n-Butanol Esterification of Butyric Acid with

Article pubs.acs.org/IECR

Kinetics of Mixed Ethanol/n‑Butanol Esterification of Butyric Acid with Amberlyst 70 and p‑Toluene Sulfonic Acid Arati Santhanakrishnan, Abigail Shannon, Lars Peereboom, Carl T. Lira, and Dennis J. Miller* Department of Chemical Engineering and Materials Science, Michigan State University, 2527 Engineering Building, East Lansing, Michigan 48824-1226, United States ABSTRACT: Esterification of butyric acid with ethanol, n-butanol, and ethanol/n-butanol mixtures was studied using Amberlyst 70 cation-exchange resin and homogeneous p-toluene sulfonic acid as catalysts. The kinetics of individual alcohol esterification were first examined in batch reactions at different temperatures and catalyst loadings, and then esterification in ethanol/n-butanol mixtures of varying concentration ratios was characterized. Both nonideal solution and ideal solution kinetic models were developed. These models accurately predict the esterification of butyric acid by the individual alcohols; a simple additive combination of the individual alcohol esterification kinetics properly describes mixed alcohol esterification, indicating that the alcohols do not compete with each other or inhibit esterification when present together. When solution density is included in the kinetic rate expression to account for the actual concentration of −OH groups in ethanol and n-butanol, butyric acid esterification kinetics with the two alcohols are described by a common rate constant. This rate constant also predicts butyric acid esterification kinetics with other alcohol combinations, suggesting a generalized esterification rate constant for simple alcohol esterification of butyric acid over Amberlyst 70 catalyst. These results provide significant predictive capabilities for simulating processes such as reactive distillation processes for mixed alcohol esterification.

1. INTRODUCTION The growing need to reduce dependence on fossil sources for fuels and chemicals has led to exploration of pathways for their manufacture from renewable sources. Esters of higher alcohols (alcohols with more than two carbons) are one such industrially important class of compounds, and economically viable processes for making them need to be designed. Blends of esters are being considered as attractive solvents or additives to biofuels because of their high energy density and favorable fuel properties. The most common route for producing esters is direct esterification of carboxylic acids with alcohols1 using either homogeneous acid catalysts such as sulfuric acid or ptoluene sulfonic acid (p-TSA) or solid heterogeneous acid catalysts such as cationic exchange resins. Mixed alcohol streams from biomass can be obtained in several ways: from condensation of lower alcohols to higher alcohols via the Guerbet reaction,2−4 via Fischer−Tropsch synthesis of alcohols from synthesis gas,5−8 or from fusel alcohols9 produced in ethanol fermentation. Esterification for biofuel or solvent applications is an attractive use of these mixed alcohol streams, as it would lead to value-added products without the need for separation into individual components. Simultaneous esterification with multiple alcohols is described in the patent literature.10−13 Since esterification reactions are thermodynamically limited, reactive distillation is a viable option for mixed alcohol processing.14,15 In simulations of reactive distillation, esterification of a mixture of amyl alcohol and n-butanol with acetic acid has been examined to compare separation-first and reaction-first schemes.16 Reaction-first schemes were determined to be more economical. Design of such reactive distillation schemes for mixed alcohols requires a good understanding of the kinetics of the reaction system, as it is generally not known whether the presence of one alcohol © 2012 American Chemical Society

accelerates or inhibits the rate of reaction of another, or if formation of mixed esters leads to transesterification that could overcomplicate the recovery process. Recent advances in producing butyric acid via fermentation of biomass carbohydrates has sparked interest in using butyric acid as a building block via esterification and other reactions.17 Apart from their potential as biofuel components, ethyl butyrate and n-butyl butyrate serve as food flavoring agents and green solvents.18 The kinetics of n-butyl butyrate formation using Dowex19 as an esterification catalyst has been previously studied and modeled using quasi-homogeneous, Eley−Rideal, and Langmuir−Hinshelwood rate models. The kinetics of ethyl butyrate formation have not been previously reported. In this study, the kinetic behavior of butyric acid esterification with mixed ethanol and n-butanol (Scheme 1) is investigated using homogeneous (p-TSA) and heterogeneous (Amberlyst 70 ion-exchange resin) catalysts. Kinetics of individual ethanol and n-butanol esterification reactions are first presented, and the results are then used to predict kinetics of butyric acid esterification with ethanol/n-butanol mixtures of varying compositions. The results provide the capability to predict butyric acid esterification reaction kinetics with any simple alcohol, a useful result for biorefinery process design.

