Preparation of Tertiary Amyl Alcohol in a Reactive Distillation Column

Jul 15, 1997 - The hydration of isoamylenes to produce 2-methyl-2-butanol (tert-amyl alcohol, or TAA) is strongly limited by chemical equilibrium to o...
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Ind. Eng. Chem. Res. 1997, 36, 3833-3844

3833

Preparation of Tertiary Amyl Alcohol in a Reactive Distillation Column. 1. Reaction Kinetics, Chemical Equilibrium, and Mass-Transfer Issues J. Castor Gonza´ lez† and James R. Fair* Separations Research Program, Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712

The hydration of isoamylenes to produce 2-methyl-2-butanol (tert-amyl alcohol, or TAA) is strongly limited by chemical equilibrium to olefin conversions of less than 50%. The general goal of this work was to determine whether reactive distillation would be a valid method to enhance the yield of TAA. The first step was to study the reaction kinetics and chemical equilibrium, using a polymeric acid catalyst (Amberlyst-15). Acetone was identified as a suitable medium to enable single liquid phase operation and also to enhance the reaction rate. It was found that the intraparticle mass-transfer resistance is negligible at temperatures below 70 °C. A kinetic expression, based on Langmuir-Hinshelwood formalism, is proposed. The forward and reverse reactions show first-order dependence on isoamylenes and TAA, respectively, while water is essentially an inhibitor of the reaction in both directions. The temperature effect on the forward reaction is quantified with an activation energy of 69.5 kJ/mol. Introduction Reactive distillation columns have gained significant importance in recent years, mainly for the preparation of ethers such as methyl tert-butyl ether (MTBE), tertamyl methyl ether (TAME), and ethyl tert-butyl ether (ETBE). These compounds are used widely as gasoline components (D’Amico, 1990; DeGarmo et al., 1992). Reactive distillation is especially useful for equilibriumlimited reactions, where the in situ separation of reactants and products enhances the progress of the reaction. In this work we explore the possibility of using a reactive distillation column for the hydration of 2-methyl-2-butene (isoamylene isomer) to produce tert-amyl alcohol (TAA). This reaction takes place in the liquid phase and in the presence of an acid catalyst, is moderately exothermic, and is limited by chemical equilibrium to olefin conversions of less than 50%. The reaction can be represented as:

CH3CHdC(CH3)2 + H2O T CH3CH2COH(CH3)2 The large difference in boiling point between isoamylene (38 °C) and TAA (102 °C) indicates an easy separation of the reaction products in a distillation column. The practical importance of this work is to demonstrate that the reactive distillation concept can indeed be used effectively to obtain very high yields of product for a reaction that is strongly limited by chemical equilibrium. The general goal of the work was to maximize the yield of TAA, ideally up to isoamylene extinction, in a single distillation column containing the catalyst that promotes the reaction. Three main working steps were identified in order to evaluate and develop a reactive column for the preparation of TAA: (1) kinetic and chemical equilibrium evaluation of the reaction; (2) distillation performance of a column containing the * To whom correspondence should be addressed. E-mail: [email protected]. † Present address: Intevep, S.A., P.O. Box 76343, Caracas 1070A, Venezuela. S0888-5885(96)00749-X CCC: $14.00

catalytic packing; (3) experimental demonstration of the concept in a small-scale column and evaluation of the effect of operating conditions using an equilibrium-based computer model. This part 1 of the paper focuses mainly on the first step of the work, i.e., the chemical equilibrium and kinetics aspects of the TAA reaction. The reactive distillation experiments and the simulation of the column will be presented in part 2. The mass-transfer characteristics and capacity of the packing containing the catalyst are discussed by Subawalla et al. (1996). A complete description of the entire work is given by Gonza´lez (1997). Previous Work The reaction of isoamylene and water to produce TAA is very similar to the well-studied etherification reactions to produce MTBE, TAME, and ETBE. All are carried out in the presence of strongly acidic macroporous resins, at moderate conditions of temperature (50-90 °C) and pressure (300-1500 kPa). The polar compound (water or alcohol) adsorbs preferentially in the resin, inhibiting favorable adsorption of the olefin. All reactions proceed by the formation of a stable tertiary carbenium ion, are thermodynamically equilibriumlimited, and are moderately exothermic (heats of reaction 25-40 kJ/mol). The TAA reaction has not been studied extensively, but the broad information available for etherification and hydration of isobutene provides a useful background. An additional problem posed in the hydration reaction is the mutual insolubility of both reactants as well as the hydrophilic character of the resin, which excludes the organic phase. For this reason, some authors have proposed the use of a solvent as a means to avoid phase splitting and also to enhance the rate of reaction. An early paper by Odioso et al. (1961) reported an isoamylene conversion to TAA of about 30%, using a fixed-bed reactor with a stoichiometric excess of water up to 350%. The results showed a strong equilibrium limitation and also very large mass-transfer resistances between the aqueous and organic phases. © 1997 American Chemical Society

3834 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997

Figure 1. Schematic of the batch reactor equipment.

