Mechanism and Kinetic Modeling of Ethanol Conversion to 1-Butanol

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Cite This: Ind. Eng. Chem. Res. 2019, 58, 12981−12995

Mechanism and Kinetic Modeling of Ethanol Conversion to 1‑Butanol over Mg and Al Oxide Derived from Hydrotalcites Amir J. Scheid,† Elisa Barbosa-Coutinho,‡ Marcio Schwaab,§ and Nina P. G. Salau*,†

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†

Departamento de Engenharia Química, Universidade Federal de Santa Maria, Avenida Roraima, 1000, CEP 97105-900, Santa Maria, Rio Grande do Sul, Brazil ‡ Departamento de Físico-Química, Instituto de Química, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, Porto Alegre, Rio Grande do Sul 91501-970, Brazil § Departamento de Engenharia Química, Escola de Engenharia, Universidade Federal do Rio Grande do Sul, Rua Ramiro Barcelos, 2777, Prédio 22202, Porto Alegre, Rio Grande do Sul 90035-007, Brazil ABSTRACT: Utilizing a mixed Mg/Al oxide derivate from hydrotalcites as catalyst for the ethanol conversation to 1butanol, catalytic tests were performed using a tubular quartz reactor at different reaction temperatures and following the central composite design for experiment design to evaluate ethanol feed molar fraction and nitrogen (carrier gas) feed flow rate. Reaction products were analyzed by gas chromatography, being qualitatively and quantitatively identified by mass spectrometer detection and by flame ionization detection, respectively. Experimental data was used to propose a mechanism of elementary reactions, which were analyzed thermodynamically to select thermodynamically favorable reactions. With the proposed mechanism, parameter estimation was performed using a particle swarm algorithm, minimizing a least-squares objective function. Results were also compared by analyzing the estimated parameters and Fisher’s test. With the best elementary reaction mechanism, a heterogeneous mechanism, which considers the adsorption, desorption, and surface reaction steps, was also proposed, and its parameters were also estimated. Despite high standard deviations of its estimated parameters, the Fisher’s test proved that it was the best model compared in this work to fit the experimental data. Finally, the results suggest that the 1-butanol production over this catalyst does not follow the Guerbet reaction scheme, because the direct condensation of two ethanol molecules is the most favorable path. According to Pang et al.,5 ethanol condensation to 1-butanol occurs in many steps, including dehydrogenation, hydrogenation, aldol condensation, and dehydration, because it is necessary that metal, base, and acid active sites are present in the catalysts. These steps are also known as the Guerbet reaction, the main mechanism proposed to explain these reactions. The Guerbet reaction for 1-butanol production from ethanol has been proposed to occur in two possible mechanisms: the direct condensation of two ethanol molecules6−12 and a threestep mechanism that involves dehydrogenation, aldol condensation, and further hydrogenation.4,8,13−18 Some authors have made efforts to support the direct condensation of two molecules of ethanol. For instance, Gines et al.12 have shown by isotropic tracer studies that the direct reaction of ethanol can occur without the intermediate

1. INTRODUCTION 1-Butanol is used in industry with multiple applications, such as solvents and paints. Still, in the last years it has been suggested that it can also play an important role as a fuel alternative, due to its high energetic value (29.2 MJ/L) compared to ethanol (19.2 MJ/L), potentially as a surrogate to gasoline.1 Two main routes for 1-butanol production can be mentioned: from biomass (biobutanol) or from fossil material (petro-butanol), the majority being produced from propylene hydroformylation. In relation to renewable processes from biomass, fermentation of bioethanol is the main route for biobutanol.2 Recently, heterogeneous catalysts have been considered as an alternative for biobutanol production from bioethanol.32 Heterogeneous catalysts are interesting as they allow higher stability and reproducibility of the proposed routes. Numerous catalysts have been proved effective in the conversion of ethanol to 1-butanol, such as alkaline earth oxides and modified MgO, hydroxyapatites with different Ca/P ratios, and mixed Mg/Al oxides.3 © 2019 American Chemical Society

Received: Revised: Accepted: Published: 12981

March 19, 2019 June 19, 2019 June 25, 2019 June 25, 2019 DOI: 10.1021/acs.iecr.9b01491 Ind. Eng. Chem. Res. 2019, 58, 12981−12995

Article

Industrial & Engineering Chemistry Research

Figure 1. Schematics of the reaction unit.

the mixed solution using a pump with 1 mL/min flow rate. After complete addition of nitrate solutions, the resulting solution has a pH of 10 and was kept agitated for additional 30 min. The final solution was then inserted into an oven at 333.15 K for 16 h for the aging process. After this step, the solution was filtered and washed using deionized water until pH 7, ensuring total removal of potassium. The obtained solid was then dried in an oven for 12 h at 373.15 K and then grinded and sifted at 300 mesh. Calcination was made at 873.15 K during 10 h, with heating rate of 278.15 K/min. 2.2. Catalytic Tests. The catalytic tests were performed in a tubular quartz reactor in a “U” shape, with internal diameter of 4 mm, where the catalyst is added in a way to form a fixed bed. The system is heated and temperature controlled. Nitrogen is used as an inert carrier gas with a controlled flow rate. Ethanol is conditioned in a temperature controlled saturator and is carried by nitrogen, which is bubbled through the ethanol solution. To avoid gas condensation, inlet and outlet lines from the reactor and the inlet line to chromatographer were heated at 413.15, 433.15, and 473.15 K, respectively. Quantification of the components (reaction products) was made by a flame ionization detector gas chromatographer (GC2014, Shimadzu) using a Carbonplot capillary column (30 m × 0.32 mm × 1.50 μm). The qualitative identification of the components was made by a gas chromatographer with a mass spectrometer detector, using the same capillary column. The schematics of the reaction unit can be seen in Figure 1. All reactions were performed using 300 mg of catalyst, at atmospheric pressure and at reaction temperatures ranging from 523.15 to 673.15 K with increments of 298.15 °C. The reactor oven was kept for 32 min at each reaction temperature to guarantee that steady-state conditions were achieved. To evaluate the effect of the ethanol feed molar fraction and the nitrogen feed flow rate, the experiments were designed according to the central composite design, with replicates at the central point (Exp 9 in Table 1). Thus, the ethanol feed molar fraction and the nitrogen feed flow rate were considered the two independent variables of the experimental design, varying in 5 levels (from −√2 to √2), and their values are shown in Table 1. The central point experiment (Exp 9 in Table 1) was performed in triplicate, and therefore, it is the average of the triplicate experiments. 2.3. Reactor Kinetics and Modeling. The model chosen to represent the reaction unit was the packed bed reactor (PBR), assuming that there are no radial variations of flow rate

