Ind. Eng. Chem. Res. 1997, 36, 1529-1534
1529
Selective Esterification of Glycerine to 1-Glycerol Monooleate. 2. Optimization Studies Nieves Sa´ nchez, Mercedes Martı´nez, and Jose´ Aracil* Facultad de Ciencias Quı´micas, Departamento de Ingenierı´a Quı´mica, Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain
The development and optimization of the synthesis of 1-glycerol monooleate over a zeolite type catalyst using a batch reactor have been carried out. A central composite design has been used in the synthesis of this surfactant. The variables chosen for the present study are temperature and catalyst concentration. The influences of both variables are positive. Response surface methodology has been found to represent adequately the yield of ester. The models obtained in this work have been tested in two scale-up experiments. Within the experimental range studied, these models showed good agreement with the experimental results. Introduction Acyl glycerides, esters of glycerine with different fatty acids, and especially those with only one ester group, in order of importance, glycerol monostearate, glycerol monooleate, and glycerol ricinoleate, are the most widely used food emulsifiers. Demand for these esters increases each day as new processes and secondary products such as DATEM are developed (Lauridsen, 1976). In the first part of this series, it was established that these esters, and, in particular, 1-glycerol monooleate, are obtained as a mixture of 35-60% monoglyceride, 35-50% diglyceride, 1-20% triglyceride, and 1-10% glycerine and fatty acids, depending on the raw materials used. By molecular distillation the amount of monoglyceride can be increased to 95%, but this operation raises the costs of the final product (Meffert, 1984). It is then necessary to develop a process capable of obtaining large quantities of monoglyceride in the most simple way and with lower costs. In our previous work we showed that the esterification process can be developed using zeolites as catalyst (Aracil et al., 1992; Sa´nchez et al.,1992). From an industrial point of view, it is necessary to optimize the process to operate in the most favorable conditions to improve the yield of reaction. The technique chosen to achieve this goal is factorial design of experiments, which uses the response surface methodology to find out the optimum catalyst concentration and temperature values for the reaction. Factorial design of experiments gives more information per experiment than unplanned approaches; it allows us to see interactions among experimental variables within the range studied, leading to a better knowledge of the process and therefore reducing research time and costs (Box et al., 1976). In part 1 of this series, an approximate pseudosecond-order kinetic model has been determined and tested for the selective esterification of 1-glycerol monooleate, showing that it reproduces the experimental results. The reaction was performed in a batch reactor to find out a relationship between the amount of ester obtained and the operating variables affecting the esterification reaction, temperature, and catalyst concentration. Commercial specifications for the final product made it * Author to whom correspondence is addressed. E-mail:
[email protected]. S0888-5885(96)00313-2 CCC: $14.00
necessary to work at a molar ratio of acid/alcohol of 1.0. The pressure and stirring were fixed to 2133 N/m2 and 600 rpm, respectively, by previous experiments. Another aim of this work was to test the statistic and kinetic models obtained in this research to extrapolate them to reactor design and industrial experimental conditions. Two experiments were carried out with a reactor 10 times larger. These models showed good agreement with the experimental results. Experimental Procedure The setup used for the present study was the same as that described in part 1 of this series except for the experiments carried out to study a possible scaleup. These were carried out in a stirred-tank reactor of 5 L, equipped with stationary baffles and a jacket. The experiments were performed and the products were analyzed according to procedures described in part 1 of this series. Results and Discussion All experiments were carried out in the absence of intraparticle resistance. The absence of intraparticle resistance was verified by comparing the yield of ester at 600 and 900 rpm. The difference between the yields was found to be less than 1%, so that the stirring was fixed at 600 rpm. The working pressure was set to 2133 N/m2, so that the water formed in the esterification process was removed continuously and the reaction could be considered as an irreversible reaction. Commercial specifications for the final product made it necessary to work at a molar ratio of acid/alcohol of 1.0. This study has been carried out to determine the effects of temperature and catalyst concentration on the yield of 1-glycerol monooleate and their optimum levels for obtaining the maximum yield of ester. We have used response surface methodology for this purpose. Response surface methodology consists of several steps. The first step is to design a set of experiments and perform them to get reliable values of the response. Factorial design was used for this purpose. The second step is to propose a suitable second-order model to find out the optimum conditions of the independent variables which produce the maximum value of the response. Response. As the problem to be studied in this work is a chemical reaction, the response chosen, Y, was the yield of ester (1-glycerol monooleate) at 30, 60, 180, and 300 min of reaction. © 1997 American Chemical Society
1530 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 Table 1. Levels of FactorssVariable Definition for the Central Composite Design max star point (+R)
max level (+1)
central level (0)
min level (-1)
min star point (-R)
designation
457.15 5.8
453.15 5
443.15 3
433.15 1
429.15 0.2
XT XC
temp (K) catalyst concn (% wt)
Table 2. 22 Factorial Experiment Matrix and Experimental Results
Table 3. Statistical AnalysissMain Effects and Interactions (Confidence Level: 95%)
exp no.
