Second order optimal rotatable design in four dimensions and its application in optimization of bioethanol yield using pineapple peels.

Abstract

An eco-friendly bio-ethanol from biomass waste is an alternative to petroleum products which are becoming scarce due to increased demand and depletion of source besides their environmental pollution effects. Most studies on optimization of process variables using Response Surface Methodology exploit Central Composite Design yet other designs exist. Optimal designs have fewer trials employed with the aim of obtaining efficient designs for fitting reduced quadratic or higher order models. Efficiency as discriminating criteria allows comparison between any design and the best design. This study sought to apply a second order optimal rotatable design in four dimensions to the ethanol production through fermentation of pineapples peels using yeast. The D-, A-, E- and T-Optimal values of the general design with their corresponding relative efficiencies were obtained. The design was used to carry out an experiment in order to determine the effects of time, pH, temperature and concentration of substrate on ethanol yield during fermentation of pineapple peels. Finally the optimum settings of time, temperature, initial pH and substrate concentration that led to optimal yield of ethanol were determined. The coded values of a design constructed by Das and Narasimham were used to obtain a design matrix X which was then used to construct a moment matrix X / X. The moment matrix was then utilized to determine the optimal values and the required efficiencies. The ratio of the optimal value of the general design to the corresponding optimal variance of the optimal design was used as a measure of relative efficiency of the design. A second order model was fit into experimental data in order to study the effects of the process variables, and the optimization through response surface plots and analytical method. The D-, A-, E- and T-Optimal values were found to be 0.6796529, 0.04104631, 0.002856958 and 1.135448 respectively, and the corresponding relative efficiencies were 98%,71.7%, 87.5% and 1% respectively. Normal probability plots and R-squared of 0.95 and Adjusted R-squared of 0.911 for E-optimal (most efficient with only 32 runs) design indicated the model fit the data well. An optimal yield of 12.35g/L of ethanol realized after 54.35 hours at 4.96 levels of pH, 34.67 0 C temperature and 28.03g/L of substrate concentration translated to 0.441g of ethanol per gram of substrate (roughly 86% of the theoretical yield of 0.511g ethanol per g of substrate) which compares well with findings from similar studies. The yield by E- optimal design was slightly lower than that of general design by 0.040g/L. The design was found reliable in modeling, optimizing and studying effects of the factors to the processes of fermentation of pineapples peels for ethanol production. A comparison of these results and the result of rotatable design with four factors constructed using balanced incomplete block design when replications are more than three the number of times pairs of treatments occur together in the design is suggested in studying the effects of the four process variables on ethanol yield and optimization of the process using pineapple peels as feedstock. Study established the factor settings for optimal ethanol yield from pineapple peels. These wastes if not properly disposed can be a major source of pollution. A cheaper fuel than fossil fuel is provided while managing wastes.