carbon dioxide mixtures in a continuous reactor

carbon dioxide mixtures in a continuous reactor

Fuel 90 (2011) 2280–2288 Contents lists available at ScienceDirect Fuel journal homepage: Biodiesel production using s...

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Fuel 90 (2011) 2280–2288

Contents lists available at ScienceDirect

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Biodiesel production using supercritical methanol/carbon dioxide mixtures in a continuous reactor José Maçaira, Aline Santana, Francesc Recasens, M. Angeles Larrayoz ⇑ Department of Chemical Engineering, ETSEIB, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain

a r t i c l e

i n f o

Article history: Received 18 November 2010 Received in revised form 14 February 2011 Accepted 15 February 2011 Available online 1 March 2011 Keywords: Biodiesel Supercritical fluids Transesterification Solid acid catalyst Vegetable oil

a b s t r a c t Fatty acid methyl esters (biodiesel) were produced by the transesterification of triglycerides with compressed methanol (critical point at 240 °C and 81 bar) in the presence of solid acids as heterogeneous catalyst (SAC-13). Addition of a co-solvent, supercritical carbon dioxide (critical point at 31 °C and 73 bar), increased the rate of the supercritical alcohols transesterification, making it possible to obtain high biodiesel yields at mild temperature conditions. Experiments were carried out in a fixed bed reactor, and reactions were studied at 150–205 °C, mass flow rate 6–24 ml/min at a pressure of 250 bar. The molar ratio of methanol to oil, and catalyst amount were kept constant (9 g). The reaction temperature and space time were investigated to determine the best way for producing biodiesel. The results obtained show that the observed reaction rate is 20 time faster than conventional biodiesel production processes. The temperature of 200 °C with a reaction time of 2 min were found to be optimal for the maximum (88%) conversion to methyl ester and the free glycerol content was found below the specification limits. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Biodiesel is one of the most famous alternative petroleum diesel fuel, which is defined as a fuel comprised of mono mono-alkyl ester of long chain fatty acids derived from vegetable oils or animal fats [1]. Conversion of these oils, consisting primarily of triglycerides, to biodiesel fuel is commonly achieved through a series of transesterification reactions involving the reaction of an alkoxy group of an ester (i.e., mono-, di-, or triglyceride) with that of a small alcohol (e.g., methanol or ethanol). The reactants are not miscible at ambient temperature and pressure; for this reason in a typical transesterification reaction the reaction system consists of two layers at the initial stage. In this sense the mass transfer controls the kinetics, until there is formation of methyl esters in the system that acts as a co-solvent because they are miscible in vegetable oil and also in methanol. However, operating the system in supercritical conditions the system becomes a single homogeneous phase, which will accelerate the reaction because there is no interphase mass transfer to limit the reaction rate [2]. Fig. 1 shows a scheme of these reactions. Transesterification process can be carried out by batch process or continuous process. The majority of studies in transesterification of vegetable oils available in the open literature deal with batch processes. However, batch processes suffer several disadvan⇑ Corresponding author. Fax: +34 934017150. E-mail address: [email protected] (M.A. Larrayoz). 0016-2361/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2011.02.017

tages compared to continuous processes: they require larger reactors volumes and hence higher capital investment; they are inherently less efficient due to start-up and shut-down; there are batch to batch variations in the quality of the products; and labor costs are higher [3]. Facing those problems and motivated by the needs to increase its production, the biodiesel industry was obliged to develop large scale continuous processes. This reaction can be catalyzed by alkalis, acids or enzymes. Synthesis of biodiesel by an alkaline catalytic transesterification reaction using a batch-type reactor has several drawbacks: it is energy intensive, recovery of glycerol is difficult, the alkaline wastewater retains fatty acids and water interferes with the reaction. In addition, alkaline transesterification is low in selectivity, leading to undesirable side reactions [4,5]. The main disadvantage of using enzyme as the catalyst for biodiesel production is that the cost is still high due to generally poor reusability as a result of poor stability of enzyme. Acid transesterification is an efficient way to produce biodiesel if the raw material oil has relative high free fatty acids content. However, environmental and economic concerns are such that a continuous process that uses a heterogeneous catalyst is much more desirable. In particular, solid acid catalysts are ideal because they are able to catalyze both transesterification and esterification reactions simultaneously, which becomes important when using lower quality feedstocks [6–8]. Although the use of solid acid catalysts for the continuous production of biodiesel is promising, only limited information exists about triglyceride transesterification rates or the extent of catalyst deactivation [6,9–13].

