Lipase-catalyzed acidolysis of sunflower oil: Kinetic behavior

Journal of Food Engineering 98 (2010) 492–497

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Lipase-catalyzed acidolysis of sunflower oil: Kinetic behavior Consuelo Pacheco, Guillermo H. Crapiste, María E. Carrín * PLAPIQUI (Universidad Nacional del Sur – CONICET), Camino La Carrindanga Km 7, 8000 Bahía Blanca, Argentina

a r t i c l e

i n f o

Article history: Received 28 September 2009 Received in revised form 23 December 2009 Accepted 22 January 2010 Available online 29 January 2010 Keywords: Enzymatic acidolysis Structured lipids Sunflower oil Lipozyme RM IM Reaction kinetic

a b s t r a c t In the present study, sunflower oil was modified with a palmitic–stearic acids blend by means of an immobilized sn-1,3 specific lipase (Lipozyme RM IM) to produce structured lipids. Products were analyzed to determine fatty acid incorporation (FM) into triacylglycerol structure and to quantify by-products as monoglycerides (MG) and diglycerides (DG). The effects of the reaction conditions (temperature, time, incorporated water) on enzymatic acidolysis were studied. Nonlinear regression methods were employed to fit experimental data with kinetic models proposed in the literature. The disappearance of reactant fatty acids (RF) over time was successfully modeled by a Ping-Pong Bi-Bi mechanism. FM was also represented with a lumped parameter model of the enzymatic mechanism. Maximum RF disappearance and FM onto sunflower oil glycerides increased with increasing reaction temperature. MG and DG concentrations in water-free systems were stabilized in low levels, while the incorporation of water to the reaction mixture produced a considerable increase in DG formation principally. Kinetic and equilibrium parameters showed temperature dependencies. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Lipids from vegetable oils are principally formed by unsaturated fatty acids being fundamental nutrients in the human diet. Also, they improve food texture and taste. However, manufactures need oils or fats to meet other characteristics related to functionality (melting point and solid fat content) and oxidative stability. Therefore, researchers and food industries have been working lately on modifying oils to reach these goals without harming human health. Enzymatic acidolysis of specific triacylglycerols (TAG) and oils has been studied during the last decades as a method to incorporate a desired fatty acid into the structure of the TAG. Nowadays there is a lot of information about reaction conditions not only at laboratory but also at pilot scale including batch and continuous processes (Camacho et al., 2007; Chopra et al., 2008; Fomuso and Akoh, 2002; García et al., 2001; Osborn and Akoh, 2002). However, there is a lack of information about experimental parameters of reaction kinetics and modeling of the acidolysis reaction behavior, especially between free fatty acids (FFA) and heterogeneous TAG, which are so necessary to design, optimize and control industrial reactors. Moreover, most published studies concerning acidolysis reactions had been focus on purified products without reporting data of not only concentration in the bulk reaction media but also information about intermediate reaction products. So, not all available results about acidolysis reactions could be used to obtain

* Corresponding author. Tel.: +54 2914861700; fax: +54 2914861600. E-mail address: [email protected] (M.E. Carrín). 0260-8774/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2010.01.032

kinetic parameters especially when a more sophisticated model is used. Most of the available modeling for acidolysis reaction is based on response surface methodology (RSM). This methodology is very helpful to optimize the studied reaction system itself, but their parameters are difficult or impossible to be compared in different conditions or systems. The magnitude of rate constants is very important not only for understanding how reaction variables affect the reaction rates but also for a rational design, optimization, scaling up and control of the acidolysis reactors (Camacho et al., 2007). Balcão and Malcata (1996) presented the mathematical modeling of a Ping-Pong Bi-Bi mechanism applied to a generic lipase-catalyzed reaction and the rate expression obtained assuming pseudo steady state. That modeling can be simplified depending on the kinetic assumptions, but hardly ever less than four lumped parameters are involved. Reyes and Hill (1994) used a Ping-Pong Bi-Bi mechanism in a simplified form to model the dynamic behavior of acidolysis reactions between FFA and TAG in the absent of solvent. They obtained two rate expressions requiring a total of five adjustable parameters and the pursuit of five component concentrations over time. Then, Ortega et al. (2004) applied that model to successfully represent the incorporation of conjugated linoleic acid (CLA) into fully hydrogenated soybean oil (FHSO) in solvent system. Xu et al. (1998) proposed a simplified kinetic model for acidolysis reactions in a solvent free system where incorporation was subject to reaction time in a similar manner as reaction velocity does with substrate concentration in the Michaelis–Menten equation. Camacho et al. (2007) postulated a grouped kinetic model for the acidolysis of a TAG with a FFA catalyzed by a sn-1,3

