Thermal decomposition kinetics of carbide slag in air atmosphere

In this study, the thermal decomposition characteristics and kinetics of carbide slag were evaluated by simultaneous measurements of thermogravimetry (TG)/differential thermal (DTA) analyses under air atmosphere. The data revealed that mass thermal decomposition processes could be divided into three stages, in which the last two stages at 400-490°C and 710-790°Cunderwent largest thermal decomposition weight loss. The thermal decomposition kinetic parameters were calculated by the Kissinger method and the corresponding apparent activation energies were estimated to 204.00 and 311.40kJ·mol−1, respectively. The respective natural logarithms of pre-exponential factor (In A) calculated by Kissinger method were 1.07×1011 and 1.77×1012. For comparison, the thermal decomposition kinetic parameters were also calculated by FWO peak maximum evolution and FWO isoconversional methods. The apparent activation energies of the two last stages were recorded as 205.71 and 313.12kJ·mol−1, respectively.


Introduction
Polyvinyl chloride (PVC) is one important plastic used worldwide in many applications. China is the world's largest producer and consumer country of PVC. The production of PVC is mainly performed from petroleum ethylene and calcium carbide acetylene. The "rich coal and little oil" principal in China [1] made the production of PVC mainly acetylene derived from hydrolysis of calcium carbide. The recent statistics suggested that PVC production by calcium carbide method accounted for 80% of total production capacity as of 2015 [2].
Carbide slag is a hydrolysis waste residue issued during hydrolysis of calcium carbide to produce PVC. The chemical reaction could be summarized by: CaC 2 +2H 2 O= C 2 H 2 +Ca(OH) 2 [3], mainly composed of Ca(OH) 2 with other metal oxides [4]. At present, many ways could be exploited to utilize carbide slag resources, including production of building materials [5] and preparation of chemical products [6] through environmental management [7]. Currently, only small portions of the enormous amounts of produced carbide slag each year in China  dumping of waste carbide slag does not only occupy the land and prevent it from being used for useful purposes but also affect the environmental sanitation and pollute the surrounding water/soil sources [8][9]. At the long run, this will cause serious environmental pollution [10]. The high calcium content of carbide slag can be used as precursor of basic adsorbents. The preparation of high-efficiency and lowtemperature calcium-based adsorbents for removal of acidic gases would achieve better waste treatment of these by-products.
In this study, the thermal decomposition kinetics and explored decomposition mechanism of carbide slag were studied by thermogravimetric analysis during temperature programming. The kinetic parameters of thermal decomposition reactions were obtained by means of the Flynn-Wall-Ozawa(FWO) and Kissinger methods.

Materials
The carbide slag derived from a chemical plant in QuJing Yunnan (China) was crushed by a shredder then dried at 110℃ for 48h. The obtained carbide slag was sieved at 200μm and used for further analysis.

Methods
The thermogravimetry experiments were carried out on a thermogravimetric-differential thermal analyzer (TGA, model, Beijing Everlasting Scientific Instrument Factory). The experimental conditions were based on Al 2 O 3 powder as reference material and sample amount of 15±5mg. After heating, air was purged into the reaction tube at gas flow rate of 10mL/min and temperature from room temperature (22℃) to 1000℃. The heating rates varied as follows: 10 K/min, 15 K/min, 20 K/min, and 25 K/min.

Thermal decomposition characteristics of carbide slag
The TG -DTG -DTA curves of carbide slag in air at different heating rates are gathered in Figure 1. Note that the carbide slag final weight loss rate was always maintained between 20~30%. These findings were similar to thermal decomposition process of carbide slag under nitrogen atmosphere [11]. The thermal decomposition characteristics of carbide slag at different heating rates are listed in Table  1. The mass thermal decomposition process could be divided into three stages. The weight loss during the first stage was the smallest, and ascribed to evaporation of adsorbed water molecules from surface of carbide slag. The maximum mass loss rate temperatures (T max ) of carbide slag during the second stage were recorded as 468.0℃, 478.4℃, 485.9℃, and 483.2℃. In the third stage, these values increased to 763.7℃, 772.3℃, 785.8℃ and 784.4℃, respectively. At peak of DTG curves of carbide slag, the DTA curves in the second stage showed downward endothermic peak ( Figure 1). Ca(OH) 2 was identified as the main component of thermal decomposition reaction of carbide slag under air atmosphere. The DTA curves of carbide slag during the third stage contained upward exothermic peak, indicating that the temperature stage was composed of combustion heat release of residual carbon in carbide slag under air. The heating rate depicted great influence on thermal mass loss. As heating rate increased, TG curve moved to high temperatures. (1) to (2) [12].
where α is the conversion rate at any time t or temperature T during thermal decomposition in % . α can be obtained using Eq. (3) [13], where m 0 is the starting mass, m t is mass at any time t or temperature T of thermal decomposition process, m f is final residual mass at the end of thermal decomposition reaction, t represents time of thermal decomposition in s, A is a pre-exponential factor of thermal decomposition in s -1 , E is the activation energy of thermal decomposition reaction in kJ/mol, R is the universal gas constant (8.314 J/molꞏK), T is the thermal decomposition temperature in K, β is the heating rate in K/min or ℃ /min, and f(α) is a function of differential kinetic mechanism determined by the type of reaction.
Here, the kinetic parameters (activation energy E, pre-exponential factor A) of carbide slag thermal decomposition reaction were obtained by the FWO and Kissinger methods. Meanwhile, the activation energy E was solved by Flynn-Wall-Ozawa (FWO) method and the results of both methods were compared. [14] is a perfect non-nuclear kinetic equation, which does not require any mechanism model to solve the activation energy of the reaction. This would prevent blindness of model selection as shown in Eq. (4):

