Investigate the kinetics of coke solution loss reaction with an alkali metal as a catalyst based on the improved genetic algorithm
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Abstract
The kinetics of coke solution loss reaction with and without sodium carbonate were investigated under the reaction atmosphere of carbon dioxide. The variables of gas flow rate and coke particle size were explored to eliminate the external and internal diffusion, respectively. Then, the improved method combining with the least square and the genetic algorithm was proposed to solve the homogeneous model and the shrinking core model. It was found that the improved genetic algorithm method has good stability by studying the fitness function at each generation. In the homogeneous model, the activation energy with and without sodium carbonate was 54.89 and 95.56 kJ/mol, respectively. And, the activation energy with and without sodium carbonate in the shrinking core model was 49.83 and 92.18 kJ/mol, respectively. Therefore, it was concluded that the sodium carbonate has the catalytic action. In addition, results showed that the estimated conversions were agreed well with the experimental ones, which indicated that the calculated kinetic parameters were valid and the proposed method was successfully developed.
Graphical Abstract
Keywords
Coking Kinetic Improved genetic algorithm Alkali metal Catalyst1 Introduction
Coke is extensively applied to metallurgy, and widely used as raw materials in many fields such as calcium carbide, foundry industry and chemical engineering (Manning and Fruehan 2001; Wang et al. 2007; Gielen and Taylor 2009). Therefore, coke plays an important role in many industries. During the last three decades, there are increasing interests in those factors that influence the gasification rate of coke (Hijiriyama et al. 1983; Zamalloa and Utigard 1995; Eatough et al. 2007; Grigore et al. 2008; Pusz et al. 2010; Zhou et al. 2010). Further, the reaction between carbon in coke and carbon dioxide is also gasification, and socalled coke solution loss reaction (Wang et al. 2016), which is the main reason leading to fragmentation and pulverization of coke in the middle and lower part of blast furnace (Wang et al. 2017). Therefore, it is believed that the coke reactivity is the core of above investigations. Because it might clarify the quantitative relationship between chemistry reaction rate and each physical factor, to provide a guiding significance in reaction optimum conditions selection and reactors design.
Some kinetic models (Miura and Silveston 1989; Belkbir et al. 2004; Nakagawa et al. 2004; Wang et al. 2009) have been reported to study coke gasification reaction with steam and CO_{2} in reactive temperature (1248–1323 K). Zhang et al. (2006) investigated the procedure of anthracite chars with steam and CO_{2} at 0.02–0.1 MPa and 1193–1323 K. They applied homogeneous model and shrinking core model to verify experimental data. Moreover, it was proved that two models well described experimental results. Therefore, the mentioned models are often used for describing the kinetic behavior of coke solution loss reaction.
Among above mentioned investigations, there is not any material as a catalyst. Furthermore, it is a known fact that addition of a range of alkali and alkaline earth metals on the substance based on carbon could enhance the efficiency of gasification. Ueda et al. (2011) studied the catalytic effect of an alkaline earth metal compound on gasification of bitumen coke in a fluidized bed reactor. Furimsky et al. (1986) used a lignite ash containing Ca, Mg, Ba, Fe, and Ni oxides as catalyst with both delayed and fluid cokes from Alberta oil sands in a fixed bed reactor. Watkinson et al. (1989) studied the addition of potassium carbonate to oil sand coke in a fluidized bed. However, the reactant in those investigations is the coke based on petroleum. Kinetic behaviors of coke solution loss reaction using alkali and alkaline earth metals as a catalyst is rarely published.
For solving above kinetic models, the accuracy of the estimated result is dependent on the calculated method. The common and reliable method is regression analysis on the basis of statistics theory, such as least square method (LS) (Axelsso 1980, 1987). However, it is difficult to solve the aforementioned models because the kinetics equations are nonlinear in most cases. Therefore, some intelligent algorithm for example the genetic algorithm (GA) (Chan et al. 2009; Delavar et al. 2010), simulated annealing, and particle swarm optimization was developed to calculate the parameters of the kinetic model in recent years. Among those methods, the GA has been widely applied to solve the problem (Mitra and Mitra 2012). In addition, fitting of nonlinear models relies on nontrivial assumptions. And, users are required to carefully ensure and validate the entire modeling. Moreover, parameter estimation is carried out using some variant of the least squares criterion involving an iterative process. Thus, researchers need to have a clear understanding of the model, its parameterization and data considered, and knowledge of model diagnostics procedures and so on (Baty et al. 2015). Therefore, the GA toolbox in MATLAB was performed to obtain initial kinetic parameters, which might deeply understand model, parameterization and diagnostics procedures and so on. To improve the computational accuracy, the least square method was also used to reestimate the parameters.
Based on above considerations, the reactive behavior of the blast furnace coke under CO_{2} as reaction atmosphere was investigated with and without sodium carbonate as a catalyst in the temperature range of 1073–1623 K. Then, two classical kinetic models were employed to describe the kinetics of coke solution loss reaction. Furthermore, kinetics parameters were estimated using the GA method combined with LS.
2 Experimental and calculation method
2.1 Materials
The raw coke material was the blast furnace coke, which came from Masteel Coking Plant. The catalyst was the reagent grade (>99.8%) sodium carbonate (Na_{2}CO_{3}) from Shanghai Hongguang Chemical Plant. A Cahn Thermax 700 thermogravimetric analyzer was used to conduct the coke solution loss reaction experiments. The protective atmosphere and the reactive atmosphere were provided with a purity >99.999% nitrogen gas and a purity >99.99% carbon dioxide, respectively, from Masteel Coking Plant.
2.2 Coke sample preparation
Proximate analysis and basic properties parameters of coke
M _{ad}  V _{daf}  A _{d}  S _{t,d} (%)  MSI (%)  SSI (%)  PRI (%) 

