Kinetic Modeling of Supercritical Interesterification with

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Kinetics, Catalysis, and Reaction Engineering

Kinetic modeling of supercritical interesterification with heterogeneous catalyst to produce methyl esters considering degradation effects Leoni N Brondani, Santhiago S Simões, Dian Celante, and Fernanda de Castilhos Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b04715 • Publication Date (Web): 20 Dec 2018 Downloaded from http://pubs.acs.org on December 22, 2018

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Industrial & Engineering Chemistry Research

Kinetic modeling of supercritical interesterification with heterogeneous catalyst to produce methyl esters considering degradation effects

L. N. Brondani, S. S. Simões, D. Celante, F. Castilhos*

Chemical Engineering Department, Federal University of Santa Maria, Avenida Roraima n° 1000, 97105-900, Santa Maria, Brazil

Abstract - In this study, it has been proposed a process model for catalytic supercritical interesterification considering degradation reactions at high temperatures. Kinetic parameters of soybean oil and methyl acetate (MeA) reaction using Ca-Mg-Al mixed oxide as catalyst considering main and intermediate reactions were estimated. Experimental data varied between 200 °C and 350 °C, a catalyst concentration of 2wt%, 5wt%, and 10wt% and molar ratio (MeA:Oil) of 20:1, 40:1 and 60:1. Degradation reactions of glyceride esters and triacetin were investigated and improved model performance. In order to avoid higher degradation rates, the presence of catalyst induces the system to achieve optimum conversions at lower temperatures, between 300 °C and 325 °C. For statistical validation of optimized parameters, the confidence intervals and the correlation coefficient between parameters were calculated. Proposed kinetic and process model fitted the experimental results very well.

Keywords: soybean oil; methyl acetate; mixed oxides; kinetic parameters; biodiesel.

1. INTRODUCTION

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Biodiesel is considered a promising alternative source to petrodiesel. Traditionally, industrial biodiesel production occurs via transesterification route between triglycerides and methanol in presence of alkali catalyst. However, some issues in glycerol production and waste management 1 are affecting the economic side for small and medium industries 2. In order to solve these problems, glycerol-free routes that generate other components to increase process profitability are widely studied. One of the options is the interesterification reaction, which produces fatty acid methyl esters (FAME) and triacetin (TA) from triglycerides (TG) and methyl acetate (MeA). Unlike glycerol, triacetin has high solubility in biodiesel and can be used as an additive because its addition to the fuel provides properties, such as cetane number and flash point temperature, similar to pure biodiesel properties 3. Casas et al.3 showed that for concentrations up to stoichiometric final product concentration (20 wt% of TA and 80 wt% of biodiesel) the triacetin can be used as a fuel additive and does not need additional separation steps like glycerol + biodiesel system, which guarantees to the interesterification process a maximum theoretical mass yield of 125%, a value greater than 100% of transesterification with methanol. Interesterification reaction has been studied for different oils in presence of enzymes 4–6, using homogeneous 7 and heterogeneous catalysts 8,9 and under supercritical conditions

10–14.

Catalyst-free interesterification reaction with methyl acetate requires

more severe temperature conditions and strong evidence of thermal degradation have been observed. Olivares and Quesada15 studied thermal decomposition during transesterification reaction with supercritical methanol and proposed that degradation reactions became evident at 300 °C. Lin et al.16 demonstrated that biodiesel decomposition mainly involves isomerization, polymerization (Diels–Alder reaction) and


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pyrolysis reactions, and they occur in the temperature ranges of 275-400 °C, 300-425 °C and higher than 350 °C, respectively. According to Laino et al.17, triacetin thermal degradation reactions results in many compounds and they are favored at high temperatures. There are just a few studies that develop kinetic models and estimate parameters for this reaction system considering products and intermediates compounds. Casas et al.7 estimated kinetic parameters for interesterification reaction considering intermediates, monoacetindyglicerides (MADG) and diacetinmonoglicerides (DAMG), for a batch system at low temperatures using potassium methoxide as homogeneous catalyst. Farobie and Matsumura14 studied continuous interesterification with supercritical methyl acetate without catalyst and proposed kinetic parameters adjusted for each experimental condition correlating them through the Arrhenius-type plot method. However, even at high temperatures degradation reactions were not considered. From our knowledge, a detailed study on reaction kinetics for FAME production with supercritical methyl acetate and heterogeneous catalyst is not available in the literature. Therefore, the aim of this work was to propose a process modelling for supercritical interesterification with heterogeneous catalyst considering degradation effects at high temperatures. Furthermore, kinetic parameters were globally estimated for the reaction of soybean oil with supercritical methyl acetate using Ca-Mg-Al mixed oxide as solid catalyst. Finally, degradation hypothesis on model development and variables

influence (temperature, catalyst concentration, and MeA excess molar ratio) were evaluated and discussed.

