Thermodynamic analysis, experimental and kinetic modeling of levulinic acid esterification with ethanol at supercritical conditions

Thermodynamic analysis, experimental and kinetic modeling of levulinic acid esterification with ethanol at supercritical conditions

Fuel 260 (2020) 116376 Contents lists available at ScienceDirect Fuel journal homepage: www.elsevier.com/locate/fuel Full Length Article Thermodyn...

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Fuel 260 (2020) 116376

Contents lists available at ScienceDirect

Fuel journal homepage: www.elsevier.com/locate/fuel

Full Length Article

Thermodynamic analysis, experimental and kinetic modeling of levulinic acid esterification with ethanol at supercritical conditions

T

Vinícius Kothea, Diego Trevisan Melfib, Kallynca Carvalho dos Santosb, Marcos Lúcio Corazzab, ⁎ Luiz Pereira Ramosa, a b

Research Center in Applied Chemistry, Department of Chemistry, Federal University of Paraná, CEP 81531-990 Curitiba, PR, Brazil Department of Chemical Engineering, Federal University of Paraná, CEP 81531-990, Curitiba, PR, Brazil

G R A P H I C A L A B S T R A C T

A R T I C LE I N FO

A B S T R A C T

Keywords: Levulinic acid Supercritical esterification Ethanol Ethyl levulinate Tubular reactor

Ethyl levulinate is an environmentally friendly biomass-derived ester that is an alternative to the classic petroleum-derived fuel additives. Several studies have been addressed to its chemical production pathways. The supercritical esterification of levulinic acid to ethyl levulinate, however, remains understudied. This work reports the effect of process variables and a kinetic study for the esterification of levulinic acid with ethanol under sub and supercritical conditions. Experimental data were obtained in a continuous tubular reactor at a fixed pressure of 100 bar. The reaction temperature varied from 220 to 280 °C, and the ethanol to levulinic acid molar ratios from (2:1) to (9:1). Ethyl levulinate was synthesized with high selectivity under all evaluated reaction conditions, achieving conversions up to 80% and 93% when ethanol to levulinic acid molar ratios of (2:1) and (9:1) were used, respectively. A PFR model approach was considered with an elementary reversible self-catalyzed rate law, and the effect of considering the mixture density behavior through the reactor using the PC-SAFT equation of state was discussed. The proposed kinetic approach was able to correlate the kinetic experimental data for all experimental conditions used in this study. Furthermore, a thermodynamic analysis was performed to elucidate trends in reaction performance.

1. Introduction The gradual decline in easily accessible petroleum reservoirs and environmental concerns related to its use have raised the need to find ⁎

sustainable alternatives for the production of energy, fuels, chemicals, and materials. Biomass stands out for this purpose due to its large availability, versatility, and low cost [1,2]. In this regard, environmentally friendly biomass-derived esters have been identified as

Corresponding author. E-mail address: [email protected] (L.P. Ramos).

https://doi.org/10.1016/j.fuel.2019.116376 Received 9 July 2019; Received in revised form 3 October 2019; Accepted 7 October 2019 0016-2361/ © 2019 Published by Elsevier Ltd.

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An HPLC pump (Shimadzu, model LC-20AT) fed the reactor with a controlled flow rate of the reaction mixture. The pressure was adjusted using a back-pressure regulator (KPB series, Swagelok). The temperature profile and the pressure inside the reactor were monitored respectively by four K-type thermocouples (1 °C uncertainty) and one pressure transducer (Huba Control, uncertainty within 0.025 MPa) connected in a field logger register (Novus). After the steady-state condition was reached, considering at least twice the spatial time at each different mass flow, samples of the reaction mixture were collected at the reactor outlet. Quantification analysis of reaction products was carried out in a gas chromatograph (Shimadzu GC 2010 Plus) equipped with an AOC 20i autosampler, a capillary Agilent CP-Wax 58 FFAP CB (50 m × 0.25 mm; 0.20 µm) column and a flame ionization detector (FID). Samples (1 µL) were injected at 200 °C in a 1:20 split ratio. The column temperature program included one isothermal step at 100 °C for 1 min, one heating ramp at 25 °C min−1 until 175 °C with an isothermal holding time of 0.5 min, a second heating ramp at 5 °C min−1 until 230 °C and a final isothermal holding time of 3 min. Quantification was carried out by external calibration. Calibration curves were built for levulinic acid (99%, Sigma-Aldrich) and ethyl levulinate (99%, Sigma-Aldrich) using standard solutions covering the concentration range of 100–1000 ppm.

