Determination of Combustion Kinetic Data of Some Agricultural Wastes from the Galicia-Northern Portugal Euroregion

Abstract

This work concerns the study of the combustion kinetic characteristics of chars made from three different biomass species, vine and kiwi pruning wastes, and gorse from forest cleaning process in a fluidized bed combustor, operating in the bubbling bed regime, at four bed temperatures, 750, 820, 850 and 920 °C. Batches of the original biomass pellets were carbonized in a nitrogen fluidized bed, either at 900 °C, for the kiwi and vine pellets, or at 800 °C for the gorse pellets. To acquire complete information on the combustion behaviour, different sizes of the char particles were subsequently burned in a bubbling fluidized bed. The evolution of the overall combustion resistance, and information on the combustion control were obtained. It was observed that for the kiwi and vine chars, the combustion was controlled through a combination of diffusion and kinetics, while for the gorse char the combustion was diffusionally controlled. In addition, the pre-exponential factors and activation energies were obtained for the kiwi and vine chars, by applying the Arrhenius law to the kinetic data for each char. Activation energy values of 246.16 kJ/mol for the kiwi char and of 155.02 kJ/mol for the vine char were obtained.

Graphic Abstract

Statement of Novelty

The present study is about the determination of kinetic and diffusive data from the bubbling fluidized bed combustion of chars made from pellets fabricated with pruning wastes of vine (Vitis vinífera) and kiwi (Actinidia deliciosa) plants, and gorse (Ulex europaeus) forestry residues. These biomass wastes were collected in the Galicia-Northern Portugal Euroregion. In this Euroregion there is a huge energy potential in agricultural and forestry wastes to be exploited and this work is a part of a wider study to evaluate such potential. It is an extension of a previous work presented at ICEER2019 [1], expanding the range of information in the study. Now it takes into account the importance of the combustion of the volatiles of the biochars on the total carbon balance, as well as the non-sphericity of the fuel particles, parameters discarded in the first study. The first paper had also no information on the combustion of gorse char particles. This new detailed information of the combustion data related to the above-mentioned biochars, leads to a more reliable set of results.

Introduction

The biomass was always one of the greatest sources of primary energy of the different human societies [2] and its importance is rising again because of the pollution issues and subsequent climatic changes, as it is considered almost a carbon dioxide neutral renewable energy source [3]. Its properties are greatly dependent upon the fuel being used and the required pre-processing [4], such as the pelletization, which is one of such pre-processing steps that is typically adopted for the energy densification of biomass [5].

The agricultural and forestry residues have being considered as an accessible and affordable source of biomass energy [6]. There is however a lack of information concerning the combustion kinetic data of many agricultural and forestry residues especially in the Galicia-Northern Portugal Euroregion, where waste values of 2 to 5 t/ha/year are common. In the present study on the fluidized bed combustion of chars made from pruning wastes of vine (Vitis vinífera) and kiwi (Actinidia deliciosa) plants and gorse (Ulex europaeus) forestry residues, diffusive and kinetic data were determined. These data are fundamental for the design, construction and adequate operation of industrial burning equipment.

The bubbling fluidized bed reactor is a good tool to determine diffusive and kinetic data for the combustion of different biomasses. It allows high heat and mass transfer rates, guarantees good temperature uniformity in the reacting region and it is indicated for the combustion of high ash content solid fuels [7, 8]. The woody biomass from Portuguese origin has been the subject of several studies. Fluidized bed combustion results of commercial and recarbonized chars of nut pine (Pinus pinea) and cork oak (Quercus suber) were discussed [9, 10], as well as the influence of the fragmentation phenomenon upon the determination of kinetic and diffusive data on the fluidized bed combustion of nut pine chars [11]. Tomé et al. [12] studied the fluidized bed combustion of chars made from biomass of Mozambican origin. This type of study was extended to Brazilian biomass, where biochars from eight species of wood obtained from the semiarid region of the Brazilian northeast known as the Cariri Paraibano, were also analyzed [13]. Following the same procedure, biochars obtained from woody biomasses from the central region of Portugal, holm oak (Quercus ilex), eucalyptus (Eucalyptus globulus), maritime pine (Pinus pinaster), and cork oak (Quercus suber), were also studied [14], and the importance of particle sphericity and fragmentation on the behavior of these four chars was discussed [15].

