Kinetics of the Hydrolysis of Palm Oil and Palm Kernel Oil - Industrial

The development of the overall rate equation for this reaction system, the ... graph by the linear-regression method using the computer software Micro...
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Ind. Eng. Chem. Res. 2006, 45, 1604-1612

Kinetics of the Hydrolysis of Palm Oil and Palm Kernel Oil Ambrose N. Anozie* and Joselin M. Dzobo Department of Chemical Engineering, Obafemi Awolowo UniVersity, Ile-Ife, Nigeria

A low-temperature, ambient-pressure, catalyzed, batch process involving hydrolysis was used to prepare fatty acids from palm oil and palm kernel oil. The acid value and saponification value were determined and used to calculate the concentration of triglycerides in solutions. The effects of water-to-oil ratio, catalyst concentration, temperature, and reaction time on the hydrolysis were studied, and the kinetics of the hydrolysis was developed. The catalyst used was a mixture of linear alkyl benzene sulfonate and sulfuric acid. The overall rate of reaction expression was used to quantify the mass transfer and chemical reaction resistances and, hence, the total resistance. The mechanism of reaction was also developed. The variation of resistances and reaction rate constant with temperature were investigated. It was found that the kinetics was one of shifting order from zero order to higher order as the reaction progressed from zero time. The total resistance represented the lumped effect of the resistances to mass transfer and chemical reaction, and it was found to be a good measure of the extent of reaction, that is, the smallest total resistance corresponded with the highest conversion and vice versa. Temperature effect on the mass transfer resistance was very weak, but temperature effect on chemical reaction resistance was strong. Introduction The hydrolysis or splitting of fats/oils produces fatty acids and glycerols. This is achieved by a variety of methods. These include the ambient-pressure, low-temperature Twitchell process with catalyst, in which the oils/fats are heated by steam spargers and closed coils in open vessels;1 the medium-pressure autoclave splitting with catalyst;2,3 the continuous, countercurrent, uncatalyzed, high-pressure splitting;2,3 and the enzymatic fat splitting.4 The stoichiometry of the hydrolysis of fats/oils is generally represented as an oversimplified reversible chemical reaction consisting of adding water to a triglyceride to produce glycerol and three molecules of fatty acids,5,6

C3H5(OCOR)3 + 3H2O h 3RCOOH + C3H5(OH)3 (1) where R represents any alkyl radical. At ordinary temperatures, oils are poorly soluble in water; the hydrolysis, therefore, proceeds extremely slowly. Catalytic agents greatly accelerate the rate of reaction at low temperatures and, therefore, have found extensive applications in commercial processing. At elevated temperatures and pressures, the solubility of oils in water is increased to such an extent that hydrolysis proceeds quite rapidly even in the absence of catalysts. Hartman7 reported that the progress of Twitchell splitting of triglycerides in the early stages before equilibrium is approached can be represented by first-order kinetics in terms of the amount of triglycerides in solution only. The mechanism was assumed to involve two or more steps, with the step in which the water molecule was involved being relatively fast. The hydrolysis of fats/oils at low temperatures in the presence of a catalyst is a complex, heterogeneous, liquid-liquid reaction. The chemical rate equation for such a nonelementary reaction may not match the stoichiometry. Moreover, the overall rate expression will have to account for the mass transfer and chemical rates. The mechanism of reaction is usually developed from the chemical rate equation. * To whom all correspondence should be addressed. E-mail: [email protected].