2. EXPERIMENTAL SECTION



2.1 Materials

Commercial refined soybean oil was obtained in a local marketplace. Methyl acetate (Reagent Plus® 99%), heptane (99%), methyl heptadecanoate (internal standard), tricaprin (internal standard) and standard references for each compound analysis were purchased from Sigma Aldrich (Brazil). Solid catalyst, hydrotalcite Ca 40%-Mg-Al with M2+/M3+ molar ratio equal 3, was synthesized based on the co-precipitation method of Reyero et al.18 and the solids were milled and sieved to reduced particle size to 300 𝜇𝑚.

2.1.1 Oil characterization

Soybean oil was characterized to determine the fatty acid profile based on a method described by Hartman and Lago19. Water content was determined by Karl-Fisher titration and the acid value was determined by titration according to AOCS Cd 3d-63 method. Fatty acid profile of soybean oil, acid value, and water content are presented in Table 1.

Table 1: Refined soybean oil characterization. Property

Measured value

Acid value [mg KOH/g] Water content (wt%)

0.145 0.08

Fatty acid profile (wt%) Palmitic acid (16:0)

10.65

Estearic acid (18:0)

3.36

Oleic acid (18:1)

22.49

Linoleic acic (18:2)

56.48

Linolenic acid (18:3)

6.24

Other

0.78


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2.2 Experimental

Interesterification kinetic experiments were performed ranging temperature reaction between 200 °C and 350 °C, solid catalyst concentration between 2 wt% and 10 wt% (based on the oil mass), molar ratio (MeA:Oil) between 20:1 and 60:1 and with an initial reaction volume of 333 mL. For molar ratio (MeA:Oil) of 20:1, 40:1 and 60:1, the soybean oil mass [g] fed into the reactor were 113.56, 70.24 and 50.84, respectively. The agitation influence on the reactional system was previously tested for a system with catalyst 10 wt% concentration. Rotations greater than 400 rpm did not show significant variations in kinetic results, thus, the experiments were performed for an upper rotation of 600 rpm to ensure that kinetics is the process limiting step. Experimental conditions investigated are shown in Table 2.

Table 2: Experimental conditions. Experiment

1

2

3

4

5

6

7

8

9

10

11

12

13

T. [°C]

250

300

350

325

300

300

325

325

300

300

325

325

200

wt% Cat.

5

5

5

5

2

10

2

10

5

5

5

5

5

MeA:O

40

40

40

40

40

40

40

40

60

20

60

20

40

Reactions were carried out in a 500 mL batch reactor (PARR 4575) with temperature and stirring controllers and pressure monitoring. Initial time was set in the beginning of heating process and not when the temperature setpoint was reached. Samples were collected in 40, 60, 70, 80, 100, 120, 150 and 180 min, centrifuged and the liquid phase was filtered in a PTFE syringe filter (0.45 𝜇𝑚). Methyl acetate excess and all the volatiles components were removed by evaporation at 80 °C and 200 mbar for 30 min.



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2.3 Analytical methods and quantification

Analytical data were based on non-volatile mass. Approximately 20 mg of sample was weighed in a 1 mL volumetric flask and completed with heptane. In the same flask was added 100 𝜇L of a 10,000 mg L-1 tricaprin solution in pyridine and 500 𝜇L of a 10,000 mg L-1 methyl heptadecanoate solution in pyridine. This mixture was injected (1 𝜇 L) into gas chromatograph (Shimadzu GCMS – QP2010) equipped with FID and ZB-5HT capillary column (15 m × 0.32 mm × 0.10 𝜇𝑚). The equipment was programmed for the following temperatures: 70 °C for 1 min, rate of 15 °C/min up to 190 °C, rate of 7 °C/min up to 260 °C and rate of 20 °C/min up to 380 °C holding for 5 min. The temperatures of the injector and detector were set at 390 °C and 380 °C, respectively. Helium was the carrier gas with constant linear velocity of 35 cm/s at 60 split ratio. Quantification of interesterification components was done through internal standard method, as shown in Eq. (1). Relative response factors were determined for the standard-analyte sets: methyl heptadecanoate to FAME and TA; tricaprin to TG, DG (dyglicerides) and MG (monoglicerides). According to Casas et al.7, the response factors of DG and MG were very similar to those of MADG and DAMG, respectively. Quantification of degraded compounds, (C)d, like heavier polymers that do not volatilize at injector temperature and are not eluted into the column, and like smaller compounds whose chromatographic peaks are not identifiable, was performed through Eq. (2).

