Kinetics of the base-catalyzed sunflower oil ethanolysis

Fuel 89 (2010) 665–671

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Kinetics of the base-catalyzed sunflower oil ethanolysis Ana V. Marjanovic´, Olivera S. Stamenkovic´, Zoran B. Todorovic´, Miodrag L. Lazic´, Vlada B. Veljkovic´ * Faculty of Technology, Bulevar Oslobodjenja 124, 16000 Leskovac, Serbia7

a r t i c l e

i n f o

Article history: Received 18 February 2009 Received in revised form 19 September 2009 Accepted 22 September 2009 Available online 7 October 2009 Keywords: Biodiesel Ethanolysis Kinetics Modeling Sunflower oil

a b s t r a c t The kinetics of the sunflower oil ethanolysis process using NaOH as a catalyst was studied at different reaction conditions. The reaction system was considered as a pseudo-homogeneous one with no mass transfer limitations. It was also assumed that the chemical reaction rate controlled the overall process kinetics. A simple kinetic model consisting of the irreversible second-order reaction followed by the reversible second-order reaction close to the completion of the ethanolysis reaction was used for the simulation of the triglyceride conversion and the fatty acid ethyl ester formation. The proposed kinetics model fitted the experimental data well. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Diesel fuels have an important part in the world industry but their increased consumption and exhaust gases have a big impact on the environment. This is the main reason why the alternative fuels have become significantly important. Alternative fuels must be technically feasible, economically competitive, environmentally acceptable and readily available [1]. One of them is biodiesel, which is a renewable, biodegradable and non-toxic fuel the use of which, when compared to the use of fossil fuels, leads to many environmental benefits: less pollution of air, water and soil and less health risk [2]. The most often used process for the biodiesel production is alcoholysis, a reaction between triglycerides (TG) found in oils and fats (from a variety of plant and animal sources) and an alcohol (most frequently methanol or ethanol) in the presence of a catalyst (such as a base, an acid or an enzyme). Methanol is the most often used alcohol in a biodiesel synthesis because of its suitable physical and chemical properties and low cost. Ethanol, which has been rarely studied, is preferable to methanol because of its superior dissolving power of vegetable oils and low toxicity [3]. The production of ethyl esters, rather than methyl esters, is of considerable interest because the ethyl ester based biodiesel is an entirely agricultural fuel and the extra carbon brought by the ethanol molecule increases both the heat content and the cetane number [4]. Ethyl esters have lower cloud and pour points than methyl esters, which

* Corresponding author. Tel.: +381 16 247 203; fax: +381 16 242 859. E-mail address: [email protected] (V.B. Veljkovic´). 0016-2361/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2009.09.025

improve the starts cold [3] and better storage properties [5]. Also, ethyl esters have a less negative effect on the environment compared to methyl ester due to low emissions of nitrogen oxides (NOx), carbon monoxide (CO) and smoke density [6]. On the other hand, ethanolysis is more energy consuming [7], traces of water in the reaction mixture seem to have dramatic effects on esters yields [8] and the separation of ethyl esters is more difficult [9]. Due to more glycerol and ethanol moving from the glycerol to the ethyl ester phase, it is necessary that the residual alcohol is removed and recovered by distillation before the water wash step [10]. If the mixture of methanol/ethanol is used for the alcoholysis reaction then this would take advantages of better solvent properties of ethanol and a desired conversion using methanol [11]. Base catalysts in homogeneous media are usually applied for the industrial biodiesel production. Alkoxides are most efficient, but NaOH and KOH are frequently used because they are cheaper and easier to handle [12]. The variables that influence the alcoholysis reaction are: the type and the amount of the catalyst, the molar ratio of methanol to vegetable oil, the reaction temperature, the agitation intensity and the purity of the reactants. High yields of methyl and ethyl esters are achieved when the fundamental reaction conditions are optimized [13,14]. The kinetics of the base-catalyzed methanolysis has been most frequently studied [15–22]. In the studies of the methanolysis reaction kinetics, three regimes are well-recognized: an initial mass transfer controlled regime (slow) followed by a chemically controlled regime (fast), and a final regime close to equilibrium (slow). In the modeling of the methanolysis kinetics only Stamenkovic´ et al. [20] included the mass transfer limitation in the initial heterogeneous reaction regime. In the study of the kinetics of