More recently, interest turned to the study of combustion of pellets made from invasive shrubs and trees, which although being considered harmful vegetable species, should in fact be considered valuable biomass energy resources [16,17,18,19]. The influence of mineral ash components in the char ashes upon the kinetic behavior during combustion was also an object of study [20, 21]. The interest of using crop and forest residues as energy sources, although going back several years, has only been more recently the target of much more scientifically orientated studies [22], although the ash-related issues have always been a subject of deep concern during biomass combustion [23].

The tested chars in the present study were made from pellets fabricated with the three mentioned biomasses. The pellets were carbonized at 900 °C (kiwi and vine) and 800 °C (gorse), in a bed fluidized by nitrogen. During solid biomass combustion, after the initial particle heating and drying phase there is the subsequent combustion of the released volatile matter, with formation of a carbonaceous solid core. The combustion of this core is the last and longer step of the solid biomass combustion process [4]. As solid fuels can be burned at temperatures up to 1000 °C, depending on the type of burner used [23], this explains the choice of the above carbonization temperatures for the production of the biochars to be tested. The objective of the experiments was thus to find out the mechanisms controlling the combustion process of such chars to optimize the operating conditions of the industrial burning equipment when using this type of agricultural waste.

Materials and Methods

The kiwi and vine biomasses from agricultural plant pruning and the gorse from forest cleaning processes, were collected in the Galicia-Northern Portugal Euroregion. Subsequently pellets were fabricated at the Viseu Polytechnic Institute in Portugal and were then carbonized at INEGI in a bubbling fluidized bed reactor. The pellets were placed inside a stainless steel mesh bag and immersed in the bed fluidized by nitrogen, to prepare the char particles. After the carbonization step, the stainless steel bag was extracted from the fluidized bed and cooled in nitrogen. Subsequently, the char particles were manually separated into five different sizes. Table 1 shows the results of the biochars proximate analysis, as well as the corresponding densities obtained through the mercury pycnometry technique.

Table 1 Proximate analysis of kiwi, vine and gorse chars

The laboratory scale fluidized bubbling bed that was initially used as a carbonizing and subsequently as a combustion reactor, was built with a refractory steel tube with an internal diameter of 80 mm and 1500 mm length. The bed was formed by silica sand particles with an average diameter of 283 μm and 200 mm height., supported by a stainless steel distributor containing 101 orifices with 0.3 mm diameter. In Fig. 1 there is an overall scheme of the experimental setup.

Fig. 1

Scheme of the experimental setup

The bed is externally heated by an electrical resistance of 4 kW, controlled by a PID controller. Two K type thermocouples (ST1 and ST2) measure the bed temperature. The ST1 is connected to the PID controller of the bed heating electrical resistance, while the readings from ST2 are sent to a data acquisition board PD2, installed in a desktop computer. A stainless steel suction probe, located above the bed free surface, collects samples of exhaust combustion gases.

The sampled flow of combustion gases is sent to a condenser and then to a volumetric sampling pump, and afterwards the cooled dry gas flow is directed to a CO₂ gas analyzer. The infrared CO₂ analyzer (Signal, model 7000FM GFC) is connected to a data acquisition system from Measurement Computing. This data acquisition system is composed by two independent boards, PCI-DAS-TC (PD2) and PCI-DAS16JR/16 (PD1), receiving signals from the thermocouples and the gas analyzer, respectively. The registration of the collected data was managed by the DasyLab software and data treatment was carried out by means of the Spyder software, a Python scientific environment [24].

For each experimental test, the char particles were selected and classified according to their sizes. The extremities of the char particles were cut to give them a cylindrical morphology, with diameters ranging from 5 to 6 mm, for kiwi and vine char particles, and from 4 to 5 mm for the gorse char particles. The corresponding lengths allowed the definition of several classes of particle classification, as specified in Table 2, five for kiwi and vine chars and four for gorse chars.

Table 2 Size classes of char particles

The combustion tests were carried out for each size class characterized by the corresponding length to diameter ratio (L/D) using 2 g batches measured in a Sartorius MA 30 balance. The mass and number of particles of each test batch were registered for further analysis.

