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Prediction and Optimization of Sulphur Trioxide Yield from Calcination of Aluminium Sulfate Using Central Composite Design
Olumide Olu Olubajo Isa Yusuf Makarfi 2
1 Abubakar Tafawa Balewa University
Dass road, P. M. B. 0248, Bauchi, 740272, Nigeria
2Durban University of Technology
P. O. Box 1334, Durban, 4000, South Africa
DOI: 10.22178/pos.51 -2 LCC Subject Category: QD1-65
Received 28.09.2019 Accepted 28.10.2019 Published online 31.10.2019
Corresponding Author: Olumide Olu Olubajo ooolubajo@atbu.edu.ng
© 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 800900 °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 R2pred of 91.98% while SO3 yield via TG analysis and SO3 conversion had R2pred 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 oC and time of 155.04 minutes respectively.
Keywords: Calcination temperature and time; Conversion; Face central composite design; Sulphur trioxide; Yield.
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 sul-phonation 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.
Yk = f (Calcination temperature,
Calcination time)
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.
k k k Y = f + Z Px +Z fX + Z PjXx,, (2)
/=1 /=1 i=i(i*j)
Where Y is the SO3 yield, ffo is the coefficient constant, ft is the linear coefficient, fftt quadratic coef-
ficient effect, fa is the interaction coefficient effect and Xi Xj is the coded values of variable i and j respectively. Yi, Y2, Y3 denotes SO3 conversion, SO3 yield via TG and XRF analyses respectively. Xi is the calcination temperature and X2 is calcination time.
Table 1 indicates the experimental results for the determination of the SO3 content via Thermogra-vimetric (TG) analysis and X-ray Fluorescence (XRF) analysis obtained from the calcination of alum derived kaolin to investigate its effect of
Face central composite design was employed and the factors required include calcination temperature (Xi) and time (X2) with the responses; SO3 conversion (Yi) 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:
Yx = -4037.45 + 8.67^ + 0.86X2 -0.0045Xf - 0.000 563Xf - 0.0072Xx X2 (3)
Y2 = -4663.90 + 10.172X! + 0.79X2 -0.00 55Xf - 0.000 57Xf - 0.00 58Xx X2 (4)
= - 70 1.79 + 0.86Xx + 0. 1 1X2 (5)
The Equations (3) to (5) represent quantitative effect of the factor variables; calcination temperature and time (Xi, X2) and their interactions on the response; SO3 conversion and SO3 yield
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 F-test 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.
from TG and XRF values (Yi, Y2, Y3). The values of Xi and X2 were substituted in the equation to obtain the theoretical value of Yi 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 i.53 respectively which also confirms that the models are significant due to the fact that it has an insignificant lack of fit. Table 2 also indicates the model F values for SO3 conversion, SO3 yield for TG and SO3 yield for XRF are 62.54, 69.i6 and i25.09 respectively, thus the models are significant implying that there is 0.0i% possibility that the noise will be large.
Tables 3-5 indicate that the Predicted R2 value for the three responses were in logical conformity with the adjusted R2 value for determination of the 3 responses. The several models produced adequate precision ratios indicating a desirable signal which was greater than 4 [22].