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Nomenclature A cA cAo cBA CBo cR cS C1 Ea k2 ~ k2 ~ k2 K M (rA)

preexponential factor, Eq. (9) (min1) concentration of TG in the oil phase (mol/dm3) initial concentration of TG (mol/dm3) concentration of ethanol (mol/dm3) initial concentration of ethanol (mol/dm3) concentration of FAEE (mol/dm3) concentration of glycerol (mol/dm3) integration constant (1) activation energy of the reaction (kJ/kmol) reaction rate constant for the irreversible pseudo second-order reaction (dm3(mol min)) reaction rate constant for the forward second-order reaction (dm3(mol min)) reaction rate constant for the reverse reaction (dm3(mol min)) reciprocal value of the equilibrium constant for the k2 Þ, 1 overall ethanolysis reaction ð¼ ~ k2 =~ initial molar ratio of TG to ethanol ð¼ cAo =cBo Þ 1 rate of TG disappearance (mol/(dm3 min))

base-catalyzed ethanolysis, mass transfer limitations have not been observed, but the two latter regimes were well-recognized [3]. The ethanolysis reaction is very fast in the initial reaction period and is then getting slower in the second period towards equilibrium. The final concentration of ethyl esters was almost reached in 10 min at the temperature reaction range of 25–75 °C and the kinetic curves had an asymptotic tendency with time [3]. According to the best knowledge of the authors, the ethanolysis kinetics has not been modeled yet. In the present work, the ethanolysis of sunflower oil using NaOH as a catalyst was studied at the temperatures between 25 °C and 75 °C. The main goal was to model the kinetics of the ethanolysis reaction. A simple kinetic model, which did not require a complex computation of the kinetic constants, was intended to be used for the simulation of the TG conversion and the fatty acid ethyl ester (FAEE) formation. The reaction system was considered as a pseudo-homogeneous one with no mass transfer limitations.

R t t1 T TG xAA xAe

gas constant (kJ/(kmol K)) time (min) duration time of irreversible pseudo second-order reaction (min) temperature (K) content of TG in the FAEE/oil fraction of the reaction mixture (%) TG conversion degree, 1 equilibrium TG conversion degree, 1

Greek symbol D parameter in Eq. (6) (= 43M(1  K)  (1 + 3M)2 < 0), 1 Abbreviations TG triglycerides DG diglycerides MG monoglycerides FAEE fatty acid ethyl esters

(f) The content of free fatty acid in the oil is negligible, so the free fatty acid neutralization can be ignored. (g) The saponification reaction is negligible and the catalyst concentration remains almost constant. A low degree of saponification (about 1%) was caused by using 0.5% of NaOH as a catalyst in methanolysis of an ox fat, coconut oil and linseed oil at 60 °C [23]. A large amount of soap and a reduction in the methyl ester yield were observed when the NaOH amount was above 1.5% (based on the oil weight) [24]. According to the assumption (c), the rate of the TG formation in the first part of the reaction is as follows:

ðrA Þ ¼ 

dcA ¼ k2 c2A dt

ð1Þ

where k2 is the reaction rate constant for the irreversible pseudo second-order reaction and cA is TG concentrations in the oil phase. Since the TG concentration is related to the conversion degree of TG, xA :

2. Theoretical background

cA ¼ cAo ð1  xA Þ The overall vegetable oil ethanolysis reaction can be presented by the following stoichiometric equation: Catalyst

A þ 3B ¢

3R þ S

where A is TG, B is ethanol, R is FAEE and S is glycerol. For the purpose of modeling the described process of ethanolysis, the following assumptions are introduced: (a) The reaction mixture can be considered as a pseudo-homogeneous system where there is no mass transfer limitation. This can be expected due to high agitation intensity [18,21,22] and a high dissolving power of ethanol in oils [3]. (b) The overall process kinetics is chemically controlled. (c) The ethanolysis of TG is the irreversible pseudo secondorder reaction in the early period of the reaction. Due to the excess of ethanol and a low product concentration, one can expect the reverse reactions to be negligible. (d) Near to the equilibrium, the forward and reverse reactions follow the second-order overall kinetics. (e) The reaction mixture is perfectly mixed, ensuring its uniform composition.

