SYNTHESIS OF MALIC ACID ON MONTMORILLONITE K10: A

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Kinetics, Catalysis, and Reaction Engineering

SYNTHESIS OF MALIC ACID ON MONTMORILLONITE K10: A LANGMUIR-HINSHELWOOD KINETIC STUDY Annelorie Mattar Knesebeck, Ronald Wbeimar Pacheco Ortiz, Fernando Wypych, and Everton Fernando Zanoelo Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b00583 • Publication Date (Web): 13 May 2019 Downloaded from http://pubs.acs.org on May 13, 2019

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SYNTHESIS OF MALIC ACID ON MONTMORILLONITE K10: A LANGMUIRHINSHELWOOD KINETIC STUDY

Annelorie Mattar Knesebeck1, Ronald Wbeimar Pacheco Ortiz2, Fernando Wypych3, Everton Fernando Zanoelo1,2*

1Federal

University of Paraná, Graduate Program of Chemical Engineering, Polytechnic

Center, Jardim das Américas, 81531-980, Curitiba, PR, Brazil; 2Federal University of Paraná, Graduate Program of Food Engineering, Polytechnic Center, Jardim das Américas, 81531-990 Curitiba, PR, Brazil; 3Federal University of Paraná, Department of Chemistry, Polytechnic Center, Jardim das Américas, 81531-980, Curitiba, Paraná, Brazil.

ABSTRACT To accelerate the reaction of hydration of fumaric acid (F) to produce malic acid (M), Montmorillonite K10 (MK10) was tested as solid acid catalyst. The experiments were performed in a stirred pressurized batch reactor at a catalyst concentration of 4.7-9.4% (w:w), and temperatures of 448-493 K for times up to 36,000 s. The concentrations of F, M, and maleic acid (Mx) formed from a secondary isomerization reaction were determined at different reaction times by UPLC analysis. MK10 increased the final conversion of F of at least 20% without any observed decay of its catalytic activity for four cycles of use. A reliable catalytic model that assumes that the surface reactions of isomerization and hydration of F are the rate controlling steps was suggested. External mass transfer resistances and diffusional limitations were not important.

*

Corresponding author: Phone + 55 41 33613583, Fax: + 55 41 33613674, [email protected]


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KEYWORDS: fumaric acid; malic acid; hydration; isomerization; solid catalyst; rate expressions.

LIST OF SYMBOLS ac

external area of catalyst particles per unit of volume of liquid free of solids (m2 m3);

CF

concentration of fumaric acid (mol L1);

CF0

initial concentration of fumaric acid (mol L1);

CM

concentration of malic acid (mol L1);

CMx

concentration of maleic acid (mol L1);

DF

diffusivity of F in water (m2 s1);

D

mean surface diameter of the catalyst powder (m);

Eaj,/R ratio between the activation energy for the jth non-catalytic reaction and the gas constant (K1); Eaj,/R ratio between the activation energy for the jth catalytic reaction and the gas constant (K1); kc

particle-liquid mass transfer coefficient (m s1);

Ki

adsorption equilibrium constant for the ith species F, W, M or Mx (L mol1);

Ki,298 adsorption equilibrium constant for the ith species F, M or Mx at 298 K (L mol1); k1,

forward-rate constant of the reaction R1 in the absence of catalyst (s1);

k10,

preexponential factor of the Arrhenius equation for the forward-rate constant of the reaction R1 in the absence of catalyst (s1);

k2,

forward-rate constant of the reaction R2 in the absence of catalyst (L mol1 s1);

k20,

preexponential factor of the Arrhenius equation for the forward-rate constant of the reaction R2 in the absence of catalyst (L mol1 s1);


2


K1

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equilibrium constant for the homogeneous reaction R1 at a temperature T;

K1,298 equilibrium constant for the homogeneous reaction R1 at 298 K; K2

equilibrium constant for the homogeneous reaction R2 at a temperature T (L mol1);

K2,298 equilibrium constant for the homogeneous reaction R2 at 298 K (L mol1); kj,

forward-rate constant of the jth reaction in the presence of catalyst (mol m3 kg1 L1 s1);

kj0,

preexponential factor of the Arrhenius equation for the forward-rate constant of the jth reaction in the presence of catalyst (mol m3 kg1 L1 s1);

Re

Reynolds number defined by Equation (16);

rF,j

non-catalytic rate of consumption of F due to the jth reaction (mol L1 s1);

rF,j

catalytic rate of consumption of F due to the jth reaction (mol L1 s1);

(rF)k rate of consumption of F for a catalyst particle of radii Rk (mol L1 s1); Sc

Schmidt number (Sc=/DF);

Sh

Sherwood number (Sh=kcD/DF);

S

stirring speed (rpm);

t

reaction time (s);

T

reaction temperature (K);

XF

overall conversion of F

Greek Symbols

CF

difference between the bulk and the boundary surface concentration of F (mol L1);

Hi,298/R

ratio between the heat of adsorption for the ith specie F, W, M or Mx at 298 K

and the gas constant (K1);


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Hj,298/R

ratio between the heat of reaction for the jth reaction at 298 K and the gas

constant (K1);



relative difference between the initial mass of reactants and the one at the time the reaction was stopped (%);

m

arithmetic mean error in overall experimental mass balance (%);

k

Thiele modulus for a catalyst particle of radii Rk;

k

internal effectiveness factor for a catalyst particle of radii Rk;



kinematic viscosity of water (m2 s1);

b

bulk density of catalyst (kg m3);

c

catalyst density (kg m3);



stirrer energy dissipation rate per unit of mass of liquid (J s1 kg1).

