Continuous biodiesel production in supercritical two-step process: phase equilibrium and process design

J. of Supercritical Fluids 124 (2017) 57–71

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Continuous biodiesel production in supercritical two-step process: phase equilibrium and process design Luigi Osmieri a,b,∗ , Reza Alipour Moghadam Esfahani b , Francesc Recasens a a b

ETS d’Enginyeria Industrial de Barcelona, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028, Barcelona, Spain Politecnico di Torino, Dipartimento di Scienza Applicata e Tecnologia, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy

a r t i c l e

i n f o

Article history: Received 26 October 2016 Received in revised form 23 January 2017 Accepted 25 January 2017 Available online 28 January 2017 Keywords: Simulation Transesterification Co-solvent Vapor-liquid equilibrium Phase envelope Validation

a b s t r a c t A supercritical biodiesel production process via transesterification of vegetable oil with methanol, using CO2 as co-solvent is designed, simulated, and validated with experimental data. A preliminary study of the liquid-vapor equilibrium of the reacting mixture at different compositions was done to determine the supercritical conditions, by means of pressure-temperature diagrams. Under supercritical conditions, the presence of a single phase increases the reaction kinetics, avoiding the limitation by interphase mass transfer, and enabling to carry out the process with low residence time. The proposed process is based on two fixed-bed catalytic reactors in series, with intermediate glycerol separation. CO2 used as co-solvent decreases the critical temperature, enabling to carry out the process in milder conditions. The intermediate glycerol separation displaces the chemical equilibrium towards higher conversion of triglyceride, increasing biodiesel yield. The results of a complete experimental study are used to validate the model, through a comparison with the simulations result. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Biodiesel is a fatty acid methyl esters mixture which has been widely used as an engine fuel over the last decades. Interestingly, one of the first fuels tested by Rudolf Diesel in the late 19th century were vegetable oils. In his Rational Heat Engine [1], Diesel developed the idea that the very high compression of the cylinder can raise the temperature to values high enough to auto-ignite the fuel. Compression-injection engines rapidly spread in Europe and North America for electricity generation because of their practical efficiency (due to the higher compression ratios used and the non-expensive gas-oil). An interesting property of biodiesel is its similarity to oilderived gas-oil as a compression-ignition fuel, both in terms of cetane number and heating value. Biodiesel is mainly produced by transesterification reaction, and could be considered a totally renewable fuel as it can be produced using vegetable oils and a bioalcohol (e.g., bio-ethanol). If methanol (MeOH) synthesized from fossil fuels-derived (e.g., coal) syngas is used for its production, biodiesel can be only considered as partially renewable. The type of glycerides to be used as raw material, depends on the local availabil-

∗ Corresponding author at: Politecnico di Torino, Dipartimento di Scienza Applicata e Tecnologia, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy. E-mail addresses: [email protected], [email protected] (L. Osmieri). http://dx.doi.org/10.1016/j.supflu.2017.01.010 0896-8446/© 2017 Elsevier B.V. All rights reserved.

ity. The products of transesterification of vegetable oils also offer the advantage of low viscosity and clean combustion. Demirbas compared supercritical (SC) transesterification process with other potential processes [2]. A summary on available biodiesel manufacturing processes was given by Dimian and Sorin Bildea [3]. In this regard, the Henkel process carried out in many European plants is of interest because it uses a continuous, liquid-phase, homogeneously catalysed system based on sodium methylate catalyst. This process produces fatty acid methyl esters (FAME) and raw glycerol, with a standard capacity of 50,000 tons of biodiesel per year. Plants of the original Henkel processes are freely offered for license [4,5]. A useful review on the plants in operation in Europe, USA and Asian Pacific, with about 3 Mtons per year production (from 1992 to 2007), with a total of 12 Mtons per year production worldwide in 2008 was provided by International Energy Agency (IEA) [6]. The Lurgi process is also interesting because it uses a homogeneous sodium methylate catalyst that is converted to methanol in the process [7]. Sodium methylate, a very strong alkali, has to be produced in another plant (that could be located far-off the biodiesel plant), then shipped to the biodiesel plant, and fed continuously to the reactor. Sodium methylate is a relatively inexpensive chemical, but it is dangerous to handle, with consequent high risk during the shipping and operation, and should be neutralized within the biodiesel plant. This requires HCl consumption for NaOH neutralization and water washing for purification. However, many

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L. Osmieri et al. / J. of Supercritical Fluids 124 (2017) 57–71

small-scale local biodiesel producers operate with batch plants and recovery operations, with all sorts of available oils including spent cooking oils, using standard bases. Vila and Salguero [8] showed that using a reactor design based in the low pressure homogeneous kinetics and the Henkel patent data, the two in-series reactors are of quite large size (30 m3 each), with a powerful agitation requirement. Glisíc and Skala provided simulation studies regarding biodiesel manufacture [9]. Homogeneous and heterogeneous catalysis (or even no catalyst) can be used, depending on the type of reactor. In our previous work [10], and in another work [11], a solid cat® alyst, SAC-13 (Engelhard) was used in a packed-bed reactor in a continuous process, which is preferred for a large plant. The results ® indicate that SAC-13 , as well as other ion-exchange catalysts (i.e., ® ® Amberlyst-15 , and Dowex-50 to lesser extent), hold activity for long periods, and can be used in catalytic distillation. The use of solid acid catalysts allows the elimination of the methoxide and the water generation. He et al. described a SC transesterification process using methanol [12]. Prior to this, Madras et al. [13] studied the biodiesel synthesis with methanol (or ethanol) without a catalyst, to high conversions at 200 bar and the SC reaction using an enzymatic catalyst (lipase) in a CO2 environment with limited conversion (30% max). It seems that the CO2 solvent adversely affects interphase mass transfer and/or the fluid-phase equilibrium. This was documented by Pereda et al. [14,15], who showed that phase equilibrium problems occur in the reactor phase condition, and by Nunes da Ponte [16] for the effect of multiphase on kinetics. Härröd et al. [17] and later Ramírez et al. [18] showed that conditions of phaseequilibria are crucial for the case of catalytic (Pd/C) hydrogenations in SC propane, CO2 , and other solvents. Mac¸aira et al. experimentally demonstrated that biodiesel could be produced in a SC MeOH/CO2 mixture (8 wt.% vegetable oil + 92 wt.% of a MeOH/CO2 mixture 25/75 parts by wt.), at 150–250 bar with a solid acid catalyst, using a packed-bed reactor [10,11]. Phase equilibria at the operating pressure and temperatures were rather done by approximation with estimated data. Pereda et al. [15,19] showed the way to the engineering predictions of thermodynamics equilibrium data using Group-Contribution Equation of State (GC-EoS) [20,21], which is one of the most reliable methods available today for multiphase processes. Unless phase equilibrium is well predicted, the engineering for the process reactor (sub- or supercritical) cannot be worked out properly [22]. In this regard, Pereda et al. [23] applied this method to the separation units of the plant as well. This opens up the question as to which equations of state have to be used, as will be addressed in this work. The overall stoichiometry for the biodiesel (FAME) formation from vegetable oil by transesterification, is as follows: Triglyceryde + 3MeOH  Glycerol + 3FAME

(1)

The reaction proceeds stepwise as three reversible reactions in series, where each reaction gives one FAME molecule, but only in the last one glycerol is generated: k1

A + B D + E k2 k3

D + B M + E

(2)

k4 k5

M + B G + E k6

where: A = triglyceride, B = methanol, D = diglyceride, M = monogyceride, E = FAME, G = glycerol. It is interesting to point out that a rapid transfer of the glycerol (reaction product) to another phase will shift the chemical equilibrium toward the formation of more FAME.