Delion et al. (1987) studied the reaction in an acetone medium, with a large excess of water (about 400%) and Amberlyst-15 catalyst (strongly acidic macroporous resin). A pseudo-first-order dependency of the reaction rate on isoamylene concentration was proposed to fit the data. An activation energy of 90.4 kJ/mol was reported for the hydration of 2-methyl-2-butene. No information was given about possible intraparticle mass-transfer resistance. Prokop and Setinek (1987) focused on the effect of the ion-exchanger (catalyst) characteristics on the reaction rate. A solvent was not used to preclude formation of two liquid phases. They reported that the aqueous phase remained inside the resin because of strong hydrophilicity, at low water-isoamylene ratios. The effect of textural and hydrophilic properties of the resin on the rate was demonstrated, but no kinetic or mechanistic interpretation was given. Goto et al. (1993) worked with Amberlyst-15 catalyst in an aqueous liquid phase, bubbling isoamylene in a semibatch operation, and found first-order dependency on isoamylene concentration. Gates and Rodrı´guez (1973) found that the general acid-catalyzed dehydration of tert-butyl alcohol (acid sites as H+) is faster than the specific acid-catalyzed form (acid sites as H3O+). In the presence of an excess of water the specific form is the dominant form as the following equilibrium is established on the acid sites of the sulfonic-polymeric catalyst (Gates, 1992):

SO3-H+ + H2O T SO3- + H3O+ Ancilloti et al. (1978) proposed similar equilibria on the resin for the preparation of MTBE. In this case the specific acid site would be provided by the protonated molecule of methanol as CH3OH2+. They proposed that the reaction proceeds through an ionic mechanism, where first the olefin is protonated by the solvated proton, followed by the interaction of the carbonium ion with the nucleophile; the first reaction was proposed to

be the rate-limiting step. A similar mechanism was proposed by Krause and Hammarstrom (1987) for the etherification of isoamylenes to TAME. Many kinetic expressions have been published recently for etherification reactions, especially for MTBE. In most of the work, expressions based on LangmuirHinshelwood or Eley-Rideal formalisms have been used to account for the inhibiting effect of the polar molecule and have been written in terms of activities instead of concentrations because of the nonideality of the liquid phase. Representative endeavors have been by Rehfinger and Hoffmann (1990a), Parra et al. (1994), and Rihko and Krause (1995). Experimental Work Apparatus. A 1-gal mixing vessel was used as a batch reactor. Figure 1 shows a schematic of the equipment. The baffled vessel contained a turbine-type impeller with flat blades that could rotate at speeds between 100 and 1200 rpm. A filter (15 µm), placed in the bottom outlet of the vessel, was used to avoid carrying catalyst particles with the liquid when sampling. The vessel was surrounded by a jacket through which hot water flowed. A thermocouple and a pressure gauge provided information about internal conditions. The jacket water was heated electrically by a coil immersed in two oil baths. The internal temperature of the reactor was controlled by adjusting the oil temperature and by regulating the hot water flow. All tests were done at 600 kPa pressure in order to ensure that the chemicals remained in the liquid phase. Analytical Method. Liquid samples taken from the bottom of the batch reactor were analyzed using a GOWMAC 550 chromatograph equipped with a thermal conductivity detector (TCD) and a 3 m, stainless-steel column filled with Carbopack-B (mesh size 80-120). Helium was used as the carrier gas. Catalyst. A strongly acidic macroporous resin, Amberlyst-15 (A-15), was used. This resin, manufactured

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3835 Table 1. Properties of Dry Resin Amberlyst-15 property

value

property

value

physical form ionic form concentration of acid sites sulfur content particle size skeletal density

opaque, spherical beads hydrogen 4.9 equiv/kg 13.8 wt % 0.35-1.2 mm 1.426 g/cm3

particle density pore volume porosity average pore diameter surface area

0.927 g/cm3 0.30 cm3/g 0.35 cm3/cm3 25 nm 45 m2/g

Figure 2. Calculation of the rate of reaction for a typical batch reactor test.