C. Pacheco et al. / Journal of Food Engineering 98 (2010) 492–497

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Nomenclature A, B, C aw ET FM FMe IG Ke KI KII m0 me P

condensed kinetic parameters of model II water activity enzyme concentration units [U] fatty acid incorporation [mol/mol] fatty acid incorporation at equilibrium state [mol/mol] intermediate compound [M] equilibrium constant of model II kinetic constant of model I [h] kinetic constant of model III [1/M] SPFA/TAG molar relation [mol/mol] enzyme mass [g] released fatty acids [M]

specific immobilized lipase in a solvent system. That model requires the knowledge of three experimental parameters and only one variable over time. Çiftçi et al. (2009) presented a gene-expression programming approach comparing its predictions to a more robust neural network modeling. They found good performance applying this empirical model to represent the acidolysis reaction between triolein and palmitic acid in a solvent system. However, it utilizes 28 fitting parameters in predicting the three TAG concentrations in the involved reaction. In the present work, enzymatic acidolysis of sunflower oil (SO) with stearic and palmitic acids in solvent system was studied from the reaction kinetic point of view, using models with different degree of complexity. The effect of the reaction conditions (temperature, time and incorporated water) on kinetic and equilibrium parameters, as well as on intermediate reaction products formation (monoglycerides (MG) and diglycerides (DG)) was analyzed. The purpose of this study was to contribute to increase the knowledge about kinetic behavior of acidolysis reactions using rate expressions proposed in literature to verify its applicability to this specific system and obtain new experimental kinetic constant values at different conditions. 2. Materials and methods 2.1. Materials Refined SO was purchased from a local grocery store as a ‘‘transfree” oil (predominant fatty acid composition, mol%: oleic acid (36.7 ± 0.5) and linoleic acid (51.3 ± 0.7) (Carrín and Crapiste, 2008)). Immobilized lipases from Rhizomucor miehei (Lipozyme RM IM, immobilized on ion-exchange resin, sn-1,3 specific, with an original water content 2–3%) was a generous gift of Novo Nordish (Bagsvaerd, Denmark) and it was used as received. Palmitic– stearic acids blend (SPFA), monopalmitin (1-monopalmitoyl-racglycerol) and dipalmitin (1,3-dipalmitoyl-rac-glycerol) were purchased from Sigma–Aldrich (Germany). N-Methyl-N-trimethylsilyltrifluoroacetamide (MSTFA) was obtained from Fluka (Buchs, Switzerland). Solid phase extraction (SPE) cartouches and pyridine were obtained from J.T. Baker (Philipsburg, NJ). Fatty acid methyl esters (FAME) standards were purchased from Supelco (Bellefonte, USA). All other reagents, gases and solvents were of analytical or chromatographic grade. 2.2. Enzymatic acidolysis Enzymatic acidolysis reactions were carried out at different conditions. In general, substrates (410 mg SO (TAG initial molar concentration, [TAG]0 = 0.14 M) + 753 mg SPFA, 1:6 molar ratio)

Q RF R2, R2adj rRF t T h V VR1, VM2 W

interesterified product glycerides [M] reactant fatty acids [M] determination coefficients rate of disappearance of RF [M/h] reaction time [h] reaction temperature [°C] treatment intensity parameter [g h/mol] reaction volume [L] kinetic parameters of model III [1/(M h U)] water [M]

