Process optimization and simulation of biodiesel synthesis from waste cooking oil through supercritical transesterification reaction without catalyst

This study reports optimization and simulation of biodiesel synthesis from waste cooking oil through supercritical transesterification reaction without the use of any catalyst. Although the catalyst enhances the reaction rate but due to the presence of water contents in waste cooking oil, the use of catalyst could cause a negative impact on the biodiesel yield. The transesterification reaction without catalyst also offers the advantage of the reduction of pretreatment cost. This study comprises of two steps; first step involves the development and validation of process simulation scheme. The second step involves the optimization using Response Surface Methodology. Face-centered central composite design of experiments is used for experimental matrix development and subsequent statistical analysis of the results. Analysis of variance is employed for optimization purpose. In addition, a sensitivity study of the process parameters including pressure, temperature, and molar ration of oil-to-methanol was conducted. The statistical analysis reveals that temperature is the most influential process parameter as compared to pressure and oil-to-methanol molar ratio. The optimization study results in the maximum biodiesel yield (94.16%) at an optimum temperature of 274.8 °C, 7.02 bar pressure, and an oil-to-methanol molar ratio of 12.43.


Introduction
The ever-increasing energy demand across the world results in the gradual depletion of fossil fuels, which is mainly driven by wide motorization and industrial activities that use fossil fuels as a primary energy source. The extensive use of fossil fuels causes severe environmental issues such as global warming, ozone layer depletion due to stratospheric pollution, and rapid climate changes [1][2][3]. It is forecast that the existing production systems will not fulfill global energy demand due to the depletion of fossil fuels, which may lead to exponential prices of fossil fuels [4,5]. These issues require immediate attention to find alternative fuels with a minimal negative environmental impact [6,7].
Biodiesel is an attractive alternative to address the aforementioned issues. It has gained much attention in the past decade because it is biodegradable, green, and renewable [8,9]. Biodiesel can be used in its pure  form or blended with conventional diesel. In its pure form, it does not have a negative impact on the performance of engines [10,11]. Biodiesel is sulfur-free, and its combustion results in relatively less harmful environmental emissions, etc. The recent Paris Accord, an international treaty on climate change, and similar promising policies laid down by the member countries of the Organization for Economic Co-operation and Development are likely to result in a steady growth in biofuels production that has already increased by 14% in recent years [12]. A comparative analysis based on statistical data from 2007 to 2016 reveals a 2.5% rise in the global use of biofuels in transportation, with more than 314.5 million barrels of ethanol and 56.6 million barrels of biodiesel used as transport fuels [13]. Biodiesel is usually synthesized both from edible and non-edible vegetable oils, waste cooking oil, animal fats, and algal lipids by the transesterification of triglyceride feedstock [14,15]. Triglyceride reacts with methanol in the presence of a catalyst to produce biodiesel and glycerol (by-product) as shown in figure 1 [1].
An excess amount of methanol can be used for higher yield or shifting the reaction to the right side [16]. Both acid and alkali can be used as catalysts, but alkali usually performs better, and most industries use it to produce biodiesel. Although alkali-catalyzed transesterification offers several advantages, but the process shows some limitations in the presence of water contents and free fatty acids in the feedstock. The reaction between free fatty acid and alkaline catalyst produces soaps and water.
The water contents and free fatty acids must be removed from feedstock before the transesterification reaction. Most industries use an esterification reaction in which free fatty acid reacts with methanol in the presence of sulfuric acid. This pretreatment technique is expensive, thereby increasing the capital cost of biodiesel production. The presence of water and free fatty acid in used cooking oil is a major cause that limits its use as a feedstock for biodiesel production. An alternative technique, the supercritical methanol method, can overcome the aforementioned issues for biodiesel production [17]. The method does not require a catalyst, and soap is not formed due to the presence of water, fatty acids, and free fatty acids. In addition, esterification and transesterification occur simultaneously in this method. The comparison of biodiesel production with and without a catalyst is given in table 1.
Several studies report using supercritical conditions to synthesize biodiesel [21][22][23]. Singh et al in 2018, conducted an optimization study using response surface methodology (RSM) and genetic algorithm to synthesize biodiesel from Jojoba oil using supercritical methanol. They used a 1:30 oil to methanol ratio at 287 • C and 123 bar for 23 min reaction time [24]. Marulanda et al reported biodiesel synthesis through supercritical conditions using low-cost lipids as feedstock. The temperature range was selected to 300 • C-400 • C while the pressure was up to 41 Mpa. The molar ratio was set to be 3:1 and 6:1, and the reaction time was 2-6 min [25].
Another study reports biodiesel synthesis via supercritical methanol and candlenut oil at 115 bar and 285 • C with 1:15 and 1:30 mole ratios of oil-to-methanol and 22 min reaction time [26].
The literature indicates that several researchers tried biodiesel production without a catalyst due to its attractive advantages. The method is promising since it offsets the disadvantages of using a catalyst that eventually reduces the capital cost. However, the reaction occurs at a very high temperature and pressure, drastically increasing the energy requirements. An accurate energy assessment requires substantial data, which can be generated using experimental or simulation studies. The high-temperature-pressure experimentation has several limitations that include cost and operational challenges; therefore, an accurate simulation can provide a good estimation of energy requirements. There is less research has been conducted on the simulation of biodiesel synthesis. Therefore, a detailed simulation and optimization study is required to minimize the energy requirements.
Thus the present study scope includes the simulation and optimization of process parameters to maximize the biodiesel yield. The first part of the study will consist of choosing the appropriate thermodynamic equation of state (EOS) and developing a simulation strategy for biodiesel production from waste cooking oil without any catalyst through a supercritical transesterification reaction. The second part deals with optimizing process parameters to maximize the biodiesel yield.

