Modeling of biodiesel production:Performance comparison of Box-Behnken,face central composite and full factorial design☆

Vlada B.Veljkovic′ ,Ana V.Velikovic′ ,Jelena M.Avramovic′ ,Olivera S.Stamenkovic′

1 University of Ni?,Faculty of Technology,Bulevar osloboenja 124,Leskovac 16000,Serbia

2 Research&Development Center “Alfatec”,Bulevar Nikole Tesle 63/5,Ni? 18000,Serbia

ABSTRACT The performances of the response surface methodology(RSM)in connection with the Box-Behnken,face central composite or full factorial design (BBD,FCCD or FFD,respectively) were compared for the use in modeling of the NaOH-catalyzed sunflower oil ethanolysis.The influence of temperature,catalyst loading,and ethanol-to-oil molar ratio (EOMR) on fatty acid ethyl esters (FAEE) content was evaluated.All three multivariate strategies were efficient in the statistical modeling and optimization of the influential process variables but BBD and FCCD realization involved less number of experiments,generating smaller costs,requiring less work and consuming shorter time than the corresponding FFD.All three designs resulted in the same optimal catalyst loading (1.25% of oil) and EOMR (12:1).The reduced two-factorinteraction (2FI) models based on the BBD and FCCD defined a range of optimal reaction temperature(25°C-75°C)and 25°C,respectively while the same model based on the 33 FFD appointed 75°C.The predicted FAEE content of about 97%-98.0%was close to the experimentally obtained FAEE content of about 97.0%-97.6% under the optimal reaction conditions.Therefore,the simpler BBD or FCCD might successfully be applied for statistical modeling of biodiesel production processes instead of the more extensive,more laborious and more expensive FFD.

Keywords:Biodiesel Box-Behnken design Model reduction Face central composite design Full factorial design Optimization

1.Introduction

Biodiesel has been attracted attention all over the world because of obvious economic benefits,increased global warming,and environmental pollution.It is commonly produced from different biorenewable recourses,in excess of an alcohol,in the presence of a catalyst.Various alcohols can be used in the biodiesel production,but the most commonly used are methanol and ethanol.Methanol is mostly used because of appropriate physicochemical properties,low cost,mild reaction conditions,fast reaction and easy phase separation,whereas ethanol is characterized by its superior vegetable oil dissolving power and lower toxicity and biodegradability,compared to methanol.Despite good pouring performances of their fatty esters at low temperatures,higher and secondary alcohols are very rarely used for the biodiesel production primarily because of their high price.Currently,edible vegetable oils are the most frequently utilized feedstocks for biodiesel synthesis all over the world.Because of their high price accounting for 70%-80%of overall biodiesel price and food vs.fuel controversy,priceless or cheap oily feedstocks,such as non-edible oils,used cooking oils,and waste animal fats,are more favorable than edible oils.However,despite these facts,edible oils will continue to be the main biodiesel feedstock in the near future.Another way to increase efficiency and reduce costs of biodiesel production processes is to conduct them under optimum reaction conditions,which are usually determined using various optimization methods.

The so-called “one-variable-at-a-time”optimization method is a conventional approach that involves a number of expensive and time-consuming sequential experiments.In addition,this method does not explain the interactions among the variables.Therefore,in recent years,it is often replaced by the statistical experimental design methods.The design of experiment (DoE)and response surface methodology (RSM) are broadly utilized in the optimization of biodiesel production processes.While the DoE methodology is useful for obtaining maximum information from a minimal number of well-planned experiments by varying simultaneously all the process factors,the RSM is a collection of mathematical and statistical tools for building an empirical model connecting ester yield with the influential process factors.

Selection of the satisfactory experimental design is the first step in the use of the DoE methodology.Various experimental designs may be used for collecting the data from the investigated biodiesel production process within the adequate ranges of the process conditions.Afterward,an adequate empirical model is selected,the influential process factors are evaluated through the analysis of variance (ANOVA) that estimates their statistical significance and the parameters of the selected model are determined using the non-linear regression method.