block
xT
xC
T (K)
C (%)
Y30
Y60
Y180
Y300
1 2 3 4 5 6 7 8
1 1 1 1 1 1 2 2
0 1 1 -1 -1 0 0 0
0 1 -1 1 -1 0 0 0
443.2 453.2 453.2 433.2 433.2 443.2 443.2 443.2
3 5 1 5 1 3 3 3
40 56 29 34 32 39 40 41
57 72 49 48 44 58 59 57
68 80 74 68 63 68 69 68
80 83 76 77 71 79 78 80
t ) 30 min S ) 1.132, YC ) 39.825, Y ) 38.70 confidence range ) (2.15 curvature: C ) Y - YC ) -1.15 curvature effect: 2.53 significant influences: T(+), C(+), TC(+) t ) 60 min S ) 0.905, YC ) 57.37, Y ) 55.24 confidence range ) (1.44 curvature: C ) Y - YC ) -2.13 curvature effect: 2.04 significant influences: T(+), C(+), TC(+)
Factors. The selection of the factors was made based on a consideration of the chemical aspect of the system. The factors chosen were temperature and catalyst concentration. The pressure, initial alcohol/acid molar ratio, and stirring were fixed. Levels. The levels for each factor were selected from results obtained in a preliminary study (Sanchez, 1994). These levels are given in Table 1.
t ) 180 min S ) 0.450, YC ) 68.62, Y ) 69.87 confidence range ) (0.72 curvature: C ) Y - YC ) 1.02 curvature effect: 1.01 significant influences: T(+), C(+) t ) 300 min S ) 0.777, YC ) 79.32, Y ) 78.41 confidence range ) (1.39 curvature: C ) Y - YC ) -0.91 curvature effect: 1.75 significant influences: T(+), C(+)
Linear Stage The experimental design applied to this study was a 22 factorial design, to which four central points were added, to evaluate the experimental error. The standard experimental matrix for the factorial design is shown in Table 2. Columns 3 and 4 give the (1 coded factor levels in the dimensionless coordinate, and columns 5 and 6 give the factor levels on a natural scale. Experiments were run at random. Table 2 also shows the results, yield of ester, after 30, 60 180, and 300 min of reaction. A statistical analysis was performed on these experimental values, and the main effects and interaction effects for two variables were calculated. The analysis of the main effects and interaction for the chosen response, yield of ester together with the test of statistical significance, a two-sided test with a 95% confidence level, are given in Table 3. This analysis shows that the temperature and catalyst concentration are the significant effects. The best-fitting response functions for the significant main effects and interaction are given in Table 3. The statistical analysis of experimental results also shows that there is a significant curvature effect. It is, therefore, necessary to consider a different design, which allows us to fit our data to a second-order model. Nonlinear Stage According to the response surface methodology, a second-order model is required, because of the significant curvature effect found in the linear stage. Additional experiments (star points) must be incorporated into the two-level factorial design. Coded levels and the actual values of the two variables are summarized in Table 1, where R, the distance from the origin to the star point, is given by R ) 2n/4; in this design R ) 1.414. The corresponding model is the complete quadratic surface between response and the factors, given by the equation: 2
Y ) b0 +
∑
k)1
2
bkXk +
∑
k)1
2
bkkXk2 +
bkjXkXj ∑ k*j
Influence of Main Effects and Interactions effect
30 min
60 min
180 min
300 min
T C TC
9.5 14.5 12.5
14.5 13.5 9.5
11.5 5.5 0.5
5.5 6.5 0.5
Table 4. Full 22 Central Composite Design MatrixsMain Effects and Interactions exp no.