and hexane (3 mL/g substrate) were mixed and heated and reaction began when immobilized enzyme (8 wt.% of total substrate, total immobilized enzyme mass, me = 0.093 g) was added. In cases where water was added (50 wt.% of enzyme), this was done at the moment hexane was incorporated. Reactions were performed in a screw-capped test tube in a water bath with temperature controller and magnetic agitation at 150 rpm. Reactions were stopped removing enzymes by filtering. All reactions were performed in duplicate and mean values are reported. 2.3. Analysis methods Structured lipids (SL) or modified TAG were isolated from the reaction mixture by alkaline deacidification as was reported in a previous paper (Carrín and Crapiste, 2008). Some results of fatty acid incorporations were extracted from that work. FAME from SL were prepared by cold transesterification with methanolic KOH according to the Official Method Ce 2-66 from AOCS (2006), and were analyzed by gas–liquid chromatography (GLC) with a 4890D series gas chromatograph (Agilent, Hewlett–Packard) and a fused-silica capillary column (SP-2380, 30 m  0.25 mm  0.2 lm film thickness; Supelco Inc.). The carrier gas was hydrogen with a linear velocity of 17 cm/s. The injector was used in split mode with a ratio of 1:100. The oven temperature was programmed to be at 170 °C for 15 min, further to increase to 210 °C at a rate of 4 °C/min, and held for 10 min. The injector and detector temperatures were 220 °C. FAME were identified by comparing their retention times with authentic standards. Glycerol (G), MG and DG were prepared and analyzed by GLC according to Plank and Lorbeer (1995), using the Official Method Cd 11b-91 of AOCS (2006) with modifications. A Varian 3700 chromatograph was used with a capillary column (MXT65TG, 15 m  0.25 mm  0.10 lm; Restek, USA). Hydrogen at 45 cm/s was used as carrier gas. Split mode at 1:30 relation was used during injection. Oven temperature was programmed as follow: 40 °C for 3 min, up to 365 °C to 25 °C/min, 365 °C for 15 min. Injector and detector (FID) temperatures were 320 °C and 370 °C, respectively. The internal standard method was used to quantify each group of by-products (G, MG and DG) with a calibration curve for each one. For the case of MG, the standard used was monopalmitin, while dipalmitin was used for DG. Water adsorption capacity of enzyme-support particles was estimated gravimetrically conditioning them for 5 days in a constant-humidity chamber containing a saturated NaCl solution (aw = 0.75) (Rønne et al., 2005).

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2.4. Kinetic models 2.4.1. Kinetic model I The simpler model found in literature to represent enzyme behavior over time is the simplified model proposed by Xu et al. (1998). This model represents the variation of incorporated FFA (FM) with reaction time (t), taking the following expression:

F M ¼ F Me t=ðK I þ tÞ

ð1Þ

compound (IG), and (3) the rate-determining step is that involving rupture of the ester bond. They tested the rate expressions, rP (P appearance rate) and rRF (RF disappearance rate), associated with the three mechanisms with experimental kinetic data obtained in the absence of a solvent, founding that the following reduced version of the rate expression corresponding to their mechanism 1 (where water enters the catalytic cycle during the acylation/deacylation steps) gave the best fit:

ðV R1 ½RF½IG  V M2 ½W½QÞET ð1 þ K II ½IGÞð½RF þ ½PÞ

where KI is a constant to be determined experimentally.

r RF ¼

2.4.2. Kinetic model II A grouped kinetic model for the acidolysis of a TAG with a FFA in no water media and catalyzed by a sn-1,3 specific immobilized lipase was proposed by Camacho et al. (2007). That model represents the variation of FM with the treatment intensity h as a function of kinetic and equilibrium parameters and FM itself, as follows: h i ðkL eT =3K M Þ ð2  3F M Þðm0  3F M Þ  ð1=K e Þð3F M Þ2 dF M ¼ dh ½ðK L =K M Þð3F M Þ þ ðm0  3F M Þ½ðkL K L =kM K M Þð3F M Þ þ ðm0  3F M Þ

where VR1, VM2 and KII are kinetic parameters that together with the initial effective water concentration (W) are obtained experimentally.

ð2Þ where h is defined as:

 me t V½TG0

ð3Þ

The equilibrium constant (Ke) is obtained taking into account the value of FM at steady state condition (FMe), by Eq. (4) as follows:

Ke ¼

ð3F Me Þ2 ð2  3F Me Þðm0  3F Me Þ

Reactions were done by duplicate and each sample was analyzed twice generating four values of the same analyses. Experimental results are showed as mean values ± standard deviation. Statistical differences between values were evaluated with the ttest. A confidence value of 95% was used. Experimental data were adjusted to proposed models using lineal and no lineal regression algorithms contained within Systat computer program (Systat 5.03, 1993) and F-tests were performed to evaluate the significance of the fittings. 3. Results and discussion