In this work, our purpose was two-fold. First, as glycerol is the component with the highest boiling point (290 ◦ C) and density (1.261 g cm−3 ), we wanted to simulate its partial condensation from the fluid coming out from the reactor using a reliable equation of state (EoS). In particular, we wanted to find the pressuretemperature (P–T) ranges where glycerol separation is favored. The use of CO2 in combination with SC methanol is of fundamental value in the proposed process as a way to lower the mixture’s critical point and monitor how this evolves with the reaction advance. To this end, we followed the approach of Poliakoff et al. [24], who obtained a moving envelope on the P–T plane for critical points and retrograde condensation regions. Our last purpose was to rewrite the reactor mass balance equations for suitable use in reaction engineering, that is, in terms of unit mass of catalyst (a standard in heterogeneous catalysis). In this way, we propose a continuous two-reactor process, with inter-stage glycerol separation and recompression of the reactive mixture, as an improved method to increase triglyceride conversion to near full completion. The model used for the simulations was validated by a complete experimental study comprising several tests at 250 bar, with different space-time values (form 0.5 to 4 min), and temperatures (form 180 to 205 ◦ C). Comparing the experimental data with the ones predicted by the simulations, provided a direct proof of the validity of the results predicted by the model.

2. Phase equilibrium calculation The objective of this part is to determine the pressure (P) and temperature (T) of the reactants mixture to have SC conditions inside the first reactor. In general, SC fluids have intermediate properties between a gas and a liquid phase. Moreover, in a SC fluid there is not any surface tension, since there are not liquid-gas bonds. All the SC fluids are completely miscible by each other. Consequently, it is possible to obtain a one-phase, multi-component mixture if the critical point of the mixture is overcame. The desired condition for this process is to have in the reactor a single homogeneous reacting phase, which presence depends on chemical composition, T and P of the system. To this purpose, it is necessary to calculate the vapor-liquid equilibrium conditions for the system having the same composition of the mixture fed to the reactor (which is made by triglycerides, methanol and a co-solvent, CO2 in this case). In the experimental tests where the values of the kinetic constants used in this work were calculated, a refined sunflower oil was used [10]. Similarly to other vegetable oils, sunflower oil is a mixture of different triglycerides [3]. In this work, as an approximation, the vegetable oil was represented by a unique component, that was chosen to be triolein (glycerol trioleate). The average content of triolein in sunflower oil is about 17%, being linolein the other main triglyceride component (74%). As triolein, linolein has 18C atoms in the side hydrocarbon chains. Other two minor components of sunflower oil are stearin (3%) and tripalmitin (6%). In addition, triolein is the triglyceride for which a greater amount of thermodynamic data are available in the literature [25]. The decision to use triolein as unique component to represent the vegetable oil could be considered a good approximation if one considers the molecular structure of triglycerides and the transesterification reaction. In facts, triglycerides are glycerol tri-esters, differing from one another only for the side hydrocarbon chains. Transesterification involves only the carbonyl group and the alcoholic oxygen, and for this reason, the differences between the long side hydrocarbon chains on the reactivity have been neglected. The influence of the different triglycerides (i.e. molecular weight and chemical structure) on the physical properties of the reactant mixture has been neglected as well.

L. Osmieri et al. / J. of Supercritical Fluids 124 (2017) 57–71 Table 1 Thermodynamic methods based on predictive EoS selected for the liquid-vapor equilibrium calcualtion. Method

EoS

P and T applicability

Molecules features applicability

PENG-ROB

Peng-Robinson

RK-SOAVE

Redlich-KwongSoave Redlich-KwongAspen

High T and P, supercritical High T and P, supercritical High T and P, supercritical

Non-polar/slightly polar Non-polar/slightly polar Non-polar/slightly polar/polar mixtures of molecules having very different dimensions Non-polar/highly polar/highly non-ideal mixtures. Mixtures of non-polar and polar compounds with light gases

RK-ASPEN

SR-POLAR

Schwarzentruber- High T Renon P < 50 bar

As widely reported in the literature [26], different thermodynamic methods can be used for the calculation of a liquid-vapor equilibrium. The two most widely used methods are based on EoS and on Activity Coefficients (AC). The choice of the thermodynamic method is very important since it highly influences the results and their reliability. For this reason, an accurate choice of the most suitable thermodynamic method for the system under investigation ® must be done. The Aspen Plus User’s Guide [27] contains a series of tables and algorithms that could help in this choice. Since our aim is the presence of a unique homogeneous phase in conditions close to the critical point, the use of a model based on an EoS seems to be more favorable than the use of a model based on AC. Further reasons in support of using an EoS-based model for the calculation of the liquid-vapor equilibrium for a system at high pressure can be found in the literature [28]. In particular, the effect of P on the physical properties of the liquid phase is significant only at high P, while it can normally be neglected at low or moderate pressures. Activity coefficients are independent of P, but at high P it is equivalent to consider that the partial molar volume of a certain i-species in the mixture would be equal to the molar volume of the pure i-species. This fact, at high P, and especially in proximity of the critical region, could lead to considerably high calculation errors. At low P, the fugacity coefficient of the gas phase could be considered equal to 1, while at elevated pressure it has to be calculated from an appropriate EoS. 2.1. Thermodynamic methods based on equations of state For the calculation of the fugacities in the case of a multiphase ® mixture, EoS or AC models can be used. Aspen Plus contains many EoS-based thermodynamic methods, thus, it is necessary to do a preliminary choice to individuate the most suitable method [27,29]. To choose a suitable EoS, the characteristics of the chemical compounds constituting the mixture (i.e. polarity and dimensions of the molecules), as well as the operative P and T, have to be considered. As evident from the different steps of the transesterification (see Eq. (2)), the chemical components of our system will be: methanol, triolein, diolein, monolein, glycerol, methyl oleate (FAME) and CO2 . Thus, the system will contain one non-polar and low-molecular weight compound (CO2 ), two highly polar compounds with a low or intermediate molecular weight (methanol and glycerol) and four high molecular weight and slightly polar compounds (triolein, diolein, monolein and methyl oleate). The most severe operating conditions in terms of T and P have to be close to the critical point of the binary mixture methanol-triolein (in case of co-solvent will

59

Table 2 Values of the thermodynamic parameters for some of the chemical components not ® available in the Aspen Plus database: MW = molecular weight; Tb = boiling point at atmospheric P; Tc = critical T; Pc = critical P; Vc = critical volume; ␻ = acentric factor.