𝑥𝑖

=

𝐴𝑖 ∙ 𝑚𝐼𝑆 𝐴𝐼𝑆 ∙ 𝑚𝑆𝑎𝑚𝑝𝑙𝑒

𝑥(𝐶)𝑑 = 1 ―

∑𝑥

∙

1 𝑅𝑅𝐹𝑖/𝐼𝑆

(1) (2)

𝑖

𝑖


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where 𝑥𝑖 is the non-volatile mass fraction [ g “i”/ g “sample”] , “i” is {TA, FAME, DAMG, MADG, TG},“IS” is the reference internal standard of “i”, A is the chromatogram area [unA], m is the mass in volumetric flask [mg] and 𝑅𝑅𝐹𝑖/𝐼𝑆 is the relative response factor for “i/IS”.

To evaluate the degradation reactions, analysis of reaction medium/samples at several reactional times were also done in a Shimadzu IRPrestige-21 Fourier transform infrared (FTIR) spectrophotometer, equipped with Pike Attenuated Total Reflectance (ATR) system. ATR-FTIR was recorded at room temperature from 4400 to 600 cm−1 at a resolution of 4 cm−1. For each spectrum, 45 scans were added before Fourier transformation and the backgrounds of the spectra were subtracted.

2.4 Kinetic modelling

Kinetic models for reaction medium was developed according to the following assumptions: (a)

Reversible interesterification reaction of triglycerides with methyl acetate

through three sequential reactions (R.1, R.2, R.3), as previously proposed 7,20.

TG

+ MeA ↔ MADG + FAME

(R.1)

MADG + MeA↔ DAMG + FAME

(R.2)

DAMG + MeA↔ TA

(R.3)

(b)

+ FAME

Diglycerides and free fatty acids are at minimum concentrations in

soybean oil and do not significantly influence reaction rates. Thus, it was adopted 𝑥𝑇𝐺 = 1.00 for initial oil mass fraction.



(c)

TG

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Irreversible degradation of TG, MADG, DAMG and FAME.

→ (TG)degraded

MADG → (MADG)degraded DAMG → (DAMG)degraded FAME

→ (FAME)degraded

Due to non-traceability in degraded compounds quantification, the degradation reactions above can be generalized in R.4 reaction.

(TG, MADG, DAMG, FAME) → (TG, MADG, DAMG, FAME)degraded

(R.4)

According to Lin et al. 16, at high temperature, the main routes of ester degradation are from the double bond (isomerization and polymerization from Diels–Alder reaction) or from the breaking of covalent bonds (pyrolysis reactions). Thus, the degradation compounds rates were considered proportional to the number of unsaturation bonds and to the carbon chain of each compound (TG, MADG, DAMG and FAME) and consequently proportional to characterization and quantification of acid chains attached. For example, TG exhibits the possibility of containing (C=C) and (C-C) three times greater than DAMG, due to the number of acid chains attached.

(d)

Irreversible degradation of triacetin (R.5) was considered individually

since mechanisms of triacetin degradation

17

and mechanisms of esters and glycerides

degradation15,16 are completely different.


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TA → (TA)degraded

(e)

(R.5)

According to Liu 21, regardless of the interesterification proposed reaction

mechanism, the main event is the nucleophilic attack of negative oxygen in the anion on a positive carbonyl carbon atom in a glyceride. Therefore, the reaction rates are directly proportional to ester groups present in the glycerides and independent of fatty acid profile attached. Thus, the individual concentrations of each glyceride with the same attached fatty acid arrangement can be simplified by the total concentrations of each glyceride.

(f)

Reactions rates [mol L h-1] from R.1 – R.5 are:

𝑟𝑅.1 = 𝑘1𝐹 ∙ 𝐶𝑇𝐺

∙ 𝐶𝑀𝑒𝐴 ― 𝑘1𝑅 ∙ 𝐶𝑀𝐴𝐷𝐺 ∙ 𝐶𝐹𝐴𝑀𝐸

𝑟𝑅.2 = 𝑘2𝐹 ∙ 𝐶𝑀𝐴𝐷𝐺 ∙ 𝐶𝑀𝑒𝐴 ― 𝑘2𝑅 ∙ 𝐶𝐷𝐴𝑀𝐺 ∙ 𝐶𝐹𝐴𝑀𝐸 𝑟𝑅.3 = 𝑘3𝐹 ∙ 𝐶𝐷𝐴𝑀𝐺 ∙ 𝐶𝑀𝑒𝐴 ― 𝑘3𝑅 ∙ 𝐶𝑇𝐴

∙ 𝐶𝐹𝐴𝑀𝐸

(3)

