Kinetics of Methyl Formate Hydrolysis in the Absence and Presence of

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Ind. Eng. Chem. Res. 2011, 50, 267–276

267

Kinetics of Methyl Formate Hydrolysis in the Absence and Presence of a Complexing Agent Olatunde Jogunola,* Tapio Salmi, Johan Wa¨rnå, Jyri-Pekka Mikkola, and Esko Tirronen Process Chemistry Centre, Laboratory of Industrial Chemistry and Reaction Engineering, Åbo Akademi UniVersity, FI-20500 Åbo/Turku, Finland

The industrial processes involved in the production of formic acid were reviewed with emphasis on the hydrolysis of methyl formate. The liquid-phase hydrolysis of methyl formate in the absence and presence of an additive (a complexing agent) was studied in a laboratory-scale batch reactor. The effects of the reaction parameters such as stirring rate, excess water, the additive, and temperature were investigated too. A kinetic model that includes the mass balances and rate equations was developed for the system by assuming a quasiequilibrium hypothesis for the reaction involving the additive. The proposed model with a degree of explanation exceeding 95% was able to predict the experimental concentrations of methyl formate, methanol, the additive, and the additive-formic acid complex. 1. Introduction Formic acid (methanoic acid, HCOOH) is an alkyl carboxylic acid in which the carboxylic group is linked to a lone hydrogen atom rather than an alkyl group (like other carboxylic acids). Thus, it has an exceptionally high acidity (pKa ) 3.74), and its structure resembles those of an acid and an aldehyde.1 The biggest market of formic acid in Europe is in the agricultural sector as a silage additive. It is also used as an antisalmonella additive in animal feeds, for decontamination of feed raw materials, and for the prevention of flock infection in the poultry industry by treatment of the finished feed.2 Outside the agricultural area, the major applications include leather tanning, textile dyeing and finishing, carpet printing, chemical synthesis and pharmaceuticals, formate salts, rubber chemicals (antiozonants and coagulants), catalysts, plasticizers, fuel cell (DFAFC), and regulation of the pH of chemical processes.2-4 The world consumption of formic acid was approximately 437 000 t in 2003. Between 2000 and 2003, the world capacity for formic acid remained relatively unchanged, while world consumption grew at an average annual rate of 2%. However, it was estimated that the average annual growth rate of formic acid demand in feed additives was between 8% and 10%, when the European Union’s ban on the use of OTC (over the counter) feed antibiotics took effect in 2006.5 Formic acid is currently produced in the chemical industry by four main processes:2 preparation of free formic acid from formate salts, oxidation of hydrocarbons, hydrolysis of formamide, and methyl formate hydrolysis. Acidolysis of formate salts is the oldest industrial process for producing formic acid. For instance, aldolization reactions carried out in the presence of strong alkali yield formates as stoichiometric coproducts. The reaction between the formate salts and mineral acids such as sulfuric acid produces formic acid and a salt. The reaction is technically straightforward, but the inevitable production of the salt is a clear disadvantage of this route. For many years, a large amount of formic acid utilized was obtained as a byproduct of acetic acid produced by the oxidation of hydrocarbons. This process is complex, and the amount of formic acid produced is very small compared to the effort devoted to the process. The production of formic acid by * To whom correspondence should be addressed. Tel.: +358 2 2154427. Fax: +358 2 2154479. E-mail: [email protected].

hydrolysis of formamide played a significant role in Europe: in 1972, about one-third of the world production was obtained by this process. The disadvantages of the formamide route are the consumption of ammonia and sulfuric acid in other processes, along with the unavoidable coproduction of ammonium sulfate. Thus, the economic and environmental drawbacks of the first three processes led to the development of a process specifically dedicated to the production of formic acid, with no undesirable byproduct. In the 1970s, various enterprises developed commercially the hydrolysis of methyl formate to methanol and formic acid into an economically feasible method. Most of the formic acid plants started in recent years employ this principle of methyl formate hydrolysis.3 The production of formic acid by hydrolysis of methyl formate (methyl methanoate, HCOOCH3) consists of carbonylation of methanol and hydrolysis of the methyl formate produced. Methanol resulting from this process is fed back to the first stage. The two stages involved are represented with chemical equations and their heat of reactions below CH3OH + CO f HCOOCH3

∆HR° ) -29 kJ/mol

HCOOCH3 + H2O a CH3OH + HCOOH ∆HR° ) +16.3 kJ/mol Carbonylation of methanol in the presence of basic catalyst (sodium methoxide or potassium methoxide) is relatively problem free and has been carried out industrially for a long time. However, hydrolysis of methyl formate is demanding technologically. First, the hydrolysis is a reversible reaction with a low equilibrium constant value. So, the equilibrium is relatively unfavorable,6 but it is dependent on the water concentration in a way that favors the use of high excesses of water, with consequent problems of finding an energy-efficient method of removing the excess water. Furthermore, methyl formate is highly volatile (bp 31.5 °C) and formic acid is a sufficiently strong acid to catalyze the re-esterification. It is therefore difficult to remove unreacted methyl formate without a significant amount of re-esterification.2 Earlier publications suggest the reaction of methyl formate and a dicarboxylic acid and then distillation of formic acid from the higher-boiling esters.7 Cho et al.8 proposed the use of a continuous chromatographic reactor, which simultaneously

