Esterification Kinetics of Tributyl Citrate Production Using

Article pubs.acs.org/IECR

Esterification Kinetics of Tributyl Citrate Production Using Homogeneous and Heterogeneous Catalysts Oscar M. Osorio-Pascuas, Miguel A. Santaella, Gerardo Rodriguez, and Alvaro Orjuela* Department of Chemical and Environmental Engineering, Grupo de Investigación en Procesos Químicos y Bioquímicos, Universidad Nacional de Colombia, 111321 Bogotá D.C., Colombia S Supporting Information *

ABSTRACT: In this work, the production of tributyl citrate via catalytic and self-catalyzed esterification of citric acid with 1butanol was studied. Both, methanesulfonic acid (MSA) and Amberlyst 70 ion-exchange resin were evaluated as catalysts in the reaction. The kinetic effects of the temperature (353−393 K), the feed molar ratio of alcohol to acid (8:1 to 16:1), and catalyst loadings (0.5−1.5 wt % of MSA, and the equivalent amount of Amberlyst 70) were evaluated. Experiments were carried out using stirred batch reactors under isothermal operation. A Box−Behnken design was used to optimize the number of experiments required to obtain a valid kinetic model. Chemical equilibrium conditions were evaluated independently from kinetic experiments, reducing the number of parameters to adjust during data regression. Self-catalytic rate of reaction was also evaluated, and it was included within the overall kinetic model. The obtained models show good agreement with experiments, and they can be used for process analysis and simulation.

1. INTRODUCTION

Among the variety of citrate esters, tri-1-butyl citrate (TBC) stands out as a widely used ingredient in cosmetic products and as a raw material to produce acetyl tri-1-butyl citrate (ATBC). The acetylated tributyl citrate provides even better results as a plasticizing agent for polyvinyl chloride (PVC).10 TBC is manly produced by direct esterification of citric acid (CA) (a major fermentation-derived commodity), with 1butanol (also available from fermentation) in a sequential− parallel reaction scheme, as shown in Figure 1. At the industrial scale, TBC is produced in batch or batch fed stirred tank reactors using a homogeneous acid catalyst.12−14 Some reports also indicate the benefit of using of heterogeneous catalyst as ion exchange resins to avoid the need for corrosion-resistant materials.15 Although homogeneous catalysts can become very corrosive to equipment and could be difficult to remove, they are preferred because they are more active and efficient in reaching high conversions to the trialkyl ester below the decomposition temperature of citric acid (∼448 K).16 Each esterification step described in Figure 1 is strongly limited by chemical equilibrium. Therefore, the continuous removal of the water generated in the process and the use of alcohol excess are common practices to achieve high conversion. For that same reason, energy-intensive alcohol recovery and recycling steps are required, involving higher processing costs. To reduce energy consumption and processing costs during citrates production, intensification by reactive distillation (RD) has been proposed for citrates production, specifically for triethyl citrate.11,15 In this case, removal of ethanol excess and water was accomplished by distillation, while reaction was

Production and consumption of biobased chemicals have gained pace in recent years because of the global trend for moderating dependence on petrochemicals, the need for reducing the environmental impacts of using fossil resources, and also as a result of the public scrutiny over the potential negative effects of being exposed to harmful chemicals. In contrast to most petroleum-based chemicals, biobased products are commonly renewable, biocompatible, and suitable for biodegradation. In this regard, the substitution of petrochemicals with biobased alternatives in the formulation of consumer goods is particularly important in the plasticizers sector. These components are widely used in the fabrication and transformation of polymers, providing the flexibility and plasticity required in the final products. The current world plasticizer market amounts to c.a. 7 million tons per year, and it is extensively dominated (∼86%) by phthalic acid esters of long chain alcohols (e.g., 2-ethyl hexanol, nonanol). The remaining nonphthalate plasticizers are used mainly in niche applications.1 Although phthalates are well-known as general-purpose plasticizing agents and have been used in a variety of polymeric materials,2,3 some studies indicate that they may represent certain risks to human health and that they are not easily biodegraded.4−8 Furthermore, in the traditional phthalic anhydride synthesis processes (gas-phase oxidation of naphthalene or o-xylene3) some aromatic trace impurities may remain in the plasticizer, preventing its use in products designed for direct contact with humans. In contrast, even if biobased plasticizers such as citric acid esters (with or without acetylation) are not for general purpose, they are generally recognized as safe (GRAS) by different international regulatory agencies. This characteristic makes citrates suitable plasticizers for pharmaceutical and cosmetic applications, medical devices, food packaging, and toys.2,3,9−11 © XXXX American Chemical Society

Received: September 26, 2015 Revised: November 22, 2015 Accepted: November 30, 2015

A

DOI: 10.1021/acs.iecr.5b03608 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 1. Esterification of citric acid with 1-butanol.