Figure 2 shows the sequence procedure of the experiments: the particle sanding and storage, the batch preparation and finally the beginning of a combustion experiment with the introduction of the char particles in the bubbling fluidized bed reactor.

Fig. 2

a Particle sanding process; b particle storage; c batch weighing and d batch introduction in the bubbling bed

The combustion experiments were carried out at bed temperatures of 750, 820, 850 and 900 °C. To follow up the development of the batch combustion process the CO₂ molar concentration in the flow of exhaust gases was continuously measured and registered, as well as the bed temperature, both at a rate of 1 Hz. A detailed analysis was performed with 49 experiments using a superficial velocity ratio of U/U_mf = 2, for all tests. The U_mf values were experimentally determined: 44.0 mm/s at 750 °C; 42.1 mm/s at 820 °C; 41.4 mm/s at 850 °C; and 40.2 mm/s at 900 °C. This velocity ratio was enough for the purpose of the studies and had the advantage of minimizing the elutriation of small particles resulting from the attrition and fragmentation of the fuel particles. With this fluidizing velocity, the carbon losses from the bed was minimized, improving the overall carbon balance required for the calculation of the time evolution of fuel particle dimensions along the combustion process. Table 3 shows the mass and the particle number for each tested batch, as well as the corresponding bed temperature.

Table 3 Characterization of the tested biochar batches

The average uncertainties of the experiments were of 0.179% (v/v) for the CO₂ measurement, 0.76% for the fluidized bed temperature and in the range of 8.6 to 16.6% for the mass flow rate of the fluidization air. These values include the whole measurement chain, i.e., up to the computer output.

Results and Discussion

Evolution of the CO₂ in the Exhaust Gas Flow

Figure 3 presents typical evolutions of the molar concentration of CO₂ in the exhaust gas flow for combustion experiments with kiwi char. The curve trends are quite similar for all tested bed temperatures. In the first instants, after the introduction of the batch of char particles, there is a peak on the CO₂ release rate followed by a continuous concentration declining. Initially, in this declining region, the reduction of concentration is quite smooth, followed by a stronger concentration reduction, being this reduction stronger for lower L/D ratios.

Fig. 3

CO₂ time evolution in the exhaust combustion gases for kiwi char particles

Riaza et al. [25] analyzed images of the combustion of individual particles and registered that the first step of the combustion process is the particle heating with consequent drying and release of volatiles, and only after this initial step the combustion of the solid residues takes place. Van Loo and Koppejan [4] and Wang et al. [26], from the study of thermogravimetric (TG) curves and differential thermogravimetric (DTG) curves confirm that the combustion of solid residue only takes place after volatiles release. Volatiles are mainly composed by light hydrocarbons, carbon monoxide and dioxide. Neves et al. [27] analyzed the volatile gas composition during the fluidized bed pyrolysis of two ligneous biomasses and realized that the majority of the volatiles were released around 600 °C, although some components like ethylene, C₂H₄, methane, CH₄, and carbon monoxide, CO, reach their peak about 900 °C. In the preparation of the chars used in the present study the wood pellets pyrolysis was done at 900 °C, while the gorse was carbonized at 800 °C, and for calculation purposes it is assumed that the volatiles that might be released in their combustion is propane, C₃H₈. Not knowing the composition of the remaining volatiles that are being released during the combustion of the char particles, it is necessary a careful approach in order to carry out an adequate carbon balance. Hesketh and Davidson [28] and Ribeiro and Pinho [29] used propane to simulate the volatiles released from burning coke particles. Following such approach, in this work the volatiles released during the biochar particles combustion were assumed as propane. With this methodology, the carbon balance of the combustion process, obtained through the time integration of the CO₂ concentration in the exhaust gases, is accomplished, and a carbon recuperation close to 100% is achieved. It should be emphasized that kiwi, grapevine and gorse chars contain 14.0% (m/m), 16.6% (m/m) and 4.3% (m/m) of volatiles, respectively, as can be observed in Table 1.