0.41  2.43  13.07  0.52  62.9  94.1  24.8 
Before the kinetic experiment, it is needed to eliminate the influence of external and internal diffusion. Four different gas flows, 150, 140, 120 and 100 mL/min, were carried out in experiments to remove the external diffusion. And, coke samples were ground by a pestle and mortar and sieved into four size ranges: 0.3–0.4, 0.2–0.3, 0.075–0.2 and <0.075 mm to eliminate the internal diffusion.
2.3 Adsorption of catalyst
In our work, the reaction temperature was quickly heated to 1173 K with the rate of 20 K/min. Sodium carbonate was decomposed into sodium oxide in 1017 K. At this time, sodium oxide is a gas state, and partly raised with gas flow to low temperature zone in the blast furnace. After that, sodium oxide was cooled down and adsorbed on the surface of coke. Adsorption metal oxide is a catalyst in the process of coke solution loss reaction. Considering the cycle enrichment of alkali metals in blast furnace, the salt of Na_{2}CO_{3} was selected as a catalyst, and added with the quantity (0, 0.5, 1, 2 and 3% based on mass) to the sieved coke particles. Then, a few droplets of water (1.0 ml) were placed in those mixtures. At 373 K temperature, those waters were evaporated.
2.4 Coke solution loss experiments
Coke solution loss experiments were implemented by using a Cahn Thermax 700 thermogravimetric analyzer. A coke sample (10 mg) was placed in a crucible of the furnace under nitrogen gas and dried at 378 K for 1 h. Then, the sample was heated up with the rate of 20 K/min. When the desired temperature was reached, N_{2} was replaced by CO_{2}. And the reaction temperature was kept constant until no evident weight loss was observed. Finally, the reaction system was cooled under N_{2} flow to room temperature.
2.5 Calculation method
 Step 1: Construct the objective function. The kinetics parameters were established by optimization. The objective function was described aswhere K is the kinetics parameter, P the experimental point number, t _{m} the reactive time, \(x_{j}^{*} \left( {t{}_{m},K} \right)\) described the calculated values of the experimental molar fraction, \(x_{j} \left( {t{}_{m}} \right)\) described the carbon conversion, \(\psi\) is the value of the objective function.$$\hbox{min} \,\,\psi \left( K \right) = \left[ {\sum\limits_{m = 1}^{P} {\left[ {x_{j}^{*} \left( {t{}_{m},K} \right)  x_{j} \left( {t{}_{m}} \right)} \right]} } \right]^{2}$$(1)

Step 2: Population size. The population size was set to 20.

Step 3: Initial population. The population type was set to be a double vector, and a random initial population with a uniform distribution was created using the uniform function.

Step 4: Estimating the objective function value. Based on the experimental data, the objective function value was calculated.

Step 5: Fitness scaling operator. The rank function was used for the fitness scaling operator, which could scale the raw scores based on the rank of each individual. The fitness scaling operator converted raw fitness scores to values in a range that was suitable for the selection function.

Step 6: Select operator. The selection operator chose parents for the next generation based on their scaled values from the fitness scaling operator. The stochastic uniform was applied for the selection operator.

Step 7: Reproduction operator. The reproduction operator determined how the genetic algorithm creates children at each new generation, where the elite count was set to 2, and crossover fraction was equal to 0.8. The elite count specified the number of individuals, which were guaranteed to survive to the next generation. The crossover fraction specified the fraction of the next generation.