Despite the fact that the fatty acids processing technology has been an established industry for about a century, there exists a dearth of technical data in the literature. This study was, therefore, undertaken as part of the technical survey to generate the necessary chemical kinetic and process data for the preparation of fatty acids. These data will elucidate the process dynamics which will form the basis for further studies in the development of an indigenous fatty acids processing technology. In this study, palm oil, unlike palm kernel oil, underwent a bleaching pretreatment because of the presence of color bodies and impurities such as carotenes, gums, lecithin, and sterols. The mixture of bleached palm oil or palm kernel oil and water was heated and catalyzed by a mixture of linear alkyl benzene sulfonate and sulfuric acid which accelerated hydrolysis at atmospheric pressure.8 The effects of variation of water-to-oil ratio, concentration of catalyst, temperature, and reaction time with hydrolysis were studied by taking samples from the reaction mixture at time intervals to analyze for the acid and saponification values using volumetric analysis. These values were used to estimate the concentration of triglycerides in the reaction mixture. The kinetics of hydrolysis of palm oil and palm kernel oil at low temperatures, the overall rate expression incorporating the mass transfer and chemical rates, and the mechanism of reaction were developed. The influence of temperature on mass transfer and chemical reaction resistances and the reaction rate constant were studied. Experimental Section Materials. The palm oil and palm kernel oil were purchased from an oil mill and plantation at Benin-City. The linear alkyl benzene sulfonate (96%) was manufactured by a detergent manufacturing company in Nigeria. The concentrated sulfuric acid (98%) was manufactured by BDH Laboratory Supplies. Methods. a. Characterization of Oils. The official methods of analysis (AOAC9) were used for the determination of iodine value, saponification value, acid value, and fatty acids analysis of the oils. The evaluation of absorbance and degree of bleaching of palm oil were done using the method documented in the British Standard Institution, BSI.10

10.1021/ie0508076 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/26/2006

Ind. Eng. Chem. Res., Vol. 45, No. 5, 2006 1605

b. Hydrolysis of Oil. The process used for hydrolysis of oils in this study was a low-temperature, low-pressure, catalyzed process in which oil, water, and catalyst, in a flat-bottomed flask fitted with a reflux condenser, were heated on a thermostatic hotplate with a magnetic stirrer. This experimental setup was very close to that of the Twitchell process. This method was adopted because of its simplicity, easy adaptability, low capital requirement, and possibility of taking measurements manually as the reaction proceeded. A sample of the bleached palm oil or clean palm kernel oil was weighed into a 500 cm3 quickfit flat-bottomed flask placed on top of a Gallenkamp thermostatic hotplate. Catalyst, in the form of a mixture of linear alkyl benzene sulfonate and sulfuric acid, was used. The linear alkyl benzene sulfonate of mass 0.5% (w/w) of oil was added to the oil, which was heated and agitated using a 1.5-in. magnetic rod as the stirrer. Boiling water containing 10% (v/v) sulfuric acid of mass 25% (w/w) of oil was added to the hot oil and linear alkyl benzene sulfonate in the hydrolyzer. The temperature was set as required, and a reflux condenser was fitted to the flat-bottomed flask. The hydrolysis reaction taking place in the splitter was allowed to run for a length of time with samples taken at specific time intervals for the analysis of the acid and saponification values. The following hydrolysis parameters were varied in order to determine their influence on the hydrolysis: • The water-to-oil ratio was varied at 25%, 50%, and 75% (w/w) of oil at 0.50% (w/w) catalyst-to-oil ratio. • The catalyst level was varied at 0.25%, 0.50%, and 0.75% (w/w) catalyst-to-oil ratio for palm oil and 0.125%, 0.25%, and 0.50% (w/w) catalyst-to-oil ratio for palm kernel oil, at the optimum water-to-oil ratio and temperature. • The temperature of reaction was varied at 80, 90, 95, and 100 °C at the optimum water-to-oil ratio • The number of stages of hydrolysis was increased to two in order to push the hydrolysis to a higher level of completion. The water-to-oil ratio was varied in the second stage of hydrolysis as in the first stage. c. Analysis of Samples. The samples taken from the hydrolyzer at specific time intervals were chilled to -10 °C, whereupon the oil rapidly solidified and the reaction quenched. The sample was then melted and washed with water to remove traces of glycerol (except in the case of palm kernel oil, because it contains a lot of water-soluble fatty acids). The samples were placed in desiccators for drying. They were then analyzed for their acid and saponification values. The acid value (AV) is a measure of the free fatty acids (FFA) present in a sample. The saponification value (SV) is a measure of the free fatty acids and triglycerides present in a sample. The progress of the reaction was monitored by means of the acid value and saponification value. The moles of triglycerides in solution, NA, was calculated as follows,

NA )

[(

SV - AV M SV MW

)

]

(2)

where M is the mass of oil and MW is the molecular weight of oil. The concentration of triglycerides (reactant A) in solution was calculated by the equation

CA )

NA VT

(3)

where VT is the total volume of oil and water in liters. The

Table 1. Characterization of Oils this study unbleached bleached palm oil palm oil acid value saponification value iodine value absorbance degree of bleaching (%) avg. mol. wt. of fatty acids

