Kinetic study on the catalytic esterification of acetic acid with isoamyl alcohol over Amberlite IR-120

Chemical Engineering Science 101 (2013) 755–763

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Kinetic study on the catalytic esterification of acetic acid with isoamyl alcohol over Amberlite IR-120 Wilmar Osorio-Viana a, Miguel Duque-Bernal a, Javier Fontalvo a, Izabela Dobrosz-Gómez b, Miguel Ángel Gómez-García a,n a

Grupo de Investigación en Aplicación de Nuevas Tecnologías, Laboratorio de Intensificación de Procesos y Sistemas Híbridos, Departamento de Ingeniería Química, Facultad de Ingeniería y Arquitectura, Universidad Nacional de Colombia - Sede Manizales, Cra 27 64 – 60, Apartado Aéreo 127, Manizales, Caldas, Colombia b Grupo de Investigación en Aplicación de Nuevas Tecnologías, Laboratorio de Intensificación de Procesos y Sistemas Híbridos, Departamento de Física y Química, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Colombia - Sede Manizales, Cra 27 64 – 60, Apartado Aéreo 127, Manizales, Caldas, Colombia

H I G H L I G H T S

G R A P H I C A L


A kinetic model for the esterification of acetic acid and isoamyl alcohol in the presence of Amberlite IR-120 was fitted.
Adsorption experiments, using pure and binary mixtures, were performed.
Computational statistics estimated by a Markov Chain Monte Carlo technique were used.
Twelve possible kinetic models were considered.
A reaction rate model in terms of NRTL activity model is recommended.

Sorption (a) and kinetic (b) experimental results and simulation on the catalytic esterification of acetic acid with isoamyl alcohol over Amberlite IR-120.

art ic l e i nf o

a b s t r a c t

Article history: Received 2 February 2013 Received in revised form 16 May 2013 Accepted 9 July 2013 Available online 17 July 2013

A kinetic model was fitted for the liquid phase esterification of acetic acid with isoamyl alcohol in the presence of the heterogeneous catalyst Amberlite IR-120. The experiments were performed in the temperature range of 322–362 K in a batch reactor. Sequential experimental design, based on the divergence criterion and tools from computational statistics such as the deviance information criterion estimated by a Markov Chain Monte Carlo technique, were used to discriminate among 12 possible kinetic models. Adsorption experiments using pure substances and binary mixtures were also performed. In statistical terms, two kinetic models appear as the most appropriate for this esterification reaction: a simple, easy-to-handle model that uses molar fractions and a second model based on the NRTL activity model, which is physically more realistic due to its congruence with the resin sorption phenomena. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Kinetics Esterification Isoamyl acetate Bayesian model selection Fusel oil Amberlite IR-120

A B S T R A C T

1. Introduction The increasing worldwide tendency of ethanol production by fermentation generates each year large amounts of fusel oil. Nearly

n

Corresponding author. Tel.: +57 6 8879300x50210; fax: +57 6 8879300x50129. E-mail address: [email protected] (M.Á. Gómez-García).

0009-2509/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2013.07.009

5 L of fusel oil are obtained for each 1000 L of produced ethanol. Fusel oil, mainly constituted of isoamyl alcohol, is commonly treated as a residue (Kuçuk and Ceylan, 1998). However, it could be used as a raw material and converted to more valuable products. Synthesis of isoamyl acetate by esterification of acetic acid with isoamyl alcohol is a promising option considering the multiple applications of isoamyl acetate in food, cosmetic and chemical industries (Aslam et al. 2010; Osorio-Viana et al., 2013a;

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Saha et al., 2005a). Nevertheless, the design of an esterification process in liquid phase requires a reliable rate of reaction expression that includes both the homogeneous reaction rate and the effect of a suitable solid catalyst. As with other analogous reactions, this esterification is reversible and can be catalyzed using homogeneous mineral acids (Liu et al., 2006; Reid, 1948). The application of heterogeneous solid acid catalysts can overcome the drawbacks of the mineral acids such as: equipment corrosion, low selectivity, product contamination and recycle costs. Synthesis of isoamyl acetate by esterification of acetic acid with isoamyl alcohol in the liquid phase has been scarcely studied. Recently, DuqueBernal et al., (2013) reported a rate of reaction expression for the esterification between acetic acid and isoamyl alcohol without the use of catalyst. They showed that there is an autocatalytic effect of acetic acid on the reaction rate which equilibrium constant (≈5.0) can be considered temperature independent and correlated a rate law expression using mole fractions as a concentration variable. Previously, Teo and Saha (2004) and Saha et al., (2005b) studied the kinetics of this heterogeneously catalyzed esterification using the ion exchange resin Purolite CT175. To account the liquid phase non-ideality, UNIFAC model was used. The authors correlated a Langmuir–Hinshelwood– Hougen–Watson (LHHW) model considering only the adsorption of isoamyl alcohol and water on the catalyst and the surface reaction as the rate limiting step. Other related studies, in which kinetic models were not shown, employed catalytic membranes of poly-vinyl alcohol containing sulfonic acid groups (Castanheiro et al., 2006), heteropolyacids like partially substituted Keggin salts (Pizzio and Blanco, 2003), immobilized lipase Candida antartica enzyme (Güvenç et al., 2007) and expandable graphite catalyst (Pang et al., 2008). In this study, catalyst characterization and kinetic tests are discussed. A sequential experimental design has been used to correlate the parameters of several kinetic models for the isoamyl acetate synthesis reaction catalyzed by Amberlite IR-120 (an ion exchange resin). Experiments covered the temperature range of 322– 362 K and 1/1, 1/2, 2/1, 1/3 alcohol/acid feed molar ratios in a batch reactor. Following a literature survey on models used for similar esterification reactions, a total of twelve kinetic models (four types of rate law with three computational forms for the liquid phase activity) were fitted and compared in statistical terms using a Bayesian approach. This involved the exploration of the a posteriori probability distribution of the model parameters using a Markov chain Monte Carlo technique (Duque-Bernal et al., 2013; Laine, 2008).