Table 1 summarizes the DoEs that have been applied so far in combination with the RSM for the optimization of biodiesel synthesis through ethanolysis of different vegetable oils,for example,soybean,sunflower,rapeseed,palm,olive,castor,cottonseed,Karanja,avocado,Brassica carinata and Raphanus sativus oils.Besides alkali hydroxides and ethoxides,calcium oxide and lipases are also employed as catalysts.Wide ranges of influential process factors like ethanol-to-oil molar ratio (EOMR),catalyst amount,temperature and time are applied in the investigated transesterification reactions.The full factorial,Box-Behnken and central composite designs (FFD,BBD and CCD,respectively) have most frequently been used.For the purpose of comparison with the so far reported studies,the applied process factors and the obtained results of the present study are also shown in Table 1.

Since each experimental design has its inherent advantages and drawbacks,it is desirable to identify the most convenient one forimprovement of a biodiesel production process with respect to complexity,accuracy and validity of the derived regression equation,acceptability of the recommended optimum reaction conditions as well as the economics and efficiency of the required laboratory work.FFD allows studying the effects of all combinations of the possible levels of influential process factors on the response including main and interaction effects and testing the model curvature.It requires the largest number of experiments among the above-mentioned designs,thus creating a more reliable empirical model,but larger costs and longer time for conduction of the necessary experimental work.Moreover,FFD includes all experimental points involved in the corresponding face CCD(FCCD) and BBD whereby the experimental points of FCCD and BBD are localized at different places of the experimental cubic space.Whereas FCCD examines borderline regions,BBD does not contain the extreme factor combinations,i.e.the vertices of the experimental cubic space.Therefore,for the same number of factors,BBD has fewer experimental points and lower number of degrees of freedom than FCCD.All three DoEs can generate the second-order polynomial equation,known also as the quadratic equation,allowing estimation of first and second order terms in the model.These designs have rarely been compared to each other with respect to their performances in the modeling and optimization of biodiesel production processes [17,18].

Table 1 Statistical modeling and optimization of biodiesel production from various feedstocks and catalysts by ethanolysis.

The performances of the RSM in connection with the threefactor-three level BBD,FCCD and FFD with replication were compared to each other when applied to the NaOH-catalyzed sunflower oil ethanolysis.The influence of catalyst loading,reaction temperature and EOMR on fatty acid ethyl ester (FAEE) content was evaluated.The principal goal was to test if the simpler BBD and FCCD could successfully replace the more expensive FFD.

2.Materials and Methods

2.1.Materials,equipment,experimental designs,reaction conditions and procedure

Materials,equipment,reaction conditions and procedure applied can be found elsewhere [19].The physico-chemical properties and fatty acid composition of the used refined sunflower oil (Sunce,Sombor,Serbia) can be found elsewhere [17,19].The sunflower oil ethanolysis catalyzed by NaOH was conducted in a round-bottomed flask with a paddle agitator (600 r·min-1) and a condenser,which was set in a glass chamber.The reaction conditions were in accordance with the 33FFD(54 observations in total)[3]:temperatures of 25°C,50°C and 75°C,EOMR of 6:1,9:1 and 12:1 and NaOH amount of 0.75%,1.00% and 1.25% (of oil).This design included the experimental points of the corresponding BBD (14 data) and FCCD (16 data).The complete design matrices of the used BBD,FCCD and FFD are shown in Table 2.In order to estimate the pure error associated with repetitions,replicates of the center point were made.An HPLC chromatograph (Agilent 1100 Series)was employed to determine the chemical composition of the ester phase samples taken after 5 min of reaction [20].The standard error in the replicates is in the range between 0.02 and 3.19,with the mean value of ±0.74 (the mean relative standard error of ±0.80%) [19].

2.2.RSM,ANOVA and multiple nonlinear regression

FAEE content in the ester phase was optimized with respect to the reaction temperature,EOMR,and catalyst amount by the RSM.The ANOVA was used with a confidence level of 95% (p ＜0.05) to evaluate the significance of individual process factors and their interactions on the basis of their F-and p-values.The cubic model had terms that are aliased with one another and hence,it was not considered as a possible regression model.The second-order polynomial equation (called here quadratic model) was first derived by multiple nonlinear regression to correlate FAEE content(Y)with reaction temperature(X1),EOMR(X2)and catalyst amount(X3):

where bi,biiand bijare the regression coefficients (i,j=0,1,2,3).Then,the statistically insignificant terms were eliminated from the derived quadratic equation,leading to a simpler equation,such as the two-factor-interaction (2FI) model:

DoEs and data processing and evaluating were performed using the Design Expert software (Stat-Ease Inc.,Minneapolis,USA).