ð2Þ

it follows from the Eq. (1):



dxA ¼ k2 cAo ð1  xA Þ2 dt

ð3Þ

where cAo is the initial TG concentration reaction.Upon the integration of Eq. (3), the following equation is obtained:

xA ¼ k2 cAo t 1  xA

ð4Þ

The reaction rate constant k2 can be estimated from the slope of the dependence of xA =ð1  xA Þ on t. According to the assumption (d), the ethanolysis reaction rate close to the equilibrium is:

ðrA Þ ¼ 

dcA ~ k2 C R C S ¼ k2 cA cB  ~ dt

ð5Þ

where ~ k2 and ~ k2 are the reaction rate constants for forward and reverse reactions, respectively, and cB , cR and cS are actual concentrations of ethanol, FAEE and glycerol, respectively. The following equation is obtained by the integration of Eq. (5) [20]:

A.V. Marjanovic´ et al. / Fuel 89 (2010) 665–671

pffiffiffiffiffiffiffi ½6Mð1  KÞxA  ð1 þ 3MÞ  D pffiffiffiffiffiffiffi ¼ f ðxA Þ ln ½6Mð1  KÞxA  ð1 þ 3MÞ þ D pffiffiffiffiffiffiffi ¼~ k2 cBo t D þ C 1

667

ð6Þ

where K ¼ ~ k2 =~ K 2 is the reciprocal value of the equilibrium constant for the overall ethanolysis reaction, M ¼ cAo =cBo is the initial molar ratio of TG to ethanol (= 1/6; 1/9 or 1/12), cBo is the initial concentration of ethanol, D ¼ 4  3Mð1  KÞ  ð1 þ 3MÞ2 < 0 and C 1 is the integration constant. The reaction rate constant ~ k2 can be estimated from the slope of the Eq. (6). The reciprocal value of the equilibrium constant can be calculated from the equilibrium degree of TG conversion, xAe , which can be experimentally determined, since it is [20]:

K¼

3Mx2Ae  ð1 þ 3MÞxAe þ 1 3Mx2Ae

ð7Þ Fig. 2. The influence of the catalyst amount on the FAEE concentrations (reaction conditions: 25 °C; ethanol to oil molar ratio 6:1; catalyst amount, %: 0.75 – (d); 1.00 – (N); and 1.25 – (j); experimental data: symbols; kinetic model: straight lines).

3. Experimental 3.1. Materials Refined and edible sunflower oil (Sunce, Sombor, Serbia) was used. Absolute ethanol was purchased from Carlo Erba (Milano, Italy). Sodium hydroxide pellets of min 98% purity were purchased from Lach-Ner (Neretvice, Czech Republic). Hydrochloric acid, conc., was obtained from Centrohem (Beograd, Serbia). Methanol, 2-propanol and n-hexane, all of HPLC grade, were obtained from Lab-Scan (Dublin, Irland). The HPLC standards for ethyl esters of palmitic, stearic, oleic and linoleic acids, triolein, diolein and monoolein were purchased from Sigma Aldrich. 3.2. Equipment The reaction was carried out in a 250 mL three-neck glass flask equipped with a condenser and a two flat-blade paddle agitator. The agitation speed, kept constant with a voltage regulator, was measured with an optoelectronic counter (Laser, Leskovac, Serbia). The reactor was immersed in a glass chamber filled with water circulating from a thermostated bath (Dema, Ilirska bistrica, Slovenia) by means of a pump.

Fig. 3. The influence of the ethanol–oil molar ratio on the FAEE production (reaction conditions: 50 °C; catalyst amount: 0.75%; ethanol to oil molar ratio: 6:1 – (d); 9:1 – (N); and 12:1 – (j); experimental data: symbols; kinetic model: straight lines).

3.3. Reaction conditions The ethanolysis of sunflower oil was carried out at 6:1, 9:1 and 12:1 molar ratios of ethanol to oil and the NaOH amount of 0.75%,

Fig. 4. The influence of the reaction temperature on the FAEE content (reaction conditions: ethanol to oil molar ratio 6:1; catalyst amount: 0.75%; temperature, °C: 25 – (d); 50 – (N); and 75 – (j); experimental data: symbols; kinetic model: straight lines).