Materials and methods
The simulation and optimization are conducted for biodiesel production employing the used cooking oil that is a feedstock taken from domestic sources. Since Triolein is the most dominant oil, it is selected as the base component. Other components include methanol, m-oleate (biodiesel), and glycerol as a by-product. The non-random two liquid EOS is used for calculations. The simulation schematic diagram is illustrated in figure 2.

Design of experiment (DoE)
The response is dependent upon several input parameters, so assessing the cause of changes in the outcome is quite complex. Therefore, DoE was employed to conduct a set of experiments. We chose the face-centered central composite design (FCCD) to evaluate the interactive effect of pressure, temperature, and a mole ratio of oil to methanol on the response objective (% biodiesel yield). The FCCD is a type of central composite design that has an alpha value equal to unity. The FCCD comprises six center points, six face-centered points, and eight corner points that collectively constitute the experimental matrix, as shown in table 2. We performed the experiments as per the randomized combination of process parameters, as depicted in table 2. For the investigation and better visualization of the interactive effect of process parameters on response objective, we employed RSM. The RSM is a modeling and optimization technique that is used to investigate the relationship in the form of empirical correlations between the process parameters and response objectives [27,28]. After a due statistical analysis, it evaluates the most influential and the least influential process parameter and the impact thereof on the response objective. This makes it a robust technique for empirical model development and process optimization [29]. The 3D response surfaces developed via RSM provide effective illustrations to visualize the effect of interacting process parameters on the response objective. The empirical modeling is portrayed via the development of second-order polynomial equations. A generalized form of the second-order polynomial equation generated in RSM for biodiesel yield is given as equation (1). where; In this study, the RSM was performed for the process parameters, including temperature (A), pressure (B), and oil-to-methanol molar ratio (C). The yield of biodiesel is the response objective in this case.

Results and discussion
The statistical results achieved via analysis of variance (ANOVA) pertaining to the empirical modeling of biodiesel yield as a function of different interactions of the process parameters are illustrated in table 3. An F-value of 60.90 and the corresponding p-value less than 0.0001 indicates that the developed model is statistically significant with the desired confidence level of 95%. Therefore, the model can be used for the sake of optimization and prediction. All the process parameters appear to be statistically significant because  of a p-value lower than 0.05. Temperature is found to be the most influential process parameter because of its lowest p-value (<0.0001). Similarly, the interaction of temperature and oil-to-methanol ratio (AC) appears to be more influential (p-value = 0.0033) than the interaction of temperature and pressure, AB (p-value = 0.0077), and the interaction of pressure and oil-to-methanol mole ratio, BC (p-value = 0.8866). From amongst the interactive process parameters under consideration, it is observed that BC is not statistically significant. The ANOVA yields a second-order quadratic polynomial regression model that correlates the response objective (% yield of biodiesel) with process parameters and various interactions thereof (temperature, pressure, and oil to methanol ratio), as depicted in equation (2).
After the development of the second-order polynomial regression equation, the optimization was performed by the use of ANOVA. The ANOVA was applied to the regression equation keeping in view the statistical significance of the model and the process parameters. Other statistical parameters such as degrees of freedom, mean square, and the sum of squared deviations are also given in table 3.

