Prediction and Optimization of Sulphur Trioxide Yield from Calcination of Aluminium Sulfate Using Central Composite Design

© 2019 The Authors. This article is licensed under a Creative Commons Attribution 4.0 License Abstract. Sulphur trioxides are common toxic gaseous pollutants which can be produced from alternative routes via calcination of aluminum sulfate derived from kaolin clay. Its demand increases geometrically, thus the need to optimize the yield of SO3 from the calcination of alum is essential. The rate of alum decomposition was monitored by the formation of SO3 via thermogravimetric analysis and X-ray fluorescence analysis. This study aimed to evaluate the effect of calcination temperature and curing time on the SO3 conversion and yields using Face Central Composite Design and optimize the process conditions to evaluate the maximum yield of SO3 using response surface methodology and its effects and interactions were investigated between 800– 900 °C at 60-180 minutes. Results indicated that experimental data satisfied second order polynomial regression model for SO3 conversion and SO3 yield from TG analysis while XRF analysis satisfied first order model respectively. An increase in SO3 conversion and yields was observed as the calcination temperature and time were increased both independently and simultaneously. The calcination temperature was found to have a stronger influence compared to the calcination time. Validation indicated agreement between experimental and predicted values with a regression value of 97.8 %, 97.77 % and 97.67 % for SO3 conversion, SO3 yield via TG and XRF analyses respectively. Based on the ANOVA, the SO3 yield via XRF produced the best model with Rpred of 91.98% while SO3 yield via TG analysis and SO3 conversion had Rpred of 79.99% and 78.01% respectively. Optimization of the production of SO3 was carried out and the optimal condition for SO3 conversion, SO3 yield via TG and XRF analyes were 90.11 %, 91.67 % and 75.81 % respectively at an optimal calcination temperature of 877.43 C and time of 155.04 minutes respectively.


INTRODUCTION
Sulphur trioxide is invisible odourless but corrosive gas which is considered as an environmental pollutant [1,2]. It can be produced in an industrial scale as a precursor to sulphuric acid which has numerous industrial applications. Sulphur trioxide is an essential reagent required in sulphonation reactions. Sulfonation and sulfation are major industrial chemical processes used to make a diverse range of products, including dyes and color intensifiers, pigments, medicinal, pesticides and organic intermediates [3]. The most common production route of SO3 is the catalytic oxidation of sulphur dioxide which is formed from the oxidation of sulphur containing fossil fuels and industrial processes that treats and produces sulfur containing compounds [4]. Several routes for the production of SO3, among which the decomposition of aluminium sulfate has been considered suitable from [5] research work in which the calcination of aluminum sulfate was achieved by heating at temperature between 700-900 °C and time interval 60-180 minutes. Despite the high efficiency of the production of SO3 via catalytic oxidation of SO2., the high cost of catalyst maintainace as well as the corrosive nature of sulphur dioxide are some of its demerits [4]. The thermal decomposition of aluminum sulfate results in the yield of sulphur trioxide which can be influenced by the calcination temperature, time and particle size of the aluminium sulfate in which the particle size was considered to be constant.
Optimization is an essential technique employed in improving the existing condition of a process [6] such as sulphur trioxide (SO3) production and can be achieved through the use of Response Surface Methodology (RSM). The optimization involves either variation of a given parameter per unit time while the other parameter is held constant using RSM. Its techniques can be employed to establish functional relationships between responses of interest and some inputs [7] and based on their relationships, the dependent variables can be used to predict responses that can be compared with the experimental values [8]. The use of RSM cannot be overemphasized as it assists in the evaluation of several parameters simultaneously with their interactions by limiting the number of an experiment to be conducted, as well as optimize process parameters and estimation of interactions [9,10]. Central Composite Design (CCD) is amongst one of the several techniques of RSM employed to design experimental procedures which have the advantage of screening a wide range of parameters as well as evaluating single variable/ cumulative effect of the variables to response [11]. It can also determine the number of the experiment to be able to evaluate for optimization of variables and responses [12] and has been found to widely used for the optimization techniques for calcination processes to produce significantly better models compared to other models [13].