Fig. 1. Variations of the reaction mixture composition with the progress of the sunflower oil ethanolysis (FAEE – (s); MG – (D); DG – (h) and TG – (d)) (reaction conditions: 25 °C, ethanol to oil molar ratio 12:1 and NaOH amount 1.00%).

1.00% and 1.25% (based on the oil weight). The reaction was carried out at the atmospheric pressure and temperatures 25, 50 and 75 °C. The agitation speed of 600 rpm was applied in all experiments.

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to neutralize the NaOH and then centrifuged (3500 rpm for 15 min). The upper layer was withdrawn, dissolved in a 2-propanol/n-hexane (5:4 v/v) in a ratio 1:200 and filtered through a 0.45 lm Millipore filter. The resulting filtrate was used for HPLC analysis. 3.5. Composition of the reaction mixture The composition of the samples of the reaction mixture was determined by HPLC, as described elsewhere [19]. The conversion degree of TG was calculated from the content of TG in the FAEE/ oil fraction of the reaction mixture, TG (in%), by the following equation:

xA ¼ 1  TG=100 Fig. 5. The irreversible pseudo second-order reaction model of TG ethanolysis (open symbols; Eq. (4) – straight solid lines) and the reverse second-order reaction model of TG ethanolysis (solid symbols; Eq. (6) – straight dash lines) at various catalyst amount, %: 0.75 – (h), 1.00 – (D), 1.25 – (s) (reaction conditions: 25 °C; ethanol to oil molar ratio 6:1).

ð8Þ

a

3.4. Experimental procedure Ethanol and sodium hydroxide were agitated in the reactor at the desired temperature for about 30 min. The sunflower oil (45.96 g) was thermostated separately and added to the reactor. As soon as the mechanical stirrer was turned on, the reaction was timed. During the reaction, the samples (1 ml) were removed from the reaction mixture, immediately quenched by adding a required amount of the aqueous hydrochloric acid solution (11% vol.)

Table 1 The rate constants for the irreversible pseudo second-order and the reverse secondorder reaction model at different reaction conditions. Reaction temperature (°C)

Ethanol to oil molar ratio

NaOH amount (%)

3 3 3 dm dm dm ~ ~ k2 mol k103 mol K 2 mol min min min

The relative deviations of the calculated and the experimental xA (%)

25

6:1

0.75 1.00 1.25 0.75 1.00 1.25 0.75 1.00 1.25

1.742 3.254 4.145 1.003 4.643 7.736 3.170 6.93 11.82

0.119 0.240 0.371 0.091 0.215 0.405 0.140 0.327 0.497

5.74 9.03 11.04 1.89 4.52 6.06 11.10 45.0 111.3

4.6 2.2 4.1 7.1 4.8 4.1 1.1 1.8 9.0

0.75 1.00 1.25 0.75 1.00 1.25 0.75 1.00 1.25

5.18 6.04 6.52 4.95 8.17 9.26 10.8 13.5 17.0

0.486 0.698 0.938 0.498 0.941 1.163 0.524 0.741 1.337

8.16 11.1 12.8 3.64 5.65 7.03 34.5 74.4 135.4

5.1 4.9 4.7 8.3 4.9 1.6 2.3 6.6 1.8

0.75 1.00 1.25 0.75 1.00 1.25 0.75 1.00 1.25

6.24 7.84 8.80 7.50 9.57 12.6 10.9 16.1 20.8

0.891 1.165 1.335 1.423 1.680 1.921 1.795 2.310 2.956

12.3 14.2 14.9 5.72 6.43 7.35 82.5 135.3 201.4

2.7 4.5 3.8 2.4 2.3 2.9 0.5 1.5 2.1

9:1

12:1

50

6:1

9:1

12:1

75

6:1

9:1

12:1

b

c

Fig. 6. Arrhenius plot of the reaction rate vs. temperature for the irreversible second-order (a), the forward second-order (b) and the reverse second-order reaction (c) (ethanol to oil molar ratio 6:1; catalyst amount, %: 0.75 – (j); 1.00 – (N) and 1.25 – (d)).