2.2. Analysis. The analytic technique described here was adapted from a previous report on citrates esterification.11 CA, mono-1-butyl citrate (MBC), di-1-butyl citrate (DBC), and TBC were analyzed by using a Dionex-Ultimate 3000 HPLCSystem, using a reversed phase C18 column (Acclaim 120, 3 × 150 mm, 3 μm). The oven temperature was set at 373 K, and the mobile phase flow rate was maintained as 1 mL/min using a programmed gradient of acetonitrile (ACN)/water (pH 2.1) as follows: 0% ACN (t = 0 min), 60% ACN (t = 20 min), 90% ACN (t = 25 min), and 0% ACN (t = 28 min). Samples were diluted in acetonitrile (3/100 v/v) before injection, and the species were quantified by ultraviolet (UV) detection at a wavelength of 210 nm. CA and TBC were identified by comparison of the retention times of standards. Quantification was carried out by previous calibration and response factor determination. Solutions of known composition were prepared and analyzed by triplicate, ensuring a detector linear response. The maximum error of HPLC analysis in these components was ±0.5%. For the MBC and DBC, there were no commercial chromatography standards available. Moreover, according to the chemical structure, the occurrence of two isomers was expected for both intermediate esters (difficult to resolve by standard HPLC), because esterification can occur in the terminal or middle carboxylic group of the CA. In all reaction samples, two peaks were observed in the chromatography plots for each intermediate ester. For quantification purposes, the two unresolved peaks of each intermediate ester were considered as a single component. Because similar detector responses for CA and TBC were obtained, the response factors of the missing citrates were calculated based upon the degree of substitution. Those were obtained by interpolating a linear relationship between the molecular weight of CA and TBC and their corresponding response factors. Adequacy of this assumption was verified by keeping track of the total amount of moles of citric species that had to be constant in each experiment. Finally, the concentrations of water (H2O) and 1butanol (BtOH) were determined by reaction stoichiometry and by mole balance. By using the considerations described above, and because the response factors for some citric species were assumed, it was observed that the maximum relative error close to the total mass balance was ±5% in the sum of the experimental mass fractions of all components. This was considered acceptable taking into account the lack of commercial chromatography standards for calibration of intermediate citrates. 2.3. Heterogeneous Catalyst Pretreatment and Preliminary Tests. As-received Amberlyst 70 was washed in ethanol under agitation for 2 h using a stirred glass container.

promoted by Amberlyst 15 as catalyst. According to these reports, it is recommended that operation occur at high temperatures to benefit the reaction rate, but the temperature should be maintained below 393 K to avoid thermal damage of the catalyst.17 Despite RD having been also proposed for the production of other CA esters,12 there is a lack of kinetic and thermodynamic information in the open literature allowing process modeling and design, particularly when using commercial homogeneous or heterogeneous catalysts such as methanesulfonic acid and Amberlyst 70. Methanesulfonic acid (MSA) is widely used as a liquid catalyst in esterification processes because of its good activity, lower corrosiveness compared with stronger acids (sulfuric or hydrochloric), and less degradation of the product (color darkening). On the other hand, Amberlyst 70 ionexchange resin can operate at higher temperatures than most commercial ion exchange resins (maximum operating temperature of 463 K18), and similarly to other solid catalysts, it can be easily recovered and regenerated in continuous process systems. Although reports indicate Amberlyst 70 has lower acid sites concentration in the polymeric matrix (>2.55 eq/ kg18) than other ion exchange catalysts, it has shown good performance in different etherifications and also in esterifications of poly(carboxylic acid)s operating in RD units.19−27 In this regard, this work describes a study on the esterification of CA with 1-butanol using MSA and Amberlyst 70 as homogeneous and heterogeneous catalyst, respectively. The effect of the catalyst concentration, reactants molar ratio, and temperature over the rate of reaction was evaluated for each catalyst. Because the autocatalytic effect was considered important based on preliminary experiments, it was also studied and incorporated within the complete kinetic models. The obtained models are intended to be used in the modeling of reactive distillation processes.

