Development of a combined approach for improvement and optimization of karanja biodiesel using response surface methodology and genetic algorithm

Abstract

This paper described the production of karanja biodiesel using response surface methodology (RSM) and genetic algorithm (GA). The optimum combination of reaction variables were analyzed for maximizing the biodiesel yield. The yield obtained by the RSM was 65% whereas the predicted value was 70%. The mathematical regression model proposed from the RSM was coupled with the GA. By using this technique, 90% of the yield was obtained at a molar ratio of 38, a reaction time of 8 hours, a reaction temperature of 40 ºC, a catalyst concentration of 2% oil, and a mixing speed of 707 r/min. The yield produced was closer to the predicted value of 94.2093%. Hence, 25% of the improvement in the biodiesel yield was reported. Moreover the different properties of karanja biodiesel were found closer to the American Society for Testing & Materials (ASTM) standard of biodiesel.

Keywords

optimization of karanja biodiesel / genetic algorithm (GA) / response surface methodology (RSM) / percentage improvement in the biodiesel yield / properties of biodiesel

Introduction

Edible and non-edible oils are used for so many years as a feed stock to run the compression ignition engine. Due to the scarcity of commercial diesel available, the requirement of alternate fuels is in demand and research is being done by various academicians to develop these fuels for compression ignition engine [1]. There are some important variables which should be considered before adopting an alternative fuel in an existing engine including none or minimum modification in the design of engine, use of some storage and transportation infrastructure, biodegradable and non-toxic assuring safe handling and transportation, capability of being produced locally and low investment cost [2]. The economic benefits of the fuels, like vegetable oils, compressed natural gas, ethanol and methanol etc. compared to the traditional petroleum resources, are marginal but the environmental benefits are enormous. Thus public policies need to be revised to encourage the development of these resources [3]. Biodiesel is one of the fuels that can be used in place of diesel in the blended form. It has many advantages as compared to petro diesel such as good lubrication, less smoke and particulate matters, higher cetane number with good anti knocking property, lower carbon monoxide and hydrocarbon emissions, renewable, biodegradable and non-toxic etc. It can be produced by the magnetic mechanical stirring method, ultrasonic cavitation method, and pyrolysis etc [4,5]. Biodiesel produced from the different oils using these methods of production are optimized at particular reaction conditions. Apart from the various methods of producing biodiesel, the magnetic stirrer method is better than others as studied by various researchers. The use of vegetable oils in compression ignition engine without any modification in the design is a very old concept, since most of the properties are similar to the petro diesel, such as viscosity, flash point, cloud point, cetane number etc [6]. Vegetable oils generally contain the oils extracted from rapeseed, sunflower, soybean, peanuts and other alternatives [7]. From these oils, biodiesels can be produced by reacting with alcohol in the presence of catalyst by the use of magnetic stirring [8-11]. Most of the oils are edible and readily available in India. Some non-edible oils such as jatropha, karanja, microalgae etc. can be used which are extracted from the seeds of their respective plants. The biodiesel produced from these oils have less emission contents, higher flash point temperature, higher cetane number, lower sulphur content and lower calorific value than that of petroleum diesel fuel [12].

Studies have been conducted for different vegetable oils: castor, corn, cotton seed, linseed, peanut, canola, safflower, sesame, soybean and sunflower, and important properties of these oils like viscosity and flash point have found and analyzed [13]. It was observed that the physical and chemical properties of these vegetable oils were inferior to commercial diesel.

Schlick et al. [14] have investigated the performance of soybean and sunflower oil in a 3- cylinder engine of ford tractor and observed that a blend of 1∶3 of these vegetable oils with diesel fuel perform satisfactorily up to 200 h. After a 200 h test, there is the deposition of carbon in the combustion chamber and injector tips. Researchers have suggested that either the modification of vegetable oils or different operating conditions are required for the engine to work satisfactorily. Ramdhas et al. [15] have also observed that no significant problems are reported using B20 peanut oil with commercial diesel. Fuel consumption has been found to be 2%-5% higher than conventional diesel. Another advantage of using biodiesel in compression ignition (CI) engines is its simplicity in the preparation by only mixing the components. By using higher alcohols, better performance has been reported for the production of fatty acid alkyl ester at room temperature, but in the winter season it tends to crystallize at room temperature below 0°C and did not separate over a period of three months which is the limitation of the biodiesel fuel over the commercial diesel.