𝑟𝑅.4 = 𝑘′4𝐹 ∙ (3 ∙ 𝐶𝑇𝐺 + 2 ∙ 𝐶𝑀𝐴𝐷𝐺 + 𝐶𝐷𝐴𝑀𝐺 + 𝐶𝐹𝐴𝑀𝐸) 𝑟𝑅.5 = 𝑘′5𝐹 ∙ 𝐶𝑇𝐴

where 𝐶𝑖 is the molar concentration [mol L-1] of “i”, 𝑘′𝑗 [h-1] and 𝑘𝑗[L mol-1 h-1] are the kinetic constants of reaction “j” from the forward direction, “F”, and from the reverse direction, “R”. The rates of each component [mol L-1h-1] are:

𝑟𝑇𝐺

= ― 𝑟𝑅.1 ― 3 ∙ 𝑘′4𝐹 ∙ 𝐶𝑇𝐺

𝑟𝑀𝐴𝐷𝐺

=

𝑟𝑅.1 ― 𝑟𝑅.2 ― 2 ∙ 𝑘′4𝐹 ∙ 𝐶𝑀𝐴𝐷𝐺



𝑟𝐷𝐴𝑀𝐺

=

𝑟𝑅.2 ― 𝑟𝑅.3 ― 𝑘′4𝐹 ∙ 𝐶𝐷𝐴𝑀𝐺

𝑟𝐹𝐴𝑀𝐸

=

𝑟𝑅.1 + 𝑟𝑅.2 + 𝑟𝑅.3 ― 𝑘′4𝐹 ∙ 𝐶𝐹𝐴𝑀𝐸

𝑟𝑇𝐴

=

𝑟𝑅.3 ― 𝑟𝑅.5

𝑟(𝑇𝐺)𝑑

=

3 ∙ 𝑘′4𝐹 ∙ 𝐶𝑇𝐺

𝑟(𝑀𝐴𝐷𝐺)𝑑 =

2 ∙ 𝑘′4𝐹 ∙ 𝐶𝑀𝐴𝐷𝐺

𝑟(𝐷𝐴𝑀𝐺)𝑑 =

𝑘′4𝐹 ∙ 𝐶𝐷𝐴𝑀𝐺

𝑟(𝐹𝐴𝑀𝐸)𝑑 =

𝑘′4𝐹 ∙ 𝐶𝐹𝐴𝑀𝐸

𝑟(𝑇𝐴)𝑑

𝑟𝑅.5

(g)

=

Page 10 of 40

(4)

The Sherwood number, Sh, was calculated to determine the process

limiting phenomena using Frössling’s equation. Analyzing the values of mass transfer coefficient, 𝑘𝑐, with order of magnitude O.M = 𝑎 × 109 [dm/h] and kinetic constants of reaction reaches maximum order of magnitude along the reaction of O.M = 𝑎 × 10 ―1 [dm³ mol-1 h-1], it was concluded that chemical reaction is the rate-controlling step. Due to catalyst and molecules characteristics, the reactional system was considered only at catalyst surface, disregarding the intraparticle diffusion, and has a dependence on catalyst concentration. Temperature influence at adsorption/desorption kinetics on catalyst surface was considered by Langmuir correlation for fraction absorbed, Eq. (5) and Eq. (6), assuming as 𝑃𝑟𝑒𝑓 = 660 psi, pressure value considered as a minimum so that there is enough fraction absorbed to start the reactional system. Kinetics effects of temperature and catalyst concentration were described by Arrhenius-type function22, Eq. (7).Temperature and pressure profiles were adjusted with data monitored and registered sequentially every 5 minutes.


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𝜃(𝑇,𝑃) =

𝐾𝐴𝐷 ∙ (𝑃𝑆𝑖𝑠𝑡 ― 𝑃𝑟𝑒𝑓)

(5)

(1 + 𝐾𝐴𝐷 ∙ (𝑃𝑆𝑖𝑠𝑡 ― 𝑃𝑟𝑒𝑓) )

[

𝐾𝐴𝐷 = exp ln (𝐾𝑇𝑟𝑒𝑓 𝐴𝐷 ) ―

)]

∆𝐻𝐴𝐷 𝑇 ― 𝑇𝑟𝑒𝑓

(

𝑅𝑇𝑟𝑒𝑓

[

𝑇

)𝑗 ― 𝑘𝑗 = (𝐶𝑐𝑎𝑡 ∙ 𝜃) ∙ exp ln (𝑘𝑇𝑟𝑒𝑓 0

(6)

)]

𝐸𝐴𝑗 𝑇 ― 𝑇𝑟𝑒𝑓

(


𝑇

(7)

where 𝐾𝐴𝐷 is the equilibrium constant for adsorption/desorption [psi-1], ∆𝐻𝐴𝐷 is the

)𝑗is the adsorption enthalpy [kJ mol-1], 𝐸𝐴𝑗 is the activation energy [kJ mol-1],ln (𝑘𝑇𝑟𝑒𝑓 0 natural logarithm of specific reaction rate at reference temperature 𝑇𝑟𝑒𝑓 = 573 K, R is the ideal gas constant [kJ mol-1 K-1], T is the absolute temperature [K],𝐶𝑐𝑎𝑡 is the catalyst mass

concentration

in

relation

to

reaction

volume

[g L-1].