2. EXPERIMENTAL DETAILS 2.1. Material. For reaction experiments, anhydrous citric acid (99.9%, FG) was obtained from Sucroal S.A. (Colombia) and 1-butanol (99.5%, for analysis) was purchased from Panreac (Spain). The concentration of all chemicals was checked by gas chromatography or high-performance liquid chromatography (HPLC), and the chemicals were used without further purification. Tributyl citrate (98%, Aldrich, United States) and citric acid (99.9%, Sigma-Aldrich) standards were used for calibration purposes. Methanesulfonic acid (98%) was obtained from Alfa Aesar (Germany) and Amberlyst 70 resin was supplied by Dow Chemical Company (United States). Acetonitrile (99.9% HPLC grade, Panreac, Spain) and deionized water were used as HPLC solvents. B


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below the desired temperature, the required amount of MSA was loaded into reactor through the sampling port using a syringe. After the mixture reached the reaction temperature (it normally took 10−15 min), the reaction time was started. When operating with the self-catalytic system, the stirring rate was maintained at 700 rpm from the beginning of the operation. When using Amberlyst 70, reagents and catalyst were charged to the reactor from the beginning. Then, the reactor was closed and operated at room temperature and 700 rpm for about 10 min to allow CA dissolution. Later, the heating was started, and after the mixture reached the required temperature, the stirring rate was adjusted to 1100 rpm. At this point, the time recording was initiated. During all experiments, 0.2−0.3 cm3 samples were withdrawn at specific time intervals through the sampling port by using a syringe. The samples were transferred to an ice bath before analysis. Eight to ten samples were obtained in each 8 h reaction experiment. 2.5. Chemical Equilibrium Experiment. Reaction equilibrium experiments were carried out in sealed glass tubes of 10 mL, which were attached to a rotating rod within an isothermal oven (Figure 3). The reactants together with the MSA were

An ethanol resin volumetric ratio of 1:4 was used during this process, and it was repeated at least three times. The rinsing process was repeated with deionized water until constant conductivity of the supernatant solution was measured. Afterward, the resin was filtered and dried under vacuum at 353 K until constant weight. The dried catalyst was maintained in a hermetic container within a vacuum oven until the final use in kinetic experiments. From preliminary experiments using Amberlyst 70 as catalyst, it was found that external mass-transfer resistances were negligible when operating at stirring rates above 800 rpm. For this reason, further reactions were run above this agitation rate. Additional experiments evaluating the effects of catalyst particle sizes on the reaction rate allowed ensuring the absence of internal mass-transfer limitations when working with particle sizes below 300 μm. Because the mean particle size of highly monodisperse Amberlyst 70 beads is around 500 μm,18 the catalyst was subjected to grinding before use in the kinetic experiments. This process was performed in a mortar using liquid nitrogen to cool the solid, avoiding the temperature rise caused by friction during the milling process. To ensure the thermal stability of the acid sites, the ion exchange capacity of the resin was measured before and after the grinding process. Details of the standard method to evaluate ion exchange capacity are described elsewhere.28 The concentration of acid sites before and after this treatment was nearly constant, and it was 4.01 ± 0.12 eq/dry kg. 2.4. Batch Kinetic Experiment. The esterification reactions were performed under batch conditions in a set of three well-mixed 100 cm3 stainless steel jacketed reactors, each one equipped with a circulating oil bath for isothermal operation and a stirring plate (see Figure 2). Also, a sampling

Figure 3. Scheme of equipment used for chemical equilibrium experiments.

previously added into tubes at the desired concentrations. The stirring rate was adjusted between 90 and 100 rpm, and the temperature was maintained constant within ±0.1 K by using a PID controller. The tubes where maintained at reaction conditions for 28−72 h, and at the end the equilibrium conditions were obtained by HPLC analysis of the reactive media. Figure 2. Scheme of equipment used for batch kinetic experiments.

3. RESULTS AND DISCUSSION A Box−Behnken experimental design was implemented to reduce the required number of experiments to fit the kinetic model. Box−Behnken is a type of response surface design used when each factor has only three levels, and it is recommended when the region of interest and the region of operability are nearly the same. Because it requires fewer evaluation points, it is less computationally expensive than central composite designs (such as the factorial design).29 In our case, three different factors at three levels are considered: initial reactants molar ratio (8:1 to 16:1), reaction temperature (363−393 K), and catalyst loading (0.5−1.5 wt %). In the case of Amberlyst 70, the required weight of catalyst was calculated using the

port and a temperature probe were located over the reactor cover to follow the reaction conditions with time. Inside the reactor, at the end of the sampling port, a stainless steel filter was located to avoid catalyst removal during operation. Initially, when using the homogeneous catalyst (MSA), the desired amount of CA and BtOH were added into the reactor at room temperature. After the reactor was closed, the magnetic stirring was set at 500 rpm and maintained for 10 min to mix reactants and dissolve the CA. Thereafter, heating was initiated by allowing the bath fluid to pass through the reactor jacket, and the stirring rate was adjusted to 700 rpm. Around 5 K C