by Rohm & Haas Co., has been on the market for more than 30 years. It was chosen because of its support by a large amount of information and its wide usage. Its properties, as reported in the open literature, are shown in Table 1. The catalyst is formed by a matrix of polystyrene cross-linked with divinylbenzene (20 mol %). Sulfonic groups are attached to the benzene rings and provide the strong acid sites required for the reaction. These sulfonic groups also give the resin strong affinity for polar molecules, causing the swelling of its gel structure and generating repulsion for aliphatic molecules. The polymer structure forms a tangle of connected polymer chains that constitute the gel phase. This phase forms beads of about 30 nm (Ihm and Oh, 1984). The gel beads are grouped in particles of 0.35-1.2 mm diameter. Accessibility to the resin beads inside the particle is provided by means of macropores that have an average diameter of about 25 nm. The reagents and products must be transported through the pores and also inside the gel beads where, according to Ihm et al. (1988), 95% of the acid sites are located. In other words, only 5% of the acid sites are on the surface of the gel beads and available from the pores. Before each test, the catalyst was dried for at least 90 min in a vacuum oven at 100-105 °C and less than 1.5 kPa. Chemicals. High-purity chemicals and distilled water were used. The isoamylene was research grade obtained from Johnson and Matthey Co. and contained 92.4 wt % 2-methyl-2-butene, the remainder 2-methyl1-butene. The TAA had a purity of 99.8 wt % and was also obtained from Johnson & Matthey. Acetone of HPLC grade (99.5% purity) was obtained from EM Science Co. Hexanes of spectrophotometry grade (density: 0.664 g/cm3) were obtained from Fisher Sci-

entific Co.; this material consists essentially of three C6 hydrocarbons: normal hexane (85.5 wt %), methylcyclopentane (10 wt %), and an unknown C6H14 isomer (4.5 wt %). Procedure. Each test lasted 2-4 h at steady conditions. The mixture of solvent, water, and catalyst was heated under agitation until the temperature was about 5 °C below the desired value. At this point isoamylene was injected from a small container above the batch reactor, using N2 as the carrier, and the pressure was set to 600 kPa. The first liquid sample was taken when the desired temperature was stabilized (about 15 min after injection of isoamylene), and at this point the reaction time was defined as zero. Samples were taken every 15-30 min (5-10 samples/test) to follow the reaction progress. Reaction Rate Calculation. The slope of the straight line obtained by plotting the TAA concentration as a function of time gave the rate of TAA formation. Figure 2 shows an example of a plot done to calculate the average rate of formation of TAA during a typical test and also provides representative conditions for the reaction study. Since the amount of catalyst loaded in each test was very small (0.8-6.5 g), the extent of the reaction was also small and the concentration of chemicals during each test changed very little. For this reason the reaction rate was practically constant during the test (constant slope in plots such as Figure 2) and could be related to the time-averaged concentration of chemicals. Experimental Plan. Twenty-nine tests were carried out to evaluate the effect of the following parameters on reaction rate: catalyst concentration, stirrer speed, catalyst size, temperature, and concentrations of isoamylene, water, TAA, and solvent (acetone). Three additional tests were extended long enough to allow the

3836 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997

Figure 3. Effect of the catalyst concentration on the rate of TAA formation.

Figure 4. Effect of the acetone concentration on the rate of formation of TAA. Acetone + hexane fixed at 80 mol % of total reaction mixture.

reaction mixture to approach chemical equilibrium. In all this work the isoamylene was characterized as 2-methyl-2-butene, since this is the component available in the largest proportion in the feed and reaction products (more than 90%). Also, the chemical equilibrium constant for the isomerization between both isoamylenes favors 7-10 times larger concentrations of 2-methyl-2-butene. Results and Discussion Preliminary tests with varying catalyst concentration showed that the rate of formation of TAA per unit of equivalent acid of catalyst is independent of the catalyst concentration (see Figure 3). For this reason all the reaction rate values are reported per unit of equivalent acid of the catalyst (the catalyst concentration of acid sites is 4.9 equiv of acid/kg of dry catalyst). Reaction Medium. Acetone was chosen as the solvent in order to avoid the formation of two liquid

phases and to enhance the rate of reaction. Its salutary effect can be seen in Figure 4. Some tests were performed by partially replacing acetone by hexanes so the total amount of inert (acetone and hexanes) was kept constant at about 80 mol %. It may be noted that the reaction rate is about 15 times larger when acetone concentration is increased up to about 80 mol % (hexane-free concentration). At less than about 60 mol % of acetone (and 20% hexane), two liquid phases are formed, and the aqueous phase is sequestered inside the hydrophilic catalyst. The effect of acetone on the rate of reaction is mainly explained by its influence on the activity coefficients of the reactants. Figure 4 shows that, as the acetone content increases, the activity coefficient of water decreases, while the activity coefficient of isoamylene increases. This change in activity coefficients boosts the formation of TAA, since the reaction is first-order-dependent on the activity of isoamylenes and is inhibited by water, as will be shown later. Because of the significant improvement in the rate of reaction when acetone was used as solvent, it

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3837

Figure 5. Effect of the mixer speed on the rate of reaction.

