Estimation of kinetic parameters and diffusion coefficients for the transesterification of triolein with methanol on a solid ZnAl2O4 catalyst

Accepted Manuscript Estimation of kinetic parameters and diffusion coefficients for the transesterification of triolein with methanol on a solid ZnAl2O4 catalyst Allain Florent, Portha Jean-François, Girot Emilien, Falk Laurent, Dandeu Aurélie, Coupard Vincent PII: DOI: Reference:

S1385-8947(15)01041-4 http://dx.doi.org/10.1016/j.cej.2015.07.075 CEJ 13973

To appear in:

Chemical Engineering Journal

Received Date: Revised Date: Accepted Date:

14 April 2015 23 July 2015 24 July 2015

Please cite this article as: A. Florent, P. Jean-François, G. Emilien, F. Laurent, D. Aurélie, C. Vincent, Estimation of kinetic parameters and diffusion coefficients for the transesterification of triolein with methanol on a solid ZnAl2O4 catalyst, Chemical Engineering Journal (2015), doi: http://dx.doi.org/10.1016/j.cej.2015.07.075

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Estimation of kinetic parameters and diffusion coefficients for the transesterification of triolein with methanol on a solid ZnAl2O4 catalyst ALLAIN Florent1, PORTHA Jean-François1,2,*, GIROT Emilien1, FALK Laurent1,2, DANDEU Aurélie3, COUPARD Vincent3 1

Université de Lorraine, Laboratoire Réactions et Génie des Procédés LRGP, UMR 7274, ENSIC, F-54000 Nancy, France

2

CNRS, Laboratoire Réactions et Génie des Procédés LRGP, UMR 7274, ENSIC, F-54000 Nancy, France

3

IFP Énergies Nouvelles, F-69360 Solaize, France

Abstract The transesterification of vegetable oils by methanol implies a set of three parallel-series reversible reactions. Over a heterogeneous catalyst, reactions are limited by molecular diffusion, resulting in the use of a large excess of methanol to achieve a high conversion. This excess is detrimental to process efficiency because it involves large energy requirement for downstream separation. In order to identify the coupled physico-chemical phenomena and to optimize the process, a pilot unit was developed to perform transesterification of triglycerides with methanol over a solid ZnAl2O4 catalyst in a tubular fixed bed reactor under high pressure and temperature. The effects of different parameters such as particle diameter, temperature, residence time and molar feed ratio of methanol to triglyceride on fatty acid methyl ester (FAME) yield and triglyceride (TG) conversion were studied. A pseudo-homogeneous reactor model has been developed to identify rate laws and kinetic parameters by exploiting the experimental data in stationary regime. A set of kinetic constants was also determined for the given catalyst considering two kinetic models: an Eley-Rideal model with the reaction between TG and methanol as the rate determining step and a classical second order equilibrated reaction without adsorption. A heterogeneous model has also been established to determine molecular diffusion coefficients for each species in the mixture, through the use of experimental results in the transient regime. These molecular diffusion coefficients are dependent on the mixture viscosity and temperature. As a result, it was determined that diffusion of triglycerides and the first reaction kinetic rates are limiting the global conversion of the system. Keywords: Transesterification, Biodiesel, Reactor modeling, Kinetics, Diffusion coefficients. *

Author to whom correspondence should be sent: [email protected]. Tel: +33 383 17 50 38

1

Abbreviations: IFPen:, IFP Énergies Nouvelles; TG: triglycerides, DG: diglycerides, MG: monoglycerides, G: glycerol, FAME: fatty acid methyl ester, FAEE: fatty acid ethyl ester, MeOl: methyl oleate, NIR: near infra-red, GC: gas chromatography, HPLC: high performance liquid chromatography, SEC: size exclusion chromatography, FTIR: Fourier transform infrared, NMR: nuclear magnetic resonance, SBO: soybean oil, SiC: Silicon Carbide, NOx: Nitrogen oxides, MSTFA: N-methyl-N-trimethylsilyltrifluoroacetamide. Nomenclature: Latin Symbols




Activity of species i



Concentration of species i ( .   )




Superficial area of the solid ( .  )



Concentration at the surface of the catalyst ( .   )

,

Molecular diffusion coefficient of species i ( .   )

,

Axial dispersion coefficient of species i ( .   )

,

Effective diffusion coefficient of species i ( .  )



Catalyst particle diameter ( )




Activation energy of reaction j (.    )




Adsorption heat of methanol (.    )



Adsorption constant of glycerides



Adsorption constant of methanol



 Pre-exponential factor of reaction j ( .    .  . !"#$# )



Adsorption constant of glycerol



Equilibrium constant of reaction j

%

Mass transfer coefficient between solid and fluid (.  )

 

 Pre-exponential factor of methanol adsorption ( .   .   . !"#$# )

&

Reactor length ( )

' (

Molecular weight of species i (!.    ) +,-

() = . 0 () =

/ 1

+,-

./ 02

Pressure (bar)

Axial Peclet number Molecular Peclet number

2

3

3) =

+,- 45 62

7 7̅

Ideal gas constant (.    .  ) Particle Reynolds number Catalyst radial coordinate ( )

Apparent mean reaction rate ( .  )

7

 Rate of reaction j ( .   . !"#$# )

:

Surface of the catalyst at radius r ( )

7

Catalyst particle radius ( )

:; = 4

65

5 02

<

<>

Schmidt number Temperature ( or ° )

Critical temperature ()

?,

Characteristic time of diffusion ()

?@#"

Characteristic time of chemical reaction ()

B"

Critical volume (; .   )

BD

Volume of reactor ( )

?#

Characteristic time of mass transfer between the solid and fluid phases ()

A

Superficial fluid velocity (.   )

BC

Volume of liquid ( )

E ,

Molar volume of species i (; .    )

G

Mole fraction

H%

Bed void fraction

F

Reactor length coordinate ()

Greek symbols

H

IJ =  O P

Porosity of the catalyst K @̅ ,-

0L55 >M

Weisz criterion Associativity constant of species i Activity coefficient of species i

ΩD

Cross section of the catalytic bed ( )

S

Dynamic viscosity of the mixture (;( )

R T



Acentric factor of species i

Stoichiometric coefficient of species i in reaction j

3

U"#$

Catalyst bulk density (!.  )

V

Residence time (s)

U V

WX,

Fluid density (!.  ) Catalyst tortuosity

Superscript

Relative error on the experimental mole fraction of species Y

in

Inlet of the reactor

out

Outlet of the reactor

f

Fluid phase

s

Solid phase

1. Introduction Biodiesel, produced from vegetable oils (mainly rapeseed, soybean or sunflower oils), is an alternative to fossil fuel diesel. In order to reduce the viscosity of these oils and render them usable as diesel, they undergo a transesterification reaction by a light alcohol to form fatty acid esters. Biodiesel can then be used directly in a diesel engine or it can be mixed with conventional diesel. Several countries have been developing this technology. The main advantages of biodiesel are its low toxicity, renewability and low carbon monoxide, sulfur and particulate emissions when compared to petroleum based diesel conventionally used. Drawbacks include a higher emission of NOx and a competition for land use with crops, which are the main reason for the development of the newest generations of biofuels. Heterogeneous transesterification of vegetable oil, as a mean of biodiesel production, presents high advantages in terms of purity of both biodiesel and glycerol; catalyst separation is furthermore avoided. Studies of heterogeneous catalysts generally show that leaching of active species occurs in the effluent (especially for fine CaO, ZnO or MgO catalyst powder) which is not acceptable for an industrial unit. However, an industrial process has been developed using a zinc aluminate catalyst which promotes the transesterification without catalyst loss [1]. The stability of this ZnAl2O4 catalyst has been studied by Pugnet et al. [2] showing that no significant leaching of the zinc aluminate catalyst in glycerin or in ester occurs. Moreover, no significant deactivation has been observed (the catalyst can be recycled up to 3 times without deactivation). However, heterogeneous transesterification requires a large excess of methanol to obtain a high conversion, as well as high operating pressure and

4

temperature increasing the solubility of methanol into oil [1]. Severe operating conditions guarantee also achievement of a unique liquid phase implying no mass transfer limitations and decreasing the viscosity. The requirement of severe operating parameters needs to be addressed in order to reduce the cost of the downstream separation and the environmental impact of the industrial process. A continuous pilot unit, including two fixed bed reactors, was built to understand and identify the coupled phenomena (thermodynamic equilibrium, kinetics, external and internal mass transfer) by handling small quantities of chemicals in a large experimental data range. The influence of the methanol to oil inlet molar ratio, of reactor temperature, and of space time, among other parameters, were studied. Triglyceride (TG), diglyceride (DG), monoglyceride (MG), glycerol (G) and fatty acid methyl ester (FAME) mole fraction at the outlet of the pilot were determined through gas chromatography (GC) following the EN14105 method. Methanol was removed previously by evaporation. A stationary pseudo-homogeneous model was developed to determine the kinetic model and the corresponding constants by minimizing the difference between experimental and theoretical mole fraction of each species. A heterogeneous model was then established to determine molecular diffusion coefficient of species by exploiting experimental results in transient regime. The knowledge of these parameters allowed to better identify the limiting phenomena and then to optimize the industrial process.