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Industrial & Engineering Chemistry Research Table 1. Evaluation of Internal Mass-Transfer Resistances at Initial Reaction Conditions Using the Weisz−Prater Criterion ρcat (kg/m3) (swollen) dp (μm) (swollen) CCAo (mole fraction) (solution) wcat (kgcat/kgsol) BtOH association factor Wilke−Chang CA molar volume at TB (cm3/mol)a ε19 experimental run T (K) robs (mol CA/mol.s) ρsol (kg/m3) μliquid (cp)36 DCA (m2/s) De (m2/s) Φw ϕ η a

1000 378 0.058 0.0264 1.0 223.14 0.57 3b 363.15 9.68 × 10−6 818 0.633 1.43 × 10−9 4.63 × 10−10 0.0662 0.258 0.996

4b 393.15 4.35 × 10−5 794 0.389 2.51 × 10−9 8.16 × 10−10 0.173 0.419 0.988

Figure 5. Self-catalyzed esterification of CA with BtOH. Conditions of run 22. Molar ratio 12:1 (alcohol:acid), 393 K. (●, CA; ○, MBC; ▼, DBC; ▲, TBC; □, BtOH; ■, H2O).

Aspen Plus v. 7.3, Database.

Figure 4. Initial reaction rate of CA with BtOH for various catalyst concentrations: (●) MSA and (▽) Amberlyst 70. Experiments performed with a reactant molar ratio, 8:1 (alcohol:acid) and 378 K. (*Mass concentration of catalyst corresponding to MSA acid equivalents. Datum at 0 wt %, cat corresponds to the self-catalytic experiment.)

Figure 6. Mole fraction-based equilibrium constants (KEQ) for esterification of CA with BtOH catalyzed with MSA at different temperatures. ●, Keq 1; ○, Keq 2; ▼, Keq 3.

Table 2. Kinetic Parameters Adjusted for Self-Catalyzed Reactions

same acid equivalents of MSA in the reactive phase. Some additional experiments were carried out to analyze the effect of temperature, concentration of catalyst, and the self-catalytic reaction. Conditions of kinetic experiments are summarized in Table S1 in the Supporting Information, and the full set of kinetic plots (Figures S2−S41) are also available there. 3.1. Mass-Transfer Considerations on the Heterogeneous System of Reaction. In preliminary CA−BtOH esterification experiments using Amberlyst 70 as catalyst, negligible external liquid−solid mass-transfer limitations were observed when operating with agitation rates above 800 rpm. On the other hand, intraparticle mass-transfer effects were analyzed by taking into consideration the Weisz−Prater module (Φw). As a general criterion, absence of intraparticle masstransfer limitations can be assumed when Φw is much less than

parameter ko self,1 ko self,2 ko self,3 Eaself,1 Eaself,2 Eaself,3 Keq 1 Keq 2 Keq 3

D

units

values

confidence interval

1/s 1/s 1/s J/mol J/mol J/mol

3.207 × 10 8.873 × 106 1.166 × 107 71 433 77 346 80 894 8.68 3.56 1.04 6

±1.183 × 105 ±4.517 × 105 ±1.776 × 106 ±237 ±1099 ±3693


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Industrial & Engineering Chemistry Research Table 3. Kinetic Parameters Adjusted for Catalyzed Reaction of Homogeneous and Heterogeneous System parameter

units

MSA


Amberlyst 70


ko cat,1 ko cat,2 ko cat,3 Ea1 Ea2 Ea3 Keq 1 Keq 2 Keq 3

1/(%wt cat)*s 1/(%wt cat)*s 1/(%wt cat)*s J/mol J/mol J/mol

2.678 × 105 3.103 × 105 4.247 × 105 57 917 60 065 66 406 8.68 3.56 1.04

±4.877 × 104 ±3.333 × 104 ±2.342 × 104 ±1850 ±1114 ±585

1.543 × 105 1.275 × 105 8.255 × 104 65 582 67 529 70 561 8.68 3.56 1.04

±8.573 × 103 ±6.755 × 103 ±6.037 × 103 ±872 ±263 ±1140

′ = robs/(wcat ′ ρsol ) robs

(2)