MW [g mol−1 ] Tb [◦ C] Tc [◦ C] Pc [bar] Vc [cm3 mol−1 ] ␻

Triolein

Diolein

Monolein

Methyl oleate

885.45 554.4 704.88 3.34 3250 1.9782

621 492.03 647.2 5.05 2830 1.7632

356.55 401.82 562.06 10.56 1254 1.5324

296.49 322.93 448.02 11.03 1108 1.0494

not be used), or of the ternary mixture methanol-triolein-CO2 (in case of the use of co-solvent). Based on our previous experimental studies conducted on systems of similar composition, the P and T conditions should be in the range 200–250 bar and 150–210 ◦ C [10]. The more suitable EoS-based thermodynamic methods are summarized in Table 1, which shows their main characteristics and applicability [29]. In a first step, as a purpose of comparison, all the thermodynamic methods shown in Table 1 were used to calculate the liquid-vapor equilibrium data. Then, the method considered the most suitable one, was selected and used for the subsequent steps of process simulation (see Section 3). 2.2. Liquid-Vapor equilibrium of the binary mixture methanol-triolein The equilibrium data were calculated for MeOH–triolein mixtures with different compositions. Once the composition of the mixture was defined, the P vs. T plot (P–T diagram or PT envelope) representing the bubble and dew point curves of the mixture ® were calculated using Aspen Plus . Since some key thermodynamic properties of some of the chemicals considered in our model were ® missing in the original Aspen Plus database, we inserted manually these values collecting them from the literature [25], as shown on Table 2. Although the reactants of our SC transesterification process (MeOH and triolein) will be fed to the reactor together with a cosolvent (CO2 ), we calculated the liquid-vapor equilibrium of the binary mixture MeOH–triolein (without co-solvent) in order to compare these data with the respective values obtained in presence of the co-solvent. In this way, we could clearly point out the advantage of the use of the co-solvent to make the critical conditions of the system less severe. The P–T diagrams for the MeOH–triolein mixture are shown in Fig. 1. Three different composition were chosen: the MeOH-totriolein molar ratio of 3:1 (Fig. 1a) is the stoichiometric ratio for the transesterification reaction. The ratio 9:1 (Fig. 1b) was chosen for a hypothetical industrial process with a slight methanol excess, while the ratio 25:1 (Fig. 1c) for a hypothetical industrial process with a large methanol excess, useful to shift the chemical equilibrium of the reaction towards the products and to enhance the triolein conversion. In Fig. 1a–c the four different P–T curves shown represent the results obtained with the different thermodynamic methods described on Table 1. From the results shown in Fig. 1a–c, for all of the thermodynamic methods used the end of the bubble points curve and the start of the dew points curve do not coincide exactly in one point, showing a discontinuity zone, where the program is not able to calculate the equilibrium points. This discontinuity zone is due to convergence problems near the critical point. Nevertheless, the critical point of the system should be located inside this discontinuity region, most likely on a line connecting the extremities of the bubble and dew point curves.

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L. Osmieri et al. / J. of Supercritical Fluids 124 (2017) 57–71

Fig. 1. P–T diagrams representing the bubble point (continuous line) and dew point (dashed line) curves for the MeOH–triolein mixture in different molar ratios: (a) 3:1; (b) 9:1; (c) 25:1. (d) P–T diagrams obtained with the RK-ASPEN EoS for the MeOH–triolein mixtures having different compositions. Vapor pressure curves for pure MeOH and pure triolein are shown for comparison.

Table 3 Critical point for the mixture MeOH–triolein with different compositions calculated with different EoS. MeOH:triolein molar ratio

3:1 9:1 25:1

Mixture critical point (Tc [◦ C]; Pc [bar]) RK-ASPEN

RK-SOAVE

PENG-ROB

SR-POLAR

(670;37) (600;92) (435;140)

(670;33) (590;90) (430;135)

(653;38) (555;90) (355;115)

(610;34) (460;50) (280;54)

For all the three different mixture composition, the amplitude of the biphasic region (located inside the region delimited by the bubble and dew point curves), as well as the critical point, decrease in the order RK-ASPEN > RK-SOAVE > PENG-ROB > SR-POLAR. Moreover, the shape of the phase envelopes (P–T diagrams) calculated using RK-ASPEN, RK-SOAVE and PENG-ROB methods are similar, while the one calculated by the SR-POLAR method is very different compared to the previous ones. Table 3 reports the critical points for the different MeOH–triolein mixtures, evaluated from the P–T diagrams of Fig. 1. It is evident that increasing the MeOH:triolein ratio, the critical temperature (Tc ) of the mixture decreases, while the critical pressure (Pc ) increases. For the purpose of clarity, and to more easily compare the results obtained for the different mixture compositions, the P–T diagrams obtained with the RK-ASPEN method are shown on Fig. 1d, together with the vapor pressure curves of pure MeOH and triolein. As expected, with a low methanol:triolein ratio the mixture critical point is more similar to the critical point of the pure triolein. On the contrary, as the content of methanol increases, the mixture critical point becomes closer to that of pure MeOH, as expected.

2.3. Liquid-Vapor equilibrium of the ternary mixture methanol-triolein-CO2 A study of the liquid-vapor equilibrium was also done for the ternary mixture CO2 –MeOH–triolein, where CO2 was used as cosolvent for the purpose of lowering the critical point. Similarly to other articles on SC biodiesel production processes using MeOH, the molar% of triolein in the mixture was fixed equal to 1 [10,11,30], and remaining% of the mixture is the sum of MeOH and CO2 . The proportion MeOH:CO2 was varied to observe the influence of a higher quantity of co-solvent. Four different compositions were analyzed, as summarized on Table 4. The results obtained from the simulation with the RK-ASPEN method for the mixtures having the compositions in Table 4 are shown in Fig. 2a. It is evident that increasing the content of CO2 (at the same time the MeOH content decreases, remaining constant the triolein content), there is a reduction of the Tc and an increase of the Pc (as also evident from the critical point values reported in Table 4). As the% of CO2 increases, there is a widening of the two-phase region (see Fig. 2a).

L. Osmieri et al. / J. of Supercritical Fluids 124 (2017) 57–71

61

Fig. 2. (a) P–T diagrams for the mixture CO2 –MeOH–triolein at different molar compositions calculated with the RK-ASPEN method. (b) P–T diagrams for the mixture CO2 MeOH-triolein with the same molar composition (row 3 of Table 4) calculated with different EoS methods. (c) P–T diagram for the mixture CO2 –MeOH–triolein with the composition chosen for the process simulation. Blue and red points indicate the critical point and the operating conditions of the first reactor, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Table 4 Critical point for the CO2 –MeOH–triolein mixture with different molar (mol%) and mass (wt%) compositions. Triolein

Methanol

CO2

3. Process development and simulation 3.1. Catalytic kinetics

Critical point

Mixture

mol%

wt%

mol%

wt%

mol%

wt%

Tc [◦ C]

Pc [bar]

1 2 3 4

1 1 1 1

17.2 17.5 17.9 18.5

9 15 25 39

5.6 9.5 16.2 26.2

90 84 74 60

77.2 73.0 65.9 55.3

185 210 225 240

270 260 235 190

Fig. 2b shows the P–T diagrams obtained with the four different thermodynamic methods considered in Section 2.1 for the mixture having a molar composition 1% triolein − 25% MeOH − 74% CO2 . Also in this case the RK-ASPEN method leads to obtain the highest critical P and T values. At this point, considering the available data about the equilibrium of the CO2 -MeOH-triolein mixture, we have to make some assumptions and set some design conditions constrains, in order to go forward with the following steps of the process design.