J. Maçaira et al. / Fuel 90 (2011) 2280–2288


Nomenclature aS Ci C Si Ea ki Ki r R Re Sh Sc T t

specific surface area concentration of component i concentration of component i at the particle surface activation energy kinetic parameters reaction equilibrium constant reaction rate the universal constant Reynolds number Sherwoo number Schmidt number temperature time

In the conventional transesterification of animals fats and vegetable oils for biodiesel production, free fatty acids and water always produce negative effects, since the presence of free fatty acids and water causes soap formation, consumes catalyst and reduces catalyst effectiveness, all of which resulting in a low conversion. The transesterification of triglycerides by supercritical alcohols has proved to be the most promising process [14]. The supercritical reaction takes a shorter reaction, and the conversion rate is very high. The basic idea of supercritical treatment is a relationship between pressure and temperature upon thermo physical properties of the solvent such as dielectric constant, viscosity, specific weight, and polarity [15]. The transesterification of sunflower oil was investigated in supercritical methanol and supercritical ethanol at various temperatures and the yield of conversion raises 50–95% in a very short time (4–10 min) [16]. Several investigators have synthesized biodiesel in supercritical alcohols [17–25]. However, the synthesis of biodiesel by supercritical alcohols has a drawback with the high cost of apparatus due to the high temperature and pressure. Researches have focused on how to decrease the severity of the reaction conditions. The addition of co-solvent in combination with supercritical conditions seems to be an efficient means to reduce significantly the operating temperature. Co-solvents, such as hexane, propane and calcium oxide [26–32] with small amount of catalyst, added into the reaction mixture can decrease the operating temperature, pressure and the amount of alcohol. Just a few works are available in the open literature regarding the use of cosolvents in the supercritical transesterification, such as the use of carbon dioxide (CO2) [18,25,33,20]. In this research, production of biodiesel from vegetablesunflower-based oil under supercritical condition was carried out. CO2 was employed as co-solvent to decrease the supercritical temperature and pressure of methanol. The effect of temperature, pressure and time was investigated in supercritical methanol/ CO2. The kinetics of transesterification of sunflower oil in supercritical methanol/CO2 with solid acid catalyst and the activation energies were determined from the temperature of the rate coefficients.

Fig. 1. Transesterification raction scheme.

Greek letters adjustable parameter acentric factor reaction time catalyst density

a x s qcat

Abbreviations FAME fatty acid methyl ester TG triglyceride DG diglyceride MG monoglyceride A alcohol E esters

2. Experimental 2.1. Materials Vegetable-sunflower-based oil (S5007) was purchased from Sigma Aldrich (Barcelona, Spain). The mixture carbon dioxide/ methanol (75:25 v/v) was supplied by Abello Linde S.A. (Barcelona). The catalyst NafionÒ SAC-13 was purchased from Sigma Aldrich. The fatty acid methyl esters (FAMEs) standards and methyl hepadecanoate internal standard for the chromatography analysis were purchased from Sigma Aldrich (Barcelona, Spain).

2.2. Equipment and experimental procedure The schematic diagram of the apparatus is shown in Fig. 2. The transesterification reaction of the vegetable oil was carried out in continuous mode in a fixed bed titanium reactor, which has 152 mm of length and 15.5 mm of internal diameter. A liquefied mixture of methanol/carbon dioxide (25/75 wt.%) was pumped using a high pressure air driven piston pump to the reactor, providing a system pressure of 250 bar, which was manually set with a high-pressure regulator. The oil was pumped using a high-performance liquid chromatography pump. Both feed lines are mixed in a static mixer. The reactant mixture was preheated to the desired operating temperature before entering the reactor by a heater. The titanium reactor was heated by an electrical heating jacket. The temperature was monitored in the external reactor walls, and also inside the reactor by a thermocouple (type K, stainless steel). Pressure is measured in the inlet and outlet of the reactor, to check for pressure drops in the fixed bed reactor. The stationary states of the reactor were determined after 30 min and three samples were collected for each experiment and the average error was below 1%. After leaving the reactor the reaction mixture is continuously expanded to atmospheric pressure on an externally heated needle-valve in order to control the total flow of the reactor mixture. The tubing that follows the expansion valve is also heated by an external resistance wire to prevent freezing of the mixture due to the referred gas expansion. This effluent was then sent to a glass container, which is immersed in a heated bath in a constant temperature of 70 °C. Here the unreacted methanol is evaporated from the mixture and along with the carbon dioxide is conducted to a series of glass U-tubes, immersed in an ethylene glycol–water (40% v/v) bath held at 10 °C to condense the methanol from the carbon dioxide. The flow rate of exhaust gas (carbon dioxide)


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Fig. 2. Scheme of the experimental installation for the continuous production of biodiesel: 1 – synthetic oil; 2 – oil piston pump; 3 – line valve; 4 – check valve; 5 – CO2 bottle; 6 – line valve; 7 – check valve; 8 – CO2/methanol mixture bottle; 9 – mixture line valve; 10 – mixture check valve; 11 – compressor;12 – pressure regulator; 13 – line valve;14 – cooling device;15 – mixture pump;16 – purge valve; 17 – pressure regulator; 18 – check valve; 19 – safety valve;20 – static mixer; 21 – pre-heater; 22 – rupture disk; 23 – fixed bed reactor;24 – expansion needle-valve; 25 – sample collector; 26 – alcohol collector;27 – flowmeter; 28 – line valve.