3.Results and Discussion

3.1.Development,evaluation and verification of BBD-and FCCD-based models

3.1.1.Quadratic models

The ANOVA results of the BBD-and FCCD-based quadratic models showed that the individual factors and the interaction between catalyst loading and temperature had a statistically significant influence on FAEE content with the confidence level of 95% in the employed experimental region (Table S1,Supplementary Material);besides that,for the latter model the quadratic term of catalyst loading was statistically significant.The quadratic equations in terms of coded and actual factors are given in Table 3.The Fmodelvalues and the corresponding p-values implied both models were significant (Table S1).Also,a high R2-value (0.98) and low value of mean relative percentage deviation (MRPD) (±0.6%) proved the adequacy of the derived quadratic models.However,as it can be seen in Table S1 (Supplementary Material),the Rp2red-values(0.683 and 0.639) were not as close to the Ra2dj-values (935 and 0.947) as one might normally expect as the recommended difference between these two coefficients of determination was larger than 0.2[21].This indicated a possible problem with the developed model and/or data and the used software recommended considering response transformation,outliers,model reduction,etc.However,the used software suggested no response transformation.The data were normally distributed but outlier values were present in both analyzed datasets(Fig.S1,Supplementary Material).Hence,the developed quadratic models were compromised due to the too large difference between Rp2red-and Ra2dj-values as well as the presence of outliers,so a new model should be looked for.

3.1.2.2FI models

Instead of the compromised quadratic model,the simpler 2FI model,Eq.(2),was recommended for predicting FAEE content.The ANOVA revealed temperature,EOMR,catalyst amount and the interaction between temperature and catalyst loading as the statistically significant variables at the 95% confidence level(Table S2,Supplementary Material).The corresponding 2FI model equations in terms of coded and actual factors are given in Table 3.The BBD-and FCCD-based 2FI models were significant as concluded on the basis of their Fmodel-(23.89 and 24.75,respectively)and p-(＜0.0001) values.Also,a high R2-value (0.953 and 0.943,respectively) and a low MRPD-value (±0.8% and±0.9%,respectively) proved the adequacy of both 2FI models.Moreover,the Fvalues of the lack of fit were insignificant,which meant that the 2FI models fitted adequately the experimental values of FAEE con-tent.Furthermore,the date from both datasets was normally distributed (Fig.S2,Supplementary Material).Finally,for the BBDbased 2FI model,theof 0.834 was in reasonable agreement with theof 0.914 and for the FCCD-based 2FI model,there was no agreement between theandvalues (0.648 and 0.905,respectively),indicating a possible problem with this model and/or data.Indeed,the analyzed FCCD dataset had two outliers while no outlier was observed in the BBD dataset (Fig.S2,Supplementary Material).Therefore,the FCCDbased model was rejected despite this statistical significance,high R2-value and low MRPD-value.

Table 2 Experimental matrix and the FAEE content predicted on the basis of FFD,BBD and FCCD

Table 3 Model equations based on BBD,FCCD and FFD datasets

3.1.3.Reduced 2FI models

The 2FI models were further simplified into the reduced 2FI model equations by removing the statistically insignificant terms,i.e.the interactions of EOMR with reaction temperature and cata-lyst loading.The ANOVA (Table 4) showed that all terms of the reduced 2FI models were statistically influential on FAEE content at a confidence level of 95%(p ＜0.0001).As it can be seen in Table 3,the reduced 2FI model equations in terms of coded and actual factors are given,the linear regression coefficients were positive,indicating a positive influence of all three process factors on FAEE content,which was ascribed to the dependency of the reaction rate on the catalyst concentration,temperature,and EOMR.With increasing the catalyst concentration and temperature,the reaction rate constant increased,enabling the achievement of a higher FAEE content in a shorter time.The increase of ethanol concentration accelerated the forward reaction and moved the reaction equilibrium to the FAEE formation,resulting in a greater FAEE content,as it follows from the stoichiometric equation of the reversible transesterification reaction:

Table 4 ANOVA results for the BBD-,FCCD-and FFD-based reduced 2FI models

Having the highest F-value and regression coefficient,the NaOH amount influenced most significantly FAEE content.Although less than the NaOH amount,the reaction temperature,and the EOMR also significantly affected FAEE content;the former was more influential than the latter.The interaction of reaction temperature and catalyst amount (X3X2) had also a significant influence on FAME content.