INTRODUCTION Malic acid (M) is an organic acid mainly used as acidulant and flavor enhancer in the beverage industry,1-3 behind only citric acid in terms of market for food applications,4 but ahead of all organic acids in regard to the growth rate of demand that has been between 4 and 8% per year in the last two decades.5 It draws attention to the importance of this product, and to the few innovative way it has been produced commercially since the sixties.2 The commercial synthesis of M typically involves the hydration of maleic anhydride to form maleic acid (Mx), the isomerization of Mx to fumaric acid (F) (reaction R1), and the conversion of F into M (reaction R2). Such a set of simultaneous reactions is commonly carried out homogeneously at high temperatures (423 K) and pressures (1400 kPa) usually in the presence of mineral acids as catalysts (e.g.; hydrochloric acid, or sulfuric acid).2, 6-9 Due to the drastic reaction conditions, the cost of the reactor and the energy requirements are obviously not negligible.2 Moreover, the use of maleic anhydride as starting reactant, which is


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typically associated to skin, eye and respiratory irritations in humans,10,

11

is not only

dangerous for the health of the workers that manipulate it, but it also increases the costs of purified M that is believed to be free of such a toxic compound.

O HO

C

C

C

C

OH OH

O C C

O

O HO

C

C

C

C

+

H2O

HO

O

C

C OH

(R1)

OH

(R2)

C

O OH

O

OH C

C

C O

Some efforts to innovate the process of production of M via chemical route have been made. The use of a base, or an acid different of HCl as catalysts,8, 12 the study of the kinetics of formation of Mx that is an undesired product of the acid-catalyzed reaction of M production,13 the microwave-assisted synthesis of M with HCl as catalyst,9 the study of the influence of catalyst concentration (HCl) on the rate of production of M,9 and the employment of subcritical water (as reactant for the hydration of F) whose positive influence on the velocity of some synthesis reactions has been reported,14 are examples of investigations that have been conducted for this purpose. There are also some studies for the same reaction system by involving maleic acid as starting reactant,15 but the use of a solid catalyst with the objective of producing M from F has been rarely explored in literature.16 In this framework, the primary aim of such an investigation was to determine the kinetics of hydration of F to produce M, and of the unwanted side-reaction of isomerization of F to form Mx, by involving only F and water as starting reactants, and Montmorillonite K10 (MK10) as solid acid catalyst. The main reason to test currently MK10 is that clays, and in ACS Paragon Plus Environment

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general acid activated clays as the MK10 usually exhibit high surface acidity that increase particularly the rate of hydration reactions,17, 18 but also of isomerization ones.18 It is in general accepted that reactions like the ones currently investigated are typically catalyzed by acid solid catalysts due to the proton transfer from the Brønsted acid sites of the solid to the reactants.19-23 In the current case, it means to form protonated F that is rapidly converted to M and Mx. In other words, the rates observed of production of these products are expected to be limited by the step of protonation, that is, by the overall rates of chemical reaction over the catalyst surface instead of by the ones of chemical adsorption. It has been also reported that MK10 offers several other advantages over solid catalysts in general, such as thermal stability, high surface area, low cost, nontoxic and noncorrosive nature, and reusability.22,

23

Its

commercial availability, well-defined properties, and extensive application in organic reactions,22,

24

which avoid the time demanding steps of catalyst preparation and

characterization, are also elements that contributed positively to its selection.

MATERIALS AND METHODS Experiments The reactant species were F purchased from Neon (purity99%, São Paulo, Brazil), and Milli-Q water (Millipore, Bedford, USA). The catalyst was commercial MK10 from Sigma-Aldrich (CAS 1318-93-0, Lot STBF5340V, St. Louis, USA). From Sigma-Aldrich it was also acquired F, M and Mx of analytical grades for UPLC analysis. All of these chemicals were used as purchased, but the powder catalyst whose density was 370 kg m3 was taken to a screen analysis with a set of three Tyler standard screens (100, 170 and 200 mesh). The mass fractions of particles retained on these screens were 3.5%, 10% and 3.5%, respectively. As a consequence, the fraction of powder caught in the pan at the bottom of the stack of screens shaken mechanically was 83%. Characterization of MK10 from the same lot from which


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samples were taken to perform the current study was already performed in terms of structural, and physicochemical properties by X-ray diffraction, Fourier-transform infrared spectroscopy, nitrogen adsorption, thermal gravimetric analysis, differential thermal analysis, and by involving the potentiometric titration technique.24 The reactions were carried out in a sealed 50 mL batch reactor with PID control of temperature (model 4848, Parr Instrument Company, Moline, USA). The apparatus was also equipped with a mixer with a stirring speed controller (15 A, 220 V) mostly operated at 300 rpm. In all the reaction experiments a 35 mL homogenous mixture of Milli-Q water, and F at a concentration close to 0.02520.0008 mol L1 was fed to the reactor at ambient temperature. The tested powder catalyst was dispersed in the reactant solution to form a suspension that was uniform in distribution of solids. It was possible because fine particles suspended in an agitated liquid tend to move with the liquid. Since it took approximately 15 min to heat the slurry up to the desired temperatures of approximately 448, 463, 478 or 493 K, the reaction was assumed to start only after such an initial heating period when the conversion of F was negligible. To confirm it, a kinetic experiments was carried out, and the average conversion of F was estimated on the basis of a set of three measured species concentrations at a time of 15 min. To have the kinetic results at the quite different operating conditions shown in Table 1, the reaction was repeated without modifying any variable for six different reaction times between zero up to 36,000 s. To stop the reaction at the moment the samples were taken from the reactor, they were rapidly cooled with water, and stored at low temperatures for UPLC analysis. Most of the experiments were performed with the purchased mixture of MK10 having average diameters lower than approximately 150 m (+100 mesh: 3.5%; 100+170 mesh: 10%; 170+200 mesh: 3.5%; 200: 83%) at a concentration of 4.7% (mass of powder catalyst per unit of liquid free of solids) (runs 1 to 4 in Table 1). However, to investigate the influence