was measured with a CO2 flow meter and sent to an explosionproof absorption system. After evaporating the unreacted methanol, the samples were left, preferably overnight, in a separating funnel to let the glycerol layer separate from the esters layer. Then a sample of the upper layer was collected and stored to future analysis. 2.3. Analysis The concentration of FAMEs was analyzed off line by gas chromatography (Shimadzu 2010) with a FID detector and a capillary column (Teknokroma SupraWax-280, 30 m  0.32 mm  0.25 lm). Compounds were quantified upon analysis following the standard UNE-EN 14103 [34]. The concentrations of free and total glycerol and mono-, di- and triglycerides were analyzed by gas chromatography based on European standard EN 14105 [35]. Compounds were quantified by capillary column gas chromatography (Shimadzu 2010) equipped with a cold on-column injection. The capillary column used was a Teknokroma TRB-Biodiesel fused silica column with an internal diameter of 0.32 mm and 10 m of length. 2.4. Achieving a single phase mixture The phase separation depends on the mixture composition, temperature and pressure. Thus, a substantially homogeneous supercritical phase can be formed by choosing the right operating conditions. There are no many previous phase behavior studies in the literature on high-pressure equilibria of these systems (alcohols + CO2 as co-solvent) [36]. The most similar application found in the literature is the supercritical alcohols with propane or dimethylether as co-solvent [37,38]. In this work, vegetable sunflower-based oil (S5007) was used for the production of biodiesel. The vegetable-sunflower-based oil is composed mainly of triolein (23.1%) and trilionolein (65.6%), with

minor contents of tripalmitin (6.4%), tristearine (4.5%) and other triglycerides (0.4%). In order to simplify the problem, Glisic et al. [39] represented the complex composition of sunflower oil with a pseudo component. In this case, the selected pseudo component was triolein, since it is the components for which more thermodynamic data are available in the literature [40] The critical constants of the pure components are needed for the calculation of a(T) and b(T), but these constants are not available for compounds such as fats, since they are chemically unstable and decompose at high temperatures. For this reason the Gani method [41,42] was used to estimate the critical properties of triolein, as this method offers better results for high molecular weight molecules such as triglycerides [43]. The critical properties and other parameters of the pure components are listed in Table 1. To simplify the problem it was decided that the thermodynamic analysis would be done considering a binary system, by treating the mixture methanol/CO2 as one component and the vegetable sunflower-based oil another component. The experimental information available in the literature on high-pressure phase equilibrium of reactive mixtures is very scarce, which made difficult to determine the parameters. Thus, it was necessary to make a rough theoretical estimation of its critical properties according to the Chueh–Prausnitz approximation [47]. The estimated values are presented in Table 2.

Table 1 Critical data for pure components.



Molecular weight (kg kmol1)

Critical temperature, Tc (°C)

Critical pressure, Pc (bar)


Methanol CO2 trioleina

32 44 884

240 31 705

80 74 3.3

0.566 0.225 1.978

Parameters calculated by the Gani method.

Acentric factor,


[44,45] [44,46] [41,42]


J. Maçaira et al. / Fuel 90 (2011) 2280–2288 Table 2 Estimation of the critical properties of the Methanol/CO2 mixture by the Chueh– Prausnitz approximation. Molar composition of methanol/CO2 (mole fraction) 0.05 0.10 0.15 0.20 0.25

Critical pressure Pc (bar)

Critical temperature Tc (°C)

Acentric factor, x

90.1 103.3 113.9 122.2 128.5

47.8 63.5 78.5 92.8 106.3

0.24 0.25 0.27 0.28 0.29

Source: Ref. [47].