Adequacy tests for model developed
Adequacy tests are performed using normal plots of residuals to evaluate whether the developed model is adequate. A model is considered adequate if the data points lie closer to a straight line. In addition, the model should not follow some particular sequence or trend. In the current study, the adequacy results are portrayed in figure 3, which illustrates residual plots of the developed regression model for the % yield of biodiesel. It can be observed from the plot that most of the data points fall close to the straight line. Moreover, the data  points do not follow a particular sequence or trend. Therefore, it can be inferred that the regression model is adequate and reliable that can be conveniently used for prediction and optimization purposes.
To further examine the adequacy and reliability of the developed regression model, another technique is employed that involves the evaluation of the abnormality of data points. In this method, the outlier plot illustrates the degree of abnormality of the data points based on the extent to which the data points fall away from the allowable range (±3.0) in the outlier plot, as shown in figure 4. It can be observed from the outlier plot ( figure 4) that all of the data points fall within the allowable range, which implies that the developed regression model is adequate.
In addition to residual and outlier plots, the appropriateness of the model is also reported in terms of average absolute deviation (AAD%) and coefficient of determination (R 2 ) values. The results indicate that AAD% is 2.249%, while R-squared is 0.9774 indicating a good agreement between predicted and experimental results.

Verification tests for the model developed
It is important to validate the developed regression model (equation (2)). For this purpose, experimental and predicted data are compared. The model validation is accomplished by using five random experimental value sets of the experiment. The experimental and predicted results are illustrated in figure 5, which clearly indicates that both predicted and experimental results display a promising agreement with each other. The % error is found to be 0.7%-1.9%. The detailed analysis and verification tests imply that the regression model (equation (2)) can be used to navigate design space. Another technique to make a comparative analysis of the significance of process parameters is the use of a perturbation plot. This plot is used to compare significant parameters one at a time in the design space while keeping the other input parameters constant. In a perturbation plot, the slope of the curves corresponding to various process parameters reveals how significant a particular parameter is. The more sloppy a curve is, the higher the significance of the parameter and vice versa. In this study, the perturbation plots of process parameters (temperature, pressure, oil-to-methanol mole ratio) are illustrated in figure 6. The sharp slope of curve A in figure 6 indicates that temperature is a more significant parameter than pressure and oil-to-methanol ratio. The same is also evident by the p-values given in table 3, which shows a much lower p-value (<0.0001) of parameter A (temperature) as compared to p-values of B (pressure, 0.0006) and C (oil-to-methanol ratio, 0.0009).
The interactive effect of process parameters on response objective can best be viewed and described by developing three-dimensional response surface diagrams together with contour plots. Figure 7(a) portrays the interactive effect of temperature and pressure. In contrast, figure 7(b) shows the interactive effect of temperature and oil-to-methanol ratio on the response objective, % yield of biodiesel.
The response surface in figure 7 illustrates the integrated effect of temperature and pressure on the % yield of biodiesel. Figure 7 indicates that biodiesel yield increases with an increase in temperature and pressure. However, from the curvatures of temperature and pressure lines, it is evident that the rise in biodiesel % yield is mainly governed by temperature. The highest yield is witnessed at a maximum temperature of 300 • C and 1.0 bar pressure. This is because the temperature is a more statistically significant parameter due to its lowest p-value (<0.0001). Therefore, careful temperature monitoring is advised during the manufacturing process. The response surface also indicates a significantly high yield of biodiesel (∼94.3%) at 300 • C and marginally high pressure (∼12 bar). A relatively lower yield (∼93.6%) is achieved at the maximum temperature (300 • C) and pressure (20 bar). A negligible curvature of the pressure lines indicates that pressure has a relatively lower effect on the biodiesel yield when it comes to studying the integrated impact of temperature and pressure on % biodiesel yield. The same is vindicated if we compare the p-value of B (pressure) with that of A (temperature) such that the p-value of B is much higher than A (0.0006), which suggests pressure is not as statistically significant as the temperature is. From the response surface, it is also evident that the lowest yield of biodiesel is achieved at the minimum temperature (100 • C) and the maximum pressure (20 bar).