formation of acetaldehyde molecules, when K−CuyMg5CeOx catalysts were used. Still, Scalbert et al.,9 using hydroxyapatite as catalyst, have applied thermodynamics to prove that acetaldehyde self-aldolization is not part of the reaction pathway and that butyraldehyde would remain as the major C-containing molecule if it was an intermediate. One of the catalysts that offers the variety of active sites for the involved mechanisms is the mixed Mg/Al oxides derived from hydrotalcites, being noticeably studied mainly due to their acid/base proprieties, low cost, easy synthesis, and high superficial area.3 Utilizing mixed Mg/Al oxides from hydrotalcites as catalyst and ethanol as reagent, not only is 1-butanol produced, but also ethene, diethyl ether, acetaldehyde, butyraldehyde, and buthene are some of the observed byproducts and intermediates. Many authors have observed these compounds,1,3,5,19 allowing the proposal of more detailed mechanisms for this complex reaction scheme. Although many similar proposed mechanisms can be found in literature, there is still a gap relating the kinetic analysis of this mechanism and its validation, allowing optimizations to be made on this new 1-butanol production route. In this work, using the Mg/Al oxide obtained from hydrotalcites as catalyst and bioethanol as a biomass-derived source, all produced compounds from the reaction were identified and quantified at different experimental reaction conditions. With the identified compounds, multiple reactions were proposed and analyzed thermodynamically to evaluate which ones were favorable in the experimental conditions. After obtaining a thermodynamically favorable reaction scheme, its kinetic parameters were estimated using a particle swarm algorithm20,21 and simulations were performed to compare the result with experimental data.

2. MATERIALS AND METHODS 2.1. Catalyst Synthesis. Mg/Al oxide from hydrotalcite in the nominal molar ratio 5 (Mg2+/Al3+) was obtained using the hydrothermal method with constant pH. A total of 200 mL of magnesium nitrate hydrate (Mg(NO3)·2.6H2O, 57.64 g) and aluminum nitrate hydrate (Al(NO3)·3.9H2O, 18.76 g) was prepared with deionized water. Also prepared was a 100 mL solution of potassium hydroxide (KOH, 25.25 g) and another 100 mL solution of 1 M potassium carbonate (K2CO3, 27.64 g). The KOH and K2CO3 solutions were mixed with vigorous agitation, while the nitrates solution was slowly dripped into 12982

DOI: 10.1021/acs.iecr.9b01491 Ind. Eng. Chem. Res. 2019, 58, 12981−12995

Article


are the parameters that will be estimated using the experimental data. Tref is the reference temperature, considered in this work as 598.15 °C (the average reaction temperature of the experiments). It is important to note that eq 3 is the reparameterized Arrhenius equation described by Schwaab and Pinto20 and eq 4 is the reparameterized van’t Hoff equation. The combination of eqs 1−4 will result in a system of differential equations that was resolved numerically using a DASSL routine.22 2.4. Thermodynamic Analysis. From the data collected from the experiments, it was possible to identify the main components (those whose concentrations were significant in the majority of the experiments) being formed from the initial ethanol molecules. These main components are presented in Table 2, where a number is associated with each component, allowing better arrangement of the equations presented further in this work.

Table 1. Experimental Conditions of the Experimental Design experiment Exp Exp Exp Exp Exp Exp Exp Exp Exp

1 2 3 4 5 6 7 8 9

% EtOH

N2 (mL/min)

22.07 (+√2) 7.93 (−√2) 20 (+1) 10 (−1) 20 (+1) 10 (−1) 15 (0) 15 (0) 15 (0)

35 (0) 35 (0) 45 (+1) 45 (+1) 25 (−1) 25 (−1) 20.86 (−√2) 49.14 (+√2) 35 (0)

and concentration. It was also considered that all of the reactor was kept at the same temperature for each temperature reaction. As the same reactor was used for all the experiments, its dimensionless size (η) was used, variating from zero to one. Therefore, the variation of molar flow rate of each component (Fj) along the reactor can be calculated by the product of the reaction velocity of each component (Rj) and the total catalyst mass used (wt), according to eq 1, where NC is the number of total components. dFj dη

= wt R j

(j = 1, ..., NC)

Table 2. Main Components Identified in the Experiments

(1)

The reaction velocity of each component can be calculated by the sum of the product of each component stoichiometric coefficient in each reaction (νji) and the reaction rate of each proposed reaction (ri), as shown in eq 2, where NR is the number of proposed reactions.

