Design of Experiments for Process Optimization of the Direct Wacker-Type Oxidation of 1-Decene to n-Decanal
Abstract
:1. Introduction
Reaction System
2. Results and Calculations
2.1. Original Conditions
2.2. Seven-Factor DoE Results
2.3. Results of Optimization
2.4. Validation Experiments
3. Methodology
3.1. Materials
3.2. Experimental Setup and Analysis for the Reaction of 1-Decene to n-Decanal
3.3. Initial DoE
3.4. Optimization
4. Conclusions and Outlook
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Glossary
p-value | The p-value is a measure that helps determine the statistical significance of the observed results in a hypothesis test. It represents the probability of obtaining results as extreme as the observed results, assuming that the null hypothesis is true. In statistical analysis, if the p-value is less than a predetermined significance level (commonly 0.05), the null hypothesis is rejected, indicating that the results are statistically significant. A lower p-value suggests stronger evidence against the null hypothesis and greater statistical significance. |
VIF (Variance Inflation Factor) | The VIF is a measure used to assess multicollinearity among independent variables in a regression analysis. Multicollinearity occurs when independent variables in a regression model are highly correlated with each other. The VIF quantifies how much the variance of an estimated regression coefficient is inflated due to multicollinearity. A VIF value of 1 indicates no multicollinearity, while values greater than 5 or 10 are often considered indicative of multicollinearity. High VIF values suggest that the corresponding independent variable may be redundant or highly correlated with other variables in the model, which can affect the interpretation of regression coefficients and the overall reliability of the regression analysis. |
Effect | The effect, also known as the effect size, represents the estimated impact of an independent variable (factor) on the dependent variable (response) in a statistical model. It indicates the magnitude of the change in the dependent variable for a one-unit change in the independent variable, while holding all other variables constant. In the context of regression analysis, the effect size is typically measured by the coefficient (Coef) associated with each independent variable. |
Coef | The coefficient, also known as the estimated coefficient or parameter estimate, represents the estimated effect size of an independent variable on the dependent variable. It indicates the change in the dependent variable for a one-unit change in the independent variable, while holding other variables constant. |
SE Coef | The standard error of the coefficient measures the variability or uncertainty in the estimated coefficient. It represents the standard deviation of the coefficient’s sampling distribution. A smaller standard error suggests more precise estimates. |
t-value | The t-value is the ratio of the estimated coefficient to its standard error. It indicates the number of standard deviations that the coefficient estimate is away from zero. A larger t-value suggests a more statistically significant coefficient. Typically, t-values are used to assess whether a coefficient is significantly different from zero. |
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Term | Effect | Coef. | SE Coef. | t-Value | p-Value | VIF |
---|---|---|---|---|---|---|
Constant | 0.01786 | 0.00210 | 8.49 | 0.000 | ||
Substrate amount | −0.02920 | −0.01460 | 0.00210 | −6.94 | 0.000 | 1.00 |
Reaction temperature | 0.00914 | 0.00457 | 0.00210 | 2.17 | 0.040 | 1.00 |
Catalyst amount | 0.02024 | 0.01012 | 0.00210 | 4.81 | 0.000 | 1.00 |
Co-catalyst amount | 0.00498 | 0.00249 | 0.00210 | 1.18 | 0.249 | 1.00 |
Reaction time | 0.00141 | 0.00070 | 0.00210 | 0.33 | 0.741 | 1.00 |
Water content | −0.01899 | −0.00950 | 0.00210 | −4.51 | 0.000 | 1.00 |