10.1021/ie101045k  2011 American Chemical Society Published on Web 11/24/2010

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effected the chemical reaction and separation process. Leonard9 suggested methyl formate hydrolysis at high temperature and pressure, with subsequent reduction in pressure suddenly below 1 bar. Separation of the methyl formate-methanol mixture from the aqueous formic acid is then effected in a liquid evaporator. A great disadvantage of the methyl formate route is the formation of aqueous formic acid as a result of the hydrolysis step. Formic acid-water mixture cannot be concentrated to more than the azeotropic composition by simple distillation (the bp of formic acid is 100.7 °C). Therefore, dehydration of formic acid is an important step in the production of formic acid from methyl formate. The concentration of formic acid in the azeotropic mixture increases as distillation is carried out under pressure: at 1 bar, the formic acid content is 77.6 wt %, and the boiling point of the azeotropic mixture is 107.6 °C; however, at 3.14 bar, the formic acid content increases to 85 wt %, while the boiling point of the azeotropic mixture is 144 °C.10,11 However, the higher boiling point at high pressure also increases the decomposition rate of formic acid. Lynn et al.12 proposed the use of a number of entrainers for the azeotropic distillation. A process involving extractive distillation with N-formylmorpholine was described by Buelow et al.13 Formic acid can also be recovered by liquid-liquid extraction using secondary amides as extractive agents since formic acid binds weakly to the amide;14 thus, water can be distilled to overcome the azeotropic point. Considerable research efforts have been made and still continue on how to optimize the process development to favor higher conversions of methyl formate with lower energy costs. Several publications are available for the hydrolysis of esters in acidic and basic media by using different approaches.15-19 However, very few investigations have been published concerning the hydrolysis of methyl formate because a large part of the literature available exists in the form of patents.9,12-14,20 Some of these publications described the hydrolysis of methyl formate in acidic and basic media.6,21-23 Begum et al.24 studied the hydrolysis kinetics of methyl formate in a neutral medium. Zhi-feng et al.25 described the technology of preparing formic acid by hydrolysis of methyl formate, while Jenner26 published a review on homogeneous catalytic reactions involving methyl formate. The detailed kinetic and reactor modeling of reversible autocatalytic hydrolysis of liquid-phase alkyl formate, i.e., ethyl formate and methyl formate, was studied by our group.27 The purpose of this work is to overcome the unfavorable equilibrium position by hydrolyzing methyl formate in the presence of a suitable complexing agent. The complexing agent is an organic base, butyl imidazole.20 The scope of this work is to determine the reaction kinetics and equilibrium in a wider domain of reaction conditions, develop a mechanistic model for the reaction system, and estimate the parameters to enable its use for the optimization of the hydrolysis reaction. The influences of reaction parameters such as the additive, excess water, stirring rate, and temperature on the reaction kinetics were investigated too. 2. Experimental Section 2.1. Materials. Methyl formate, 97%; formic acid, 99.5%; methanol, >99%; acetonitrile >99%; distilled water; the additive X, 98.87; and nitrogen gas were used. Nitrogen was used as a shielding gas to protect the solution from atmospheric contamination. 2.2. Experimental Setup and Procedure. The hydrolysis reaction is carried out in a conventional 500 mL Parr autoclave, made of zirconium metal, at constant temperature and pressure. The reactor consists of feeding and reaction vessels, a heating

Table 1. Experimental Details temperature

molar ratios

expt.

(°C)

X/ MeFo

G001 G002 F001 F002 F003 F004 F005 F006 E001 E002 E003 E004 E005 H001 H002 I001 H002 B001 B002 B003 B004

80 80 90 90 90 90 90 90 100 100 100 100 100 110 110 110 110 90 90 90 90

0.00 0.60 0.00 0.20 0.40 0.60 0.75 1.00 0.00 0.20 0.40 0.60 0.75 0.00 0.60 0.60 0.60 0.41 0.41 0.41 0.41

C0A

H2O/ MeFo

FA/ MeFo

MeOH/ MeFo

(mol/kg)

1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.5 2.0 2.5 3.0

0.112 0.112 0.112 0.112 0.112 0.112 0.112 0.112 0.112 0.112 0.112 0.112 0.112 0.112 0.112 0.000 0.000 0.112 0.112 0.112 0.112

0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104 0.104a 0.104 0.104 0.104 0.104

9.91 5.71 9.91 7.94 6.62 5.71 5.14 4.40 9.91 7.94 6.62 5.71 5.17 9.91 5.71 5.90 5.90 6.81 6.51 6.12 5.76

a Indicates that the experiment was conducted at a stirring speed of 300 rpm instead of 1200 rpm that was used for the rest of the experiments.

unit, a stirrer, and a sampling line. The sampling line includes a cooling bath and a filter. Two thermocouples and cooling air are used for temperature control. Table 1 displays the experimental matrix. A known amount of formic acid, water, and additive X was fed into the reactor vessel. Methanol and precooled methyl formate were discharged into the feeding vessel. A nitrogen line to the reactor and the vent lines were connected to the system. The chemicals were used as received from the manufacturers. The initial total amount of the liquid mixture was about 300 g. The heating system and the stirrer were turned on. When the temperature reached the desired value, the mixture in the feeding vessel was charged into the reactor vessel using overpressure (20 bar), and the reaction commenced. Samples were taken in defined sample intervals (5, 10, 15, or 20 min) using reactor system pressure. The samples were analyzed during the course of the experiment to ascertain when equilibrium was reached. The reaction is stopped after equilibrium is attained. 2.3. Gas Chromatography Analysis. The calibration was done using acetonitrile as the internal standard. The samples were analyzed off-line using a gas chromatograph: Agilent 6890, injection port temperature 150 °C, oven temperature 40 °C, column DB-5 (capillary), 60 m × 320 µm × 0.5 µm, carrier gas helium (15 mL/min at 1 min), detector FID (280 °C, H2 flow 40 mL/min, air flow 450 mL/min). The analysis time for the sample was between 4 and 5 min. The calibration solution is always done before the analysis of the samples. The experimental results were based on methanol analysis due to the volatility of methyl formate and the difficulty in getting a reliable analysis method for formic acid. 3. Mathematical Modeling of the Hydrolysis Process in the Presence Of an Additive Methyl formate hydrolysis in the presence of a complexing agent can be regarded as a two-step process. In the first step, a slower water-catalyzed hydrolysis process is the dominating kinetic step. Methanol and formic acid are being produced. As the reaction proceeds and more H+ is released from the dissociation of formic acid, a faster complexation step takes precedence over the hydrolysis step.