block
xT
xC
T (K)
C (%)
Y30
Y60
Y180
Y300
1 2 3 4 5 6 7 8 9 10 11 12
1 1 1 1 1 1 2 2 2 2 2 2
0 1 1 -1 -1 0 0 -R 0 a 0 0
0 1 -1 1 -1 0 0 0 a 0 -R 0
443.2 453.2 453.2 433.2 433.2 443.2 443.2 429.2 443.2 457.2 443.2 443.2
3 5 1 5 1 3 3 3 5.8 3 0.2 3
40 56 29 34 32 39 40 39 44 32 43 41
57 72 49 48 44 58 59 50 63 58 59 57
68 80 74 68 63 68 69 60 73 77 71 68
80 83 76 77 71 79 78 67 81 82 84 79
Main Effects and Interactions effect
30 min
60 min
180 min
300 min
T C TC TT CC
2.27 7.60 12.5 -5.37 2.62
10.08 8.16 9.50 -5.62 1.375
11.76 3.45 0.5 0.75 4.25
6.64 2.19 0.5 -4.12 1.87
Table 4 shows the standard orthogonal central composite design matrix. It includes actual and coded levels, experimental results, and the main effects and their interactions obtained from statistical analysis. The best-fitting response surfaces are given in Table 5. The coefficients were obtained by multiple regression analysis. This analysis includes all the independent variables and their interactions, regardless of their significance levels.
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1531 Table 5. Response Surface Models 0.5 h 1h 3h 5h
Statistical Models r ) 0.97 Y ) 40 + 1.137XT + 3.80XC + 6.25XTXC - 2.687XT2 + 1.312XC2 Y ) 57.5 + 5.039XT + 4.082XC + 4.75XTXC - 2.812XT2 + 0.687XC2 r ) 0.89 Y ) 68.25 + 5.88XT + 1.728XC + 0.25XTXC + 0.375XT2 + 2.125XC2 r ) 0.99 Y ) 79.25 + 3.32XT + 1.094XC + 0.25XTXC - 2.0625XT2 + 0.9375XC2 r ) 0.81
0.5 h 1h 3h 5h
Industrial Model Y ) -599.4 + 8.3137T + 53.24C + 0.3125TC - 0.0268.8T2 - 0.3281C2 Y ) -733 + 9.3496T - 39.3653C + 0.2375TC - 0.0281T2 + 0.1718C2 Y ) 72.68 - 0.7245T - 4.5835C + 0.0125TC + 0.00375T2 ( 0.55375C2 Y ) -566.4 + 7.3069T - 2.4839C + 0.0125TC - 0.0206T2 + 0.2344C2
Figure 1. Response surface plot of the statistical model and experimental data for t ) 0.5 h.
The statistical model is obtained from coded levels giving the real influence of each variable on the process and the technological model from the real values of the variables. Figures 1-4 show the response surface plots and contour plots for the experimental values of ester yield and the predicted values for the experimental range of temperature and catalyst concentration, at four different reaction times. These contour plots and dimensional surfaces are the most useful approach in terms of visualization of the reaction system. A good fit of the surface obtained to the experimental data can be observed.
r ) 0.97 r ) 0.89 r ) 0.97 r ) 0.81
Figure 2. Response surface plot of the statistical model and experimental data for t ) 1 h.