∑ νjiri

(i = 1, ..., NR) (2)

i

Each reaction rate is obtained according to the mechanisms proposed, where the elementary reaction mechanism considers all reactions to be elementary and reversible. For the heterogeneous mechanism, the reaction rates are obtained by considering the Langmuir−Hinshelwood−Hougen−Watson (LHHW) hypothesis, which considers the adsorption, desorption, and surface reaction steps. For both models, the kinetic constant of each reaction (ki,m) and the adsorption equilibrium constant (KAD,j) are presented in eqs 3 and 4, respectively, where i stands for each reaction, m for the model, and j for each component adsorbed. ÉÑ ÄÅ ÅÅ Ei , m ji T − Tref zyÑÑÑ Tref ÅÅ jj zzÑÑÑ ki , m = expÅÅln(ki , m ) + ÅÅ R ·Tref jk T z{ÑÑÑ ÅÇ (3) Ö ÅÄÅ ÑÉ ΔHj ij T − Tref yzÑÑÑ ÅÅ Tref Å j z KAD , j = expÅÅln(K AD , j) + j zÑÑÑ ÅÅ R ·Tref jk T z{ÑÑÑ ÅÇ (4) Ö T

In these equations, ln(ki,mref),

Ei , m R ·Tref

T

ref , ln(KAD,j ), and

ΔHj R ·Tref

component

1 2 3 4 5 6 7 8 9

ethanol diethyl ether ethene acetaldehyde butyraldehyde butanol 1-butene water dihydrogen

From these components, a total of 9 reactions and side reactions were proposed as possible paths for the ethanol condensation to 1-butanol; these reactions were already proposed by other authors and are presented in Table 3.

NR

Rj =

number

Table 3. Proposed Reactions for the Ethanol Conversion to Butanol and Side Reactions index

are,

reaction

refs

R1 R2 R3

2 ethanol ⇌ diethyl ether + water diethyl ether ⇌ ethanol + ethene ethanol ⇌ ethene + water

R4

ethanol ⇌ acetaldehyde + dihydrogen

R5

2 acetaldehyde ⇌ butyraldehyde + water

R6 R7 R8

2 ethanol ⇌ butanol + water butanol ⇌ butene + water butyraldehyde + dihydrogen ⇌ butanol

R9

2 acetaldehyde +2 dihydrogen ⇌ butanol + water

5, 13, 19, 30,31 32 1, 3, 5, 7, 8, 13, 30, 33−35 1, 8, 9, 13, 14, 17, 18, 30 1, 8, 9, 13, 14, 17, 18, 30 6−9, 11 3, 32, 35−37 1, 8, 9, 13, 14, 17−19, 30 9

Knowing the possible reactions, it is possible to evaluate if the experimental concentration of the identified components is thermodynamically favorable, i.e., if their concentration is below the equilibrium concentration of these reactions, the last one being defined by thermodynamics. This method of analyzing reversible reactions is presented and explained by Meunier, Scalbert, and Thibault-Starzyk,23 where the authors define the reaction quotient (Q) and the

respectively, the natural logarithm of the kinetic constant of reaction i in the reference temperature, the activation energy for reaction i divided by the gas constant and reference temperature, the natural logarithm of the adsorption equilibrium constant of component j in the reference temperature, and the adsorption enthalpy for component j divided by the gas constant and reference temperature. They 12983


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where the numerator is the difference in the number of parameters between the models and the denominator the degrees of freedom of the model with more parameters. If F is lower than or equal to Fcrit, the model with a lower number of parameters can be considered statistically equal to the one with more parameters. The equation to calculate F is eq 8, where FO is the objective function value of the model, p is the number of parameters, and n is the total number of experimental points. Subscript 1 refers to the model with a lower number of parameters and subscript 2 to the model with a higher number of parameters.

equilibrium constant (KEQ). The reaction quotient is the product of each component’s activity, each raised to the power of the corresponding stoichiometric coefficient for each given reaction. When working in the gaseous phase and under moderate pressures, each component’s activity can be approximated by its partial pressure. Therefore, eq 5 presents one example, the reaction quotient of R9 from Table 3. Q=

PWater ·PButanol PDi ‐ hydrogen 2·PAcetaldehyde 2

(5)

ij FO1 − FO2 yz jj p − p zz 2 1 { F= k jij FO2 zyz jn−p z k 2{

At the beginning of the reaction, there are no products formed; therefore, Q must be equal to zero. As the reaction starts to occur, Q increases, and if given enough time, Q will reach the thermodynamic equilibrium and will be equal to KEQ. Therefore, the approach-to-equilibrium (η), defined as the ratio between Q and KEQ, takes a maximum value of one when at equilibrium, meaning it should remain lower or equal to unity, i.e., η = Q/KEQ ≤ 1. Any η above unity would mean that the reaction is not thermodynamically favorable in that direction.23 The value of KEQ is related to the standard Gibbs free energy of each reaction (−ΔG0R) as presented in eq 6. −ΔG0R can be calculated using the thermodynamic parameters of the involved components, which can be found in the literature.24,25

3. RESULTS AND DISCUSSION 3.1. Thermodynamic Analysis. Reactions R1 to R9 were analyzed thermodynamically to evaluate their approach-toTable 4. Maximum η for Reactions R1 to R7

ij −ΔGR0 yz zz KEQ = expjjj j RT zz (6) k { 2.5. Parameter Estimation. After defining the reaction scheme for each mechanism, the kinetic parameters of each reaction were estimated by minimizing the least-squares objective function (OF), presented by eq 7.

