than 0.90, indicating a good fit.

The Ginstling-Brounstein model showed the better fit, and the obtained results are shown in Table 2.

Agro-industrial wastes | Heating rate | Temp range | Kinetics parameters | Statistical parameters | ||
---|---|---|---|---|---|---|

β (K/min) | (K) | E (KJ/mol) | A (s−1) | R2 | σ | |

Sawdust | 5 | 450 565 | 90.96 | 1.34 × 10^{7} | 0.90 | 7.31 × 10^{−8} |

10 | 450 560 | 98.62 | 1.91 × 10^{8} | 0.98 | 3.44 × 10^{−8} | |

15 | 442 561 | 99.80 | 5.10 × 10^{8} | 0.91 | 6.13 × 10^{−8} | |

Plum pits | 5 | 400 480 | 81.42 | 1.94 × 10^{7} | 0.97 | 4.27 × 10^{−8} |

10 | 503 620 | 90.66 | 3.92 × 10^{6} | 0.99 | 1.96 × 10^{−8} | |

15 | 555 644 | 99.88 | 6.26 × 10^{6} | 0.91 | 8.91 × 10^{−8} | |

Olive pits | 5 | 387 477 | 70.23 | 1.59 × 10^{6} | 0.91 | 7.09 × 10^{−8} |

10 | 476 679 | 80.45 | 1.22 × 10^{6} | 0.98 | 3.21 × 10^{−8} | |

15 | 488 578 | 87.46 | 1.07 × 10^{7} | 0.92 | 8.91 × 10^{−8} |

Figures 7–9 show the comparison of experimental data and the predicted values at different heating rates for the char combustion stage. The Ginstling-Brounstein model showed the better fit too, and the obtained results are shown in Table 3.

Agro-industrial wastes | Heating rate | Temp range | Kinetics parameters | Statistical parameters | ||
---|---|---|---|---|---|---|

β (K/min) | (K) | E (KJ/mol) | A (s−1) | R2 | σ | |

Sawdust | 5 | 670 1073 | 98.19 | 1.20 × 10^{2} | 0.97 | 2.85 × 10^{−9} |

10 | 670 1073 | 58.17 | 8.33 × 10^{0} | 0.99 | 4.32 × 10^{−9} | |

15 | 670 1073 | 40.11 | 1.03 × 10^{0} | 0.95 | 6.67 × 10^{−9} | |

Plum pits | 5 | 670 1073 | 60.25 | 1.00 × 10^{1} | 0.90 | 8.15 × 10^{−9} |

10 | 670 1073 | 41.50 | 1.03 × 10^{0} | 0.87 | 1.78 × 10^{−8} | |

15 | 670 1073 | 38.64 | 1.11 × 10^{0} | 0.92 | 1.49 × 10^{−8} | |

Olive pits | 5 | 670 1073 | 46.40 | 1.01 × 10^{0} | 0.98 | 6.44 × 10^{−9} |

10 | 670 1073 | 24.10 | 1.01 × 10^{0} | 0.89 | 1.49 × 10^{−8} | |

15 | 488 578 | 49.34 | 3.50 × 10^{0} | 0.98 | 6.01 × 10^{−9} |

This model describes the biomass waste gasification characteristics, and it assumes that the process rate is limited by the diffusion of the reaction products from the surface, the reaction surface decreases during the process, and it can be assumed that the solid phase has the form of ball-shaped grains [29].

The obtained activation energy values vary between 70 and 100 kJ/mol and 24–98 kJ/mol for the pyrolysis and char gasification stages, respectively, for all studied agro-industrial wastes. The highest value of the energy activation was predicted for plum pits at heating rate of 15 K/min for pyrolysis stage. Also, the highest value for the same parameter was predicted for sawdust at 5 K/min for char combustion stage. The calculated values of E vary slightly with the heating rate for each biomass and indicate the existence of a complex multistep mechanism that occurs in the solid state. The increasing of heating rate leads to a simultaneous increase of the heat effect. So, the maximum decomposition rate tends to increase at higher heating rates because it provides a greater thermal energy facilitating the heat transfer around and within the samples [30, 31]. The smallest value of this parameter was calculated for olive pit at 5 K/min. The found activation energy values are similar to obtained values by other authors [30, 32].

On the other hand, the pre-exponential factor value was obtained for each agro-industrial waste at the different heating rates. This parameter varies too with the heating rate; however, it is important to consider that it was obtained from a model-based method and it is tainted by association with the reaction model that must be assumed to permit its calculation.