As can be seen in Table 2 the introduction of the CO2 co-solvent decreases the critical properties of the mixture. As the quantity of methanol increases in the binary mixture (decrease in the percentage of CO2) the critical pressure and temperature increase. The molar composition chosen to work with was a mixture of 25% of methanol. Methanol in excess is needed to enhance the forward reaction. The maximum reaction temperature of the catalyst is 210 °C. With the critical properties defined for the methanol/CO2 defined, this mixture was treated as one component, and the vegetable sunflower-based oil (triolein) was treated as another. The determination of the critical point was calculated for the system (CO2 + methanol) – vegetable sunflower – based oil at different temperatures, estimating the kij values from the ratio of the fugacity coefficients obtained with the PR-EOS [48–50]. The calculations were performed with the PE 2000 [51] in terms of the convergence pressure [49,50]. Although this is a rough approximation, the mixture of (CO2/methanol)–oil binary mixture exhibits a convergence pressure around 200 bar and temperature is 150 °C, which is quite above that reported in previous work [36] for the CO2–methanol system (130 bar and 70 °C), which compares favorably with the vapor phase estimated in this study [52,53]. The critical pressures for each temperature were determined by both the convergence of vapor and liquid equilibrium lines [54] and are presented in Table 3. The pressure was kept constant (250 bar) over the operating pressure range 200–245 bar to ensure the supercritical single phase condition. 2.5. Design of experiments The experimental design for the transesterification reaction was carried out using a continuous fixed bed reactor. Based on the above phase equilibrium consideration, the temperature was varied in the range from 150 to 205 °C and space time from 0.5 to 4.0 min. The chosen variables in this study were reaction temperature and space time and the ester content in the biodiesel samples was selected to be the response variable. The total system pressure, the molar ratio methanol:oil and catalyst mass were kept constant at 250 bar, 25:1 mol and 9 g, respectively. Once these levels were selected the central composite design of experiments was applied. The experimental conditions in this work are presented in Table 4. In a Response Surface Regression

Table 4 Experimental condition: central composite design. Run

Real values

1 2 3 4 5 6 7 8 9 10 11 12

Temperature (°C)

Space time (min)

180 180 205 150 205 180 180 205 150 150 205 150

0.5 2.1 2.1 0.5 3.9 3.9 1.0 0.5 1.0 3.9 1.0 2.1

consisting of two variables, the total number of experiments was determined to be 12. 2.6. Statistical analysis MINITAB Release 16 statistical software was used for regression analysis of the experimental data. The responses (y) of the transesterification process were used to develop a quadratic polynomial equation that correlates the yield of biodiesel as a function of the independent variables and their interactions as shown in the following Eq. (1) [55]:

y ¼ bo þ

k X i¼1

bi xi þ

k X

bii x2i þ



bij xij þ 2


where y is the response; k is the variable number; xi and xj are the uncoded independent variables; bo is a constant and bi, bij and bij are regression coefficients. The quality of developed model was determined by the value of correlation (R2) while analysis of variance (ANOVA) was used to evaluate the statistical significance of the model by the values of regression and mean square of residuals.

3. Kinetics modeling Reaction kinetics were carried out using a continuous fixed bed reactor. The temperature range studied was 150–205 °C and pressure was kept constant at 250 bar to provide a dense supercritical medium at all temperatures. The thermal transesterification reaction is divided into three steps. Transesterification with alcohol is multiple reactions consisting of a number of consecutive and reversible reactions. Triglyceride (TG) is converted stepwise to diglyceride (DG), monoglyceride (MG) and finally glycerol (GL). At each reaction step, one molecule of methylated compounds is produced for each molecule of methanol consumed. As a result, six different rate constants of the reaction are reported for the whole reaction as discussed by Eqs. (2)–(5) [47]. The overall reaction: catalyst  3E þ GL TG þ 3A  !


Stepwise reactions: Table 3 Estimated critical pressure for transesterification reaction at different temperatures. Mixture molar composition

Temperature (°C)

Pressure (bar)

Methanol/CO2 (99%)* + triolein (1%)

150 180 205

200 240 245

Source: Ref. [54]. * 25%wt METOH in CO2.

k1  DG þ E TG þ A  ! k2



 MG þ E DG þ A  !


k5  GL þ E MG þ A  !




where A and E denote the alcohol and ester respectively.


J. Maçaira et al. / Fuel 90 (2011) 2280–2288

Table 5 Operating conditions and FAME’s content on strongly acidic catalyst resin (Nafion SAC-13) = 9 g, pressure = 250 bar, molar ratio methanol:oil = 25:1 and supercritical methanol + CO2 mixture as medium.


Temperature (°C)

Space time (min)

Solvent flow rate (g/min)

Oil flow rate (g/min)

Space time (min)

MG* (wt.%)

DG* (wt.%)

TG* (wt.%)

FAMEs* Yield (wt.%)

Total glycerol* (wt.%)


0.5 1.0 2.0 4.0

16.2 8.2 4.2 2.3

1.4 0.7 0.4 0.2

0.5 1.0 2.0 4.0

0.20 0.60 0.6 0.02

6.7 8.5 9.7 2.9

85.4 79.3 64.8 16.6

7.5 11.2 24.1 77.6

0.3 0.4 0.9 2.8


0.5 1.0 2.1 3.9

16.2 8.2 4.2 2.3

1.4 0.7 0.4 0.2

0.5 1.0 2.0. 4.0

1.7 1.2 1.3 1.2

8.7 5.8 4.7 2.3

51.5 27.5 16.8 6.0

31.6 58.2 69.3 81.4

6.5 7.0 7.9 9.1


0.5 1 2.1 3.9

16.2 8.2 4.2 2.3

1.4 0.7 0.4 0.2

0.5 1.0 2.0 4.0

2.0 1.6 1.1 0.9

4.2 3.1 1.0 0.8

12.7 7.3 0.8 1.1

73.4 79.7 88.0 88.2

7.6 8.3 9.2 9.1

Relative standard deviation for MG, DG, TG, FAMEs and glycerol for each process was less than 1%.