1.1. Reaction set of vegetable oils transesterification Biodiesel is produced by transesterification of triglycerides with a stoichiometric excess of methanol following the reaction given by equation (1). Glycerol (G) and fatty acid methyl ester (FAME) are produced. TG + 3MeOH ↔ G + 3FAME

(1)

This global reaction can be decomposed in three parallel-series reactions, each consuming one mole of methanol and producing one mole of FAME. The set of reactions is given by equations (2), (3) and (4). TG + MeOH ↔ DG + FAME

(2)

DG + MeOH ↔ MG + FAME

(3)

MG + MeOH ↔ G + FAME

(4)

5

These reactions can be catalyzed in different ways: homogeneously, heterogeneously, or with enzymes. Homogeneous catalysis is the most common one when it comes to industrial applications, but heterogeneous catalysis is also possible and can solve some of the problems of homogeneous catalysis, such as the separation of the catalyst from the reaction mixture and the absence of waste streams. Enzymatic catalysis will not be addressed in this paper. Both bases and acids have been used as homogeneous and heterogeneous catalysts. However, even without catalyst, for high temperatures and high molar ratios (around 220°C and a ratio of 21 between methanol and soy bean oil) and after 10 hours of reaction, 85% in mass of methyl ester can be found in the oil phase (which do not contain any ester at the beginning), as observed by Diasakou et al. [3]. However, the third reaction producing glycerol tends to be kinetically very slow in the absence of catalyst, as monoglyceride levels tended to stay high and glycerol content low. Irreversible kinetics parameters were determined based on second order reactions to fit the experimental data for this non-catalytic reaction. Moreover, no by-products were detected.

1.2. Homogeneous catalysis Homogeneous catalysts such as sodium hydroxide or sulfuric acid are used in several processes of transesterification of fatty acids [1], [4]. Freedman et al [5] studied the transesterification of soybean oil with methanol and butanol with H2SO4, NaOBu or NaOCH3 as catalysts. Influence of temperature and ratio of alcohol to soybean oil were studied. Their experiments confirmed the three successive and parallel second order reactions for the case of butanol with a alcohol:oil molar ratio of 6:1. With increasing ratios, the kinetics tends towards first orders. They also showed that for the case of methanol, at a methanol:oil ratio of 6:1, the best description would be a combination of the second order consecutive reactions set (equation 2-4) combined with a forth order kinetics describing the global reaction (equation 1). Indeed, ester was appearing experimentally too fast with methanol to only be obtained through second order rate laws. The smaller size of methanol compared to butanol could explain this phenomenon, as several methanol molecules could react simultaneously with the triglyceride.

6

Noureddini et al. [6] studied the homogeneous kinetics of transesterification of soybean oil by methanol with NaOH as catalyst in a stirred tank reactor. Variations in temperature and mixing was studied, where the alcohol to oil ratio and catalyst amount were kept constant. Activation energies were determined and they proposed a mechanism in which a mass transfer controlled region is followed by a kinetically controlled one. Indeed, the system is first controlled by the transfer between the oil and alcohol phases. As ester is formed, the solubility of the two phases increases, leading to a monophasic system, and the reaction is then limited by kinetics. Kinetic mechanism is determined to be a second order for each reaction (for forward and reverse reactions). With increasing stirring speed, the apparent reaction rate increases, methyl ester conversion occurs earlier and the equilibrium is reached earlier. The same goes for temperature. The global reaction considered by Freedman et al. [5] was discarded in that study as it did not help fitting the experimental data. Moreover they did not observe any inhibition effect due to the formation of glycerol in the last step of the reaction.

1.3. Heterogeneous catalysis Heterogeneous catalysis presents several advantages over the homogeneous counterparts. No soaps are formed during the reaction (for base catalysis), the catalyst is easily recovered and the downstream separation is simplified, leading to an easy recovery of glycerol with purity higher than 98 % in mass [1]. However, in order to reach a sufficiently high level of TG conversion and of FAME yield by shifting the thermodynamic equilibrium, the molar feed ratio of methanol to oil needs to be increased in the heterogeneous process. Catalysts consisting of a mix of Mg and Al were used by Kapil et al. [7] in the determination of kinetics for the transesterification of triglycerides. They compared three different models of kinetics (Eley-Rideal (ER), Langmuir-Hinwhelwood-Hougen-Watson (LHHW) and Hattori) with different assumptions on the rate determining step. Activities, calculated with the UNIFAC method, were used to take into account the non-ideality of the mixture. They identified the LHHW model with methanol adsorption as the limiting step to be the most accurate one for their experiments. Dossin et al. [8], [9] also used the Eley-Rideal model with activity coefficient (based on the UNIFAC method) for the transesterification of acetic acid with methanol and later applied it to the transesterification of triglycerides. They again assumed that methanol adsorption was the rate limiting step, which enabled them to transfer

7

this model from acetic acid to triglycerides, that all three reactions had the same rate constant, and that their equilibrium constants were equal to one. The transesterification of palm oil with biodiesel on a KF/Ca-Mg-Al hydrotalcite solid base catalyst was studied by Xiao et al. [10]. They used isopropyl ether to solubilize oil and methanol and obtain a homogeneous system. An Eley-Rideal type mechanism with adsorption of methanol and reaction with non-adsorbed glycerides was developed for the global reaction given by Equation (1). The rate determining step was assumed to be the reaction between adsorbed methanol and non-adsorbed triglyceride. Pugnet et al. [2] studied the reaction of transesterification of rapeseed oil with methanol in a batch reactor on the same ZnAl2O4 catalyst that is used in the present work, considering several catalyst sizes, mixing speeds, molar ratio of methanol to oil and temperatures. They showed that the thermal activity of the reactions could not be neglected in their case, except for the third reaction which is not activated without catalyst, confirming the results of Diasakou et al. [3]. A kinetics model without adsorption was used and the first reaction was determined to be the limiting one in terms of kinetics. The third reaction is highly promoted by the addition of a catalyst. The catalyst was determined to not be affected by attrition, and to be stable in time. It was also showed that the use of the catalyst as powders of less than 500

S in diameters leads to a kinetic regime, not limited by diffusion. Stirring speed is needed to be high enough, above 800 rpm to avoid limitation due to external mass transfer. Melero et al.

[11] proposed a review of several heterogeneous acid catalysts available for transesterification of oils. Lee and Wilson [12] present a review on heterogeneous transesterification explaining how new synthetic materials based upon solid acids and bases with tailored pore architecture can improve diffusion to the active sites. Davison et al. [13] published a pertinent overview on kinetic reaction and diffusive transport modelling of the heterogeneously catalyzed triglycerides transesterification. In this paper, a model system of tributyrin transesterification in the presence of MgO catalysts is used and recommendations are provided on multicomponent diffusion calculations, which is quite uncommon. Excluding this article form Davison et al., a majority of the presented studies does not consider the possibility of diffusion limitations due to the large size of the triglycerides molecules. Even though the kinetics and thermodynamic equilibrium of such reactions have been studied, they might not entirely explain the high amount of methanol required with respect to stoichiometry to achieve a high conversion in an industrial process. Therefore this

8

problem of a high number of limiting parameters is addressed in this paper, as some of them are still to be identified. This present work is presented with an aim for future work to optimize the industrial production process of heterogeneous biodiesel synthesis.

2. Materials and methods Experiments were conducted on a pilot unit and the products were analyzed for quantification after a step of phases separation. The experimental results enable us to observe the influences of temperature, molar ratio and residence time on the glycerides and ester contents in the oil phase. It was then possible to determine the value of the parameters of the kinetic rate law that is the most adapted to the case study, by optimizing a pseudo-homogeneous plug-flow reactor model with regards to the mole fractions of the oil phase in the steady state regime for different parameters values. First, a literature review applied on transesterification monitoring is presented; second, the pilot unit and the analysis method used are described.