suitable replacements to petroleum-derived chemicals in various areas such as pharmaceuticals, transportation fuels, plasticizers, solvents, food flavors, coating, and fragrance [3–6]. Levulinic acid, also known as 4-oxopentanoic acid, is a renewable carboxylic acid that can be obtained from lignocellulosic materials such as corn starch, sugarcane bagasse, wheat straw, rice husks, paddy straw, sorghum grain, water hyacinth, paper mill sludge, tobacco chops, and olive tree pruning [7,8]. This acid has been selected by the US Department of Energy (DOE), with ethanol and other compounds, as part of the 15 carbohydrate-derived chemical building blocks for the development of biorefineries, owing to its potential to serve as a green platform chemical [9]. Ethyl levulinate, among the levulinate esters, has gained attention because it can be applied for fragrance manufacturing, as neat fuel and as additive for diesel and biodiesel [10–13]. Several studies have been performed so far to elucidate and optimize its chemical production pathways either from raw biomass [14–17], carbohydrates [17–19], or directly from levulinic acid [20–25]. Chemical routes starting from levulinic acid and ethanol are particularly attractive since they combine two environmentally friendly compounds of high interest for biorefineries. Levulinic acid esterification to ethyl levulinate exhibits low reaction rates under auto-catalyzed and low-temperature conditions. Russo et al. [21] reached only 25% of levulinic acid conversion after 1 h at 60 °C using a (5:1) ethanol to levulinic acid molar ratio. Thus, this reaction has been carried out with homogeneous catalysts such as sulfuric acid [20,21], as well as with heterogeneous catalysts such as enzymes [22], ion-exchange resins [21,23], sulfonated hydrothermal carbons [20], transition metal salts [24], zeolites, and sulfated oxides [25]. Although different catalytic systems have led to high levulinic acid conversions, these routes lead to subsequent complications such as consumption, deactivation, separation, and recovery of catalysts, and low selectivity in some cases. Bankole and Aurand [26] attempted to bypass these issues by conducting the auto-catalyzed esterification of levulinic acid at high temperatures, reaching about 60% conversion at 250 °C using an ethanol to levulinic acid molar ratio of (1:1). This was an interesting approach because supercritical ethanol has been successfully used for esterification and transesterification in various reaction systems [27–29]. However, Bankole and Aurand [26] did not evaluate the effect of high temperatures and different molar ratios. Also, because the pressure was not measured in their study, it is not possible to infer the thermodynamic conditions of the system and if ethanol indeed reached its critical point (pressure above 61.48 bar and temperature above 240.75 °C). This work provides consistent experimental data and the mathematical modeling of a tubular isobaric and isothermal reactor where the levulinic acid esterification under ethanol supercritical conditions took place. The information and the proposed modeling approach are fundamental to understand and provide basic parameters for modeling, designing and optimization of an alternative process regarding the supercritical esterification of levulinic acid to ethyl levulinate.

2.2. Design of experiments A 23 factorial design was performed keeping the inlet volumetric flow at ambient conditions fixed at 2 mL∙min−1, and using temperature, ethanol to levulinic acid molar ratio and pressure as factors. The levels were chosen to include ethanol subcritical and supercritical conditions according to the following maximum and minimum values: 220 and 280 °C, 100 and 200 bar, and ethanol to levulinic acid molar ratios of (1:1) and (9:1). The center point of the factorial design (250 °C, 150 bar and molar ratio of 5:1) was performed in three replicates. 2.3. Kinetic modeling Kinetic data for the levulinic acid esterification were acquired under ethanol subcritical (P = 100 bar; T = 220 °C) and supercritical conditions (P = 100 bar; T = 250 and 280 °C) at two different ethanol to levulinic acid molar ratios (MR = 2:1 and 9:1). At each reaction condition, the mass flow (ṁ ) was varied from 0.1 to 4.7 g min−1 and each corresponding outlet amount of ethyl levulinate was measured. The kinetic of levulinic acid esterification with ethanol at high temperatures and high pressures was assumed to follow an elementary and self-catalyzed rate law, as represented in Eq. (1). Thus, Eq. (2) was used to calculate the corresponding reaction rate (rA ), k1