was decided to conduct the reaction in this medium, which would also avoid problems associated with a second liquid phase inside the reactive column. Mass-Transfer Effects. Three mass-transfer resistances were considered to affect the observed rate of reaction: (1) transport through the solid-liquid interface film; (2) transport inside the catalyst pores; (3) transport inside the gel phase of the catalyst. The first two resistances were evaluated by changing stirrer speed and catalyst particle size, respectively. The third resistance was not evaluated experimentally, but an assessment of its importance was made, based on published data. Liquid-Solid Mass Transfer. Figure 5 shows the effect of stirrer speed on the rate of reaction. It was found that above 600 rpm there was no effect on the rate, indicating no significant resistance to mass transport between the liquid phase and the external part of the catalyst. For this reason, most of the tests were made at 800 rpm. A theoretical assessment of the importance of the solid-liquid resistance to the transport of isoamylene was made using the dimensionless Biot number. This number relates the mass transport velocity across the liquid-solid interface to the mass transport velocity inside the solid. For spherical particles the Biot number can be written as

θKLrp 3De

(1)

De ) Dθ/τ

(2)

Bi ) where

The mass-transfer coefficient KL was estimated using the Boon-Long correlation for suspended solids in agitated vessels, given by Oldshue (1983). A tortuosity value of 1.3 was taken, based on information for the same catalyst given by Rehfinger and Hoffmann (1990b) and by Velo et al. (1990). The molecular diffusion coefficient for isoamylene in acetone at infinite dilution was calculated using the Wilke-Chang correlation (1955) and was corrected for nondilute, nonideal conditions using the Vignes equation (1966) and UNIFAC-

predicted activity coefficients. The value of the Biot number was found to be about 10, which indicates that the transport across the liquid-solid interface is about 1 order of magnitude larger than the transport inside the pores of the catalyst. Mass Transfer in the Catalyst Pores. The original catalyst as supplied by the manufacturer has a range of particle sizes between 0.35 and 1.2 mm. This material was sieved into three fractions in order to evaluate the particle size effect on the rate of reaction. The ranges of catalyst particle diameter used for this purpose were 0.35-0.42, 0.42-0.60, and 0.60-0.80 mm. Particles larger than 0.8 mm and smaller than 0.35 mm were in very small amounts and were discarded. Figure 6 shows the effect of particle size on the rate of formation of TAA at 60 and 70 °C. There appears to be no significant effect of catalyst particle size, which indicates that the mass transport inside the catalyst particles is fast enough to enable elimination of this resistance in relation to the rate of reaction. A theoretical verification of the intraparticle masstransfer effect was made assuming a pseudo-first-order dependency of the reaction on isoamylene, as proposed by Delion et al. (1987) and Goto et al. (1993), taking into account that measurements were made at conditions far from chemical equilibrium. The catalyst particles were essentially isothermal, since the maximum temperature difference from the center to the surface, calculated through a heat balance in the particle, was less than 0.2 °C. Satterfield (1970) indicates that a theoretical calculation of the catalyst effectiveness factor can be made using a modulus Φ, which can be readily calculated from the observed rate of reaction and the concentration on the particle surface (same as bulk concentration here, since there is no significant solid-liquid resistance). For the transport of isoamylene, which is likely to be the limiting species on the acid site, this modulus is calculated as v rp2RTAA Φ) DIC5,eCIC5

(3)

The rate of reaction per unit volume of catalyst particle was calculated from the observed rate of reaction plus the values of particle density and acid site

3838 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997

Figure 6. Effect of the catalyst size on the rate of formation of TAA. Table 2. Results of the Tests To Evaluate the Chemical Equilibrium

concentration in the catalyst v RTAA ) RTAA(CH+)(Fp)/3600

feed (wt %)

(4)

Taking the rate of reaction from Figure 6, the calculated values of the Φ modulus were between 0.07 (at 60 °C with the smallest particles) and 0.41 (at 70 °C with the largest particles). Satterfield (1970) gives a plot that shows that the effectiveness factor is unity when Φ is less than 0.7, for the case considered here. At higher values, the effectiveness factor begins to decrease, and a reduction of the rate of reaction may be noticed. These calculations confirm the experimental data which showed no significant resistance for the transport of isoamylene in the catalyst pores. Mass Transfer in the Gel Phase. Several authors have evaluated this effect for the hydration of isobutene in polymeric acid catalysts. Leung et al. (1986) estimated the value of the Thiele modulus in the gel phase of A-15 as about 10-3. On the basis of this low value, they concluded that the hydration of isobutene is very unlikely to be affected by the resistance to mass transport inside the very small gel particles of the catalyst (30 nm). Satterfield (1970) and Gupta and Douglas (1967) reported that the diffusion coefficient of isobutene in the gel phase of the catalyst is only 1 order of magnitude smaller than the molecular diffusion coefficient in the liquid. This relatively high value of the coefficient in the gel phase was explained by Gupta and Douglas on the basis that the main mechanism of transport is by surface diffusion as deduced by the inverse effect of temperature. Although the transport of species in the gel phase is slower than in the pores (1 order of magnitude), the mass-transfer resistance is smaller in the gel phase because the much smaller particle size (4 orders of magnitude) is the dominant effect. An estimated value of Φ in the gel phase was also made for the hydration of isoamylene, assuming that the diffusion coefficient of the isoamylene in the gel phase is 10% of the effective diffusion coefficient in the catalyst pores, following the findings of Satterfield and Gupta and Douglas. Using a value of 3 × 10-8 m for the radius of the gel beads, Φ for the isoamylene

test

temp (°C)