2.1. Transesterification monitoring: literature review Different methods can be applied to monitor and to analyze the proceedings of the transesterification reaction of triglycerides, depending on the nature of the products (fatty acid methyl ester, FAME or fatty acid ethyl ester, FAEE) and the level of accuracy desired. Online measurement of the yield of ester obtained in the process can be achieved through viscosity control [14]–[15]. The oil phase density can also be used, as shown by Filippis et al., who were able to establish a good correlation between the oil phase density of the mix and the ester content, provided that it is in the 85-100 % in mass range [16]. Raman spectroscopy can also be used with near infra-red (NIR) sources for control of FAEE. However the Raman spectrums of FAME and triglycerides present fewer variations than that of FAEE and triglycerides, limiting possible applications of Raman spectroscopy to FAME formation reactions [17]. Fourier transform infra-red (FTIR) can also be used to monitor FAEE content [18] and FAME content [19]. Finally, nuclear magnetic resonance (H-NMR) measurements based on the α-CH2, glyceridic and methyl ester protons can be used to monitor

9

the fractions of FAME (or FAEE but with a little more difficulties) and total remaining glycerides simultaneously [19]–[22]. To fully analyze the mole fraction of monoglycerides (MG), diglycerides (DG), triglycerides (TG), glycerol (G) and fatty acid ester produced, chromatographic methods are available. Gas Chromatography (GC) [23], High Performance Liquid Chromatography (HPLC) [24] and Size Exclusion Chromatography (SEC) [25] are all available and the reader should refer to the review by Meher et al. [26] for more details. European standards for biodiesel are ruled by the norm EN 14214 [27] and analysis can be performed following the norm EN 14105 [28], [29], which uses gas chromatography. In this paper, chromatography analyses were based on this norm, and therefore GC was used. Analysis of the methanol and glycerol content in the polar alcohol phase cannot always be obtained with the previously mentioned methods, and in particular cannot be obtained with the GC method, EN 14105, used in this paper. Those mole fractions were not obtained in the present work as they are not necessary to the determination of the kinetics, but they could be obtained through a different GC method [30]. In the present work, they were obtained based on mass balances between the inlet and outlet of the pilot unit and the experimental conversions of all the glycerides.

2.2. Pilot unit Methanol of analytical grade was obtained from Sigma Aldrich. Purified triolein (98.5 % in mass) and rapeseed oil methyl ester (99.1 % in mass) were obtained from IFP Energies Nouvelles (Solaize, France). Calibration standards for gas chromatography analysis were purchased from Agilent Technologies (Agilent Technologies, Colorado Springs, CO, USA) and reference standards (glycerol tricaprate, butanetriol) from Sigma-Aldrich (Sigma-Aldrich, Saint-Louis, MO, USA). Heptane and pyridine of analytical grade were also purchased from Sigma-Aldrich (Sigma-Aldrich, Saint-Louis, MO, USA). A simple schematic of the pilot unit is presented in Figure 1 and a picture is given in Figure 2. Figure 1: Simplified schematics of the pilot unit.

Figure 2: Picture of the pilot unit developed in the LRGP.

10

Two cylinders of 6 mm of diameter and 5 mL volume were used as reactors and place inside a Heraeus oven (Thermo Scientific, USA). The reactors were filled with either catalyst or SiC depending on the experiment. A smaller tube filled with SiC was used as a static mixer to ensure a good mixing of methanol and triolein before reactors. This mixer was also placed inside the oven. Pressure inside the system was regulated at the outlet with a Brooks 5866 series pressure controller linked to a Brooks control panel. The inlet flow of triolein was regulated with the use of a 307 Gilson pump (Middleton, WI, USA) and measured with a mini cori-flow flow-meter (Bronkhorst, Ruurlo, Netherlands). The inlet flow of methanol was regulated with the use of a similar 307 Gilson pump and measured with a liquid-flow flowmeter (Bronkhorst, Ruurlo, Netherlands). Set points for the flow rates were entered through a graphical Lab-view interface developed at the laboratory on an Optiplex 740 computer (Dell, USA). Sufficient pressure drops between the inlet and outlet of the flow-meters were assured through the use of two Swagelok pressure regulators (Solon, OH, USA) to ensure a good flow-rate regulation. Flow-rates of triolein and methanol ranged respectively from 1 to 20 g/h and from 1 to 15 g/h. The mesoporous ZnAl2O4 catalyst was provided by IFPen (Solaize, France), in the form of extrudates of size 2.5 mm. It was grinded down to a smaller size for this study around 355400 µm; particles are then supposed to be spherical. This catalyst presents a high resistance to deactivation and to attrition. No leaching of active phase in glycerin or in ester has been experimentally observed. The characteristic of the catalyst are given in Table 1. Table 1: Catalyst properties.

Molar ratio Zn/Al

0.3

Specific area (m2/g)

160

Size of mesopores (nm)

9 -100

Density (kg/m3)

1188

Tortuosity

2.5

Porosity

0.512

11

After placing the catalyst in the reactors, water was removed from the catalyst by flowing methanol in the pilot until complete removal. The amount of water was followed by Karl Fisher titration of regular sampling at the outlet, and the drying was considered complete when water levels were equal between the inlet and the outlet of the pilot unit.

2.3. Preparation of samples Methanol was removed from samples using a TurboVap LV evaporator (CaliperLife Sciences, Hopkinton, MA, USA) with a stream of N2 at 15 psi and a bath temperature of 45°C as it was previously done in the literature [31]. Samples were then placed in storage at 4°C until GC analysis. Samples of 10 mg were placed in a GC vial and set in the automated preparation and injection tray on the gas chromatograph. Solutions of reference standards in pyridine were prepared manually with concentrations of 8 mg/ml for glycerol tricaprate and 1 mg/ml for butanetriol. 8 µl of the butanetriol solution, 10 µl of the glycerol tricaprate solution and 10 µl of N-methylN-trimethylsilyltrifluoroacetamide (MSTFA) (Sigma-Aldrich, Saint-Louis, MO, USA) were added to the sample. It was then agitated for 5 min and let to rest for 30 min before adding 800 µl of heptane.

2.4. Analysis The samples were analyzed for TG, DG, MG, FAME and free glycerol (solubilized glycerol in the oil phase) by gas chromatography analysis according to the European standards method EN 14105 from 2003 and 2011 [28], [29]. Analysis was performed on an Agilent 7890A chromatograph with automated preparation/injection tray, equipped with a Cool On Column (COC) injector, a Flame-Ionization Detector (FID) and an Agilent Chemstation software (Agilent Technologies, Colorado Springs, CO, USA). The column used was an Agilent J&W 10 m x 0.32 mm x 0.1 µm DB5-HT capillary column (Agilent Technologies, Colorado Springs, CO, USA), with H2 (Air liquide) at 5 mL/min as the carrier gas. The injector temperature was set to track oven mode (oven temperature plus 3°C) and the FID to 380°C. Oven temperature started at 50°C for 1 min, increased to 180°C at a rate of 15 °C/min, then

12

increased to 230°C at a rate of 7 °C/min, increased to 370 °C at a rate of 10°C/min were it was held at this temperature for 5 min. The injected volume of prepared sample was 1 µl. 2.5. List of experiments The studied parameters are the methanol to oil molar ratio M, the reactor space time τ and the reactor temperature T. M is defined as the ratio between the molar stream of methanol and the molar stream of oil in the feed. The list of experiments given in Table 2 was determined to be the most representative ones as for the determination of the pre-exponential factor and activation energies as well as the equilibrium constants of the model of kinetics of Equations (2), (3) and (4). An algorithm developed to maximize the information obtained on the parameters during each experiment was used to get the list in Table 2. It ensures a good precision on the parameters. It however needs to be initialized with several experimental results, and therefore experiments 1 through 8 were conducted before the use of that algorithm [32]. Table 2: List of experiments.

Total

n°

V(s)

M

1

3070

27.6

180

2

6.19

2

1260

18.4

180

2

6.19

3

1025

23

180

2

6.19

4

1025

27.6

140

2

6.19

5

1025

27.6

160

2

6.19

6

1025

27.6

200

2

6.19

7

1025

27.6

180

2

6.19

8

1025

27.6

180

1

3.57

9

790

2

200

1

4.36

10

740

20

200

1

4.36

11

740

9

170

1

4.36

12

740

9

200

1

4.36

13

740

9

185

1

4.36

Experience

T(°C)

Number of reactors

catalyst mass (g)

13

14

750

3

185

1

4.36

15

740

20

185

1

4.36

16

740

13

185

1

4.36

17

740

4

185

1

4.36

18

840

5

200

1

4.36

19

1200

5

200

1

4.36

20

1800

5

200

1

4.36

21

2640

5

200

1

4.36

22

2160

4

200

1

4.36

Th1

1200

6

160

1

0

Th2

720

12

180

1

0

Th3

720

12

200

1

0

Experiments 4 – 8 enable to have the influence of temperature on the system for a residence time equal to 1025 seconds and a molar ratio equal to 27.6. Experiments 11-13 enable to observe the influence of temperature for a lower residence time equal to 740 seconds and a lower molar ratio equal to 9. Experiments 13 – 17 are performed to observe the influence of the molar ratio M on the system for a given residence time of 740 seconds and a temperature of 185 °C. Experiments 18-21 give us information on the influence of residence time for a given molar ratio and temperature. Experiments Th1, Th2 and Th3 were designed to evaluate the conversion due to thermal activity only, without the presence of the catalyst as the literature suggested high activity for the first and second reactions even without catalyst. Results of these blank experiments show that homogeneous reactions are negligible under the considered operating conditions, the values of triolein conversion and ester yield being lower than 5 %. The choice of the oven in the pilot unit was essential. Indeed it provides a homogeneous distribution of heat to avoid the presence of hot spots, which are known to cause homogeneous reactions. Experiments 12 and 13 were each reproduced once for consistency and to evaluate the reproducibility of results.