A + Et + A⟷E + W + A k2

rA = (−k1 CA CEt + k2 CE CW ) CA

(1) (2)

where A, Et , E , and W represent levulinic acid, ethanol, ethyl levulinate and water, Ci is the concentration of each “i ” compound, and k1 and k2 are the forward and backward kinetic rate constants, respectively. This approach is representing the self-catalytic feature of acid esterification under near and supercritical conditions of ethanol [27]. Therefore, the acid appears in both sides of the equations because it is considered to act as reagent and catalyst in this reaction system. A steady-state plug flow reactor model was assumed to represent the reaction system. Therefore, the dispersion effects were neglected and the differential material balance for each i compound was expressed as shown in Eq. (3),

2. Materials and methods 2.1. Experimental section The esterification of levulinic acid (99%, purchased from SigmaAldrich) and ethanol (99.8%, purchased from Vetec®), without pretreatment of the reagents, was carried out inside a continuous tubular reactor as described by Santos et al. [28]. Briefly, the reactor consisted of a stainless-steel column (316 1/8″ OD × 0.91 cm, Swagelok) with 22 ± 1 mL capacity (free volume) that was inserted into an electric furnace, whose maximum operating temperature was 420 °C (Sanchis, Brazil). Further details of this reaction system can be obtained from the schematic diagram that has been included in Supplementary Material (Fig. SM-1).

dFi = ri dV

(3)

where Fi is the mol flow of each i component and V is the reactor 2

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volume. Since a single reaction is assumed to occur (see Section 3.2), the levulinic acid conversion ( X ) is defined as represented in Eq. (4). The material balance and the concentrations of individual components were rewritten on the basis of this variable as shown in Eqs. (5)–(9),

FA0 − FA FA0

X=

OF =

j

(15)

i

X jiExp

X Calc ji

where and are the experimental and its corresponding calculated conversion (Eq. (13)) for each point i of each experimental condition j , M is the number of points in each isothermal condition and N is the number of the experimental conditions evaluated in this work. Root mean square deviation (RMSD ) was used to compute the correlation between the model predictions and the experimental data as shown in Eq. (16).

(4)

dX −rA C (k C C − k2 CE CW ) = = A 1 A Et dV FA0 FA0

N

2 ∑ ∑ (XjiExp − X Calc ji )

(5)

M

CA =

FA C = A0 (1 − X ) pmix ρ0mix V̇

(6)

CEt =

FEt C = A0 (MR − X ) ρmix ρ0mix V̇

(7)

CE =

FE C = A0 Xρmix ρ0mix V̇

(8)

FW C = A0 Xρmix ρ0mix V̇

(9)

CW =

RMSD = 100

3.1. Experimental design as a preliminary assessment As a preliminary study to investigate the reliability of the proposed reaction system and to collect some basic information for the development of the kinetic modeling, a 23 factorial design was performed. The conditions selected and the resulting levulinic acid conversion are presented in Table 1, and the statistical analysis are presented in Supplementary Material. Temperature and ethanol to levulinic acid molar ratio were identified as the most significant process parameters influencing levulinic acid conversion to ethyl levulinate, as shown in the Pareto plot presented in Supplementary Material (Fig. SM-2). Despite slightly significant (p > 0.05) in the statistical analysis of the reaction performance, pressure was chosen to be fixed at 100 bar for the kinetic modeling. Besides, the effect of pressure on reaction yield was minor compared to other reaction variables.

ρ0mix

molar mass (MMA andMMEt ) and ethanol to levulinic acid molar ratio (MR ).

CA0 xA0 1 = = ρ0mix MM0mix MM0mix (MR + 1) 1 = 1 MR MM MMEt (MR + 1) + A MR + 1 MR + 1

(

)

3.2. Selectivity analysis (10)

In this study, the reaction selectivity was monitored by GC–MS analysis. This evaluation was needed because levulinic acid has two functional groups (ketone and carboxylic acid), and since the reaction system is subject to high pressure and temperature, parallel reactions may take place (i.e., lactonization or cyclization of levulinic acid) leading to the formation of undesirable products. The results obtained at every reaction condition of the experimental design of Table 1 suggested the absence of byproducts. The GC–MS run of one representative reaction aliquot is given in Supplementary Material (Fig. SM-3), in which no residual levulinic acid is observed. Hence, the supercritical esterification of levulinic acid with ethanol was highly selective for ethyl levulinate, allowing the assumption of a single reaction taking place at the experimental conditions used in this study (Section 2.2).