IC5

water yield (%)

TAA

Kea

eq 1 eq 2 eq 3

70.1 59.7 59.4

10.04 10.04 9.83

1.82 1.82 3.82

15.7 19.8 29.6

0.33 0.44 0.41

a

Ke: chemical equilibrium constant (experimental, eq 5).

hydration is about 1 × 10-4. This value clearly indicates that the transport of isoamylene in the gel phase is very fast, and thus the gel phase does not offer significant mass-transfer resistance. Considering the experimental results and the dimensionless numbers discussed above, we can summarize the relative resistance to the mass transport of species as catalyst gel phase , liquid-solid film < catalyst pores < reaction rate. Based on this analysis, the data taken in these tests were considered essentially representative of the intrinsic rate of reaction and free of mass-transfer effects. Chemical Equilibrium. Three tests were made in the batch reactor using large amounts of catalyst (27 g) and waiting until the TAA concentration did not change with time. Table 2 shows a summary of the main results of these tests. The mole ratio of water to isoamylenes in the feed for the first two tests was about 0.7, and that value was increased to 1.5 for the third test. Notice that the maximum isoamylenes conversion to TAA was 30% at 60 °C and a 1.5 ratio of water to isoamylene. The experimental values of the chemical equilibrium constant were calculated using the following equation:

Ke )

aTAA aIC5aW

(5)

The activity of each species was calculated using the experimental mole fraction values, and the activity coefficients were calculated using the UNIFAC predictive method (Gmehling et al., 1982) as

ai ) xiγi

(6)

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3839

expression that permits the calculation of the chemical equilibrium constant as a function of temperature:

Table 3. Calculation of the Heat of Reaction and Chemical Equilibrium Constanta quantity ν sensible heat (25-60 °C) sensible heat (25-80 °C) H°L G°L

units

TAA

2-methyl2-butene

water

kJ/mol kJ/mol kJ/mol kJ/mol

1 +7.3 +12.0 -379.8 -125.1

-1 +5.5 +8.9 -68.2 +60.2

-1 +2.6 +4.1 -286.0 -229.0

T ) 25 °C

T ) 60 °C

T ) 80 °C

25.6 0.23

26.4 0.14

26.6 0.08

heat of reaction (-∆Hr), kJ/mol equilibrium constant (Ke)

a Heats and Gibbs free energies of formation were taken from TRC Thermodynamics Tables, Hydrocarbons and Nonhydrocarbons (1986).

The increase of Ke from 0.33 to 0.41-0.44 when the temperature was reduced from 70 to 60 °C follows the expected trend for an exothermic reaction. From the experimental data, the average heat of reaction (-∆Hr) could be calculated as

( )(

-∆Hr ) R ln

)

Ke1 1 1 Ke2 T1 T2

-1

(7)

In this equation the subscripts 1 and 2 refer to the tests at 60 and 70 °C, respectively. The experimental value of the heat of reaction was calculated to be 20.5-27.2 kJ/mol. The heat of reaction, which is a function of temperature, can also be calculated from the heats of formation of reactants and products in the liquid phase at 25 °C using the following expression:

∆Hr(T) )

∑i (υiH°L,i) + ∑i (υi∫298Cpi dT) T

(8)

This expression includes the sensible heat (liquid) to convert the heat of reaction to the desired temperature. The required data and calculated values of -∆Hr are given in Table 3. Note that the values of the heat of reaction obtained at 60 and 80 °C (26.4 and 26.6 kJ/ mol) agree reasonably well with the experimental values (20.5 and 27.2 kJ/mol). It can also be noticed that, in the range of interest (25-80 °C), the heat of reaction is relatively constant, so an average value of 26.5 kJ/mol was taken for all purposes in the subsequent steps of this work. The chemical equilibrium constant at 25 °C can be obtained from the Gibbs free energy of formation of each compound in the liquid phase:

(

Ke ) exp -

)

∑i (υiG°i) RT

(9)

The dependence of the equilibrium constant on temperature is given by the van’t Hoff equation:

d(ln Ke) ∆Hr ) dT RT2

(10)

Considering that the heat of reaction is relatively constant in the range of temperature considered here (25-80 °C), eq 10 can be integrated between the standard and the reaction temperatures to give an

Ke ) Ke0 exp

( (

))

-∆Hr 1 1 R T T0

(11)