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269

K2CCCXR

(2)

CCX )

Differentiating eq 2 with respect to time t (R is constant) gives

(

)

dCCX dCC dCX + RCXR-1 C ) K2 CXR dt dt dt C

The complexing agent due to its nucleophilic nature, i.e., the presence of a lone pair of electron on the pyridine-like nitrogen atom, abstracts proton from the acid forming an ionic liquidlike complex (ion pair) called n-butyl imidazolium formate. As more H+ accumulates, the complexation step, i.e., abstraction of free formic acid from the solution, enhances the equilibrium conversion of methyl formate. The complexation step is de facto a neutralization step. However, it is important to know that the pH of the solution decreases as the reaction progresses due to the formation of formic acid. The acid can be recovered from the additive by simple distillation. 3.1. Stoichiometry and Rate Equation. Several variations of kinetic models were tried in this work but the best model was chosen and will be discussed in details. In the present case, we consider the hydrolysis of methyl formate in the presence of an additive, i.e. a complexing agent (X). The additive does not react with the reactants but with the desired product C, thus shifting the equilibrium to the side of the products. The reactions involved are denoted as follows where A ) methyl formate, B

) water, C ) formic acid, D ) methanol, X ) additive, and CX ) the product-additive complex (adduct). In the mathematical modeling, we assume that the system can be treated as a pure liquid-phase system, and the role of the gas phase, including the volatilization of the components can be ignored since vaporization was prevented by carrying out the reaction under pressure and the gas volume was very small compared to the liquid volume in the reactor. Also, the hydrolysis reaction is autocatalyzed without the additive since the formic acid formed in the hydrolysis reaction catalyzes the hydrolysis reaction. The velocity of the process is expressed by

(

r1 ) f CACB -

1 C C K1 C D

)

(1)

where f is a kinetic factor that includes catalyzed and noncatalyzed contributions. For instance, the noncatalyzed contribution is described by a rate constant (k), while the catalytic contribution is typically expressed by the product of the rate constant (k′) and the catalyst concentration (Ccat): k′Ccat. The stoichiometric coefficient of X in the reaction is in general not unity but represented by a general coefficient R. In sequel, we assume that the second reaction is fast, and thus quasi-equilibrium hypothesis can be applied to it. The concentration of CX, which unfortunately cannot be determined from chemical analysis, can thus be obtained by using the concept of quasi-equilibrium

(3)

3.2. Batch Reactor with Quasi-Equilibrium and Kinetic Steps. An isothermal batch reactor model was applied. The results of the modeling are summarized in Table 2, and the details of the model derivation are given in Appendix A. The hydrolysis reaction is temperature dependent. The following temperature dependencies were assumed for the rate and equilibrium constants k ) k0e-Ea/RT

(4)

Keq ) K0eqe-Eq/RT

(5)

where Keq ) equilibrium constant and Eq ) activation parameter of the equilibrium. To suppress the mutual correlation of the pre-exponential factors and the activation energies in parameter estimation, a transformed temperature (z) was introduced, and eq 4 becomes k ) k0e-Eaz/R

(6)

j (T j is a reference temperature (in Kelvin), where z ) 1/T -1/T chosen to be close to the average temperature of the experiments, and T is the temperature of the set point), and eq 5 obtains the forms for the actual reactions Keq1 ) K0eq1e-Eq1z/R

(7a)

Keq2 ) K0eq2e-Eq2z/R

(7b)

where Keq1 ) K1 and Keq2 ) K2 in the sequel. The hydrolysis rate is obtained from eq 1. The autocatalytic effect of the reaction product (formic acid) and the effect of the additive (X) were taken into consideration in the kinetic factor, f f ) k + k'CC + k''CX However, in the parameter estimation, k′ tended toward zero, so it is neglected in the above equation. Thus, the equation reduced to f ) k + k″CX

(8)

Inserting the temperature dependence, eq 6 into eq 8 gives ′′

f ) k0e-Eaz/R + k′′0e-Eaz/RCX which is rewritten as

[

f ) k0e-Eaz/R 1 +

( )

k″0 -Ea e k0

E″a

Ea

-1 z/R

]

CX

For the sake of simplicity, let B ) k0′′/k0 and EB ) E′′/E a a.

(9)

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Table 2. Summary of the Mathematical Modeling concentration of components (mol/kg)

rate equation (kg min/mol)

CA

dCA ) -r1 dt

CB ) CA - COA + COB

dCB ) -r1 dt

CC )

( [

β - CA 1+

dCC R2K2(β - CA)CXR-1 ) 1- 1+ dt (1 + K2CXR )2

K2CXR

where β ) COA + COC + COCX CD ) COA - CA + COD

dCD ) r1 dt

CX

dCX R2K2(β - CA)CXR-1 )- 1+ dt (1 + K2CXR )2

CCX )

[ [

(β - CA)K2CXR

dCCX R2K2(β - CA)CXR-1 ) 1+ dt (1 + K2CXR )2

1 + K2CXR

(

Reaction rate

r1 ) f CACB where

[

1 C C K1 C D

f ) k0e-Eaz/R 1 +

Finally, inserting this expression of f, eq 1 gets the form

[

CCCD r1 ) k0e-Eaz/R[1 + Be[-Ea(EB-1)z]/RCX] CACB K1

]

1 + K2CXR

RK2CXR

) )

1 + K2CXR

-1

K2CXR

1 + K2CXR

))

r1

r1

r1

E′′a Ea

-1 z/R

CX

]

n

Q(f) )

∑ [(y

i

- yˆi)2]

(12)

i)1

(10)