Kissinger method results. The Kissinger method
where T max is peak decomposition temperature in K. The physical meanings of the remaining parameters are the same as in Section 3.2.1.
Linear fitting was performed according to Eq. (4) with In(β/T 2 max ) as ordinate and T -1 max /10 -3 K -1 as abscissa. The slope of the fitted straight line was identified as -E/R and intercept as In(AR/E). These two plots allowed obtaining E and A. The second and third stages carbide slag thermal decomposition showed maximum peaks, which can be obtained from TG-DTG curve (Figure 1). The obtained data can be processed according to Figure 1 (β, lgβ, T max /K, In(β/T 2 max ), (T -1 max /10 -3 K -1 ). The analyses of DTG curves are presented in Table 2.
The results of fitting are shown in Figure 2. The linear equation of the second stage can be obtained from the plot of Y=-24.53715X+22.19173. The thermal decomposition activation energy E was estimated to 204.00 kJꞏmol -1 with pre-exponential factor A of 1.07×10 11 . The linear equation of the third stage was identified as: Y=-37.4552X+24.57829, with thermal decomposition activation energy E of 311.40 kJꞏmol -1 and A of 1.77×10 12 .

Flynn-Wall-Ozawa method.
The activation energies were also calculated using the FWO [15] peak maxima and FWO isoconversional methods, and the results were compared with those of Kissinger method (Eq. (5) for FWO): where G(α) is the integral kinetic mechanism function determined by the reaction type, T a is temperature at the same conversion rate at different heating rates in K, and the physical meanings of the remaining parameters are the same as in Section 3.2.1.
Under different heating rates (β), the conversion rates α max at peak decomposition temperatures T max looked approximately equal. Meanwhile, T a in Eq. (5) was replaced by T max , and ln(β) was plotted as ordinate and 1/T max as abscissa. After fitting, the slope of the straight line obtained after fitting was identified as -0.4567E/R, and allowed determination of E. The relevant data and processing (β, T max , ln(β), (1/T max ) × 10 3 ) obtained by combining with Figure 1 are listed in Table 3, and the linear fittings are depicted in Figure 3. To verify that conversion rate α max at peak decomposition temperature T max was approximately equal under different heating rates β , mass m t in TG curve was obtained from T max of DTG curve for all four graphs in Figure 1. Note that m 0 and m f were known parameters. From Eq. (1), the peak conversion rate α max at thermal decomposition of carbide slag can be calculated at peak decomposition temperature. The relevant data processing (m 0 , m t , m f , α max ) are gathered in Table 3. The α max values at different heating rates β looked similar, with average of 48.1% and 89.3%, respectively. Therefore, α max can be approximated as a fixed value, consistent with literature reports [16] and indicating the applicability and effectiveness of the proposed method.

Conclusions
The thermal decomposition process of carbide slag under air could be divided into three stages. The first stage was characterized by evaporation of adsorbed water molecules on the surface of carbide slag. The second stage produced Ca(OH) 2 as main component of carbide slag thermal decomposition reaction. The third stage was characterized by exothermic combustion of carbon particles in carbide slag. The thermal decomposition kinetic parameters in the second and third stages in terms of activation energies were calculated by Kissinger and FWO peak maximum evolution isoconversional methods. The obtained activation energy values were similar, indicating that both methods were suitable for solving the thermal decomposition kinetics of carbide slag.