In this situation, the mass fraction of carbon ${f}_{c}$, in a given sample of biochar to be burned, is the summation of the fixed carbon and the carbon in the volatiles

$$\mathop f\nolimits_{c} = \mathop f\nolimits_{cf} + \mathop f\nolimits_{cv}$$

(1)

where ${f}_{cf}$ is the mass fraction of the fixed carbon and ${f}_{cv}$ is the carbon mass fraction in the volatiles determined by means of

$$\mathop f\nolimits_{cv} = \frac{{\mathop 3\nolimits_{{}} \mathop M\nolimits_{C} }}{{\mathop M\nolimits_{C3H8} }}\mathop f\nolimits_{v}$$

(2)

In Eq. 2M_C and M_C3H8 are respectively the molecular masses of carbon and propane and f_v is the volatiles mass fraction in the char particles. From the calculation the following values are determined, f_cv = 11.45% and f_c = 83.20%.

Figure 4 shows the CO₂ released evolution during an experiment for kiwi char particles with a L/D ratio of 1 and a bed temperature of 750 °C, and as can be observed it is possible to identify two stages: the first stage (red line) represents the time evolution of the CO₂ formed during the propane (volatiles) combustion, as the release of volatiles occurs at the beginning of the combustion process, of a given batch of coal particles; and the second stage (blue line) which refers to the CO₂ released through the combustion of the carbonaceous solid residue. As observed the initial CO₂ release peak stays inside the initial red zone (Fig. 4).

Fig. 4

CO₂ time evolution in the exhaust combustion gases for kiwi char particles L/D = 1 and a bed temperature of 750 °C

During the second stage, the combustion of the solid carbonaceous residue, the smaller the particles, the faster is the combustion reaction because of the higher surface area available for the heterogeneous phase reaction of carbon oxidation to carbon monoxide. There is so a higher reaction rate as detected by the stronger slope in the curves shown in Fig. 3. At the end of the solid residue combustion, the reaction rate increases due to the particle fragmentation [11, 15, 30], which increases the superficial reaction area, leading to a stronger decaying of the CO₂ curve. It is also clear that the higher the bed temperature the stronger is the CO₂ decay meaning that the value of the kinetic and diffusive resistances are becoming smaller (Figs. 3, 5 and 6).

Fig. 5

CO₂ time evolution in the exhaust combustion gases for vine char particles

Fig. 6

CO₂ time evolution in the exhaust combustion gases for gorse char particles

The combustion behavior of the vine char is similar to the kiwi char. Figure 7 shows equally time evolutions of the CO₂ concentration in the combustion exhaust gases for different L/D ratios and four bed temperatures, namely 750, 820, 850 and 900 °C. The same initial peak of the CO₂ curve, and again the same CO₂ evolution corresponding to the combustion of the carbonaceous solid residue. For the same assumption of considering that propane is representative of the released volatiles, the following results are obtained for vine char particles, f_cv = 13.60% and f_c = 85.00%.

The gorse char has a lower volatiles percentage, 4.3% (w/w), leading to a different time evolution of CO₂ in the first stage and, as expected, the peak magnitude decreases when compared to the others biochars previously presented, Fig. 6. However, concerning to the combustion of the solid carbonaceous residue, its behavior is similar to the previously biochars, the kiwi and the vine char. The carbon content in the volatiles and in the carbonaceous residues are respectively f_cv = 3.5% and f_c = 88.3%.

Overall Resistance to Combustion

From the integration of the CO₂ versus time curve, and knowing the number of particles composing a batch under combustion, it is possible to determine for each time instant the burned mass fraction of carbon, the particle size and the instantaneous reaction rate and finally the time evolution of the overall resistance to combustion [9,10,11]. To determine the carbon burned m_cf up to a given time instant, the CO₂ versus time curve is integrated according to Eq. 3 of the trapezium rule,

$$\mathop {m^{i} }\nolimits_{cf} = \mathop M\nolimits_{C} \mathop {\dot{V}}\nolimits_{air} \mathop {\tilde{n}}\nolimits_{{}} \frac{{\mathop {x^{i} }\nolimits_{CO2} + \mathop {x^{i - 1} }\nolimits_{CO2} }}{{\mathop 2\nolimits_{{}} }}\left( {\mathop {t^{i} }\nolimits_{{}} - \mathop {t^{i - 1} }\nolimits_{{}} } \right) + \mathop {m^{i - 1} }\nolimits_{cf}$$

(3)

where i represents the present time instant while i-1 represents the former time instant, ñ is the generic molecular concentration in the exhaust gas flow, t is a generic time instant and $\mathop {\dot{V}}\nolimits_{air}$ is the volume flow rate of air, assumed equal to the flow rate of the combustion products.