For the design of the biodiesel production process, the mass balances of our previous work [10] were used, but now with the correct assumptions for the fluid phase, and not with pseudohomogeneous assumption. The three stepwise equilibrium reactions in series described by Eq. (2), were assumed to occur simultaneously on the catalyst surface, with the following kinetics: r1 = k1 CA CB − k2 CD CE

(3.1)

r2 = k3 CD CB − k4 CM CE

(3.2)

r3 = k5 CM CB − k6 CG CE

(3.3)

where ri are the net forward catalytic rates, ki are the second order kinetic constants and Ci are the molar concentrations. Then, the differential change of mole flow of a product, dFi, along an element of bed volume dV, will be: dFi = d (v0 Ci ) = ri dW = ri B dV

1) The choice of the thermodynamic method to be used for the process simulation. We decided to use the RK-ASPEN method for two reasons. First, among the four methods considered, it provides always the more extended biphasic region, and the highest values of critical P and T, that is, it is the more “conservative” one. Second, on the basis of the characteristics of the different methods considered (see Table 1), the RK-ASPEN seems to be the most suitable to represent the ternary mixture CO2 -MeOHtriolein, and the multi-component mixture which will be formed inside the reactor as long as the reaction will proceed. Both these mixtures contain molecules having very different dimension, which are highly polar (methanol and glycerol) or slightly polar molecules (triglyceride, diglyceride, monoglyceride, FAME), as well as a light non-polar gas (CO2 ). Conversely, both the PENGROB and RK-SOAVE methods are more suitable for non-polar or slightly polar mixtures. Regarding the SR-POLAR, although it is described as good to represent highly polar mixtures and nonideal systems, its accuracy is low at high P, and it provided the less conservative results in our calculations. 2) The composition of the mixture fed to the first reactor. It was chosen equal to the row 3 of Table 4 (1% triolein, 25% MeOH, and 74% CO2 on molar basis) because it provides a sufficiently high content of vegetable oil (almost 18 wt.%), a considerably high MeOH excess (25 mol of MeOH per mole of oil, which represents more than 8 times the stoichiometric value) in order to displace the chemical equilibrium towards the products of the reaction. In addition, the high co-solvent content enables to reduce considerably the Tc . In facts, without co-solvent (see Section 2.1) the MeOH-triolein mixture has a Tc of ∼435 ◦ C, which is too high ® for both the operative range of the catalyst (Nafion SAC-13 ) and the thermal stability of the vegetable oil molecules. On the contrary, using CO2 as co-solvent, the Tc decreases to ∼225 ◦ C, assuring the presence of a homogeneous phase at a considerably lower T. However, the drawback is the increase of the Pc (from ∼140 to ∼230 bar). 3) The operative conditions of the first reactor. They were defined considering the available data about the liquid-vapor equilibrium. The choice of the operating P and T is represented by the red point in Fig. 2c. Specifically, since the critical point is Tc = 225 ◦ C and Pc = 235 bar, we selected the conditions of 230 ◦ C and 250 bar as sufficiently far from the biphasic zone boundary to assure the presence of a unique homogeneous phase inside the reactor.

(4)

where B is the bulk catalyst density in the packed bed. In Eqs. (3.1)–(3.3), two kinetic constants for each reaction are necessary, thus six in total. We have shown in a previous work that the molar concentrations are related to the compressibility factor of the high P gas mixture [31], so it is advantageous to use Ci , instead of fugacities or activities provided that mixture compressibility factor is available [32]. In Eqs. (3.1)–(3.3) the rates ri are expressed in moles per unit mass of catalyst per unit time, and the T-dependence is contained in the kinetic constants k(T), through the Arrhenius expression, with a pre-exponential factor Ai and activation energy Ei , as:

 E  i

ki = Ai exp −

RT

(5)

where R is the gas constant, and T is the absolute temperature. In our previous work [10] we performed four integral-reactor runs with different space times at three different T (twelve experimental runs in total), that are sufficient to calculate the rate coefficients and consequently their respective pre-exponential constants and activation energies. Because we previously used pseudo-homogeneous concentrations (i.e. neglecting the presence of catalyst as a solid phase), the reaction rates per unit catalyst mass could not be calculated [10]. On the other hand, in that work it was shown that interphase mass-transfer rate was not limiting. Then the radial concentration gradients and T gradients inside the reactor were absent [10]. Therefore, it was assumed without proof that ® the effectiveness factor of the SAC-13 catalyst was 100%, despite the extremely high intrinsic rates observed (see Section 3.2). This is quite unlikely, and opens up the question as to which phase mass transfer occurs if there is no such solid phase. Hence, further exper® iments for this process on SAC-13 catalyst have to be performed to verify these assumptions. As expressed in Eqs. (3.1)–(3.3), the Ci are those prevailing in the fluid phase flowing in the boundary layer the catalyst particles. Considering one dimensional cylindrical packed tube reactor, where a mass of catalyst dW occupies a volume dV of tube, an isothermal, steady-state balance for components can be written in terms of reactor volume and fluid-phase concentrations, as follows: −

dFA = r1 B dV

(6.1)

−

dFB = (r1 + r2 + r3 ) B dV

(6.2)

L. Osmieri et al. / J. of Supercritical Fluids 124 (2017) 57–71

dFD = (r1 − r2 ) B dV

(6.3)

dFM = (r2 − r3 ) B dV

(6.4)

dFG = r3 B dV

(6.5)

dFE = (r1 + r2 + r3 ) B dV

(6.6)

Since the volumetric flowrate v0 is constant in a run, Eqs. (6.1)–(6.6) can be written in terms of concentrations (Ci ) and ␶, as: d (v0 Ci ) dCi dC =  i  = dV d d V/v0

(7)

Thus, the conservation Eqs. (6.1)–(6.6) become: −

dCA = r1 B d

(8.1)

−

dCB = (r1 + r2 + r3 ) B d

(8.2)

dCD = (r1 − r2 ) B d

(8.3)

dCM = (r2 − r3 ) B d

(8.4)

dCG = r3 B d

(8.5)

dCE = (r1 + r2 + r3 ) B d

(8.6)

with the initial conditions:CA0 = 0.3 kmol m−3 , CB0 = 7.5 kmol m−3 , CD0 = CM0 = CG0 = CE0 = 0 at ␶ = 0 [10]. The rates r1 to r3 are given before by Eqs. (3.1)–(3.3) in terms of fluid concentrations. At constant T, the volumetric flowrate v0 at high pressure is constant, and it can be explicitly expressed as the new variable space-time (␶). In Eqs. (8.1)–(8.6) B = 314 kg m−3 is the bulk packing density (packing factor) of the catalyst in the reactor tubes [10]. It is important to note that ␶ is the time during which the fluid is in contact with the catalyst within the reactor (average residence time). The values of the kinetic constants (ki ) calculated from Eq. (8.1)–(3.6) using the above packing factor B , and the initial conditions, are reported in Table 5, so that catalytic rate coefficients have been calculated. In Fig. 6 of Mac¸aira et al. [10] the tri-, di-, and monoglycerides, biodiesel and residual MeOH concentrations, were measured in the fluid phase in the reactor, as a function of ␶. It is important to note that the values of ␶ for the experimental reactor are very small, so that, only 2 min are necessary to reach the chemical equilibrium conditions. This indicates the very short reac® tion time in SC fluid conditions using SAC-13 catalyst. On Table 5, the activation energies and Arrhenius pre-exponential factors for the respective ki values are reported as well. With these reaction ® kinetics values, the process simulator software Aspen Plus was used to simulate the two-reactor system proposed in this work. For these high intrinsic rates, the catalyst effectiveness factor may be much less than unity. 3.2. First reaction stage: the industrial plant Before starting the simulation, the molar (or mass) streams of reactants were set under the hypothesis that the biodiesel production plant will treat an annual amount of 50,000 tons of vegetable oil. This represents an amount comparable to the capacity of an industrial plant of intermediate dimensions in western Europe [3]. Assuming that the composition of the mixture fed to first reactor is the one indicated at the end of Section 2.3 (1% triolein – 25%