2. MATERIALS AND METHODS 2.1. Materials. Reagent-grade ethanol (200 Proof, Decon Laboratories, Inc., King of Prussia, PA), n-butanol (99.9%, Sigma Aldrich Corp., St. Louis, Missouri), n-butyl butyrate Received: Revised: Accepted: Published: 1845

August 23, 2012 November 15, 2012 December 28, 2012 December 28, 2012 dx.doi.org/10.1021/ie302267s | Ind. Eng. Chem. Res. 2013, 52, 1845−1853

Industrial & Engineering Chemistry Research

Article

Scheme 1. Esterification of Butyric Acid with Ethanol and n-Butanol

Table 1. Summary of Experiments and Conditions molar feed ratios run

temp. (°C)

catalyst

ethanol:acid

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

60 80 100 120 60 80 100 120 60 60 60 80 80 80 80 80 80 60 80 100 120 60 80 100 120 60 60 60 80 80 80

A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 A-70 p-TSA p-TSA p-TSA p-TSA p-TSA p-TSA p-TSA p-TSA p-TSA p-TSA p-TSA p-TSA p-TSA p-TSA

4.3 2.8 8.7 6.6

0.5 2.6 0.9 1.5 4.5 2.0 0.8 1.9 0.6 2.9 2.8 3.7 3.7

0.4 3.6 5.0 0.5 1.9 3.7

n-butanol:acid

3.7 4.4 4.5 3.3 4.7 2.6 4.2 1.7 3.9 1.9 3.8 2.2 3.0

2.0 3.0 2.8 3.7 1.8 3.3 1.0 2.7 1.9 0.9

(>98%, Sigma Aldrich Corp., St. Louis, MO), ethyl butyrate (>99%, Sigma Aldrich Corp., St. Louis, MO), water (HPLC solvent, JT Baker Reagent Chemicals. Phillipsburg, NJ), ptoluene sulfonic acid monohydrate (Spectrum Quality Products, Inc., Gardena, CA), butyric acid (>99%, natural, Sigma Aldrich Corp., St. Louis, MO), acetonitrile (HPLC grade, Emanuel Merck Damstadt Chemicals, Philadelphia, PA), methanol (Sigma Aldrich Corp., St. Louis, MO), and ethyl octanoate (Sigma Aldrich Corp., St. Louis, MO) were used without further purification. Gas chromatographic (GC) analysis of the aforementioned chemicals showed no significant presence of impurities except trace amounts of water. Hydranal-

solution density (ρ) (kmol m−3)

catalyst loading (kg cat./kg soln)

14.9 15.0 15.0 14.9 10.9 10.9 10.9 10.9 14.9 12.8 11.5 12.6 12.9 12.6 11.5 12.6 11.5 14.8 14.9 15.0 15.0 10.9 10.9 10.9 10.9 11.4 13.0 14.4 11.4 12.6 14.0

0.0100 0.0101 0.0075 0.0099 0.0096 0.0101 0.0101 0.0115 0.0109 0.0085 0.0099 0.005 0.0105 0.0077 0.0093 0.0196 0.0097 0.0012 0.0013 0.0012 0.0013 0.0013 0.0013 0.0014 0.0013 0.0012 0.0013 0.0013 0.0013 0.0014 0.0014

coulomat E solution (Riedel-de Haën, Seelze, Germany) was used in Karl Fischer titrations. Helium (99.995%, AirGas, USA) was used as carrier gas for GC. The properties of the heterogeneous cation-exchange resin catalyst Amberlyst 70 (Dow Chemical Co., Midland, MI) are reported in the literature.20 2.2. Heterogeneous Catalyst Conditioning. As-received Amberlyst 70 (A-70) was sieved in a series of US-standard sieves (Dual Manufacturing Co., Chicago, IL), and the −45 + 60 mesh (0.25−0.35 mm diameter) fraction was used in kinetic experiments. The resin was washed with methanol multiple times until the supernatant liquid was colorless and then filtered 1846