The evolution of the overall combustion resistance, as a function of the mean diameter of the particles, is calculated using mathematical models developed for the fluidized bed combustion of char particles, assuming that they are spherical. However, this hypothesis normally does not occur and accordingly the combustion data must be analyzed taking the particle non-sphericity into account. In the present study cylindrical particles with different length to diameter ratios L/D, were considered. The sphericity of the particles must then be taken into consideration, in order to reach a better characterization of the volume and surface area of the particles composing a given batch of char particles.

The corrected spherical diameter of the particle is the product of the diameter of a sphere with the same volume as the particle $\mathop d\nolimits_{s}$ with the particle sphericity [15],

$$\mathop d\nolimits_{{}} = \mathop \phi \nolimits_{p} \mathop d\nolimits_{s}$$

(4)

being ${\phi }_{p}$, the particle sphericity, given by,

$$\mathop \phi \nolimits_{p} = \frac{{\mathop A\nolimits_{s} }}{{\mathop A\nolimits_{p} }}$$

(5)

and taking into account the real L/D ratio of the particle,

$$\mathop \phi \nolimits_{p} = \left( {\frac{{\mathop 3\nolimits_{{}} }}{{\mathop 2\nolimits_{{}} }}} \right)\frac{{\left( {{{\mathop L\nolimits_{{}} } \mathord{\left/ {\vphantom {{\mathop L\nolimits_{{}} } {\mathop D\nolimits_{{}} }}} \right. \kern-\nulldelimiterspace} {\mathop D\nolimits_{{}} }}} \right)^{{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}}} }}{{\left( {{{\mathop L\nolimits_{{}} } \mathord{\left/ {\vphantom {{\mathop L\nolimits_{{}} } {\mathop D\nolimits_{{}} }}} \right. \kern-\nulldelimiterspace} {\mathop D\nolimits_{{}} }}} \right) + \mathop 1\nolimits_{{}} }}$$

(6)

In Table 4 are the corresponding sphericities for all the particles tested.

Table 4 Sphericities of the char particles as a function of the corresponding L/D ratios

This type of approach has already been used in several experimental studies [15, 31]. The correct use of the particle sphericity leads to a precise understanding of the combustion control mechanisms. Figure 9 presents the overall combustion resistance as a function of the particle diameter for combustion experiments of vine char at 850 °C, with and without the sphericity correction. If, for a given situation, the influence of the particle non-sphericity is not accounted for, a wrong interpretation of the results might occur. In Fig. 7, it is possible to observe the influence of the L/D ratio on the control of the combustion process. The left side plots, Fig. 7a and c, were obtained by non-applying the sphericity correction leading to the erroneous idea of a purely kinetically controlled combustion process. The right side plots, Fig. 7b and d, were obtained using the non-sphericity correction, leading to a correct interpretation of the relative influence of diffusion and kinetics upon the combustion control.

Fig. 7

Influence of the sphericity correction on the evaluation of the overall combustion resistance

Kinetic and Diffusive Results

To determine the kinetic and diffusive information from the evolution of the overall combustion resistance, the transient initial and final regions of this evolution were discarded and only data in the 30 to 70% burned mass fraction were considered. Accordingly, the next plots, Figs. 8, 9 and 10 show the 1/K versus corrected d for the kiwi, vine and gorse char pellets respectively. Only 10% of the experimental points are presented in the plots, to keep them readable. However, the calculations were carried out with all the available experimental points.