Table 3 includes values of the Gibbs free energy of formation in the liquid phase at 25 °C, which are used for the calculation of the equilibrium constant at several temperatures. The experimental values of Ke reported in Table 2 at 60 and 70 °C are about 3 times larger than corresponding thermodynamic values shown in Table 3. This difference was also noticed by Delion et al. (1987), who reported that the experimental values of the equilibrium constant were between 3.9 and 5.6 times larger than the theoretical values. The difference between experimental and predicted values of the chemical equilibrium constant may be due to experimental error, but Gonza´lez (1997) offers an alternate explanation based on the distribution coefficient concept introduced by Helfferich (1962), which considers that the activities of species in the liquid bulk are different from those inside the catalyst gel phase where the reaction takes place. Reaction Kinetics. The effects of temperature and concentrations of product and reactants on the rate of reaction were also evaluated. Figure 7 shows the effect of temperature on the reaction rate. Note that the catalyst with the smallest particle size (0.39 mm) was used in order to minimize possible intraparticle masstransfer resistance, especially at 75 °C. The data in Figure 7 were regressed according to the Arrhenius expression, considering concentrations to be constant, in order to obtain a preliminary value of the activation energy for the forward reaction. A value of 66.6 kJ/mol was found by this approach and was used to locate the continuous line in this figure. As shown below, the regression of the entire data, to fit a kinetic model, gave an activation energy of 69.5 kJ/mol. This value is smaller than the values reported by Delion et al. (1987), which were 82.9 and 90.4 kJ/mol for the hydration of 2-methyl-1-butene and 2-methyl-2-butene, respectively. For the hydration of isobutene, Leung et al. (1986) reported an activation energy of 67 kJ/mol, while Velo et al. (1988) reported 73.7 kJ/mol. In any case, the value of the activation energy found in this work seems to match reasonably well the values reported previously for the hydrations of isoamylene and isobutene. The effect of isoamylene and water mole fractions on the rate of formation of TAA is shown in Figure 8. The rate of reaction clearly shows a first-order dependency on isoamylene mole fraction. On the other hand, water is an inhibitor of the forward reaction at concentrations higher than 5 mol %. This probably results from the strong affinity of the catalyst for polar molecules, which makes the concentration of water on the acid sites very large, reducing the availability of those sites for isoamylene adsorption and further reaction to TAA. Figure 9 shows the effect of TAA and water on the rate of TAA decomposition (reverse reaction) at conditions far from chemical equilibrium. Again, the effects are the same as those for the case of the forward reaction: first-order dependency on TAA composition and an inhibiting effect of water. It should be mentioned that, for the range of water concentrations studied, changes in the acid character of the catalyst are not expected, since the water concentrations are high enough to prevent the formation of SO3H+ acid

3840 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997

Figure 7. Effect of the temperature on the rate of TAA formation.

Figure 8. Effect of isoamylene and water on the rate of formation of TAA.

groups from H30+ ions. This would enhance the rate of reaction, according to Gates (1992). All the data gathered in this work, including the equilibrium runs (zero rate of reaction) and the reverse reaction runs (negative rate of formation of TAA), were used to develop a kinetic expression. Several models were formulated in terms of activities instead of concentrations, to account for the highly nonideal character of the liquid mixture. Activity coefficients were obtained from the UNIFAC model (Gmehling et al., 1982). The effect of temperature was modeled using the Arrhenius expression for both the forward and reverse reactions. The activation energy for the reverse reaction was expressed as a function of the forward activation energy and the theoretical value of the heat of reaction (-∆Hr ) 26.5 kJ/mol):

Er ) Ef + (-∆Hr)

(12)

Three different kinetic models were evaluated with the data generated in this work:

(1) Simple power law (PL):

( )

RTAA ) Af exp -

Ef a R1a R2 RT IC5 W (Ef/R + 3170) aTAAR3 (13) Ar exp T

(

)

(2) Langmuir-Hinshelwood (L-H). This model assumes that the reaction takes place between one molecule of water and one of isoamylene, both adsorbed on two different acid sites. The summation in the denominator accounts for all the adsorbed species that share the largest portion of acid sites:

RTAA )

(() )

Ef + 3170 Ef R Af exp aIC5aW - Ar exp aTAA RT T (1 + Kiai)2 (14)

( )

∑

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3841

Figure 9. Effect of TAA and water on the rate of decomposition of TAA.

(3) Eley-Rideal (E-R). In this case the reaction takes place between one molecule adsorbed on one acid site and one nonadsorbed molecule from the liquid phase. Again, the summation in the denominator accounts for the distribution of sites among the different species.

RTAA )

(() )

Ef + 3170 Ef R Af exp a a - Ar exp aTAA RT IC5 W T 1 + Kiai (15)

( )

∑

The derivation of the basic equations corresponding to the L-H and E-R formalisms can be found elsewhere (Carberry, 1976). Several options were considered for the L-H model, depending on which species are considered to be adsorbed onto the catalyst sites. Water is, of course, the most likely to occupy the acid sites; TAA and acetone are probably the next candidates in preference for adsorption, while isoamylene is unlikely to occupy a significant fraction of the active sites. A fourth model was also tested, in which the adsorption of water into the gel phase of the resin is assumed to follow an exponential distribution. The R exponent of the water activity is an empirical parameter that can be found by regression with other parameters. Further details on this empirical approach may be found in Gonza´lez (1997).