Here, robs is the rate of reaction per unit volume of reacting liquid phase. In this study, this is evaluated as the consumption rate of CA with time. In eq 2, wcat ′ is the catalyst loading (kilogram of catalyst per kilogram of reacting phase), and ρsol is the density of reacting phase. In preliminary tests, it was found that dry Amberlyst 70 particles could swell up to double their volume when contacted with BtOH. Therefore, the particle diameter at reacting conditions (dp) can be calculated as d p/d pdry =

3

(VPswollen/VPdry )

Taking into account that after the catalyst was grinded before use, obtained particle size distribution was in-between 150 and 300 μm. The higher value of this interval (300 μm) was used to estimate the swollen particle diameter with eq 3, obtained a dp value of 378 μm. The particle diameter used in this calculation was conservative taking into account that Weisz−Prater module increase with the particle size. Alcohol adsorption within the macroreticular structure of Amberlyst 70 modifies its density because of the swelling effect. The catalyst density under reaction conditions has been previously reported as 1000 kg/m3 in similar reactive media,19,32,33 so this value was used for Weisz−Prater module evaluation. The effective diffusivity (De) was calculated based upon the liquid-phase diffusion coefficient (DCA) estimated from the Wilke−Chang model,34 using eq 4.

Figure 7. Calculated data versus experimental data for esterification between citric acid and 1-butanol catalyzed with methanesulfonic acid (●, CA; ○, MBC; ▼, DBC; △, TBC; ■, BtOH; □, H2O).

De = (ε/τ )DCA = ε 2DCA

(4)

As observed, effective diffusivity was computed as the quotient of particle porosity (ε) and pore tortuosity (τ), or assuming that ε is the inverse of τ.32,33 Then, the observed Weisz−Prater modulus can be used to calculate the effectiveness factor of the reaction (η) taking into consideration the Thiele modulus (ϕ) for spherical particles using the following expression:

Figure 8. Calculated data versus experimental data for esterification between citric acid and 1-butanol catalyzed with Amberlyst 70 resin (●, CA; ○, MBC; ▼, DBC; Δ, TBC; ■, BtOH; □, H2O).

ΦW = ηϕ2 = 3(ϕ coth ϕ − 1)

the unity. For a spherical particle the Weisz−Prater module can be calculated as30,31 ′ )ρcat (d p/6)2 /(DeCCAo) ΦW = (robs

(3)

(5)

Equation 5 represents the Weisz−Prater modulus for a spherical pellet assuming a first-order reaction in CA, which is considered to be a valid assumption in this case because of the large excess of alcohol used in experiments. The calculated values of Φw for an initial molar ratio of 16:1 (BtOH:CA) and at 363.15 and 393.15 K are shown in Table 1. Results indicate that the main effect in the reaction is the kinetic one because Φw ≪ 1 (internal mass-transfer resistance can be negligible30) and the effectiveness factor is nearly unity.30,35 As observed, this analysis was performed in the

(1)

where robs ′ is the observed rate of reaction per mass of catalyst and ρcat and dp are the catalyst density and particle diameter, respectively. De is the effective diffusivity of CA within the catalyst particle, and CCAo is the concentration of CA in the bulk liquid at the beginning of the reaction. For the calculation of the observed reaction rate (robs ′ ) the following equation can be used: E


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temperature limits of the kinetic study, ensuring that observed reaction rates during experiments corresponded to intrinsic kinetics. This was also experimentally confirmed by performing kinetics runs using different catalyst particle sizes. As shown in Figure S1 of the Supporting Information, there are no differences when working with particles below 250 μm. 3.2. Effect of Catalyst Loading. The effect of varying the catalyst concentration (MSA and Amberlyst 70) in the reaction is presented in Figure 4. In this case, only the reaction rate at time zero for the first step of esterification (CA consumption) was considered. As observed, for both homogeneous and heterogeneous catalysts, reaction rate is directly proportional to catalyst loading. Additionally, the slope of the trend line for Amberlyst 70 is smaller than that for MSA. This indicates that for an equivalent amount of active sites, MSA is more effective as catalyst than Amberlyst 70 resin. This was expected because of the mobility of the homogeneous catalyst. Another important finding of these preliminary experiments is that reaction occurs even without catalyst. This indicates that is important to consider the self-catalytic reaction, which is expected to be more significant at high temperatures. Another important finding of these preliminary experiments is that reaction occurs even without catalyst. This indicates that is important to consider self-catalytic reaction, which will be more significant at high temperatures. 3.3. Self-Catalytic Reaction. Self-catalytic reaction was evaluated according to conditions reported in Table S1 (runs 17−25). The temperature and molar ratio ranges correspond to those evaluated for the catalytic systems. In this case, the reaction is promoted by the acidic groups of the citric species (CA, MBC, and DBC). A typical reaction profile of selfcatalytic reaction is observed in Figure 5. All the kinetic profiles obtained in the self-catalytic experiments are also available in the Supporting Information. 3.4. Kinetic Model Description. In a batch reactor, the change in the composition of the chemical species can be expressed as follows: dNi /dt = NT(dxi /dt ) = θirv , iV