Table 1 - Experimental Design and Results
Run Temp °C, X1 Time min, X2 Conversion %, Y1 SO3 TGA %, Y2 SO3 XRF %, Y3
1 800 60 8.30 7.55 6.33
2 800 120 12.60 12.97 8.63
3 800 180 16.97 17.46 11.59
4 850 60 48.55 49.95 25.62
5 850 120 68.29 70.25 45.91
6 850 180 80.16 82.47 57.28
7 900 60 97.40 94.44 93.75
8 900 120 97.40 97.26 95.49
9 900 180 97.40 97.36 97.23
Table 2 - ANOVA for Response Surface Quadratic Model Analysis of Variance for Conversion and Percentage SO3 Yield for XRF & TG analyses with Central Composite Design CCD_
Source Sum of Squares DF Mean Square F Value Prob > F
Model Yi ii558.43 5 23ii.69 62.54 < 0.000i
Xi i0780.62 i i0780.62 29i.65 < 0.000i
X2 270.4i i 270.4i 7.32 0.0304
Xi2 357.8 i 357.8 9.68 0.0i7i
X22 ii.35 i ii.35 0.3i 0.5968
X1X2 i8.79 i i8.79 0.5i 0.4989
Residual 258.75 7 36.96
Lack of Fit 258.75 3 86.25 2.34 0.8240
Model Y2 ii567.i7 5 23i3.43 69.i6 < 0.000i
Xi i0506.86 i i0506.86 3i4.08 < 0.000i
X2 342.77 i 342.77 i0.25 0.0i5
Xi2 5i2.73 i 5i2.73 i5.33 0.0058
X22 i7.68 i i7.68 0.53 0.4908
XiX2 i2.22 i i2.22 0.37 0.5647
Residual 234.i7 7 33.45
Lack of Fit 234.i7 3 78.06 2.33 0.8240
Model Y3 ii53i.76 2 5765.88 i25.09 < 0.000i
Xi ii259.73 i ii259.73 244.29 < 0.000i
X2 272.03 i 272.03 5.09 0.0355
Residual 460.93 i0 46.09
Lack of Fit 460.93 6 76.82 i.53 0.ii76
Table 3 - Model Summary Stal tistics/ Sequential Model Sum of Squares for CCD for SO3 Conversion
Source Linear 2FI Quadratic Cubic
Sum of Squares ii05i.04 i8.79 4.88.60 247.98
DF 2 i 2 2
Mean square 5525.52 i8.79 244.3 i23.99
F value 72.i2 0.23 6.61 57.54
Prob> F < 0.000i 0.6406 0.0244 < 0.0004
Std. Dev. 8.75 9.ii 6.08 i.47
R2 0.9352 0.9368 0.9781 0.9908
Adj. R2 0.9222 0.9i57 0.9625 0.9978
Pred. R2 0.87i73 0.752 0.7801 0.894i
PRESS i5i6.96 2930.38 2598.21 i25i.95
Suggested Suggested Aliased
Authors [23] and [24] reported that a fitted model is said to be acceptable when the R2 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 indicated R2 values for 97.81 %, 98.02 % and 96.16 % respectively while R2adj value for SO3 conversion, SO3 yield via TG and XRF analyses were 96.25 %, 96.60 % and 95.39 % respectively, indicating appropriateness of the developed model in predicting the SO3 conversion, SO3 yield via TG and XRF analyses for the two factors with R2 and R2adj value close to unity. Authors [25] and
[26] stated that a better empirical model fit was obtained with the experimental data when the R2 value is close to unity and observed that a relatively high R2 value does not imply that the model is adequate, thus, [25] suggested that a R2adj of above 90% is most appropriate to evaluate the model adequacy for the three responses which were closer to unity. Thus, indicating a good fit of the model to experimental results.
The analysis of variance showed the significant effect of the independent variables on the responses and determine the responses which were significantly affected by the various interactions. The following model terms Xi, X2, X12 were
considered significant while the model terms greater than 0.10 were considered not significant for experimental SO3 conversion and SO3 yield via TG analysis whereas, SO3 yield via XRF analysis showed that only the linear model terms Xi, X2 were considered significant. The calcination temperature, (Xi) obtained a F value of 291.65, 314.08 and 244.29, while for the calcination time (X2) produced a F value of 7.32, 10.25 and 5.09 for the experimental SO3 conversion, SO3 yield for TG and XRF analyses respectively. The high F values are a strong indication that the effect of
the calcination temperature is far more significant compared to the calcination time for all the models. The quadratic term of the temperature obtained a F values of 9.68 and 15.33 respectively with p values falling within p< 0.05 or p < 0.10 respectively. The quadratic term of the calcination time as well as the product of the calcination temperature and time obtained low F values, thus indicating that their effect is insignificant for the first two responses. It could be concluded that both factors X1 and X2 significantly affected the three responses.