For this kinetic study, some assumptions were made: (i) the reaction rates constants are determined by two different ways: considering the reaction as irreversible and in one single step, and other considering the reaction as a series of three consecutive reversible reactions; (ii) as the vegetable sunflower-based oil is refined, the proportion of free fatty acids was negligible, and then the free fatty acid neutralization was not significant; (iii) mass transfer limitation in the reaction system was neglected. Based on the above assumptions, the differential equations characterizing the stepwise reactions were as follows [56,57]:

d½TG ¼ k1 ½TG½A þ k2 ½DG½E dt d½DG ¼ k1 ½TG½A  k2 ½DG½E  k3 ½DG½A þ k4 ½MG½E dt d½MG ¼ k3 ½DG½A  k4 ½MG½E  k5 ½MG½A þ k6 ½GL½E dt d½GL ¼ k5 ½MG½A  k6 ½GL½E dt d½E ¼ k1 ½TG½A  k2 ½DG½E þ k3 ½DG½A  k4 ½MG½E dt þ k5 ½MG½A  k6 ½GL½E d½A d½E ¼ dt dt

4.1. Effect of the inlet flowrate and temperature


Twelve experiments were carried out varying the temperature inside the reactor and the mixture inlet flow rate, and thus the space time inside the reactor. The oil flow rate was calculated in each run so the methanol/oil molar ratio was kept constant throughout the experiments, and equal to 25:1. The pressure and catalyst mass were also kept constant at 250 bar and 9 g, respectively. In Table 5 are presented the operating conditions in each run and the content (mass percentage) of each sample in terms of fatty acid methyl esters. As shown in the Table 5, the FAMEs yield ranged from 7.5% to 88.2%, depending on the conditions of experiments. These results can be fitted into a second order quadratic model of coded unit given in Eq. (13):


yFAMEs% ¼ 70:295 þ 27:693X T þ 13:167X s  12:966X 2T

ð6Þ ð7Þ

 11:867X 2s  4:343X s X T ð10Þ ð11Þ

where k1 to k6 are reaction rate constants (L/mol min); [TG], [DG], [MG], [GL], [A] and [E] are mole concentrations of TG, DG, MG, GL, alcohol, and esters in a reaction mixture (mol/L). The concentration change of each component with time could be obtained experimentally and the nonlinear curve fitting software MATLAB (the Maths Work Inc.) was used for fitting the system of differential equation into the experimental data. The initial values for the variables, at reactor entrance are [TG]0 = 0.30 mol/L and [A]0 = 7.5 mol/L, calculated from the mixture of density. From k-values obtained at different temperatures, the activation energy for each transesterification step was estimated using the Arrhenius equation:

k ¼ k0 eEa =RT

4. Results and discussion


where k0 = frequency factor; Ea = activation energy; R = gas constant. The activation energy and the preexponential factor for each consecutive reaction can be obtained by plotting the logarithm of the calculated rate constants for the catalyzed reaction versus the reciprocal of absolute temperature.


in which y is the response factor, fatty acid methyl ester content (% (w/w)). XT and Xs are the values of the independent factors, reaction temperature (°C) and space time (min), respectively. The model was found to have correlation value (R2) of 0.94, which means that 94% of the total variables investigated, indicating that the regression proposed has a good prediction for the system. At low reaction temperature of 150 °C, the yield of biodiesel is affected by space time. However, at higher reaction temperature, its relevancy to the argumentation of yield is enormous. Fig. 3 shows the time variation of conversion at different temperatures. The conversion and reaction rate increased with increase in temperature. Complete conversions are obtained at 205 °C at less than 3 min (Fig. 3). The condition at 150 °C did not reach the equilibrium in 4 min (Fig. 3). Contrary to results from other authors like Noureddini and Zhu [57], and Vicente et al. [58], the triglyceride conversions are very high even using high values of flow rate that result in low contact times between the inlet mixture and the catalyst. For each experiment done, the FAMES content was determined and can be seen in Fig. 3. Because the transesterification of vegetable oil into methyl esters is a three step series of reversible reactions, the conversion of triglycerides is not equal to the FAMEs content in each sample, due to the formation of intermediate species (see Fig. 4). The content of free glycerol in each sample performed with the temperature 200 °C and at different reaction time is presented in


J. Maçaira et al. / Fuel 90 (2011) 2280–2288

depends on conditions of state, so as the reaction is carried out in supercritical conditions, the mass transfer coefficients are not available easily in open literature. In supercritical conditions mass transfer is studied specially in extraction problems, where some correlations have been proposed [61]. In Fig. 5 are plotted the mass transfer coefficients determined and those predicted by the correlations chosen. The mass transfer coefficients were determined using a correlation proposed by Abaroudi et al. [65], and compared to those predicted by the correlations presented in Table 7. This correlation is proposed by these authors in supercritical conditions with carbon dioxide and a variable amount of toluene as a co-solvent.