2. Experimental 2.1. Catalyst characterization Table 1 presents the properties of the ion exchange resin Amberlite IR-120, as reported by Rohm and Haas. The resin was preconditioned previous to every reaction test. This procedure was based on successive washings with HCl and NaOH aqueous solutions as follows: (1) treatment with HCl solutions increasing the concentration stepwise: 0.5 M; 1 M; 2 M, followed by a continuous treatment with 3 M; then, washing with HCl solutions of stepwise decreasing concentrations: 2 M; 1 M and 0.5 M; (2) washing with deionized water; (3) stepwise treatment with NaOH solutions: 0.1 M; 0.5 M; 1 M; 0.5 M and 0.1 M; (4) washing again with deionized water; (5) stepwise treatment with HCl solutions: 0.5 M; 1 M; 2 M; 1 M and 0.5 M, (6) washing with water, (7) finally, a cation exchange was performed with 1 M HCl to obtain the resin in its H+ form (Zagorodni, 2007). Next, the resin was dried in an oven at 70–75 1C and under vacuum pressure of 40–50 Torr for

Table 1 Properties of ion exchange resin Amberlite IR-120 (Rohm and Haas) as reported by the manufacturer. Physical form Matrix Functional group Ionic form as shipped Total exchange capacity Moisture holding capacity Shipping weight Maximum reversible swelling Maximum operating temperature

Amber spherical beads Styrene divinylbenzene copolymer Sulfonic acid H+ ≥ 1.8 eq/L (H+ form) 53–58% (H+ form) 800 g/L Na+-H+≤11% 135 1C

approximately 8 h, time at which a constant weight was obtained. To estimate the cation exchange capacity of the resin, standard titration using an automatic burette (Titrino Metrohm SM 702) was performed with an aqueous solution 0.1 M in NaOH supersaturated with NaCl (Helfferich, 1995). Particle size distribution was measured using a screening sieving machine with 6 Tyler plates (1–0.15 mm screen size) and mechanical agitation for 20 min, using approx. 200 g of resin saturated with atmospheric moisture. The retained weight of resin in each sieve was measured. When the resin is brought into contact with a liquid, some of the liquid is incorporated inside the resin. As this phenomenon also involves the solid bulk phase (absorption) and not only its surface (adsorption), here the term sorption is used to include both as suggested by the IUPAC recommendations (IUPAC, 2004). Resin swelling and sorption equilibria were estimated as proposed by Gregor et al. (1951). Dry resin density was measured with a 10 mL picnometer (class A) in which a given quantity of resin was brought into contact with heptane (Merck), a solvent which does not swell the resin due to its non-polarity (Gregor et al., 1951). Then, dry resin was brought into contact with each of the reaction substances during 24 h; then, the liquid–solid mixture was separated by centrifugation; the swollen resin density was determined as stated before, using the corresponding substance instead of heptane. For sorption experiments, three binary non-reactive mixtures were prepared (alcohol–acetate, acid–acetate and acid–water) at several initial concentrations. For each mixture a dry resin sample of 2 g was mixed, using a shaker, with a given mass of the solution in a 50 mL beaker at 20 1C for at least 24 h. Next, a sample of the liquid in equilibrium with the resin was measured by gas chromatography (Perkin-Elmer, FID detector) and automatic titration (Titrino Metrohm SM 702) with NaOH for the binary mixtures with acetic acid. For all tests, the following reactive grade chemicals were used without further purification: isoamyl alcohol (Merck, 98%), isoamyl acetate (Merck, 99%), acetic acid (Panreac, 99.7%), HPLC grade water (Thermo Scientific Barnsted Nanopure unit, resistivity at 25 1C: 18.0 MΩ cm). Resin swelling at room temperature was estimated assuming additive volumes and using the experimental data for densities of: solvents (ρliq), dry resin (ρdr) and wet resin (ρH). It is reported in terms of the absorbance ratio (RW) and the swelling ratio (RH), which are defined as follows: RW ¼