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Table 2 Activation energy of alkali-catalyzed alcoholysis at atmospheric pressure.

a

Oil

Alcohol

Catalyst/ quantity (% of oil)

Molar ratio of alcohol to oil

T (°C)

Reaction mechanism; kinetics model

Activation energy (kJ/mol)

References

Palm

Methanol

KOH 1.0

6:1

55–65

26.8–61.5

[15]

Soybean

Butanol

NaOBu 0.5 and 1.0

30:1

20–60

46.9–72.0

[16]

Butanol

NaOBu 1.0

6:1

20–60

Methanol

NaOCH3 0.5

6:1

20–60

Soybean

Methanol

NaOH 0.2

6:1

30–70

Brassica carinata oil

Methanol

KOH 0.5–1.5

6:1

25–65

Sunflower

Methanol

KOH0.5–1.5

6:1

25–65

Sunflower

Methanol

KOH 1.0

6:1

10–30

Sunflower

Ethanol

NaOH 0.75, 1.00 and 1.25

6:1, 9:1 and 12:1

25–75

Three consecutive reversible reactions; second-order a Three consecutive reversible reactions; pseudo-first order forward and second-order reverse reactions Three consecutive reversible reactions; second-order Combination of consecutive and shunt reactions; second and forth order for consecutive and shunt reactions, respectively Three consecutive reversible reactions; second-order Three consecutive reversible reactions; second-order Three consecutive reversible reactions; second-order Irreversible second-order overall reaction in the middle period; the reversible second-order overall reaction in the final period Irreversible second-order overall reaction in the initial period; the reversible second-order overall reaction in the final period

34.2–71.5 56.8–83.8

21.7–83.1

[18]

12.0–104.8

[22]

6.0–41.6

[21]

33.2–53.5

[20]

3.4–43.9

This work

Only the forward reactions were considered.

4. Results and discussion 4.1. Ethanolysis reaction analysis The variations of the reaction mixture composition with the progress of the sunflower oil ethanolysis at a set of reaction conditions (25 °C, ethanol to oil molar ratio 12:1 and NaOH amount 1.00%, based on the oil weight) are presented in Fig. 1. The shape of the curve representing the variations of FAEE fraction with time indicated two periods of the reaction. In the initial stage of the process the formation of FAEE was fast and then it became slower as the reaction approached the completion. No mass transfer limitation was observed in the initial reaction period. This type of the ethanolysis reaction kinetics has already been observed [3,25]. A decrease in the TG concentration followed the increase in FAEE concentration. The concentrations of intermediate products, monoglycerides (MG) and diglycerides (DG), increased at the beginning of the reaction achieving their maximum, then decreased and finally stayed nearly constant. The concentrations of MG and DG were smaller than 0.5% and 2%, respectively. The reaction rate increased by increasing the catalyst amount in the range of 0.75–1.25%, based on the oil weight, and consequently the reaction approached the completion in a shorter time (Fig. 2). These results agreed with those reported by Encinar et al. [3,25] for NaOH and KOH catalyzed ethanolysis of Cynara cardunculus L. oil and the used frying oil. They found that the optimal catalyst concentration is 1% referred to the total mixture, which corresponded to 1.25% based on the oil weight for the ethanol to oil molar ratio of 6:1. There was less influence of the catalyst amount on the reaction rate at higher ethanol–oil molar ratios. This can be explained by a small difference in the total catalyst amount in the reaction mixture when the ethanol quantity is increased. The initial ethanol–oil molar ratio affected both the FAEE production rate and the FAEE yield, as it can be seen in Fig. 3. The variation of the FAEE moles (not the FAEE concentration) with time was analyzed because the FAEE concentration was reduced with increasing the ethanol to oil molar ratio at a constant oil mass, due to the increase of the total reaction mixture volume. When the initial ethanol to oil molar ratio was increased from 6:1 to 12:1 both the reaction rate and the FAEE yield in moles generally increased.