Fig. 8

Straight-line fitting for the kiwi char overall combustion resistance

Fig. 9

Straight-line fitting for the vine char overall combustion resistance

Fig. 10

Straight-line fitting for the gorse char overall combustion resistance

In the batch combustion experiments carried out in the fluidized bed, the solid particles are assumed spherical and burn at a constant density, nm and reducing size. It was also considered that the particle carbon burns to CO according to C + ½ O₂ → CO and the CO formed burns away from the particle according to CO + ½ O₂ → CO₂ [32], which is a further evolution from the initial model established by Avedesian and Davidson [33]. Thus, the oxygen consumption rate at the surface of the particle is then half the carbon consumption rate and the heterogeneous phase reaction that takes place at the particle surface is a first order reaction,

$$\mathop {\dot{N}}\nolimits_{{O_{2} }} = \frac{{\mathop 1\nolimits_{{}} }}{{\mathop 2\nolimits_{{}} }}\mathop R\nolimits_{0} = \mathop \pi \nolimits_{{}} \mathop d\nolimits_{{}} \mathop {Sh}\nolimits_{{}} \mathop D\nolimits_{G} \left( {\mathop C\nolimits_{p} - \mathop C\nolimits_{s} } \right) = \frac{{\mathop 1\nolimits_{{}} }}{{\mathop 2\nolimits_{{}} }}\mathop k\nolimits_{c} \mathop \pi \nolimits_{{}} \mathop d\nolimits_{{}}^{2} \mathop C\nolimits_{s}$$

(7)

where ${\dot{N}}_{{O}_{2}}$ is the molar oxygen flow rate reaching the particle surface, ${R}_{0}$ is the carbon molar consumption rate, Sh is the particle Sherwood number, d is the diameter of the burning particle, ${D}_{G}$ is the oxygen diffusivity in the air, ${C}_{p}$ and ${C}_{s}$ are respectively the molar concentrations of oxygen in the particulate phase of the bed and at the surface of the burning particle. ${k}_{c}$ is the reaction rate constant for the heterogeneous phase reaction occurring at the surface of the char particle. Manipulating the above equation, it is possible to write that,

$$\mathop R\nolimits_{0} = \mathop 2\nolimits_{{}} \mathop \pi \nolimits_{{}} \mathop K\nolimits_{{}} \mathop d\nolimits_{{}}^{2} \mathop C\nolimits_{p}$$

(8)

wherein, 1/K is the overall combustion resistance [10, 11] for the combustion of batches of carbon particles in a bubbling fluidized bed combustor. As can be seen from Eq. 9, after a mathematical manipulation of the Eq. (8) [10, 11], the first term of the second member is the particle external diffusion resistance, while the second term concerns the heterogeneous phase carbon-to-carbon monoxide reaction resistance.

$$\frac{{\mathop 1\nolimits_{{}} }}{{\mathop K\nolimits_{{}} }} = \frac{{\mathop d\nolimits_{{}} }}{{\mathop {Sh}\nolimits_{{}} \mathop D\nolimits_{G} }} + \frac{{\mathop 2\nolimits_{{}} }}{{\mathop k\nolimits_{c} }}$$

(9)

It is understandable that from the slope of the 1/K versus d diffusive information can be gathered through the Sherwood number, while from the intercept the heterogeneous reaction rate constant k_c is determined. Table 5 presents the determined kinetic and diffusive data.

Table 5 Kinetic and diffusive results for the three tested chars

From the analysis of the results available in Table 5, it can be concluded that the reaction control is shared by the diffusion and the heterogeneous phase reaction kinetics, for the kiwi and vine chars, while for the gorse char above 850 °C the combustion control is purely diffusive. The values of the Sherwood number are similar to those found in other studies of the same group covering Brazilian, Mozambican and Portuguese biochars [10, 12,13,14].