Peterson et al. [16] have observed that the effective method to produce biodiesel is trans esterification and has been proven to be worldwide. It is the process of reacting triglyceride with an alcohol in the presence of catalyst to produce fatty acid esters and glycerol. Various reaction variables like reaction temperature, mixing intensity, reaction time, catalyst concentration and alcohol to oil ratio have been observed that affect the yield of biodiesel to a greater extent. Similarly optimization of karanja biodiesel has been done by various researchers that significantly influence the reaction conditions of the biodiesel yield [17,18]. The physical and chemical properties of karanja biodiesel were observed with the obtained biodiesel. A comparison chart between the commercial diesel and karanja biodiesel were prepared to describe the behaviour of karanja based biodiesel in compression ignition engines. Different experimental design techniques such as Taguchi, response surface methodology etc. have been studied to find out the optimum variables for the biodiesel yield. Chary et al. [19] have optimized the oil agglomeration process variables for maximum recovery of coal fines using statistical approach based on Taguchi methodology. Very few academicians have optimized the reaction variables for predicting the biodiesel yield of karanja oil. It has been observed from different papers that the biodiesel yield mainly depends upon controllable variables like molar ratio of alcohol to oil, reaction time, reaction temperature, catalyst concentration and mixing speed with the selection of magnetic stirrer condition and mixing environment. The work described in this paper deals with the optimization of karanja biodiesel using response surface methodology and genetic algorithm (GA) to understand the effect of different variables on biodiesel yield. Besides, the properties of produced biodiesel have also been measured by the authors’ own standard measuring instruments.

Materials and methods

Analytical grade chemicals such as ethanol (99.5%), catalyst KOH in the pallet form were used as base catalyst for a reaction. Karanja oil was purchased from the local market. A magnetic stirrer was used to perform the experiments with the addition of the above chemicals with the karanja oil for different speeds. The biodiesel yield was obtained from these mixtures of chemicals. There are various ways to produce biodiesel with different design techniques of optimization such as taguchi, response surface methodology, artificial neural network (ANN), GA, and etc. This paper deals with the production of biodiesel by using Design Expert 6 of Stat Ease, Inc. and GA for optimizing the reaction variables that affect the biodiesel yield. By selecting the response surface methodology (RSM) and central composite design (CCD), five factors with half fraction were used to observe the experimental response of different combination of variables. The experiments were conducted in UIET, M.D.U Rohtak to measure the biodiesel yield.

Apparatus

A biodiesel processor of 4L was developed in UIET Maharshi Dayanand University Rohtak Haryana India, which mainly consisted of a reaction vessel (1-L capacity) and a water bath (4-L capacity). There was a provision to control the speed of the magnetic stirrer. The reactor was heated in the water bath where a 1500 W electric heater was used to increase the temperature. Different temperature sensors were attached to the reactor with their controller to control the power supply to the water bath for maintaining the required temperature in the reactor. Condenser space was provided in the vessel to evaporate the ethanol during the process.

Problem formulation

Before beginning with the design, the variables which affect the biodiesel yield were observed from the papers published and limits of these variables were also analyzed [20-22]. Five important reaction variables with their constraint values that affect the response were mainly observed. The biodiesel yield was observed to vary with these combinations of variables. Therefore, the biodiesel yield can be represented by the function of five variables as

\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}=f({\mathrm{X}}_{\mathrm{1}},{\mathrm{X}}_{\mathrm{2}},{\mathrm{X}}_{\mathrm{3}},{\mathrm{X}}_{\mathrm{4}},{\mathrm{X}}_{\mathrm{5}}),

where X₁ is the molar ratio in %; X₂, reaction time in hour; X₃, reaction temperature in ºC; X₄, catalyst concentration in %; and X₅, mixing speed of the magnetic stirrer in r/min.

Constraint function

There are certain limits for all the variables which affect the production of biodiesel, which were discussed previously, as shown in Table 1. Therefore, the variables were to be optimized for different ranges of molar ratio, reaction time, reaction temperature, catalyst concentration and mixing speed.

Theory of trans esterification

Reactions were performed between karanja oil, ethanol in the presence of catalyst KOH by mixing these chemicals with the help of the magnetic stirrer. Two products, biodiesel and glycerol, were obtained during each experiment, which were to be separated and distilled in a particular beaker. Calculations of the percentage of karanja oil, catalyst and ethanol are as follows:

Molecular weight of triglycerides: 870 g.

Molecular weight of ethanol: 46 g.

1 gram mol of karanja oil: 870 g.