∑ ∑ (yijexp − yijmod )2

reaction index

T (K)

KEQ

Q

η = Q/KEQ

R1 R2 R3 R4 R5 R6 R7

673.15 548.15 673.15 623.15 673.15 673.15 673.15

2.4817 41.506 1490.4 3.9301 443.10 1411.6 39502

0.3690 0.0378 0.0701 5.0 × 10−5 20.2695 0.0491 0.2686

0.1487 0.0091 5.0 × 10−5 1.3 × 10−4 0.0458 3 × 10−5 1 × 10−5

Table 5. η Results for R8 for the Central Point Experimental Data

Nexp NC

OF =

(8)

(7)

T (K)

KEQ

Q

η = Q/KEQ

where Nexp is the number of experiments, NC is the number of mod components, and yexp are molar fractions of organic ij and yij compounds in each experiment and in the model prediction, respectively. As it is not possible to measure experimentally the concentration of dihydrogen and water (it can only be inferred by the calculation of the atom balance), only the molar fraction of the organic compounds was used on this calculation. For the minimization of the OF, a hybrid algorithm that first uses the particle swarm method was used to search for a global best20,21 followed by a Gauss−Newton derivative method that further improves the estimation based on the best solution found. For all the estimated parameters, the confidence interval and the standard deviation were also calculated. 2.6. Fisher’s Test. Aiming to compare statistically the results between the two models, Fisher’s test was performed. This test was chosen as it allows a simple and direct comparison between model performances. More sophisticated tests, such as the chi-squared test,26,27 require a high number of experimental replication for an appropriate evaluation of experimental variances, going beyond of the scope of the present work. Fisher’s test is applied to decide if a model with a lower number of parameters is statistically equal to a model with more parameters, what can be used to justify the reduction of some parameters. In summary, this test compares a calculated F to the critical F (Fcrit), obtained from the Fisher distribution,

523.15 548.15 573.15 598.15 623.15 648.15 673.15

3.192 1.267 0.530 0.232 0.106 0.050 0.024

0.0 1280.16 2713.86 1736.74 2230.23 2233.03 238.174

0.0 1010.48 5117.93 7473.91 21050.15 44668.31 9801.58

i=1 j=1

Table 6. η Results for R9 for the Central Point Experimental Data T (K)

KEQ

Q

η = Q/KEQ

523.15 548.15 573.15 598.15 623.15 648.15 673.15

204025.46 27313.42 4347.07 805.18 170.48 40.64 10.77

0.0 89745.94 111955.21 30721.33 34658.45 34581.17 0.0

0.0 3.286 25.754 38.154 203.295 850.916 0.0

equilibrium and whether each one of them is favorable for the data collected on these experiments. For the reaction quotient calculation, the central point data was used, mainly due to the fact that this experiment was done in triplicate. From the proposed reactions, all of them, except R8 and R9, had η values very close to 0 (maximum 0.14 for R1 at 673.15 K). This result is summarized in Table 4, where the maximum 12984


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Industrial & Engineering Chemistry Research Table 7. Estimated Parameters for the Elementary Reaction MechanismModel 1 parameter T

ln(k1,1ref) T ln(k2,1ref) T ln(k3,1ref) T ln(k4,1ref) T ln(k5,1ref) T ln(k6,1ref) T ln(k7,1ref) E1,1

RTref E2,1 RTref E3,1 RTref E4,1 RTref E5,1 RTref E6,1 RTref E7,1 RTref OF =

value

lower limit

upper limit

standard dev.

−1.13 −0.85 −25.86 −3.33 7.95 −1.50 −2.04

−1.15 −0.92 −749.54 −3.37 7.77 −1.54 −2.23

−1.12 −0.78 697.81 −3.30 8.12 −1.45 −1.86

0.01 0.03 368.18 0.02 0.09 0.02 0.10

28.73

28.37

29.09

0.18

7.85

7.10

8.60

0.38

−149.67

−5197.46

4898.12

2568.15

0.36

−0.03

0.75

0.20

−21.91

−24.71

Table 9. Proposed Reactions from Model 2 index

reaction

R1 R2 R3 R4 R5 R6

2 ethanol ⇌ diethyl ether + water diethyl ether ⇌ ethanol + ethene ethanol ⇌ acetaldehyde + dihydrogen 2 acetaldehyde ⇌ butyraldehyde + water 2 ethanol ⇌ butanol + water butanol ⇌ butene + water

Table 10. Estimated Parameters for the Elementary Reaction MechanismModel 2 parameter

value

lower limit

upper limit

standard dev.

ln(kT1,2ref) ln(kT2,2ref) ln(kT3,2ref) ln(kT4,2ref) ln(kT5,2ref) T ln(k6,2ref)

−1.1494 −0.8375 −3.3118 7.9316 −1.4894 −2.0334

−1.1896 −0.9059 −3.3457 7.7576 −1.5349 −2.2188

−1.1092 −0.7691 −3.2779 8.1056 −1.444 −1.8479

0.0205 0.0348 0.0173 0.0885 0.0231 0.0943

28.9663

28.4153

29.5173

0.2803

7.5997

6.8332

8.3663

0.39

−1.0963

−1.4498

−0.7428

0.1799

−19.4514

−21.9437

−16.9591

1.268

11.2685

10.6343

11.9027

0.3227

10.5614

8.1275

12.9954

1.2383

E1,2 RTref

−19.11

1.42

E2,2 RTref

11.21

10.57

11.86

0.33

E3,2 RTref

10.61

8.15

13.07

1.25

E4,2 RTref

3.60478

E5,2

obtained η is presented for reactions R1 to R7. It is clearly seen that all of these reactions are far from equilibrium, can be considered thermodynamically favorable for the experimental conditions of this work, and therefore will be considered as the possible reaction path for the parameter estimation. As for reactions R8 and R9, Tables 5 and 6 represent their results for all the reaction temperatures in the central point experiment, where R8 presented values of η on the order of 105 while R9 presented values on the order of 103. This result is very important as it shows that this reaction is more favorable in the opposite direction of the Guerbet mechanism. As a consequence, these reactions will not be considered in the proposed mechanisms in this work. Moreover, this result shows that the Guerbet reaction pathway is not thermodynamically favorable in this experimental condition, where the direct condensation of two ethanol molecules appears to be the most favorable path to form 1-butanol. 3.2. Parameter Estimation. Considering that R1 to R7 will be the reactions considered as the pathway for 1-butanol production from ethanol over this Mg/Al catalyst, two different approaches were considered. One of them considers