Triglyceride Conversion %

100 90 80 70 60 50 40 150ºC





10 0 0.00





Space Time (min)

% (w/w)

Fig. 3. Variation of conversion with time at different temperatures. Pressure = 250 bar, catalyst mass = 9 g and methanol/oil molar ratio = 25.

Sh ¼ aRe0:8 Sc0:33

0:295 < a < 0:589

Given the scarce data available in this area of study, this correlation seemed the most appropriate to determine the mass transfer coefficients and to assess the resistance of mass transfer from fluid to solid in the system. In theory the mass transfer coefficients are independent of temperature [60], and as can be seen from Fig. 5 these values vary very little with the temperature. The rate of mass transfer between the fluid and solid phase can be calculated from the determined valued according to Eq. (15) [66].

rqcat ¼ ksi aS ðC i  C Si Þ

Space Time (min) Biodiesel Yield

Triglyceride Conversion

Fig. 4. Comparison between the triglyceride conversion and the FAMEs content in each sample obtained at 205 °C, 250 bar, catalyst mass of 9 g, and methanol/oil ratio of 25.

Table 5. The highest yield in biodiesel was produced with at the temperature of 200 °C and space time of 2 min and the free glycerol content below than 0.02% (w/w) as established in the European [59] quality standard for commercial biodiesel, EN 14214. This fact makes a stage of separating and purification unnecessary for the process developed in this work. The results clearly indicate that the supercritical process can produce a biodiesel fuel that complies with the glycerol content requirements and almost without further refining steps downstream of the supercritical reactors (see Table 6).



The triglyceride concentration in the catalyst surface was determined and compared to that verified in the bulk. The values are presented in Table 8 in form of percentage. As can be seen from this table, the difference between the two concentrations can be safely neglected as the maximum value for this difference is 0.00009%.

4.3. Kinetic approach 4.3.1. One step irreversible reaction scheme In the transesterification process to get a higher conversion of the reaction in the supercritical methanol, a high molar of methanol to oil is needed. Due to this high molar ratio, the reverse reaction was ignored, and the concentration of methanol can be regarded as invariant. Considering only the forward reaction and assuming the whole reaction as a first order reaction, the reaction can be modeled as: k

TG þ 3A ! 3E þ GL


The apparent rate constant of the reaction, k can be given by Eq. (17).

4.2. External mass transfer Mass transport limitations can seriously interfere with a fast reaction, and great care should be taken to eliminate these as much as possible in kinetic investigation [60]. The mass transfer coefficients were calculated and the unmeasured surface concentration is determined and compared to that in the bulk to assess the mass transfer resistance in the system. As heat transfer, mass transfer Table 6 Free glycerol content of biodiesel produced at 205 °C. Space time (min)

FAMEs% (w/w)*

Free glycerol% (w/w)*

0.5 1 2.1 3.9

64 78.1 81.6 79.2

0.0104 0.0101 0.0104 0.0123

* Relative standard deviation for FAMEs and glycerol for each process was less than 1%.

d½TG ¼ k½TG dt


The reaction rate constants at different reaction temperature were calculated for each experiment using the Eq. (17) and are presented in Table 9. As expected the maximum reaction rate constants correspond to high flow rates, or low space time values as the concentration of reactants is maximum and of products is minimum. The exception is for 150 °C as equilibrium is no reached, and for the range of flow rates studied the reaction rate does not change significantly (as can be seen from the slopes of the curve of 150 °C of Fig. 3. In Table 9 are some reported values for the reaction rate constants. These values are drawn from authors that made the same kinetic consideration of one step irreversible transesterification reaction. Because, until the date of this work, there are not reported works that combine supercritical state of the reaction mixture with a solid catalyst, the comparison has to be made between


J. Maçaira et al. / Fuel 90 (2011) 2280–2288

So far it have not been reported works done using solid catalysts under supercritical conditions, so the values determined have to be compared to those reported in similar processes. The value determined in this work is similar to that found by Vujicic et al. [67]. This last author also determined the activation energy of the reaction in the diffusion regime to be 32 kJ/mol, indicating that value determined in this work corroborated the conclusion taken from Section 4.2 that there were no mass transfer limitations between the liquid phase and the catalyst and that the reaction is in the kinetic regime.

0.12 Wakao and Kaguei (1982)

Kg m/s

0.10 0.08

Lim et al. (1989)

0.06 0.04 0.02

150 ºC 180ºC 205ºC

Tan et. al (1988 )

0.00 0






Re Fig. 5. Comparison of predicted values of solid to fluid mass coefficients determined and for some correlations.