Discussion The influence of variables, reaction temperature, and catalyst concentration on the ester yield will now be discussed. The influence of the main factors and interactions will be discussed from statistical models. Influence of Temperature. From statistical analysis, it can be concluded that, for the experimental range, temperature is the most important factor on the esterification process. It has a positive influence on the response; that is, ester yield increases with increasing temperature. At 5 h of reaction time, the change in conversion with temperature was found not to be uniform in the whole temperature range. In the tem-
1532 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997
Figure 3. Response surface plot of the statistical model and experimental data for t ) 3 h.
Figure 4. Response surface plot of the statistical model and experimental data for t ) 5 h.
perature range between center point and star point [(0,0)(R,0)] the total increase in conversion was only 3%, which corresponds to an increase of 0.21%/°C. However, for the lower temperature range [(-R,0)(0,0)] the conversion increased 12%, i.e., 0.86%/°C. The lower conversion increase observed for higher temperatures can probably be due to formation of byproducts, glycerol dioleate and glycerol trioleate. Influence of the Initial Catalyst Concentration. The initial catalyst concentration has a positive influence on the process, but it changes from being the most important factor at low times of reaction to progressively decreasing its influence. This can be explained by the decrease in reaction rate at long reaction times, because reactant concentrations are lower than those at initial times. Influence of Interactions. The above-mentioned effects explain the temperature-catalyst concentration crossed influence. The same as for the effects mentioned previously, its importance decreases along the reaction. This is due in part to formation of byproducts and to the low concentration of reactants at long times of reaction. The interaction has a positive influence which implies that although reaction rate is smaller at
long times the effect of temperature is larger than the low concentration of reactants. Analysis of Response: Yield of Ester. The shapes of the three-dimensional surfaces and contour plots, representing ester yield versus temperature and catalyst concentration, are quite similar, so that the conclusions are valid for all reaction times. The experimental results, confirmed by contour plots, show that the best conditions, from an economical point of view, of the operating variables to obtain the maximum yield of reaction are 180 °C temperature and 5% catalyst concentration. Figures 5 and 6 show the plots of experimental values versus predicted values and the residual analysis for 3 h of reaction. Analogous curves have been obtained for the other times studied. Kinetic and Technological Model Validation To finish the study, both the kinetic model proposed in part 1 of this series and the technological model obtained from the design were compared using a 5 × 10-3 m3 batch reactor for the scaleup of the process. The reactor was provided with baffles along the circumfer-
Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1533 Table 6. Scaleup Working Conditions temperature (K) pressure (N/m2) catalyst concentration (% by weight) glycerine/oleic acid molar ratio reactor volume (m3) time of reaction (h)
453.15 2132.6 5 1:1 3 × 10-3 5
Experimental Conversion to Glycerol Monoleate (%) experiment 1
experiment 2
79
78
technological model
kinetic model
Theoretical Results to Glycerol Monoleate (%) 81 90 Fiability (%) 97
87
Consider that for any volume element, ∆V, of the reactor the conservation principle requires that the mass of species i obeys the following statement:
{rate of i into volume of element} {rate of i out of volume element} + {rate of production of i within the volume element} ) {rate of accumulation of i within the volume element} in our case as we work in batch conditions: Figure 5. Experimental values versus predicted values for t ) 3 h.
{rate of production of 1-glycerol monooleate} ) {rate of accumulation of 1-glycerol monooleate} VRRMO ) dNMO/dt
(1)
RMO ) νMOrMO VRRMO ) -dNAC/dt
(2)
In terms of reaction rate:
-rAC ) νMOIMO + νDIrDI
(3)
where
∫0X
t ) CAC0
Figure 6. Normal probability plot for t ) 3 h.
ence to improve the mixing. The optimum values for temperature and catalyst concentration obtained from the central composite design were chosen. Two additional experiments were carried out, in these conditions. The molar ratio of reactants was fixed to 1, temperature was set at 453 K and the catalyst concentration was 5% by weight. The other conditions, working pressure and stirring speed, were maintained as above.