To get adequate information from the kinetic data it must be taken into account that

$$\mathop k\nolimits_{c} = A\,\exp \,\left( {{{ - \mathop E\nolimits_{a} } \mathord{\left/ {\vphantom {{ - \mathop E\nolimits_{a} } {\left( {\overline{R} T_{p} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\overline{R} T_{p} } \right)}}} \right)$$

(10)

where $\stackrel{-}{R}$ is the universal gas constant and T_p the particle temperature, A the pre-exponential factor and E_a the activation energy. From a logarithmic plot of ln k_c versus 1/T_p,

$$\mathop {\ln }\nolimits_{{}} \mathop k\nolimits_{c} = \mathop {\mathop {\ln }\nolimits_{{}} A}\nolimits_{{}} {{ - \mathop E\nolimits_{a} } \mathord{\left/ {\vphantom {{ - \mathop E\nolimits_{a} } {\left( {\mathop {\overline{R}}\nolimits_{{}} \mathop T\nolimits_{p} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\mathop {\overline{R}}\nolimits_{{}} \mathop T\nolimits_{p} } \right)}}$$

(11)

a linear trend line can be theoretically obtained and, from its slope and interception, information on the activation energy and on the pre-exponential factor is obtained. However, to get the right information from the kinetic results it is necessary to know the burning particle temperature, which is normally above the fluidized bed temperature. However, the measurement of the wandering particles temperature is impossible. The option adopted in this work, as in many other previous works of the group [13, 14, 34], is to carry out an energy balance of the particle and from it obtain the corresponding particle temperature. The scheme of the energy balance of a carbonaceous particle is in Fig. 11.

Fig. 11

Energy balance at the surface of the burning particle [34]

Figure 11 shows the energy transfer, taking place at the surface of a burning carbon particle. Assuming that for short time intervals there is no heat transferred towards the particle interior, and taking into account that the process can be considered a steady state one, the energy balance is simplified to:

$$\mathop {\dot{m}}\nolimits_{C} \mathop h\nolimits_{C} + \mathop {\dot{m}}\nolimits_{O2} \mathop h\nolimits_{O2} - \mathop {\dot{m}}\nolimits_{CO} \mathop h\nolimits_{CO} = \mathop {\dot{m}}\nolimits_{c} \mathop {\Delta h^{^{\prime}} }\nolimits_{{}}$$

(12)

where, $\dot{{m}_{\text{C}}}{h}_{\text{C}}$ is the energy of the carbon; $\dot{{m}_{{\text{O}}_{2}}}{h}_{{\text{O}}_{2}}$ is the energy of the oxygen flow; $\dot{m}_{CO} h_{CO}$ is the energy of the carbon monoxide flow and $\Delta {h}^{^{\prime}}$ is the heat of combustion of ${\text{C}}+1/2{\text{O}}_{2}\to {\text{CO}}$ at the bed temperature. The result is then [34],

$$\mathop {\dot{m}}\nolimits_{C} \mathop {\Delta h^{^{\prime}} }\nolimits_{{}} + \mathop {\dot{m}}\nolimits_{C} \mathop c\nolimits_{pg} \left( {\mathop T\nolimits_{p} - \mathop T\nolimits_{b} } \right)\frac{{\mathop {\exp }\nolimits_{{}} \left( { - \frac{{\mathop {\dot{m}}\nolimits_{C} \mathop c\nolimits_{pg} }}{{\mathop 2\nolimits_{{}} \mathop \pi \nolimits_{{}} \mathop d\nolimits_{{}} \mathop k\nolimits_{tg} }}} \right)}}{{\mathop 1\nolimits_{{}} - \mathop {\exp }\nolimits_{{}} \left( { - \frac{{\mathop {\dot{m}}\nolimits_{C} \mathop c\nolimits_{pg} }}{{\mathop 2\nolimits_{{}} \mathop \pi \nolimits_{{}} \mathop d\nolimits_{{}} \mathop k\nolimits_{tg} }}} \right)}} + \mathop \varepsilon \nolimits_{p} \mathop \pi \nolimits_{{}} \mathop d\nolimits_{{}}^{2} \mathop \sigma \nolimits_{{}} \left( {\mathop T\nolimits_{p}^{4} - \mathop T\nolimits_{b}^{4} } \right) = \mathop 0\nolimits_{{}}$$