dx.doi.org/10.1021/ie302267s | Ind. Eng. Chem. Res. 2013, 52, 1845−1853


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study. This is because low loadings of catalyst (∼0.1 wt % pTSA and 1 wt % A-70), low ratios of alcohol to acid (∼3:1− 6:1), and relatively low temperatures were used in the experiments. 3.1. Mass Transfer Considerations. Accurate characterization of reaction kinetics requires that experiments be conducted in the kinetic regime, i.e., at conditions where external and internal mass transfer resistances do not affect the reaction rate. Preliminary experiments at varying stirring speeds showed that conversion rates were unaffected above 600 rpm, implying that the external mass transfer resistances are negligible at a stirring speed of 800 rpm. To estimate the influence of intraparticular mass transfer resistance in the heterogeneous catalyst reaction, the Weisz−Prater criterion was used.21 The observable modulus was first calculated by eq 1

to remove excess methanol. The resin was then dried in an oven at 373 K for 2 days. The dried resin was stored in a sealed container in a desiccator and removed in required amounts for reactions. Fresh catalyst was used for each experiment. To find the ion-exchange capacity of the catalyst, a known quantity of dry A-70 was submerged in ethanol for 4−5 h and then titrated with NaOH. The average ion-exchange capacity was found to be 2.35 ± 0.1 equiv of H+/kg, in reasonable agreement with the value reported by the manufacturer.20 2.3. Kinetic Experiments. Isothermal kinetic experiments were carried out in 75 mL batch reactors in a Parr 5000 Multireactor system (Parr Instrument Co., Moline, IL). The reactor system is equipped with temperature and stirring speed control and with a dip tube on each reactor to collect liquid samples during reaction. The end of the dip tube is fitted with a 2 μm stainless steel filter to avoid withdrawing solid catalyst along with liquid sample. To begin an experiment, ethanol and n-butanol were weighed out alone or in predetermined molar ratios and added to the reactor with a known amount of catalyst (A-70 for heterogeneous catalysis and p-toluene sulfonic acid for homogeneous catalysis). The reactor was sealed and heated until it stabilized at the desired reaction temperature. Stirring was set to 800 rpm unless otherwise specified. Once the desired temperature was reached, a specified amount of butyric acid was added to the reactor through the sample port in a single shot; the moment of addition was taken as time zero of the reaction. Total reactant weight came up to approximately 0.040 kg per reaction. Samples of 0.5−1 mL were withdrawn at specified time intervals during the kinetic regime (0−6 h) using 3 mL Luer-Lok tip syringes (Becton Dickson and Co., Franklin Lakes, NJ) and stored in hermetically sealed vials in a standard refrigerator at 277 K. Samples to characterize reaction equilibrium were taken 24−48 h after the start of reaction. 2.4. Analysis. The initial water concentration in the reactants was determined by Karl Fischer titration in an Aquacounter coulometric titrator AQ-2100 (JM Science Inc., Grand Island, NY) and taken into account in calculations. Analysis of reaction samples was carried out in a Varian 450 gas chromatograph outfitted with a thermal conductivity detector (Varian Medical Systems Inc., Palo Alto, CA). Reaction samples were diluted 10-fold in acetonitrile containing 11.11 wt % ethyl octanoate as an internal standard. Separation was done on a 0.53 mm i.d, Aquawax-DA 30 m capillary column with 1.0 μm film thickness. Helium carrier gas flow rate was set to 10 mL min−1. The following temperature program was used: initial column temperature 313 K for 2 min, ramp at 10 K min−1 to 423 K, ramp at 30 K min−1 to 503 K, hold 2 min. Detector temperature was held at 513 K. Standards of known composition in the range of interest were prepared and run in the chromatograph before and after reaction samples to calibrate the response factor of each component of the reaction.