The solution of the differential Eq. (5) is the conversion profile along the reactor volume (Vr ). The knowledge of the conversion profile allows estimating the mixture density along the reactor volume. With this, the residence time (tr ) was calculated for each experimental point according to Eq. (11), V = Vr

∫V =0

1 dV = V̇

V = Vr

∫V =0

ρmix dV ṁ

(11)

where ṁ states for the mass flow. Eq. (12) was obtained by the differentiation of Eq. (11),

V̇ dtr = dV

(12)

then a change of variable in Eq. (5), with Eq. (12), led to Eq. (13), which provides the conversion profile along the reaction residence time.

dX −rA·V̇ = = (k1 CA CEt − k2 CE CW )(1 − X ) dtr FA0

Table 1 Experimental conditions used in the 23 factorial design developed for the levulinic acid esterification with ethanol and the resulting levulinic acid conversion.

(13)

An Arrhenius-type Eq. (14) was applied to express the kinetic constants for Eqs. (5) and (13).

ki =

Ea ⎛− i ⎞ 10 k 0, i e⎝ RT ⎠

(16)

M·N

3. Results and discussion

where CA0 is the levulinic acid inlet concentration, V̇ is the volumetric flow, and ρ0mix is the mixture density in the inlet reactor condition. As the density of the mixture ( ρmix ) varies through the reactor volume, the treatment given to this variable is further detailed in Section 3.4. Also, the CA0 ratio in Eqs. (6)–(9) is expressed in Eq. (10) in terms of reagent

tr =

N

2 ∑ j ∑i (X jiExp − X Calc ji )

i = 1, 2

(14)

Therefore, the parameters to be adjusted were the pre-exponential (or frequency) factors (k 0,1 and k 0,2 ) and the activation energies (Ea1and Ea2 ). The stochastic Particle Swarm Optimization (PSO) algorithm [30] was applied to minimize the objective function (15) by pre-estimating the kinetic parameters, which were optimized afterwards using the “fminsearch” subroutine from Matlab®, 3

Temperature (°C)

Ethanol to levulinic acid molar ratio

Pressure (bar)

Levulinic acid conversion (%)

220 220 220 220 250 250 250 280 280 280 280

1:1 1:1 9:1 9:1 5:1 5:1 5:1 1:1 1:1 9:1 9:1

100 200 100 200 150 150 150 100 200 100 200

49.4 53.1 41.2 43.5 72.6 71.1 71.5 61.7 63.1 78.0 83.4

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analysis of the simulated P-T diagrams revealed also that the behavior at low and high molar ratios (with one critical line and without azeotrope) were similar, suggesting that the reaction systems involving ethanol, levulinic acid, ethyl levulinate and water follows a Class I – Type I phase behavior according to the Konynenburg and Scott classification [33]. This was so because such compounds are highly associative to one another [34]. As expected, the simulated diagrams of Fig. 1 are predicting that the impact reaction conversion on the thermodynamic behavior is more pronounced at lower ethanol to levulinic acid molar ratios. Hence, with an increase in molar ratio, the system composition becomes less sensible to levulinic acid conversion due to the presence of ethanol in excess. It can also be noticed that the bubble points are more sensible to the reaction extension than the dew points and both always require higher pressure to be achieved at the same temperature in relation to an increase in reaction conversion. As the esterification took place, the critical point decreased probably due to the consumption of levulinic acid, which is the compound with the highest critical temperature and pressure in the system. Thus, as the reaction proceeds, the system becomes more soluble on the account of ethyl ester to ethanol and water to ethanol interactions. Santos et al. [27] came to similar observations while modeling the esterification of fatty acids using the same thermodynamic approach. 3.4. Mixture density evaluation As described previously, the mixture density varies through the reactor volume because, at fixed pressure-temperature conditions, it is a function of composition and/or reaction conversion. Hence, the Aspen Plus V8.4 (30.0.033) sensitivity analysis was performed to evaluate changes in mixture density with changes in reaction conversion (Fig. 2) using the PC-SAFT EoS to deal with non-idealities of this complex mixture. For this, the pure component parameters are given in Table 2 and all binary interaction parameters were set equal to zero (kij =0). Fig. 2 reveals that, at all evaluated conditions, the reaction causes the system to expand. Also, the density of the reactant mixture was more sensible to conversion at high temperatures, reaching 15% and 12% of deviation at 280 °C with ethanol to levulinic acid molar ratios of (9:1) and (2:1), respectively. Thus, despite the assumption that incompressible fluid fits well under subcritical conditions (for the evaluated conditions implying a maximum of 6% deviation at 220 °C and an ethanol to levulinic acid molar ratio of 2:1), rigorous modeling of supercritical reactors should consider density variations or at least perform a similar thermodynamic analysis. A 4ª order polynomial equation (such as ρmix = a·X 4 + b·X 3 + c·X 2 + d·X + e ) was used to adjust the simulated mixture density data presented in Fig. 2 for each temperature and molar ratio evaluated in this study. This approach was used to include in the kinetic modeling the density dependence as a function of composition at constant pressure and temperature, thus avoiding an extra computational effort in adding a subroutine for the PC-SAFT EoS.