Fig.1.Predicted versus actual FAEE contents for the BBD reduced 2FI model(data included in the derivation of the BBD model;the data that were not included into the derivation of the BBD model:the data located at the vertices of the FFD cube ■ and the rest of the data corresponding to the combinations of the process factors where two of them were at middle levels).

Fig.2.Predicted versus actual FAEE contents for the FCCD reduced 2FI model (data included in the derivation of the FCCD model; and the rest of the data that were not used into the derivation of this model).

Several statistical criteria were analyzed to assess how the derived model fitted the experimental data.On the basis of its Fvalue (BBD:43.19 and FCCD:44.37) and p-value (＜0.0001),these models were statistically significant.The R2-values (BBD:0.950 and FCCD:0.942) indicated a high goodness of fit of the reduced 2FI models.The value of(BBD:0.872 and FCCD:0.867)agreed well with the value of(BBD:0.918 and FCCD:0.920),demonstrating a very good FAEE content prediction by the model.The MRPD of ±0.9% (based on 14 and 16 data for the BBD-and FCCDbased models,respectively) indicated an outstanding compliance between the models and the experiment(Figs.1 and 2).Moreover,the lack of fits was insignificant (p=0.157 ＞0.050 and 0.158 ＞0.050 for the BBD-and FCCD-based models,respectively),which was desirable.Furthermore,the data from both datasets was normally distributed and no outlier was observed (Fig.S3,Supplementary Material).Finally,these models were validated using the sub-FFD datasets that were not used in their derivation.The MRPD values for these sub-datasets were ±1.4% (28 data) and±1.2% (24 data;Table 2),proving a good fitness of both BBD-and FCCD-based models even for the vertices of the cube,i.e.the extreme levels of the process factors and the combinations of the process factor levels,which were out of the experimental region employed in their derivation.

Table 5 Comparison of the regression models developed on the basis of the 33 BBD,FCCD and FFD

3.2.Analysis of 33 FFD models

3.3.Response surface analysis

FAEE content is graphically represented as a function of the temperature,EOMR and NaOH amount by response perturbation,interaction,contour and surface plots using the reduced 2FI model developed from the BBD.

3.3.1.Perturbation plots

The perturbation plot,shown in Fig.3,demonstrates the effect of changing one process factor while holding the other two process factors as constant.It measured FAEE content from the center point of the experimental region (X1=50°C,X2=9:1 and X3=1.0%) in each of the three axes and helped to compare the influence of all process factors at any particular point.Since the developed reduced 2FI model included only individual process factors and the interaction of the catalyst with loading temperature,the effects of all three process factors were illustrated by the straight lines.Thus,it could be concluded that the response surfaces would be flat.On the basis of the slope of the straight lines,it was concluded that FAEE content was the most sensitive to the catalyst amount and the most insensitive to the EOMR.The perturbation plot demonstrated that increasing all process factors resulted in the increase of FAEE content.

3.3.2.Interaction plots

Fig.3.Perturbation plot for FAEE content,which is based on the BBD reduced 2FI model (center point of the experimental region:X1=50°C,X2=9:1 and X3=1.0%).

Fig.4 shows the interaction plots of reaction temperature (X1)versus catalyst loading (X3) at low,middle and high EOMRs (X2).Generally,a higher FAEE content was obtained at the larger catalyst amount at any temperature and EOMR.Moreover,independently of the EOMR,FAEE content increased with increasing the reaction temperature at smaller catalyst amounts (0.75% and 1.00% of oil) with the slope of the straight line much larger for the smaller catalyst amount.However,the reaction temperature did not affect FAEE content at the largest catalyst amount (1.25%of oil) in the whole range of EOMR.