(6)

where Ni is number of moles of component i, NT the total number of moles in the reactor, xi the mole fraction of component i in the liquid reactive media, θi the stoichiometric coefficients of component i, and rv,i the volumetric reaction rate for component i. Because of the large excess of alcohol required to dissolve CA, the mixture density can be considered nearly constant with time. For this reason, and taking into account that the total number of moles is conservative, eq 6 can be simplified to eq 7. dxi /dt = −ri

(7)

According with literature, the esterification reaction can be described by using a power law kinetic model assuming an Arrhenius-type temperature dependence and a first order with respect to each reactant.11 Therefore, for a typical esterification, the kinetic model can be expressed in a pseudohomogeneous model as rj = Ccatk w, j(xAcidxAlcohol − x Esterx Water /KEQ, j)

(8)

where CCat is the catalyst or active sites concentration and kw and KEQ are the reaction rate constant and the equilibrium constant of reaction j, respectively. Here, an approximate mole fraction-based model is used when a thermodynamic model is

Figure 9. Esterification of CA with BtOH. Molar ratio 8:1 (alcohol:acid), 393 K, and 1 wt % of catalyst loading. (a) MSA, (b) Amberlyst 70, and (c) Self-catalytic (●, CA; ●, MBC; ▼, DBC; ▲, TBC; □, BtOH; ■ H2O). F


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Industrial & Engineering Chemistry Research θ

not available to describe phase equilibria of the reactive media (otherwise, an activity-based model is preferred). For a catalytic esterification, the rate constant of reaction j is termed kCatj, and it can be expressed as k Catj = ko,Catj exp[− Ea Cat, j/(RT )]

KEQj = Πxi , ij,j

Here, θi,j is the stoichiometric coefficient of component i in the reaction step j. The values of the equilibrium constants were determined by measuring the final concentration of reaction (after 3 days or more) at temperatures between 342 and 373 K. MSA was used as catalyst during these experiments because its activity is higher than that of Amberlyst 70, and no solid−liquid equilibria might affect results. In addition, the higher activity of MSA helps to ensure a real chemical equilibrium condition in the time frame of the experiments. The temperature dependence of the chemical equilibrium constants are presented in Figure 6 as the linear form of a van’t Hoff-type relationship. The equilibrium constant for the formation of MBC (Keq 1) was measured only at 373 K adding 5 wt % of water to the reactive mixture. This was done because after several attempts to determinate the chemical equilibrium constant, the final concentration of CA was well below the uncertainty of the chromatographic technique. The addition of water helped to shift the chemical equilibrium to the reactants, allowing measurable concentrations of CA, and to obtain a reproducible experiment. The other equilibrium constants, Keq 2 and Keq 3, were evaluated with initial mixture of CA and BtOH only, at all temperatures. As observed, molar-based equilibrium constants are nearly independent of temperature, indicating that reactions are virtually thermoneutral (i.e., negligible heat of reaction). The averaged Keq 1, Keq 2, and Keq 3 values obtained were 8.68, 3.56, and 1.04, respectively. 3.6. Determination of Kinetic Parameters. The kinetic parameters (pre-exponential factors and energies of activation) were calculated from the numerical integration of the kinetic rate expressions. The model was integrated using a commercial software (Matlab), solving eqs 12−14 (without catalyst) and eq 15−17 (with catalyst) via an ODE23 function (fourth-order Runge−Kutta), using the initial mole fraction concentration of components (t = 0) as the initial condition in the solution of the set of ordinary differential equations. The molar balance was calculated to determine the concentration profiles of species in the batch reactor, as described in eqs 19−24.