Step 8: Crossover operator. The crossover operator combined two individuals, or parents, to form a new individual, or child, for the next generation. The scattered function was used as a crossover function. The scattered function created a random binary vector.

Step 9: Mutation operator. The mutation operator made small random changes in the individuals in the population, which provided genetic diversity and could the GA to search a broader space (Beasley et al. 1993; Johnson and RahmatSamii 1997). The Gaussian function was introduced for the mutation operator. The average amount of mutation is controlled by scale and shrink. In this case, scale and shrink were both set as 1.0.

Step 10: Migration operator. The migration operator was the movement of individuals if population size was set to be a vector of length greater than 1. The best individuals often replace the worst individuals. The direction function was used to control the migration.

Step 11: Stopping criteria. The stopping criteria operator determined what caused the algorithm to terminate. The specified the maximum number of iterations was equal to be 100. Function tolerance, tall generations and stall time limit were set as 0.000001, 50, and 20, respectively.

Step 12: Estimating the kinetic parameters. The kinetic parameters obtained by GA were set as the initial kinetic parameters. Then, the kinetic parameters were obtained by the LS method that was solved using the lsqnonlin function in Matlab. If the objective function value was greater than 10^{−8}, the initial kinetic parameters were afresh set as the results obtained from the LS method. Then, the NLS method was newly carried out until the objective function value was less than 10^{−8}.
3 Results and discussion
3.1 Elimination of coke samples diffusion
3.1.1 Influence of gas flow rate
3.1.2 Effect of coke particle size on reaction conversion
Furthermore, it was reported that the fine coke particle size range from 0.038 to 0.053 mm was adopted in kinetics investigation (Semagina et al. 2011). Therefore, the coke particle size of (I) was implemented in our work.
3.1.3 Effect of loaded catalyst quantity
3.2 Kinetic modeling
3.2.1 Kinetic model
3.2.2 Stability of calculation method
The best and the mean values of the fitness function at each generation were shown in Fig. 5, respectively. The points at the bottom of the plot denoted the best fitness values, while the points above them denoted the averages of the fitness values in each generation. The best and the mean values in the current generation were also numerically displayed at the top of Fig. 5, respectively. It was concluded that the best fitness value was improved rapidly in 15th generations before, when the individuals were far from the optimum. The best fitness value improved more slowly to near 1.2866 × 10^{−6} after the 30th generation, whose populations were closer to the steady point. Hence, the improved GA method in our work has good stability.
3.2.3 Kinetic parameters
The scattered symbols expressed the experimental data. And, the lines were calculated values that were estimated with the LSGS method. Obviously, both of them agree very well, indicating that calculated values are acceptable.
Kinetic parameters of coke samples for the homogeneous model and the shrinking core model
Sample  Activation energy E (kJ/mol)  Preexponential A (s^{−1})  

Homogeneous  Shrinking core  Homogeneous  Shrinking core  
Raw coke samples  95.56  92.18  0.8548  0.5656 
Samples adsorbed Na_{2}CO_{3}  54.89  48.83  0.0230  0.0108 
4 Conclusions
The kinetics of coke solution loss reaction with and without sodium carbonate were investigated with CO_{2} as a reaction atmosphere using the thermogravimetric analyzer. In the primary experiment, two variables (gas flow rate and coke particle size) were studied. As the results showed, 120 mL/min is sufficient to avoid the external mass diffusion, and the internal diffusion is negligible when the particle size is lower than 0.075 mm. The improved method combined the least square with the genetic algorithm was implemented to solve the homogeneous model and the shrinking core model. By investigating the fitness function at each generation, it was found that the improved genetic algorithm method has good stability to solve two models. Based on estimated reaction rate constant, kinetic parameters were obtained using the Arrhenius Law. In the homogeneous model, the activation energy with and without sodium carbonate was 54.89 and 95.56 kJ/mol, respectively. And, the activation energy with and without sodium carbonate in the shrinking core model was 49.83 and 92.18 kJ/mol, respectively. Therefore, it was obvious that Na_{2}CO_{3} has a catalytic action during coke solution loss reaction. The estimated carbon conversions obtained from two models with the LSGA method agreed well with experimental datum, indicating that the calculated kinetic parameters were valid and the method combined the least square with the genetic algorithm was successfully developed.
Notes
Acknowledgements
Financial supports for this work from the National Natural Science Foundation of China (21476001) and Key Project of Anhui Provincial Department of Education (KJ2017A045) are gratefully acknowledged. The Project was also supported by Open Fund of Shaanxi Key Laboratory of Energy Chemical Process Intensification (No. SXECPI201601).
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