63

MeOH – 74% CO2 on molar basis), and that the plant is operating continuously during one year (365 days), the molar flow rate of triolein to be fed will be 6,46 kmol h−1 . MeOH and CO2 flow rates were calculated proportionally, according to the desired composition. The simulation of the first reaction stage considered the units MIXER1, HEATER1 and REACTOR1 in the flow-sheet scheme shown in Fig. 3. HEATER1 represents a hypothetical unit that heats-up and pressurizes the reactants to the T and P desired at the reactor inlet (T = 230 ◦ C; P = 250 bar). REACTOR1 represents an ideal isothermal plug-flow catalytic reactor, where the transesterification reaction occurs following the kinetic equations described in Section 3.1. It must be considered that the unit REACTOR1 is an approximation of the real reactor, which would be a tubular (or multi-tube) fixed bed catalytic reactor, since in the simulations, pressure drops and nonuniform axial and radial heat distributions were not considered, and the fluid dynamics regime was considered as an ideal plugflow. Regarding the reactor diameter (D) and length (L), we initially set the value of 1 m for both of them. To vary the residence time (␶), we modified the reactor length accordingly, keeping the diameter constant and equal to 1 m. Then, we simulated the process with different ␶ (changing the reactor length), in order to determine the composition of the mixture at the reactor outlet in function of ␶. Fig. 4a shows the mass fraction composition of the stream at the outlet of the first reactor vs. the residence time. The trend of the biodiesel yield (YFAME ) vs. ␶ is shown in Fig. 4b. The biodiesel yield is defined as the ratio of the moles of biodiesel (FAME) produced and the moles of biodiesel theoretically producible (which correspond to the triple of the moles of triolein fed to the process), as shown by Eq. (8) [33]: YFAME =

molFAME,out 3 · moltriolein,in

(8)

From Fig. 4b, it is evident that YFAME reaches a “plateau” corresponding to ∼ 92% at ␶ ∼ 4 min (which corresponds to a reactor length of 8 m), indicating that the reaction almost reached the equilibrium. Operating with higher ␶ does not lead to any significant yield increase, thus, to obtain an increase of YFAME , it is necessary to displace the chemical equilibrium. This will be done by the intermediate glycerol separation and the second reaction step described in the following Sections 3.3 and 3.4. At this point, it is necessary to make a design decision about the reactor length according to the desired ␶ to assure an adequate conversion (Z) and biodiesel yield. We decided to assume ␶ = 2 min, (that corresponds to L = 4 m). This value enables to obtain YFAME = 88.6%, which is very close to the chemical equilibrium conditions (see Fig. 4). Doubling the reactor length value only lead to obtain an increase of 3.8% in YFAME . As evidenced by the results presented in Fig. 4a, using the detailed kinetic model with three consecutive reactions for the vegetable oil transesterification in SC conditions, the chemical equilibrium can be reached in the first reactor with a short residence time of the order of few minutes. This detailed kinetic model enables to calculate the Z of the triglyceride and the YFAME , as well as to quantify the presence of unreacted intermediates (diglyceride and monoglyceride). Moreover, in Fig. 4a it is evident that the amounts of diolein and monolein are considerably smaller (almost two orders of magnitude) compared to methyl ester. This confirms that this continuous supercritical acid-catalysed transesterification process carried out in a fixed bed reactor is very effective in terms of yield and productivity. The study of phase equilibrium described in Section 2, which enables the determination of the T and P necessary to have a unique SC phase at the reactor inlet, is only the pre-requisite necessary to carry out all the transesterification process in SC conditions. In facts, even if assuming the T and P to remain constant, as long as the reactions occur, the system composition changes, and new

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Table 5 Revised second order catalytic kinetic constants ki (in L2 mol−1 kgcat −1 min−1 ) based on molar concentrations of the fluid flowing outside the catalyst. Activation energies and pre-exponential factors are also given.

T = 150 ◦ C T = 180 ◦ C T = 205 ◦ C Ea [kJ mol−1 ] Ai [L2 mol−1 kgcat −1 min−1 ]

k1

k2

k3

k4

k5

k6

0.167 2.965 4.809 105.6 2.38 1012

0.780 9.586 66.56 135.7 4.47 1016

0.624 3.885 10.096 85.8 2.60 1010

25.446 48.408 50.00 21.4 1.21 104

3.94 93.63 792.99 162.5 4.73 1020

6.019 45.22 287.58 117.5 1.86 1015

®

Fig. 3. Scheme of the flowsheet used for the simulation of the process with Aspen Plus .

phases could appear [16,22,34]. Thus, it is necessary to determine the phase equilibrium conditions of the multi-component mixture inside the reactor (which composition is changing as a function of ␶), with the purpose to verify whether condensation is occurring. If so, this should be avoided, e.g. by stopping the reaction and operating a separation, or varying T and/or P in order to restore the SC conditions. This investigation can be done using the P–T diagrams at a fixed chemical composition [16,24], as in Section 2. Reporting on the same diagram the phase equilibrium conditions obtained for the system having the chemical composition at reactor outlet with different ␶, we can determine how the biphasic region varies as long as the reaction goes on, and we can verify if the system conditions lie outside the biphasic region. Fig. 4c shows these P–T diagrams for the first reactor (REACTOR1). Each curve corresponds to a different ␶. The results show that the extent of the biphasic (liquid-vapor) region decreases with the increase of ␶, that is, approaching the chemical equilibrium. This is logical, because with the reaction progress high molecular weight compounds (tri-, di- and monoglycerides) are consumed, and at the same time lighter molecules are produced (FAME and glycerol). From an operative point of view, it must be considered that pressure drops in the catalytic bed (not considered in this simulation) are likely to occur, and that the transesterification reaction is globally exothermic [35]. Thus, if the reactor cooling system would not allow to have a totally uniform temperature distribution (that is, local T increases will be present), the pathway of T and P conditions as long as the reaction proceeds, could be similar to the one indicated in Fig. 4c by the arrow. The white and black points represent the conditions at the reactor inlet and outlet, respectively. To avoid the formation of a biphasic system inside the reactor, the “trajectory” of the point representing T and P of the system inside the reactor must always be located outside the biphasic region corresponding to the different residence times. Thus, for example, for ␶ = 2 min, the point representing the T and P conditions of the system, must be outside the orange phase envelope, which was calculated for a mixture composition corresponding to a ␶ in the reactor of 2 min (see Fig. 4c). As a conclusion, on the first view of process development, we decided to assume the length of the first catalytic reactor = 4 m, which corresponds to a ␶ = 2 min. It is remarkable that with a such low reaction time, the biodiesel yield achieved by this SC process is already near 90%, closely approaching chemical equilibrium.