(9)

As for the self-catalyzed reaction kSelf j, it can be expressed as k Selfj = ko,Selfj exp[− EaSelf, j/(RT )]

(10)

Herein, R is the ideal gas constant and T is the absolute temperature; koi and Eai are the pre-exponential factor and the activation energy of reaction i, respectively. Regarding the CCat parameter in eq 8, for the catalytic reaction, it can be assumed as the catalyst loading in weight percent (wcat, kilograms of catalyst/100 kilograms of reactive phase). In the case of the self-catalytic system, CCat can be expressed as the molar concentration of acid equivalents from citric species (xacid):11 xacid = 3xCA + 2xMBC + xDBC

(11)

Here, we assumed that the self-catalytic activity is proportional to the total concentration of hydrogen ions present in CA (three hydronium ions), MBC (two hydronium ions), and DBC (one hydronium ion). Differently from the catalytic reaction, in the self-catalytic system the concentration of active sites (xacid) changes with time; having its maximum at time zero and gradually decreasing over time until reaching a value near to zero. Taking into account the above, the kinetic models for the self-catalytic reactions during CA esterification can be defined as follows: rSelf,1 = xacidk Self,1(xCAxBtOH − xMBCx H 2O/KEQ1)

(12)

rSelf,2 = xacidk Self,2(xMBCxBtOH − xDBCx H 2O/KEQ2)

(13)

rSelf,3 = xacidk Self,3(xDBCxBtOH − xTBCx H 2O/KEQ3)

(14)

(18)

In this case of the catalytic reaction, there is a synergic effect of the self-catalytic reaction. For this reason, the kinetic model is described as the linear combination of both effects as follows: r1 = (xacidk Self,1 + wCatk Cat,1)(xCAx BtOH − xMBCx H2O/KEQ1) (15)

r2 = (xacidk Self,2 + wCatk Cat,2)(xMBCxBtOH − xDBCx H 2O/KEQ2) (16)

r3 = (xacidk Self,3 + wCatk Cat,3)(xDBCxBtOH − x TBCx H 2O/KEQ3) (17)

Equations 15−17 are the complete kinetic models that describe CA esterification with BtOH using either homogeneous or heterogeneous catalyst. Because the number of parameters is large (15 in total) to fit with few kinetic experiments, and there is lack of thermodynamic models to calculate the phase and chemical equilibrium of the system, the kinetic equations were mole fraction-based as a simplification, and the equilibrium constants were experimentally obtained. Additionally, the kinetic parameters of self-catalytic reaction were obtained by fitting data from noncatalytic experiments only (runs 17−25). 3.5. Reaction Equilibrium Constants. The chemical equilibrium constants for the three reaction steps can be estimated in a mole fraction-basis as follows:

dxCA /dt = −r1

(19)

dxMBC/dt = r1 − r2

(20)

dx DBC/dt = r2 − r3

(21)

dx TBC/dt = r3

(22)

dx BtOH/dt = −r1 − r2 − r3

(23)

dx H2O/dt = r1 + r2 + r3

(24)

The kinetic parameters were determined by the minimization of the objective function described in eq 25, using a genetic algorithm method from Matlab libraries. NC

Fmin = [∑ (xi ,exptl − xi ,calcd)2 ]/NC i=1

(25)

Here, NC is the number of citric species; xi,exptl and xi,calcd are the experimental and calculated mole fractions, respectively, obtained from the concentration profiles with time. Initially, the kinetic parameters for self-catalytic system were calculated. Later, the same optimization function was used to fit the catalytic parameters including the self-catalytic parameters G



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previously calculated. The final values of the kinetic parameters are presented in the Tables 2 and 3. Fmin values obtained in each optimization were 1.19 × 10−5, 2.68 × 10−5, and 1.97 × 10−5 for self-catalytic, homogeneous, and heterogeneous systems, respectively. As expected, the MSA catalyst showed lower energies of activation and higher pre-exponential factors in each reactions step than the heterogeneous catalyst. This agrees with the higher turnover frequency (∼6 times higher) for the same amount of acid equivalents, as observed in the slopes of the trend lines of Figure 4. The kinetic parameters here obtained agree with similar reports on esterification reaction of poly(carboxylic acid).11,19 Figures 7 and 8 are parity plots of the whole set of experiments compared with calculations from the developed models. Also, Figure 9 presents the good agreement between experimental and calculated kinetic profiles under different catalysts and operating conditions. The whole set of experiments and plots are included in the Supporting Information. As observed, there is good agreement between the obtained kinetic expressions and the experimental observations. This indicates that the obtained models can be used with confidence for process design and up-scaling purposes. Figure 9 presents the agreement of the experimental and calculated kinetic profiles under different catalysts and conditions. The whole set of experiments and plots are included in the Supporting Information.