RTAA )

(() )

Ef + 3170 Ef R Af exp aIC5aWR - Ar exp aTAA RT T (1 + KWaWR)2 (16)

( )

The data were processed using a nonlinear regression method, based on the Gauss-Newton algorithm, with all four kinetic models described here. A commercially available software package was used to carry out the

regressions and to obtain values of the parameters for each model, as well as statistical information that allows a comparison of models and selection of the one most appropriate. The main results of the regression of the data for each model and the corresponding statistical indicators are shown in Table 4. The three indicators used to evaluate the quality of the model in relation to the prediction of the reaction rate were as follows: (1) The sum of squares (SS) is the minimized variable and is calculated as the sum of the squares of the differences between the predicted and experimental values. (2) The coefficient of determination (COD) is a measure of the fraction of the total variance accounted for by the model. As the COD approaches unity, the experimental error and other effects not considered in the model tend toward zero. (3) The F-value (also used for the Fisher test) is an indicator that considers the variance accounted by the model as well as the number of parameters. When the number of model parameters decreases or the fraction of variance accounted by the model increases, the F-value also increases, indicating a better model. Table 4 shows that the PL model does not give a good fit of the data, since the SS value is above 100 and the COD value indicates that this model only accounts for 77.3% of the variance of the data. The failure of the PL model results from its inability to consider the inhibiting effect of water over the reverse reaction. Three cases were considered using the L-H model (Table 4): the first case assumes only significant water adsorption on the acid sites, the second considers both water and acetone adsorbed, and adsorbed water and TAA are accounted for in the third. As can be noted, there is a significant improvement in relation to the PL model, as the SS is reduced to 13.0 and the model accounts for 98.1% of the variance of the data. The predicted values of the reaction rate for these three cases are practically the same, since the model parameters are very close and the adsorption terms for acetone and TAA are negligible compared with the water term. The F-value indicates that the L-H model, which

3842 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 4. Results of the Kinetic Model Evaluation model power law (eq 13) Langmuir-Hinshelwood (eq 14) water adsorption Langmuir-Hinshelwood (eq 14) water adsorption acetone adsorption Langmuir-Hinshelwood (eq 14) water adsorption TAA adsorption Eley-Rideal (eq 15) water adsorption modified L-H (eq 16) water adsorption

parameter

statistical indicator

Af ) 3.30 × 1012 mol/h/equiv of acid Ar ) 1.02 × 1018 mol/h/equiv of acid Ef ) 78.6 kJ/mol R1 ) 1.00; R2 ) -1.08; R3 ) 1.23 Af ) 8.37 × 1015 mol/h/equiv of acid Ar ) 1.93 × 1020 mol/h/equiv of acid Ef ) 69.8 kJ/mol KW ) 138.6 Af ) 1.06 × 1016 mol/h/equiv of acid Ar ) 2.45 × 1020 mol/h/equiv of acid Ef ) 70.1 kJ/mol KW ) 146.6; KA ) 0.075 Af ) 1.12 × 1016 mol/h/equiv of acid Ar ) 2.60 × 1020 mol/h/equiv of acid Ef ) 70.1 kJ/mol KW ) 149.9; KT ) 0.092 Af ) 1.61 × 1015 mol/h/equiv of acid Ar ) 4.45 × 1019 mol/h/equiv of acid Ef ) 72.7 kJ/mol KW ) 657.9 Af ) 1.01 × 1014 mol/h/equiv of acid Ar ) 1.95 × 1017 mol/h/equiv of acid Ef ) 69.5 kJ/mol KW ) 26.2 R ) 3.64

SS ) 157.1 COD ) 0.773 F ) 14.2

includes only water adsorption, is a better model as it can account for the same variance with one less parameter. The E-R model does not produce as good results as the L-H model, since its SS is almost twice the value for the L-H model. The reason is because the inhibition effect of water over the forward reaction cannot be properly accounted for, since the water activities in the numerator and denominator tend to cancel (Kwaw > 1). The last model tested was the modified L-H that considers non-linear distribution coefficients for the activity of water inside and outside the gel phase of the resin. The structural indicators for this model are very similar to those for the nonmodified L-H versions. However, the values of the parameters and the predicted reaction rates with the simple L-H (eq 15) and modified L-H (eq 16) are different. A further comparison of the L-H and modified L-H models was made by evaluating their residuals (difference between the experimental and predicted reaction rate values). The analysis of the residuals showed that the errors were not evenly distributed for the case of the L-H model (eq 15). In fact, the only cases in which the residuals were negative (experimental rate < predicted rate) for the forward reaction case were those in which the water activity was very high. This means that eq 15 overpredicted the reaction rate for high water concentrations, while the rate was slightly underpredicted for the cases where the water mole fraction was lower than 15 mol %. Furthermore, most of the unaccounted variance of the L-H model (eq 15) came from the high water activity points. On the other hand, the modified L-H model (eq 16) gives a more uniform distribution of residuals, and it is not biased toward any particular set of data. Because of its better handling of the water effect, the modified L-H model was finally selected as the kinetic expression for calculating the reaction rate:

