4.1. Pyrolysis of RPC
RPC, similar to other types of plant biomass, is composed of cellulose, hemicellulose, lignin, and smaller amounts of other organic compounds, but the content of individual components can vary with the rapeseeds originating from different plantations. In addition, RPC contains a certain amount of unpressed oil, as well as moisture and 5–11 wt.% of nonvolatile mineral substances [
7,
8,
23]. Useful information about the composition of biomass and its thermal characteristics is provided for thermogravimetric analysis.
The TG profile for the pyrolysis of the RPC sample in an inert argon atmosphere at a sample heating rate of 10 °C/min are shown in
Figure 2. The DTG data (
Figure 3) show that the thermal decomposition of RPC can be divided into several weight loss stages occurring at different temperatures.
The total main weight loss of rapeseed oil cake was determined to be 70% at temperatures up to 600 °C, and there was only a slight weight loss (∼5 wt.%) in the high temperature range (600–1000 °C) due to evaporation and thermal cracking of the higher-molecular-weight primary pyrolysis products filling pores of the solid residue [
24].
To elucidate the process mechanism, a deconvolution of the DTG curve into individual peaks was performed using the NETZSCH Peak Separation software, and the results are shown in
Figure 3. The experimental data were fitted as an additive superposition of peaks, where each single peak was represented by the Fraser–Suzuki profile. The best fit to the DTG curve was achieved for a system consisting of six peaks. The correlation coefficient was 0.999. The peak position and the area fraction expressing a percentage of total mass loss of RPC in each single stage are given in
Table 3.
In the first stage, the moisture adsorbed on the char was evaporated at temperatures below 200 °C. A major sample weight loss occurred between 170–600 °C due to thermal degradation of the carbohydrates, mainly hemicellulose cellulose and lignin components (peaks II, III, V). Similar results were reported in a previous study related to TG analysis of the pyrolysis of RPC [
5,
7]. According to the literature, the second peak, exhibiting a maximum at approximately 229 °C on the DTG curve as a shoulder of the peak with a maximum at 318 °C, should be attributed to the thermal degradation of hemicellulose [
25]. The third weight loss step, which occurred between 250 and 370 °C, could be related to the degradation of the rapeseed oil cake cellulose. Smets et al. [
7] showed that the fourth peak, which reaches the maximum at 380 °C, can be identified as the volatilization of triglycerides and their partial decomposition to fatty acids. Lignin decomposed over a higher temperature range [
25]; therefore, decomposition of this component could be represented by the weight loss peak V with the maximum at approximately 442 °C.
The solid residue remaining after pyrolysis consists mainly of the mineral fraction and the deposited carbon formed at the earlier stages of the process. The solid is porous, with the pores being partly filled with molten volatile primary decomposition products (high-molecular-weight hydrocarbons). The oxidation of fixed carbon and thermal cracking of the substances filling pores takes place at sufficiently high temperatures, and these processes range from 600 to 1000 °C. Peak VI represents the abovementioned processes.
4.2. Kinetics of Char Gasification
The TG curves obtained under isothermal CO
2 gasification experiments were converted to carbon conversion on an ash-free basis, defined as:
where
m0,
m and
mF represent the weight, % or mg, related to the initial mass of the sample, a given moment and a final solid residue of the process, respectively [
26,
27].
The formula can be used with an assumption that the ash decomposition is negligible. The experimentally obtained conversions are shown in
Figure 4. These results demonstrate the effects of the temperature and CO
2 concentration on the reaction times needed for complete gasification. The raw data are shown in the form of symbols, while the meaning of the lines is explained later in the text.
Figure 4 also presents a dependence of reactivity (conversion rate
dX/dt) of RPC char in CO
2 gasification on conversion. A maximum appears on the reactivity curves at a conversion of approximately 30%–40%. From this result, it follows that for the correct kinetic interpretation of the experimental data, the rate equation of the RPM model should be applied, as mentioned in
Section 2.
To estimate the model parameters, a two-step procedure was applied. In the first step, approximate values of unknown model parameters were estimated, and in the second step, their final values were determined using nonlinear regression by minimization sum of squares of residual, SSR (deviations predicted from empirical values of conversions). A range of conversions from 0.05 to 0.9 was used for the model evaluation due to the uncertainty of the data obtained in the initial and final stages of the experiments.
At the beginning of the process, the reaction rate constants
ks for different temperatures and CO
2 concentrations were calculated as the slopes of the plots (shown in
Figure 5) obtained by linearization of the experimental data with the integral form of the RPM rate equation, Φ, given in
Table 1. The symbols on the plots represent the experimental data from
Figure 4, and the solid lines represent their linear fits, as calculated by regressions.
The structural parameter ψ needed to calculate Φ in the RPM model can be estimated from the experimental conversion values where the reaction rate is the maximum
Xmax [
28]. However, as shown in
Figure 4, the position depends on the temperature and CO
2 concentration. In such a situation, a better approach to estimate the structural parameter seems to be a method used by Everson et al. [
29], where ψ was calculated by fitting Equation (4) to all experimental results:
where
tX and
t0.9 are the times after which the conversion reaches
X and 0.9, respectively. A comparison of the conversions calculated from Equation (4) and the experimental results is shown in
Figure 6 for
ψ = 6.8, which was determined to be the optimal value for this parameter.
Then, using the reaction rate constants calculated at different temperatures and CO
2 concentrations, the approximate values of the activation energy, the pre-exponential factor, and the reaction order were estimated and used as initial values in further calculations. The effect of temperature over the range 800 to 900 °C with three concentrations of CO
2, as shown in
Figure 7a, and the effect of carbon dioxide concentration over the range 0.1 to 1.0 mole fraction for two extreme temperatures, as shown in
Figure 7b, show very similar trends, which made it easier to determine the parameters.
As mentioned earlier, in the second stage of kinetic model identification, the final values of the model parameters were determined using nonlinear regression of the experimental data with the model rate equations. The Arrhenius parameters, the reaction order with respect to the carbon dioxide mole fraction, and the structural parameter were estimated by minimizing the objective function of the following form:
where
Xexp. and
Xcal. are the char conversions determined experimentally and calculated from the model equations given in
Table 1,
M is the number of experimental runs, and
N is the number of experimental data points in each run (in this case,
M = 7 and
N = 17). The optimal values of the model parameters are given in
Table 4, and some fit statistics are included in
Table 5.
The optimal value of 6.1 for the structural parameter found in this study is similar to the
ψ value of 6 reported for rice husk char obtained by Gao et al. [
30], while it is considerably lower than the values of 16.9–42.6 reported for coconut-shell chars [
31]. When the
ψ value is higher than 2, pore growth increases the surface area of the solid reactant and the reaction rate during the initial stage of gasification [
32]. The lower values of rice husk chars indicate that the chars would undergo limited pore development in the gasification process [
33]. The values for the reaction order with respect to the carbon dioxide mole fraction (0.57) and the activation energy (222.1 kJ/mol) are within the ranges published in the literature [
19].