An understanding of the interaction of the factors is essential in evaluating their relationship because their interactions are difficult to be determined using the one-factor-at-a-time approach [14]. The three stages in implementing response surface techniques include the design of experiment i.e. Box-Behnken or Central Composite Design (CCD), development of a model equation through statistical and regression analysis and finally optimization of parameters via model equation [15]. RSM has found applications in numerous experimental designs ranging from palm oil transesterification [16], extraction processes [8], drilling process [17], biodiesel production [18], prediction of blended cement properties [19,20,21] and decomposition as well as other areas of engineering.
The aim of this paper is to investigate the effect of aluminum sulfate calcination temperature and time on the production of SO3 through response surface methodology using central composite design (CCD) and interactions studied. The comparison of the SO3 yields via TG and XRF techniques and SO3 conversion to ascertain which produces the best yield. It also involves optimization of the process conditions for the production of SO3 from the decomposition of aluminium sulfate derived from kaolin.

EXPERIMENTAL DESIGN
The summary of the design for responses; Sulphur trioxide conversion and yield estimation for XRF and TG values with calcination temperature and time as factors. The following parameters were chosen as independent variables: calcination temperature (800 °C , 850 °C , 900 °C ), while the calcination time (60 min, 120 min, 180 min). Face central composite factorial design (3 level 2 factors) with 9 runs (1 block) (design expert 6.0) where -1 denotes low value of the independent variable (800 °C , 60 min), 0 used for the medium value (850 °C , 120 min) and the high value (900 °C , 180 min) were employed to investigate the effect of the above factors on the responses. A model was fitted to the response surface generated by the experiment.
Design-Expert 6.0.8 software was employed to analyze the best fit data and to estimate the optimal value of the factors considered. RSM was used to determine the optimal process parameters to obtain maximum SO3 content. CCD at 3 levels, 2 factors was selected as independent variables and the interaction of variables were estimated. 9 runs were carried out to fit the general model of equation (1) and to obtain economically optimum conditions for the SO3 removal efficiency.
Where Y is the SO3 yield, βo is the coefficient constant, βi is the linear coefficient, βii quadratic coef-ficient effect, βij is the interaction coefficient effect and Xi Xj is the coded values of variable i and j respectively. Y1, Y2, Y3 denotes SO3 conversion, SO3 yield via TG and XRF analyses respectively. X1 is the calcination temperature and X2 is calcination time. Table 1 indicates the experimental results for the determination of the SO3 content via Thermogravimetric (TG) analysis and X-ray Fluorescence (XRF) analysis obtained from the calcination of alum derived kaolin to investigate its effect of calcination temperature and time on the SO3 formation. The statistical analysis of the results was carried out by ANOVA to evaluate the model and its parameters were tabulated in Table 2.
The statistical significance was achieved by the Ftest of the experimental result obtained. The model terms were selected or rejected based on the probability value with 95 % confidence level. Then, the response surface contour plots are generated to visualize the individual and the interactive effects of the variables. Face central composite design was employed and the factors required include calcination temperature (X1) and time (X2) with the responses; SO3 conversion (Y1) and SO3 yield from TG (Y2) and XRF (Y3) analyses. The factors and the response variables were investigated and the effect of the various factors on the responses were determined using design expert 6.0.8. Results indicated that a quadratic equation was obtained for SO3 conversion and SO3 yield from TG analysis whereas SO3 yield from XRF analysis satisfied linear model: The Equations (3) to (5) represent quantitative effect of the factor variables; calcination temperature and time (X1, X2) and their interactions on the response; SO3 conversion and SO3 yield from TG and XRF values (Y1, Y2, Y3). The values of X1 and X2 were substituted in the equation to obtain the theoretical value of Y1 Y2 and Y3 respectively. Based on the experimental design and factor combination, linear model was found to be significant for SO3 via XRF analysis amongst other responses which were significant for quadratic models. Table 2 indicates the analysis of variance (ANOVA) for SO3 conversion, SO3 yield from TG analysis and SO3 yield from XRF analysis, all gave F value for lack of fit was 2.34, 2.33 and 1.53 respectively which also confirms that the models are significant due to the fact that it has an insignificant lack of fit. Tables 3-5 indicate that the Predicted R 2 value for the three responses were in logical conformity with the adjusted R 2 value for determination of the 3 responses. The several models produced adequate precision ratios indicating a desirable signal which was greater than 4 [22].  Authors [23] and [24] reported that a fitted model is said to be acceptable when the R 2 is not less than 80% and greater than 75 % respectively. In this study, the predicted values for developed models had a good correlation with the experimental results as shown in Table 3   From the experimental results, statistical testing was carried out employing Fishers test for ANOVA and the statistical significance of the second-order model indicated that the regression is statistically significant (P<0.0001) for the first two responses while the third response statisti-cal data satisfied linear model; however, the lack of fit is not statistically significant at 99% confidence level, thus the residual variance for the models were insignificant [27,28]. The analysis of variance indicated significant effect of the independent variables on the responses.      Contour and 3D Plots. The correlation between the responses and the factors were further explained via contour and response surface plots. The diagnostic plots represented by Figures 4-6 employed to estimate the adequacy of the regression model which shows the response plots (3D) and the contour plots for the effect of factors X1 (calcination temperature), X2 (calcination time) on the first response Y1 (SO3 conversion), second response Y2 (SO3 yield with TG analysis) and third response Y3 (SO3 yield with XRF analysis) respectively. The response surface curves illustrate the interaction between the factors and determination of the optimal level of the factors for maximum response. The non-parabolic nature of contours implies no significant interaction between both factors [29] as observed in Figure 6.