Table 4 - Model Summary Statistics/ Sequential Model Sum Of Squares for CCD for SO3 Yield with TG analysis_
Source Linear 2FI Quadratic Cubic
Sum of Squares 10849.63 12.22 705.32 227.42
DF 2 1 2 2
Mean square 5424.82 12.22 352.66 113.71
F value 57 0.12 10.54 84.28
Prob> F < 0.0001 0.7401 0.0077 0.0001
Std. Dev. 9.76 10.22 5.78 1.16
R2 0.9194 0.9204 0.9802 0.9994
Adj. R2 0.9032 0.8939 0.966 0.9986
Pred. R2 0.8403 0.6755 0.7999 0.9336
PRESS 1884.27 3829.56 2361.51 783.86
Suggested Suggested Aliased
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.
Table 5 - Model Summary Statistics/ Sequential Mode Sum of Squares for CCD for SO3 Yield with XRF values
Source Linear 2FI Quadratic Cubic
Sum of Squares 11531.76 0.79 197.1 248.28
DF 2 1 2 2
Mean square 5765.88 0.79 98.55 124.14
F value 125.09 0.015 2.62 42.08
Prob> F < 0.0001 0.9037 0.1412 < 0.0007
Std. Dev. 6.79 7.15 6.13 1.72
R2 0.9616 0.9616 0.9781 0.9988
Adj. R2 0.9539 0.9488 0.9624 0.997
Pred. R2 0.9198 0.8478 0.7808 0.8571
PRESS 962.12 1830.36 2628.47 1714.22
Suggested Aliased
Normal Probability and Predicted vs Actual Plots. Figures 1 (b), 2 (b) and 3 (b) also indicated that there is a strong relationship between the pre-
dieted and actual values for SO3 conversion, SO3 yield for TG and XRF values respectively based on the results obtained.
Figure 1 - (a) Normal Plot of residuals indicating
significance of the model developed for SO3 conversion and (b) Predicted vs Actual plot of the model developed for SO3 conversion
Figure 3 - (a) Normal Plot of residuals indicating significance of the model developed for SO3 yield with XRF and (b) Predicted vs Actual plot of the model developed for SO3 yield with XRF
It could be inferred that the predicted model obtained from the Design Expert software was significantly adequate in predicting SO3 conversion and SO3 yield for TG and XRF values respectively. Tables 6-8 illustrate the predicted values, actual values and residual errors of SO3 conversion and SO3 yield via TG and XRF analyses respectively.
Table 6 - Diagnotistic Case Statistics for SO3 Conversion
Temp Time Actual Predicted Resid
°C min value % Value % ual %
800 60 8.3 3.07 5.23
800 120 12.6 i3.97 -1.37
800 180 16.97 20.83 -3.86
850 60 48.55 59 -10.45
850 120 68.29 67.74 0.55
850 180 80.16 72.43 7.73
900 60 97.4 92.i8 5.22
900 120 97.4 98.75 -1.35
Figure 2 - (a) Normal Plot of residuals indicating significance of the model developed for SO3 yield with TG analysis and (b) Predicted vs Actual plot of the model developed for SO3 yield with TG analysis
Table 7 - Diagnotistic Case Statistics for SO3 Yield via TG Analysis
Temp °C Time min Actual value % Predicted Value % Residual %
800 60 7.55 2.51 5.04
800 120 12.97 14.35 -1.38
800 180 17.46 21.12 -3.66
850 60 49.95 59.73 -9.78
850 120 70.25 69.82 0.43
850 180 82.47 74.85 7.62
900 60 94.44 89.7 4.74
900 120 97.26 98.04 -0.78
Table 8 - Diagnotistic Case Statistics for SO3 Yield via XRF Analysis
Temp °C Time min Actual value % Predicted Value % Residual %
800 60 6.33 -1.94 8.27
800 120 8.63 4.79 3.84
800 180 11.59 11.53 0.064
850 60 25.62 41.38 -15.76
850 120 45.91 48.11 -2.2
850 180 57.28 54.85 2.43
900 60 93.75 84.7 9.05
900 120 95.49 91.43 4.06
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 Xi (calcination temperature), X2 (calcination time) on the first response Yi (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.
Figure 4 - Response surface plot (Contour and 3 D
surface) showing the effect of different factors (Xi: Calcination temperature, X2: calcination time) for SO3 yield with TG analysis for quadratic model
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.