ð4Þ

Some hypothesis are postulated to obtain the previous model: (1): as a positional specificity sn-1,3 was assumed, only fatty acids in that positions of the TAG are involved in the reaction; (2): the substitution in one position is independent of the nature of the fatty acid present in the other possible position to be substituted, namely both positions are equivalents; (3): DG concentration reaches stationary state in short reaction time and remains at low level; (4): acyl-enzyme complexes are the only intermediates with appreciable life where enzyme participates, being in equilibrium with FFA; (5): acyl-enzyme concentrations are large with respect to free enzyme concentration. A reduced model is obtained by grouping parameters:

h i A ð2  3F M Þðm0  3F M Þ  ð1=K e Þð3F M Þ2 dF M ¼ dh ½Bð3F M Þ þ ðm0  3F M Þ½ðBCÞð3F M Þ þ ðm0  3F M Þ

2.5. Result analysis

MG and DG formation was analyzed over the reaction time and at different conditions (temperature and added water) (Figs. 1 and 2). Essays with added water were conducted to simulate the reaction system behavior when reactants are more hydrated than analytical grade ones, as could occur at industrial scale. Water activity in the reaction system was estimated to be 0.52 and 0.08 when water was and was not added, respectively, from models presented by Black et al. (1948). Water adsorption capacity of enzyme-support was 2.8% when an atmosphere equilibrated with a water

20

15

ð5Þ

where A, B and C were chosen as the condensed kinetic parameters taking into account their meanings: A = kLeT/(3KM) (relation between formation kinetic constant of acyl-enzyme complex from original TAG, active enzyme concentration and equilibrium constant of the acyl-enzyme complex formation from free reactant fatty acids), B = KL/KM (relation between equilibrium constants of the acyl-enzyme complexes formation from free released/reactant fatty acids) and C = kL/kM (relation between DG esterification kinetic constants towards original/new TAG formation). This expression of the model was used to adjust experimental data.

% IG

 h¼

ð6Þ

10

5

0

0

10

20

30

40

50

t [h] 2.4.3. Kinetic model III Reyes and Hill (1994) postulated three different mechanisms to describe the interesterification reaction between TAG and FFA, differing from one another with respect to the point at which the water molecule enters the catalytic cycle. Authors assumed: (1) all the fatty acids released from the triglyceride substrate can be lumped together in a single product (P), (2) lower glyceride species (G, MG and DG) can be lumped together in a single intermediate

DG - 40ºC

DG - 50ºC

DG - 60ºC

MG - 40ºC

MG - 50ºC

MG - 60ºC

Fig. 1. Intermediate glyceride (IG) concentration (wt.%) in the reaction product as a function of time and temperature (without added water). DG: diglycerides, MG: monoglycerides.

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60

Table 1 Parameters of model I, FMe and KI, at different temperatures.

% IG

40

20

0 0

10

20

30

40

50

t [h] DG

DG w

MG

MG w

Fig. 2. Intermediate glyceride (IG) concentration (wt.%) in the reaction product as a function of time and added water (T = 60 °C). DG: diglycerides, MG: monoglycerides, w: experience with added water.

activity equal to 0.75 was surrounding it. It means that the added water of 50% (aw = 0.52) was high enough to maintain the liquid phase hydrated in a similar level over time even though solids adsorbed water. So, it is to remark that added water was not only in the surroundings of the enzyme, as could be the case when water was not added or when immobilized enzyme is conditioned in an atmosphere of known activity water (as other authors had analyzed (Rønne et al., 2005; Kim et al., 2008)), but also throughout the liquid phase. Glycerol was not observed during chromatographic essays, not even when water was added to the reaction media and reaction time was long enough to allow the enzyme to complete hydrolysis reaction in all three positions if it was possible. So, this fact allows us to confirm the sn-1,3 specificity of the R. miehei enzyme. MG content in the reaction products was maintained below 3.3 wt.% (7.4 molar%) when water was not added to the reaction system. On the other hand, DG formation showed a continuous increase over the first 24 h of reaction time for all considered temperatures. At 40 °C, DG formation continued increasing up to 48 h of reaction. Conversely, at 50 and 60 °C DG formation showed a stationary state from 24 h of reaction time. When water was added to the reaction media (Fig. 2) at 60 °C, MG formation increased up to its maximum after 16 h of reaction and then decreased and reached stationary state, showing that hydrolysis reaction at this point on is not favored anymore over the esterification one. The maximum MG proportion obtained was 9.2 molar%, while the level obtained at the same temperature without added water was 2.5 molar%. DG formation significantly increased compared to the case without added water, reaching a mass level four times higher than the latter case (3.4 times higher in molar percentage) at 48 h of reaction. So, it is concluded that at such a high level of aw (0.52) in the reaction media the partial hydrolysis reaction seems to be favored to the detriment of the esterification reaction, in accordance with Zhao et al. (2007).