3.3. Intermediate separation From the results of the simulation, the YFAME at the end of the first reaction stage is 88.6%, obtained with ␶ = 2 min. To maximize YFAME , a separation stage is placed in the process after the first reactor, with the purpose of separating as much glycerol as possible from the mixture. In this way, one of the products of the transesterification process is almost totally eliminated, enabling the chemical equilibrium to be more displaced towards a complete reactants conversion. This will lead to the formation of more methyl oleate. The following step of the process will be to send the glycerol-free FAME-rich stream to a second fixed bed SC catalytic reactor, to go further with the transesterification reaction, increasing the YFAME . The separation of the glycerol from the mixture can be obtained with a P and T decrease by means of a flash separation. Since glycerol is almost insoluble in methyl oleate, two liquid phases will form after the flash separation: one rich in glycerol, and another one rich in FAME (biodiesel). On the other hand, the residual vegetable oil (triolein) and the intermediates (diolein and monolein) that can further react, are mainly miscible in the biodiesel. Thus, the separation of the methyl oleate alone (which would have enabled a further displacement of the chemical equilibrium), is not viable. This flash separation was simulated using the unit FLASH1 (see Fig. 3), which represents the set of an expansion valve (throttling valve), a cooled/heated tank, and a gravimetric decanter (to enable the separation of the liquid phases), where the formation of one vapor phase and two liquid phases occurs. In the ® simulation with Aspen Plus , this operation is simulated by the calculation of a vapor–liquid–liquid equilibrium. The outlet of FLASH1 is represented by three different streams: one vapor stream (VAP) containing the most volatile components (mainly CO2 and MeOH), one liquid stream rich in biodiesel (LIQ1), and one liquid stream rich in glycerol (LIQ2). In particular, LIQ2 also contains a not negligible amount of methanol, which should be separated from the glycerol and recovered. This could be done for example by a distillation column. However, this distillation was not considered in this work, for our purpose is the viability of the SC transesterification in two reaction steps. The MeOH hypothetically recovered by this distillation column can be reused as reactant, and it is represented in the process flowsheet by the stream named ADMEOH (see Fig. 3), representing the MeOH contained in LIQ2 (which was theoretically recovered by distillation). To make the separation process occurring in FLASH1 effective, it is necessary to find its most adequate operative conditions. The ® Aspen Plus unit for the calculation of vapor–liquid–liquid equi-

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65

Table 6 List of process units of Fig. 6. Unit

Description

TK-101 TK-102 P-101 P-102 P-103 E-101 R-101 V-101 V-102 C-101 R-102 P-104 T-101 P-105 E-105 E-106 E-102 R-102 V-103 V-104 T-102 E-107 E-108 E-103 C-102 E-104 TK-103

CO2 (liquid) storage tank MeOH storage tank pump for vegetable oil pressurization pump for CO2 pressurization pump for MeOH pressurization heat exchanger for heating the first reactor feed first reactor flash vessel for intermediate glycerol separation decanter for intermediate biodiesel–glycerol separation compressor for pressurization of the flash vapour phase second reactor pump for pressurization of flash biodiesel-rich liquid phase distillation column for the intermediate glycerol–MeOH separation pump for pressurization of the MeOH separated in T-101 head condenser of column T-101 bottom reboiler of column T-101 heat exchanger for heating the second reactor feed second reactor flash vessel for final separation decanter for final biodiesel–glycerol separation distillation column for final glycerol–MeOH separation head condenser of column T-102 bottom reboiler of column T-102 methanol condenser CO2 compressor CO2 condenser glycerol storage tank

496 kg h−1 ). Therefore, the temperature of the flash must enable to have at least 496 kg h−1 · 0.995 = 493.52 kg h−1 of glycerol in LIQ2. The temperature is 36 ◦ C, and we set this value for the simulation of the FLASH1 unit. For the simulation of the second reaction step, the MeOH amount to be re-fed (ADMEOH stream) was assumed to be equal to the MeOH flow rate present in LIQ2 (521 kg h−1 ). 3.4. Second reaction stage

Fig. 4. (a) Mass fraction composition at the outlet of the first SC catalytic reactor (REACTOR1) at different residence times. (b) Biodiesel yield at end of the first reaction stage at different residence times. (c) P–T diagrams calculated with RK-ASPEN EoS for the multicomponent system having the composition of the stream at the outlet of the first reactor at different residence times.

librium requires to fix two of the following four parameters: T, P, heat duty and vapor fraction. We decided to fix T and P. In particular, the expansion in the flash was conducted at atmospheric P, and the operating T was found by a sensitivity analysis. In this case, the sensitivity analysis was used to determine the influence of the flash T on the amount of glycerol recovered in the stream LIQ2 (in terms of flow rate). To choose the operating temperature of the flash unit, we assumed that the goal of the separation stage was to recover in the stream LIQ2 an amount of glycerol equal to 99.5% of the glycerol produced in the first reaction step (which was

In the second reaction stage, more FAME will be produced due to the displacement of the chemical equilibrium caused by the glycerol separation, starting from the molecules (triglyceride, diglyceride and monoglyceride) not completely converted in the first reactor. The simulation of the second reaction stage considers the units MIXER2 (mixing together the streams VAP, LIQ1 and ADMEOH), HEATER2 (that heats-up and pressurizes the reactants to the T and P desired at the reactor inlet) and REACTOR2 (see Fig. 3). As REACTOR1 in the first reaction stage, REACTOR2 is a catalytic plug flow reactor. The choice of the T and P at which REACTOR2 operates was made based on the phase envelope diagram for the multi-component system with a chemical composition equal to the stream MIXTURE2 (see Fig. 5a). For this mixture the critical point is located at T = 195 ◦ C and P = 200 bar. As a consequence, in order to be in SC conditions, we assumed the P and T of the second catalytic reactor to be 210 ◦ C and 210 bar, respectively. To vary the residence time in REACTOR2, as previously done for REACTOR1, we ran different simulations changing the length of the reactor, and keeping the diameter constant and equal to 1 m. YFAME was calculated according to Eq. (8), and its variation with ␶ is shown in Fig. 5b. With ␶ = 4 min (corresponding to L = 8 m), the reaction almost reached the equilibrium, with YFAME = 98.3%. Increasing ␶ up to 10 min (L = 20 m) only leads to a YFAME increase of 0.1%. Thus, the L of REACTOR2 was set to 8 m in the simulation. In the first reaction step, the maximum YFAME obtainable was ∼ 92.5%, and at the first reactor outlet we got YFAME = 88.6%. Thus, performing the intermediate glycerol separation and the second reaction stage, we increased YFAME of about 10%, obtaining a

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Fig. 5. (a) P–T diagram for a system having the same composition of the stream fed to the second catalytic reactor. Blue and red points indicate the critical point and the operative conditions of the second reactor, respectively. (b) Biodiesel yield in function of residence time in the second reactor. (c) P–T diagrams for the multicomponent system having the composition of the stream at the outlet of the second reactor at different residence times. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

L. Osmieri et al. / J. of Supercritical Fluids 124 (2017) 57–71 Table 7 Properties of experimental reactor and solid catalyst. Reactor Type Dimensions Volume Heating resistance

Ti tube (Eurotechnica, Germany) 152 × 15.5 mm 26.8 cm3 2.5 kW

67

Table 8 Ranges of the experimental reactor conditions. Temperature Pressure Space-time, V/v0 Vegetable oil Feed Oil mass flowrate Solvent (25/75 MeOH/CO2 ) mass flowrate

150–205 ◦ C 250 bar 0.5–4 min Sunflower 0.2–1.4 g min−1 16.2–2.3 g min−1

Catalyst Designation Mass in reactor Type ® Nafion content Pellets Pore volume, Vg Surface area, Sg Skeletal density Acidity Acid type ® Nafion clusters Moisture Internal porosity Pore diameter Packing density ® SAC-13 vs. pure Nafion activity Hammet value