The initial composition of the liquid was known, which gives the initial condition for the equation mass balances. The concentrations (mol/kg) were obtained from Ci ) ni/mL, where ni is the number of moles of the component and mL is the mass of the liquid mixture. The concentrations CB, CC, CCX, and CD were calculated from the equations collected in Table 2. 3.3. Parameter Estimation Procedure. The mathematical model used in this work consists of ordinary differential equations (ODEs) (see Table 2). A vector of the ODEs can be written as follows dC _ ) f(C _ , t) dt

]( ]( -1

K2CXR

)

( )

k′′0 -Ea e k0

]( -1

(11)

which is solved with the initial condition known, i.e., concentrations C ) C0 at t ) 0. The ODE systems arising from chemical kinetics are often stiff because some of the reaction steps are rather slow, while others are very rapid, approaching equilibrium. Thus, a stable algorithm is used. In our work, we used MODEST software.28 In the software, the ODEs are solved by linear multistep methods implemented in ODESSA, which is based on the LSODE software.29 Different optimization algorithms can be used to find the correct value of the parameters. This is usually done by leastsquares optimization, where the objective function to be minimized is defined as

where yi is the experimental value of component i in the mixture and yˆi is the corresponding model prediction. In the present work, yi and yˆi represent the experimental and predicted concentrations of methanol. The concentrations were solved numerically from eq 11 during the minimization of the objective function, eq 12. The minimization was carried out with a hybrid simplex-Levenberg-Marquardt algorithm implemented in MODEST. The extent or degree of explanation R2 of the kinetic model is defined as follows R )12

∑ (y ∑ (y

i

- yˆi)2

i

- jyi)2

(13)

where jyi is the mean value of the observations. 4. Physical Properties and Qualitative Kinetic Results 4.1. Vapor Pressure and Volatilization. The influence of the gas phase on the system was taken into consideration due to the volatility of methyl formate. The gas volume of the system was minimized. The validity of the hypothesis that the effect of the gas phase can be discarded in the mathematical treatment was checked by calculating the vapor pressure of the feed and vapor compositions using the liquid phase activity coefficient method, NRTL, in ASPEN Plus software. The vapor pressures of the pure components of the liquid mixture at different temperature were calculated by using the modified Antoine equation.30

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log10 P ) A' +

B' + C' log10 T + D'T + ET2 T

(14)

271

Table 3. Vapor Pressures of the Pure Components of the Liquid Mixture vapor pressure (bar)

where P is the vapor pressure (torr). A′, B′, C′, D′, and E are empirical constants whose values are listed in the Appendix as Table B1. The calculated values of the vapor pressure of the pure components of the hydrolysis mixture at the experimental temperatures are collected in Table 3. The compositions of the feed and product streams (calculated as a flash with Aspen plus) are listed in Table 4. The role of the gas phase can be estimated from these data. The initial total load in the reactor was about 300 g. At 110 °C, the estimated liquid density is 0.87 kg/L, which gives a liquid volume of 345 mL. The volume of the impeller, sampling system, and other accessories is around 55 mL. Thus, the estimated gas volume, VG ) 500 mL - 345 mL - 55 mL ) 100 mL. The estimated feed vapor pressure is 4.14 bar (Table 4), and the methyl formate mole fraction is 0.313 (Table 4). Thus, the partial pressure of methyl formate is 0.313 × 4.14 bar ) 1.30 bar. From the ideal gas law, we then obtain the amount of methyl formate in the gas phase: nA ) PAVA/RT ) 4.08 mmol. The initial amount of methyl formate was 1.5 mol. Thus, only (4.08 × 10-3/1.5) × 100% ) 0.27% of methyl formate was in the gas phase. The other components are less volatile, and their roles in the gas phase are minor. 4.2. Density. The density of the reaction mixture is expected to vary with temperature and liquid-phase composition. The temperature dependence of the density of each individual component of the reaction mixture was described by Yaws.30

[

FL ) A''B''-

1 -

T TC

]

n

(15)

Tabulated values of A′′, B′′, n, and TC are given as Table B2 in the Appendix. The density of the additive (X) was obtained at different temperatures with the aid of a pycnometer. The densities of the pure components of the mixture at the reaction temperatures are listed in Table 5. The reaction mixture density was calculated based on the assumption of an ideal mixture with constant partial molar volumes, and the contribution of the adduct (CX) formed between formic acid and the additive was ignored. The density of the mixture was calculated directly from the pure component densities as follows Fmix )

[

wH2O wFA wMeOH wX wMeFo + + + + FMeFo FH2O FFA FMeOH FX

]

-1

(16)

The calculated mixture density showed very little changes during the course of the reaction; hence, an average density was taken for each reaction temperature. The average density decreases linearly as the temperature increases. Thus, the density was 0.91-0.87 kg/dm3 from 80 to 110 °C. 4.3. Effect of the Reaction Parameters. Several experiments were carried out to study the effects of reaction parameters, such as temperature, stirring rate, the additive, and excess water on the reaction kinetics and equilibria. 4.3.1. Effect of Stirring Speed. Two experiments were performed at a minimum stirring speed of 300 and 1200 rpm. The experiment indicated that 300 rpm was enough for the reaction. 4.3.2. Effect of Excess Water. The presence of excess water improves the yield of formic acid in the hydrolysis of methyl formate without the presence of any additive. This is, of course,

compound

80 °C

90 °C

100 °C

110 °C

formic acid methanol methyl formate water

0.52 1.80 4.67 0.47

0.73 2.55 6.07 0.71

1.0 3.53 7.74 1.0

1.33 4.79 9.73 1.43

Table 4. Equilibrium Pressures and Gas Phase Compositions (NRTL Method) feed stream temperature (°C) pressure (bar)

80 1.94

90 2.52

110 4.14

125 5.87

80 2.03

90 2.66

110 4.43

125 6.32

product stream temperature (°C) pressure (bar) component

feed stream mole fraction

product stream mole fraction

H2O MeOH MeFo FA X

0.533 0.031 0.313 0.027 0.095

0.353 0.212 0.133 0.207 0.095

Table 5. Densities of Pure Components of the Mixture at 80-110°C temperature

MeFo

H2O

FA

MeOH

X (pycnometer)