T [°C]

FMe [molar%]

KI [h]

R2

40 50 60

50.91 51.52 53.90

6.42 3.33 2.89

0.9986 0.9990 0.9947

ratio was high, led us to accept the fifth hypothesis of model II in cases where water was not added (Camacho et al., 2007). For kinetic model I, experimental data were fitted to Eq. (1) at different temperatures (Table 1). The obtained FMe values were slightly smaller than those reported by Xu et al. (1998) for two systems at 60 °C and the same substrate ratio as ours: 62.5 molar% for fish oil with capric acid, and 65.36 molar% for medium chain TAG with free fatty acids from SO. The found differences could be attributed to differing substrates and enzymes. From Eq. (1), the kinetic equation representing the variation of FM with time is obtained:

dF M =dt ¼ ðF Me K I Þ=ðK I þ tÞ2

ð7Þ

From this expression and Eq. (5), experimental data were fitted and grouped parameters A, B and C corresponded to Eq. (5) were obtained (Table 2). Comparison of obtained parameters with those reported by Camacho et al. (2007) were performed through a Student t-test at a 95% confidence level, assuming they had the same variance and this one equal to the highest variance obtained from our data at all temperatures analyzed. At 40 °C, the equilibrium constant and parameter A were smaller (p = 0.0477 and 9.6  105, respectively) and parameter B was higher (p = 0.0106) than values reported by Camacho et al. (2007) for triolein and caprylic acid at 30 °C (1.26, 0.00782 mol/g h and 2.17, respectively). Parameter C (kL/kM) was kept close to 1 indicating that the reaction between DG and acyl-enzyme complex was very fast and that temperature did not affect the contact probability between them. This conclusion could be the explanation to the fact that DG concentration was kept low when water was not added to the reaction system. This result was also found by Camacho et al. (2007). The dependency of obtained parameters and equilibrium constant upon temperature was also studied. Parameter B did not show any specific dependency in the temperature range studied. Equations obtained for A and Ke are presented in Tables 3 and 4, respectively. Once numerical values of parameters from Eq. (5) were calculated, numerical integration of this equation was carried out to obtain the incorporation profiles as time functions (Fig. 3). It is observed that the lumped model selected represents satisfactorily the analyzed reaction system. Therefore, a simple three empirical parameters model was validated for the prediction of the behavior of acidolysis reaction assisted by immobilized enzymes during batch production.

Table 2 Parameters of model II (Eq. (5)).

3.1. Kinetic representation through models I and II High degrees of fatty acid incorporation were obtained. This could be related to the affinity of the enzyme for the fatty acids. This item, together with the fact that the used SPFA/TAG molar

T [°C]

A [mol/g h]

B [mol/g h]

C [mol/g h]

Ke

R2

40 50 60

0.0038 0.0075 0.0089

3.63 3.68 3.53

1.000 0.9999 1.000

0.6358 0.8795 1.4169

0.9974 0.9949 0.9928

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3.2. Kinetic representation through model III Data concerning the molar concentration of reactant free fatty acids (RF) in the reaction mixture over time are consolidated in Table 3 Dependency of parameter A from Eq. (5) upon temperature. Functionality

A0 [mol/g h]

A1 [mol K/g h]

R2

A ¼ A0  AT1

0.0936

28.000

0.9611

Table 4 Dependency of equilibrium constant (Ke) from Eq. (5) upon temperature. Functionality

K0

K1 [K]

R2

ln K e ¼ K 0 þ K 1 T

13.019

0.0401

0.9881

FM [molar fraction]

0.6

Table 5 Kinetic parameters of model III (Eq. (6)).