ϕw =

* )ρ ⎛ d p ⎞ (robs CAT ⎜ ⎟ Deff C BA ⎝ 6 ⎠

2

(1)

where r*obs is the observed rate of reaction per weight of catalyst, ρCAT is the density of catalyst (assumed to be 1000 kg m−3), CBA is the liquid-phase concentration of butyric acid, dp is the swelled diameter of catalyst at reaction conditions (eq 2) d p = d p,dry ×

Vp,swollen 3

Vp,dry

(2)

where dp is 0.30 mm and Vp,swollen/Vp,dry is determined from a simple measurement to be 2.0 for both alcohols. The effective diffusivity Deff of butyric acid in alcohol is estimated in eq 3, where pore tortuosity τ is assumed to be equal to the inverse of particle porosity ε, and DBA is bulk diffusivity of butyric acid in alcohol estimated from the Wilke−Chang equation22 ⎛ε⎞ Deff = DBA ⎜ ⎟ = DBA ε 2 ⎝τ⎠

(3)

The Thiele modulus (φ) and effectiveness factor (η) for butyric acid esterification are calculated from the observable modulus ϕw = ηφ2 assuming the reaction is pseudo-first order in butyric acid (i.e., excess alcohol) and thus η = ((tanh(φ))/(φ)). Values of η were evaluated for butyric acid in each of the alcohols (Table 2) and found to be ∼0.93 and ∼0.96 for ethanol and nbutanol esterification, respectively. These values of η indicate that intraparticular resistances can be neglected. 3.2. Reaction Equilibrium Constants. The equilibrium constant for a given experiment was estimated by determining the unchanging composition of the reaction solution after 24− Table 2. Intraparticle Effectiveness Factors for A-70Catalyzed Butyric Acid Esterification molar feed ratio

3. RESULTS A list of all experiments conducted along with their conditions (temperature, initial reactant molar ratio, weight fraction of catalyst) is given in Table 1. Control experiments to investigate autocatalysis of the reaction showed negligible rates over the temperature range studied. Although etherification side reactions have been observed in other studies involving the esterification of n-butanol7,13 and ethanol8 at temperatures above 386 K, no ethers (di-n-butyl ether, diethyl ether, or ethyl n-butyl ether) were observed in the reaction samples in this 1847

run

temp. (°C)

ethanol:acid

1 2 3 4 5 6 7 8

60 80 100 120 60 80 100 120

4.3 2.8 8.7 6.6

n-butanol:acid

η

3.7 4.4 4.5 3.3

0.99 0.99 0.99 0.98 0.99 0.98 0.98 0.98



Article

Figure 1. van’t Hoff plots for equilibrium constants of ethanol and n-butanol esterification of butyric acid: (⧫) ethanol ideal solution; (●) ethanol activity based; (■) n-butanol ideal solution; (▲) n-butanol activity based. Error bars for each temperature represent one standard deviation.

48 h of reaction. The activity-based equilibrium constant Ka,m for reaction m is given in eq 4.

is the rate of reaction m per unit volume, and xi is the mole fraction of component i in the liquid mixture. The parameter θi,m is the ratio of stoichiometric coefficients of component i with respect to the reference component in reaction m. For this esterification system, eq 5 can be expressed in terms of total molar density of the liquid phase (ρ = NT/V) because the total number of moles is conserved and the reaction volume is constant during reaction.

NC

K a, m = Kx , mK γ , m =

∏ (xiγi)νEQ i ,m

i=1

(4)

Here xi, γi, and vi,m represent the equilibrium mole fraction, activity coefficient at equilibrium, and stoichiometric coefficient, respectively, of component i in the reaction mixture. The molefraction-based equilibrium constants (Kx,m) were calculated directly from the equilibrium composition of the reaction mixture. The ratio of activity coefficients (Kγ,m) accounts for deviation from ideal behavior; values of activity coefficients were estimated using UNIFAC (universal functional activity coefficient).23 The experimental values of Kx and Ka for butyric acid esterification with ethanol and n-butanol with A-70 ionexchange resin or p-TSA as catalyst are presented together in Figure 1. Consistent values of the equilibrium constants were observed with both catalysts. Scatter in the values of the equilibrium constant is a result of uncertainty arising from the necessity measuring the concentration of every species (including water) participating in the reaction at the equilibrium state. The enthalpy of reaction (ΔHr), obtained from the slope of the trend line in Figure 1, is +18 kJ for ethanol and +12 kJ for n-butanol esterification of butyric acid, indicating that the reactions are mildly endothermic. Although previous studies have reported temperature-independent values of equilibrium constants in kinetic models,19 here the data in Figure 1 were used to calculate temperature-dependent equilibrium constants in the kinetic model described below. 3.3. Kinetic Model Description. In a batch reactor, the change in number of moles Ni of component i participating in M reactions can be expressed as