For

𝑘𝑗,

= [L2 h-1 mol-1 gCat-1], and for 𝑘′𝑗, 𝑘𝑇𝑟𝑒𝑓 = [L h-1 gCat-1]. 𝑘𝑇𝑟𝑒𝑓 0 0 For reaction (R.4), kinetics effects were considered to be dependent only by thermal influence, Eq. (8), with 𝑘𝑇𝑟𝑒𝑓 = [h-1]. 0

[

)4 ― 𝑘′4𝐹 = exp ln (𝑘𝑇𝑟𝑒𝑓 0

)]

𝐸𝐴4 𝑇 ― 𝑇𝑟𝑒𝑓

(


𝑇

(8)

2.5 Process modelling

The process model was developed according to the following assumptions: (a)

Likely transesterification and esterification reactions with methanol, the

interesterification reaction with methyl acetate present distinct characteristics and phase equilibrium during heating up to high temperatures. Fang et al.23 reported the phase



Page 12 of 40

equilibrium data for the mixtures of supercritical methanol + C18 methyl esters and observed that these systems present significant changes becoming a homogeneous 𝑀𝑖𝑥 supercritical phase at mixing critical properties, 𝑇𝑀𝑖𝑥 𝐶 and 𝑃𝐶 , and also that these values

are close to critical properties of the more volatile compound. In the present work, mixing critical properties were calculated according to the 𝑀𝑖𝑥 pseudocritical approach, Eq (9). Since 𝑇𝑀𝑖𝑥 𝐶 and 𝑃𝐶 depend on the mixture composition

and critical properties of pure substances, the highest values for

mixing critical

temperature and pressure for the system studied in this work are found for the initial reaction concentrations, where the system is a binary mixture of MeA and TG, since TG is the highest 𝑇𝑐 compound. Therefore, for MeA:Oil molar ratios of 20:1, 40:1 and 60:1 the highest values of 𝑇𝑀𝑖𝑥 and 𝑃𝑀𝑖𝑥 from initial concentrations are respectively 𝐶 𝐶 [255.84 °C, 659.83 psi], [244.90 °C, 674.73 psi] and [241.13 °C, 679.86 psi]. Since all experimental temperatures are higher than 250 °C, it can be concluded that reactions were performed mostly at supercritical conditions.

𝑌𝑀𝑖𝑥 𝐶 =

∑𝑥

𝑖

(9)

∙ 𝑌𝑖𝐶

𝑖

where 𝑌𝑀𝑖𝑥 is the critical mixing property, 𝑥𝑖 is the molar fraction of “i” and 𝑌𝑖𝐶 is the 𝐶 critical property of pure component “i”. The critical properties of pure interesterification glycerides were approximated by esterification compounds available in the literature 24, and for MeA , 𝑇𝑀𝑒𝐴 = 233.4 °C and 𝑃𝑀𝑒𝐴 = 690.38 psi 25. 𝐶 𝐶 Therefore, it was proposed to divide the reaction system into two stages according to critical mixing properties namely as pre-critical and supercritical stages.


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Pre-critical stage: below mixing critical properties, there is the coexistence of three phases: a bottom liquid-solid phase composed of interesterification compounds, methyl acetate and suspended solid catalyst in equilibrium with a top phase of methyl 𝑀𝑒𝐴 acetate in the gaseous state (𝑇𝑀𝑒𝐴 ≤ 𝑇 < 𝑇𝑀𝑒𝐴 ≤ 𝑇 < 𝑇𝑀𝑖𝑥 𝑏 𝐶 ) or supercritical state (𝑇𝐶 𝐶 ).