0.4

0.2

0

Fig. 4. The quality of the fitting to kinetic model III is shown in this figure and the corresponding values of the obtained kinetic parameters are summarized in Table 5. The effect of temperature and added water on the disappearance of reactant fatty acids RF and kinetic parameters are also shown. The obtained values of VR1 and VM2 parameters are in accordance with those reported by Ortega et al. (2004) for R. miehei at 75 °C and in absence of solvent (p = 0.7505 and 0.0735, respectively). However, KII values are too different (p = 0.0006) to disregard the fact that reaction conditions, substrates and enzyme preparation are different. The behavior of VR1 and VM2 parameters with temperature (in cases where water was not added in the reaction media) was analyzed finding that the VR1/VM2 ratio presented a more lineal and constant tendency than each one alone (Fig. 5A). This conduct could be explained by the fact that both parameters are relations of kinetic constants, so the quotient between them smoothen the variations of each other with temperature. Moreover, the tendency of this ratio to increase with temperature showed that the acidolysis reaction was more favored than the hydrolysis one from the kinetic point of view. KII also increased with temperature with a lineal trend (Fig. 5B). Taking into account

T [°C]

VR1a [1/(M h U)]

VM2a [1/(M h U]

KII [1/M]

R2

R2adj

40 50 60 60 wb

19.71 26.89 18.64 7.20

13.70 13.94 8.68 5.03

280 334 400 150

0.97 0.96 0.99 0.96

0.95 0.93 0.98 0.94

a Parameters are expressed per unit of immobilized enzyme (U), defined as the amount of immobilized enzyme necessary to incorporate 1 lmol of B per hour, at the considered temperature. b Experience with added water.

0

10

20

30

40

50

t [h] 2.5

A

V R1/V M2

Fig. 3. Incorporation of SPFA into SO during enzymatic acidolysis as a function of time and temperature (N: 40 °C, : 50 °C, j: 60 °C): fitting of experimental values extracted from Carrín and Crapiste (2008) to kinetic model II. Mean value ± standard deviation.

0.82

2.0

1.5

0.78 1.0

RF [M]

0.74

35

40

45

50

55

60

65

T [ºC]

0.70 450

B

0.66

0.58

0

10

20

30

40

50

K II [1/M]

400

0.62

350 300

t [h] 40ºC

50ºC

60ºC

60ºC w

40ºC

50ºC

60ºC

60ºC w

250

35

45

55

65

T [ºC] Fig. 4. Disappearance of reactant fatty acids (B) from the reaction media over time (t) at different temperatures. Lines represent data fitting to kinetic model III. w: experience with added water.

Fig. 5. Relationship between kinetic parameters of model III and temperature. A: VR1/VM2; B: KI. Straight lines represent lineal fittings.

C. Pacheco et al. / Journal of Food Engineering 98 (2010) 492–497

that this parameter relates the kinetic constants of the IG incorporation/liberation from enzyme complexes, the higher its value the more favored the IG–enzyme complexes formation is. So this behavior is in accordance with that found for VR1/VM2. When water was added to the reaction system (60 °C), VR1/VM2 and KII diminished from the values obtained when water was not added. This is a clear representation of the behavior of the enzyme in different systems. A higher water activity in the reaction media (more than the amount needed for the reaction to begin) favors the hydrolysis reaction and the liberation of IG from enzyme complexes avoiding the esterification reaction (last stage of the desired acidolysis reaction) to proceed. Statistical analyses were performed to determine the regression models significance obtaining p-values lower than 1  106 for the three models, showing that regressions are highly significant. Moreover, model I has the higher F/Fc ratio value (771) being followed by model II (194) and III (80), in that order. It is to say that the simplest model predicts the kinetic behavior with higher significance. However, the application of each of these models is not supposed to be exactly the same. The availability of models that take into account different independent variables could be helpful to describe different situations, from a simple representation of incorporation data over time to a more sophisticated simulation or control of the process in which intermediate products concentrations are required. 4. Conclusion Kinetic behavior of enzymatic acidolysis of sunflower oil with palmitic and stearic acids were investigated. Intermediate reaction products were analyzed over time at different temperatures and added water, finding that hydrolyzes was not completed (G was not found in any sample). MG and DG formation increased principally by the presence of excessive water in the reaction media. Three models were tested and validated to represent the behavior of the reaction system with different complexity. Parameters of each one were obtained making possible its applicability in future design, optimize, or control processes. The advantage of counting on different models parameters to represent the same reaction system resides in the possibility for future users to evaluate what variables they are interested in representing or controlling and decide what model they would use. Acknowledgements This work was financially assisted by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), the Agencia Nac-

497

ional de Promoción Científica y Tecnológica (ANPCyT), and the Universidad Nacional del Sur (UNS) of Argentina.

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