CAPITULO III - Planteamiento del Problema
4. Se configuró la sesión de chat
It is possible to try and increase the yield of ketone 4.3 by increasing the limits for acetone eq and NaOH flow rate, however it is worth considering if the increase in reagent eq would be worth the financial and material cost, especially for reaction scale up. Especially as doubling the eq of 4.2 only resulted in an increase of 1% yield. Although yield was the target function for the optimisations so far, previous research has shown how yield is not the best target and other metrics such as E-factor, process mass intensity (PMI), material cost and reaction productivity can be a better target for an efficient manufacturing process.12, 17, 18, 27, 181 The advantage of a statistical model means that additional responses can be calculated and new models fitted without carrying out further experiments, whereas algorithm optimisations need new experiments to find new optima.
Therefore, metric analyses were carried out by calculating the values for different metrics from the experiments used to fit the existing models. The new metrics were PMI, a measure of the total chemical resource per mass unit
-0.2 0 0.2 0.4 0.6 0.8 1 1 2 4 Compound number
Summary of Fit
R2 - original R2 - extended Q2 - original Q2 - extended Validity - original Validity - extended Reproducability - original Reproducability - extended
𝑃𝑀𝐼 = ∑ 𝑄𝑚(𝑖)
𝑛 𝑖=1
𝑄𝑛(𝟒. 𝟏) 𝑌 𝑀𝑊(𝟒. 𝟑)
(4.25)
where 𝑄𝑚 is mass flow rate, 𝑄𝑛 is molar flow rate, 𝑌 is yield and 𝑀𝑊 is molecular weight;182
Space time yield (STY), the mass of product per unit volume per unit time
𝑆𝑇𝑌 =𝑄𝑛(𝟏)𝑀𝑊(𝟑)
𝑉 (4.26)
where 𝑉 is reactor volume; and material cost per mass unit of ketone 4.3 produced 𝐶𝑜𝑠𝑡 = ∑ 𝑄𝑣(𝑖) £(𝑖)𝐶0(𝑖)
𝑛 𝑖=1
𝑄𝑛(𝟒. 𝟏) 𝑌 𝑀𝑊(𝟒. 𝟑)
(4.27)
Figure 4.13 Summary of fit for the new metrics. Green - 𝑹𝟐, blue - 𝑸𝟐, yellow – validity, turquoise – reproducibility.
New models for these metrics were fitted using MLR with R2 values of 0.93 (PMI), 0.92 (STY) and 0.90 (cost); and Q2 values of 0.86 (PMI), 0.86 (STY) and 0.83 (cost). Each model also had high reproducibility (> 0.9) and no evidence of lack of fit (Figure 4.13).
Table 4.6 Effect of different metrics on the product composition of compounds 1, 3 and 4
Metric target 4.1 / % 4.3 / % 4.4 / % PMI / kg kg-1 STY / g L-1 h-1 Cost / £ kg-1 Yield 3.22 65.62 3.01 18.48 633.20 33.45 PMI 4.54 47.90 6.02 13.81 614.36 27.92 STY 3.06 62.15 4.45 19.11 872.69 34.50 Cost 4.15 58.81 4.13 14.30 798.39 26.72 Yield PMIa 4.28 55.32 4.70 13.99 729.52 26.91 PMI Costb 2.96 64.81 3.66 16.35 769.93 29.57
The first column shows the metric target, responses are shown in the rows. Maximized values are highlighted in bold, minimized values and highlighted in italics. Unformatted values display the models’ predicted values. amaximize the yield of 3, minimize the PMI; bminimize both PMI and cost.
Table 4.6 shows how the model responses change with optimum conditions for different metric targets. The maximum yield has poor responses for PMI, STY and cost, showing that high yielding reactions are wasteful and unproductive. The optimum response for PMI is the least productive and predicts the lowest yield of ketone 4.3. There is good correlation between the responses of PMI and cost for all the metric targets. This should be expected as they are calculated by the ratio of product to substrates and reagents. The raw material cost calculation aims to put bias on reducing the excess of expensive material, although this reaction example is perhaps not the best to show this as all substrates are relatively inexpensive. It should be noted, however, that lower cost promotes a higher yield rather than lower PMI, indicating that raw material cost could be the most important metric, assuming that a cheaper reagent does not increase the complexity, and therefore cost, of work-up and purification.
The conditions for the optimal responses are shown in Table 4.7. The flow rate of 4.2 is towards its upper limits for every target which reduces the residence time, therefore increasing the reaction productivity (STY). The acetone equivalents are generally lower than the self-optimisation thus limiting the reagent waste (PMI and cost). Strict temperature control is required to both maintain the high yields of 4.3 and minimise polymer formation.
Table 4.7 Predicted conditions for the optimum responses to different metric targets
Metric target 4.1 flow rate / mmol min-1
NaOH flow rate / mmol min-1 4.2 / mol eq Temperature / °C Yield 0.741 0.112 12.4 47.2 PMI 0.846 0.044 6.0 44.1 STY 1.000 0.150 13.9 42.2 Cost 0.986 0.067 9.2 47.1 Yield PMIa 0.915 0.055 7.5 45.5 PMI Costb 0.998 0.096 10.5 46.8
amaximize the yield of 3, minimize the PMI; bminimize both PMI and cost.
4.4 Conclusions
The yield of ketone 4.3 in a Claisen-Schmidt condensation was self-optimised using an automated flow reactor equipped with an at-line HPLC system and feedback loop with SNOBFIT algorithm. With the data obtained from the self-optimisation, response surface models were fitted to the main compounds of interest in the reaction (4.1, 4.3 and 4.4). After analysis of the models and self-optimisation data, it was decided to carry out further optimisations in a larger chemical space. The second experimental optimisation improved upon the yield of 4.3 and the increased correlation between the new optimum and surrounding experimental points, provided a greater range of conditions at which optimal yields could be obtained. The subsequent statistical models of the extended optimisation predicted similar optimal conditions and exhibited an overall improved model fit.
It should be noted that the choice of algorithm in the initial self-optimisation step is critical to achieving a good fit to the RSM. The simplex algorithm and modifications thereof,137-139, 183 is a popular choice in self-optimising systems.12, 14-17, 23, 25, 27 However, during its operation it will only execute experiments with an improved predicted response therefore not providing any information about experimental space that does not lie between the initial and optimum points. The execution of random conditions and exploration of free space offered by SNOBFIT provides a scatter of data, without which the additional response surface fitting would not be possible. In this study, the increased robustness resulting from the additional experimental points around the optimum would also have been forfeited with a simplex approach.
Because the experimental optimum was identified at the edge of the initial optimisation space, prediction of the optimum via the statistical model was compromised due to its inability to fit a polynomial to changes induced by the cliff edge. The experimental self-optimisation, however, freely explored the edge of the optimisation space to identify the point of maximum yield. For these reasons, it can be concluded that self-optimisation is the superior technique for chemical process optimisation. However, when used in tandem the subsequent response fitting of self- optimisation data can predict the responses of different species and even alternate metrics without additional experimentation. It therefore follows that self-optimisation and DoE can be interdependent, rather than conflicting techniques, which can combine to provide a wealth of information in the scale-up and process optimisation of chemical systems.