Fang et al.23 demonstrated for a similar system of methanol and C18 methyl esters that even when the conditions are lower than the critical mixing properties, the mole fractions of the more volatile compound in the vapor are very close to unity. Therefore, it was considered that the MeA molar fraction in gas phase was 𝑦𝑀𝑒𝐴 = 1 during the pre-critical stage. As the vaporization rate to gas phase has low influence on the variation of MeA concentration at liquid phase due to the large methyl acetate excess in the system, it was considered that liquid 𝐶𝑀𝑒𝐴 only changes due to the reaction volume expansion. At the pre-critical stage, the reactions have low rates and occurred only in liquid phase, which volume expansion dependence with composition and temperature was calculated by liquid mixtures correlations proposed by Spencer and Danner 26. Besides, the sampling effects were also considered according to Eqs (12) – (16). Supercritical stage: above mixing critical properties, there is a single supercritical phase composed of interesterification compounds, methyl acetate and catalyst uniform suspension with constant volume and equal to reactor nominal size. Sampling does not affect the reaction volume, that is, it was constant due to supercritical fluid properties. All 96 experimental points used for kinetic parameters optimization, except for the 40 min point of Exp. 1, are on supercritical stage.

(b)

Batch reactor model for two stages was defined by 11 differential

equations, Eq. (10). Agitation used was sufficient for a homogenous dispersion of catalyst in solution and does not form reaction dead zone.



𝑑(𝐶𝑖 ∙ 𝑉) 𝑑𝑡

Page 14 of 40

(10)

= 𝑟𝑖 ∙ 𝑉

where 𝐶𝑖 is the molar concentration [mol L-1] of “i”, V is the reaction volume [cm³], “i” = {MeA, TA, FAME, DAMG, MADG, TG, (TA)d,(FAME)d, (DAMG)d, (MADG)d, (TG)d}, and (𝐶(𝑇𝐴)𝑑 + 𝐶(𝐹𝐴𝑀𝐸)𝑑 + 𝐶(𝐷𝐴𝑀𝐺)𝑑 + 𝐶(𝑀𝐴𝐷𝐺)𝑑 + 𝐶(𝑇𝐺)𝑑) = 𝐶(𝐶)𝑑 .

(c)

The non-volatile mass variation throughout the extent of reaction between

sampling was described by mass balance, Eq. (11).

𝑀′ = 𝑀′𝑖𝑛 + (𝑛𝑖𝑛 𝑀𝑒𝐴 ― 𝐶𝑀𝑒𝐴 ∙ 𝑉) ∙ 𝑀 𝑀𝑒𝐴

(11)

where 𝑀′𝑖𝑛, is the initial non-volatile mass [g], 𝑛𝑖𝑛 𝑖 is the initial mols of “i”, 𝑉 is the reactional volume [L] and 𝑀′𝑖𝑛 is the molar mass of “i” [g mol-1]. The second term represents the mass increase due to MeA consumption, R.1 – R.3.

(d)

At sampling times, the variables were calculated and updated by the

following relations:

𝑊

= 𝑊𝑜𝑢𝑡 ― (𝑊𝑜𝑢𝑡/𝑉) ∙ 𝑉𝑠

(12)

𝑛𝑖

= 𝑛𝑜𝑢𝑡 ― 𝑉𝑠 ∙ 𝐶𝑜𝑢𝑡 𝑖 𝑖

(13)

𝑉

= 𝑉𝑜𝑢𝑡 ― 𝑉𝑠

(14)

𝑥𝑀𝑜𝑑 = (𝐶𝑜𝑢𝑡 𝑖 𝑖 ∙ 𝑉 ∙ 𝑀 𝑖) / 𝑀′

𝑜𝑢𝑡


(15)

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𝑀′ = 𝑀′

𝑜𝑢𝑡

― 𝑉𝑠 ∙

∑𝑀

𝑖

∙ 𝐶𝑜𝑢𝑡 𝑖

(16)

𝑖

where 𝑌𝑜𝑢𝑡 is the reactional variable Y at time sampling, the W is the catalyst mass [g], 𝑥𝑀𝑜𝑑 is the calculated non-volatile mass fraction [ g “i”/ g “sample”] and 𝑉𝑠 is the sample 𝑖

volume [10 mL].

2.6 Models comparation and parameters optimization

With the kinetic and process modelling, reactions reversibility hypothesis of R.1, R.2 and R.3 was initially tested considering triacetin degration (R.5) in order to obtain the best set of Arrhenius parameters, resulting in 2 models: M.1) Due to high MeA excess, reverse reactions can be neglected, or M.2) Reverse reactions were considered. Afterward, the influence of triacetin degradation hypothesis, R.5, were tested. For the 2 models, Arrhenius parameters were concomitantly estimated by minimizing the least squares objective function, Eq. (17). Data from experimental conditions shown in Table 2 were used. However, Exp. 4 data was reserved to validate the models and Exp. 13 data was neglected for not reacting under 200°C, 5 wt% catalyst content and molar ratio (MeA:Oil) of 40.

