Krunal A. Shah A, Jigisha K. Parikh B, Kalpana C. Maheria A,*

Optimization studies and chemical kinetics of silica sulfuric acid catalyzed biodiesel synthesis from waste cooking oil

Krunal A. Shah a, Jigisha K. Parikh b, Kalpana C. Maheria a,*

*Corresponding author:

Dr. Kalpana C. Maheria, Assistant Professor, Applied Chemistry Department, SardarVallabhbhai National Institute of Technology, Ichchhanath, Surat, Gujarat, India – 395007.

Contact No.: 0261-2201793

E-mail:

SUPPLEMENTARY INFORMATION

Taguchi method

The Taguchi method, a fractional factorial design approach, is an important technique to determine theoptimal and robust product or process characteristics with minimum sensitivity to noise. Using theTaguchi method, a systematic and efficient plan for performing experiments can be formulated andquantitative information can be extracted with fewer experiments. The Taguchi method thus helps toprovide useful information with reduced time, materials and cost.

The method was developed by Genichi Taguchi as an important tool to find out the optimal and robust product or process characteristics having minimized sensitivity to noises. It gives a systematic approach to optimize the design for performances, quality and cost. This method is different from other experimental design methods in two ways:

1. Parameters affecting the process can be designated as controlling and non-controlling.

2. This method can be used to investigate the parameters for more than two levels.

The Taguchi method for optimizing a process can be performed in following steps:

To select process parameters to be evaluated: It is usual that many of the parameters can affect the process. However, only a few of them are truly important or active. In transesterification of RCSO, the major factors selected for the purpose of optimization were oil to methanol ratio, reaction temperature, reaction time and catalyst dosage.
To determine the number of parameter levels for the process: four level of parameters viz. maximum, minimum and intermediate were taken for experimental design.
To select the appropriate orthogonal array and assignment of process parameters to the orthogonal array: The orthogonal array is the shortest possible matrix of combinations. In orthogonal array, all the parameters are varied at the same time and their effects studied simultaneously to determine which factors have more or less influence. To analyze the significance of four factors at four different levels, a full factorial experimentation would require 44 (=256) experiments (table 2) to find the influencing parameters, while the Taguchi design involves only sixteen experiments using an OA L16 (44).
To conduct the experiments based on the arrangement of the orthogonal array.
To identify and calculate the performance characteristic i.e. signals to noise ratio (S/N ratio):The S/N ratio is simply a quality indicator by which the effect of changing a particular process parameter on the performance of the process is evaluated. Usually, there are three categories of performance characteristics in the analysis of the S/N ratio: ‘smaller is better,’ ‘nominal is better’ and ‘higher is better’. The S/N ratio for each level of the process parameters can be computed based on the S/N analysis. In present experiments, aim is to maximize the yield, hence, ‘higher is better’ characteristic was selected in this study for which equation is given as:

(S1)

Where, n is the number of repetition done for a given experiment and yi is the yield of ith experiment.

To analyze the experimental result using the performance characteristic: The performance characteristics were chosen as the optimization criteria i.e. to select the optimal levels of process parameters. After calculating the S/N ratios at each level for various parameters, the optimum level, that is the highest S/N ratio among all levels of the parameters, can be determined.
Analysis of variance (ANOVA):ANOVA is performed to see which process parameters are statistically significant. For this, total variation, ST, and individual variations, SA, are to be calculated. Total variation gives the total magnitude of variations of the experimental data and individual variation signifies the contribution of individual factor to the final response variable and their equation can be written as:

(S2)

Where, n is the total number of experiments and i denotes value at ith experiment.

(S3)

Where A is the factor selected for the study, i is the level number of the specified factor A, k is the repetition of each level of the factor A and Ai is the sum of S/N ratio involving this factor and level i.

The relation between total variation and individual variation is presented by the equation:

(S4)

Where A is the factor for given set of experiment, n denotes number of factors involved and Se denotes variation due to unaccounted factors.

Variance (V) is defined as the individual variation divided by the degree of freedom (D) of that factor.

(S5)

Degree of freedom is associated with each piece of information that is estimated from the data or it is the number of independent comparisons that can be made in the data.

F-test is a qualitative analytical tool to see which process parameters have a significant effect on the process. Usually, the larger the F-value, the greater is the effect on the process due to the change of the process parameter.

F- value can be found by the equation:

(S6)

The percentage contribution of each factor (CF) is useful for quantitative evaluation as given by the following equation:

To verify the optimal process parameters through the confirmation experiment.

Figure 1S: Reaction mechanism for SSA catalyzed transesterification of WCO