dXAC -rA
AC
(4)
Substituting in eq 3 the equation we previously obtained for the rate of reaction and operating, we obtain, for the experimental conditions used, a value of acid conversion to glycerol-1-oleate of 90%. From the technological model obtained for 5 h of reaction, we obtain a final conversion to glycerol-1-oleate of 81%. Taking the results obtained from the two additional experiments as shown on Table 6 and comparing them with those obtained from both theoretical models, we obtain 88% when the kinetic model is considered and a fiability of 97% when the technical model from the design of experiments is considered. Both results show the process can be accurately described by the models. Therefore, the models can be used to study the scaleup of the process. The kinetic model is valid for the design of the reactor. The technological model is useful to find the best conditions for working in an industrial plant. Conclusions In this study, a fully central composite design has been applied to optimize the synthesis process of
1534 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997
1-glycerol monooleate. A full two-factorial design has proved effective in the study of the influence of the variables on the process. Central composite design procedure has been followed to optimize the variables that determine the yield of ester. A response equation has been obtained for the yield of ester. From this equation, it is possible to predict adequately the operating conditions required to obtain a well-defined amount of ester. The study of the factors affecting the yield of ester shows that, within the experimental range considered, the most important factor is temperature. This factor has a positive influence. The initial catalyst concentration has a positive influence although it decays during reaction. According to these results, in the experimental condition range the maximum yield of ester (84%) is achieved at intermediate temperature (180 °C) and maximum initial catalyst concentration (5% by weight). The models obtained in the present work, kinetic and technological, have been found to be valid for the scaleup of the process. A change of scale was carried out, and the models were found to predict the experimental results with over 90% accuracy. Therefore, those models have proved to be valid for use on an industrial scale. Acknowledgment Prof. A. Corma (Instituto de Tecnologı´a Quı´mica del Paı´s Valenciano) is gratefully acknowledged for the zeolite preparation and synthesis.
r ) correlation coefficient rAC ) rate of reaction t ) time (h) T ) reaction temperature (K) VR ) reactor volume xk ) natural value for factor K and xjk ) mean natural value for factor K xK ) coded level for factor K XAC ) acid conversion YC ) estimated response at the center points Yt ) estimated response for the experiments (acid conversion) at time t Greek Letters νI ) stoichiometric coefficient for species i
Literature Cited Aracil, J.; Martı´nez, M.; Sa´nchez N.; Corma, A. Formation of a Jojoba Oil Analog by esterification of oleic acid using zeolites as catalysts. Zeolites 1992, 12, 233-236. Box, G.; Hunter, J.; Hunter, J. Statistics for Experiments; John Wiley & Sons: New York, 1976. Lauridsen, I. B. Food Emulsifiers: Surface Activity, Edibility, Manufacture, Composition and Application. J. Am. Oil Chem. Soc. 1976, 53, 400-407. Meffert, A. Technical uses of fatty acid esters. J. Am. Oil Chem. Soc. 1984, 61, 255-258, Sa´nchez, N. Design of Zeolite Systems as Catalysts for the Synthesis of Fine Chemicals (Disen˜o de Sistemas Zeoliticos como Catalizadores de sı´ntesis de productos de Quı´mica Fina). Ph.D. Dissertation, Universidad Complutense, Madrid, Spain, 1994. Sa´nchez, N.; Martinez, M.; Aracil, J.; Corma, A. Synthesis of Oleyl oleate as a jojoba oil analog. J. Am. Oil Chem. Soc. 1992, 69 (11), 1150-53.
Nomenclature C ) initial catalyst concentration (% by weight) CACO ) initial acid concentration d ) unit of variation from x to xj i ) species, monoester, diester, or acid K ) factor; either C (initial catalyst concentration) or T (temperature) Ni ) mole number at time t of species i RA ) intrinsic reaction rate of production
Received for review June 3, 1996 Revised manuscript received January 8, 1997 Accepted January 13, 1997X IE960313W
X Abstract published in Advance ACS Abstracts, March 15, 1997.
