bioethanol is one of the most employed liquid biofuels due to the easy adaptability of this fuel to existing engines and because this is a cleaner fuel with higher octane rating than gasoline .
ethanol market grew from less than a billion liters in 1975 to more than 39 billion liters in 2006 and is expected to reach 100 billion liters in 2015 .   among the widely used substrates for ethanol production
are the molasses , the wastes byproduct of sugar industries from sugarcane and sugar beet .
this is because they are cheap raw materials , readily available , and ready for conversion with limited pretreatments as compared with starchy or cellulosic materials , as all sugars are present in a readily fermentable form .  
ongoing research and development seeking to improve methods by minimizing the numbers of experiments provide information about the direct additive effects of the study variables and interaction effects using design of experiment methods .
recently , this statistical technique has been successfully applied in many fields [ 58 ] .
response surface methodology ( rsm ) is a combination of mathematical and statistical techniques and is used for the modeling and analysis of problems in which a response of interest is influenced by several variables , and the objective is to optimize this response .
the most popular rsm design is the central composite design ( ccd ) for analysis of experimental data .
the ccd is efficient and flexible , providing sufficient information about the effects of variables and overall experimental error with a minimum number of experiments .
center points in ccd design are usually repeated 46 times to get a good estimate of experimental error ( pure error ) .
five center points are created by default for each factor : alpha , with negative , zero and positive values ( 1 , 0 , and 1 ) . in this study ,
alpha value was taken as one resulting in 3 levels , lowest ( 1 ) , middle ( 0 ) , and highest ( + 1 ) which is more specifically known as central composite face centered design ( ccfd ) , in an attempt to optimize the variables : incubation period , initial ph , incubation temperature , and molasses concentration , which affect bioethanol production .
the main goal of the present work was to maximize bioethanol production from sugarcane molasses in batch fermentation process using previously isolated saccharomyces cerevisiae y-39 .
the application of ccfd and rsm assisted in designing , modeling , and optimizing the fermentation process by performing a series of controlled laboratory experiments .
sugarcane molasses was purchased from sugars and integrated industries egyptian distillation plants in hawamdeia city , giza , egypt and stored at 4c until use .
wickerham wh medium prepared according to wickerham   was used for maintenance and inoculum preparation .
medium for fermentation experiments was prepared as follows : 2  g kh2po4 , 10  g ( nh4)2so4 , 1  g mgso4    7h2o , and 2  g yeast extract were dissolved in 1  l distilled water , molasses concentration and ph were then adjusted according to the experimental conditions before sterilization , at 121c for 20  min to avoid contamination .
a yeast strain saccharomyces cerevisiae y-39 , previously isolated for its ability to produce bioethanol from different saccharides , was used in this study .
active cultures for fermentation experiments were prepared by growing y-39 in wh medium for 48  h at 30c in shaking incubator 150  rpm .
harvested cells were washed twice with sterile saline ( 8.5  g nacl per 1  l distilled water ) and then resuspended in sterile saline to be used as a fresh and pure stock for inoculation .
the types of sugars in molasses were determined by high performance liquid chromatography ( hplc ) , according to the method reported by madian et al . .
ashes were quantified by gravimetric analysis after burning samples at 550c for 3  h , and minerals concentrations were determined by atomic absorption spectrophotometer in central analytical lab . in egyptian petroleum research institute .
all other chemical characterizations of molasses were done in agricultural research center , giza , egypt .
ethanol yield was measured by gas chromatography ( model 6890 , agilent ) , equipped with flame ionization detector and nominal capillary column ( 60  m  530  m  5.00  m ) .
all experiments were carried out in triplicates , and the listed results are the average .
batch fermentations were done in 100  ml erlenmeyer flasks fitted with rubber stoppers , containing 50  ml of culture media , inoculated with 5  ml of fresh yeast inoculum stock ( 10  mg fresh yeast / ml ) .
incubation was performed in shaking incubator 100  rpm , set at temperatures according to the required experimental conditions .
samples for analyses were taken at the beginning and end of fermentation at the prescribed incubation periods .  