800.00 825.00 350.00 S75.00 900.00
A: Calcination temoerature
A: Calcination temperature
Figure 5 - Response surface plot (Contour and 3 D
surface) showing the effect of different factors (X1: Calcination temperature, X2: calcination time) for SO3 conversion for quadratic model
Figures 8 and 9 illustrate the effect of calcination time on the SO3 yield via TG and XRF analysis at various constant calcination temperature. From the predictive model for the determination of the SO3 via TG analysis, it could be observed that the SO3 yield increased as the calcination time progressed from 60-180 minutes while the calcination temperature was held constant at 800, 825, 850, 875 and 900 °C respectively. The SO3 yield via TG analysis increased from 24.32-43.54 %, 49.93-65.67 % as the calcination time progressed from 60-180 minutes at constant calcination temperature of 850 and 900 °C respectively. This increase in SO3 yield could be attributed to the increase in the duration of calcination stemming from the increase in kinetic energy gained by the molecules to overcome the activation energy resulting in increased SO3 yield.
Figure 6 - Response surface plot (Contour and 3D surface) showing the effect of different factors (X1: Calcination temperature, X2: calcination time) for SO3 yield with XRF for quadratic model
Similar trend of an increase in the SO3 yield via XRF analysis as the calcination time progressed at constant calcination temperature of 800, 825, 850, 875 and 900 °C respectively. The SO3 yields via XRF analysis were found to be higher compared to those obtained from TG analysis. The values of SO3 yield via XRF were also significantly close to SO3 conversion values at various calcination temperatures and time compared to those of SO3 yield via TG analysis. This could be attributed to the accuracy of the analyses of the SO3 yield. 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].
Figure 7 - Response surface plot (3D surface and Contour) indicating the optimal conditions (Xi: Calcination
temperature, X2: calcination time) for SO3 conversion
80
60
40 O 40 t-
ca
S 0
m
20
-20
-40
-800oC 825oC 850oC 875oC 900oC
Calcination time mins
Figure 8 - Effect of calcination time on the SO3 yield via TG analysis at various calcination temperatures
100
80
X 60
. s
2 40
20
-20
800oC 825oC 850oC 875oC 900oC
180
Calcination time mins
Figure 9 - Effect of calcination time on the SO3 yield via XRF at various calcination temperatures
0
100
80
X 60
s
T5
Hi 40
m
o
m
20
-60 mins - 90 mins 120 mins -150 mins 180 mins
-20
810 820 830 840 850 860 870 880 890 900
Calcination temperature oC
Figure 10 - Effect of calcination temperature on the SO3 yield via XRF at various calcination times
80
60
40
<
(J I—
2 ' >
33
OJ
■ >. 20
m
O
1/1
0
-20
-40
-60 mins - 90 mins -120 mins -150 mins 180 mins
900
Calcination temperature oC
Figure 11 - Effect of calcination temperature on the SO3 yield via TG analysis at various calcination times
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 %, SO3 yield via TG analysis of 91.67 % and SO3 yield via XRF of 75.81 % at an optimal calcination temperature of 877.43 °C and time of 155.04 minutes. Figures 12-13 indicated similar trend of an increase in the SO3 conversion and SO3 yield obtained via TG and XRF analyses as the calcination temperature and time of the aluminum sulfate was simultaneously increased as illustrated by the response surface plots.
0
Figure 12 - Response surface plot (3D surface and Contour) indicating the optimal conditions (X1: Calcination temperature, X2: calcination time) for SO3 yield via TG analysis respectively
Figure 13 -Response surface plot (3D surface and Contour) indicating the optimal conditions (X1: Calcination temperature, X2: calcination time) for SO3 yield via XRF
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 (R2 =97.8%, R2adj = 97.06%) (97.77%, R2adj=97.03) and (R2 =97.67 R2adj=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 (R2pred = 91.98%) compared to SO3 yield via TG analysis (R2pred=79.99 %) and SO3 conversion (R2pred=78.01 %) respectively.
ACKNOWLEDGEMENTS
The authors wish to thank National Metallurgical Development Centre, Jos and the Department of Chemical Engineering of Ahmadu Bello University Zaria for providing infrastructure, facilities and their support to this research work.
REFERENCES
CONFLICT OF INTEREST
The authors declared that they have no conflict of interest.
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