Fig. 1. Pressure-temperature diagrams simulated on Aspen Plus V8.4 (30.0.033) for the synthesis of ethyl levulinate using ethanol to levulinic acid molar ratios of (a) (2:1) and (b) (9:1) at different simulated reaction conversions.

3.3. Phase behavior analysis of the reactant mixture Depending on its temperature, pressure and composition, systems containing supercritical fluids may be homogeneous or non-homogeneous [31]. Due to the absence of mass transfer limitations, single phase systems are desirable to maximize the reaction rate. Thus, to verify if the kinetic study is restricted to the homogeneous region, a phase behavior analysis was performed by simulating pressure-temperature diagrams at different reaction conversions (X = 0, 20, 40, 60, 80, and 100%). Fig. 1(a) and (b) depict the results of the simulations for both molar ratios that were used in this study (2:1 and 9:1, respectively). For this thermodynamic analysis, PC-SAFT EoS was used to predict the phase behavior for the levulinic acid esterification with ethanol, where all binary interaction parameters were set equal to zero (kij = 0) following the same approach used in previous studies [27,28,32]. All simulations were performed using the Aspen Plus V8.4 (30.0.033), with the PC-SAFT pure compound parameters described in Table 2. Fig. 1 demonstrates that the defined experimental conditions are placed in a homogeneous region, however, some of them are close to the vapor-liquid region predicted using the PC-SAFT equation, particularly at 280 °C for an ethanol to levulinic acid molar ratio of (9:1). Since the two-phase region was estimated and therefore subjected to prediction errors, there is no certainty in stating that all reactions experiments were performed under homogeneous conditions. The

3.5. Kinetic study Levulinic acid esterification under sub and supercritical conditions of ethanol were acquired in a tubular reactor. A steady-state PFR model approach was considered and an elementary reversible self-catalyzed rate law was assumed. As discussed in Section 3.4, the mixture density varies through the reactor volume. Earlier studies have neglected such variations in similar systems by taking the assumption of incompressible flow [27,28]. This approach is simpler to implement than the detailed kinetic modeling of Section 2.2 and was followed for the acquired data to provide a discussion about the effects of such theoretical assumption. The adjusted kinetic parameters for the esterification of levulinic acid, assuming and neglecting mixture density variations, are presented 4

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Table 2 Critical properties and PC-SAFT parameters of pure components. Parameter

ASPEN name

Levulinic acid1 [40]

Ethyl levulinate2 [40]

Ethanol [41]

Water [41]

mi εi/ κ (K ) σi (Ȧ )

PCSFTM PCSFTU PCSFTV

2.0311 266.4953 4.1241

6.4558 226.9371 3.0938

2.3827 198.24 3.1771

1.0656 3.0007 366.51

κ Ai Bi

PCSFAU

0.0171



0.032384

0.034868

ε Ai Bi·κ −1 (K ) Assoc. Aceptor Assoc. Donor

PCSFAV

4578.3655

0

2653.4

2500.7

P SAT AAD%

– – –

1 1 1.07%

2 0 0.13%

1 1 0.99%

1 1 1.88%

ν[a]or ρ[b] AAD%



0.06%[b]

1.18%[b]