14.4 204.0 55.8 0.276

12.3 209.1 60.5 0.027 90.24

262.3

255.6

this Ooi & Pee12 study Ooi & Pee12 palm oil 2-15 196-202 48-56

palm kernel oil

palm kernel oil

26.3 3-17 253.8 243-249 14.3 16.2-19.2

208.4

fractional conversion was then calculated as

XA ) 1 -

CA CA0

(4)

where CA0 is the concentration of triglycerides at the beginning of the reaction. Fractional conversion was used in this work rather than degree of hydrolysis, which was defined as the ratio of acid value to saponification value of a sample.11 Results and Discussion Characterization of the Oils. The results obtained from the analysis of the unbleached palm oil, bleached palm oil, and palm kernel oil are presented in Table 1. These results agree favorably well with literature values.12 Effects of Varying Operating Parameters. The effects of varying the initial water concentration, CB0, on the reaction are shown in Figures 1 and 2 for palm oil and palm kernel oil, respectively. By varying the initial water-to-oil ratio, the catalyst concentration was varied as well. It was found that a 25% (w/ w) water-to-oil ratio with an initial catalyst concentration of 0.018 gmol/L offered the best local optimum value for the hydrolysis of palm oil and that a 50% (w/w) water-to-oil ratio with an initial catalyst concentration of 0.015 gmol/L was optimum for palm kernel oil. The results were different because the oils were different and showed that, in the hydrolysis of oils, the optimum water-to-oil ratio and catalyst concentration have to be determined experimentally. It was also observed that, at the optimum water-to-oil ratio, palm oil had a higher conversion than palm kernel oil, but palm kernel oil took a shorter time to reach maximum conversion than palm oil. The effects of varying catalyst level on the hydrolysis are shown in Figures 3 and 4 for palm oil and palm kernel oil, respectively. It was observed that, above a certain limit, there was so much emulsification that there was excessive foaming of the reaction mixture, causing the reaction vessel to be flooded. Below a certain level of catalyst, too, the rate of hydrolysis became too low, especially for palm oil. The catalyst-to-oil ratio of 0.50% (w/w) was found to be the best local optimum level for the hydrolysis of both oils. The results obtained by varying the temperature at which the hydrolysis was carried out are presented in Figures 5 and 6 for palm oil and for palm kernel oil, respectively. It was observed that the rate and completeness of the hydrolysis decreased with a decrease in temperature. The effect of double-stage operation is presented in Figures 7 and 8 for palm oil and palm kernel oil, respectively. It was observed for palm oil that the variation of water-to-oil ratio with conversion in stage two was also of the same trend as in stage one (Figure 1). For palm kernel oil, the optimum water-to-oil ratio in stage two (50% (w/w)) was also the same as in stage

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Figure 1. Effect of water-to-oil ratio on the hydrolysis of bleached palm oil.

Figure 2. Effect of water-to-oil ratio on the hydrolysis of palm kernel oil.

one (Figure 2), but the variations of 25% (w/w) and 75% (w/ w) water-to-oil ratios with conversion in stage two were the reverse of that in stage one. The double-stage operation increased the conversion from 0.72 to 0.96 for palm oil and from 0.65 to 0.86 for palm kernel oil in 6 h, and the total reaction time was 12 h. It was further observed in stage two that, at the optimum water-to-oil ratio, palm oil had a higher conversion and took a shorter time to reach maximum conversion than palm kernel oil. Search for the Kinetic Model. The kinetics of the reaction was developed in terms of the concentration of triglycerides during the reaction, CA, and the initial catalyst concentration, CC0. Typical graphs of concentration of triglycerides versus time during hydrolysis are presented in Figure 9 for palm oil at 25% (w/w) water-to-oil ratio and Figure 10 for palm kernel oil at 50% (w/w) water-to-oil ratio. It was found that the best fit to the experimental data began with a straight line portion followed after some hours by a curved portion. This showed that the reaction was one of shifting order, which began with zero order and then moved to a higher order n. The order n was determined using the differential method. The shifts in the order of reaction

Figure 3. Effect of catalyst on the hydrolysis of bleached palm oil using 25% (w/w) water-to-oil ratio.