(13)

where, $\Delta {h}^{^{\prime}}=9211 \rm {kJ}/\rm {kg}$ at 25 °C, ignoring its temperature dependence. $\mathop T\nolimits_{p}$ is the particle temperature, T_b is the bed temperature, ${\upvarepsilon }_{p}=0.95$ is the emissivity of a carbon particle, $\upsigma$ is the Stefan–Boltzman constant, ${k}_{tg}$ is the thermal conductivity of the gas evolving the burning carbon particle, which was assumed equal to the thermal conductivity of the air at bed temperature. ${c}_{pg}$ is the specific heat of the gas evolving the burning carbon particle; $d$ is the diameter of the burning carbon, and $\dot{{m}_{\text{C}}}$ is the burning rate of the carbon particle, given by [34],

$$\mathop {\dot{m}}\nolimits_{C} = \mathop 2\nolimits_{{}} \mathop M\nolimits_{C} \mathop \pi \nolimits_{{}} \mathop d\nolimits_{{}}^{2} \mathop K\nolimits_{{}} \mathop C\nolimits_{p}$$

(14)

being C_p the average molar O₂ concentration inside the bed dense phase, and 1/K the overall fluidized bed combustion resistance.

By means of Eq. 13 the instantaneous particle temperatures were determined for each experiment. Table 6 presents the average particle temperature for each bed temperature and biomass species through a program routine as well as the corresponding reaction rate constants and the average temperature difference between the bed and the burning particle temperature.

Table 6 Average temperatures of the char burning particles and corresponding heterogeneous phase reaction rate constants

Figures 12 and 13 present the plot of ln k_c versus 1/T and the corresponding fitting straight lines for kiwi and vine chars. As above a bed temperature of 820 °C, the gorse char combustion has a pure diffusive control, no kinetic data can be obtained for this last char.

Fig. 12

Arrhenius fitting for kiwi char

Fig. 13

Arrhenius fitting for vine char

Table 7 shows the activation energy and the pre-exponential factor for the kiwi and vine chars, determined from the Arrhenius straight-line fitting.

Table 7 Activation energy and pre-exponential factor for kiwi and vine chars

The activation energies are comparable with those from other authors. Rangel and Pinho [10] present activation energies in the 54 to 117 kJ/mol range for nut pine (Pinus pinea) and cork oak (Quercus suber) chars, while Tomé et al. [12] got values in the 56.6 and 169.3 kJ/mol range for chars made with african woods (Afzelia quanzensis, Millettia stuhlmannii and Pterocarpus angolensis). Pereira and Pinho [14] obtained values in the 39 to 121 kJ/mol range, for holm oak (Quercus ilex), eucalyptus (Eucalyptus globulus), maritime pine (Pinus pinaster) e cork oak (Quercus suber) chars. Janse et al. [35]. present a large set of data collected from the literature from different authors and refer activation energies from 84.9 to 160 kJ/mol for several types of wood chars. Adánez et al. [36] using a modified Arrhenius equation got values in the 55 to 63 kJ/mol range for pine and eucalyptus chars.

However, the activation values obtained on the present study are on the high side, especially for vine char, being slightly above the values obtained from the majority of the studies that were cited. The vine data, Fig. 13, show some discrepancies towards the straight fitting line, as opposed to the kiwi char. Looking at the higher ash content of the vine char and, compared to the kiwi char, the minor ash components, specially alkaline-earth and non-metallic ones like phosphorus, might have an important impact upon the temperature evolution of the reaction rate constant [20].

Conclusions

In this study on the bubbling fluidized bed combustion of chars, made from vine and kiwi agricultural pruning wastes, and gorse forest residues, it was found that the combustion depends on both, the particle external diffusion process and the heterogeneous phase reaction kinetics, for the kiwi and vine chars. For the gorse char the combustion is purely controlled by the diffusion process.

The activation energy values, 246.16 kJ/mol for the kiwi char and 155.02 kJ/mol for the vine char, are on the high side of the activation energy value ranges, obtained in several other studies for wood chars. In the scientific literature there are not available such activation energy values for agricultural wastes, as is the case of the kiwi and vine pruning wastes chars.

Another important conclusion to report here, is that the influence of the particle non-sphericity must be clearly accounted for, otherwise, wrong conclusions concerning the dominating mechanism of the char combustion can be drawn, and supposition of a pure kinetic combustion control could appear. The present work is in line with the interest of agro-forestry residues as an energy source, and how the study of combustion problems arising from some of the minor ash components of these biomasses [23, 37], is becoming an important request for the understanding of the phenomena occurring inside the reaction zone.