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of catalyst deactivation, and catalyst concentration, some tests were also done only by replacing the raw catalyst by a reused one (runs 5 and 6 in Table 1), and by increasing the amount of catalyst in the reactor to 7.05% (b70 kg m3) and 9.4% (b94 kg m3) (7 and 8 in Table 1). The procedure of catalyst regeneration consisted of washing it for five times with distilled water at ambient temperature, passing the dispersion through a 15 μm pore size filter (Qualy, São José dos Pinhais, Brazil), and drying the wet catalyst in an oven (SL 100, Solab, Piracicaba, SP, Brazil; Olifef CZ, Ribeirão Preto, SP, Brazil) at 343 K, and 373 K for 24 hours. For the purpose of examining the importance of external and internal mass transfer resistances on reaction rates, experiments were conducted by modifying exclusively those variables to which these resistances are typically sensitive. For instance, runs 9 and 10 were performed at different stirring speeds (450 rpm, and 600 rpm), while runs 11 and 12 used samples of catalyst that were only different in particle size (+100 mesh, and 170+200 mesh), respectively. In a summarized way, the results that emerged from these experiments will be applied in the following to estimate the effect of stirring speeds on reaction rates, to evaluate the difference between the bulk and the boundary surface concentration of F, and to calculate the internal effectiveness factor. The detailed operating conditions for all the experimental runs are shown in Table 1. It is important to underline that in the cases of runs 5 to 12, the species concentrations were determined at no more than two reaction times (7200 s only, or 7200 and 14400 s for runs 5 and 6). The concentrations of F, M and Mx in the aliquots filtered through a 0.45 μm pore size cellulose acetate filter (Sartorius Stedim Biotech, Goettingen, Germany) were determined by liquid chromatography (model Acquity UPLC H-Class, Waters, Milford, USA). The samples automatically injected in a C18 1.7 µm column (2.150 mm, Acquity UPLC BEH, Waters,


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Milford, USA) were examined by refractive index and photodiode array detectors (Waters, Milford, USA). The mobile phase was an ultra pure water solution at a pH of 2 (5 mM H2SO4), and a flow rate of 0.6 mL min1. The chromatographic conditions were according to the AOAC standard method.25

Chemical mechanism and kinetic model The set of Equations (1) to (3) written from F, Mx, and M balances on an ideal batch reactor represents the currently suggested kinetic model. The right-side terms in these ordinary differential equations (ODE's) are the non-catalytic (rF,j) and catalytic (rF,j) rates of consumption of fumaric acid due to the jth reactions.

dC F  rF ,1  rF ,1  rF ,2  rF ,2  dt

(1)

dC Mx  rF ,1  rF ,1  dt

(2)

dC M  rF ,2  rF ,2   dt

(3)

For the reactions of isomerization (R1 or j=1) and hydration (R2 or j=2) of F in the absence of catalyst, the rate laws are given by Equations (4) and (5) by involving rate constants for the forward reactions whose change with absolute temperature was computed by Arrhenius (see Equation 6) on the basis of known values of frequency factors and energies of activations shown in Table S1 (available as supplementary material).14


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rF ,1  k1, C F 

k1, K1

rF ,2  k 2 , C F CW 

C Mx

k 2 , K2

(4)

CM

 E aj ,  k j ,  k j 0 , exp    RT 

(5)

j=1,2

(6)

For the reactions R1 and R2 exclusively catalyzed by MK10, the rate expressions are of the form of classical models for heterogeneous catalysis commonly referred to as Langmuir-Hinshelwood (LH), or Hougen-Watson models.26-28

  C F  C Mx K 1 rF ,1  k1,  b K F   1  K F C F  K W CW  K M C M  K Mx C Mx 

(7)

  C F CW  C M K 2 rF ,2   k 2 ,  b K F K W  2   1  K F C F  K W CW  K M C M  K Mx C Mx  

(8)

with the rate constants for the forward reactions (k1,, and k2,), and the adsorption equilibrium constants for the ith species (KF, KW, KM, and KMx) computed from Arrhenius (Equation 9), and van't Hoff (Equation 10) relations. The Langmuir-Hinshelwood formulation to kinetics of fluid-solid catalytic reactions as the ones currently investigated was first described by Hinshelwood,29 and few years later developed in detail by Hougen and Watson.30 Nowadays, it is described for the most part in almost all the classical books of chemical engineering


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kinetics.31,

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In any case, Table S2 (available as supplementary material) summarizes the

steps involved to develop Equations (7) and (8).