Figure 4. Effect of catalyst on the hydrolysis of palm kernel oil using 50% (w/w) water-to-oil ratio.

for different initial water-to-oil ratios investigated are presented in Table 2. It was assumed that the rate of reaction was proportional to catalyst concentration within the catalyst concentration range used. The general rate equation, which can account for the shift from zero order to n order, was proposed to be of the form

-rA )

k′CC0CnA k′′ + CnA

(5)

where rA is the rate of reaction of the triglycerides, CC0 is the initial concentration of catalyst, and CA is the concentration of the triglycerides. Also, the shift from zero order to first order was proposed to be of the following form:

-rA )

k′CC0CA k′′ + CA

(6)

From eqs 5 and 6, it is seen that, at high CA (CA . k′′), the

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Figure 5. Effect of temperature on the hydrolysis of bleached palm oil using 25% (w/w) water-to-oil ratio. Figure 7. Double-stage hydrolysis of bleached palm oil to determine the effect of water-to-oil ratio on the second stage.

Figure 6. Effect of temperature on the hydrolysis of palm kernel oil using 50% (w/w) water-to-oil ratio.

reaction is of zero order and is given by

-rA ) k′CC0 (high CA, zero order)

(7a)

From eq 5, at low CA (CA , k′′), the reaction is of n order and is given by

-rA )

k′ C Cn (low CA, n order) k′′ C0 A

(7b)

From eq 6, at low CA (CA , k′′) the reaction is of first order and is given by

-rA )

k′ C C (low CA, first order) k′′ C0 A

(7c)

It has been stated that this type of rate equation is used to represent the kinetics of surface-catalyzed reactions.13 Earlier workers7,14 had proposed a first-order kinetic model with respect to the triglycerides only. The general chemical rate eqs 5 and 6 were tested by integral analysis. Integration of eq 5 between the limits of concen-

Figure 8. Double-stage hydrolysis of palm kernel oil to determine the effect of water-to-oil ratio on the second stage.

tration, CA0 to CA, and time, 0 to t, gave the following equation:

CA0 - CA C1-n A

-

C1-n A0

)

(

CC0t - k′′ + k′ 1-n n-1 CA - C1-n A0

)

n>1

(8)

Similarly, integration of eq 6 gave the following equation:

( )

CA0 - CA CC0t ) -k′′ + k′ CA0 CA0 ln ln CA CA

(9)

Equations 8 and 9 were tested using concentration versus time data extracted from the smooth curves of concentration versus time, the order, and the duration of reaction in Table 2. Figure 11 shows the test of eq 8 on bleached palm oil at 25% (w/w)

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Figure 9. Concentration versus time in the hydrolysis of bleached palm oil at 25% (w/w) water-to-oil ratio.

Figure 11. Test of the integral analysis, eq 8, for bleached palm oil at 25% (w/w) water-to-oil ratio.

Figure 10. Concentration versus time in the hydrolysis of palm kernel oil at 50% (w/w) water-to-oil ratio. Table 2. Shift in the Order of Reaction in the Hydrolysis of Palm Oil and Palm Kernel Oil oil palm oil

initial water-to-oil ratio, %(w/w)

duration, h

order, n

25

0-5 5-18 18-24 0-9 9-18 18-24 0-12 12-24 0-4 4-7 7-12 0-3.4 3.4-12 0-6 6-12

0 2.86 termination 0 2.50 termination 0 1 0 10.53 termination 0 5.12 0 2.86

50 75 palm kernel oil

25 50 75

water-to-oil ratio and Figure 12 shows the test of eq 9 on bleached palm oil at 75% (w/w) water-to-oil ratio. Figure 13 shows the test of eq 8 on palm kernel oil at 50% (w/w) waterto-oil ratio. It is seen from Table 2 that palm kernel oil did not

Figure 12. Test of the integral analysis, eq 9, for bleached palm oil at 75% (w/w) water-to-oil ratio.

have a reaction with a shift from zero to first order and eq 9 was not applicable to it. A linear relationship was obtained which showed that the kinetic model developed was meaningful. The data points in Figures 11-13 were calculated by a computer program written in FORTRAN language, and the straight lines were fitted by the linear-regression method using the computer software Microcal Origin. Overall Rate Equation. The development of the overall rate equation for this reaction system, the integral analysis of the overall rate equation, and equations for the evaluation of resistances to mass transfer and chemical reaction are given in the Appendix. Integral analysis equations, eqs A8 and A9, were applied to the linear portion and curved portion, respectively, of the concentration versus time graph. Only in the case of the first-order reaction was eq A8 applied to the curved portion of the graph. The data points generated for each case were used to fit a straight line graph by the linear-regression method using the computer software Microcal Origin. Very good fits were