RTref E6,2 RTref OF =

3.62691

all the reactions to be elementary, being called the Elementary Reaction Mechanism, while the other considers the adsorption, desorption, and surface reaction steps, the so-called the Heterogeneous Mechanism. 3.2.1. Elementary Reaction MechanismModel 1. Considering reactions R1 to R7 to be elementary and reversible reactions, it is possible to define each reaction rate, as shown in eqs 9 to 15. The subscript “1” represents Model 1. ij P P yz r1,1 = k1jjjjP12 − 2 8 zzzz j KEQ 1 z{ k

(9)

Table 8. Kinetic Constant for Each Experimental Reaction TemperatureModel 1 ki,1 k1,1 k2,1 k3,1 k4,1 k5,1 k6,1 k7,1

523.15 K 5.23 1.39 1.23 3.39 6.56 4.48 2.83

× × × × × × ×

−3

10 10−1 10−2 10−2 104 10−2 10−2

548.15 K 2.34 2.09 4.97 3.45 2.09 8.04 4.93

× × × × × × ×

−2

10 10−1 10−6 10−2 104 10−2 10−2

573.15 K 9.19 3.03 4.00 3.51 7.36 1.37 8.17

× × × × × × ×

−2

10 10−1 10−9 10−2 103 10−1 10−2

598.15 K 3.22 4.27 5.86 3.57 2.83 2.23 1.30 12985

× × × × × × ×

−1

10 10−1 10−12 10−2 103 10−1 10−1

623.15 K 1.02 5.85 1.45 3.62 1.18 3.50 1.98

× × × × × ×

10−1 10−14 10−2 103 10−1 10−1

648.15 K 2.95 7.82 5.71 3.67 5.23 5.30 2.94

× × × × × ×

10−1 10−17 10−2 102 10−1 10−1

673.15 K 7.90 1.02 3.36 3.71 2.46 7.79 4.23

× × × × ×

10−19 10−2 102 10−1 10−1


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Industrial & Engineering Chemistry Research Table 11. Kinetic Constant for Each Experimental Reaction TemperatureModel 2 ki,2

523.15 K

548.15 K

573.15 K

598.15 K

623.15 K

648.15 K

673.15 K

k1,2 k2,2 k3,2 k4,2 k5,2 k6,2

0.005 0.1455 0.0427 45294.04 0.0448 0.0288

0.0226 0.2164 0.0403 16408.71 0.0807 0.05

0.0896 0.3107 0.0382 6500.803 0.138 0.0826

0.3168 0.4328 0.0365 2783.877 0.2255 0.1309

1.0122 0.587 0.0349 1276.145 0.3543 0.1999

2.9562 0.7776 0.0335 621.3516 0.5376 0.2955

7.9841 1.0091 0.0323 318.8479 0.7913 0.4245

Table 12. Adsorption Equilibrium Constants constant

adsorbed component

KAD,1 KAD,2 KAD,3 KAD,4 KAD,5

ethanol water acetaldehyde butyraldehyde butanol

Table 13. Estimated Parameters for the Heterogeneous MechanismModel 3 parameter

value

lower limit

upper limit

standard dev.

T ln(k1,3ref) T ln(k2,3ref) T ln(k3,3ref) T ln(k4,3ref) T ln(k5,3ref) ln(kT6,3ref) ref ln(KTAD,1 ) Tref ln(KAD,2) ref ln(KTAD,3 ) ref ln(KTAD,4 ) ref ln(KTAD,5 )

21.2832 −0.0028 7.8158 7.0761 20.5817 −1.6167 −10.2086 −14.6918 1.3634 9.278 0.2564

19.8182 −0.1221 7.096 4.3438 19.1251 −19.6744 −10.958 −39210.7 0.0221 8.8877 −17.7908

22.7482 0.1166 8.5356 9.8084 22.0383 16.441 −9.4592 39181.3 2.7046 9.6682 18.3036

0.7453 0.0607 0.3662 1.39 0.741 9.1867 0.3812 19940.6 0.6824 0.1985 9.1813

17.5782

16.1858

18.9706

0.7084

7.4353

6.3098

8.5609

0.5726

−1.8233

−2.3876

−1.259

0.2871

−23.1069

−27.0602

−19.1536

2.0112

5.0466

3.5327

6.5605

0.7702

21.337

−110.02

152.694

66.8265

ΔH1 RTref

3.5735

2.1818

4.9652

0.708

ΔH2 RTref

34.9379

−135621.0

135690.0

69013.3

ΔH3 RTref

−4.5341

−6.603

−2.4653

1.0525

ΔH4 RTref

31.4081

26.4149

36.4012

2.5402

ΔH5 RTref

−10.5704

−142.259

121.118

66.9952

FO =

3.35376

E1,3 RTref E2,3 RTref E3,3 RTref E4,3 RTref E5,3 RTref E6,3 RTref

Figure 2. Heterogeneous mechanism proposed in this workModel 3.

ij PP yz r2,1 = k 2jjjjP2 − 1 3 zzzz j KEQ 2 z{ k ij P P yz r3,1 = k 3jjjjP1 − 3 8 zzzz j KEQ 3 z{ k

(10)

(11) 12986


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Industrial & Engineering Chemistry Research Table 14. Kinetic and Adsorption Constants for Each Experimental Reaction TemperatureModel 3 ki,3, KAD,j