3.3.3.Response surface and contour plots

Fig.5 shows the 3D and contour plots for FAEE content as a function of the temperature and the catalyst amount at the EOMR of 12:1 resulted from the reduced 2FI model derived from the BBD dataset.The BBD gave similar response surfaces to those obtained on the basis of the FFD [19].It is obvious that the increase of the temperature led to higher FAEE content,which was ascribed to the positive impact of the temperature on the reaction rate and the reduction of the viscosity of the reaction mixture.A similar impact of the temperature on ethanolysis was observed for sunflower [1],Karanja [14]and avocado [13]oil.Independently of the EOMR,the influence of the temperature on FAEE content was more significant at smaller catalyst amount,becoming less significant at larger NaOH loading while its effect was insignificant at the 1.25% catalyst.This behavior could be attributed to very fast reaction rate at higher catalyst amount when the reaction was completed in only a few minutes (below 5 min).At the 1.25% catalyst and any temperature in the range 25°C-75°C,FAEE content was almost constant for each EOMR.The catalyst amount positively influenced FAEE content at all reaction temperatures and EOMRs.The most significant,positive impact of catalyst loading on FAEE formation has already been reported [1,10].However,the effect of NaOH amount depended on the reaction temperature,as it was thoroughly discussed by Silva et al.[10].The highest impact of the catalyst amount was observed at 25°C and decreased at higher temperatures.Such a behavior can be ascribed to the positive influence of the temperature on the ethanolysis reaction rate,which was more dominant at higher temperatures [10].

Fig.4.Interaction plots of reaction temperature (X1) versus catalyst loading (X3),which are based on the BBD reduced 2FI model,at various EOMRs (X2):(a) 6:1,(b)9:1 and(c)12:1(model,X3,%:0.75—black line and 1.25—red line;design points,X3,%:●0.75,▲1.00 and ■1.25).

Fig.5.Response surface (a) and contour plots(b) for FAEE content as a function of and catalyst loading,based on the BBD reduced 2FI model,at the EOMR of 12:1.

3.4.RSM optimization on the basis of the BBD-based reduced 2FI model

For the selection of the optimal operating conditions using the developed BBD-based reduced 2FI model,the criterion of optimization was to get the maximum FAEE content in the range up to 100%with the process factors limited to the employed experimental region.According to 3D figures(Fig.5),the maximum FAEE content of 98%or higher can be obtained at any temperature between 25°C and 75°C if the EOMR of 12:1 and catalyst amount of 1.25% were applied.The same result was suggested by the used software on the basis of the reduced 2FI model.The predicted FAEE content under the optimum operating conditions was about 98.2% while the experimental FAEE content was in the range 96.6%-97.6%depending on the reaction temperature.

3.5.Comparison of the BBD-,FCCD-and FFD-based models

For comparing performances of three models based on the FFD and incorporated BBD and FCCD,several criteria can be used,like complexity,validity,and accuracy of the derived regression models,the acceptability of the recommended optimum reaction conditions as well as the cost and duration of the required experimental work.Some data used for this comparison are presented in Table 5.Apparently,the realization of BBD and FCCD involves a much smaller number of experiments,generates smaller costs,requires less work and consumes shorter time than the corresponding FFD.All three models led to the same optimum EOMR(12:1) and catalyst loading (1.25% of oil).The reduced 2FI models based on the BBD and FCCD defined a range of optimal reaction temperature (25°C-75°C) and 25°C,respectively while the same model based on the 33FFD appointed 75°C.The FAEE content of the crude biodiesel,produced under the optimum reaction conditions was above the limit specified by the biodiesel quality standard (＞96.5%).All three models were characterized with similar statistical criteria like R2,,C.V.and MRPD.On the basis of the comparison,it could be concluded that the BBD and FCCD had the advantage of smaller costs,less work and shorter time of experimentation over the corresponding FFD and hence,both could be suggested for optimizing biodiesel production processes.