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Figure 13. Test of the integral analysis, eq 8, for palm kernel oil at 50% (w/w) water-to-oil ratio. Table 3. Effects of Initial Water-to-Oil Ratio and Catalyst on Mass Transfer and Chemical Reaction Resistances in the Hydrolysis of Palm Oil and Palm Kernel Oil Using the Overall Rate Equation

oil palm oil

palm kernel oil

initial linear portion initial catalyst water-to-oil conc., CC0, ratio, %(w/w) gmol/L RM RC RT 25 50 75 25 50 75

0.018 0.015 0.013 0.018 0.015 0.013

0.69 0.27 2.87 0.20 0.96 3.67

4.29 9.13 16.52 5.79 3.90 14.04

4.98 9.40 19.39 5.99 4.86 17.17

curved portion RM

RC

RT

2.87 6.46 5.35 4.55 3.32 8.34

6.78 3.20 3.20 8.42 7.33 3.09

9.65 9.66 8.55 12.97 10.65 11.43

obtained for all the cases. From these straight-line graphs, the resistance to mass transfer was calculated using eq A10 and the resistance to chemical reaction was calculated by either eq A11 or eq A12. The reaction rate constant for the zero-order reaction was calculated by eq A13. The mass transfer and chemical reaction resistances in the hydrolysis of palm oil and palm kernel oil were calculated for different initial water-to-oil ratios and catalyst concentrations and are summarized in Table 3. By varying the initial waterto-oil ratio, the initial concentration of the catalyst, containing linear alkyl benzene sulfonate and sulfuric acid, was varied as well. It was observed in the linear portion of the concentration versus time data for palm oil that the minimum resistance to mass transfer of 0.27 occurred at a 50% (w/w) water-to-oil ratio and an initial catalyst concentration of 0.015 gmol/L, and the minimum resistance to chemical reaction of 4.29 occurred at a 25% (w/w) water-to-oil ratio and an initial catalyst concentration of 0.018 gmol/L. For palm kernel oil, the minimum resistance to mass transfer of 0.20 occurred at a 25% (w/w) water-to-oil ratio and an initial catalyst concentration of 0.018 gmol/L, and the minimum resistance to chemical reaction of 3.90 occurred at a 50% (w/w) water-to-oil ratio and an initial catalyst concentration of 0.015 gmol/L. The catalyst acted both as surface-active agent and hydrolyzing acid. The surface activity of the catalyst influenced the mass transfer resistance, while the acidic action influenced the chemical reaction resistance.

The way the catalyst (and water, indirectly) influenced the resistances to mass transfer and chemical reaction for the two oils were different. The total resistance gave the lumped effect of the actions of the catalyst and water and is the parameter to be used in investigating the overall rate of reaction. The variations of total resistance with initial water-to-oil ratio for palm oil and palm kernel oil were in conformity with experimental observations in Figures 1 and 2. For palm oil, the smallest total resistance of 4.98 was obtained at the optimum water-to-oil ratio of 25% (w/w). Also, palm kernel oil had the smallest total resistance of 4.86 at the optimum water-to-oil ratio of 50% (w/w). Similarly, the total resistances in the curved portion of the concentration versus time graph gave meaningful results. For palm oil, considering only water-to-oil ratios with an n-order reaction, the smallest total resistance was 9.65 at the optimum water-to-oil ratio of 25% (w/w). The total resistance of 8.55 for palm oil was obtained for the first-order reaction at a 75% (w/w) water-to-oil ratio. For palm kernel oil, all water-to-oil ratios have an n-order reaction, and the smallest total resistance of 10.65 was obtained at a 50% (w/w) water-to-oil ratio. Search for the Reaction Mechanism. The hydrolysis of palm oil and palm kernel oil was found to be well-correlated by the rate equation, eq 5. This was hypothesized by a twostep elementary reaction mechanism,

nA +

1

3

+ nQ + C I* + 3nB 98 3nP C h 2 catalyst water fatty acids glycerol (10)

where I* is an intermediate complex. In the first step, the oil reacts with the catalyst to produce an intermediate by a reversible reaction. In the second step, this intermediate reacts with water to form the free fatty acids and glycerol, regenerating the catalyst. This mechanism is similar to the MichaelisMenten15 mechanism for the enzyme-substrate reaction. The initial catalyst concentration was assumed to be equal to the free catalyst concentration and the concentration of catalyst attached to reactant and was written as follows:

CC0 ) CC + CI*

(11)

The second assumption was the steady-state assumption made by Briggs and Haldane:16

dI* )0 dt

(12)

Using these two assumptions, it was derived that

nk3CC0CnA k′CC0CnA -dA dQ ) ) ≡ dt dt k2 + k3 k′′ + CnA + CnA k1

( )

(13)

When CA . k′′ w zero order and high CA, and when CA , k′′ w n order and low CA. The kinetics and mechanism of reaction suggested that the overall reaction could be represented as follows: CC0,3nCB0

nA 98 3nP + nQ

(14)

CC0,3nCB0

i.e., nC3H5(OCOR)3 98 3nRCOOH + nC3H5(OH)3 (14a) There is a reaction between water and the intermediate complex

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Table 4. Effect of Temperature on Resistances and Reaction Rate Constant in the Hydrolysis of Palm Oil and Palm Kernel Oil Using the Overall Rate Equation and Zero Order Kinetics oil

T, K

RM

RC

RT

%RM

k′, h-1

palm oil

373 368 363 353 373 368 363 353

0.17 0.17 0.40 408.67 0.08 0.40 1.58 0.74

4.99 6.57 7.95 4444.17 4.62 6.41 9.84 17.22

5.16 6.74 8.35 4852.84 4.70 6.81 11.42 17.96

3.3 2.5 4.8 8.4 1.7 5.9 13.8 4.1

59.71 47.17 37.48 0.93 80.65 60.29 41.65 25.88

palm kernel oil

which does not appear in the overall reaction. The kinetics and mechanism of reaction do not match the stoichiomatry as given by eq 1. Even though water did not appear as a reactant in the above equation, it indirectly influences the concentration of triglycerides as given by eq 3. Variation of Resistances and Reaction Rate Constant with Temperature. The resistances to mass transfer and chemical reaction, the total resistance, and the reaction rate constant were evaluated at different temperatures at the optimum initial waterto-oil ratio and for zero-order kinetics only using eqs A8, A10, A11, and A13. The results are summarized in Table 4. Lower values of the resistance to mass transfer compared to the chemical reaction resistance showed that chemical reaction was the rate-determining step. The total resistance, which combined the double action of the catalyst, decreased with an increase in temperature. It was observed that at 80 °C the resistances in palm oil increased by a large factor and also the reaction rate constant decreased to a very small value compared to the values at 90-100 °C. Increase in resistances and a decrease in the reaction rate constant at 80 °C compared to those at 90-100 °C for palm oil could mean a very slow reaction at 80 °C becoming faster at 90-100 °C. It was also observed that an increase in temperature increased the chemical reaction rate constant and decreased the chemical reaction resistance. This suggested that higher temperatures would enhance the hydrolysis reaction.

and is given by

1 kAGa

+

pA

1

(A2)

HA HA + kALaE kCBfL

where 1/(kAGa) is the gas film resistance, HA/(kALaE) is the liquid film resistance, and HA/(kCBfL) is the liquid bulk resistance. Equation A2 can be written for the liquid-liquid (here oil-water) reaction system using concentration terms rather than partial pressure to give the following expression: -r0A )

1 oil film resistance + water film resistance +

CA 1 kCBfL (A3)

In the hydrolysis of fats/oils, it is reasonable to assume that the water film resistance is much larger than the oil film resistance for the diffusion of oil through both films. Second, since our interest in this study is simply to quantify the resistances to mass transfer and chemical reaction, the total film resistances can be lumped together. Therefore, the overall rate expression can simply be written as

-r0A )

1 C R M + RC A

(A4)

where RM is the resistance to mass transfer and RC ) 1/kCBfL is the resistance to chemical reaction. Second-order kinetics, eq A1, was used to derive the overall rate expression of eq A2. According to Levenspiel,13 since no analysis is available for other than second-order reactions, other reactions such as the rate equation, eq 5, can be replaced with a second-order approximation as follows,

-rA )

Conclusions

1

-r0A )

k′CC0CnA

) k′CC0CA

k′′ + CnA

[ ] Cn-1 A

k′′ + CnA

≡ k′CC0CACB (A5)