Table 7 Correlations used for the prediction of the mass transfer coefficients. Correlation

Range of validity


Sh ¼ 1:5Re0:43 Sc1=3

5.6 < Re < 28.1


Sh ¼ 0:38Re0:83 Sc1=3

2 < Re < 55 4 < Sc < 16 4 < Re < 135


8 < Re < 90 1.5 < Sc < 10


 2 1=3 1=4 Sh Sc ¼ 0:128 Re Gr ðRe1=2 Sc1=3 Þ3=4 ðScGrÞ1=4  1=3  3=4 2 Sc1=3 þ1:1398 Re Sc  0:01634 h Sh  0:3 ¼ ð0:269Re0:88 Sc0:3 Þ ð0:3 þ 0:001ðScGrÞ






Table 8 Mass transfer coefficients fluid to solid using Abaroudi correlation. Exp.

Temperature (°C)




kg (m  s1)

C TG;bulk C TG;surface C TG;bulk

1 2 3 4


57 29 15 8

7.4 7.4 7.4 7.4

25 14 8.5 5.2

5.73  102 3.31  102 1.97  102 1.22  102

0.0000061 0.0000058 0.0000080 0.0000473

5 6 7 8


80 43 21 13

6.2 6.2 6.2 6.2

30 18 10 7.1

9.13  102 5.53  102 3.14  102 2.15  102

0.0000228 0.0000238 0.0000346 0.0000194

9 10 11 12


73 39 19 12

5.6 5.6 5.6 5.6

28 17 9.4 6.5

9.36  102 5.66  102 3.22  102 2.20  102

0.0000871 0.0000102 0.0000163 0.0000005


Source: Ref. [65].

the conventional reaction done with solid catalysts and with the conventional supercritical method. As can be seen, the values determined in this work are much higher than those reported, even when compared with higher temperatures. The combination of the supercritical state of the reaction mixture with a catalyst apparently has advantages when comes to the reaction rate.

4.3.2. Three-step reversible reaction scheme In the previous section the reaction was considered as a one step irreversible reaction and first order to the triglyceride concentration. Now the reaction will be considered as a three-step reversible reaction as showed in Eqs. (3)–(5). In this kinetic study the three-step reversible reactions were considered elementary reactions so there is expected that the forward and reverse reactions to follow second order overall kinetics. Thus mass balance equations regarding each component are indicated in Eqs. (6)–(11). The calculation of the effective rate constants requires the integration of the differential equation system presented, and the subsequent resolution of the resultant equation system. Due to the complexity of the problem, this resolution was carried out using numerical methods. The mathematical program Matlab (The Maths Works Inc.) was used because it has built-in differential equations functions that enable the resolution of ordinary differential equation systems. Fig. 6 shows the product concentration during the reaction. The methyl ester formation rate increased from the beginning of the reaction until the equilibrium was approached. The triglyceride initial concentration decreased with the space time while monoglyceride and diglyceride content increased to a maximum before further decreasing toward a quasi-total disappearance. Examination of the curve-fitting results showed a good fit of the kinetic model to the experimental results. From the fitting of the experimental results obtained at three temperatures, the reaction rate constants were calculated and are presented in Table 10. Reaction rates almost always increase with temperature for elementary irreversible reactions but multiple and reversible reactions occasionally exhibit an optimal temperature with respect to the yield of a desired product. In this case this all the reaction rate constants increased with temperature. The reverse reaction of transformation of monoglycerides and FAMEs into triglycerides and alcohol was the less affected by temperature, being almost insensitive to temperature. The same reaction but in the forward way (diglyceride to monoglyceride) was enhanced by temperature as was verified to all the other reactions. The activation energies and rate constants obtained in this study were compared with previously reported values [68,69] and the calculated activation energies are slightly lower. The activation energies are illustrated in Table 11. Comparing these results with those obtained considering a first order single step irreversible reaction, there are obvious differences. Although the reaction rate constants cannot be compared directly, as they are referent to different order reaction rates, the

Table 9 Reported values of the rate constants and activation energy for the reaction. Oil type

Temperature (°C)

Methanol/oil molar ratio


Activation energy (kJ/mol)

Rate constant (L/mol min)


Vegetable oil (S5007) Sunflower Mustard Palm Sunflower Soybean RBD palm

150–205 120 300 300 300 220–235 200–400

25 6 30–80 10–50 40 – –

Nafion SAC-13 CaO – – – – –

128 101–161 59 9–15 3 117–128 105

0.3–26.4 0.221 0.220 0.114 0.058 – –

This work [67] [25] [21] [18] [68] [69]

J. Maçaira et al. / Fuel 90 (2011) 2280–2288

Fig. 6. Content of methyl esters, triglycerides, diglycerides, monoglycerides, glycerol and methanol in the products obtained at 205 °C, 250 bar, catalyst mass of 9 g, and methanol/oil ratio of 25.

