High Yield Dihydroxystearic Acid (DHSA) Based on Kinetic Model from Epoxidized Palm Oil

In recent years, studies related to the epoxidation of fatty acids have garnered much interest due to the rising demand for eco-friendly epoxides derived from vegetable oils. From the epoxidation reaction, there is a side reaction involving epoxide and water. This reaction produces a by-product – dihydroxystearic acid (C18H36O4, DHSA). DHSA is one of the chemical precursors in the production of cosmetic products. Therefore, a kinetic model was developed to determine the optimised epoxidation process and concentration of DHSA, where each of the reactions was identified. The kinetic rate, k parameters obtained were: k11 = 6.6442, k12 = 11.0185, k21 = 0.1026 for epoxidation palm oleic acid, and k41 = 0.0021, k51 = 0.0142 in degradation process. The minimum error of the simulation was 0.0937. In addition, DHSA yield optimisation was done through Taguchi method, and the optimum conditions obtained were H2O2/oleic acid – OA unsaturation molar ratio 1 : 1 (level 2), formic acid – FA/OA unsaturation molar ratio 0.5 : 1 (level 1), temperature 35 °C (level 1), and agitation speed 100 rpm (level 1). A high yield of DHSA can be achieved under these conditions.


Introduction
The growth in vegetable oil demand has increased compared to the petroleum-based polymer. 1 Since petroleum causes environmental pollution concerns, vegetable oil has become an alternative in the production of the epoxide. In the epoxidation reaction of vegetable oil, oxirane ring-opening, known as epoxide ring degradation, will occur. 2 The oxirane ring-opening depletes the yield and can cause high peroxide values of epoxidized vegetable oils, so the opening needs to be minimised. 3 The commercial production of palm oil is quite high compared to that of other vegetable oils. 4 The low cost of palm oil makes studies on the synthesis and oxirane cleavage of palm oil more practical and economical. 5 Epoxidized palm oil (EPO) can be obtained by reacting to the double bond of oil with peroxy acid that is generated in situ by reacting with concentrated hydrogen peroxide (H 2 O 2 ) and formic acid (CH 2 O 2 , FA) in the presence of mineral salt as a catalyst. 2 The EPO can be used as a raw material in the manufacture of a wide range of products, such as paint, plastic, and adhesives. Besides, EPO is obtained from renewable resources, and can be regarded as biodegradable and non-toxic. Hence, it is suitable in replacing petroleum, since petroleum is toxic and harmful to the environment.
In this study, the oxirane-ring degradation of epoxidation palm oil was determined through MATLAB simulation. Ode45 is one of the tools in MATLAB designed to work with differential equations. The benefit of this tool is its ability to determine the reaction rate of the epoxidation and degradation of EPO. Nevertheless, the epoxy that reacts with water produces DHSA. The physical appearance of DHSA is white and tasteless with an acid odour, and is non-irritating to the skin. 6 It is suitable for cosmetic ingredients. As the cosmetic industry is gradually increasing, it is suitable to produce a large amount of DHSA. 7 However, literature on the optimisation of DHSA production is still lacking and has only a few references. Thus, in this paper, the optimisation of DHSA production will be studied by the Taguchi method, and by referring the data from the simulation.
To determine the rate coefficient numerically, parametric studies were conducted. There were two computing processes involved, which solved a set of differential equations (Eqs. 6-14) numerically, and computed the errors between the experimental and the simulation. The Ode45 function of MATLAB was used to solve the differential equation by numerical integration using the fourth-order Runge-Kutta method. The parameter values were predicted using a genetic algorithm in MATLAB software. The algorithm can search for the optimal value of the process variable. 8 The reliability of the parameters was verified by minimising the error, e, between the experiment and the simulation, as shown in Fig. 1.

Optimisation procedure
In recent research, the design of experiment (DOE) had been applied by implementing the Taguchi method ap-proach. The method was developed by Taguchi and Kinoshi to enhance the process parameters and increase the quality of components that were industrial. 9 This method employs a set of orthogonal arrays; with reaction parameters, optimisation is performed using the lowest possible number of experimental runs. 10 A few parameters, such as reaction temperature, FA to OA unsaturation molar ratio, H 2 O 2 to OA unsaturation molar ratio, and agitation speed can affect the reaction of epoxidation. All these parameters were explored with the diversity of levels, as shown in Table 1. Therefore, the optimal reaction conditions of these vital reaction temperatures were analysed based on a DOE approach. The diversity of factors was studied by crossing the orthogonal array of the control parameters. The result obtained was further analysed manually using the signal to noise (S/N) ratio and analysis of variance (ANOVA). The optimum combination of reaction conditions projected by the Taguchi method was then tested and validated by running a confirmation reaction at the optimal predicted reaction conditions.  3 Results and discussion 3.1 Reaction rate of DHSA production Kinetic model for catalytic epoxidation of palm oleic acid based on palm oil (PO) was developed by MATLAB simulation. The kinetic data for the epoxidation and degradation of palm oil corresponded to the initial concentration.
The Genetic Algorithm (GA) method was used to fit the experimental data and the Runge-Kutta fourth-order method was applied using the Ode45 tool to solve the system of differential equations. There were 27 experiments run in the simulation, in order to ensure the optimal value of epoxidation. The experimental data was obtained from the previous experiments, and the simulation was based on that data. The initial concentration of formic acid (FA), hydrogen peroxide (H 2 O 2 ), and oleic acid (OA) from previous experimental data was chosen as a reference to find the kinetic rate constant, k. On the other hand, the kinetic rate was used to determine the concentration of DHSA in oxirane cleavage. This occurred when the epoxide reacted with water. It corresponded to the objective of this study.

Optimisation of DHSA through Taguchi method
To determine the optimum reaction conditions for the production of DHSA, the Taguchi method was used, as presented in Table 3. Signal to noise (S/N) ratio is an analytical medium used to evaluate the most influential level of each factor that contributes to the optimum response value. L-27 orthogonal array with four factors and three levels for each factor was selected. The Taguchi orthogonal array experimental design is presented in Table 3, where the estimated concentration of DHSA was obtained from the simulation. The "larger-the-better" S/N ratio indicated better performances regardless of the performance characteristics. According to the previous research, 6 the optimum level for all parameters would be the level with the greatest S/N ratio. The 27 experimental runs based on Taguchi method suggested that the optimum DHSA was obtained at H 2 O 2 /OA unsaturation molar ratio of 1 : 1 (level 2), FA/OA unsaturation molar ratio 0.5 : 1 (level 1), temperature of 35 °C (level 1), and agitation speed of 100 rpm (level 1). These results were plotted for each parameter in Fig. 2.