M

dxi 1 = (∑ θi , mrm) dt ρ 1

The rate of formation of ester in reaction m, rm, is based on the law of mass action (e.g., a “power law” model) with the driving force for the reversible reaction described in terms of species activity (ai = xiγi), reflecting the role of chemical potential in describing reaction equilibrium. For esterification in neat mixtures of reactants (e.g., no solvent) that constitute a nonideal liquid phase, the activity of each species is multiplied by solution density to account for the absolute concentration of each species (−OH and −COOH) in the reaction mixture. This inclusion of solution density is necessary to compare reaction rates for different alcohol−acid combinations because the molar concentration of −OH groups decreases as alcohol molecular weight increases (Table 1). This approach has been previously defined and used for liquid-phase reactions.24,25 The rate of formation (rm) of butyrate ester (BE) in reaction m can be expressed in terms of the activity of butyric acid (BA), alcohol (OH), butyrate ester (BE), and water (W), wCAT, the catalyst loading in the reaction mixture, ρ, the total molar density of the reacting fluid, k0,m, the pre-exponential factor, and Ea,m, the activation energy of the rate constant for reaction m. ⎛ Ea, m ⎞⎡ rm = wCATρ2 k 0, m exp⎜ − ⎟ ⎢x γ x γ ⎝ RT ⎠⎢⎣ BA BA OH OH

M

dNi dx = NT i = (∑ θi , mrm)V dt dt 1

(6)

(5)

−

where NT is the total number of moles in the reactor, M is the number of reactions in the system, V is the reaction volume, rm 1848

x BEγBEx W γW ⎤ ⎥ ⎥⎦ K a, m

(7)



Article

Table 3. Optimized Kinetic Parameters with 95% Confidence Limits and Equilibrium Constants from Experimental Data (T in Kelvin) n-butanol

ethanol parameter

ideal

activity

ideal

activity

Ka Amberlyst 70 ko ((kg soln·m3)/ (kg cat.·s·kmol)) Ea (kJ/kmol) p-toluenesulfonic acid ko ((kg soln·m3)/(kg cat.·s·kmol)) Ea (kJ/kmol)

exp(8.18−2654/T)

exp(8.85−2207/T)

exp(7.50−2339/T)

exp(6.88−1365/T)

4.1 ± 0.5 × 103 45 900 ± 3400

6.2 ± 1.6 × 103 47 300 ± 6100

6.8 ± 1.4 × 103 46 800 ± 290

11.9 ± 0.5 × 103 48 300 ± 155

22.9 ± 1.4 × 103 44 900 ± 182

26.2 ± 1.7 × 103 45 200 ± 192

21.3 ± 2.6 × 103 44 900 ± 375

71.8 ± 6.8 × 103 48 300 ± 300

By inserting the appropriate rate expression (eq 7), eq 6 can be written for every species in the reaction mixture to give a set of ordinary differential equations describing the esterification system. For the individual ethanol−butyric acid system and the n-butanol−butyric acid system, these equations were integrated numerically and reaction parameters determined using the functions nlinfit and ode23 from the optimization toolbox in Matlab 7.12.0. Both the activity-based model described above and an ideal solution model with all activity coefficients γi set to unity were regressed to give rate parameters for the individual reactions. Optimization was done by minimizing Fmin, where Fmin2 is defined (eq 8) as the sum of squared differences between calculated (xi‑calcd) and experimental (xi‑exp) species mole fractions for all species in all esterification reactions conducted. 2 Fmin =

1 n

NC

∑ ∑ (xi− exp − xi− calcd)2 samples i = 1

(8)