1ðρliq =ρdr Þ 1ðρliq =ρH Þ

RH ¼ RW

ρdr ρH

ð1Þ

ð2Þ

Using both the RW and the experimental binary sorption data, the mass fraction of component A inside the resin ðwSA Þ in equilibrium with the liquid can be computed considering global and component material balances, according to Eq. (3), where RS stands for

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the ratio of initial liquid solvent mass/resin mass: wSA ¼ wLA þ

RSðw0A wLA Þ RW1

ð3Þ

2.2. Kinetic tests Reaction experiments were carried out in a glass batch reactor, provided with magnetic stirrer (700 rpm), temperature jacket and a reflux condenser. The temperature of the jacket was fixed to the desired value and the temperature of the reaction mixture was controlled using a PT-100 sensor (7 0.01 1C). First, the cold reactor was loaded with glacial acetic acid and heated to the reaction temperature through the jacket; preconditioned dry catalyst was loaded to the reactor using 5 wt% of the feed fluid mixture. Next, preheated isoamyl alcohol was added to the reactor and this was taken as time zero for reaction. Reagent masses were measured (70.2 g) to fill a volume of approximately 120 mL. Samples of 0.4–0.5 mL (10–15 per run) were taken every 10– 90 min, depending on the extent of the reaction in each run, through a stainless steel needle attached to 1 mL disposable syringes. They were frozen with liquid nitrogen, stored in ice and analyzed three times by automatic titration with standardized 0.1 N NaOH to find the mass fraction of acetic acid, hereafter called acidity. Thus, the experimental values of acidity, as a function of time, were collected in each experimental run. Some samples were also analyzed by gas chromatography to check mass balances. No quantifiable peaks of other substances were detected. Hence, no secondary reactions are considered in this study. Nine experimental runs (Table 2) were conducted with the experimental setup described above. Test runs RC2–RC6 were distributed according to a 22+1 factorial design, at which the temperature and the initial alcohol to acid molar ratio were varied. The conditions for RC7 and RC8 experimental runs were chosen to maximize the divergence criterion among models that so far had given a better fit in a preliminary regression analysis using data from RC2 to RC6. The divergence criterion in sequential experimental design allows a better model discrimination with a reduced number of experimental runs (Englezos and Kalogerakis, 2001). Test runs RC1 and RC9 introduced variations to the conditions in test run RC2, considering effects of the agitation speed Table 2 Experimental runs used in the study of the heterogeneous esterification reaction. Variation Runa Mean in T (K)b value of T (K)

RC1 RC2 RC3d RC4 RC5 RC6 RC7 RC8 RC9

362.36 361.90 322.65 322.41 362.05 347.46 342.34 328.47 361.46

0.76 0.47 0.14 0.22 0.47 0.21 0.14 0.09 0.35

Reagents loaded (mole fraction) %Cat

XHAc

XROH

XE

Total run time (h)

4.720 4.833 4.928 5.023 4.856 4.922 4.947 4.848 5.087

0.666 0.666 0.661 0.340 0.345 0.500 0.324 0.601 0.6618

0.334 0.334 0.339 0.660 0.655 0.500 0.346 0.202 0.3382

0.000 0.000 0.000 0.000 0.000 0.000 0.330 0.000 0.000

6.09 5.39 21.80 47.01 25.08 6.37 9.40 16.08 5.75

Conversion at the end of the runc (%)

86.8 86.8 87.4 86.2 86.6 67.8 64.3 45.5 80.3

Runs R2–R6 were performed according to a 22+1 factorial design.

757

(influence of external mass transfer resistance) in RC1 and the ion exchange capacity of the resin in RC9. Influence of external mass transfer resistance during kinetic test runs was evaluated changing the velocity of agitation in the reactor vessel from 700 to 1100 rpm, at conditions of maximum intrinsic reaction rate: high temperature and acetic acid in excess (see Table 2 for runs RC1 and RC2). The obtained results for acidity versus time showed that there is no appreciable difference between the runs at a different velocity of agitation (not shown here). This means that the measured reaction rates are free of external mass transfer resistance above 700 rpm. No internal mass transfer resistance was considered due to the low mean particle size of the resin according to the criteria of Quinta and Rodrigues (1993) and Pääkkönen and Krause (2003).