In the hydrolysis of palm oil and palm kernel oil to fatty acids at low temperatures, the kinetics was found to be one of shifting order, from zero order to higher order n with respect to the concentration of triglycerides. The rate of reaction was also proportional to the initial catalyst concentration used. The catalyst influenced the mass transfer and chemical reaction resistances. The total resistance was in agreement with the extent of reaction. The resistance to chemical reaction was the ratedetermining step. The temperature effect on the mass transfer resistance was very weak, but the temperature effect on chemical reaction resistance was strong. This showed that higher temperatures would greatly improve the hydrolysis reaction.

and the overall rate equation, similar to eq A4, was derived as

Appendix

where k′′/(k′fLCC0Cn-1 A ) is the chemical reaction resistance for the curved portion and CnA/(k′fLCC0Cn-1 A ) is the chemical reaction resistance for the linear portion. The integral analysis of this equation was carried out as follows:

Development of the Overall Rate Equation and Evaluation of Mass Transfer and Chemical Reaction Resistances and Rate Constant. For a gas-liquid reaction system with secondorder kinetics,

-rA ) kCACB

(A1)

where subscripts A and B refer to reactants, the overall rate expression based on the two-film theory has been developed13

-r0A )

CA RM +

Cn-1 A

k′fLCC0 k′′ + CnA -r0A )

-

CA

)

1

RM +

k′′ + CnA k′fLCC0Cn-1 A

1 CnA k′′ RM + + k′fLCC0Cn-1 k′fLCC0Cn-1 A A

CA

(A6)

1 dt k′′ 1 1 )) RM + + 0 n dC C f k′C rA fLk′CC0CA A A L C0

∫0t -dt ) ∫CC

A

A0

[

]

1 k′′ 1 RM + + dCA CA f k′C Cn fLk′CC0 L C0 A

Ind. Eng. Chem. Res., Vol. 45, No. 5, 2006 1611

-t ) RM ln

1-n CA k′′(C1-n (CA - CA0) A - CA0 ) + + CA0 fLk′CC0 fLk′CC0(1 - n)

[ ( )] [ ( )]

1-n CA - CA0 C1-n A - CA0 k′′ 1 + ) C C k′fL C ln A k′(1 - n)fL CC0 ln A C0 CA0 CA0 linear portion curved portion

-RM -

t (A7) CA ln CA0

This equation contained concentration terms for the linear and curved portions of the concentration versus time graph. It was used to analyze the cases of zero-order, n-order, or first-order reactions. For a high CA and zero-order reaction, which represents the linear portion of the concentration versus time graph, and neglecting the curved portion of the reaction, eq A7 reduced to

[ ( )] CA0 - CA CA0 CC0 ln CA0

) -k′fLRM + k′fL

( ) t CA0 ln CA

n ) 0 or 1 (A8)

For a low CA and n-order reaction, which represents the curved portion of the concentration versus time graph, and neglecting the linear portion of the reaction, eq A7 reduced to

( ( ))

( )

1-n -k′(n - 1)fL k′(n - 1)fL C1-n A - CA0 t RM + ) CA0 CA0 k′′ k′′ CC0 ln ln CA0 CA n > 1 (A9)

For the special case when n ) 1, that is, a first-order reaction, eq A7 reduced to eq A8. Therefore, eq A8 was also used to handle first-order reactions. The resistance to mass transfer was calculated from the straight-line graph of eq A8 or A9 as

intercept RM ) slope

(A10)

The resistance to chemical reaction for a zero- or first-order reaction was calculated from eqs A6 and A8 as follows,

RC )

CA,avg 1 ) n ) 0 or 1 -1 slope × CC0 (k′fL)CC0CA

1 n-1 ) n>1 k′fL slope × CC0Cn-1 n-1 A,avg C C k′′ C0 A

( )