14

3. Modeling Kinetics parameters are determined for the given system of triglyceride transesterification, and several kinetic models from the literature are considered in the rest of the article. 3.1. Kinetic scheme Two sets of kinetic expressions are considered in this paper. One does not involve adsorption, and can be described with Equations (5), (6) and (7). It will be referred to as “classical”.

7 =  exp ]− 7 =  exp ]− 7 =  exp ]−


 1 _ ]
`
 −
0
% _ 3< 


 1 _ ]
0
 −

% _ 3<  
 1 _ ]

 −
C
% _ 3< 

(5) (6) (7)

A second set of kinetic expressions based on the Eley-Rideal model with the methanol adsorption as the rate limiting step (RLS) and reaction between adsorbed methanol and bulk phase glycerides is considered in equations (8), (9) and (10). FAME is directly released in the bulk phase, without having to desorb, but DG and MG are subject to a desorption step, which is not limiting. The reaction scheme is as follow [9]:

')bc + ∗ → ')bc∗ (3&:) ')bc∗ +
')bc ∗ + h ↔ 'h ∗ +  ')bc∗ + 'h ↔ h ∗ +  h ∗ ↔ h +∗

'h ∗ ↔ 'h +∗

h ∗ ↔ h +∗

The adsorption constant of DG and MG are supposed equal, to a unique value noted  . The

glycerol adsorption constant is noted  and the one of methanol  . The corresponding rate laws are given in Equations (8), (9) and (10).

15

7 = 7 = 7 =


 1
0
% k j
 − k 3< 
` 

1 + 0 % + 
0 +
 + 
C 
`

  exp j−

(8)


 1

% k j
 − k 3< 
0 

1 +  % + 
0 +
 + 
C 
0

  exp j−

(9)


 1

% k j
 − k 3< 
C 

1 +  % + 
0 +
 + 
C 
C

  exp j−

(10)

All three reactions consider the same kinetic constant, corresponding to the adsorption of methanol, the rate determining step. This model will be referred to as “Eley-Rideal”. For each model, activities are considered in order to take into account the highly non ideal behavior of the system, especially for glycerol. The activities are calculated with the concentration and activity coefficient of species i, as given in Equation (11).


 = P 

(11)

Numerical values of the activity coefficients obtained for a given composition with the

UNIFAC-LLE correlation are given in Table 3 as an example, with G the molar fraction of species Y. Details on the UNIFAC-LLE method are given in appendix A.

Table 3: Example of activity coefficient values calculated with the UNIFAC-LLE method for T = 453 K.

G

P

TG

MeOH

DG

MG

G

MeOl

0.2

0.4

0.05

0.05

0.05

0.25

0.84

1.02

0.95

1.29

30.26

1.18

Glycerol presents a very strong deviation from ideality with an activity coefficient of 30.26. This tends to accentuate the need to take into account these activity coefficients in the model.

16

3.2. Reactor modeling Two reactor models were developed. The first one is a plug flow pseudo-homogeneous model and it was used in order to determine the kinetic parameters of the reaction by regression of the experimental results at steady state in chemical regime. The second reactor model takes into account the transient regime, the mass transfer between the catalyst and the liquid phase as well as axial dispersion in the fixed bed and diffusion inside the catalyst. This model is capable of simulating the whole pilot unit including tubes and a static mixer, and is used in order to exploit the transient regime results and to obtain the molecular diffusion coefficients of the species in the system. The assumption of a plug-flow reactor was made for the determination of the kinetic

parameters, neglecting mass transfer limitations in the catalyst, given its diameter of  =

375 S. Pugnet et al. [2] showed the absence of mass transfer limitations on this catalyst for particle smaller than 500 µm considering the same reaction of transesterification of vegetable

oils by methanol. Moreover, the model was validated a posteriori after getting kinetic parameters and diffusion coefficients by studying the Weisz criterion and characteristic times of the system for diffusion of species Y, ?,, , interfacial mass transfer of species Y, ?#, and reaction of triolein, ?@#",` defined as follow:

?,, ?#, =

  _ 6 = ,

(12)

 /6 %, (1 − H% )

(13)

]

?@#",` =

`p 7p

, = , H /V

(14) (15)

with  the catalyst diameter, , the molecular diffusion coefficient of species i in the

mixture, H the catalyst porosity, V the catalyst tortuosity, , the effective diffusion coefficient of species Y in the mixture, %, the mass transfer coefficient between the fluid and

the catalyst for species Y and H% the bed porosity, `p the concentration of triolein at reactor inlet and 7p the reaction rate of the first reaction (equation 2) at reactor inlet.

17

Diffusion times for the experiments were estimated to be around 60 s, transfer time between liquid and solid was estimated around 10 s and reaction time around 450 s. When compared to the global residence times comprised between 600 and 1200 seconds, diffusion and mass transfer between the two phases are actually negligible in the reactor. The Weisz criterion, given in equation (16) was also calculated: J I,

 7s r  = 36 , ,

(16)

with 7sr the apparent reaction rate of reaction tand , the concentration of species Y at the

J surface of the catalyst. It was calculated based on triolein. Its value is around I,` = 0.2

which places the system at the limit of the kinetically controlled region, validating the pseudohomogeneous model for the catalyst particle diameter of around  = 375 S. Kinetics

parameters are then assessable thanks to a pseudo-homogeneous model neglecting internal and external mass transfer limitations. The first model is a pseudo-homogeneous perfect plug-flow reactor developed with the following hypotheses: -

steady state regime,

-

no axial nor radial dispersion,

-

isobaric and isothermal conditions,

-

homogeneous liquid phase.

This leads to the pseudo-homogeneous one-dimensional model described for species i by a molar balance given by equation (17):

A

   = w T 7 F 

(17)

with A the superficial velocity of the fluid, F the length coordinate of the reactor,  the 

concentration of species Y, T the stoichiometric coefficient of species Y in reaction t and 7 the reaction rate of reaction j in relation to the volume of the bed.

Transesterification reactions are regularly considered isothermal in the literature as their standard reaction enthalpy are close to 0 .   .

18

The reactor is considered isobaric and this hypothesis is verified afterwards through the Ergun equation given in equation (18):

( 150S (1 − H% ) A 1.75(1 − H% )U A = − − F H%  H% 

(18)

with S the dynamic viscosity of the fluid mixture, U its density, H% the void fraction of the catalytic bed and A the superficial fluid velocity. The pressure drop was calculated for each experiments, and lead to pressure drops of around 0.1 bar, which are considered negligible.

The second model of reactor is a heterogeneous model developed with the finite volume method. The hypotheses are as follow: -

transient regime,

-

isobaric and isothermal conditions,

-

homogeneous liquid phase,

-

spherical catalyst particles.

The model is based on elementary mass balances in the fluid and solid phases that are given in equations (19) and (22) respectively, boundary conditions are given in equations (20), (21), (23) and (24): xA  − , 

y  z HΩ yF { % D 

=

 xA 



y y   ~BD +  BC − ,  z H% ΩD + %,
 }  − ,@ yF {|,{ y? 





A ,p = A  − , H% 5

>€

{

− , x:

5

>€ {

at the inlet of the bed

= 0 at the outlet of the bed

y  y  y   z + w T 7 U"#$ B = − , x: z + H B y7 @ y7 @,@ y? 