Table 10 Reaction rate constants. Temperature (°C)

150 180 205

Rate constants (L/mol min) k1






0.0524 0.931 1.51

0.245 3.01 20.9

0.196 1.22 3.17

7.99 15.2 15.7

1.24 29.4 249

1.89 14.2 90.3

Table 11 Activation energies and preexponential factors. Reaction direction

Rate constants (L/mol min)

Ea (kJ/mol)

k0 (L/mol min)


k1 k2 k3 k4 k5 k6

16.20 20.48 13.02 3.29 24.56 17.69

10.24 14.95 8.83 4.78 19.87 14.72

Notes: Ea – activation energy; k0 – preexponential constant.

activation energies determined are much lower than the 128 kJ/mol value previously determined. This fact makes it clear that for the kinetic study of this reaction, the intermediate species should be included, and a three-step reversible reaction scheme should be considered. Also, in most cases the published work regarding kinetics for single step irreversible reaction considers that the FAMEs percentage is equal to the triglyceride conversion. This is obviously a rough estimation and assumes full conversion of intermediate species, and shouldn’t be considered as it leads to different values of reaction rate constants. This is true even when using a large excess of alcohol, as it is shown is this work, where the use of a molar ratio of methanol to oil of 25 did not made the reaction irreversible. 5. Conclusions Our work combines the existing technologies of heterogeneous catalysis and the supercritical process, making the most of the


advantages of each to create a continuous process. The continuous production of biodiesel under supercritical conditions, using a solid acid catalyst and carbon dioxide as co-solvent, was successfully accomplished. It was observed that highest FAMEs content (88.2%) was produced at a temperature of 200 °C and residence time of 2 min, without purification steps and the free glycerol content was found below the specification limits. The reaction rate can be 20 times faster than the conventional process. These particular experimental conditions are more attractive to scale up the biodiesel production, when compared to the the experimental conditions at which supercritical transesterification process are usually conducted (temperature > 350 °C and methanol:oil ratio 40:1), because the costs associated with the pumping, preheating, and recovery of excess methanol are minimized. The mass transfer coefficients were determined using several correlations available in the literature, for the operations conditions used, there were no mass transfer limitations. This agrees with published claims that the one phase supercritical condition and the presence of co-solvent reduces the transport limitations and increases the reaction rates. The results obtained from supercritical transesterification reaction showed that, whenever possible, the three-step reversible reaction scheme should be considered, as the reversible reactions are important and that they should be accounted for in this process. The determined observed reaction rates and the reaction rates constants were compared to those present in published works. The determined reaction rates were much higher, and the activation energy was found to be similar, considering a single irreversible step. Considering a three step irreversible reaction scheme, the activation energies for each were found be lower than those published, which is an indication that the developed process has advantages over the conventional ones. The results show that is possible to have a continuous process that results in very high conversion of triglycerides (99.4%) in a very short contact time (2 min), and with reasonable fatty acid methyl esters content (88%), making this process a possibility for the production of biodiesel in a larger scale. The other advantage is that the separation of the products as well as the byproducts can be achieved efficiently under the supercritical conditions. The amount of insignificant reaction time needed make this technology very attractive compared to other processes. This technology is environmental good, since it has less effluent, and the secondary product, glycerin, will have a really good high quality. Acknowledgments The authors would like to acknowledge Spanish Ministry of Science, Technology and Innovation (Grant No. ENE 2009-14502) for the financial support given. References [1] Vicente G, Martínez M, Aracil J. Optimization of integrated biodiesel production. Part I. A study of biodiesel purity and yield. Bioresour Technol 2007;98:1724–33. [2] Pinnarat T, Savage PE. Assessment of noncatalytic biodiesel synthesis using supercritical reaction conditions. Ind Eng Chem Res 2008;47:6801–8. [3] Darnoko D, Cheryan M. Continuous production of palm esters. J Am Oil Chem Soc 2000;77:1269–72. [4] Noureddini H, Gao X, Philkana RS. Immobilized Pseudomonas cepacia lipase for biodiesel fuel production from soybean oil. Bioresour Technol 2005;96:769–77. [5] Nie KL, Xie F, Wang F, Tan TW. Lipase catalyzed methanolysis to produce biodiesel: optimization of the biodiesel production. J Mol Catal B: Enzym 2006;43:142–7. [6] Lotero E, Liu Y, Lopez DE, Suwannakarn K, Bruce DA, Goodwin JG. Ind Eng Chem Res 2005;44:5353. [7] Kulkarni MG, Dalai AK. Waste cooking oils an economical source for biodiesel: a review. Ind Eng Chem Res 2006;45:2901–13.


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