response surface methodology ( rsm ) was used to optimize bioethanol production process from sugarcane molasses and investigate the influence of different fermentation process variables on the bioethanol yield . the central composite face
the experimental runs were carried out according to a 2 full factorial design for the four identified design independent variables , namely , incubation period h ( x1 ) , initial ph ( x2 ) , incubation temperature , c ( x3 ) , and molasses concentration wt.% ( x4 ) , with low ( 1 ) and high ( + 1 ) levels .
the total number of experiments ( runs ) was given by the simple formula [ 30 = 2 + 2k + 6 ] , where k is the number of independent variables ( k = 4 ) , this includes 16 factorial points from 24 full factorial ccfd were augmented with 6 replicates at the center point to assess the pure error .
the design factors ( variables ) with low 1 and high + 1 levels , are , namely , x1 [ 24 and 72  h ] , x2 [ 5 and 7 ] , x3 [ 20 and 40c ] , and x4 [ 15 and 25  wt.% ] . the central values ; zero level chosen for experimental design were 48  h , 6 , 30c , and 20% for x1 , x2 , x3 , and x4 , respectively ( table 1 ) .
once the experiments were preformed , the next step was to perform a response surface experiment to produce a prediction model to determine curvature , detect interactions among the design factors ( independent variables ) , and optimize the process , that is , determine the local optimum independent variables with maximum yield of bioethanol .
the model used in this study to estimate the response surface is the quadratic polynomial represented by the following equation : 
 ( 1)y=o+i=14ixi+i=13j = i+14ijxixj+i=14iixi2 , 
 where y is the bioethanol yield ( g / l ) , o is the value of the fixed response at the center point of the the design , i , ij , and ii are the linear , interactive , and quadratic coefficients , respectively .
xi and xj are the independent variables ( factors ) under study .   the statistical software design expert 6.0.7 ( stat - ease inc . , minneapolis , usa ) was used for design of experiments , regression and graphical analyses of the data obtained , and statistical analysis of the model to evaluate the analysis of variance ( anova ) .
sugarcane molasses is a dark viscous fluid with ph value of 5 and very rich in nutrients required by most microorganisms .
carbon , nitrogen , phosphorus , sodium , and potassium contents are 64 , 6 , 0.3 , 0.33 , and 5.5 ( wt.% ) , respectively .
non - nitrogenous compounds ( e.g. , citric acid , oxalic acid ) represent 28% ( wt.% ) .
molasses is found to be rich in calcium 0.7% and contains significant quantities of trace minerals copper ( 2.2  ppm ) , zinc ( 3.91  ppm ) , manganese ( 4.74  ppm ) , iron ( 78.37  ppm ) , and magnesium ( 1370  ppm ) .
sugarcane molasses is rich in fermentable sugars 55% ( wt% ) and non - fermentable sugars recorded 5% ( wt% ) .
most of the chemical parameters determined in this study were in close agreement to those reported by chen and chou , who found molasses containing 4555% total sugars , 2025% reducing sugars , 2535% sucrose , 1016% ash , 0.40.8% calcium , 0.10.4% sodium , 1.55% potassium and ph 55.5 .
soil and climate , the variety and maturity of the cane , and the processing conditions in the factory all influence molasses composition .
consequently , considerable variation may be found in nutrient content , flavor , color , and viscosity of molasses .
based on ccfd and experimental results , rsm was used to optimize fermentation process design factors ( independent variables ) .
the statistical combinations of variables in coded and actual values along with the predicted and experimental responses are presented in table 2 . the regression equation characterizing the influence of different considered variables on process yield was obtained : 
 ( 2)y=177.4 + 6.34x10.41x23.33x32.39x4  33.32x1x2 + 28.51x1x322.11x1x4  27.60x2x3 + 30.38x2x416.39x3x4  0.56x1292.58x22 + 44.08x3266.47x42 .
positive sign in front of the terms indicate synergetic effect , whereas negative sign indicates antagonistic effect .
pareto chart figure 1 , was used in this work to make it much easier to visualize the main and interaction effects of all factors to the response variable , that is , bioethanol yield .