[

a a - 1.95 × (-8359 T ) -11544 exp( a ]/(1 + 26.2a ) (17) T ) 3.64

RTAA ) 1.01 × 1014 exp 1017

IC5 W

3.64 2

TAA

W

SS ) 13.0 COD ) 0.981 F ) 352 SS ) 13.1 COD ) 0.981 F ) 270 SS ) 13.3 COD ) 0.981 F ) 265 SS ) 25.6 COD ) 0.963 F ) 176 SS ) 13.8 COD ) 0.980 F ) 256

Figure 10. Parity plot comparing predicted and experimental rates of reaction.

Figure 10 shows the parity plot comparing the experimental and predicted values using eq 17. Although a good agreement between experimental and predicted data may be observed, further and more fundamental work will be needed to provide proper understanding and to model properly the equilibrium distribution of water between the gel and liquid phases. Conclusions Reaction kinetics, chemical equilibrium, and intraparticle mass-transfer issues have been evaluated for the hydration of isoamylene in the presence of an acid macroporous resin as catalyst. Acetone was identified as a suitable reaction medium to ensure a single liquid phase; the rate is 15 times faster than when two liquid phases are present, and problems with a second liquid phase in the distillation column are avoided. No significant intraparticle mass-transfer resistance was noticed, using commercially available samples of Amberlyst-15 catalyst at temperatures less than 70 °C in

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3843

the acetone medium. The formation of TAA is strongly limited by thermodynamic chemical equilibrium, with a maximum conversion of isoamylenes of about 30% at 60 °C and a 1.5 molar ratio of water to isoamylenes. The reaction is moderately exothermic with a heat of reaction of 26.5 kJ/mol. A reaction rate expression was developed using a modified Langmuir-Hinshelwood model that considers a nonlinear distribution of water between the gel phase of the catalyst and the liquid phase. The forward and reverse reactions show first-order dependence on isoamylenes and TAA, respectively, while water is essentially an inhibitor of the reaction in both directions. The temperature effect over the forward reaction was quantified with an activation energy of 69.5 kJ/mol. Acknowledgment The authors thank Intevep, S.A., the Research and Technological Support Center of PDVSA (Petro´leos de Venezuela, S.A.), for funding this work. Nomenclature Af ) Arrhenius preexponential factor of the forward reaction, mol/h/equiv of acid Ar ) Arrhenius preexponential factor of the reverse reaction, mol/h/equiv of acid ai ) activity of the ith species Bi ) Biot number, dimensionless Ci ) concentration of the ith species, mol/m3 CH+ ) concentration of catalyst acid sites, 4.9 equiv of acid/ kg of dry catalyst COD ) coefficient of determination Cpi ) specific heat of the ith species, J/mol/K D, Di ) diffusion coefficient of the ith species, m2/s De, Di,e ) effective diffusion coefficient of the ith species inside the catalyst pores, m2/s Ef ) activation energy of the forward reaction, J/mol Er ) activation energy of the reverse reaction, J/mol F ) Fisher statistical value (F-value) G°i ) Gibbs free energy of formation of species i in the liquid phase, J/mol H°L,i ) heat of formation of species i in the liquid phase, J/mol ∆Hr ) negative value of the heat of reaction in the liquid phase, J/mol Ke ) chemical equilibrium constant Ke0 ) chemical equilibrium constant at 298 K Ki ) adsorption constant of compound i in kinetic equations (13)-(15) KL ) liquid-solid film mass-transfer coefficient, m/s KW ) water adsorption constant in kinetic equation (16) R ) gas law constant, 8.32 J/mol Ri ) rate formation of species i, mol/h/equiv of acid Rvi ) rate of formation of species i per unit of dry catalyst volume, mol/s/m3 rp ) particle radius of the catalyst, m SS ) sum of squares T ) temperature, K (or °C) T0 ) reference temperature (298 K) xi ) mole fraction of the i species in the liquid phase Greek Symbols Φ ) modulus defined by eq 3 R, Ri ) power constants in kinetic expressions (i is a number) γi ) activity coefficient of species i νi ) reaction stoichiometric coefficient of compound i θ ) catalyst porosity (pore volume fraction)

Fp ) particle density of the catalyst, kg/m3 τ ) catalyst tortuosity Subscripts (Chemical Compounds) A ) acetone IC5 ) isoamylene TAA ) tert-amyl alcohol W ) water

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Received for review November 26, 1996 Revised manuscript received May 13, 1997 Accepted May 14, 1997X IE960749B

X Abstract published in Advance ACS Abstracts, July 15, 1997.