>€M



>€M @

@

= 0 in the center of the particle

= %, (  − ,@- ) at the surface of the particle 

(19)

(20)

(21)

(22) (23) (24)

with , the axial dispersion coefficient of species Y, ΩD the cross section of the bed, %, the

solid to liquid mass transfer coefficient of species Y,
 = 6(1 − H% )/ the superficial area of

19

the solid,  the fluid concentration of species Y, ,p the fluid concentration of species Y at 



the inlet of the reactor,  the concentration of species Y in the solid, BD the elementary volume of reactor contained between F and F + F, BC the volume of liquid in BD , ,

the effective diffusion coefficient of species Y in the catalyst, 7 the rate of reaction t, U"#$ the

catalyst bulk density, : the surface of the catalyst at radius 7, B the elementary volume of catalyst contained between 7 and 7 − 7 and 7 the catalyst radius. The volume of liquid BC contained in the volume of reactor BD is given by:

BC = (H% + (1 − H% )H )BD

(25)

The mass balance applied to the fluid phase (equation (19)) is composed of two convectiondiffusion terms, one term of transfer between solid and fluid and one term of accumulation. The mass balance applied to the solid phase (equation (22)) is composed of two terms of diffusion, one term of reaction and one term of accumulation. External mass transfer is

effected at the boundary at 7 =  /2 (equation (24)). More details are provided in previous

work [33]. Similar mass balances as the one applied to fluid (equation (19)) are used to model the empty tubes and the static mixer of the pilot unit. The transfer term between solid and fluid phase is then removed. Axial dispersion coefficients of each species in the reactors are calculated using the corrected Gun correlation [34]-[35]:  1 () () 5 1 (1 −  ) + = (1 − ) ]exp ]− − 1__ + () 5 25 (1 − )() V ()

(26)

with () the axial Peclet number, () the molecular Peclet number, V the bed tortuosity, considered equal to a value of √2 for spherical particles, and  a parameter defined by:

=

0.48 1 0.48 75:; + ] − .… _ exp ]− _ .… :; 2 :; ()

(27)

S U 

(28)

with :; the Schmidt number defined as follow:

:; =

with S the fluid mixture dynamic viscosity and U its density.

Axial and molecular Peclet numbers are defined as follow for species Y:

20

 A H% ,

() , =

(29)

 A H% ,

(), =

(30)

In a liquid laminar flow, the axial Peclet number is generally considered equal to a value of 0.5. However, when the molecular Peclet number falls under the value of 100, axial Peclet number can increase to a value higher than 1. Moreover, if the Schmidt number decreases to values under circa 1000, the axial Peclet number also increases. Table 4 gives an example of the ranges of axial and molecular Peclet number that are characteristic in this pilot unit for

three experimental conditions. The axial Peclet number () is calculated with equation (26) while the molecular Peclet number () depends on a molecular diffusion coefficient estimated with the Wilke and Chang correlation for mixtures:

, = 7.4 ×

10‡ ˆO'< . S T,

(31)

with O' = ∑Š G O ' , where O is the associativity constant of species t (equal to 1 except for methanol, for which O is equal to 1.9), ' the molecular weight of species t and E , the

molar volume of species Y. This correlation is only used to have an order of magnitude for axial dispersion. Molecular diffusion coefficients are determined later from experiments. The Reynolds number of particle, 3) is defined by equation (32).

3) =

A U S

(32)

Table 4: Values of the Reynolds number ‹Œ, axial and molecular Peclet numbers ŒŽ and Œ for different working conditions.

'

V ()

< (° ) 185

0.52

0.7-1.5

13-113

5

2640

200

0.16

0.9-2.2

2.6-30

20

740

185

0.64

0.8-1.5

14-82

9

740

3)

()

()

The development of this heterogeneous model is useful to precisely determine the molecular diffusion coefficient from experimental results in transient regime as well as from

21

experimental results on a higher diameter catalyst, which leads to diffusion limitations inside the catalyst particles that have to be considered with a heterogeneous model.

4. Results 4.1. Experimental results

Samples were obtained at regular time intervals at the outlet of the pilot unit. These samples were prepared according to the previously given procedure and analyzed with gas chromatography. Margins of error were calculated on the two points that were repeated (3 and 13) and are given in table 5. Table 5: Relative error due to manipulations and chromatography analysis on the global molar composition of each species.

WX, (%)

TG

MeOH

DG

MG

G

FAME

20.0

1.0

2.7

1.1

4.6

3.6

The relative error on FAME molar fraction seems to be low, but should actually be considered as the sum of the absolute error on every other species, since ester molar fraction is obtained by difference to unity. The error on triglyceride is high. This is due to the analysis method and the use of a single reference compound for quantification of all the glycerides, triglyceride being the farther away from this reference compound on the chromatogram. The composition of the oil phase was determined and the global molar composition of the mixture was derived from the results through steady state mass balances applied on the reactors. Figures 3 to 5 show the outlet molar fractions at steady state as a function of

temperature < (figure 3), inlet molar ratio ' (figure 4) and residence time V (figure 5) respectively.

Figure 3: Evolution of global molar compositions at the outlet of the reactors at steady state as a function of reactor temperature; classical model with concentration and experimental results. M=9, ‘ =740s, ’“” =4.36g, •– =355-400—.

22

Figure 4: Evolution of global molar compositions at the outlet of the reactors at steady state as a function of inlet methanol to oil molar ratio; classical model with concentration and experimental results. T=185°C, ‘ =740s, ’“” =4.36g, •–=355-400—. Legend: see Figure 3.

Figure 5: Evolution of global molar compositions at the outlet of the reactors at steady state as a function of residence time; classical model with concentration and experimental results. M=5, T=200°C, ’“” =4.36g, •–=355-400—. Legend: see Figure 3.

Ester and glycerol content increase with temperature as well as with residence time as seen on figures 3 and 5. However, they decrease with the increase of the inlet molar ratio as pictured on figure 4, and so do the glycerides content. Indeed, these molar fractions are global, which become smaller due to dilution when the overall quantity of methanol rises as M increases. Triglycerides and diglycerides contents decrease with the increase of temperature, but monoglycerides seems to remain at a constant level of around 1.8%mol/mol, as pictured on figure 3(a). Monoglycerides level also do not change with increasing residence time whereas triglycerides and diglycerides decrease with increasing residence time, as pictured on figure 5(a). These results tend to show that consumption and production rates of monoglycerides are equal in our experiments at steady state for a large spectrum of parameters values. The second and third reactions reach therefore thermodynamic equilibrium and their reaction rates equal one another. The thermodynamic equilibrium of the first reaction is however not reached as the triglycerides content is decreasing with increasing residence time.

4.2. Determination of kinetic parameters Experimental results were used in the determination of the kinetic parameters. First, the

parameters  and 
 from the “classical” kinetic model as well as the equilibrium constants

˜, are determined using both concentrations and activities in the rate laws. Second, kinetic

parameters form the “Eley-Rideal” model are estimated, using concentration in place of activities in the rate laws, as the optimization using activities did not lead to any exploitable results.

23

In order to determine the values of the kinetic constants, the pre-exponential factors and activation energies are transformed into parameters better fitted to optimization. These new parameters are defined as follow:


 ™ = ln ] _ 3 κ = ln( ) −

(33)


 3<

(34)

For all the kinetic models being optimized, the least squares criterion chosen to be minimized is the following:

&: = w(G"#%" − G 

)

žŸ 

(35)

The molar fractions used for determination of the least-square criteria are the ones in the mixture that were deduced from the oil phase. The results of the optimizations are given in Tables 6 and 7 for the “classical” rate laws without adsorption (Eq. 5-7) for temperatures ranging from 140°C to 220°C. Comparison with the literature is provided, where temperatures were varied between 180°C and 210°C. Confidence intervals with 15 degrees of freedom at a 95% significance level are provided for reaction rate function of concentrations. Table 6: Kinetics parameters and least square criterion values for the kinetic rate law without adsorption ¦ (Eq 5-7) for temperatures between 140°C and 220°C.  ¢¡ in £ . ¤¥¦ . §¦ .  ‘¦ ’“”“ , ¨“¡ in  ©. ¤¥ .

function of:
















Concentrations

1.26 × 10

8.88 × 10

1.28 × 10¬

64.6

31.8

17.0

Reaction rate

Activities Concentrations (Results from reference [2])

±7.4 × 10« 1.31 × 10 1.7 × 10

±2.8 × 10

0.78 × 10… 94

±3.3 × 10‡ 1.80 × 10¬ 3.7

&:

±2.4

±1.5

±2.4

0.022

55.0

27.4

17.2

0.058

82.0

103.0

88.0

-

24

Table 7: Equilibrium constants and least square criterion values for the kinetic rate law without adsorption (Eq 5-7) for temperatures between 140°C and 220°C.