0.79%[a]

6.83%[a]

1 2

Values in brackets provide the reference for the experimental dada; Induced association modeling approach.

in Table 3. It is worth emphasizing that these parameters were obtained from global estimation, considering all evaluated isotherms for both ethanol to levulinic acid molar ratios simultaneously. To assure the accuracy of the reported parameters, a sensitivity analysis was performed by perturbating each parameter at a time (by 5–15%) and reoptimizing the others. A plot of the minimum obtained RMSD (%) for each perturbed parameter is presented in Supplementary Material (Fig. SM-4). Both methodologies displayed low RMSD values and fitted well the experimental data. The slightly lower RMSD acquired neglecting the mixture density variations through the reactor volume suggests that the system thermodynamic behavior might not have been well predicted by PC-SAFT EoS or that some neglected aspects such as pressure loss, temperature variations and dispersion effects may be even more significant than density variations. These aspects will be evaluated for rigorous modeling in future work. Fig. 3(a) and (b) show, for each isothermal condition at ethanol to levulinic acid molar ratios of 2:1 and 9:1, respectively, the experimental levulinic acid conversion and the corresponding calculated profile with the adjusted parameters assuming compressible flow as described in Section 2.2. The error bars at the central isotherm were established from duplicated experimental runs and from the previous experience of the group with the employed experimental apparatus. These errors were classified as type B according to the “Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results” [35]. Results obtained in this work shows that the proposed reaction approach led to higher reaction rates for the levulinic acid conversion than other approaches presented in the literature. For example, at 280 °C with an ethanol to levulinic acid molar ratio of (9:1), 85% of levulinic acid conversion was experimentally acquired after a relatively short residence time of less than 25 min (Fig. 3a). Table 4 summarizes some reaction conditions that already have been reported for levulinic acid esterification, as well as the needed residence time to reach similar reaction conversions. Fig. 3 also depicts that increases in the feed (ethanol and levulinic acid at different molar ratios) and temperature generally led to higher conversions and initial reaction rates, which can be better visualized by the kinetic model adjusted to the set of experimental data obtained in this study. Higher initial rates were obtained for reactions performed at lower molar ratios of 2:1 (CA0 = 1.05 ± 0.15 mmol.L−1) (Fig. 3a) compared those of higher molar rations of 9:1

Fig. 2. PC-SAFT EoS simulation on Aspen Plus V8.4 (30.0.033) of the mixture density at 100 bar in relation to levulinic acid conversion using ethanol to levulinic acid molar ratios of (a) (2:1) and (b) (9:1).

Table 3 Adjusted kinetic parameters for levulinic acid esterification with ethanol at supercritical conditions. Compressible Flow

10 k 0,1 (L∙mol−1)2min−1

10 k 0,2 (L∙mol−1)2min−1

Ea1∙R−1 (K−1)

Ea2∙R−1 (K−1)

RMSD (%)

Neglected Assumed

62866.89 155665.37

4935.06 8081.87

8061.45 8494.82

7230.15 7466.63

4.82 5.12

5

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Table 5 More accurate values for gaseous enthalpy and free Gibbs energy of formation of levulinic acid, ethyl levulinate, ethanol and water.

ΔG fo

( ) kJ kmol

Reference

ΔH fo

( ) kJ kmol

Reference

Levulinic acid

Ethyl levulinate

Ethanol

Water

−491695*

−443200

−167285

−228510

[37] −613100

[This work] −620065

[38] −234531

[38] −241818

[37]

[39]

[38]

[38]

* Calculated directly from the reported formation enthalpy and entropy using the Gibbs free energy definition.

molar ratio than the other chemical pathways mentioned in Table 4. However, it presents significant advantages for high levulinic acid conversions such as lower residence times and no need of adding an exogenous catalyst. Also, this work serves as a reference material for the development of scaled-up reactor projects and optimization within the applied range of temperature and ethanol to levulinic acid molar ratios. 3.6. Chemical equilibrium analysis In order to perform the chemical equilibrium analysis for the levulinic acid esterification with ethanol, the equilibrium constant (Keq) was obtained by Eqs. (17) and (18),

ΔGR = ΔHR − T ΔSR = −RT ln(KEQ )