Substrate amount*Catalyst amount | −0.01621 | −0.00811 | 0.00210 | −3.85 | 0.001 | 1.00 |
Substrate amount*Water content | 0.01439 | 0.00720 | 0.00210 | 3.42 | 0.002 | 1.00 |
Reaction temperature*Reaction time | −0.01108 | −0.00554 | 0.00210 | −2.63 | 0.015 | 1.00 |
Catalyst amount*Co-catalyst amount | 0.01136 | 0.00568 | 0.00210 | 2.70 | 0.013 | 1.00 |
Central points | −0.00137 | 0.00631 | −0.22 | 0.829 | 1.00 |
Term | Effect | Coef. | SE Coef. | t-Value | p-Value | VIF |
---|---|---|---|---|---|---|
Constant | 0.39393 | 0.00885 | 44.49 | 0.000 | ||
Substrate amount | −0.13843 | −0.06921 | 0.00885 | −7.82 | 0.000 | 1.00 |
Catalyst amount | 0.10872 | 0.05436 | 0.00885 | 6.14 | 0.000 | 1.00 |
Reaction time | 0.04246 | 0.02123 | 0.00885 | 2.40 | 0.024 | 1.00 |
Water content | 0.06036 | 0.03018 | 0.00885 | 3.41 | 0.002 | 1.00 |
Substrate amount*Catalyst amount | −0.08659 | −0.04330 | 0.00885 | −4.89 | 0.000 | 1.00 |
Substrate amount*Water content | −0.04622 | −0.02311 | 0.00885 | −2.61 | 0.015 | 1.00 |
Catalyst amount*Water content | 0.05650 | 0.02825 | 0.00885 | 3.19 | 0.004 | 1.00 |
Central points | 0.0012 | 0.0266 | 0.05 | 0.963 | 1.00 |
Term | Effect | Coef. | SE Coef. | t-Value | p-Value | VIF |
---|---|---|---|---|---|---|
Constant | 0.07691 | 0.00103 | 72.07 | 0.000 | ||
Reaction temperature | −0.01486 | −0.00743 | 0.00103 | −6.96 | 0.000 | 1.00 |
Catalyst amount | 0.00884 | 0.00442 | 0.00103 | 4.14 | 0.004 | 1.00 |
Co-catalyst amount | 0.01273 | 0.00637 | 0.00103 | 5.97 | 0.000 | 1.00 |
Central points | 0.00217 | 0.00178 | 1.17 | 0.262 | 1.00 |
Term | Effect | Coef. | SE Coef. | t-Value | p-Value | VIF |
---|---|---|---|---|---|---|
Constant | 0.4946 | 0.0127 | 39.03 | 0.000 | ||
Catalyst amount | 0.1168 | 0.0584 | 0.0127 | 4.61 | 0.002 | 1.00 |
Co-catalyst amount | 0.0652 | 0.0326 | 0.0127 | 2.57 | 0.033 | 1.00 |
Central points | 0.0385 | 0.0220 | 1.75 | 0.118 | 1.00 |
Factors: | 7 | Basic experimental plan: | 7; 32 | Resolution: | IV |
Runs: | 36 | Replications: | 1 | Fraction: | ¼ |
Blocks: | 1 | Central points (total): | 4 |
Factors | Steps | ||
---|---|---|---|
(−) | Origin | (+) | |
(A) Substrate amount (mL) | 0.5 | 2.25 | 4 |
(B) Reaction temperature (°C) | 30 | 55 | 80 |
(C) Catalyst amount i (mg) | 10 | 30 | 50 |
(D) Co-catalyst amount i (mg) | 10 | 35 | 60 |
(E) Homogenization temperature (°C) | 30 | 55 | 80 |
(F) Reaction time (h) | 0.5 | 12.25 | 24 |
(G) Water content (mL) | 0.001 | 0.25 | 0.5 |
Factors: | 3 | Basic experimental plan: | 3; 8 |
Runs: | 12 | Replications: | 1 |
Blocks: | 1 | Central points (total): | 4 |
Resolution | IV | Fraction | ¼ |
Factors | Steps | ||
---|---|---|---|
(−) | Origin | (+) | |
(B) Reaction temperature (°C) | 70 | 85 | 100 |
(C) Catalyst amount (mg) | 50 (4.9 eq) | 65 (6.4 eq) | 80 (8 eq) |
(D) Co-catalyst amount (mg) | 50 (14 eq) | 65 (18 eq) | 80 (23 eq) |
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Bouveyron, T.; Bratenberg, P.; Bell, P.; Eisenacher, M. Design of Experiments for Process Optimization of the Direct Wacker-Type Oxidation of 1-Decene to n-Decanal. Catalysts 2024, 14, 360. https://doi.org/10.3390/catal14060360
Bouveyron T, Bratenberg P, Bell P, Eisenacher M. Design of Experiments for Process Optimization of the Direct Wacker-Type Oxidation of 1-Decene to n-Decanal. Catalysts. 2024; 14(6):360. https://doi.org/10.3390/catal14060360
Chicago/Turabian StyleBouveyron, Thomas, Patricia Bratenberg, Peter Bell, and Matthias Eisenacher. 2024. "Design of Experiments for Process Optimization of the Direct Wacker-Type Oxidation of 1-Decene to n-Decanal" Catalysts 14, no. 6: 360. https://doi.org/10.3390/catal14060360
APA StyleBouveyron, T., Bratenberg, P., Bell, P., & Eisenacher, M. (2024). Design of Experiments for Process Optimization of the Direct Wacker-Type Oxidation of 1-Decene to n-Decanal. Catalysts, 14(6), 360. https://doi.org/10.3390/catal14060360