51.2

53.1

12.2

Reaction rate function of: Concentrations Activities Concentrations [2]

&: 0.022

±3.9

±4.6

±0.6 144

0.058

0.17

1.21

0.87

-

83

144

For the “classical” model without adsorption, the activation energies obtained in the present work are lower than the ones from the literature, as observed in table 6, and the preexponential factors are also lower. However, when comparing the rate constants as calculated ®#

in table 8, that shows the values of the rate constants  =  exp (− D`€ ) for different

temperatures, the literature and the present results lead to similar rate constants. Indeed, according to the results of Pugnet et al. [2], at a temperature of 185 °C, the first reaction has a

 rate constant of 7.6 × 10  .    .  . !"#$# , the second reaction has a rate constant

of

 4.2 × 10‡  .    .  . !"#$#

and

the

third

a

rate

constant

of

 1.6 × 10¯  .    .  . !"#$# . This results could show a high correlation between the

pre-exponential factors  and the activation energies 
 . More experiments could help to de-correlate those parameters.

Table 8: Values of the rate constants in £ . ¤¥¦ . §¦ .  ‘¦ ’“”“ for different temperatures for the kinetic rate law (Eq 5-7) with activity coefficients equal to one.

T (°C) 160 185 200

Reaction 1

Reaction 2

Reaction 3

2.1 × 10

1.3 × 10¯

1.1 × 10¯

9.3 × 10

2.7 × 10¯

1.7 × 10¯

5.6 × 10

2.1 × 10¯

1.5 × 10¯

Figures 3-5 shows the fitting of the “classical” model with the experiments using concentrations instead of activities (activity coefficients equal to one), as the mole fraction are plotted against temperature, molar ratio and residence time.

25

The classical kinetics with concentrations, despite being the simplest of all proposed models, is the one that fits the best the experimental results. Its least square criterion is indeed the smallest, and the fitting appears to be better on the figures. The addition of a kinetics rate law for the global reaction of equation (1) did not improve the results in any way. The first reaction clearly limits the system kinetically, with values of rate constants being between 3 and 5 times lower than the ones of the second reaction and 1 to 2 times lower than the ones of the third reaction. The third reaction is the least affected by temperature change, the first one being the most affected. The rate constant of the third reaction is only multiplied by 1.6 when temperature increases from 160°C to 200°C whereas the one of the first reaction is multiplied by 4. This behavior is linked to the values of the activation energies, which is 3 times higher for the first reaction than for the third one. The first reaction also limits the system thermodynamically, its equilibrium constant  being the lowest of the three with a

value of 29.5.

Tables 9 and 10 present the results for the “Eley-Rideal” model for temperatures between 140°C and 220°C. Comparison with the literature is provided, for temperatures between 30°C and 50°C.

Table 9: Kinetics parameters, equilibrium constants and least square criterion values for the kinetic rate law with adsorption (Eq 8-10) function of the concentration of the species.  ¢°Œ±² in ³ . §¦ .  ‘¦ ’“”“ and ¨“°Œ±² in  ©. ¤¥¦ .

 

This study Dossin et al. [9]

2.08 × 10 1.48 × 10


 43.09 20.1



21.3



46.5



LS

30.7

0.044

1.0

-

Table 10: Adsorption coefficients and least square criterion values for the kinetic rate law with adsorption (Eq 8-10) function of the concentration of the species. ´Ž , ´µ and ´°Œ±² in ³ . ¤¥¦.

This study Dossin et al. [9]



4.3 × 10



1.54 × 10

5.29 × 10



3.53 × 10

LS 0.044 -

26

The parameters optimization for the “Eley-Rideal” model leads to a higher least square criterion than the classical model, and therefore do not describe the experimental results as well. The difference in the results concerning the model with adsorption when compared to the literature comes from the fact that Dossin et al. [9] used kinetic parameters determined on the transesterification of acetic acid, a molecule with a very short chain of carbon when compared to triolein, with significant hypotheses such as equilibrium constants of one for all reactions and the consideration of only one adsorption equilibrium constant for all species. Temperature is also extremely lower.

4.3. Determination of the molecular diffusion coefficients of species in the mixture Molecular diffusion coefficients correlations can be based on the assumption given in equation (36) for small variations of temperatures [36]:

¶ S¶ = <

(36)

with C a constant, ¶ the diffusion coefficient of solute A in solvent B, T the temperature and S¶ the viscosity of solvent B. In the case of the Wilke and Chang equation, the constant takes the following value: = 7.4 ×

»

·¸ (¹º )K ½.¾ ¼2,1

with '¶ the molecular weight of solvent B,

E , the molar volume of solute A and I the association factor of solvent B. This assumption was considered in our case with the solvent being the mixture of all species. The dynamic viscosity of mixture was calculated using the Teja and Rice method [36]:

ln(S H ) = ln(¿H)(D)

+ Àln(SH)(D) − ln(SH)(D) Á

R − R (D) R (D) − R(D)

(37)

with R1 and R2 two reference fluids, chosen in our case to be the methanol and the ester, S is the dynamic viscosity and R the acentric factor; H is a parameter defined by: /

VÄ ε= (<" ')/

(38)

Details of the calculations are given in appendix B.

27

The molecular diffusion constant of each species in the mixture was then determined by optimization on the experimental results. A first step was conducted, considering the transient regime results of the experiment presented in the present paper, on small diameter catalyst

particles ( = 375 S), and the optimization was then refined on results of experiments

previously conducted on a larger catalyst diameter of  = 2.5  at steady state [33]. The results of those experiments are not given in the present paper.

Optimization of the molecular diffusion constants was realized with the heterogeneous model with axial dispersion and considering mass transfer between the fluid and solid phase as well as in the solid particles. The optimization was conducted on Matlab with the use of the fmincon function, on 63 different experimental points. Results are given in table 11 and a set of examples, comparing the optimized results with the Wilke and Chang equation adapted for liquid mixture is given in table 12. Table 11: Values of the constants , S /< for each species.

Species

, S × 10 <

TG

MeOH

DG

MG

G

FAME

0.083

8.233

1.879

7.428

4.667

4.359

Table 12: Comparison between molecular diffusion coefficients of species ¡ in the mixture, , , obtained by the Wilke and Chang equation adapted for mixtures and by optimization, in ¦¢Å Æ . §¦ . Comparison with the results obtained by Davison et al. for tributyrin transesterification on MgO. Ç¡ is the global mole fraction of species ¡.

Species

TG

MeOH

DG

MG

G

FAME

0.1

0.6

0.05

0.05

0.05

0.15

Wilke-Chang correlation

2.57

20.37

3.76

5.51

14.42

5.55

Optimization

0.17

17.00

3.88

15.34

9.63

9.00

0.03

0.82

0.03

0.02

0.01

0.09

0.995

-

1.2

1.52

1.68

2.28

G (mol/mol) G (mol/mol)

Davison et al. [13] (tributyrin transesterification)

The main differences are a lower diffusion coefficient for triglycerides and glycerol as well as an increased coefficient for monoglycerides and FAME. The values for methanol and

28

diglycerides remain in the same order of magnitude. Another method to calculate diffusion coefficients, proposed by Davison et al. [13], can be used. This method is based on the following sequential calculations: -

estimation of the infinite dilution diffusion coefficient (Wilke and Chang correlation),

-

estimation of the normal diffusion coefficient taking into account the diffusion coefficients calculated by Wilke and Chang and using mole fractions,

-

estimation of the squeezing effect of large molecules through a pore already full of molecules,

-

estimation of the non-ideality of the solution using viscosity data.

This method, applied for a model system of tributyrin transesterification (diffusion coefficient calculated in a mix with a large mole fraction of methanol equal to 0.82), give results in the same order of magnitude than those obtained for a triolein transesterification (see Table 12). Figures 6 to 8 picture the fitting of the model with the experimental results for different sets of parameters from experiments 2, 3, 6, 9 and 14. Mass fraction in the oil phase is plotted as a function of time. The influence of inlet molar ratio ' (figure 6), temperature < (figure 7) and residence time V (figure 8) is respectively represented.

Figure 6: Evolution of the mass content in the oil phase as a function of time. Influence of the molar ratio of methanol to oil, °. T=185°C, ‘ =740s, ’“” =4.36g, •– =355-400—.

Figure 7: Evolution of the mass content in the oil phase as a function of time. Influence of the temperature È, ° = Æ¢, ‘ =740s, ’“” =4.36g, •–=355-400—.

Figure 8: Evolution of the mass content in the oil phase as a function of time. Influence of the residence time ‘ . T=200°C, ° = É, ’“” =4.36g, •– =355-400—.