3. Mathematical modeling 3.1. Kinetic models for the catalytic esterification reaction The esterification reaction of acetic acid with isoamyl alcohol is an equilibrium-limited chemical reaction: CH3COOH+(CH3)2CHCH2CH2OH2CH3COOCH2CH2CH(CH3)2+H2O In general, reported rate laws can be classified into two groups: (i) pseudo-homogeneous model (PH), Langmuir–Hinshelwood–Hougen–Watson (LHHW) or Eley–Rideal (ER) classic rate law expressions that neglect the liquid–polymer phase equilibrium and use concentration variables (molar fraction, density or activity) in the liquid phase (Akbay and Altıokka, 2011; Lee et al., 1999, 2000, 2001; Pöpken et al., 2000; Yu et al., 2004); (ii) rate law expressions (LHHW, ER, etc.) in terms of the activity of the substances incorporated into the resin, in conjunction with a model for liquid–polymer phase equilibria and an activity model for the polymer gel phase (Mazzotti et al., 1997; Sainio et al., 2004). In this work, four rate laws are adopted, as described in Table 3: PH, LHHW, Pöpken et al. (2000) type model and a proposed model, all as a function of a concentration variable in the liquid phase. For each of these models, three activity models were also considered: ideal liquid phase, UNIFAC-Dortmund (Gmehling et al., 2002) and non-random two liquid (NRTL) model (DuqueBernal et al., 2013; Osorio-Viana et al., 2013b). Thus, a set of 12 different alternatives were analyzed based on experimental data of the reaction rate between acetic acid and isoamyl alcohol. The rate constant k1, based on an Arrhenius-type equation, can be expressed with two adjustable parameters:
 Ea 1 1  ð4Þ lnk1 ðTÞ ¼ lnk0 ðT 0 Þ  T T0 R where T0 is a reference temperature, in this case 363.15 K and Ea is the apparent activation energy for the reaction. The use of a reference temperature is recommended for curve fitting procedures (Englezos and Kalogerakis, 2001). On the other hand, the equilibrium constant Keq is assumed to be temperature independent (Duque-Bernal et al., 2013) and an adjustable parameter. It has not been estimated from thermochemical data due to the associated uncertainty with such computation in esterification reactions (Wyczesany, 2009). The adsorption equilibrium constants Ki are taken as temperature independent (Akbay and Altiokka, 2011; Pöpken et al., 2000).

a

Runs RC1 and RC9 have the same reagents loading than run RC2 but differ in speed of agitation and resin exchange capacity respectively. RC1 and RC9 not included in model correlation. b Computed as 1.96 times the standard deviation of measured values along the experimental run. c Not all experimental runs reached a state of chemical equilibrium. d Time zero for this run for an acetic acid conversion of 20.70% due to experimental conditions.

3.2. Objective function Using the observed values of acidity as a function of ! time, y obs ðtÞ, collected in seven experimental runs, a regression analysis was performed for each model presented in Table 3. In a Bayesian approach, the a posteriori probability of the adjustable

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Table 3 List of kinetic models evaluated for the heterogeneous esterification reaction. Models

Type

Rate law

MC1ua MC1nb MC1xc

PH


 aL aL r ¼ k1 aLHAc aLROH  KE L W

MC2u

LHHW

eq

Proposed

MC4u

Pöpken et al. (2000)


 a′ a′ k1 a′HAc a′ROH  KE S W eq

MC4n MC4x

c


 aL aL k1 aLHAc aLROH  KE S W

r¼ 2 1 þ aLHAc kads;HAc þ aLROH kads;ROH þ aLW kads;W

MC3u MC3x MC3n

b

lnk0 ðT 0 Þ; Ea ; lnK Leq

eq

MC2n MC2x

a

Adjustable parameters

r¼ 2 a′HAc þ a′ROH þ a′E þ a′W   k1 a″HAc a″ROH ða″E a″W =K Seq Þ r¼   2 a″HAc þ a″ROH þ a″E þ a″W

lnk0 ðT 0 Þ; Ea ; lnK Seq ; lnkads;HAc ; lnkads;ROH ; lnkads;W ; K

ads;i a′i ¼ aLi  K ads;w ¼ aLi  K rel;i

a″i ¼

aLi

PM i

K

ads;i  K ads;w ¼

lnk0 ðT 0 Þ; Ea ;

aLi PM i

 K rel;i

lnK Seq

lnkrel;HAc ; In krel;ROH ; lnkrel;E

Models MC1u–MC4u uses UNIFAC Dortmund for liquid phase activity. Models MC1n–MC4n uses NRTL for liquid phase activity. Models MC1x–MC4x uses molar fractions for ideal liquid phase.

! parameter vector θ in model M j was evaluated, assuming a normally distributed error for acidity, and assigning a Gaussian prior to the estimated parameters (Duque-Bernal et al. 2013). This probability is given by (Tarantola, 2005) !! ! ! pð θ j y obs ; M j Þ ¼ constant  exp ð½SData ð θ Þ þ SPrior ð θ ÞÞ ð5Þ ! where SData ð θ Þ represents the sum of squares on the data (i.e., a measure of how different the model predictions are from the ! experimental data) and SPrior ð θ Þ represents the sum of squares on the prior (i.e., a measure of the difference between the a priori information on the parameter and their currently estimated values). Assuming a Gaussian distribution on the error and the prior, the following equations are obtained: ! 1 ! ! ! ! SData ð θ Þ ¼ ð y obs  y calc ÞT  C D 1  ð y obs  y calc Þ 2