In eq 8, n is the number of experimental samples withdrawn in all experiments regressed and Nc is the number of reacting components in those experiments. Optimized kinetic parameters with 95% confidence limits are reported in Table 3 for ethanol−butyric acid and n-butanol− butyric acid esterification with A-70 and p-TSA catalysts. The activation energies in Table 3 are in the expected range of values (45 ± 10 kJ mol−1) for esterification of small aliphatic carboxylic acids with aliphatic alcohols. The temperaturedependent expression for the thermodynamic equilibrium constant Ka is reported for each reaction in Table 3. A comparison of the experimental and predicted mole fraction profiles for individual alcohol esterification is given in Figure 2 for A-70 heterogeneous catalyst and in Figure 3 for pTSA homogeneous catalyst. It can be seen that the kinetic model fits the individual alcohol esterification reactions reasonably well. The kinetic parameters reported in Table 3 for individual ethanol−butyric acid and n-butanol−butyric acid esterification reactions were combined, without adjustment or additional regression, to model the mixed ethanol/n-butanol esterification of butyric acid. Comparison of both ideal solution and nonideal activity-based model predictions of mixed alcohol esterification with experimental data for several experiments is shown in Figure 4 for A-70 catalyst and Figure 5 for p-TSA. These plots clearly show that the simple combined model fits the experimental data well. The average deviation of the kinetic model prediction from experimental data at a given data point is described in eq 9.

Figure 2. Experimental and predicted concentration profiles of individual ethanol and n-butanol esterification in the presence of 1 wt % A-70: (a) run 2 (ethanol, T = 80 °C); (b) run 5 (n-butanol, T = 60 °C). () Ideal solution model prediction; (---) activity-based model predictions; (⧫) butyric acid; (■) ethanol; (▲) ethyl butyrate; (×) water; (○) n-butanol; (●) n-butyl butyrate.

fABS =

1 Ncn

NC

∑ ∑ |xi− exp − xi− calcd| samples i = 1

(9)

For ethanol−butyric acid esterification, the average deviation per data point over all experiments with A-70 was 0.012 and 1849



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Figure 3. Experimental and predicted concentration profiles of individual ethanol and n-butanol esterification in the presence of 0.1 wt % pTSA: (a) run 20 (ethanol, T = 100 °C); (b) run 23 (n-butanol, T = 80 °C). () Ideal solution model predictions; (---) activity-based model predictions; (⧫) butyric acid; (■) ethanol; (▲) ethyl butyrate; (×) water; (○) n-butanol; (●) n-butyl butyrate.

with p-TSA was 0.015. For n-butanol−butyric acid esterification, the average deviation per data point over all experiments with A-70 was 0.016 and p-TSA was 0.020. These values indicate that the experimental data are indeed reasonably represented by the kinetic models. For the mixed alcohol esterification, the average deviation of the predicted values from experimental data was 0.011 for A-70 and 0.013 for p-TSA. The similarity of these deviations with those from the fitted individual alcohol experiments is verification that the combined model is a good representation of mixed alcohol esterification. These deviations thus represent the scatter in the experimental data collection and analysis procedure, the largest contributor to which was measurement of water concentration using Karl Fischer analysis. The uncertainty in the rate constants at the 95% confidence level (Table 3) are quite reasonable, given the relatively small number of data points (ranging from 32 to 60 depending on the data set) used in each regression and the relatively low

Figure 4. Experimental and predicted concentration profiles of mixed alcohol esterification in the presence of 1 wt % A-70: (a) run 13 (ethanol:n-butanol = 1.15:1, T = 80 °C); (b) run 11 (ethanol:nbutanol = 0.21:1, T = 60 °C); (c) run 9 (ethanol:n-butanol = 1:1, T = 60 °C). () Ideal solution model predictions; (---) activity-based model predictions; (⧫) butyric acid; (■) ethanol; (▲) ethyl butyrate; (×) water; (○) n-butanol; (●) n-butyl butyrate. 1850