523.15 K

548.15 K

573.15 K

598.15 K

k1,3 k2,3 k3,3 k4,3 k5,3 k6,3 KAD,1 KAD,2 KAD,3 KAD,4 KAD,5

1.41 × 108 3.43.10−1 3.22 × 103 3.25 × 104 4.21 × 108 9.31 × 10−3 2.21 × 10−5 2.78 × 10−9 7.49 1.18 × 102 5.88

3.52 × 108 5.06.10−1 2.93 × 103 9.73 × 103 5.48 × 108 2.84 × 10−2 2.66 × 10−5 1.72 × 10−8 5.91 6 × 10 × 102 3.39

8.13 × 108 7.21.10−1 2.68 × 103 3.24 × 103 6.97 × 108 7.83 × 10−2 3.15 × 10−5 9.08 × 10−8 4.76 2.72 × 103 2.05

1.75 × 109 9.97.10−1 2.48 × 103 1.18 × 103 8.68 × 108 1.99 × 10−1 3.69 × 10−5 4.16 × 10−7 3.91 1.07 × 104 1.29

ij P P yz r4,1 = k4jjjjP1 − 4 9 zzzz j KEQ 4 z{ k

ij P P yz r5,1 = k5jjjjP4 2P9 − 5 8 zzzz j KEQ 5 z{ k

(12)

ij P P yz r7,1 = k 7jjjjP6 − 7 8 zzzz j KEQ 7 z{ k

(14)

P P zy ji r6,1 = k6jjjjP12 − 6 8 zzzz j KEQ 6 z{ k

623.15 K 3.54 1.34 2.30 4.68 1.06 4.67 4.25 1.69 3.26 3.77 8.46

× 109 × × × × × ×

103 102 109 10−1 10−5 10−6

× 104 × 10−1

648.15 K 6.79 1.77 2.15 1.99 1.28 1.03 4.85 6.16 2.76 1.21 5.72

× 109 × 103 × 102 × 109 × 10−5 × 10−6 × 105 × 10−1

673.15 K 1.24 2.28 2.02 9.02 1.52 2.14 5.49 2.04 2.36 3.54 3.98

× 1010 × 103 × 101 × 109 × 10−5 × 10−5 × 105 × 10−1

of them have positive activation energy and presented much more consistent results in terms of standard deviation. The negative activation energy was also obtained for reaction R5. For this particular case, although there is evidence that the compound 2-butenal takes part as an intermediate in this reaction,6,19 with the experimental data of this work it was not possible to identify significant quantities of this compound, which does not allow its consideration for the reaction pathway and impedes the parameter estimation for this possible reaction. Therefore, reaction R5 will still be considered for the reaction pathway, highlighting that further investigation should be made regarding its mechanism. Considering what was discussed regarding R3, a new elementary reaction mechanism was proposed, where R3 does not take part in the mechanism. The reactions were renamed by keeping R1 and R2, but R4 became R3, R5 became R4, and so on, as presented in Table 9. 3.2.2. Elementary Reaction MechanismModel 2. By removing R3 from the proposed mechanism, a new mechanism was proposed and the reaction rates can be seen in eqs 16 to 21. Tables 10 and 11 present the new estimated parameters and the kinetic constant evaluated at the experimental reaction temperatures, respectively.

(13)

(15)

Using the reactions rates presented and the data from all experiments, the kinetic parameters were estimated and the result is presented in Table 7. To understand better the kinetic meaning of the estimated parameters for the experimental conditions evaluated on this work, the kinetic constant k was calculated for each reaction and reaction temperature, as shown in Table 8. By analyzing the data presented in Tables 7 and 8, it is possible to observe that reaction R3 presents some unexpected values for its kinetic rate and activation energy, such as (i) high standard deviation for the kinetic constant and activation energy, making the confidence region of these parameters contain the zero value, which could mean that these parameters are nonsignificant; (ii) negative activation energy, which goes directly against the statement that this reaction should benefit from high reaction temperatures;3,6 (iii) extremely low values for the kinetic constant at the experimental reaction temperatures, reaching orders of 10−19, meaning that the R3 reaction rate would be very close zero, presenting very little effect in the conversion of reagents to products in the proposed mechanism. As shown by Revell and Williamson,28 an elementary step, by definition, must occur in one single step and present positive activation energy. Although it is common to encounter negative activation energies in experiments, this happens when the considered reaction is not an actual elementary step, as there must be a mechanism of two or more elementary reactions (with positive activation energy) that represents the conversion of those reagents to products.28,29 According to the above discussion, it can be observed that the proposed mechanism already covers this situation, since reactions R1 and R2 represent the global reaction R3 and both

P P zy ji r1,2 = k1jjjjP12 − 2 8 zzzz j KEQ 1 z{ k ij PP yz r2,2 = k 2jjjjP2 − 1 3 zzzz j KEQ 2 z{ k

(16)

ij P P yz r4,2 = k4jjjjP4 2P9 − 5 8 zzzz j KEQ 4 z{ k

(18)


(20)

ij P P yz r3,2 = k 3jjjjP1 − 4 9 zzzz j KEQ 3 z{ k

(17)


(19)

(21)

From Table 10, it is possible to see that none of the estimated parameters that had high standard deviation contained zero in their confidence regions. It is also possible 12987


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Figure 3. continued

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Figure 3. continued

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Figure 3. Simulations for Model 2 and experimental data (●, ethanol data; − ethanol model; ◀, diethyl ether data; --, diethyl ether model; ▲, ethene data; ··, ethene model; ▶ − acetaldehyde data; -·, acetaldehyde model; ■, butyraldehyde data; --, butyraldehyde model; ⧫, 1-butanol data; −, 1-butanol model; ▼, butene data; ···, butene model) as a function of the reaction temperature for the experiments: (a) Exp 1, (b) Exp 2, (c) Exp 3, (d) Exp 4, (e) Exp 5, (f) Exp 6, (g) Exp 7, (h) Exp 8, and (i) Exp 9 (Table 1).