ð6Þ

! ! ! 1 ! ! SPrior ð θ Þ ¼ ð θ  θ prior ÞT  C θ 1  ð θ  θ prior Þ 2

ð7Þ

If additionally it is assumed that the error on acidity data follows a normal probability distribution with standard relative deviation of srel ¼0.016 (as inferred from experimental data) the sum of squares on the data can be written: ! SData ð θ Þ ¼

! !2 N yobs;u ycalc;u ð θ Þ 1 ∑ yobs;u 2s2rel u ¼ 1

ð8Þ

where ycalc,u denotes the calculated values for acidity using a given model, yobs,u corresponds to the measured value of acidity and the sum goes along the values of all experimental runs for one given model. The use of relative error in the residuals reflects the error structure of the analytical methods employed. The data collected in this study allows the application of a noninformative prior to all model parameters. The a posteriori probability distribution of the parameters, as given by Eqs. (6) and (7), may be sampled by means of Monte Carlo Methods (Tarantola, 2005). It is also useful to have a negative loglikelihood function, minimization of which gives the fitted parameters with maximum likelihood. This function is a sum of squares as given by h ! ! !i LML ð θ Þ ¼  SData ð θ Þ þ Sprior ð θ Þ ð9Þ

No prior information on the parameter values was assumed, ! which makes Sprior ð θ Þ ¼ 0. For the objective function, the batch reactor molar balance, in terms of the extent of the reaction, was used to calculate the predicted acidity (ycalc,u) versus time. The heterogeneous reaction rate model (to be fitted) and the homogeneous reaction rate (Duque-Bernal et al., 2013) were both included. A maximum estimated fraction of 4% of the total observed rate is attributable to the homogeneous reaction at high reactants concentration.

3.3. Regression algorithm and criteria for model comparison Initially, each set of model parameters was separately fitted by minimizing Eq. (9) with the Levenberg–Marquardt algorithm (Laine, 2007). Thus, the models were linearized around the minimum to evaluate the marginal confidence intervals and a covariance matrix for the parameters of each model (Englezos and Kalogerakis, 2001). These sets of parameter values were taken as initial values in a Markov chain Monte Carlo sampling of Eq. (7) using a Delayed Rejection Adaptive Monte Carlo (DRAM) algorithm (Bishop, 2006). Computations were performed with the MatLabs toolbox DRAM mcmcstat. A separate Markov chain was launched for each model and its convergence was verified each time by evaluating Geweke's criterion. The resulting Markov chains were used to evaluate the deviance information criterion (DIC) applied for model comparison (Ntzoufras, 2009). Upon repetition of computations, a change in the estimated DIC below 2% indicates the convergence of the Markov chains. DIC is suggested here as the statistic to assess the relative goodness of fit of the different models. Additionally, a linear relationship between the DIC (a global measure of model performance) and the smallest adjusted correlation coefficient r 2aj per experimental run was found (DuqueBernal et al., 2013). This correlation would not be expected if a single experimental run were more prone to error than the others; yet, this result is not sufficient proof of the data integrity. Therefore, for each model, an adjusted correlation coefficient was calculated with individual data of each experimental run and the smallest of the obtained values was taken as the model correlation coefficient, which might a more familiar goodness of fit statistic than DIC for some readers.

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4. Results and discussion 4.1. Catalyst characterization The measured cation exchange capacity of preconditioned resin Amberlite IR-120 of 4.7 70.3 meq/g (95% confidence interval) was in agreement with the value reported by the manufacturer (Table 1) as well as by Musante et al. (2000). Integral analysis of particle size distribution was evaluated in terms of mass and the number of particles for each fraction. Uniformity and curvature coefficients, mean diameter and fraction of fines are presented in Table 4. A complete distribution of particle sizes was approximated to a probability density distribution function using statistical methods (Fig. 1) as described elsewhere (Fieller et al., 1992). The mass distribution of particle sizes is mono-disperse with a mean value of 677 mm and presents a better fit to a normal distribution than to a log-normal one. It can be seen that the fraction of fines with a diameter lower than 300 mm has a large number of particles (415%) but its weight fraction is lower than 1%. Dry and wet resin densities are presented in Fig. 2, along with the corresponding uncertainties. The dry resin has a higher density (aprox. 1.43 g/mL) than the wet one as expected. The standard deviations of the experimental data increases in the following order: water4acetic acid4dry resin4ester4alcohol. So, the density measurements for the resin swelling with isoamyl alcohol and isoamyl acetate are more prone to error. However, these solvents present lower vapor pressures than those of water and acetic acid and thus a low evaporation rate is expected. Consequently, the deviations could be related to fluctuations of room temperature and, simultaneously, the high vapor pressure of heptane which explain the high standard deviation for the measured density of the dry resin. Fig. 3 presents the measured resin absorbance ratio for pure solvents together with the calculated values of RW using Eq. (1). The following affinity of the resin to the solvents, on mass basis,

Table 4 Uniformity and curvature coefficients. Mean diameter and fraction of fines from particle size distribution analysis of ion exchange resin Amberlite IR-120. Parameter

Uniformity coefficient Fraction of fines ( o 300 mm) Mean diameter (mm) Curvature coefficient

This work Distribution in number

Distribution in mass

Reported by manufacturer (Rohm and Haas)

2.4 15%

1.5 o 1%

≤1.8 2% max

515 1.0

677 1.3

620–830 –

Fig. 1. Resin particle size integral analysis by weight. Inserted legend shows estimated mean mass diameter and the density of probability for each correlation. Fit based on a modified maximum likelihood criterion (Fieller et al., 1992).