SAC-13 (Engelhard-DuPont, USA) 9g SAC/SiO2 composite 13% 1 × 4.5 mm 0.6 cm3 g−1 200 m2 g−1 2.23–2.25 g cm−3 0.13 meq g−1 −CF2 –SO3 H 20 − 60 nm in size 1 − 3% 57% 12 nm 0.314 g cm−3 118.7 times larger (liquid Dodecene-1 isomerization rate at 70 ◦ C) −14 to −10

value very close to 100%. This result is obtained with a residence time in the reactor of only 4 min. Fig. 5c shows the P–T diagrams at different ␶ for the second reactor. As for the first reactor, also in this case the extent of the two-phase zone decreases as chemical equilibrium is approached. As described in Section 3.2, if P and T are kept constant inside the reactor, the reacting mixture will remain in a homogeneous SC phase. 3.5. Final separation stage The stream at the outlet of the second catalytic reactor (OUTR2) contains methyl oleate, unreacted MeOH, CO2 , glycerol, and small quantities of triolein, diolein and monolein that were not completely converted to methyl oleate. Therefore, it is necessary to carry out another separation process with a double purpose: to recover CO2 and MeOH (that will be recycled to process start) and to purify the biodiesel produced as much as possible. This final sep® aration stage is represented in the Aspen Plus flowsheet by the unit FLASH2 (see Fig. 3), which calculates the vapor–liquid–liquid equilibrium (similarly to the unit FLASH1 described in Section 3.3). Here, the multi-component mixture outgoing from REACTOR2 is separated into: one vapor phase (VAP2) containing mainly CO2 and MeOH, one liquid phase rich in methyl oleate (BIODIES), and one liquid phase mainly containing glycerol and MeOH (LIQ3). The calculation of the three-phase equilibrium, as for the intermediate separation between the two reactors, was simulated fixing the values of T and P. Since the separation of the different phases is better at low P, the flash was operated at atmospheric pressure. On the other hand, for the choice of the optimal temperature, we again used sensitivity analysis. The sensitivity analysis was run with T as manipulated variable in the simulation. As controlled variables, we used the mass fraction of methyl oleate in the biodiesel-rich phase (BIODIES), and the amount of glycerol separated in the other liquid phase (LIQ3). Concerning the mass fraction of methyl-oleate in the biodiesel-rich stream, we adpted the European Standard EN14214, so that the minimum FAME in biodiesel for commercialization must be 96.5 wt.%. On the other hand, regarding the quantity of glycerol separated, we must consider the glycerol mass flow at the second reactor outlet (that is 85.53 kg h−1 ), trying to recover as much glyc-

erol as possible in the stream LIQ3. In addition, according to the European Standard EN14214, the maximum amount of glycerol allowed in biodiesel is 0.25 wt.%. Using the sensitivity analysis, we monitored the variation with T of: (i) the mass fraction of methyl oleate in the stream BIODIES, and (ii) the mass flow rate of glycerol in the stream LIQ3. As expected, as T increases, the methyl oleate mass fraction in the biodiesel-rich phase increases, while the amount of glycerol in LIQ3 decreases. As a consequence, the optimal T for FLASH2 was chosen as a compromise to be the T that allows to have at least 96.5% of methyl oleate in the BIODIES stream, minimizing at the same time the quantity of glycerol. This temperature was found to be 57 ◦ C, and this value was thus set in the simulation. 3.6. SC biodiesel process in two reaction steps with intermediate glycerol separation As a conclusion, we present in Fig. 6 the process flow diagram for the biodiesel production process developed in this work. The aim is to show that, since the flowsheet of Fig. 3 may appear relatively simple, it prevents to understand the actual complexity of the related industrial process which may be possibly developed starting from the one simulated in this work, in terms of quantity of process units. For example, the flash units (FLASH1 and FLASH2) have to be considered as a set of expansion valve + heated/refrigerated tank + decanter, and the heating/pressurizing units (HEATER1 and HEATER2) have to be considered as a set of pumps/compressors + heat exchangers. Another important aspect that increases the complexity of the plant is the recirculation of the unreacted MeOH and CO2 . This recirculation was not considered in our simulations (see Fig. 3). However, it would be necessarily present in an industrial plant. In Fig. 6, the process units are identified by an alphanumeric code according to the rules for the drafting of a process flow diagram, and their function is briefly described in Table 6. 4. Experimental validation 4.1. Previous experimental background – reactor operation and experimental methods In order to validate the process proposed, the first step of the process was simulated in the same conditions used in the experiments carried out with the setup present in the laboratory. This setup was used to determine the kinetic constants for the transesterification reactions. A summary of the experimental conditions used in the reaction is given in Tables 7 and 8. A detailed engineering diagram for the continuous flow packed bed catalytic reactor is reported elsewhere, as well as the experimental procedures [10]. These include transesterification of triglyceride with methanol in presence of CO2 . The Engelhard catalyst used is described in Table 7 ® as SAC-13 (13% Nafion on silica composite), which is a solid superacid catalyst. It is worth mentioning that SAC-13 is very active ® ® (much more active than Amberlyst-15 or Dowex-50 ), hence intra-particle mass transfer calls for further study, which is outside the scope of this work.

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Fig. 6. Flowsheet of the supercritical biodiesel production process in two-step reaction with intermediate glycerol separation developed in this work. The numbers identify the different streams and the alphanumeric codes identify each different process unit.

The reactor effluent produced at different reaction T and spacetimes, was expanded to atmospheric pressure and analyzed after complete fractionation. It was first done, by condensation in a heating bath at 70 ◦ C, followed by condensation at a lower T (−10 ◦ C). The first condensate was analyzed for the glycerides, glycerin, and FAMEs, while the second one was analyzed for unreacted MeOH. The remaining gas (CO2 ) was counted in a precision gas-meter and vented to an explosion-proof hood. The fractionation method and all the analytical procedures were detailed in our previous work [10]. 4.2. Validation of the model with experimental data We modeled the process in the first reactor in the same conditions used in the experiments, concerning: reactor dimensions (length and diameter), mass of catalyst, composition of the inlet mixture, P, T, and reactant mixture flow (affecting the residence time), as described in our previous work [10] (see Table 8), in order to compare the composition of the mixture at the reactor outlet with the composition obtained in the experimental runs. It is important to remark that the P–T diagram for the mixture CO2 –MeOH–triolein with the same composition of the fluid fed to the reactor inlet in the experiments was calculated with the same thermodynamic model previously used to simulate the process using RK-ASPEN method. In this regard, it is interesting to read

the work of Weber et al. [36]. Therefore, this provides a direct check not only on the validity of kinetics but also on the thermodynamic method used to describe vapor-phase equilibrium. Comparing the experimental results with the results of our simulations enables to have an experimental evidence that the calculations and predictions performed by the model are correct, and thus they can be used for the design of SC biodiesel production processes with confidence. The wt.% composition of the reactants + co-solvent mixture used in the experiments is the following: 7.95% triolein, 23.03% MeOH, and 69.10% CO2 (which corresponds to a molar% composition of 0.39% triolein, 31.28% MeOH, and 68.33% CO2 ). Observing the corresponding P–T diagram shown in Fig. 7a, it is evident that the operative conditions of the experimental reactor are SC, being the three working points (corresponding to P = 250 bar and T = 150, 18, and 205 ◦ C respectively) outside the two-phase region envelope. These results were confirmed by the experimental evidences reported in previous works [10,11]. Based on the results previously shown about the restriction of the two-phase region in the P–T diagram with reaction (see Figs. 4c and 5c), it is possible to infer that the system will remain vapour inside the reactor as reaction proceeds, as long as P and T values are maintained. The simulation of the transesterification process in the same conditions of the experimental tests was carried out using the first part of the flowsheet shown in Fig. 3 (that is, the first reaction