𝑁.𝐸𝑥𝑝

𝐹𝑂𝑏𝑗 =

∑ ∑ (𝑥 ― 𝑥 𝑖

𝑁

𝑀𝑜𝑑 2 𝑖

)

(17)

𝑖

where “i” = {TA, FAME, DAMG, MADG, TG, (C)d,}. The used optimization algorithm was composed by stochastic Particle Swarm Optimization (PSO)

27

and thus the solution was refined using the MatLab® built−in



routine nlinfit with trust-region-reflective algorithm option. ODE system was solved through MatLab® built−in routine ode15s (a variable-step, variable-order solver based on the numerical differentiation formulas of orders 1 to 5). PSO search limits used for EA were between 10 and 150 kJ mol-1, for ∆𝐻𝐴𝐷 were between -250 and 250 kJ mol-1, and

) and ln (𝐾𝑇𝑟𝑒𝑓 for ln (𝑘𝑇𝑟𝑒𝑓 𝑗 𝐴𝐷 ) were between -15 and +15. For statistical validation of optimized parameters, the confidence intervals through elliptical confidence region approximation and the correlation coefficient between all combinations of two parameters were calculated using the MatLab® built−in routine nliparci. In order to validate the triacetin degradation hypothesis, R.5, Student’s t-test and Fisher’s exact test were used.

3. RESULTS AND DISCUSSION

3.1 Thermal degradation

Soybean oil is rich in unsaturated fatty acids in content (85.11%), as shown in Table 1, especially in linoleic and oleic acids, which makes the reactional system very susceptible to thermal degradation reactions, mainly isomerization and polymerization 16,28,29.

As shown in Figure 1, when the temperature set point rises up there is an increase

in intensity and quantity of chromatographic peaks from parallel reaction products. This behavior is consistent with the profile of degraded compounds, Figure 2, which demonstrates an increase in reaction rates over residence time and temperature set point.


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Figure 1.Chromatograms overlay of samples at reaction time of 120 min, 40:1 molar ratio (MeA:Oil), 5wt% catalyst concentration and different temperatures. Highlighted regions show the location of peaks for some degraded compounds.



Figure 2.Experimental mass fraction of degraded compounds, (C)d, versus time at 40:1 molar ratio (MeA:Oil), 5wt% catalyst concentration and different temperatures. Data were linked for better visualization.

To study the degradation mechanisms over reactional time, FTIR analyses were carried out. Figure 3 shows the profiles, in transmittance along wavelength, for Exp. 3 samples. As shown in Figure 3, throughout reaction time it is observed that peaks corresponding to (C=O) stretching and to (C-H) deformation present modifications, which is pertinent with interesterification reactions.


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Figure 3. FTIR spectra overlay of samples at different reaction time, 40:1 molar ratio (MeA:Oil), 5wt% catalyst concentration and 350 °C.

The (C=C) stretching, (C=C) cis and (C=C) trans transmittance peaks from Exp. 3 were quantified and are shown in Figure 4. It is observed that in first 60 min, the decrease of (C=C) stretching profile, Figure 4(a), is proportional to increase of (C=C) trans profile, Figure 4 (c), indicating that initially, the route of thermal degradation is mainly due to isomerization, and therefore there is no great increase in C(d), Figure 4 (d), since isomers have almost identical chemical properties and gas chromatographic retention times, causing them to be quantified as the major products by Eq. (1). Above 60 min, (C=C)



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trans transmittance profile, Figure 4 (c), reaches equilibrium and the profiles of (C=C) stretching, Figure 4 (a), and (C=C) cis, Figure 4 (b), show slight growth rates, indicating that polymerization reactions become the main route of degradation at higher times. It is observed that the growth rate of (C=C) stretching transmittance above 60 min, Figure 4 (a), is proportional to the increase of C(d), Figure 4 (d), since the heavier polymeric compounds do not volatilize at injector temperature and do not elute in column, presenting a large linear correlation of R = 0.9850. The order of predominant reactions, first isomerization and after polymerization, was also demonstrated by Lin et al. thermal decomposition reactions of biodiesel.


16

in

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Figure 4. Transmittance at (a) 3008 cm-1, (C=C)stretching; (b) 721 cm-1, (C=C)cis; (c) 966 cm-1, (C=C)trans; and (d) experimental mass fraction of degraded compounds from Exp.3 samples.