Fig. 2. Box diagrams for experimental dry and wet resin densities in different solvents. Numbers in brackets indicate repetitions for each solvent.

Fig. 3. Box diagrams for experimental and calculated resin absorbance ratio in different solvents. Numbers in brackets indicate repetitions for each solvent.

can be seen: water4acetic acid4isoamyl alcohol≈isoamyl acetate. The dispersion of the experimental data is similar to that of Fig. 2 because the experimental data of Fig. 2 and Eq. (1) were used to obtain Fig. 3. This affinity order is related to the molecular weight (and molecular size) of the solvents which are 18, 60, 88 and 130 kg/kmol, respectively. The higher affinity was measured for the smallest molecule, water. Experimental resin sorption equilibria for three binary nonreactive mixtures (acetic acid (1)/water, isoamyl alcohol (1)/ isoamyl acetate, acetic acid (1)/isoamyl acetate) are shown in Fig. 4. That figure presents the molar fraction of component (1) in the resin (resin free) as function of its liquid phase activity. Data for isoamyl alcohol/water are not shown due to liquid–liquid phase splitting. Comparison of the binary mixtures shows that, on molar basis, the adsorption of isoamyl alcohol is higher than the isoamyl acetate one and that of isoamyl acetate is higher than the acetic acid one, and finally that of acetic acid is slightly higher than water one. Consequently, the order of adsorption, based on binary measurements on molar basis, is isoamyl alcohol 4 isoamyl acetate 4 acetic acid≈water. As compared to resin absorbance ratio for pure components water has the highest affinity, on mass basis, but this is the case when its concentration is high and its liquid phase activity is close to one. However, for intermediate and low liquid phase activities, the isoamyl alcohol showed a higher affinity than the other solvents. Fig. 4 also shows that the adsorption of a component in a binary mixture is similar for all binary mixtures as its activity coefficient in the liquid phase is closer to one. This order of adsorption in terms of liquid phase activity coefficients will be used below to evaluate the kinetic models proposed for the esterification of isoamyl alcohol.

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Table 6 Maximum likelihood estimates and marginal confidence intervals for correlated parameters for heterogeneous kinetic models. computed with a 95% confidence level. ln kads,HAc or ln kads,ROH or ln kads,W or ln keqL or Model ln K0 (T0) Ea (mol/g h) (kJ/mol) ln krel,HAc ln krel,ROH ln krel,E ln keqs

Fig. 4. Experimental resin sorption equilibria distribution diagrams for three binary non-reactive mixtures. Molar fraction inside the resin versus activity of the same component in the liquid phase. ●: acetic acid (1)/water (2) mixture. ■: acetic acid (1)/isoamyl acetate (2) mixture. ○: isoamyl alcohol (1)/isoamyl acetate (2). Activity coefficient model NRTL. Tendency solid lines are included to guide the view. Includes a 451 dashed line for comparison.

Fig. 5. Acidity versus time plots for catalytic reaction test runs in Table 2.

MC1u

 0.366 70.089

54.4 7 3.1

–

–

–

3.254 70.061

MC2u

 0.102 70.265

53.6 7 3.0

 4.389 7 2.116

 1.463 7 1.523

 3.905 7 2.369

3.249 70.056

MC3u

0.162 70.156

49.6 7 2.9

2.952 7 0.393

2.178 7 0.411

1.948 7 0.619

0.167 70.264

MC4u

0.163 70.153

49.7 7 3.0

4.161 7 0.401

3.767 7 0.429

3.928 7 0.629

0.165 70.293

MC1n

 0.474 70.120

52.5 7 4.2

–

–

–

2.828 70.096

MC2n

0.185 70.450

51.6 7 3.8

 3.955 7 2.465

 0.314 7 0.704

 2.604 7 3.018

2.825 70.097

MC3n

0.209 70.192

54.5 7 3.2

2.194 7 0.522

1.776 7 0.637

1.421 7 0.847

0.399 70.475

MC4n

0.206 70.187

54.5 7 3.2

3.415 7 0.511

3.383 7 0.629

3.418 7 0.822

0.375 70.454

MC1x

 0.349 70.088

53.0 7 3.1

–

–

–

1.618 70.059

MC2x

0.034 70.234

52.2 7 2.7

 4.319 7 2.166

 0.813 7 0.692

 3.577 7 3.004

1.606 70.054

MC3x

0.117 70.113

51.6 7 2.6

1.422 7 0.286

0.702 7 0.314

0.571 7 0.426

0.165 70.263

MC4x

0.116 70.118

51.6 7 2.7

2.621 7 0.302

2.286 7 0.328

2.535 7 0.463

0.158 70.258

Table 5 Goodness of fit statistics for the heterogeneous reaction rate models. Model Type