1 gram mol of ethanol: 46 g.

Quantity of karanja oil taken: 100 g.

Sample calculation for biodiesel yield:

Amount of ethanol for 100 g of vegetable oil

\mathrm{F}\mathrm{o}\mathrm{r}\mathrm{6}:\mathrm{1}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}=(\mathrm{46}/\mathrm{870})\times \mathrm{100}\times \mathrm{6}=\mathrm{31.7} \mathrm{g},

\mathrm{4.5}:\mathrm{1}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}=(\mathrm{46}/\mathrm{870})\times \mathrm{100}\times \mathrm{4.5}=\mathrm{23.7} \mathrm{g}.

Catalyst KOH taken: 1% by weight of oil.

Quantity of biodiesel produced: 90 g (say).

Quantity of ethanol: 31.7 g. (for 6∶1 molar ratio).

\begin{array}{l}\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}=(\mathrm{Q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{f}\mathrm{b}\mathrm{i}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\mathrm{d}/\mathrm{Q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{f}\mathrm{o}\mathrm{i}\mathrm{l}\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{e}\mathrm{n})\times \mathrm{100}\\ =(\mathrm{90}/\mathrm{100})\times \mathrm{100}\\ =\mathrm{90}\%.\end{array}

Design of experiments

To find out the optimum value of biodiesel yield, the experiments were performed using Design Expert 6, which helped to create the design matrix according to the number of variables and output. The response was measured and accordingly analysis of variance (ANOVA) based on the above experiments was found to optimize the response at particular combination of variables. To start the experiments, first, the levels of the variables affecting the biodiesel yield were determined [23-29]], as shown in Table 1. The coded and actual values of these factors were represented in Table 2. The regression model of the response was developed using the popular RSM design technique using central composite design (CCD) for certain experiments with the consideration of five significant factors, as listed in Table 3. Three groups of design points, which were fraction factorial, axial (also called star points) and center points, according to the CCD method were used for finding the coefficient of quadratic model. Five levels of each variable were taken into account. By using fractional factorial, the number of experiments was reduced to 32. It has 16 factorial points, 10 axial points and 6 center points. The experiments were conducted in the magnetic stirrer according to the design matrix obtained from the RSM with the CCD, as shown in Table 3. The response was measured from these experiments by the combination of reaction conditions.

Results and discussion

Analysis of variance for significant testing of variables

After performing the experiments, ANOVA was created which predicted the regression equation and the significance of the proposed model. As tabulated in Table 4, by comparing the different F- values of various possible regression equation terms, the quadratic model was observed to be significant for the given response.

The mathematical regression model for biodiesel yield from experimental data was obtained as

(1)$$\begin{gathered} Y=-\mathrm{79.16246}+\mathrm{4.13281}{X}_{\mathrm{1}}+\mathrm{20.02192}{X}_{\mathrm{2}}-\mathrm{0.31084}X\mathrm{3}+\mathrm{8.69357}{X}_{\mathrm{4}} \\ -\mathrm{0.041313}{X}_{\mathrm{5}}-\mathrm{0.034268}{X}_{\mathrm{1}}^{\mathrm{2}}-\mathrm{0.58586}{X}_{\mathrm{2}}^{\mathrm{2}}+\mathrm{7.21262}\times {\mathrm{10}}^{-\mathrm{4}}{X}_{\mathrm{3}}^{\mathrm{2}} \\ -\mathrm{0.097403}{X}_{\mathrm{4}}^{\mathrm{2}}+\mathrm{2.22635}\times {\mathrm{10}}^{-\mathrm{5}}{X}_{\mathrm{5}}^{\mathrm{2}}-\mathrm{0.23958}{X}_{\mathrm{1}}{X}_{\mathrm{2}}-\mathrm{6.25}\times {\mathrm{10}}^{-\mathrm{3}}{X}_{\mathrm{1}}{X}_{\mathrm{3}} \\ -\mathrm{0.071429}{X}_{\mathrm{1}}{X}_{\mathrm{4}}+\mathrm{2.05357}\times {\mathrm{10}}^{-\mathrm{3}}{X}_{\mathrm{1}}{X}_{\mathrm{5}}+\mathrm{0.010606}{X}_{\mathrm{2}}{X}_{\mathrm{3}} \\ -\mathrm{0.69048}{X}_{\mathrm{2}}{X}_{\mathrm{4}}-\mathrm{9.52381}\times {\mathrm{10}}^{-\mathrm{4}}{X}_{\mathrm{2}}{X}_{\mathrm{5}}+\mathrm{0.010390}{X}_{\mathrm{3}}{X}_{\mathrm{4}} \\ +\mathrm{1.42857}\times {\mathrm{10}}^{-\mathrm{4}}{X}_{\mathrm{3}}{X}_{\mathrm{5}}-\mathrm{2.65306}\times {\mathrm{10}}^{-\mathrm{3}}{X}_{\mathrm{4}}{X}_{\mathrm{5}}. \end{gathered}$$