 E aj ,  k j ,  k j 0 , exp    RT 

  H i ,298 K i  K i ,298 exp  R 

1  1     T 298 

j=1,2

i=F,W,M,Mx

(9)

(10)

The proposed rate law for the catalytic isomerization of F supposes that the surface reaction is the rate-limiting step. In the case of MK10 catalyzed hydration, Equation (8) was written by assuming that such a reaction is between F and water adsorbed on the catalyst surface, with the surface reaction as the rate-controlling mechanism. Both Equations (7) and (8) also consider the following key simplifications: i) the adsorption of F, W, M and Mx occur at discrete points (sites on the surface of MK10) with equal activity; ii) each molecule is accommodated on a single site that has no interaction with a vacant or occupied adjacent one; iii) the amount adsorbed is not higher than the one obtained when all the active sites are covered (i.e., a monomolecularlayer is formed); iv) the rate of desorption of a specie i is only dependent on its amount adsorbed on the surface of MK10; v) the step of surface reaction is always described by simple first- and second-order rate expressions;30 vi) chemisorption occurs at a much quicker rate than surface reaction. The procedure of tuning of the rate parameters consisted of first adjusting the constants of Equation (8) to reproduce the observed variation in the rates of production of M (rM,=rF,2) as a function of the measured concentrations of F, M and Mx. In a second step, the constants on which k1, and K1 are dependent in Equation (7) were tuned on the experimental concentrations of Mx.


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In both these individual steps of tuning, the Simplex method of optimization was used to minimize the sum of the squared differences between the experimental and calculated responses (i.e., rM, in a first moment, and CMx in a second turn).33 However, to tune the parameters of Equation (7), it was necessary to solve numerically the system of ODE given by Equations (1) to (3), which was done by applying the implicit BDF method.34 In other words, a differential method was used to determine the rate law parameters k2,, KF, KW, KM and KMx in Equation (8), while the estimation of k1, and K1 in Equation (7) involved the use of an integral procedure for treatment of the experimental data. The reason for such a difference in the use of these methods was the low sensitivity of rMx, (or rF,1 since rMx,=rF,1) with respect to changes in the rate parameters k1, and K1. To have heats of adsorption for the considered adsorbed species that were of the same magnitude as the expected heats of chemical reactions31, 35, the optimization routine restricted the search for the optimal Hi,298 to values between 21 and 630 kJ mol1. The equilibrium constant for the reaction R2 as a function of temperature was estimated with the van't Hoff relation (Equation 11) based on parameters available in the literature.13 However, in order to have an expression for rMx, that was consistent with the observed variation in CMx with time, it was necessary to tune K1,298 and H1,298, but by involving Equation (11) yet. This is not unusual,13 since very small uncertainties in the Gibbs free energy and standard enthalpies of formation of Mx and M at 298 K have a significant impact on K1.

  H j ,298 K j  K j ,298 exp  R 

1  1     T 298 

j=1,2

(11)

RESULTS AND DISCUSSION


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The first remarkable issue with respect to the proposed mechanism of catalyzed conversion of F is whether it is consistent with the current experimental observations. Preliminary simulations at the optimal set of model parameters revealed that the denominator of Equation (7) and (8) were approximately constants during the reaction, at all the reaction conditions currently examined. It allowed to have simplified rate expressions that are identical to the ones that would be obtained for reversible elementary reactions taking place in an homogeneous system:

rF ,1  k1*,  b C F  C Mx K 1 

(12)

rF ,2   k 2*,  b C F CW  C M K 2 

(13)

where, k1*,, and k2*, are rate constants computed with Equation (9) yet, but by involving preexponential factors k10*,, and k20*,, respectively. The full set of kinetic parameters to be used with these simplified rate expressions is shown in Table S1 (available as supplementary material). Figures 1a and 1b confirm that these simplified rate expressions represent the experimental rates of production of M (rM, or rF,2), and the experimental concentrations of Mx (CMx) very well. In fact, under both these circumstances, the coefficient of determination R2 was approximately 0.9. Mean relative errors lower than 3% also indicate that the residuals are not predominantly positive or negative. The reliability of the kinetic experimental results is at least in part also indicated by an almost normal distribution of errors in the overall mass balances (Figure 1c). The mean error was approximately 1%, and except for a single experiment, they were always lower than 10%.


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The experimental overall conversions of F and the ones estimated on the basis of the suggested rate laws (i.e., the ones given by Equations 12 and 13) with the kinetic parameters presented in Table S1 are illustrated in Figure 2. It is promptly noticed that the consumption of F with time was properly described at the four different examined temperatures. A still more important finding revealed from such a plot under all the examined conditions is that the used solid acid catalyst was effective in increasing the reaction rates. At the end of the reaction, the conversions of F in the presence of MK10 were at least 20% higher than those estimated without taking the catalytic conversion into account. Such a minimum difference was observed at the highest investigated temperature of 493 K, but as the temperature is reduced the importance of the thermal conversion falls, and the benefit of using the catalyst becomes more evident. For instance, the difference between computed XF with and without catalyst is increased to 42% at 448 K. Plots of M and Mx concentration against time demonstrate that the model also describes correctly the amount of appropriate (M) and undesired (Mx) products that were formed experimentally (Figures 3 and 4). Because Mx rapidly approaches its equilibrium concentration, the computed concentrations of Mx become more sensitive to the equilibrium constant for the isomerization reaction. It means that small uncertainties in the Gibbs free energy and standard enthalpies of formation of F (GF,298=655 kJ mol1; HF,298=812.2 kJ mol1) and Mx (GMx,298=630.4 kJ mol1; HMx,298=789.4 kJ mol1) at 298 K36 may be responsible for large deviations between experimental and computed results of CMx. In fact, it was concluded that an uncertainty of only 0.4% in the available values of GF,298 and GMx,298, as well as of just 2.6% in HF,298 and HMx,298 may lead to the values of K1,298 and H1,298 currently adjusted to have modeling results that match well with the experimental behavior. From a practical point of view, it is important to recognize that the differences between using and not using MK10 are smaller than one would expect for a catalyst to be used to