(17)

k ΔHR ΔSR ln(KEQ ) = ln ⎛ 1 ⎞ = − + k RT R 2 ⎝ ⎠

(18)





where changes in the reaction enthalpy and entropy were obtained by fitting Keq versus T−1. Keq values were obtained by the forward and backward reaction rate constants (k1 and k2), which were assessed from the adjusted pre-exponential factors and the activation energies presented in Table 3. Fig. 4 shows a plot for the Eq. (18) where the obtained parameters were ΔHR = -8548.37 J∙mol−1 and ΔSR = 24.59 J.mol−1∙K−1. Two different approaches were considered to calculate the levulinic acid equilibrium conversion under the applied experimental conditions: the kinetic and the thermodynamic approaches. The kinetic approach uses a simulation of the proposed modeling with adjusted parameters to identify the levulinic acid conversion that corresponds to the infinity residence time (equilibrium conversion) at each reaction condition. By contrast, the thermodynamic approach consisted in simulations of the Aspen Plus V8.4 (30.0.033) “Equilibrium reactor” block, with the PCSAFT EoS parameters presented in Table 2 and additional pure compound parameters retrieved from Aspen Plus Databank at each reaction condition. This block calculates the standard enthalpy, entropy and Gibbs free energy of formation of pure compounds and correct them to the reaction conditions. Therefore, it estimates the equilibrium constant as well as the equilibrium conversion without any kinetic information. Considering the parameters retrieved from Aspen Plus Databank, the two approaches conducted to different results, with the kinetic approach always leading to lower equilibrium conversions (Table 6). As discussed by Voll et al. [36], a small variation in parameters such as the standard Gibbs free energy of formation and the standard formation

Fig. 3. Experimental and calculated conversion profiles for levulinic acid esterification under sub and supercritical conditions of ethanol, using ethanol to levulinic acid molar ratios of (a) (2:1) and (b) (9:1). The initial concentration of levulinic acid at each reaction condition was calculated according to Eq. (10).

(CA0 = 3.45 ± 0.23 mmol.L−1) (Fig. 3a). Also, at lower molar ratios the reaction reached equilibrium conversion values lower than those obtained at 9:1. However, conversions were statistically identical at 250 °C and 280 °C after ~ 70 min residence time for both molar ratios. Therefore, from a process engineering point of view, reactions at 250 °C, even at lower molar ratios of 2:1, might be more feasible than reactions at 280 °C because lower temperatures and ethanol to levulinic acid molar ratios demand lower energy consumption in the reactor setup and in the downstream ethanol recovery. In addition, as previously pointed out in Section 3.3, the most severe reaction condition (molar ratio of 9:1 at 280 °C) approaches the simulated vapor-liquid envelop (Fig. 1). With this, mass transfer limitations may have been present if the reaction was not completely homogeneous. In general, the supercritical esterification of levulinic acid with ethanol required higher temperature and ethanol to levulinic acid Table 4 Reaction conditions reported to reach about 85% levulinic acid conversion. Esterification Homogeneously catalyzed by sulfuric acid [21] Homogeneously catalyzed by Novozym 435 [22] Heterogeneously catalyzed by FE2(SO4)3 [24] Uncatalyzed esterification [This work]

Experimental conditions −3

CCAT = 80 mol·m ; T = 70 °C; MR = 5 CCAT = 10 mg·mL−1; T = 37.5 °C; MR = 4 CCAT = 108 mol·m−3; T = 50 °C; MR = 3 T = 280 °C; MR = 9

CCAT and MR refer to the catalyst concentration and ethanol to levulinic acid molar ratio, respectively. 6

Residence time (min)

Conversion (%)