The response surface in figure 8 illustrates the interactive effect of temperature and oil-to-methanol ratio on the response objective (% biodiesel yield). It is observed that the biodiesel yield increases with an increase in temperature and oil-to-methanol ratio. The maximum yield (95.7%) is observed at the highest values of  temperature and oil-to-methanol ratio, that is 300 • C and 20 • C. In this case, the curvatures of both temperature and oil-to-methanol ratio lines in the response surface clearly indicate that temperature is more influential than oil-to-methanol ratio, which is also evident by the much lower p-value of temperature (<0.0001) as compared to the p-value of oil-to-methanol ratio (0.0009). If we consider the singular contour  lines of temperature and oil-to-methanol ratio, it can be observed that the % yield of biodiesel increases rapidly with temperature increase. However, a relatively lower tendency of increase in % yield of biodiesel is witnessed with an increase in the oil-to-methanol ratio. The minimum biodiesel yield (∼90%) is achieved at the lowest temperature and oil-to-methanol ratio, which is 100 • C and 5. A moderately high oil-to-methanol ratio (∼12.5) at 300 • C also results in a significantly high yield (∼94.7%). At the highest temperature (300 • C) and lowest oil-to-methanol ratio (5), the % yield is close to 93.4%, still better than the minimum yield (∼90%). In this case, the temperature also appears to be more influential than the other parameter (oil-to-methanol ratio in this case), yet again vindicates the higher statistical significance of temperature. These results again justify our ANOVA results, indicating that the statistical significance of process parameters follows an ascending order such that the significance of temperature is higher than the oil-to-methanol molar ratio and the significance of the molar ratio of oil-to-methanol is higher than pressure. This implies that temperature is the most influential process parameter for biodiesel synthesis in this particular study.
One of the main objectives of the current study is parametric optimization. Table 4 lists goals, parameters, and their ranges used for the optimization such that the main aim was to maximize the % yield of biodiesel. Multi-objective optimization tool is used for this purpose that makes a unique combination of input variables at which all the response objectives provide the best result at the same time.
A set of various solutions for optimization is listed in table 5. The best solution (solution #1) with a desirability = 1 is chosen for optimization. The calculated maximum % yield results to be 94.16% at optimum values of temperature = 274.8 • C, pressure = 7.02 bar, and molar ratio = 12.43. The contour and three-dimensional desirability plots for the optimized solution are illustrated in figures 9 and 10, respectively.
The optimization results of our study are significantly important when compared with the results of similar studies reported in the literature. For example, a study used RSM and genetic algorithm to synthesize biodiesel from Jojoba oil by using supercritical methanol with a 1:30 oil-to-methanol ratio at 287 • C and 123 bar for 23 min reaction time [24]. The pressure employed (123 bar) is tremendously high and demands highly robust equipment to sustain this high pressure. This increases the capital cost. In the current study, the optimum pressure required is only 7.023 bar, much lower than 123 bar.
Similarly, another study reports biodiesel synthesis via supercritical methanol and candlenut oil at 115 bar and 285 • C with 1:15 and 1:30 mole ratios of oil-to-methanol and 22 min reaction time [26]. This study also employed a huge pressure (115 bar) that not only adds to the capital cost but also increases the operational and maintenance costs of the overall manufacturing process. Our study used an optimum

Conclusion
The simulation and optimization of biodiesel production from the transesterification of used cooking oil have been explored in this research. ChemSep is used to simulate the process, and RSM is used to optimize the process condition for maximum biodiesel yield. FCCD is employed for the DOEs and ANOVA. The ANOVA results indicate that temperature is the most influential process parameter, with the oil-to-methanol ratio being the second. The model was tested using experimental results and found that the agreement between experimental and simulation results is promising. The developed model is statistically significant, with a percentage AAD (%AAD) of 2.249% and an R-squared value of 0.9774. This implies that the regression model developed in this study can be useful for optimization and prediction purposes. The optimization results indicate a maximum yield of 94.16% at an optimum temperature of 274.8 • C, a pressure of 7.02 bar, and an oil-to-methanol molar ratio of 12.43.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).