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produce commercially malic acid (see Figure 2 again). It seems particularly bad when one considers how efficient is hydrochloric acid to accelerate homogeneously the same reaction.9, 13, 14

However, the possibility of reusing solid catalysts, in general, is an aspect that may

contribute for making MK10 more attractive for the malic acid industry. In this framework, kinetic experiments with recycled MK10 were performed at conditions shown in Table 1 (runs 5 and 6). The results reported in Figure 5 make it clear, at least on the basis of three recycling tests, that there was no significant decay of activity of the reused catalyst. In fact, it has been noticed that MK10 can be reused many times without loss in catalytic efficiency.22,

37

It

cannot be forgotten that the operation of catalyst regeneration consisted of only washing it with distilled water, and drying it at the moderate temperatures of 343 K (Figure 5a1-5c1), and 373 K (Figure 5a2-5c2). As may be noticed in Figure 5, the drying temperature had no influence on the catalytic activity. To determine experimentally in what extent the amount of catalyst could increase the rate of reaction, two additional experiments were conducted. The operating conditions were the same as for run 3, except for the concentration of MK10 that was increased by a factor of 1.5 and 2 (runs 7, and 8 in Table 1). The increase of the examined factor (i.e., [MK10] or b) contributed lightly to accelerate the conversion of the limiting reactant F into products (see Figure 6a). However, the good agreement between calculated and experimental data not only further validates the kinetic model, but it also confirms that the catalytic rates of reaction are linearly dependent on [MK10] (i.e., rF,j  b). It means that a packed bed of MK10 with a bulk density of catalyst that approaches the catalyst density (c=370 kg m3) would increase noticeably the yield of the examined reaction (see the curve for b=c in Figure 6a). It could make MK10 suitable for a commercial production of malic acid. The effect of species mass transfer between the fluid and the catalyst surface on the reaction rates was also evaluated. Such an analysis was motivated by the typical low relative


15

Page 17 of 31 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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


velocities between particle and liquid in slurries.31 Some experiments that involved measurements of F concentration at a time of 7200 s were initially performed by varying the stirring speeds, and maintaining all other variables constants (runs 3, 9 and 10 in Table 1). However, because the change of the examined factor typically does not alter markedly the relative velocity between the dispersed particles and the aqueous solution, the F conversion was constant (see Figure 6b). In other words, it is not possible to state that the reason for the negligible influence of the stirring speed on XF was a minor role that mass convection played in the rates of disappearance of F. A much more consistent result to support that neglecting external mass transfer resistances led to insignificant errors in the rate is given by the small difference between the bulk and the boundary surface concentration of F from Equation (14) (CF109 mol L1):

C F 

 rF ,1  rF ,2  k c ac

(14)

where, the numerator in the right-side of this expression is the determined rate of consumption of F in the reactions R1 and R2 (107 mol L1 s1 for any run), kc represents the particleliquid mass transfer coefficient in the agitated reactor computed with Equation (15) as a function of the Reynolds number suggested by the Kolmogoroff's theory of isotropic turbulence (Equation 16),31,

38-40

and ac is the external area of catalyst particles per unit of

volume of liquid free of solids (Equation 17).31

Sh  0.69 Re1 2 13 Sc


(15)

16


 D 4 Re   3  

ac 

  

Page 18 of 31

13

6 b D c

(16)

(17)

In Equation (16),  is the ratio between the stirrer power and the mass in the agitated reactor, D is the mean surface diameter of the catalyst powder from the data of particle size classification, and  is the kinematic viscosity of water. The thermophysical properties from which kc and ac were calculated are summarized in Table S3 (available as supplementary material). To investigate the importance of internal mass transfer on the rates of reactions R1 and R2 with MK10 as catalyst, two independent kinetic experiments were performed under operating conditions that were only different in terms of size of catalyst (see runs 11 to 12 in Table 1). The determined rates of disappearance of F were 5.34107 mol L1 s1 and 5.52107 mol L1 s1 for particles of MK10 whose radii were approximately 7.35105 m and 4.05105 m, respectively. From the ratio between the Thiele modulus 1 and 2, and between the internal effectiveness factor 1 and 2 for reactions of first-order take place in the presence of spherical catalyst particles of radii R1 and R2, a system of nonlinear algebraic equations may obtained:31, 32

1 

R1 2 R2


(18)

17

Page 19 of 31 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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


 rF 1 R1 2 1 coth1   1   rF 2 R2 2  2 coth 2   1

(19)

where (rF)1 and (rF)2 are currently the rates of consumption of F for the experiments with catalysts particles of radii R1 and R2. The pair of values of Thiele modulus obtained by finding the roots of the nonlinear equations by Newton (1=0.87 and 2=0.48) were used to calculate the internal effectiveness factors k for the particles of radius Rk:

k 

3

k 2

 k coth k   1

(20)