the model identified that within the studied range of experiments , the quadratic effect of incubation temperature and the interactive effect of initial ph and molasses concentration and that of incubation period and temperature have highly significant positive influence on the bioethanol yield .
that is , with increment of both incubation period and temperature , the bioethanol yield increases , and the same occurred with increment of both ph and molasses concentration . but
incubation period has a relatively low significant positive effect on bioethanol yield , while the quadratic effect of initial ph and molasses concentration , and the interactive effect of incubation period and initial ph as well as interactive effect of incubation temperature and initial ph have highly significant inverse effect on the bioethanol yield .
the interactive effect of incubation period and molasses concentration and that of incubation temperature and molasses concentration have a significant negative impact on the bioethanol yield .
initial ph , incubation temperature , molasses concentration , and the quadratic effect of incubation period seem to have negative impact on bioethanol yield .
thus , bioethanol yield decreases with increase of the initial ph and incubation period , incubation temperature and initial ph , incubation period and molasses concentration or incubation temperature and molasses concentration .  
the validity of the fitted model was evaluated , and its statistical significance was controlled by f - test .
the analysis of variance ( anova ) for the response surface full quadratic model is given in table 3 .
it can be indicated that the model is highly statistically significant at 95% confidence level , with f - value of 82.14 , and very low probability p value of < 0.0001 .
the values of the determination coefficients , r  and  radj which measure the model fitting reliability for model ( 2 ) , were calculated to be 0.9871 and 0.9751 , respectively .
this suggests that approximately 98.71% of the variance is attributed to the variables and indicated a high significance of the model .
thus , only 0.0129 of the total variations can not be explained by the model which ensures the good adjustment of the above model to experimental data .
confirmation of the adequacy of the regression model was reflected also by the good agreement between experimental and predicted values of response variables as shown in table 2 .
the lack of fit test is performed by comparing the viability of the current model residuals to the variability between observations at replicate settings of the factors .
the lack of fit was statistically significant with f - value of 53.24 and p value of 0.0002 .
a significant lack of fit suggests that there may be some systematic variation unaccounted for in the hypothesized model .
this may be due to the exact replicate values of the independent variable in the model that provide an estimate of pure error .  
the relationship between predicted and experimental values of bioethanol yield is shown in figure 2 .
it can be seen that there is a high correlation ( r = 0.9853 ) between the predicted and experimental values indicating that the predicted and experimental values were in reasonable agreement .
it means that the data fit well with the model and give a convincingly good estimate of response for the system in the experimental range studied .  

figure 3 shows the normal probability plots of the standardized residuals for bioethanol production efficiency .
a normal probability plot indicates that if the residuals follow a normal distribution , in which case the points will follow a straight line .
since some scattering is expected even with the normal data , as shown in figure 3 , it can be assumed that the data is normally distributed .
thus , the obtained normal probability plot indicates a good validity for the approximation of the quadratic regression model .  

, points of observed runs were scattered randomly within the constant range of residuals across the graph .
that is , the model is adequate , and there is no reason to suspect any violation of the independence or constant variance assumption in all runs .
the standardized residuals versus run plot represented in figure 4(b ) shows randomly scattered points ranged between 2.8 ; the errors were normally distributed and insignificant .  
the perturbation plot figure 5 shows the comparative effects of all independent variables on bioethanol yield .
the sharp curvature of the three factors : initial ph , incubation temperature , and molasses concentration shows that the response , bioethanol yield , was very sensitive to these three variables .
the comparatively semiflat incubation period curve shows less sensitivity of bioethanol yield towards the incubation period .
thus , the incubation period with the studied range of experiments has no major function in the fermentation process compared to the other three factors .
the empirical predicted quadratic model for response ( bioethanol yield ) in terms of process variables ( incubation period , initial ph , incubation temperature , and molasses concentration ) are plotted in three - dimensional diagrams ( figure 6 ) , to investigate the interaction among the variables and to determine the optimum condition of each factor for maximum bioethanol yield . 