(A12)

where CA,avg is the average concentration for the portion considered. The rate constant for the linear portion of the concentration versus time graph was calculated from eq A8 as follows:

k′ )

slope fL

Nomenclature a ) interfacial area per unit volume, m2/m3 C ) concentration, gmol/L E ) enhancement factor for mass transfer with reaction fL ) volume fraction of liquid H ) Henry’s law constant for gas-phase systems, Pa‚m3/mol I* ) intermediate complex k′ ) reaction rate constant for zero-order kinetics, h-1 k" ) constant, (mol/L)n k1, k2, k3 ) reaction rate constants for mechanism studies k ) reaction rate constant for second-order kinetics in the general overall rate equation kG ) mass transfer coefficient of the gas film, mol/m2‚Pa‚s kL ) mass transfer coefficient of the liquid film, m3/(m2 of surface) M ) mass of triglycerides, g MW ) molecular weight of triglytcerides n ) order of reaction N ) amount of triglycerides, gmol pA ) partial pressure of component A, Pa r ) rate of reaction, (mol/L) h-1 r0 ) overall rate of reaction, (mol/L) h-1 RM ) resistance to mass transfer RC ) resistance to chemical reaction RT ) total resistance t ) time, h T ) temperature, K or °C VT ) total volume of oil and water, L X ) fractional conversion Subscripts A ) triglycerides B ) water C ) catalyst 0 ) initial Literature Cited

(A11)

and the resistance to chemical reaction for an n-order reaction was calculated from eqs A6 and A9 as follows,

RC )

Supporting Information Available: The supporting information includes (1) concentration versus time graphs for palm oil at 50% (w/w) and 75% (w/w) and for palm kernel oil at 25% (w/w) and 75% (w/w) water-to-oil ratio; (2) further details about the development of integral equations from the rate equations; and (3) FORTRAN coding for the testing of the integral equations. This material is available free of charge via the Internet at http://pubs.acs.org.

(A13)

(1) Sonntag, N. O. V. Fat Splitting. J. Am. Oil Chem. Soc. 1979, 56 (II), 729A-732A. (2) Muckerheide, V. J. Industrial Production of Fatty Acids: Fatty Acids; Their Chemistry, Properties, Production and Uses, Part 4, 2nd ed.; Interscience Publishers: New York, 1967; pp 2679-2702. (3) Sonntag, N. O. V. New Developments in the Fatty Acid Industry. J. Am. Oil Chem. Soc. 1979, 56 (II), 861A-864A. (4) Linfield, M. W.; Barauskas, R. A.; Sivieri, L.; Serota, S. I.; Stevenson, R. W., Sr. Enzymatic Fat Hydrolysis and Synthesis. J. Am. Oil Chem. Soc. 1984, 61 (2), 191-195. (5) Morrison, R. T.; Boyd, R. N. Organic Chemistry, 4th ed.; Allyn and Bacon Inc.: New York, 1983. (6) Yunus, R.; Fakhru’l-Razi, A.; Ooi, T. L.; Iyuke, S. E.; Idris, A. Development of Optimum Synthesis Method for Transesterification of Palm Oil Methyl Esters and Trimethylolpropane to Environmentally Acceptable Palm Oil-Based Lubricant. J. Oil Palm Res. 2003, 15 (2), 35-41. (7) Hartman, L. Kinetics of the Twitchell Hydrolysis. Nature 1951, 167, 199-200. (8) Twitchell, E. Benzenestearosulphonic Acid and Other Sulphonic Acids Containing the Stearic Radical. J. Am. Chem. Soc. 1900, 22, 22.

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(9) AOAC. Official Methods of Analysis; Association of Official Analytical Chemists: Washington, DC, 1990. (10) BSI. Determination of Carotene in Vegetable Oils, British Standard Methods of Analysis of Fats and Fatty Oils; British Standard Institution: London, 1977; Vol. BS 684 (No. 2), p 20. (11) Sturzenegger, A.; Sturm, H. Hydrolysis of Fats at High Temperatures. Ind. Eng. Chem. 1949, 43 (2), 510-515. (12) Ooi, S. L.; Pee H. P. Processing for Industrial Fatty Acids II. J. Am. Oil Chem. Soc. 1985, 62 (2), 348-351. (13) Levenspiel, O. Chemical Reaction Engineering, 3rd ed.; John Wiley & Sons: New York, 1999.

(14) Cox, C. B. An Approach to Continuous Twitchell Fat Splitting. Trans. Inst. Chem. Eng. 1949, 27, 123-137. (15) Michaelis, L.; Menten, M. L. The kinetics of invertin action. Biochem. Z. 1913, 49, 333. (16) Briggs, G. E.; Haldane, J. B. S. A note on the kinetics of enzyme action. Biochem. J. 1925, 19, 338.

ReceiVed for reView July 9, 2005 ReVised manuscript receiVed December 18, 2005 Accepted December 22, 2005 IE0508076