considered to be the surface reaction step). All other steps (adsorption and desorption) were considered to be in equilibrium. From the mechanism proposed in Figure 2, the reaction rates were determined by following the Langmuir−Hinshelwood−Hougen−Watson (LHHW) hypothesis, and they are presented in eqs 22 to 28. In addition to the kinetic constant of each reaction, there is also the adsorption equilibrium constant (KAD,j), where the considered adsorbed component products are shown in Table 12, and the vacant activate site concentration, represented by C∗. The vacant active site concentration comes from a numeric balance that considers the total concentration of active sites, the vacant active sites, and the sites where reactants or products are adsorbed. The value of the total concentration of active sites is incorporated to the kinetic constant.

to observe that the objective function (FO) had very little change from Model 1 (3.60478) to Model 2 (3.62691), which represents an increase of less than 1%. Regarding activation energies, Model 2 presents again two negative values, for R3 and R4 (unless stated, from now on consider Table 9 as reference for the reactions). R4 was already discussed previously, as it is the former R5 from Table 3, but R3 (former R4 from Table 3) presents a new situation. Looking back at Table 7, it is possible to see that the activation energy for this reaction was close to zero, and now at the new estimation, despite being negative, it is again close to zero. It is hard to take any conclusion from this value as it is not possible to rule out that this value is related to experimental errors. Furthermore, no intermediate for this reaction was identified, so for now this negative activation energy will only give us a hint to look deeper into this reaction. Table 11 presents the kinetic constants for all experimental reaction temperatures. It is clearly perceptible that the orders for all kinetic constants are similar for all reactions, except for that of R4, which presents a higher order. By looking at the equation rate for R4 in eq 18, this high value for the kinetic constant can be understood as this value needs to compensate the low concentrations of the reactants to form a high concentration of the product butyraldehyde. Acetaldehyde and dihydrogen, the reactants of this reaction, are formed in the same reaction R3, and their low concentration and the high concentration of the product butyraldehyde will be clearer when the molar fraction graphs are shown and later discussed in this work. 3.2.3. Heterogeneous MechanismModel 3. By defining which elementary reactions would take part in the mechanisms proposed, each elementary reaction was broken down into adsorption, surface reaction, and desorption steps. The literature covers some mechanisms involved for many catalysts that have similar properties and for the Mg/Al oxide derived from hydrotalcites,3,7,13,14,17,30 and the mechanisms proposed in this work try to combine the ideas from all of them. Figure 2 presents the proposed heterogeneous mechanism for the reactions, based on the Model 2 elementary reactions. It is important to note that, as this is the first approach, the acidic and basic sites were simplified as a single active site (*). The global reactions are shown in bold, and the ratedetermining step is underlined (all limiting steps were

ij P P yz r1,3 = k1KAD ,12C 2jjjjP12 − 2 8 zzzz *j KEQ 1 z{ k ij PP yz r2,3 = k 2C jjjjP2 − 1 3 zzzz *j KEQ 2 z{ k

(22)

ij P P yz r4,3 = k4KAD ,32C 2jjjjP4 2P9 − 5 8 zzzz *j KEQ 4 z{ k

(24)

P P zy ji r6,3 = k6KAD ,5C jjjjP6 − 7 8 zzzz *j KEQ 6 z{ k

(26)

ij P P yz r3,3 = k 3KAD ,1C jjjjP1 − 4 9 zzzz *j KEQ 3 z{ k

(23)

ij P P yz r5,3 = k5KAD ,12C 2jjjjP12 − 6 8 zzzz *j KEQ 5 z{ k

(25)

(27)

1 C = * K P+K P +K P +K P +K P AD ,1 1 AD ,2 8 AD ,3 4 AD ,4 5 AD ,5 6 (28)

Following the estimation of the parameters, Table 13 presents the estimated values, with their lower and upper limit 12990


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Figure 4. continued

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Figure 4. continued

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Figure 4. Simulations for Model 3 and experimental data (●, ethanol data; −, ethanol model; ◀, diethyl ether data; --, diethyl ether model; ▲, ethene data; ··, ethene model; ▶, acetaldehyde data; -·, acetaldehyde model; ■, butyraldehyde data; --, butyraldehyde model; ⧫, 1-butanol data; −, 1-butanol model; ▼, butene data; ··, butene model) as a function of the reaction temperature for the experiments: (a) Exp 1, (b) Exp 2, (c) Exp 3, (d) Exp 4, (e) Exp 5, (f) Exp 6, (g) Exp 7, (h) Exp 8, and (i) Exp 9 (Table 1).