figure 6(a ) represents the effects of varying , incubation period and initial ph on bioethanol yield at constant incubation temperature 38c and molasses concentration 18  wt% .
however , increase in bioethanol yield occurred with an increase in incubation period at ph range from 5.5 to 6.5 .
further increase in initial ph would decrease the bioethanol yield . according to this interaction effects ,
a significant positive impact is detectable ; that is , bioethanol yield increased with the increase of incubation temperature and time .
figure 6(c ) shows the interactive effect of incubation period h and molasses concentration wt.% on bioethanol production at constant initial ph 5.6 and incubation temperature 38c .
it is obvious that with the increase of molasses concentration above 20  wt% , bioethanol yield decreases .
g / l obtained at higher incubation period 72  h and 20  wt.% molasses concentration .  

figure 6(d ) shows the cooperative effect of incubation temperature and initial ph on bioethanol yield at constant incubation period 72  h and molasses concentration 18  wt% . as shown in figure 6(d ) , at low and high ph values , the bioethanol yield decreases . the maximum bioethanol yield 257 
g / l was obtained at high incubation temperature 40c and initial ph of 6 .  

figure 6(e ) illustrates the interactive effect of initial ph and molasses concentration on bioethanol yield at constant incubation period 72  h and temperature 40c .
where , bioethanol yield is low at both low and high molasses concentrations and initial ph .
but bioethanol yield increases within ph range 5.56.5 and molasses concentration 18%22% with maximum yield of 257 
g / l at ph and molasses concentration of 6 and 20% , respectively .  

figure 6(f ) represents the interactive effect of incubation temperature and molasses concentration on bioethanol yield at constant incubation period 72  h and initial ph 5.6 .
it is obvious that with the increase in temperature , the bioethanol yield increases reaching its maximum at 40c , while at low and high molasses concentrations the yield decreases and increased within 18%22% .
g / l is obtained at molasses concentration and incubation temperature of 20% and 40c .  
the optimization process was carried out to determine the optimum value of bioethanol production efficiency , using the design expert 6.0.7 software . according to the software optimization step , the desired goal for each operational condition ( x1 incubation period , x2 initial ph , x3 incubation temperature , and x4 molasses concentration ) was chosen  within  the studied range .
the response ( bioethanol production ) was defined as maximum to achieve the highest performance .
the program combines the individual desirability into a single number and then searches to optimize this function based on the response goal .
accordingly , the optimum working conditions and respective bioethanol production were established , and the results are presented in table 4 . an additional experiment was then performed to confirm the optimum results . as shown , the maximum bioethanol production was 255 
g / l at incubation period of 71  h , initial ph 5.6 , incubation temperature 38c , and molasses concentration of 18% .
recording average of 1.08 and 0.87% , respectively , indicating that process optimization by ccfd was capable and reliable to optimize bioethanol production from sugarcane molasses using saccharomyces cerevisiae y-39 .
rsm and ccfd proved to be reliable and powerful tool for modeling , optimizing and studying the interactive effects of four process variables ( incubation period , initial ph , incubation temperature , and molasses concentration ) of bioethanol production from batch fermentation of sugarcane molasses using locally isolated saccharomyces cerevisiae y-39 .
a highly significant ( r = 0.9871 , p < 0.0001 ) regression quadratic model equation was obtained by analyzing the data of a 2 factorial design . the maximum predicted and actual bioethanol yields are 253 and 255 
 a statistical model was developed in this study to describe bioethanol production through a batch fermentation process of sugarcane molasses by locally isolated saccharomyces cerevisiae y-39 . 
 response surface methodology rsm based on central composite face centered design ccfd was employed to statistically evaluate and optimize the conditions for maximum bioethanol production and study the significance and interaction of incubation period , initial ph , incubation temperature , and molasses concentration on bioethanol yield . with the use of the developed quadratic model equation , a maximum ethanol production of 255  
 g / l was obtained in a batch fermentation process at optimum operating conditions of approximately 71  h , ph 5.6 , 38c , molasses concentration 18%  wt.% , and 100  rpm . 
1. Introduction
2. Materials and Methods
3. Results and Discussion
4. Conclusion