The temperature dependence of the reaction rate is shown in Fig. 4. As it can be seen, all the reactions were very rapid, achieving very high ethyl esters concentrations. The reaction rate was slightly lower at 25 °C, but the FAEE content was essentially the same after approximately 20–30 min for all the temperatures. Thus, an increase of the temperature is not indispensable if the reaction time is longer. Our results were in conformity with other reports [3,25–28]. In addition, some authors [29] found that at high reaction temperatures the ester yield decreased due to accelerating the saponification of the TG by the alkaline catalyst before the completion of alcoholysis. We did not observe this effect. 4.2. Reaction kinetics model According to the assumptions (c) and (d), the kinetic model involved the irreversible pseudo second-order reaction mechanism in the initial period and the reverse second-order model close to equilibrium. Fig. 5 shows the dependences of the left side of Eqs. xA with time in the ini(4) and (6) on time. The linear variation of 1x A

tial part of the process confirms that the ethanolysis of TG is the irreversible pseudo second-order reaction in the early period of the reaction. The variation of f ðxA Þ, defined by Eq. (6), with time in the final part of the process is also linear verifying that the ethanolysis follows the reverse second-order reaction kinetics. The reaction rate constants were calculated from the slopes of the corresponding linear curves and are given in Table 1; the values of the TG conversion degree, produced by the Boltzman function of the experimental data, were used in these calculations. The values of xA constant corresponding to the reverse reaction were small, the 1x A especially at the lower temperature and the lower ethanol to oil molar ratio. This could be caused by the immiscibility of ethyl esters and glycerol which involved a mass transfer resistance in that direction. All the rate constants increased with increasing both, the reaction temperature and the catalyst amount. Generally, the rate constants increased with increasing the ethanol to oil molar ratio. k2 Þ and ln ð~ k2 on 1=T The linear dependences of ln (k2), ln ð~ (Fig. 6) confirm that the Arrhenius equation could be applied for determining the activation energies for the ethanolysis reactions:

k ¼ A  expðEa =RTÞ

ð9Þ

A.V. Marjanovic´ et al. / Fuel 89 (2010) 665–671

670

a

tions of the calculated and the experimental TG conversion degree were in the range from ±0.5% to ±9.0% in all experiments (Table 1). The TG conversion degree based on the proposed kinetic model was calculated from the following equations: – for 0 < t 6 t1 (the irreversible pseudo second-order reaction)

xA ¼

k2 cAo t 1 þ k2 cAo t

ð10Þ

– for t P t1 (the reversible pseudo second-order reaction)

xA ¼

b

pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi D  expð~ k2 cBo t D þ C 2 Þ pffiffiffiffiffiffiffi ½6Mð1  KÞ½1  expð~ k2 cBo t D þ C 2 Þ

½ð1 þ 3MÞ 

ð11Þ

The kinetic model and the experiment were also compared based on the variations of the molar concentrations of TG and FAEE. As it can be seen in Fig. 7, the kinetic model agreed well with the experimental data. The molar TG concentration was calculated by Eq. (4). The molar FAEE concentration was calculated using the TG conversion degree corrected for the MG and DG formation. 5. Conclusions

c

The NaOH catalyzed sunflower oil ethanolysis was studied under various reaction conditions in order to analyze the effects of the reaction conditions on both the FAEE yield and the reaction rate and to model the ethanolysis reaction kinetics. A good agreement between the simple model and the experimental data verified that the reaction mixture could be considered as a pseudohomogeneous system with no mass transfer limitations in the initial reaction period. This is an important difference from the basecatalyzed methanolysis, which is a well-known mass transfer controlled in the initial region. The ethanolysis process kinetics was only chemically controlled. As the methanolysis reaction after the initial mass transfer controlled regime, the ethanolysis reaction also followed the irreversible second-order reaction kinetics in the early period of the reaction and the reversible second-order reaction close to its completion. Acknowledgment This work has been funded by the Ministry of Science and Environmental Protection of the Republic of Serbia (Project 19062TR). References

Fig. 7. The comparison of TG and FAEE concentrations calculated by the kinetic model (straight lines) with the experimental data (TG – (d) and FAME – (N)) at (a) 25 °C, (b) 50 °C and (c) 75 °C (reaction conditions: ethanol to oil molar ratio 9:1; catalyst amount 1.25%).

where A is the preexponential factor, Ea is the activation energy, and R is the gas constant. The activation energies were calculated to be in the range 8.3–35.1, 22.3–43.9 and 3.4–34.6 kJ/mol for the irreversible second-order reaction, the forward second-order reaction and the reverse second-order reaction, respectively. Generally, the calculated activation energies are slightly lower than those for the alcoholysis reaction obtained in other studies, as it can be seen in Table 2. 4.3. Simulation of the ethanolysis process The proposed kinetic model satisfactorily fitted the changes of the FAEE concentration with the reaction time. The relative devia-

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