The calcination temperature and time both caused an increase in the SO3 conversion and yield % when their values were increased from lower level to higher level as observed from the 3D surface plots. The plotted response surface curves were employed to elucidated the interaction of the factors and to determine the optimal level of each factor for a maximum response. From the predictive model, an increase in the calcination temperature from 800-900 °C at constant time of 60, 120 and 180 minutes led to a significant increase in the SO3 conversion respectively as illustrated in Figure 7. Similar trends of an increase in the SO3 yield from TG and XRF analyses were observed as the calcination temperature was increased at constant times of 60, 120 and 180 minutes illustrated in Figures 5-6 respectively. A significant increase in the SO3 yield via TG and XRF analyses was experienced as both factors were gradually increased. Similarly, an increase in the SO3 conversion was experienced as the calcination time was gradually increased from 60 to 180 min at constant calcination temperature of 800, 850 and 900 °C.  The increase in yield of SO3 from the decomposition of alum derived from kaolin clay could be attributed to the increase in amount of kinetic energy required to propagated the decomposition reaction as the temperature was increased or the calcination time progressed [29].  It could be observed in Figure 10 and 11, that as the calcination temperature was gradually increased from 800-900 °C, there was a steady increase in the SO3 yield for both XRF and TG analyses respectively. On the other hand, the predictive model for the determination of the SO3 yield via XRF analysis, it could be seen that as the calcination time was held constant at 180 minutes and the calcination temperature was increased from 800-900 °C, the SO3 yield via XRF increased from 6.01-92.01 %. Similar trend of an increase in the SO3 yield via XRF was observed for other calcination time at 60, 90, 120 and 150 minutes respectively.
Optimization. Optimization of the production of SO3 was conducted and the optimal conditions for optimal SO3 conversion of 90. 11

CONCLUSION
An increase in the calcination temperature and time between 800-900 °C and 60-180 minutes led to an increase in the SO3 conversion, SO3 yield via XRF and TG analyses respectively. Based on experimental results, an empirical relationship between the response and factors was obtained and found SO3 conversion and SO3 yield via TG analysis best suited with quadratic models whereas SO3 yield via XRF satisfied a linear model. The SO3 yields and conversion were established by the response surface and contour plots of the model-predicted responses. The SO3 conversion and SO3 yields via TG and XRF analyses of 90.11 %, 91.67% and 75.81 % were obtained under optimal value of process parameters for calcination temperature of 877.43 °C and time of 155.04 minutes respectively. Analysis of variance for SO3 conversion and SO3 yields via TG and XRF analyses indicated a high coefficient of determination value for SO3 conversion and yields (R 2 =97.8%, R 2 adj = 97.06%) (97.77%, R 2 adj=97.03) and (R 2 =97.67 R 2 adj=97.06) respectively. Thus, a satisfactory agreement of the second-order regression and first order model with the experimental data for TG and XRF analyses respectively. The calcination temperature provided the most significant effect on the SO3 yields and conversion compared with calcination time. It was also observed from the ANOVA that SO3 yield via XRF gave the best model with (R 2 pred = 91.98%) compared to SO3 yield via TG analysis (R 2 pred=79.99 %) and SO3 conversion (R 2 pred=78.01 %) respectively.