Article

sensitivity of the objective function to values of the kinetic parameters. This low sensitivity arises from the well-known “compensation effect”, wherein different combinations of preexponential factors and activation energies can give nearly the same values of rate constants over a narrow range of temperatures. The values of actual rate constants at a given temperature, however, are unique in their fit and thus useful for design or comparison between systems. The rate of esterification with homogeneous p-TSA catalyst is substantially higher than with heterogeneous A-70 resin. Using catalyst loadings, the A-70 acid site density of 2.35 equiv of H+/kg, and initial species concentrations, the initial turn over number (TON, kmol BA/kmol H+/h) for ethanol on p-TSA is 70.8 and on A-70 is 16.8. For n-butanol, the initial TON is 40.7 on p-TSA and 11.3 on A-70. The ratio of TON for the two catalysts is approximately four for both alcohols. We attribute the lower TON in A-70 not to mass transport effects (see Table 2) but most likely to steric effects associated with limited access of acid and alcohol to an anchored acid site in the porous solid catalyst versus the unhindered access acid and alcohol have to free acid in solution. The similarity in activation energies over the two catalysts supports this postulate and suggests that the reaction mechanism is the same on homogeneous p-TSA and heterogeneous A-70. The ability of individual alcohol kinetic models to fit mixed alcohol esterification over a wide range of alcohol molar ratios is strong evidence that the alcohols are not competing or inhibiting each other during esterification. It is consistent with the accepted mechanism of acid-catalyzed esterification in which the carboxylic acid is protonated by the acid site, followed by the slow, rate-limiting attack of nucleophilic alcohol on the electron-deficient carbonyl carbon. There is evidently a high enough concentration of protonated butyric acid in the present case to provide ample opportunity for either ethanol or n-butanol to attack without interference. The results described here are in accordance with a similar study examining mixed acid esterification, which reported that the additive combination of both esterification reactions also predicted the kinetics of the mixed acid system well.26 3.4. Generalized Rate Constant for Butyric Acid Esterification. The absolute rate of butyric acid esterification (kmol/m3/s) in ethanol is higher than in n-butanol for both catalysts. This is expected because the absolute concentration (kmol/m3) of ethanol in solution is higher than n-butanol, and thus, the hydroxyl group concentration is higher.27 However, in the rate expression developed here for each catalyst, the rate constants for ethanol and n-butanol esterification at a given temperature, determined from the pre-exponential factors and activation energies for each reaction in Table 3, have the same values within experimental uncertainty. This result is true for both heterogeneous A-70 and homogeneous p-TSA catalysts. The activity kinetic model with solution density included (eq 7) thus unifies esterification of butyric acid with ethanol and nbutanol. The generalization of esterification rate was extended by applying the rate expression (eq 7) to the initial rates of a set of C2−C8 alcohol esterification reactions with butyric acid conducted previously in our laboratory27 over A-70 catalyst. The resulting rate constant at 60 °C for each of the alcohols examined is given in Table 4. It can be clearly seen that the values of the rate constant are strikingly similar for all alcohols examined. This results strongly supports the concept of a

Figure 5. Experimental and predicted concentration profiles of mixed alcohol esterification in the presence of 0.1 wt % p-TSA: (a) run 31 (ethanol:n-butanol = 4.1:1, T = 80 °C); (b) run 29 (ethanol:n-butanol = 0.18:1, T = 80 °C); (c) run 30 (ethanol:n-butanol = 1:1, T = 80 °C). () Ideal solution model predictions; (---) activity-based model predictions; (⧫) butyric acid; (■) ethanol; (▲) ethyl butyrate; (×) water; (○) n-butanol; (●) n-butyl butyrate. 1851



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dp = swelled diameter of catalyst in reaction conditions, m Ea,m = activation energy of the rate constant for reaction m, kJ kmol−1 Fmin = square root of mean of squared absolute residues fabs = average deviation of predicted vs experimental mole fraction in kinetic modeling Ka,m = activity-based equilibrium constant for reaction m Kx,m = mole-fraction-based equilibrium constant for reaction m Kγ,m = ratio of activity coefficients of species in reaction m k0,m = pre-exponential factor of reaction m, kg soln·m3(kg cat.)−1 s−1 kmol−1 NC = number of components in reaction Ni = number of moles of species i in the reaction mixture, kmol NT = total number of moles in the reactor, kmol rm = rate of reaction m per unit volume of liquid phase, kmol s−1 m−3 r*obs = observed rate of reaction per weight of catalyst, mol s−1 kg−1 R = ideal gas constant V = volume of reaction liquid phase, m3 Vp,swollen = bulk volume of swollen catalyst, m3 Vp,dry = dry bulk volume of catalyst, m3 wCAT = catalyst loading in the reaction mixture, kg catalyst (kg solution)−1 xi = mole fraction of component i in the liquid mixture