The triglycerides and ester profiles on all figures 6-8 (a,d) clearly show a double spike in concentration on the model. This behavior is also recognizable on the experimental results. The first spike corresponds to the dispersion through the reactor and tubes when no reaction is

29

occurring, the ester being progressively replaced by triglycerides and methanol. The glycerides have not yet diffused in the catalyst pellets, and the reaction is not occurring. When the triglyceride content starts to decrease, and the ester one increases, chemical reaction is starting. Triglycerides are consumed, and it is the point where mono and diglycerides, which are produced, start to flow out of the reactors as seen on figures 6-8 (b,c). The dynamic behavior of the reactor is well reproduced by the heterogeneous model that was developed. Figure 7 pictures the evolution of the mass content in the oil phase as a function of time for

different temperatures, at a high molar ratio of ' = 20. The model seems to have some difficulties to reach the correct steady state, even though the transient part is well described. This comes from the initial assumption of equation (36) on which is based the optimization of the diffusion constants. The mixture viscosity might not be well determined at a high molar ratio like the one considered in this figure. It is possible that the estimated viscosity is too high when compared to the real values, which we unfortunately cannot measure. This shows one of the limits of this model, where a high molar ratio might lead to large uncertainties. 5. Conclusions The heterogeneous transesterification of vegetable oils by methanol requires a large excess of methanol in order to lead to a high conversion. This is due to several limitations in the process, both physical and chemical. Those limitations were identified through the use of experimental results and simulation. The work leads to a kinetic rate law for the transesterification of triolein with methanol over a ZnAl O« catalyst. Experiments were

conducted in a pilot unit developed at the laboratory. The small size of the catalyst particles,

and therefore the absence of mass transfer limitations, allowed the use of a pseudohomogeneous model for the determination of the kinetic parameters. The rate law that was determined to be the most efficient in reproducing experimental results consists of three second order expressions taking into account thermodynamic equilibrium. Reaction rates including adsorption of methanol as the rate determining step with an Eley-Rideal mechanism were also considered but lead to less accurate results when the kinetic constants of both models were optimized. Activity coefficients were calculated in order to account for the nonideality of the mixture but kinetic models considering the concentrations of the species instead of their activities lead to better results. Equilibrium constants are relatively high when compared to the literature, and were considered constant with temperature, which is not actually the case. The values of these equilibrium constants could be improved. Molecular

30

diffusion coefficients were also obtained with use of the transient regime results that were obtained on the pilot unit. Using a heterogeneous model and taking into account the mass

transfer phenomena in the system, optimization of the constant , S /< was possible,

leading to simple correlations for the molecular diffusion coefficients of the species in the

mixture. The entire process of biodiesel synthesis through heterogeneous transesterification has now to be optimized to reduce the amount of methanol needed, as well as to reduce the energy consumption of the separation steps required to achieve a high conversion. Acknowledgments The authors wish to acknowledge CNRS and IFP Energies Nouvelles for its financial support.

31

References [1] L. Bournay, D. Casanave, B. Delfort, G. Hillion, and J. A. Chodorge, New heterogeneous process for biodiesel production: A way to improve the quality and the value of the crude glycerin produced by biodiesel plants, Catal. Today 106 (2005) 190– 192. [2] V. Pugnet, S. Maury, V. Coupard, A. Dandeu, A.-A. Quoineaud, J.-L. Bonneau, and D. Tichit, Stability, activity and selectivity study of a zinc aluminate heterogeneous catalyst for the transesterification of vegetable oil in batch reactor, Appl. Catal. Gen. 374 (2010) 71–78. [3] M. Diasakou, A. Louloudi, and N. Papayannakos, Kinetics of the non-catalytic transesterification of soybean oil, Fuel 77 (1998) 1297–1302. [4] U. R. Kreutzer, Manufacture of fatty alcohols based on natural fats and oils, J. Am. Oil Chem. Soc. 61 (1984) 343–348. [5] B. Freedman, R. O. Butterfield, and E. H. Pryde, Transesterification kinetics of soybean oil 1, J. Am. Oil Chem. Soc. 63 (1986) 1375–1380. [6] H. Noureddini and D. Zhu, Kinetics of transesterification of soybean oil, J. Am. Oil Chem. Soc. 74 (1997) 1457–1463. [7] A. Kapil, K. Wilson, A. F. Lee, and J. Sadhukhan, Kinetic Modeling Studies of Heterogeneously Catalyzed Biodiesel Synthesis Reactions, Ind. Eng. Chem. Res. 50 (2011) 4818–4830. [8] T. F. Dossin, M. F. Reyniers, and G. Marin, Kinetics of heterogeneously MgO-catalyzed transesterification, Appl. Catal. B Environ. 62 (2006) 35–45. [9] T. F. Dossin, M. F. Reyniers, R. J. Berger, and G. B. Marin, Simulation of heterogeneously MgO-catalyzed transesterification for fine-chemical and biodiesel industrial production, Appl. Catal. B Environ. 67 (2006) 136–148. [10] Y. Xiao, L. Gao, G. Xiao, and J. Lv, Kinetics of the Transesterification Reaction Catalyzed by Solid Base in a Fixed-Bed Reactor, Energy Fuels 24 (2010) 5829–5833. [11] J. A. Melero, J. Iglesias, and G. Morales, Heterogeneous acid catalysts for biodiesel production: current status and future challenges, Green Chem. 11 (2009) 1285–1308. [12] A.F. Lee, K. Wilson, Recent developments in heterogeneous catalysis for the sustainable production of Biodiesel, Catal. Today 242 (2015) 3-18. [13] T. J. Davison, C. Okoli, K. Wilson, A.F. Lee, A. Harvey, J. Woodford, J. Sadhukhan, Multiscale modelling of heterogeneously catalysed transesterification reaction process: an overview, RSC Advances, 3 (2013) 6226–6240. [14] M. E. Borges, L. Díaz, J. Gavín, and A. Brito, Estimation of the content of fatty acid methyl esters (FAME) in biodiesel samples from dynamic viscosity measurements, Fuel Process. Technol. 92 (2011) 597–599. [15] N. Ellis, F. Guan, T. Chen, and C. Poon, Monitoring biodiesel production (transesterification) using in situ viscometer, Chem. Eng. J. 138 (2008) 200–206. [16] P. D. Filippis, C. Giavarini, M. Scarsella, and M. Sorrentino, Transesterification processes for vegetable oils: A simple control method of methyl ester content, J. Am. Oil Chem. Soc. 72 (1995) 1399–1404. [17] G. F. Ghesti, J. L. de Macedo, I. S. Resck, J. A. Dias, and S. C. L. Dias, FT-Raman Spectroscopy Quantification of Biodiesel in a Progressive Soybean Oil Transesterification Reaction and Its Correlation with 1H NMR Spectroscopy Methods, Energy Fuels 21 (2007) 2475–2480. [18] G. Zagonel, Multivariate monitoring of soybean oil ethanolysis by FTIR, Talanta 63 (2004) 1021–1025.

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[19] G. Knothe, Monitoring a progressing transesterification reaction by fiber-optic near infrared spectroscopy with correlation to 1H nuclear magnetic resonance spectroscopy, J. Am. Oil Chem. Soc. 77 (2000) 489–493. [20] G. Gelbard, O. Brès, R. M. Vargas, F. Vielfaure, and U. F. Schuchardt, 1H nuclear magnetic resonance determination of the yield of the transesterification of rapeseed oil with methanol, J. Am. Oil Chem. Soc. 72 (1995) 1239–1241. [21] G. F. Ghesti, J. L. de Macedo, V. S. Braga, A. T. de Souza, V. C. Parente, E. S. Figuerêdo, I. S. Resck, J. A. Dias, and S. C. Dias, Application of raman spectroscopy to monitor and quantify ethyl esters in soybean oil transesterification, J. Am. Oil Chem. Soc. 83 (2006). 597–601. [22] M. Morgenstern, J. Cline, S. Meyer, and S. Cataldo, Determination of the Kinetics of Biodiesel Production Using Proton Nuclear Magnetic Resonance Spectroscopy (1H NMR), Energy Fuels 20 (2006) 1350–1353. [23] C. Plank and E. Lorbeer, Simultaneous determination of glycerol, and mono-, di- and triglycerides in vegetable oil methyl esters by capillary gas chromatography, J. Chromatogr. 697 (1995) 461–468. [24] M. Holčapek, P. Jandera, J. Fischer, and B. Prokeš, Analytical monitoring of the production of biodiesel by high-performance liquid chromatography with various detection methods, J. Chromatogr., 858 (1999) 13–31. [25] G. Arzamendi, E. Arguiñarena, I. Campo, and L. M. Gandía, Monitoring of biodiesel production: Simultaneous analysis of the transesterification products using sizeexclusion chromatography, Chem. Eng. J. 122 (2006) 31–40. [26] L. Meher, D. Vidyasagar, and S. Naik, Technical aspects of biodiesel production by transesterification - a review, Renew. Sustain. Energy Rev. 10 (2006) 248–268. [27] AFNOR, EN 14214 - Automotive fuels - Fatty acid methyl esters (FAME) for diesel engines - Requirements and test methods (2013). [28] AFNOR, EN 14105 - Fat and oil derivates - Fatty Acid Methyl Esters (FAME) Determination of free and total glycerol and mono-, di-, triglyceride contents (2003). [29] AFNOR, EN 14105 - Fat and oil derivates - Fatty Acid Methyl Esters (FAME) Determination of free and total glycerol and mono-, di-, triglyceride contents (2011). [30] M. Mittelbach, G. Roth, and A. Bergmann, Simultaneous gas chromatographic determination of methanol and free glycerol in biodiesel, Chromatographia 42 (1996) 431–434. [31] E. Revellame, R. Hernandez, W. French, W. Holmes, and E. Alley, Biodiesel from activated sludge through in situ transesterification, J. Chem. Technol. Biotechnol. 85 (2010) 614–620. [32] F. Mathieu, J. M. Commenge, L. Falk, and S. Lomel, Technologies comparison for iterative data acquisition strategies, Chem. Eng. Sci. 104 (2013). 829–838. [33] J. F. Portha, F. Allain, V. Coupard, A. Dandeu, E. Girot, E. Schaer, and L. Falk, Simulation and kinetic study of transesterification of triolein to biodiesel using modular reactors, Chem. Eng. J. 207–208 (2012) 285–298. [34] J. M. P. Q. Delgado, A critical review of dispersion in packed beds, Heat Mass Transf., 42 (2006) 279–310. [35] D. J. Gun, Axial and radial dispersion in fixed beds, Chem. Eng. Sci. 42 (1987) 363– 373. [36] B. Poling, J. Prausnitz, and J. O’Connell, The Properties of Gases and Liquids. McGraw Hill Professional, New-York, 2000.