For the largest particles of MK10 used in the kinetic experiments (100 mesh or 147 m in diameter) whose mass fraction in the powder catalyst was lower than 4%, the effectiveness factor was 0.95. It means that the particle sizes were sufficiently small to eliminate virtually any diffusion resistances. It is also important to emphasize that montmorillonite, raw material to produce MK10, are ellipsoidal tactoids about 1.2 nm long and between 100 to 400 nm wide, which tend to be reduced in size after the acid/thermal activation.42 It means that the solid that was currently evaluated as catalyst was in fact agglomeration of particles that have many micropores that contribute to the reduction of the diffusion resistances. In the impossibility of purchasing MK10, this activation can be easily performed in any available montmorillonite, obtaining catalysts that are similar to the commercial available MK10.43

CONCLUSIONS


18


Page 20 of 31

Commercial montmorillonite K10 demonstrated to be effective in promoting the reaction of hydration of F to synthesize malic acid without any noticed significant loss of its catalytic activity. The kinetics of hydration and isomerization of F was properly described by classical Langmuir-Hinshelwood rate models on the basis of experiments in the absence of mass transfer limitations. The surface hydration reaction was between F and water adsorbed on MK10, and the rate limiting steps for the isomerization and hydration reactions were the reactions over the catalyst.

SUPPORTING INFORMATION Rate parameters (Table S1), steps for writing the rate expressions (Equations 7 and 8) in terms of species concentration in the fluid phase (Table S2), and thermophysical properties necessary to estimate kc (5.45103 m s1) and ac (2104 m2 m3) at 478 K (Table S3).

REFERENCES (1) Wang, X.; Gong, C. S.; Tsao, G. T. L-Malic acid production from fumaric acid by a laboratory Saccharomyces Cerevisiae strain SHY2. Biotechnol. Lett. 1996, 18, 1441. (2) Kirk-Othmer. Encyclopedia of Chemical Technology; Wiley: Hoboken, 2007. (3) Grand View Research. Malic acid Market Analysis by Application (Beverages, Confectionary & Food) And Segment Forecast to 2020; Grand View Research Inc.: San Francisco, 2015. (4) Francis, F. J. Wiley Encyclopedia of Food Science and Technology; Wiley: Hoboken, 1999. (5) Goldberg, I.; Williams, R. Biotechnology and Food Ingredients; Springer: New York, 1991.


19

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(6) Bender, M. L.; Connors, K. A. A non-enzymatic olefinic hydration under neutral conditions: the kinetics and mechanism of the hydration of fumaric acid monoanion. J. Am Chem. Soc. 1962, 84, 1980. (7) Bada, J. L.; Miller, S. L. The kinetics of hydration of fumaric acid between pH 0 and 6. J. Am. Chem. Soc. 1969, 91, 3948. (8) Ramsey, S. H.; Schultz, R. G. Preparation of malic acid; US Patent 5210295, 11 May 1993. (9) Ortiz, R. W. P.; de Jesus, B. G.; Franceschi, E.; Dariva, C.; Cardozo-Filho, L.; Zanoelo, E. F. Microwave-assisted synthesis of malic acid involving hydrochloric acid as catalyst. Reac. Kinet. Mech. Cat. 2017, 122, 793. (10) NOAA. CAMEO Chemicals version 2.7; 2016. (11) TOXNET. U.S. National Library of Medicine; https://toxnet.nlm.nih.gov/cgibin/sis/search/a?dbs+hsdb:@term+@DOCNO+183, 2018. (12) Erickson, L. E.; Alberty, R. A. Kinetics and mechanism of the base-catalyzed hydration of fumarate to malate. J. Phys. Chem. 1959, 63, 705. (13) Ortiz, R. W. P.; Benincá, C.; Cardozo-Filho, L.; Zanoelo, E. F. High-pressure acidcatalyzed isomerization and hydration of fumaric acid in a homogeneous nonisothermal batch reactor. Ind. Eng. Chem. Res. 2017, 56, 3873. (14) Mattar Knesebeck, A.; Ortiz, R. W. P.; Cardozo-Filho, L.; Zanoelo, E. F. Isomerization and hydration of fumaric acid under catalytic and noncatalytic conditions. Reac. Kinet. Mech. Cat. 2018, 125, 521. (15) Gao, Z.; Chen, W.; Chen, X.; Wang, D.; Yi, S. Study on the Isomerization of Maleic Acid to Fumaric Acid without Catalyst. Bull. Korean Chem. Soc. 2018, 39, 920. (16) Zheng, L. Preparation process of malic acid; Chinese Patent CN1560016A, 17 May 2006.


20


Page 22 of 31

(17) Atkins, M. P.; Smith, D. J. H.; Westlake, D. J. Montmorillonite catalysts for ethylene hydration. Clay Minerals 1983, 18, 423. (18) Comelli, N.; Avila, M. C.; Volzone, C.; Ponzi, M. Hydration of -pinene catalyzed by acid clays. Cent. Eur. J. Chem. 2013, 11, 689. (19) Aronson, M. T.; Gorte, R. J., Farneth, W. E. The influence of oxonium ion and carbenium ion stabilities on the alcohol/H-ZSM-5 interaction. J. Catal. 1986, 98, 434. (20) Janik, M. J.; Macht, J.; Iglesia, E.; Neurock, M. Correlating acid properties and catalytic function:

a

first-principles

analysis

of

alcohol

dehydration

pathways

on

polyoxometalates. J. Phys. Chem. C 2009, 113, 1872. (21) Glazneva, T. S.; Sadovskaya, E. M.; Suknev, A. P.; Goncharov, V. B., Simonova, L. G.; Paukshtis, E. A.; Bal'zhinimaev, B. S. Brønsted acidity study of fiberglass materials by H/D-exchange. Appl. Catal. A Gen. 2009, 366, 262. (22) Hechelski, M.; Ghinet, A.; Louvel, B.; Dufrénoy, P.; Rigo, B.; Daïch, A.; Waterlot, C. From Conventional Lewis Acids to Heterogeneous Montmorillonite K10: EcoFriendly Plant-Based Catalysts Used as Green Lewis Acids. ChemSusChem 2018, 11, 1249. (23) Liu, Y. X.; Zhang, X.; Guo, L.; Wu, F.; Deng, N. S. Photodegradation of Bisphenol A in the Montmorillonite KSF Suspended Solutions. Ind. Eng. Chem. Res. 2008, 47, 7141. (24) Kanda, L. R. S.; Corazza, M. L.; Zatta, L.; Wypych, F. Kinetics evaluation of the ethyl esterification of long chain fatty acids using commercial montmorillonite K10 as catalyst. Fuel 2017, 193, 265. (25) AOAC. Food Compositions; Additives, Natural Contaminants (Official Method AOAC 986.13: quinic, malic, citric acid in cranberry juice cocktail and apple juice); AOAC: Arlington, 1990.


21

Page 23 of 31 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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(26) Pandhare, N. N.; Pudi, S. M.; Mondal, S.; Pareta, K.; Kumar, M., Biswas, P. Development of Kinetic Model for Hydrogenolysis of Glycerol over Cu/MgO Catalyst in a Slurry Reactor. Ind. Eng. Chem. Res. 2018, 57, 101. (27) Venstrom, J.; Davidson, J. H. The kinetics of the heterogeneous oxidation of zinc vapor by carbon dioxide. Chem. Eng. Sci. 2013, 93, 163. (28) Pandey, N. K.; Reddy, R.; Mishra, S.; Murali, R.; Boshi, J. B. Study on the Kinetics of Catalytic Hydrogenation of U(VI) in Nitric Acid Solution Using a Bubble Reactor. Ind. Eng. Chem. Res. 2018, 57, 3482. (29) Hinshelwood, C. N. Kinetics of Chemical Change; Oxford University Press: London, 1940. (30) Hougen, O. A.; Watson, K. M. Chemical Process Principles; John-Wiley & Sons: New York, 1947. (31) Smith, J. M. Chemical Engineering Kinetics; McGraw-Hill: Singapore, 1981. (32) Fogler, H. S. Elements of Chemical Reaction Engineering; Prentice Hall: London, 1992. (33) Jenson, V. G.; Jeffreys, G. V. Mathematical Methods in Chemical Engineering; Academic Press: New York, 1977. (34) Petzold, L. R. A. Description of DASSL: A Differential/Algebraic System Solver, Report SAND82-8637; Sandia: Albuquerque, 1982. (35) Barrow, G. M. Physical Chemistry, McGraw-Hill: Singapore, 1988. (36) DIPPR. The DIPPR Information And Data Evaluation Manager (DIADEM), Version 1.2; AIChE: New York, 2000. (37) Rani, C. S.; Suresh, N.; Rao, M. V. B.; Pal, M. Montmorillonite K10 catalyzed one-pot synthesis of 2-aryl substituted N-(4-oxo-1,2-dihydroquinazolin-3(4H)-yl)aryl or alkylamide derivatives under ultrasound irradiation. Arabian J. Chem. in press.


22


Page 24 of 31

(38) Levins, D. M.; Glastonbury, J. R. Aplication of Kolmogoroffs theory to particle-liquid mass transfer in agitated vessels. Chem. Eng. Sci. 1972, 27, 537. (39) Batchelor, C. K. Mass transfer from small particles suspended in turbulent fluid. J. Fluid Mech. 1980, 98, 609. (40) Armenante, P. M.; Kirwan, D. J. Mass transfer to microparticles in agitated systems. Chem. Eng. Sci. 1989, 44, 2781. (41) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The properties of gases and liquids; McGraw-Hill: New York, 1977. (42) Cadene, A. A.; Durand-Vidal, S.; Turq, P.; Brendle, J. Study of individual Namontmorillonite particles size, morphology, and apparent charge. J. Colloid Interf. Sc. 2005, 285, 719. (43) Zatta, L.; Ramos, L. P.; Wypych, F. Acid activated montmorillonite as catalysts in methyl esterification reactions of lauric acid. J. Oleo Sci. 2012, 61, 497.


23

Page 25 of 31 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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Operating conditions for the reaction experiments. CF0=(2.520.08)102 mol L1. Run T (K)

[MK10] (%)

Cycles of reuse

S (rpm)

Mesh

Replicates

1

448

4.7 (b=46.75 kg m3)

0

300

100

2

2

463

4.7 (b=46.75 kg m3)

0

300

100

2

3

478

4.7 (b=46.75 kg m3)

0

300

100

3

4

493

4.7 (b=46.75 kg m3)

0

300

100

2

5

478

4.7 (b=46.75 kg m3)

3 (dried at 343 K)

300

100

3

6

478

4.7 (b=46.75 kg m3)

3 (dried at 373 K)

300

100

1

7

478

7.05 (b=70.13 kg m3)

0

300

100

1

8

478

9.4 (b=93.51 kg m3)

0

300

100

1

9

478

4.7 (b=46.75 kg m3)

0

450

100

1

10

478

4.7 (b=46.75 kg m3)

0

600

100

1

11

478

4.7 (b=46.75 kg m3)