Table 4. Generalized Rate Constants for Butyric Acid Esterification Over A-70 for Different Alcohols

a

alcohol

ρi, kmol·m−3

k × 104 (60 °C) kg soln·m3 (kmol·kg cat.·s)−1

methanol ethanol ethanol propanol n-butanol n-butanol isobutanol 2-EHA 4-heptanol 1-heptanol 1-octanol

23.5 16.4 16.4 12.8 10.4 10.4 10.4 6.2 6.8 6.8 6.1

5.0b 2.3a 3.0b 2.2b 3.0a 3.0b 1.9b 2.8b 2.5b 0.9b 0.9b

This work. bReference 27.

generalized rate constant for esterification of butyric acid over A-70 catalyst with any alcohol. As a further generalization of butyric acid esterification, we calculated the initial reaction rate for n-butyl butyrate formation over Dowex 50Wx8-400 resin19 at 110 °C and a 4:1 BA:nBuOH initial feed ratio. Adjusting the value of the resulting rate constant to 60 °C using an activation energy of 38 200 kJ/ kmol19 and accounting for the differences in acid site density between Dowex resin and Amberlyst 70, the rate constant for their system in a form equivalent to that presented in Table 4 is 1.98 × 10−4 m3 soln·kg soln/(kg cat.·kmol·s), a remarkably similar value, given the differences in the reaction system.

Greek

γi = activity coefficient of component i in the reaction mixture ε = particle porosity η = intraparticle effectiveness factor ΦW = Weisz−Prater observable modulus φ = Thiele modulus ρ = molar density of reacting liquid phase, kmol m−3 ρCAT = density of catalyst particles, kg m−3 θi,m = ratio of stoichiometric coefficient of component i with respect to the reference component in reaction m τ = pore tortuosity vi,m = stoichiometric coefficient of component i in reaction m

4. CONCLUSIONS The kinetics of ethanol and n-butanol esterification of butyric acid in the presence of homogeneous p-toluene sulfonic acid and heterogeneous ion-exchange resin catalyst Amberlyst 70 have been accurately described by an activity-based kinetic model with solution density included. Mixed alcohol esterification kinetics are accurately predicted by an additive combination of esterification rates of the individual alcohols, indicating that alcohols do not compete with each other or inhibit each other in simultaneous esterification reactions. By including solution density to describe actual concentrations of −OH and −COOH in solutions of neat reactants, butyric acid esterification kinetics with simple C2−C8 alcohols are described by a single rate constant, which serves as a generalized rate constant for butyric acid esterification over Amberlyst 70. The additivity of rates and existence of a generalized rate constant greatly simplifies the simulation of actual biorefinery esterification processes with single or multiple alcohols.

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Abbreviations

AUTHOR INFORMATION

Corresponding Author

*Tel.: (517) 353-3928. E-mail: [email protected].

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Notes

The authors declare no competing financial interest.

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A-70 = Amberlyst 70 BA = butyric acid BE = butyrate ester BB = n-butyl butyrate But = n-butanol EB = ethyl butyrate EQ = equilibrium Eth = ethanol OH = alcohol p-TSA = p-toluene sulfonic acid UNIFAC = universal functional activity coefficient W = water

REFERENCES

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NOMENCLATURE AND UNITS ai = activity of species i in reaction solution CBA = concentration of butyric acid in liquid phase, kmol m−3 Deff = effective liquid-phase diffusivity of butyric acid, m2 s−1 DBA = bulk diffusivity of butyric acid in alcohol, m2 s−1 1852



Article

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n-Butanol Esterification of Butyric Acid with

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