When comparing the model terms, it was apparent that the feed-to-solvent ratio had the most definite impact on the yield. A low feed-to-solvent ratio was equivalent to a high surfactant concentration, and thus the yield increased with a decrease in the feed-to-solvent ratio. Both, the agitator speed and the column capacity had a less significant influence on the yield.
The model was assessed based on the normal probability of a residual vs. run plots. The corresponding plots regarding the yield model are presented in appendix A 19. The normal probability plot was a function of the internally standardized residuals. That assessment was the most important for the model diagnostics. A precise and stable model had all data points close to the linear function. The developed model for the yield give satisfying results, and no outliers were observed. Additionally, a residual vs. run plots indicated which measuring points differed more from its predicted value. While there were some values, which were further of the predicted value, all measuring points were within the coded confidence level of 3. Thus, the total fluctuation of the residuals was no cause for concern, since it illustrates that they vary only due to common-cause variations [171]. Overall, the residual diagnosis confirms the quality of the model which provided reasonable results.
In Figure 6.6, the surface contour plots for the agitator speed and capacity (a) and the feed-to-solvent ratio and capacity (b) are illustrated.
Figure 6.6: Contour plots of the yield as a function of the feed-to-solvent ratio (ν) and capacity (b) at agitation speed (n) = 40 rpm (plot a), and as a function of n and b at ν = 8 (plot b). Colored for the yield; at T = 40°C.
The influence of the feed-to-solvent ratio on the yield (Figure 6.6a) was pronounced at 40 rpm and feed-solvent-ratio = 8. Overall, when the feed-to-solvent ratio was the highest (10), a yield of approx. 22 % was reached at average agitator speed.
By decreasing the feed-to-solvent ratio to the minimum (6), the obtained yield was nearly doubled.
Contrary to the expectations, the agitator speed did not dominate the yield change through the control of the surfactant dispersion in the column (Figure 6.6 b). A possible reason for this could be the fact that the phase ratio between the aqueous and micellar phase at the narrow surfactant concentration range in the mixing zone did not change significantly. Thus, an increase in the stirring speed would lead to a better dispersion of the similar amount of surfactant-rich phase. Hence, no significant improvement in the mass transfer rate could be reached [170].
Furthermore, a high column capacity had an adverse effect on the yield. The agitator speed – capacity contour plot at a constant average feed-to-solvent ratio (Figure 6.6 b) confirmed the limited significance of the column capacity. Additionally, a considerable area of the plot was restricted due to the stress limit. The reason for that is the multilinear constraint, which allows the highest surfactant concentration in the raffinate only at low column capacities.
Overall, according to the model, the best yield value was located in one of the corner points of the surface plot, at a moderate agitator speed and the lowest feed-to-solvent ratio. The highest yield was calculated at a column capacity of 1 l·h-1, agitator speed of 40 rpm and a feed-to-solvent ratio of 6. At these conditions, a maximum yield of 43.9 % and enrichment factor of 3.2 (calculated according to
Equation 2-13) were reached. An experiment under the described operation conditions was able to obtain a yield of 42.5 %, which confirms the calculated result of the model.
However, during the batch CPE, a yield of 79 % was reached. Contrary to the expectation, the yield of a continuous process at 3 wt% Triton X-114 in the mixing zone reached the half of the corresponding single-stage value. The reason for this could be the limited residence time in the column. When conducting the batch experiments, the solubilization of CA occurred 24 hours before the subsequent phase separation. On the other hand, at the continuous process, the solubilization and phase separation took place simultaneously, with a residence time of the feed of approx. one hour. In comparison, Ingram et al. were able to extract vanillin in the continuous cloud point extraction system with a yield of 76.7 wt% at 40 °C [43]. However, the feed flow was lower and the residence time in the column higher due to the lower applied column capacity. Further, the authors were able to use an increased agitation of 100 rpm, which was not possible in this work due to the stress limit. The different operating conditions could be the reason for the significantly reduced mass transfer, and thus for the reduced yield. The productivity, on the other hand, was enhanced in comparison to the batch experiment and previous works [43]. Nevertheless, it was possible to develop a quadratic model, which provided valid results for the estimation of the yield of the continuous cloud point extraction.
6.1.4 PRODUCTIVITY OPTIMIZATION
In this chapter, the results for the achieved productivity of the continuous CPE of CA are discussed. The productivity was calculated according to Equation 2-15 for all conducted experiments. Hence, the response within the system varied between 34.8 and 113.6 (see table in appendix A 18). The fit of four different models was investigated for the productivity. As for the yield, the different model statistics are presented in appendix A 20.In order to model the productivity, a linear model was
recommended by Design-Expert. The r-squared value of the quadratic model was with 0.920 slightly higher than the r-squared value of the linear model with 0.903.
However, the linear model excelled in a lower standard deviation, PRESS and especially in a much better predicted R-squared value. Overall, the linear model had the better quality and was chosen as the model for the productivity. Although the cubic model had the highest R-squared, it was aliased and cannot be applied.
The “Sequential Model Sum of Squares” and “Lack of fit”-tests confirm the quality of the linear model for the productivity and are listed in appendix A 20 as well.
Hence, s linear equation was developed to model the productivity (Equation 6-3).
5ˆ‰ = 37.3 ∙ ? − 0.1 ∙ − 9.0 ∙ ν + 90.7