3.2 Kinetic parameters, hypotheses and model validation

Estimated parameters and their confidence region are shown in Table 3 for both models. Although M.2 model has the lowest FObj value (1.0809), the large parametric uncertainties of confidence limits, especially for reverse reactions parameters, demonstrate the irrelevance of irreversibility hypotheses under experimental conditions studied and the model super parameterization, which justifies its lower FObj value. For M.1 model (FObj = 1.2604), even with a smaller number of parameters (12), the confidence intervals are consistent with estimated values and demonstrate small parametric uncertainties. In addition, parametric correlation coefficients for this model present values lower than 0.8 indicating low parametric correlations, good parameterization, estimation and good hypothesis postulate. Since M.2 model is superparametric, comparative statistical analysis, Student’s t-test and Fisher’s exact test, need not be performed. Therefore, M.1 model was accepted as the best one to predict experimental data and will be used in the course of this work. The M.1 values of activation energies presented similarity to results previously published in literature 14,30.

Table 3: Estimated kinetic parameters and confidence interval for models (P ± C.I). Reaction (R.1) (R.2) EA

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(R.3) (R.4) (R.5) (R.1)

"F" "R" "F" "R" "F" "R" "F" "F" "F"

M.1 M. 2 75.40 ± 5.64 71.66 ± 5.99 -104.37 ± 155 89.03 ± 14.38 73.56 ± 17.78 -36.52 ± 87.48 89.69 ± 30.79 91.77 ± 100.44 -58.86 ± 161 96.30 ± 17.41 99.68 ± 15.71 59.61 ± 21.33 50.77 ± 60.48 -2.95 ± 0.07 -3.04 ± 0.06


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(R.2)

) ln (𝑘𝑇𝑟𝑒𝑓 𝑗

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(R.3) (R.4) (R.5) ∆𝐻𝐴𝐷 ln (𝐾𝑇𝑟𝑒𝑓 𝐴𝐷 ) Parameters FObj

"R" "F" "R" "F" "R" "F" "F"

--2.82 ± 1.25 -3.30 ± 0.11 -3.23 ± 0.12 --1.19 ± 0.55 -3.24 ± 0.24 -2.56 ± 0.66 -0.29 ± 1.22 -3.44 ± 0.17 -3.54 ± 0.16 -1.74 ± 0.59 -1.94 ± 0.56 -154,75 ± 1,12 -118 ± 19755 -3,85 ± 0,50 12 1.2604

3,10 ± 471 18 1.0809

Highlighted cells present a confidence interval values of 50% or more of the parameter value.

To evaluate the triacetin degradation hypothesis, new parameters were adjusted for modified M.1 model (without R.5, 𝑟𝑅.5 = 0). Figure 5 shows the effect of TA degradation hypothesis on model fitting. It is noticeable the improvement on prediction capability of the model for TA mass fractions, corroborating the relevance of TA degradation hypothesis on model performance.



Figure 5. Experimental (□) and predicted triacetin mass fractions from M.1 model with ( ― ) and without ( ― ― ) R.5 hypothesis at 40:1 molar ratio (MeA:Oil), 5 wt% catalyst

concentration and (a) 325 °C; (b) 350 °C.

Table 4 presents the Student’s t test and the Fischer's exact test results (95% of confidence) for M.1 model with and without the influence of reaction R.5, where 𝜇 is the


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mean value of “i” and 𝜎2 is the variance of “i”. There is statistical equivalence between and 𝜇𝑀𝑜𝑑 if means of experimental and model data are contained into intervals from 𝜇𝐸𝑥𝑝 𝑖 𝑖 Student’s t test. Likewise, the 𝜎²𝑀𝑜𝑑 are equivalent to 𝜎²𝐸𝑥𝑝 if ratios of experimental and 𝑖 𝑖 model data variances are into the lower and upper limits from Fischer's exact test. For M.1 with R.5 reaction (FObj = 1.2604), the model presents variances and means consistent with experimental data for all “i”. However, for M.1 without R.5 reaction (FObj = 1.7297), 𝜎2 and 𝜇 values do not present equivalence between model and experimental data, which indicates that there is no satisfactory fitting.

Table 4: Student’s t test Fischer's exact test [lower limit < (𝐹 = 𝜎2𝐸𝑋𝑃/𝜎2𝑀𝑂𝐷) < upper limit] for mass fraction of “i” (95% of confidence).

Student’s t test

“i”

Fischer's exact test

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TA FAME DAMG MADG TG (C)d.

Experimental 0.0263 < μ < 0.0345 0.3670 < μ < 0.4360 0.0575 < μ < 0.0703 0.1322 < μ < 0.1702 0.1888 < μ < 0.2584 0.0991 < μ < 0.1331

M.1 with R.5 (FObj = 1.2604)

M.1 without R.5 (FObj = 1.7297)

0.0225 < μ < 0.0306 0.3706 < μ < 0.4400 0.0535 < μ < 0.0692 0.1331 < μ < 0.1714 0.1889 < μ < 0.2856 0.0994 < μ < 0.1371 0.6610 < 𝐹

Kinetic Modeling of Supercritical Interesterification with

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