Number of SMEa LML Run with Lowest raj2 DIC parameters [Eq.(9)] lowest raj2

MC1u MC2u MC3u MC4u MC1n MC2n MC3n MC4n MC1x MC2x MC3x MC4x

3 6 6 6 3 6 6 6 3 6 6 6

a

PH LHHW Proposed Pöpken PH LHHW Proposed Pöpken PH LHHW Proposed Pöpken

1.92 1.49 1.74 1.74 2.37 1.47 1.53 1.53 1.84 1.14 1.30 1.28

0.3339 0.3173 0.3169 0.3168 0.5301 0.4344 0.3269 0.3267 0.2939 0.2399 0.2270 0.2272

RC3 RC3 RC3 RC3 RC3 RC3 RC3 RC3 RC3 RC3 RC3 RC3

0.8599 0.8433 0.8613 0.8583 0.7588 0.8325 0.8228 0.8221 0.8621 0.9084 0.8826 0.8835

0.360 0.328 0.359 0.359 0.572 0.428 0.375 0.374 0.317 0.263 0.260 0.262

Square mean error.

4.2. Goodness-of-fit statistics for kinetic models correlation Acidity versus time plots, for test runs in Table 2, are presented in Fig. 5. Using the proposed algorithm, independent regressions

for the 12 considered models and their corresponding goodnessof-fit statistics have been calculated and are shown in Table 5 (square mean error, log-likelihood function Eq.(9), adjusted correlation coefficient r 2aj and deviance information criterion DIC). The correlated parameters for each model are presented in Table 6. In order to illustrate how models correlate with experimental data, predicted and experimental parity plots for acidity are compared in Fig. 6. 4.3. Analysis and model selection Parity plots (Fig. 6) show that no one of the correlated models has a significant deviation from experimental data. However, all models have a low correlation coefficient for the test run RC3, which is the run with the lowest value of r 2aj (Table 5). This low correlation of predicted reaction rate can be attributed to the lack of more experimental data at conditions similar to that of run RC3: low temperature and feed with an excess of acetic acid. According to the values of goodness-of-fit statistics (Table 5), the proposed kinetic models that are function of the molar fractions (ideal liquid phase) seems to be more likely that those in terms of

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Fig. 6. Predicted and experimental parity plot for acidity using correlated kinetic models.

activities. A similar conclusion was obtained for the homogeneous rate law (Duque-Bernal et al., 2013). Among the four models with molar fractions, no one seems to be better than the others (Fig. 6). The MC1x pseudo-homogeneous model (PH), with the lowest DIC value among PH models, is unlikely because it does not take into account adsorption of any substance on the resin surface. The resin absorption of the liquid mixture occurs in the bulk polymer phase, but as more mass of a particular substance is absorbed inside the resin, more frequently will be the collisions between these molecules and the catalytic sites and consequently the substance adsorption will increase. Therefore, it can be speculated that measured absorbance ratios should correspond to adsorption affinities. It must be pointed out, as discussed previously in Section 2.1, that both absorption and adsorption phenomena occurs simultaneously in the resin and no attempt was made here to differentiate the contribution of each one in the sorption process. For models MC2x, MC3x and MC4x (all with six adjustable parameters) statistical criteria show similar results and discrimination is difficult without additional experiments. The LHHW model (MC2x) presents a low square mean error (SME) and it skips isoamyl acetate adsorption term (which does not agree with resin binary adsorption measurements). Model MC2x shows a higher adsorption constant for alcohol than for water (Table 6), which agrees to the experimental adsorption measurements for binary mixtures (Fig. 4). If the UNIFAC-Dortmund (Gmehling et al., 2002) and NRTL (Duque-Bernal et al., 2013; Osorio-Viana et al., 2013b) models are used to evaluate the equilibrium constant of the esterification at experimental conditions, a value of approximately 1.0 is calculated using a minimization of the Gibbs free energy. This is close to the equilibrium constant adjusted from reaction experiments (Table 6) for the kinetic models based on activities: MC3u, MC4u, MC3n, MC4n. These models correspond to those that take into account the adsorption of all species in the esterification reaction. These models also predict with enough accuracy the experimental reaction rate measurements. However, models MC3n and MC4n are attractive reaction rate expressions for the esterification of acetic acid with isoamyl alcohol because the use of NRTL model, with parameter values recently reported for this mixture, has superior capabilities for the vapor–liquid–liquid equilibria prediction (Osorio-Viana et al., 2013b). The goodness of fit statistics for these two models, presented in Table 5, is quite similar and cannot be used to discriminate between them. Model MC3n predicts the same order of adsorption than the one found from binary experiments (Fig. 4), except for acetic acid. So, it seems that this model is better than the other ones because it implies