(°C)

kg/L

kg/L

kg/L

kg/L

kg/L

80 90 100 110

0.8800 0.8625 0.8443 0.8254

0.9755 0.9656 0.9556 0.9454

1.1433 1.1297 1.1157 1.1013

0.7333 0.7225 0.7113 0.6996

0.9005 0.8925 0.8845 0.8765

true also in the presence of a suitable additive. According to the principle of Le Chatelier, increasing the concentration of one of the reactants in a reversible reaction shifts the equilibrium in favor of the forward reaction. It was possible to monitor the effect of excess water on the reaction kinetics by varying the water/MeFo molar ratio from 1.5 to 3.0. The value of the equilibrium conversion was obtained by taking the average of the experimental conversions when the reaction had attained the equilibrium. The increment is the difference between the succeeding and preceding values of the conversion at equilibrium. The result demonstrating the effect of excess water is illustrated in Figure 1. It can be deduced from Figure 1 that the equilibrium conversion increases as the water/MeFo molar ratio increases, but the increment decreases as the water/MeFo molar ratio increases. For example, the equilibrium conversions for the water/MeFo molar ratios of 1.5, 2.0, 2.5, and 3.0 are 0.56, 0.64, 0.68, and 0.70, respectively. Thus, the increments are 0.08 (0.64 - 0.56); 0.04 (0.68 - 0.64); and 0.02 (0.70 - 0.68). So, it is

Figure 1. Effect of excess water on the reaction kinetics and equilibrium conversion at 90 °C; X/A molar ratio ) 0.4.

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Table 6. Influence of Additive X on the Equilibrium Conversion of Methyl Formate at 90°Ca

a

X/MeFo molar ratio

equilibrium conversion (mol %)

increment

0.00 0.20 0.40 0.60 0.75 1.00

0.30 0.49 0.61 0.66 0.69 0.71

0.00 0.19 0.12 0.05 0.03 0.02

H2O/MeFo ) 1.8.

not economically viable to increase the amount of water just to get a minor change in the conversion because of the cost of separating formic acid from water. Therefore, there should be a point of process optimization in terms of capacity and energy requirement in water removal. Therefore, the water-to-MeFo molar ratio should be between 1.5 and 2.0. 4.3.3. Effect of the Additive. The molar ratio of the additive X to that of MeFo was varied from 0.0 to 1.0. The influence of the additive in the hydrolysis of methyl formate is very pronounced, as demonstrated by Table 6. As the X/MeFo molar ratio increases, the equilibrium conversion also increases. However, the cumulative effect decreases as the molar ratio increases. It can be deduced that the addition of the additive (X) to the reaction mixture improved the equilibrium conversion considerably while using a smaller amount of excess water. The additive forms a not too strong adduct (X-HCOOH) with formic acid and in the process shifts the hydrolysis reaction in favor of the products. Then, the formic acid can be removed from the additive by simple distillation. Furthermore, the additive also increases the rate of the reaction as the X/MeFo molar ratio increases since the probability of more reactant collisions increases. The pH of the solution decreases as the reaction progresses due to the formic acid

formed and remains virtually constant at equilibrium. For example, at molar ratios of X/MeFo ) 0.6 and H2O/MeFo ) 1.8, the pH at the beginning and end of the reactions is 6.64 and 5.20, respectively. 5. Kinetic Modeling Results 5.1. Parameter Values. The model fit to the experimental data was achieved with MODEST software using a combined Simplex-Levenberg-Marquardt method. The differential equations describing the mass balances of the organic components were solved by the backward difference method during parameter estimation. Several modifications of the ionic model were tried, but the model version with the best fit was selected (Table 2). The kinetic model was fitted to all the experimental data (experiments with different temperatures and additive-to-methyl formate molar ratios), and the model was able to predict well the experimental behavior with an almost 96% degree of explanation. Different activation energies were used for the rate and equilibrium constants because an attempt to give the same approximate value for them gave an unsatisfactory result in the parameter estimation. The parameter estimation was carried out by calculating the value of the objective function several times with different values of the rate and equilibrium constants. Also, in the model, when R (stoichiometric coefficient of additive X) was fixed at 1.5, the model gave less satisfactory results. However, when R was allowed to vary between 0 and 10, the model was satisfactory with an objective function value of 1.33 and an R value of about 0.54. This indicates that the stoichiometric of the additive X in the reaction is not 1. An average temperature of 95 °C was used for the model. The values of the estimated parameters are collected in Table 7.

Figure 2. Comparison of simulated model and experimental values (a) at 80 °C, molar ratio of X/A ) 0.6, and (b) at 90 °C, molar ratio of X/A ) 0.2.

Figure 3. Comparison of simulated model and experimental values at 100 °C with (a) molar ratio of X/A ) 0.4 and (b) molar ratio of X/A ) 0.75.

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273

a

Table 7. Parameter Estimation Results: Global Parameters

Eq1

Eq2

Ea

parameters

k0

B

K1

K2

(kJ/mol)

(kJ/mol)

(kJ/mol)

EB

R

value standard deviation (%)

0.22 5.5

0.58 10.4

0.18 4.5

875 53.2

7.9 62.9

88.3 43.8

81.4 7.1

0.68 18.2

0.54 5.9

a

The parameters are explained by eqs 7a-10 and Table 2.

Figure 4. Sensitivity analysis of fairly identified parameters: (a) k0 and well-identified parameters: (b) Ea, (c) Eq1, and (d) R.