0

300

+100

1

12

478

4.7 (b=46.75 kg m3)

0

300

170+200

1


24

(a)

(b)

6 4 2 0 0

Page 26 of 31

2

4

6

8

(rM,)exp.x107 (mol L1 s1)

0.6

(c)

12 0.4

8

F()

8

(CMx)calc.x104 (mol L1)

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(rM,)calc.x107 (mol L1 s1)


0.2

4 0 0

4

8

12

(CMx)exp.x104 (mol L1)

0 -30 -20 -10

0

 

10 20 30

Figure 1. A comparison between the experimental and calculated catalytic rates of production of malic acid (a), and concentration of formed maleic acid (b) at a catalyst concentration of 4.7% and temperatures between 448 K and 493 K (runs 1 to 4 in Table 1). Mass balance error distribution for the kinetic experiments (c) (m=0.95.4 %).


25

Page 27 of 31

(b) 0.8

XF

XF

(a) 0.8 0.4

0.4 0

0 0

10

20

3

t x10

30

0

40

(s)

10

(d) 0.8

XF

(c) 0.8

XF

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4

20

3

30

t x10

(s)

10

15

40

0.4 0

0 0

5

10

3

t x10

15

20

25

0

5

3

t x10

(s)

20

25

(s)

Figure 2. Calculated (lines) and experimental (symbols) conversion of fumaric acid in the absence of MK10 in an electric-heated batch reactor (dashed lines and squares),14 and with MK10 at a concentration of 4.7% (solid lines and circles), and at 448 K (a), 463 K (b), 478 K (c) and 493 K (d) (runs 1 to 4 in Table 1). Reprinted in part with permission from ref 14. Copyright 2018 Springer Nature.


26

(a)

1.6 0.8 0 0

10

20

3

t x10

(c)

30

40

(s)

CM x102 (mol L1) CM x102 (mol L1)

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2 1 CM x102 (mol L1) CM x10 (mol L )


Page 28 of 31

(b) 1.6 0.8 0 0

10

(d)

20

3

30

t x10

(s)

10

15

40

1.6

1.6

0.8

0.8 0 0

5

10

3

15

20

25

0 0

5

3

20

25

t x10 (s) t x10 (s) Figure 3. Variation in the concentration of produced malic acid with time without MK10 in an

electric-heated batch reactor (dashed lines and squares),14 and with MK10 at a concentration of 4.7% (solid lines and circles) at 448 K (a), 463 K (b), 478 K (c) and 493 K (d) (runs 1 to 4 in Table 1; lines: calculated results; symbols: experimental data). Reprinted in part with permission from ref 14. Copyright 2018 Springer Nature.


27

(a)

16 12 8 4 0 0

10

(c)

3

t x10

16 12 8 4 0

0

20

5

10

3

30

40

(s)

15

CMx x104 (mol L1) CMx x104 (mol L1)

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4 1 CMx x104 (mol L1) CMx x10 (mol L )

Page 29 of 31

(b) 16 12 8 4 0 0

10

(d)

16 12 8 4 0

20

25

0

5

20

3

30

t x10

(s)

10

15

3

20

40

25

t x10 (s) t x10 (s) Figure 4. Formed maleic acid in the kinetic experiments without MK10 in an electric-heated

batch reactor (dashed lines and squares),14 and with MK10 at concentration of 4.7% (solid lines and circles) at 448 K (a), 463 K (b), 478 K (c) and 493 K (d) (runs 1 to 4 in Table 1; lines: calculated results; symbols: experimental data). Reprinted in part with permission from ref 14. Copyright 2018 Springer Nature.


28


3 2 1 0

0

5

(b1)

10

3

t x10

15

20

25

2 1 CMx x104 (mol L1) CM x10 (mol L ) C x102 (mol L1) F

(a2)

(a1)

2 1 CMx x104 (mol L1) CM x10 (mol L ) C x102 (mol L1) F

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 31

3 2 1 0

0

5

(b2)

(s)

1.6

10

3

t x10

15

20

25

20

25

20

25

(s)

1.6

0.8

0.8

0 0

(c1)

5

16 12 8 4 0 0

5

10

3

15

t x10

(s)

10

15

3

20

25

0 0

(c2)

5

16 12 8 4 0

20

25

0

5

10

3

15

t x10

(s)

10

15

3

t x10 (s) t x10 (s) Figure 5. Concentrations of F, M and Mx from experiments with virgin (circles) (run 3 in

Table 1) and recycled MK10 (squares) (runs 5 and 6 in Table 1) at a concentration of 4.7% and a temperature of 478 K. Solid lines: computed concentrations; a1-c1: catalyst regeneration at 343 K; a2-c2: catalyst regeneration at 373 K.


29

(a) 0.8

(b) 0.4

bc

b94

0.6

XF

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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


b70

XF (at t=7200 s)

Page 31 of 31

b47  =0.0 b

0.4 0.2

0.3 0.2 0.1 0

0 0

10

20

30

300

450

600

S (rpm) t x10 (s) Figure 6. Effect of catalyst concentration (a: run 3, 7, and 8 in Table 1) and stirring speed (b: 3

run 3, 9 and 10 in Table 1) on the conversion of F. XF at [MK10]=0 in an electric-heated batch reactor (or b=0.0 kg m3) is from Mattar-Knesebeck et al.14 Reprinted in part with permission from ref 14. Copyright 2018 Springer Nature.


30

SYNTHESIS OF MALIC ACID ON MONTMORILLONITE K10: A

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