experiment, showing on the same plot the experimental data (points) used for the estimation. The results can be seen in Figure 3 for Model 2 and in Figure 4 for Model 3. For the simulations and experimental data, the components were divided into two different plots for each experiment, according to their molar fraction, facilitating the visualization of components with lower molar fractions. Another important characteristic of Figures 3 and 4 is that water and dihydrogen were not plotted on the graphs, as these compounds are not measured in the experiments and, therefore, would not be comparable. Therefore, the only compounds presented in these figures will be the organic compounds. One of the first findings observed in Figures 3 and 4 is that there is no significant difference between Models 2 and 3, since all components presented the same behavior for both simulations. Thus, both results will be elucidated together in the next paragraphs. Considering the ethanol, its molar fraction continuously drops when the reaction temperature is increased, which is expected and observed in the experimental data. It was also demonstrated by the simulations performed in this work. The high conversion at higher temperatures of ethanol is mainly explained by the formation of olefins, in this case ethene, where its formation is favored when the reaction temperature is increased. The olefin formation also explains the behavior observed for diethyl ether and for 1-butanol, where their molar fraction increases with the increase of reaction temperature up to a point where the formations of ethene and butene start to be more favored. The aldehydes are the compounds that had the greater discrepancies, as the simulation failed to predict some of their behavior. Analyzing first acetaldehyde, it is possible to observe that on experiments 1, 4, 5, and 6, where the experimental data showed a peak of maximum formation, the simulation succeeded in representing its molar fraction, despite the slightly dislocated peak of formation. However, for the remaining experiments, acetaldehyde formation appeared to be favored by the increase of the reaction temperature, a situation that was not predicted by the simulations. Butyraldehyde is the component that presents the most unstable behavior, as its molar fraction is relatively low for all the experiments except experiments 5 and 6, where it represents around 45% of the total organic components in

Table 15. Fisher’s Test for Comparison of Models comparison

lower × higher parameter number

F

Fcrit

1 2 3

Model 2 × Model 1 Model 2 × Model 3 Model 1 × Model 3

1.3168 3.4126 3.9201

3.0172 1.8533 1.9605

and standard deviation, and the objective function value. Although the objective had decreased about 8% compared to Model 2, it is clear to see that that many parameters had a high standard deviation and that the confidence region contained the zero value. It may be highlighted that, due model nonlinearity, some estimated parameters are highly correlated to each other, which makes a precise parameter estimation difficult; however, this is an intrinsic characteristic of the kinetic models with a large number of parameters that are estimated simultaneously. This simulation involves a total of 22 parameters that are parts of a complex system of differential equations, which may cause a lot of conflicts during their estimation. As made for the other models, Table 14 presents the kinetic constants and adsorption equilibrium constants evaluated at the experimental reaction temperatures. Again, the complexity of the system makes the interpretation of these values harder than the interpretation for the previous Models 1 and 2, where each kinetic constant was related to only one reaction rate. Now, not only is the kinetic constant related to the reaction rate, but also the adsorption equilibrium constants and the vacant active site concentration are, the latter requiring all adsorption equilibrium constants to be evaluated during its calculation. Considering the results and the complexity of the heterogeneous system, a deeper analysis should be performed, perhaps trying to constrain the reaction paths by starting not from ethanol but from other compounds like acetaldehyde, which hopefully would increase the intermediate component concentration, enhancing their analysis, and also decrease the number of reactions involved, allowing better parameter estimation without as many dependencies. 3.3. SimulationsModels 2 and 3. With the estimated parameters and the reactions rates proposed in the last section, a MatLab routine was also implemented to solve numerically the system of differential equations of Models 2 and 3, where the resulting molar fractions (lines) were plotted for each 12993


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Industrial & Engineering Chemistry Research Notes

the latter one. This substantial change in behavior was not predicted by the simulations, and this result reinforces the necessity of a deeper analysis of the reactions involved in its formation. Overall, it can be seen that the simulations represent quite well the experimental data in the majority of the experiments, by presenting close molar fraction values and presenting a similar behavior from the apparent tendency from the experimental data. Some discrepancies, especially the ones for the aldehydes, again strengthen the necessity of performing more experiments, where feeding the reactor with an intermediate component, such as aldehyde, might be crucial to further understand the mechanisms involved in this reaction scheme. 3.4. Fisher’s Test. Fisher’s test was performed to compare statistically one model to another and evaluate if they can be considered as equal when representing the data. Table 15 presents the results obtained for this test. It can be seen that the calculated F for the comparison between Model 2 and Model 1 was lower than the critical F, showing that Model 2 can be considered statistically equal to Model 1, supporting the decision to remove one of the reactions from the scheme. When comparing Model 2 to Model 3, the calculated F was higher than the critical F; therefore, Model 3 can be considered as a better model to fit the experimental data than Model 2, despite the higher standard deviations. To be sure Model 3 is also statistically better than Model 1, this comparison was also done, where the calculated F again was higher than the critical F, proving that Model 3 is also a better model to fit the experimental data than Model 1.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank the National Council of Technological and Scientific Development (CNPq), the Coordination for the Improvement of Higher Education Personnel (CAPES), and the Research Support Foundation of Rio Grande do Sul (FAPERGS) for the financial support for this project.

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4. CONCLUSION The experimental data from the conversion of ethanol to 1butanol over Mg and Al oxides derived from hydrotalcites, performed at different reaction temperatures, allowed a kinetic modeling of this complex system reaction for the experimental conditions presented in this work. The results showed that the Guerbet reaction pathway, where ethanol is converted to 1-butanol in a sequence of steps, does occur, but only up to the formation of butyraldehyde, where the final conversion of this intermediate to 1-butanol is not thermodynamically favorable for the experimental conditions studied. Rather, it was possible to show that the direct condensation of two ethanol molecules to 1-butanol was the most favorable path for this conversion to occur, where a mechanism of six elementary reactions was proposed and its kinetic parameters were estimated using a particle swarm algorithm. Estimations resulted in a good representation of the experimental data; still, further work must be made to better understand the mechanisms involved in the formation of the Guerbet reaction intermediates. A heterogeneous mechanism was also proposed, and although this model presented high standard deviations for the estimated parameters, Fisher’s test proved that it was the best model evaluated in this work.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*(N.P.G.S.) E-mail: [email protected]. Phone: +55-55-32208448. Fax: +55-55-3220-8030. ORCID

Nina P. G. Salau: 0000-0002-6139-7369 12994


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Mechanism and Kinetic Modeling of Ethanol Conversion to 1-Butanol

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