The rate constants for the noncatalyzed k0 and the additiveenhanced k0′′ steps are 0.22 kg/mol min and 0.13 kg2/mol2 min, respectively (B ) k0′′/k0), while the activation energies for the noncatalytic and the additive-enhanced steps are 81.4 and 55.4 kJ/mol, respectively (EB ) E′′/E a a). According to the model, the addition of the complexing agent into the hydrolysis mixture lowered the activation energy by 26 kJ/mol, while the reaction enthalpy of the hydrolysis process in the absence of the complexing agent is consistent with the earlier value reported by our group27 and from the literature.31 Furthermore, from the value of the equilibrium constant for the complexation step, it can be deduced that the products are strongly favored. 5.2. Fit of the Model. The fit of the model for some experiments (molar ratio of B/A ) 1.8) is presented in graphical form in Figures 2 and 3. The difference between the simulated and experimental values was minor, when the hydrolysis process took place in the absence of the complexing agent, and as the temperature increases, the model fit improved slightly. The rate of the hydrolysis reaction increases with increasing temperature but

has no pronounced influence on the equilibrium conversion. This can be explained by the weak temperature dependence of the equilibrium constant, i.e., the low value of the reaction enthalpy (∆H ) +7.7 kJ/mol).31 At a temperature of 80 °C, it took more than 3.5 h to reach the equilibrium, whereas the reaction attained the equilibrium in less than an hour at 110 °C. However, equilibrium conversion was approximately the same. The reaction cannot be performed at a very high temperature because it might affect the decomposition of formic acid and increases the volatility of the methyl formate. According to the model predictions, formic acid (C) is in most cases captured by the additive (X), and the complex (CX) is formed quantitatively. However, for the ratio X:MeFo ) 0.2, some free formic acid is left in the solution at 90 °C as depicted by Figure 2. This is due to the fact that the additive is not enough to complex all the formic acid produced. However, as more additive is added especially at lower temperatures (80 and 90 °C), almost all the formic acid is taken up. Also, at higher experimental temperatures (100 and 110 °C), some free formic acid is visible according to the model (Figure 3) even when

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Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011

there is enough additive (molar ratio of X/MeFo ) 0.75 at 100 °C) to complex them. Therefore, from the model results, X/MeFo ) 0.6 at 100 °C is enough to complex the formic acid. This statement is also supported by the experimental data in Table 6. Furthermore, the initial S-shape of the methanol concentration curve is not always very well predicted by the model. A reason might be that the autocatalytic effect of the formic acid was neglected in the final version of the model. Minor temperature fluctuation cannot explain the S-shape. 5.3. Sensitivity Plots. The sensitivity of the objective function with respect to the kinetic parameters was investigated by calculating the objective function as a function of one of the parameters, while keeping the other parameters at the values of the objective function minimum. The objective functions as a function of parameters k0, Ea, Eq1, and R (Table 7) are plotted in Figure 4. It can be seen that the objective function has sharp minima in Figure 4b-d which implies that the corresponding parameter is well-defined. 5.4. Role of the Complexing Agent. In the absence of the complexing agent, high excesses of water are required to achieve a desirable methyl formate conversion, but with the complexing agent, little excess water (molar ratio of H2O/MeFo ) 1.8) is needed to get a better result. Therefore, reducing the energy cost of the water removal and minimizing corrosion-related problems, the use of a complexing agent is favorable. The complexing agent by capturing the free formic acid prevents the re-esterification of the reaction products, thus unreacted methyl formate can be removed from the process. The optimum amount of the complexing agent required to obtain a good conversion and achieve a reasonable complexation of the acid product according to the experimental data and model fit is moderate (molar ratio of X-to-ester ) 0.6). Even smaller amounts can be used. The significance of the complexing agent in the hydrolysis process, apart from improving the formic acid yield, is that it also eliminates the formation of an azeotropic mixture between water and formic acid. Furthermore, there is no byproduct in the process, and the complexing agent, X, can be recovered and recycled. However, the choice of a suitable complexing agent is very vital to the hydrolysis process. Thus, a very weak complexing agent is incapable of shifting the equilibrium, while a too strong agent will form a stronger adduct with the formic acid product, therefore making it difficult for the formic acid to be separated easily from the adduct. Thus, the advantage of n-butyl imidazole is that it formed a salt-like bond with formic acid which can be easily removed by simple distillation without any decomposition. 6. Conclusions Kinetics and thermodynamics of the hydrolysis of an ester in the presence of an additive were accomplished with an advanced model involving the description of slow ester hydrolysis and rapid complexation of the product with an additive (X). Different activation energies were assumed for the equilibrium and rate constants, the values of which were estimated with regression analysis. The main advantage of the kinetic model applied is that it is based on the analytical data of one of the components, the alcohol formed only. The concentrations of the other components, including the additive (X) and its adduct (CX) with the carboxylic acid, are predicted by the model. The fit of the model to the experimental data was very acceptable; the parameters were well identified; and the standard

errors were reasonable. The effects of reaction parameters on the reaction kinetics were investigated, too. It turned out that the additive is an effective complexing agent; the methyl formate conversion can be shifted from 0.2 (in the absence of the complexing agent, X) to as high as 0.7 with the aid of X. The agent can be separated from the formic acid by distillation. Process intensification is accomplished in two aspects: the equilibrium is shifted favorably, and the use of a large excess of water is avoided. This leads to smaller process equipment (reactor) and saved energy costs in the separation stages. Finally, the kinetic models proposed can be used for process design and simulation. Acknowledgment This work is part of the activities of the Åbo Akademi Process Chemistry Centre (PCC) within the Finnish Centre of Excellence Programme (2006-2011) by the Academy of Finland. Notation C ) concentration, mol/kg C ) concentration vector Ea ) activation energy of the noncatalyzed step, kJ/mol Ea′′ ) activation energy of the additive-enhanced step, kJ/mol Eq1 ) activation parameter of the equilibrium for the noncatalyzed step, kJ/mol Eq2 ) activation parameter of the equilibrium for the additive enhanced step, kJ/mol f ) rate function H ) enthalpy, kJ/mol k ) rate constant for the noncatalyzed step, kg/mol min k′ ) rate constant for autocatalyzed step, kg2/mol2 min k′′ ) rate constant for the additive-enhanced step, kg2/mol2 min K1 ) equilibrium constant for the noncatalyzed step K2 ) equilibrium constant for the additive-enhanced step KC ) concentration-based equilibrium constant m ) mass, kg n ) number of moles, mol P ) vapor pressure, torr PA ) partial pressure of methyl formate, bar pH ) power of hydrogen pKa ) acid dissociation constant Q ) objective function R ) gas constant, J/mol K R2 ) degree of explanation r ) reaction rate, mol/kg min T ) temperature; set point temperature, K t ) time, min V ) volume, mL w ) weight fraction z ) transformed temperature, K-1 R ) stoichiometric coefficient of the additive ∆ ) change ∑ ) summation F ) density, kg/L - ) average Subscripts and Superscripts cat ) catalyst eq ) equilibrium G ) gas i ) component index L ) liquid mixture R ) reaction

Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011

CA - C0A ) CB - C0B ) -(CD - C0D)

° ) standard state 0 ) initial value

Furthermore, stoichiometry gives the relation

AbbreViation ACN ) acetonitrile bp ) boiling point CX ) adduct (complex formed between formic acid and additive) DFAFC ) direct formic acid fuel cell FA (C)) formic acid FID ) flame ionization detector GC ) gas chromatograph H2O (B) ) water LSODE ) Livermore solver for ordinary differential equations MeFo (A) ) methyl formate MeOH (D) ) methanol mix ) mixture NRTL ) non-random two liquid ODESSA ) ordinary differential equation solver with explicit simultaneous sensitivity analysis OTC ) over the counter rpm ) revolutions per minute X ) additive

Appendices A. Batch Reactor Mass Balances. The mass balances of the components in the batch reactor are expressed as

dCX dCCX ) -R dt dt which upon integrating gives CCX ) C0CX +

rA ) rB ) -r1

(A.1.1)

rC ) r 1 - r 2

(A.1.2)

rD ) r1

(A.1.3)

rX ) -Rr2

(A.1.4)

rCX ) r2

(A.1.5)

dCCX dCC dCA ) -r1, ) r2, ) r 1 - r2 dt dt dt imply that dCA dCC dCCX + )0 + dt dt dt

dCA dCD dCB )) dt dt dt

Integration of eq A.4 with the limits [C0i, Ci] gives CA - C0A + CCX - C0CX + CC - C0C ) 0 Recalling that CCX ) K2CCCXR (eq 2), we get CC(1 + K2CXR ) ) C0A - CA + C0C + C0CX ) 0

CC )

Thus, we get an expression for CC and CCX (taking eq 2 into consideration) CC )

D

E

27.9278 -2.60 × 10 -7.25 × 10 6.41 × 10 3.94 × 10-6 45.6171 -3.24 × 103 -1.40 × 101 6.64 × 10-3 -1.05 × 10-13 28.9576 -2.36 × 103 -7.48 × 100 -7.44 × 10-10 2.70 × 10-6

-10

2.42 × 10-9

CCX )

1 + K2CXR

(A.5)

(β - CA)K2CXR 1 + K2CXR

(A.6)

dCA d(CC + CCX) )dt dt De facto CC + CCX ) (1 + K2CXR )CC (CCX is obtained from eq 2) dCA d{(1 + K2CXR )CC} )) r1 dt dt

1.81 × 10-6

Table B2. Density Parameters of the Pure Components

formic acid methanol methyl formate water

β - CA

From eq A.4

0

29.8605 -3.15 × 103 -7.30 × 100

1 + K2CXR

CC(1 + K2CXR ) ) C0A + C0C + C0CX - CA ) β - CA, where β ) C0A + C0C + C0CX

Table B1. Empirical Constants for Vapor Pressure of the Pure Components C

C0A - CA + C0C + C0CX

We denote

(A.2)

Integrating eq A.2 with limits [C0i, Ci] gives B. Tables of Constants for Components.

3

(A.4)

and

From eqs A.1.1-A.1.5, we can directly conclude that

B

1 (C - CX) R 0X

The relations obtained from eqs A.1-A.1.5

(A.1)

where i ) A, B, C, D, X, and CX in the present case. The reaction scheme gives us

A

(A.3)

and finally

dCi ) ri dt

formic acid methanol methyl formate water

275

Differentiation gives

A

B

n

Tc

0.36821 0.27197 0.34143 0.3471

0.24296 0.27192 0.25838 0.274

0.23663 0.2331 0.2768 0.28571

580 512.58 487.2 647.13

(1 + K2CXR ) which gives

dCC dCX + RK2CCCXR-1 ) r1 dt dt

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Ind. Eng. Chem. Res., Vol. 50, No. 1, 2011

dCC r1 RK2CCCXR-1 dCX ) dt 1 + K2CXR 1 + K2CXR dt

(A.7)

Substituting CC (eq A.5) into eq A.7 gives dCC r1 RK2(β - CA)CXR-1 dCX ) dt dt 1 + K2CXR (1 + K2CXR )2

(A.8)

For the complex (CX), we have the stoichiometric relation (eq A.4) dCA dCC dCCX )dt dt dt which gives dCCX r1 RK2(β - CA)CXR-1 dCX ) r1 + dt dt 1 + K2CXR (1 + K2CXR )2 which on simplification gives dCCX K2CXR RK2(β - CA)CXR-1 dCX ) r + 1 dt dt 1 + K2CXR (1 + K2CXR )2

(A.9) Furthermore, eq A.3 is inserted into eq A.9, and (dCX)/(dt) is solved

[

dCX R2K2(β - CA)CXR-1 )- 1+ dt (1 + K2CXR )2 Equation A.3 gives dCCX/dt

[

dCCX R2K2(β - CA)CXR-1 ) 1+ dt (1 + K2CXR )2

](

RK2CXR

-1

](

1 + K2CXR

r1

(A.10)

K2CXR

-1

)

1 + K2CXR

)

r1

(A.11)

The time derivative of C is obtained from eq A.4, and the relation (dCA)/(dt) ) -r1 dCCX dCC ) r1 dt dt and finally we have

( [

dCC R2K2(β - CA)CXR-1 ) 1- 1+ dt (1 + K2CXR )2

]( -1

K2CXR

))

r1 1 + K2CXR (A.12)

In reality, the solution of the entire set of equations can be obtained just by solving the differential equations of the two key components, A and X, with the initial conditions CA ) C0A and CX ) C0X at t ) 0.