33

Appendix A The thermodynamics model used to compute the activity coefficients is the UNIFAC model with parameters from the LLE modification. Each species considered in the model is decomposed into groups, and the number of groups for each molecule is given in table A.1. Table A.1: Number Í¡  of groups   in each molecule ¡ for the UNIFAC-LLE method.

Groups

OH

CH3

CH2

CH

CH=CH CH2COO

TG

0

3

41

1

3

3

MeOH

1

1

0

0

0

0

DG

1

2

28

1

2

2

MG

2

1

15

1

1

1

G

3

0

2

1

0

0

FAME

0

2

13

0

1

1

The activity coefficient of species Y, P is obtained with the set of equations (A.1) to (A.12).

ÎP = ln P> + ÎPD

(A.1)

with P> the molecular contribution and PD the residual contribution. P> is obtained with equations (A.2) to (A.7):

ÎP>

pÒ

I Ð I = Î + 5Ï Î +  − w F%Ñ F I F

(A.2)

F Ï pÒ ∑ F Ï

(A.3)



where F is the molar fraction of species Y, Î: the total number of species and:

Ð =

I =

where:

F 7 pÒ ∑ F 7

 = 5(7 − Ï ) − (7 − 1) p

7 = w TÓ 3Ó Ó

(A.4) (A.5)

(A.6)

34

p

Ï = w TÓ ÔÓ

(A.7)

Ó

with 3Ó the volume parameter of group , ÔÓ the surface area parameter of group  and Îh

the total number of groups. Values for TÓ are given in table A.1 and values for 3Ó and ÔÓ are given in table A.2.

Table A.2: Values of ‹  and Õ  for the UNIFAC-LLE method for the different groups.

OH

3Ó

CH3

1

ÔÓ

1.2

CH2

CH

CH=CH CH2COO

0.9011 0.6744 0.4469

1.1167

1.6764

0.848

0.867

1.42

0.54

0.228

The residual contribution PD is obtained with equations (A.8) to (A.12):

where ΓÓ and

ΓÓ

ÎPD

p

= w TÓ }ÎΓÓ − ÎΓÓ ~

(A.8)

Ó

are respectively the residual activity coefficients of group  in the mixture

and the residual activity coefficient of group  in a solution only containing species Y. p

p





ÎΓÓ = ÔÓ ×1 − ln Øw Ð ÙÓ Ú − w ΨÓ = exp j− Ð =


Ó k <

Ð ΨÓ Ü ∑p  Ð Ψ

(A.9) (A.10)

Ý Ô ∑p  Ý Ô

(A.11)

 ∑pÒ  T F Ý = pÒ p  ∑ ∑ T F

(A.12)

with < the temperature,
Ó the group interaction parameter for the interaction between groups  and , given in table A.3.

Table A.3: Group interaction parameters for the UNIFAC-LLE method.

Groups

OH

OH

0

CH3

644.6

CH3

CH2

CH

CH=CH CH2COO

382.2

382.2

382.2

470.7

195.6

0

0

0

74.5

972.4

35

CH2

644.6

0

0

0

74.5

972.4

CH

644.6

0

0

0

74.5

972.4

CH=CH

724.4

292.3

292.3

292.3

0

-577.5

CH2COO

180.6

-320.1

-320.1

-320.1

485.6

0

Appendix B The mixture dynamic viscosity was calculated using the Teja and Rice method [36]:

ln(S H ) = ln(¿H)(D)

+ Àln(SH )(D) − ln(SH)(D) Á

R − R (D) R (D) − R(D)

(B.1)

with R1 and R2 two reference fluids, chosen in our case to be methanol and the ester. S is the dynamic viscosity and R the acentric factor. H is a parameter defined by: /

VÄ (<" ')/

(B.2)

R = w G R

(B.3)

'% = w G '

(B.4)

ε= With:





B", = w w G G B", <", =





∑ ∑ G G <", B",

B", =

/

B",

(B.5)

/ 

}B", + B", ~ 8

(B.6) /

<" B" = Þ }<", <", B", B", ~

(B.7)

where Þ , close to the value of one, is regressed on experimental values. In this paper, it is taken equal to unity. The reference viscosities S (D) and S (D) are not calculated at the temperature of the system, <, but at

``ß,€ `ß,2

.

36

100 (b) FAME, MeOH

8

z (%mol/mol)

z (%mol/mol)

10 (a) TG, DG, MG, G

6 4 2 0 140

TG, exp G, exp

160

180 T (◦ C)

TG, model G, model

200

220

DG, exp FAME, exp

80 60 40 20 0 140

160

DG, model FAME, model

180 T (◦ C)

MG, exp MeOH exp,

200

220 MG, model MeOH, model

80

15

z (%mol/mol)

z (%mol/mol)

(a) TG, DG, MG, G

10 5 0

5

10

15 M

20

(b) FAME, MeOH

60 40 20 0

5

10

15 M

20

(b) FAME, MeOH

z (%mol/mol)

z (%mol/mol)

20 (a) TG, DG, MG, G 15 10 5 0

1,000

1,500

2,000

τ (s)

2,500

50 40 30 1,000

1,500

2,000

τ (s)

2,500

(a) Triglycerides

60

(b) Diglycerides wD (%w/w)

wT (%w/w)

10 40 20 0

0

2

4

6

8

5

0

10

0

2

t (h)

6

8

10

t (h) 100

8 (c) Monoglycerides 6

wE (%w/w)

wM (%w/w)

4

4 2

(d) FAME

80 60 40

0

0

2

4

6

8

10

0

2

4 t (h)

t (h) M = 9 experiment M = 9 model

6

M = 20 experiment M = 20 model

8

10

(b) Diglycerides

8 wD (%w/w)

wT (%w/w)

30 20 10 0

10

(a) Triglycerides

0

2

4

6

8

6 4 2 0

10

0

2

t (h)

6

8

10

t (h) 100

(c) Monoglycerides wE (%w/w)

wM (%w/w)

6

4

4 2

(d) FAME

90 80 70

0

0

2

4

6

8

10

t (h) T=185 ◦ C experiment T=185 ◦ C model

0

2

4

6 t (h)

T=200 ◦ C expriment T=200 ◦ C model

8

10

60

(a) Triglycerides

(b) Diglycerides

20 0

wM (%w/w)

wD (%w/w)

40

0

2

4

6 t (h)

8

10

5

0

12

0

2

4

6 t (h)

8

100

10 (c) Monoglycerides 8 wE (%w/w)

wT (%w/w)

10

6 4

10

12

(d) FAME

80 60

2 0

0

2

4

6 t (h)

8

10

12

τg = 1200 s experiment τg = 1200 s model

40

0

2

4

6 t (h)

τg = 2640 s experiment τg = 2640 s model

8

10

12

Highlights Heterogeneous transesterification of triolein to produce Biodiesel is studied. Experiments have been performed on a pilot unit including two fixed bed reactors. A pseudo-homogeneous model has been developed to determine kinetic parameters. A heterogeneous model has been used to estimate molecular diffusion.

37