3.6.Comparison of the present and previously reported studies

One of the main results of the present study was that the all three process factors,namely the NaOH amount,the reaction temperature and the EOMR,significantly affected FAEE content,provided that the NaOH amount was more influential than the other two.This accorded with most results of the statistical analysis of batch ethanolysis reactions,which showed a positive impact of EOMR and catalyst amount on FAEE content,while the impact of temperature seemed to depend on the type of oily feedstock.Avhad et al.[13]reported a significant,positive influence of the reaction temperature,EOMR,and catalyst amount on the avocado oil ethanolysis catalyzed by CaO.Exceptionally,for the ethanolysis of R.sativus stokes oil catalyzed by sodium ethoxide,Valle et al.[3]reported no significant effects of the EOMR and the catalyst loading on FAEE yield,and a greatest,but negative influence of the agitation intensity.However,Domingos et al.[2],who optimized the NaOH-catalyzed ethanolysis of R.sativus L.oil,reported the insignificant influence of the reaction temperature.The difference in the observed impacts of reaction temperature on the ethanolysis of the same feedstock might be ascribed to different catalysts used in the two studies.In line with the major observance,Silva et al.[10]found all three process factors statistically significant for the ethanolysis of soybean oil catalyzed by NaOH,while Tippayawong et al.[11]did not prove the significant influence of the reaction temperature on the ester yield.Several other research groups reported also that the reaction temperature had no statistically significant impact [2,4,5,9].The temperature was significant for the KOH-catalyzed sunflower oil ethanolysis but not significant for the B.carinata oil ethanolysis,whereas the catalyst loading had a positive impact on FAEE yield,independently of the type of oil[1].The negative impact of the reaction temperature on FAEE yield was observed for the palm [15]and rapeseed [8]oil ethanolysis.Verma and Sharma [14]observed for the Karanja oil ethanolysis catalyzed by KOH that FAEE yield increased with increasing the reaction temperature and then decreased.This was attributed to the reduction of the viscosity that enabled the faster formation of alkyl esters[23].Only Poppe et al.[16]observed a negative impact of reaction temperature on the enzymatic ethanolysis of olive and palm oils,which was attributed to the loss of enzyme activity,while the amount of biocatalyst and substrate molar ratio had a positive effect for olive and palm oil,respectively.The same effect was observed in the ultrasound-assisted ethyl ester synthesis from palm oil in the presence of KOH,where the EOMR,catalyst amount and ultrasonic amplitude positively affected FAEE yield while the influence of reaction temperature was negative [15].The negative effect of the catalyst loading was observed only for the castor oil ethanolysis using an alkaline catalyst [6].

The optimum reaction conditions and maximum FAEE yields or contents for ethanolysis of various oily feedstocks using various catalysts are given in Table 1.Most studies,including the present one,have reported the optimum reaction temperature lower than 40°C,most frequently 25°C or 30°C.The exceptions are Karanja[14],avocado[13],and soybean[12]oils that require much higher temperature(above 60°C)and longer reaction time(1 or 2 h).The optimum EOMR is mainly in the range from 9:1 to 12:1,although some researchers have found smaller(5:1) [1]or higher (20:1)[9]optimum EOMR values.It is interesting that these exceptions,related to sunflower oil,B.carinata oil (5:1),and cottonseed oil(20:1),are at lower reaction temperatures (25°C-30°C) and the catalyst loading of about 1%.The optimum alkali catalyst (alkali hydroxides and ethoxides) loading is in the range between 1.0%and 1.5%,while solid and enzyme catalysts are used with larger loadings,which may be attributed to their lower catalytic activity in the liquid-liquid-solid reaction systems,compared to homogeneous catalysts.The maximum FAEE yield/content is mostly higher than 90%,but in some cases,it is lower than the prescribed limit for biodiesel (96.5%).

4.Conclusions

In the present study,the performances of three multivariate strategies,namely the RSM combined with the three-factor-three level BBD,FCCD,and FFD with replication were compared to each other in the case of the FAEE synthesis by the NaOH-catalyzed sunflower oil ethanolysis.All three multivariate strategies were efficient in the statistical modeling and optimization of the influential process variables and pointed out to the same optimum reaction conditions and the predicted FAEE content in the ester phase of the reaction mixture.The predicted FAEE content (about 98%) agreed with the FAEE content (about 97%) experimentally achieved under the optimum reaction conditions.Being economically advantageous over the FFD with repetition,the BBD and FCCD combined with the RSM are recommended for the optimization of biodiesel production processes.

Nomenclature

b0constant regression coefficient

bilinear regression coefficient

biiquadratic regression coefficient

bijregression coefficients of two-factor interactions(i,j=1,2,3)

C.V. coefficient of variation

MRPD mean relative percent deviation,%

p probability values

R2coefficient of determination

X1reaction temperature,°C

X2ethanol-to-oil molar ratio,mol·mol-1

X3NaOH amount based on,% the oil mass

Y FAEE content,%

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2018.08.002.