250 187.5 50 25

about 85 84.7 about 84 85.1

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performed a new simulation considering the reaction condition described by Bankole and Aurand [26] (uncatalyzed esterification, 1:1 ethanol to levulinic acid molar ratio and 250 °C), which is similar to the reaction conditions evaluated in this study. Since these authors did not measure the pressure on their reaction system, it was assumed to be 35 bar (slightly above predicted bubble pressure on the equilibrium condition), which is coherent with their described experimental apparatus. Under such experimental conditions (250 °C, 35 bar, 1:1 molar ratio), the thermodynamic approach for levulinic acid equilibrium conversion predicted 62.72%. This value agrees well with the results of Bankole and Aurand [26], which corresponded to a 60.8% levulinic acid conversion after 180 min of reaction time. 4. Conclusion In this work, the levulinic acid esterification under sub and supercritical ethanol conditions was investigated in a continuous tubular reactor. A PFR model approach with an elementary reversible autocatalytic rate law was proposed. The mixture density profile through the reactor volume was estimated using the PC-SAFT equation of state. The results found suggested that as the reaction proceeds the reactional mix expands, at all evaluated conditions. The proposed kinetic model showed good agreement with the experimentally measured values of levulinic acid conversion (RMSD = 5.12%). The reaction was highly selective for ethyl levulinate regardless of the applied experimental conditions, and levulinic acid conversions of up to 80% were reached after a fair residence time (around 15 min at 280 °C using an ethanol to levulinic acid molar ratio of 9:1), showing that the supercritical esterification of levulinic acid may be a promising chemical pathway to produce ethyl levulinate.

Fig. 4. Linearized plotting of the equilibrium constant natural logarithm as a function of the inverse of the temperature for levulinic acid esterification under ethanol sub and supercritical conditions.

enthalpy of the acid and the ester can lead to huge variations in the esterification equilibrium conversion. To illustrate this effect a Tornado plot is presented in Fig. 5 for the experimental conditions (a) and (d) as specified in Table 5, considering a deviation of 1.50% for each reaction parameter. Fig. 5 shows that small variations in the parameters of formation significantly affect conversion. Therefore, due to its high sensibility to several parameters, the thermodynamic approach should not be trusted to predict equilibrium conversion unless the fundamental thermodynamic parameters are known with great confidence for all involved compounds. In any other situation, the kinetic approach is found to be more reliable. The standard formation enthalpy and entropy of gaseous levulinic acid were reported by Reichert et al. [37] with good precision, the standard formation Gibbs free energy and enthalpy are well known for water and ethanol [38] and there are some studies about the enthalpy of formation of ethyl levulinate due to its use as fuel [39]. However, to the best of our knowledge, there is still a lack of information about the Gibbs free energy of formation of ethyl levulinate. The Gibbs free energy of formation of ethyl levulinate was fitted in order to provide small deviation between the equilibrium conversion acquired through the kinetic and the thermodynamic approaches. These new simulations were performed using Aspen Plus V8.4 (30.0.033) “Equilibrium reactor” block with the PC-SAFT EoS parameters presented in Table 2, the more accurate values for enthalpy and free Gibbs energy of formation (Table 5) and additional pure compound parameters retrieved from Aspen Plus Databank, at each evaluated reaction condition. The results are summarized in Table 6. Lastly, in order to validate the estimated Gibbs free energy of ethyl levulinate and the thermodynamic approach as a whole, it was

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors want to thank CNPq (Brazil, grants 406737/2013-4, 305393/2016-2 and 309506/2017-4), COPEL (Companhia Paranaense de Energia, grant PD 2866-0470/2017) and Fundação Araucária (PI 07/ 2018 Horizon 2020, grant 004/2019) for financial support and scholarships. This work was also financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brazil (CAPES) – Finance Code 001. Appendix A. Supplementary data Supplementary data to this article can be found online at https://

Table 6 Equilibrium conversions obtained from the proposed kinetic modeling and Aspen Plus V8.4 (30.0.033) “Equilibrium reactor” block, with PC-SAFT EoS parameters presented in Tables 2, 5 and additional pure compound parameters retrieved from the Aspen Plus Databank at each reaction condition. Reaction condition

a b c d e f

Ethanol to levulinic acid molar ratio

2:1

9:1

Temperature (°C)

220 250 280 220 250 280

Equilibrium conversion (%) Kinetic

Thermodynamic*

Thermodynamic**

78.69 80.14 81.39 95.29 95.77 96.17

97.01 97.19 97.46 99.29 99.38 99.54

78.74 80.40 82.41 93.36 94.52 96.09

* Simulation performed with the more accurate enthalpy and Gibbs free energy of formation. ** Simulation performed with enthalpy and Gibbs free energy of formation retrieved from Aspen Plus Databank. 7

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Fig. 5. Tornado plot sensitive analysis for the levulinic acid conversion response under 1.50% independent perturbations on standard formation enthalpy and entropy of levulinic acid and ethyl levulinate for experimental conditions (a) and (d) according to Table 5.

doi.org/10.1016/j.fuel.2019.116376.

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