(3) Ullmann. Encyclopaedia of Industrial chemistry, 6th ed.; WileyHCH: Weinhein, 2003. (4) Aguilo, A.; Horlenko, T. Formic acid. Hydrocarbon Process. 1980, 59, 120. (5) Bizzari, S.; Yagi, K. Chemical Economics Handbook Report: Formic acid; SRI Consulting: USA, June 2004. (6) Schultz, R. F. Studies in ester hydrolysis equilibria: Formic acid esters. J. Am. Chem. Soc. 1939, 61 (6), 1443. (7) Ullmann. Encyclopaedia of Industrial chemistry, 4th ed.; WileyVCH: Weinhein, 1999. (8) Cho, B. K.; Robert, W.; Carr, Jr.; Aris, R. A continuous chromatographic reactor. Chem. Eng. Sci. 1980, 35, 74. (9) Leonard, J. B. Preparation of formic acid by hydrolysis of methyl formate. Eur. Patent 5998, Dec. 12, 1979. (10) Ito, T.; Yoshida, F. Vapour-liquid equilibria of water-lower fatty acids systems. J. Chem. Eng. Data 1963, 8, 315. (11) Gil’burd, M. M.; Moin, F. B.; Pazderskij, Yu. B.; Los, V. G. Calculation of azeotropic composition in the system water-formic acid at high pressure. J. Appl. Chem. USSR 1985, 59, 250. (12) Lynn, J. B.; Homberg, O. A.; Singleton, A. H. Formic acid synthesis by lower alkyl formate hydrolysis. U.S. Patent 3907884 to Bethlehem Steel Corp., Sept. 23, 1975. (13) Buelow, H.; Hohenschutz, H.; Schmidt, J. E.; Sachsze, W. Purification of formic acid by extractive distillation. U.S. Patent 4076594 to BASF, Feb. 28, 1978. (14) Hohenschutz, H.; Schmidt, J. E.; Kiefer, H. Preparation of formic acid. U.S. Patent 4218568 to BASF, Aug. 19, 1980. (15) Dash, A. C.; Mohanty, A. K. Reactions in micellar solutions. Indian J. Chem. 1989, 28A, 661. (16) Pradhan, G. C.; Nandra, R. K.; Dash, A. C. Kinetics of acid & base hydrolyses. Indian J. Chem. 1988, 27A, 905. (17) Bunton, C. A.; Hadwick, T. Tracer studies in ester hydrolysis. Part 9: phenyl and diphenylmethyl trifluoroacetate. J. Chem. Soc. 1961, 943. (18) Long, F. A.; Paul, M. A. Application of The H0 Acidity Function To Kinetics And Mechanisms Of Acid Catalysis. Chem. ReV. 1957, 57, 935. (19) Bell, R. P.; Dowding, A. L.; Noble, J. A. The kinetics of ester hydrolysis in concentrated aqueous acids. J. Chem. Soc. 1955, 9, 3106. (20) Anderson, J. J.; Hamlin, J. E. Process for the preparation of formic acid. Eur. patent 126 524B2 to BP Chem. Ltd., June 24, 1992. (21) Marlier, J. F.; Frey, T. G.; Mallory, J. A.; Cleland, W. W. Multiple isotope effect study of the acid-catalyzed hydrolysis of methyl formate. J. Org. Chem. 2005, 70, 1737. (22) Pranata, J. Ab initio study of the based-catalyzed hydrolysis of methyl formate. J. Phys. Chem. 1994, 98, 1180. (23) Marlier, J. F. Heavy-atom isotope effects on the alkaline hydrolysis of methyl formate. J. Am. Chem. Soc. 1993, 115, 5953. (24) Begum, S.; Zeb, M. A.; Pirzada, N. Hydrolysis of methyl formate in aqueous solutions and the evaluation of rate constants. J. Chem. Soc. Pak. 2000, 22 (4), 250. (25) Zhi-feng, L.; Liang, C.; Jiang-hong, Z.; Lin, S.; Zhi-li, F.; Xiangyu, L. Study on the technology of preparing formic acid by hydrolysis of methyl formate. Tianranqi Huagong 2002, 27 (3), 1 (translated from Chinese to English). (26) Jenner, G. Homogenous catalysis reactions involving methyl formate. Appl. Catal., A 1995, 121, 25. (27) Jogunola, O.; Salmi, T.; Era¨nen, K.; Wa¨rnå, J.; Kangas, M.; Mikkola, J.-P. Reversible autocatalytic hydrolysis of alkyl formate: kinetic and reactor modelling. Ind. Eng. Chem. Res. 2010, 49, 4099. (28) Haario, H. ModEst 6-A User’s Guide; ProfMath: Helsinki, 2007. (29) Hindmarsh, A. C. A Systematic Collection of ODE-Solver. In Scientific Computation; Stepleman, R., Eds.; IMACS: Amsterdam, 1983. (30) Yaw, C. L. Chemical properties handbook: physical, thermodynamics, enVironmental, transport, safety, and health related properties for organic and inorganic chemicals; McGraw-Hill: New York, 1999. (31) Lide, D. R. CRC Handbook of Chemistry and Physics, 85th ed.; CRC Press Inc.: Boca Raton, FL, 2004.

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ReceiVed for reView May 7, 2010 ReVised manuscript receiVed October 12, 2010 Accepted October 21, 2010 IE101045K