F-test was used to check the significance of the model which was defined as the ratio of between group mean square values to within group mean square values. The p-values were used to investigate the significance of each coefficient which also showed the interaction strength of each variable. A smaller value of p indicated higher significance of corresponding coefficient. The software automatically checked the F-test and calculated the probability of all regression equation terms. If probability>F for the proposed model<0.05, it was significant. As given in Table 5, the F-value of 3.01 indicated that there was only 3.21% chances that F-value of a model could occur due to the fact that the noise and p-value of .0321 was less than 0.05, which showed that the model was significant. By analyzing the coefficient of determination (R²), the goodness of fit was checked. The value of R²= 84.55% demonstrated that 15.45% was not explained by the model. The coefficient of variance was also high, with a value of 8.18, due to the large difference in the actual and predicted values of biodiesel yield. A negative predicted R-squared value implied that the overall mean was a better predictor of the response than the current model. As shown in Table 5, adequate precision was a measure of signal to noise ratio, with a value of 5.841 that was greater than 4, which proved the precision and reliablility of the experiments. In the regression model, X₅, X₁², X₃², X₁X₂, X₁X₃, X₁X₅, and X₂X₄ were significant terms, which were only included in order to improve the predicted model. The lack of the fit value of 0.0779 implied that it was not significant relative to pure error. A reduced model that is a function of most significant variable is

(2)\mathrm{F}\mathrm{A}\mathrm{E}\mathrm{E}=-\mathrm{79.16246}-\mathrm{0.041313}{X}_{\mathrm{5}}-\mathrm{0.034208}{X}_{\mathrm{1}}^{\mathrm{2}}+\mathrm{7.21262}\times {\mathrm{10}}^{-\mathrm{4}}{X}_{\mathrm{3}}^{\mathrm{2}}-\mathrm{0.23958}{X}_{\mathrm{1}}{X}_{\mathrm{2}}-\mathrm{6.25}\times {\mathrm{10}}^{-\mathrm{3}}{X}_{\mathrm{1}}{X}_{\mathrm{3}}+\mathrm{2.05357}\times {\mathrm{10}}^{-\mathrm{3}}{X}_{\mathrm{1}}{X}_{\mathrm{5}}-\mathrm{0.69}{X}_{\mathrm{2}}{X}_{\mathrm{4}}.

The mathematical model, Eq. (1), could be plotted in the response surface contours for various values of reaction variables of the biodiesel yield. As depicted in Fig. 1 with the variation in molar ratio and reaction time the biodiesel yield was affected. In the curved lines, the yield was constant with the combination of variables. When moving away from the origin in the contour plot, biodiesel yield was found to increase and at certain point it reached the maximum. The optimum design point in Fig. 1 meant that at this point biodiesel production was the maximum between the two combination of variables with a constant temperature of 145°C, catalyst concentration of 8.5% by wt. of oil, and a mixing speed of 425 r/min.

Figure 2 showed the effect of molar ratio and temperature on biodiesel yield. In the curved lines, the yield is constant at a reaction time of 8.5 hours, a catalyst concentration of 8.5%, and a mixing speed of 425 r/min. With the increase in molar ratio and temperature, the yield first increased from 57.14 to 58.284 and at a certain point it reached the maximum, which was the design point or optimum point of the biodiesel yield. After that, the yield decreased to 58.284, and finally came to a minimum value of 57.1469.

The effect of molar ratio and catalyst concentration on biodiesel production was illustrated in Fig. 3 at a reaction time of 8.5 hours, a reaction temperature of 145ºC, and a mixing speed of 425 r/min. Similar trend occurred in this case as that shown in Fig. 2. Here curved lines indicated that the yield was constant. With the increase of the molar ratio from 14 to 30 and the catalyst concentration from 5 to 12, the yield first increased and then decreased. During these changes, the optimum yield was obtained which was the design point for different combinations of factors. Similar variation of yield was seen in the case of molar ratio and mixing speed, as shown in Fig. 4, but here the curved lines were different compered to those in Figs. 2 and 3.