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69

Fig. 7. (a) P–T diagram representing the bubble point (continuous line) and dew point (dashed line) curve for the mixture CO2 –MeOH–triolein with the same composition of the reacting mixture of the experimental runs. (b–f) Comparison between experimental points (dots) and simulation (continuous lines) wt.% of each different component of the mixture at the reactor outlet (unreacted MeOH and CO2 free-basis).

step), comprising the process units named MIXER1, HEATER1, and REACTOR1. In the experimental tests, the different residence times (␶) were obtained varying the mass flow rate of the reactants and co-solvent, keeping constant the composition of the mixture fed (see Table 8 for the operating conditions). The same parameters were set in Aspen ® Plus , and the flow rates were varied accordingly to vary ␶. The different simulations were run at 250 bar, setting the corresponding T in the unit HEATER1. The results in terms of wt.% composition of the mixture at the outlet of REACTOR1 are summa-

rized in Table 9, together with the results of the experimental tests. The same results are also graphically shown in Fig. 7b–f. There, a comparison between the experimental and simulation results obtained at different T is made separately for each component. For the tests carried out at 205 ◦ C (green curves and points in Fig. 7b–f), there is an acceptable agreement between the experimental and simulation results. In facts, for all the five components considered (triolein, diolein, monolein, glycerol and FAME), the experimental points are close to the trend provided by the simulation. The highest differences are observed for monolein, especially

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Table 9 Experimental and simulation results at different T and ␶ regarding the wt.% composition (unreacted MeOH and CO2 free-basis). P = 250 bar, reactor inlet composition: 7.95% triolein, 23.03% MeOH, and 69.10% CO2 . Component [wt.%]

Experimental

T = 150 ◦ C Triolein Diolein Monolein Glycerol FAME

␶ [min] 0.5 85.4 6.7 0.2 0.3 7.5

1.0 79.3 8.5 0.6 0.4 11.2

0.5 51.5 8.7 1.7 6.5 31.6

1.0 27.5 5.8 1.2 7.0 58.2

0.5 12.7 4.2 2.0 7.6 73.4

1.0 7.3 3.1 1.6 8.3 79.7

T = 180 ◦ C Triolein Diolein Monolein Glycerol FAME

␶ [min] 2.0 64.8 9.7 0.6 0.9 24.1

4.0 16.6 2.9 0.02 2.8 77.6

0.78 86.26 7.10 0.48 0.18 5.97

1.55 74.37 10.29 0.86 0.76 13.72

2.0 16.8 4.7 1.3 7.9 69.3

4.0 6.0 2.3 1.2 9.1 81.4

0.68 15.67 14.18 0.61 5.79 63.75

1.36 3.12 3.84 0.63 8.40 84.00

2.0 0.8 1.0 1.1 9.2 88.0

4.0 1,1 0.8 0.9 9.1 88.2

0.59 12.90 5.33 0.36 7.34 74.07

1.18 2.45 1.03 0.47 8.89 87.17

␶ [min]

T = 205 ◦ C Triolein Diolein Monolein Glycerol FAME

Simulation

3.02 56.59 11.54 1.10 2.20 28.58

5.62 34.48 9.29 1.22 4.55 50.46

2.67 0.30 0.84 0.72 9.06 89.08

4.92 0.10 0.55 0.66 9.13 89.55

2.31 0.28 0.24 0.55 9.19 89.74

4.24 0.13 0.17 0.50 9.22 89.97

␶ [min]

␶ [min]

␶ [min]

considering the trend at low ␶ values. However, since the amount of monolein present in the mixture is considerably lower compared to the other components (between 0.25 and 2 wt.%), these deviations can be considered acceptable. The results obtained at 180 ◦ C (red curves and points in Fig. 7b–f) show a higher deviation between experiments and simulations for triolein and FAME compared to the results at 205 ◦ C, especially at intermediate values of ␶ (1 and 2 min). A good agreement is observed for glycerol. Regarding the runs at 150 ◦ C (black curves and points in Fig. 7b–f), there is a good agreement between experimental and simulation results at low ␶ for all the components. On the contrary, for ␶ = 4 min, the discrepancies are remarkable, except for glycerol. This happens in particular, for triolein, diolein and monolein, which show considerably lower values in the experiment than in the simulation. Consequently, exactly the opposite behavior is observed for FAME. An important consideration to be made concerning the three series of simulation runs at three different T is that, despite the mass flow rates are the same, the corresponding experimental ␶ values reported in our previous work [10], and then in Table 6 and in Fig. 7b–f do not change. Nevertheless, these ␶ values should vary. In fact, varying the operating T, the density of the fluid should changes accordingly, and consequently this causes a change of ␶. Otherwise, this fluid density change is accounted for by the model in the simulations (see. Table 6): here, keeping constant the mass flow, ␶ increases with the decrease of T. This consideration has to be considered in the plots in Fig. 7b–f. Additional reasons for the discrepancy between the experimental and the simulations results could be due to unaccuracies in the gas-chromatographic analysis of the components, and to uncomplete separation of MeOH and CO2 in the GC, causing some erro in the determination of the wt.% composition of the mixture. All these errors, in turn, could have affected the calculation of the kinetic constants through the mathematical procedure described in our previous work [10]. However, the deviations between experiments and simulations can be considered acceptable, and are comparable to what is reported in other articles on biodiesel processes [22,37–39]. In summary, according to our results, we can conclude that the thermodynamic and kinetic model that we used to simulate

the process proposed in this work can be considered validated by experimental evidence. 5. Conclusions and future work In this work, the development of a biodiesel production process by transesterification of triglycerides (vegetable oil) in SC conditions is presented. The process involves two stages of reaction in catalytic fixed bed reactors, with an intermediate separation of glycerol, with the purpose to shift the chemical equilibrium towards a higher triglycerides conversion and biodiesel yield. The ® different stages of the process were simulated with Aspen Plus . The first part of the work describes the calculation of the liquidvapor equilibrium data (P–T diagrams) with Equation of State methods for the oil–MeOH mixture at different compositions (with and without co-solvent), in order to individuate the SC conditions of the mixture, and consequently the operating conditions of the first reactor. The advantage of using CO2 (co-solvent) has been pointed out, in terms of reduction of the critical point of the system, allowing the process to be carried out within the catalyst conditions. In the second part, the kinetic model for the transesterification reaction is described, and then used to simulate the process. The process description is divided in different steps: (i) first catalytic reactor, (ii) intermediate glycerol separation, (iii) determination of the operating conditions of the second reactor, (iv) second catalytic reactor, and (v) final separation. The results obtained point out that this continuous SC catalytic process in fixed bed reactors enables to carry out the transesterification reaction for the production of biodiesel with high conversion and yield, and with a very short reaction time compared to other processes reported in the literature (e.g. the liquid process with homogeneous catalyst). In particular, it is remarkable that for this SC process the residence times in the first and second reactor are of only 2 and 4 min, respectively. This allows a considerable reduction in reactor volumes. Moreover, the presence of the intermediate separation stage, together with the second catalytic reactor, leads to obtain a biodiesel yield of 98.3%, compared to 88.6% in the case of a single reactor. The comparison between the experimental results and the results of the simulations run in the same conditions confirmed the validity of both the thermodynamic and kinetic models used to

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