## 5. Exergetic analysis to biomass gasification

The syngas composition and exergetic efficiency of the gasification process were studied with the lignocellulosic waste composition, gasifier temperature, and *ER* and *SBR* variation. *ER* was varied from 0.15 to 0.3, SBR from 0 (gasification with air only) to 3, and gasifier temperature in the range of 650–950°C. The moisture content of wastes was set at about 6% by weight.

### 5.1. Influence of gasifier temperature

In order to analyze the syngas composition and exergetic efficiency with the gasifier temperature variation, SBR value was set at 2, and the ER value was 0.25. Figure 10 shows that the exergetic efficiency increases when the gasifier temperature augments. This is consistent with Zhang results [33]; he informed that higher efficiencies can be achieved by increasing the gasification temperature. In the studied temperature range, the highest value to this parameter was calculated for olive pits (64% at a temperature equal to 950°C), and the lowest value was predicted for the sawdust (41% at a temperature equal to 650°C). The lower temperatures favor the exothermic reactions of CH_{4} and CO_{2} formations. The higher temperatures favor the endothermic reactions as the H_{2} and CO formation reactions. Therefore, in the product, moles of H_{2} and CO increase and consequently the exergy efficiency of the process. Therefore, the molar fraction of these gases in the syngas increases the process' exergy efficiency.

### 5.2. Influence of ER

To study the *ER* influence on the gasification efficiency and syngas composition, the gasifier temperature was set at 850°C and *SBR* at 1.5. Figure 11 shows that the exergetic efficiency diminishes with the increase of *ER*. It is because the O_{2} content in the gasifying agent promotes the combustion reactions. During the gasification process, these reactions are not desirable because they compete with the reactions to transform the biomass in syngas rich in H_{2} and CO contents. Increasing the *ER* value, H_{2}, CO, and CH_{4} contents decrease; thus the calorific value of the produced gas and the exergetic efficiency decrease. In addition, the CO_{2} and H_{2}O presences in the syngas composition diminish its calorific value and the exergetic efficiency. For the Olive pits, when *ER* increases, the H_{2} and CO contents in syngas decrease about 20% and 15%, respectively.

### 5.3. Influence of SBR

Considering the influence of *SBR* in the gasification efficiency and syngas composition, this parameter was varied when *ER* value was equal to 0.25 and the gasifier temperature equal to 850°C. Figure 12 shows the exergetic efficiency decrease with the growth of *SBR*. The lowest value of this parameter corresponds to *SBR* = 1.5; then the exergetic efficiency value increases softly. The decrease is due to the physical exergy of the steam used as the gasifying agent. This decrease is produced because it is necessary to supply energy to the water to transform it in steam. Then, it is partially offset by the increase of H_{2} content in the produced syngas.

Comparing the gasification process of olive pits (*SBR = 0*) using air as gasifying agent and an steam–air mixture (*SBR = 1*), the CO content into the produced syngas decreases 38% approximately when the mixture is used; however, the H_{2} content increases around 31%.

For the Olive pits, exergetic efficiencies equal to 60.13% and 60.11% were obtained for air and steam/air (SBR = 3) gasification, respectively, considering that the variation is not very noticeable. Physical exergy is related to the syngas sensible heat, and this is lost when the gas cools and it influences the exergetic efficiency value. Increasing the SBR value, the water content in the produced gas flow increases, and also it contributes to the physical exergy. The exergy content of syngas is the sum of physical and chemistry exergies. The physical exergy of biomass steam gasification is higher than the exergy of air gasification due to the higher temperature of the steam, resulting in the exergetic efficiency of air gasification higher to the efficiency of steam gasification.

## 6. Conclusions

Two main stages defined the thermal process, named pyrolysis and gasification.

When heating rate increases, the TG curves are shifted to the right, to the higher temperature region, and the peak height of the DTG curves increases. This shifting occurs because sample solid requires more reacting time at high heating rates.

To describe the kinetic behavior during the pyrolysis stage, different models were selected. The three-dimensional diffusion (Ginstling-Brounstein) model showed the best fitting for all experiments, assuming that the diffusion is the controlling step of the reaction rate. The kinetic parameters were calculated using this model.

The variation of E values with the heating rate indicates the existence of a complex multistep mechanism that occurs in the solid state.

The results of the proposed model suggest to work at high temperatures using an air-vapor mixture as gasifying agent. While the vapor increases the H

_{2}content in the produced syngas, the exergetic efficiency decreases due to the necessary energy to convert water into steam.