ACKNOWLEDGMENTS This work was supported by “Departamento de Administrativo de Ciencia, Tecnologiá e Innovación − Colciencias”, under the Project named “Producción de plastif icantes a partir de ácido ́ ́ citrico usando procesos hibridos de reacción y separación simultánea”, code: 1101-569-33201. M.A.S. thanks “Jardiń Botánico de Bogotá José Celestino Mutis” for partial support of his research.

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ACN = Acetonitrile ATBC = Acetyl Tri-n-butyl citrate or Acetyl Tri-1-butyl citrate BtOH = 1-butanol CCat = Catalyst or active sites concentration CCAo = Concentration of CA in the bulk liquid at beginning of the reaction CA = Citric acid Cat = Catalyst/catalytic dp = Catalyst particle diameter swollen dp dry = Catalyst particle diameter dry DBC = Di-n-butyl citrate or Di-1-butyl citrate De = Effective diffusivity of CA in the catalyst particle Ea = Energy activation (J/mol) Fmin = Minimization function H2O = Water HPLC = High performance liquid chromatography kj = Reaction rate constant of forward of “j” (1/s) koj = Pre-exponential factor of forward reaction “j” (1/s) kw,j = Reaction rate global constant of “j” (1/s) Keq = Equilibrium constant MBC = Mono-n-butyl citrate or mono-1-butyl citrate MSA = Methanesulfonic acid NC = Number of citric component evaluated Ni = Number of moles of component “i” NT = Total number of moles in the reactor o in the reaction mixture PID = Proportional−integral−derivative (control system) PVC = Polyvinyl chloride R = Ideal gas constant RD = Reactive distillation Rf = Initial molar ratio (alcohol:acid) r1 = Reaction rate for MBC production or AC consumption r 2 = Reaction rate for DBC production or MBC consumption r3 = Reaction rate for TBC production or DBC consumption ri = Reaction rate of component “i” (1/s) robs = Observed rate of reaction r′obs = Observed rate of reaction per mass of catalyst (mol/ kgcat.s) rv,i = Volumetric reaction rate of component “i” (1/cm3.s) Self = Self-catalysis t = Time T = Temperature (K) TBC = Tri-n-butyl citrate or tri-1-butyl citrate UV = Ultraviolet V = Volume (cm3) VP = Catalytic particle volume wcat = Catalyst loading (% wt) wcat ′ = Catalyst loading, kg of catalyst per kg of reacting phase xacid = Mole fraction of acid species in self-catalytic reaction

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b03608. List of kinetic experiments performed for citric acid (CA)/1-butanol (BtOH) esterification, kinetic profiles obtained with Amberlyst 70 using different particle diameters, and kinetic profiles obtained in experiments (PDF)

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NOMENCLATURE

List of Symbols and Abbreviations

4. CONCLUSIONS A kinetic study of the esterification of citric acid with 1-butanol using methanesulfonic acid and Amberlyst 70 resin as a catalyst was performed. Experimental runs were carried out at different temperatures (353−393 K), feed molar ratios (8:1 to 16:1), and catalyst loadings (0.5−1.5 wt % equivalent to MSA). Independent experiments allowed obtaining the chemical equilibrium constant for the three steps of reaction, and they were found to be nearly temperature-independent. A preliminary analysis indicated that self-catalytic reactions had to be considered during the catalytic process, and the parameters of a mole fraction-based were obtained for selfcatalytic and catalytic reactions. As expected, the homogeneous catalyst demonstrated higher activity in the esterification reaction. After comparison with the whole set of experiments, the models show good agreement and can be used for process design and up-scaling purposes.

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Article

AUTHOR INFORMATION

Corresponding Author

*Phone: (+57) 1 3165000, ext. 14303. E-mail: aorjuelal@unal. edu.co. Notes

The authors declare no competing financial interest. H


Article

Industrial & Engineering Chemistry Research xi = Mole fraction of component “i”

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Greek Letters

ε = Particle porosity η = Effectiveness factor of reaction θi = Ratio of stoichiometric coefficients of component “i” ρcat = Catalyst particle density ρsol = Density of reacting phase τ = Pore tortuosity ϕ = Thiele modulus Φw = Weisz−Prater modulus Subscripts and Superscripts

calcd = Calculate data exptl = Experimental data i = component identification j = reaction step identification (1, 2, or 3)

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REFERENCES

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