Figure 5 displayed the actual and predicted biodiesel yields. It could be observed that these values were closer and standard error was observed by representing graphically. A minimum of 44 and 70 were obtained experimentally by different combinations of variables. For the observed biodiesel yield of 44%, the predicted yield obtained from the regression model was 46%. Other similar comparisons showed that there were small standard errors between these two yields.

As shown in Fig. 6, residuals vs. experimental runs, the residual differences were very large due to the presence of noise in the experiments. The number of experiments were shown in abcissa and studendized residuals were in ordinate. In every run, there was noise, due to which the actual yield differed from the predicted yield of regression equation.

The normal probability plot of biodiesel yield depicted in Fig. 7 indicated that the model was significant since small deviations from the actual probability line were obtained. By indicating the different points in Fig 7, comparison was done between the various values of observed and predicted yield with the reference yield line. It was observed that the actual yields were closer to that of the predicted.

GA

A GA was applied to the regression model obtained from the response surface method for optimization of different process variables to maximize biodiesel yield. It gave information in probabilistic selection for producing a population of problem solutions. First of all, an initial population had to be created and consequently generations were generated according to a prespecified breeding to fix the certain mutation value. When the GA was run in the MAT Lab, it automatically generated initial population according to constraints mentioned in Table 6. The program was run repeatedly with these GA parameters using the regression equation from the RSM till the best response was reported. The variation of parameters used were population size, crossover function, elite count, crossover fraction, mutation fraction and the number of generation. This best solution was generally called elite solution.

The different steps to apply the GA are shown in Fig. 8. The fitness function was generated with the use of regression equation and with the variation of parameters shown in Table 6. For each population, the fitness function had to be created and run in the MAT Lab. The population generation is generally called parents, whose terms are computing best fitness, for each set of population; sorting best fitness as elite; crossover; and mutation, referred as reproduction. Crossover and mutation was the correction algorithm (Fig. 8) since their values could be varied to obtain the best yield. This process remained in continuation until the limit of stopping condition. As could be referred from Fig. 9, by plotting the number of generations and biodiesel yield, the best and mean solution obtained from the GA was 94.2093% by repeatedly running the similar parameters related to the GA.

Validation experiments under optimum conditions obtained from RSM approach and GA

To check the accuracy of the predicted model by the two approaches, a minimum of six experiments were conducted at optimum reaction conditions as shown in Table 7. An average yield of 65% was obtained from these experiments under the regression model as compared to the predicted yield of 70%. The output produced was low since the requirement of the response was to maximize it, and another GA approach was applied. The regression model obtained from the RSM was used in the fitness function of the GA. For the reaction conditions mentioned in Tables 6 and 7, a yield of 94.2093% was predicted and the following parameter variations were proposed: Population size 5000, crossover function two point, mutation function uniform, elite count 1, crossover fraction 0.9, mutation fraction 0.01 and number of generation 20. To validate the proposed output, similar experiments were conducted using optimum reaction conditions under the GA. It was observed that an average yield of 90% was obtained.

Improvement of biodiesel yield and comparison of its properties with American Society for Testing & Materials (ASTM) standard of biodiesel

The different experiments were performed for the optimum reaction conditions using the RSM and it was observed that an average yield of 65% was obtained, but a yield of 90% was observed using optimized variables of the GA. It was analyzed that the optimum yield of biodiesel from the GA was 25% more than that obtained by the RSM approach, as shown in Table 7. Also, as shown in Table 8, the biodiesel produced using optimum reaction variables under the GA had cetane number of 48 which was closer to the ASTM standard of biodiesel. The rest of the properties were also close to the standard values. The performance of this biodiesel in compression ignition engine did not have large variations in the power output as compared to commercial diesel.

Conclusions

Based on the results of this work, the following specific conclusions are drawn:

1) A GA approach with five input variables was used to optimized the biodiesel yield. An average yield of 90% of given karanja oil was obtained for a molar ratio of 38, a reaction time of 8 hours, a reaction temperature of 40°C, a catalyst concentration of 2%, and a mixing speed of 707 r/min.

2) A 25 percent improvement in the average biodiesel yield was reported by the GA approach in comparison to the RSM using the same reaction variables.

3) The fuel properties of produced biodiesel were closer to the ASTM standard of biodiesel. Therefore, it could be concluded that karanja biodiesel could be used as a fuel by blending it with commercial diesel to run compression ignition engines.

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