Fig. 7. Evaluation of the effect of resin exchange capacity. Extent of reaction and reaction rate profiles over time for experimental reaction test runs at different resin exchange capacity (RC2: 4.7 meq/g and RC9: 2.7 meq/g).

an equilibrium constant value which agrees with that calculated from minimization of the Gibbs free energy. Additionally, it reproduces reaction rate experiments with a low square mean error, involves an activity model that predicts the liquid–liquid–vapor equilibrium of the mixture and contains adsorption constants that agree with binary adsorption experiments, except for acetic acid. 4.4. Effect of resin exchange capacity In the resin reusability experiment, a fresh and preconditioned resin (exchange capacity 3.9 meq/g) was washed with water and dried under vacuum pressure for 8 h at 80 1C. Its exchange capacity was measured (3.6 meq/g) and it was used for a replication experiment. After the second experiment, the resin was washed and dried and its exchange capacity measured once again (3.4 meq/g). Between the two reaction tests, the resin suffers color change from amber (fresh) to the brown-black one (used) and a ca. 6.5% reduction in its exchange capacity. However, no statistically significant differences were observed in the experimental data of the two reactions test due to the almost constant exchange capacity of the resin. In order to evaluate the influence of resin exchange capacity on reaction rate, reaction test RC9 reproduces the operating conditions of reaction test RC2 (Table 2), this time using a resin with a reduced exchange capacity of 2.7 meq/g (obtained by treating a

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preconditioned resin with NaCl aqueous solution). Fig. 7 shows the extent of the reaction profiles measured over time for the two test runs. The experiment RC9 shows a lower reaction rate than that in RC2. Fig. 7 also shows the reaction rate profiles over time by using smoothing cubic spline curve to approximate the extent of the reaction profile and calculate its derivative. Initial reaction rate drops from 4.4 mol/(g h) (RC2) to 0.8 mol/(g h) (RC9) corresponding to ca. 80% reduction in initial reaction rate for a reduction of ca. 40% in resin exchange capacity at 90 1C and 2:1 acid/alcohol feed molar ratio. This result shows that the rate of reaction depends on the ion exchange capacity of the resin, although this dependence is not necessarily linear (Beránek and Kraus, 1978).

5. Conclusions Applying Bayesian statistics, twelve kinetic models for the heterogeneous esterification of acetic acid with isoamyl alcohol over Amberlite IR-120 have been compared and discriminated to find the most likely form to represent the experimental data. Among the considered models, those with ideal liquid phase have the lowest square mean errors (SME). Experimental sorption on Amberlite IR-120 shows, with binary mixtures and based on molar fractions and liquid phase activities, that the resin has the following affinity to the mixture components: isoamyl alcohol 4isoamyl acetate4acetic acid≈water. Among the adjusted models for the esterification reaction catalyzed by Amberlite IR-120, from a phenomenological perspective, model MC3n based on activities (with NRTL model from Osorio-Viana et al., 2013b), is the most congruent with experimental observations. Model MC3n has values of its adsorption equilibrium constants clearly related with the resin sorption affinities (except for acetic acid), its equilibrium constant has the same order of magnitude as the calculated by thermodynamics and predicts the kinetic behavior with a low and acceptable error. Nevertheless, from an engineering perspective, both model MC3n and model MC2x (LHHW type, based on molar fractions) makes similar reaction rate predictions and are both equally probable in statistical terms. Model MC2x is most suitable for its ease of implementation in a process simulation software (like ASPEN Pluss).

Nomenclature H W RW RH RS IC a ρ w r k ki x K eq T T0 Ea R t ! y obs ! y calc

percentage volume swelling, % absorbance or percentage swelling on a mass basis, % absorbance ratio, – swelling ratio, – ratio of initial liquid solvent mass/resin mass, – interchange capacity, meq/g activity, – density, g/mL mass fraction, – reaction rate mol/(gcat h) Reaction rate constant mol/(gcat h) adsorption equilibrium constant for i, – liquid molar fraction, – equilibrium constant, – temperature, K reference temperature, K activation energy, kJ/mol universal gas constant kJ/(mol K) time, h observed values of acidity, – calculated values of acidity, –

! θ M p SData SPrior srel N LML r 2aj

vector of adjustable model parameters, – kinetic model, – probability function, – sum of squares on the data, – sum of squares on the prior – standard relative deviation, – number of experimental runs, – log-likelihood function, – correlation coefficient, –

Superscripts S L o

gel phase (polymer) liquid phase reference condition

Subscripts HAc ROH E W A i Cat ads rel j u o liq dr H het

acetic acid isoamyl alcohol isoamyl acetate water component component catalyst adsorption Relative to water model type experimental run reference condition liquid dry resin wet resin heterogeneous

Abbreviations PH LHHW ER DIC DRAM SME

pseudo-homogeneous model Langmuir–Hinshelwood–Hougen–Watson Eley–Rideal deviance information criterion delayed rejection adaptive Monte Carlo square mean error

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