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Calculating the Thermodynamic Characteristics and Chemical Equilibrium of the Stepwise Transesterification of Triolein Using Supercritical Lower Alcohols Dan Zeng, Ruosong Li, Tianwei Jin, and Tao Fang* School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, People’s Republic of China ABSTRACT: A comparative study of triolein transesterification using three individual supercritical alcohols (methanol, ethanol, and isopropanol) was performed using thermodynamic analysis. The correlative properties were calculated for all components, including boiling point, critical parameters, acentric factor, enthalpy, entropy, and constant-pressure heat capacity. Chemical equilibria of the three reaction systems were discussed and diagrams of reaction enthalpy, Gibbs free energy and the chemical equilibrium constant as a function of temperature were constructed for the temperature range from 300 to 700 K. The results illustrated that, in the supercritical state, the triolein transesterification reaction proceeds primarily with methanol under the proper reaction conditions, but rarely occurs with ethanol or isopropanol. This observation was consistent with the experimental results reported in literature. This study provides a reliable method for analyzing analogous reaction systems for biodiesel synthesis with supercritical fluids. Previous work in the application of supercritical fluids to biodiesel production has been focused predominantly on the optimization of process variables and understanding the kinetics and phase equilibrium of oil transesterification in batch or flow reactors.4,15−20 There have been a few investigations of chemical equilibria in the transesterification reaction using supercritical lower alcohols.8,21−23 For instance, Anikeev21,23 provided the thermodynamic data for all compounds participating in the transesterification reaction and constructed phase diagrams for these materials. Furthermore, Anikeev22 studied the chemical equilibria that occurred during the stepwise transesterification reactions between mixed triglycerides and methanol, thus leading to the prediction of the transesterification behavior of mixed triglycerides in the supercritical state. Thermodynamic studies have proven particularly useful for predicting the reaction equilibria and evaluating the thermodynamic feasibility of a given process. However, to date, there have been virtually no thermodynamic investigations of the transesterification of triglycerides with supercritical ethanol or isopropanol. Very few reports are available to thermodynamically justify the selection of methanol as the most suitable alcohol for transesterification with triglycerides. The intention of this study is to investigate the differences between the main three transesterification reaction systems, triolein and supercritical methanol (T&SCM), triolein and supercritical ethanol (T&SCE), and triolein and supercritical isopropanol (T&SCI), using thermodynamic analysis. Additionally, this work intends to explain why methanol has conventionally been selected as the appropriate alcohol for biodiesel production and how the equilibrium constant for the

1. INTRODUCTION Continued use of petroleum-based fuels is now widely recognized as unsustainable, because of diminishing supplies and the contribution of these fuels to the accumulation of carbon dioxide in the environment.1 Biodiesel, produced from renewable resources, is becoming more attractive due to its positive environmental benefits.2,3 This fuel is sustainable, biodegradable, nontoxic, and generates lower emissions in comparison with petroleum-based diesel. The consumption of biodiesel will promote the balance sought between agriculture, economic development, and the environment.4−6 Conventional biodiesel synthesis technologies include direct use, blending, microemulsification, and pyrolysis. There remain some limitations associated with all of these processes, thus current research in the field is focused on overcoming these shortcomings by developing alternative production methods. Transesterification using supercritical fluids, which needs no catalysts, is a new and highly attractive approach to biodiesel production. It is insensitive to water or free fatty acids (FFA) in the feedstock, requires relatively short reaction time, and results in a relatively high ester conversion yield.7−9 From a previous comparative study on transesterification methods for the production of biodiesel reported in the literature,10 triglyceride transesterification using supercritical lower alcohols, such as methanol, ethanol, and propanol, has proven to be the most promising process. The alcohol is selected in this process with cost and performance in mind. Among the common alcohols, methanol is used commercially, due in part, to its low cost and its physical and chemical attributes (highly polar molecule with shortest aliphatic moiety).11−13 However, ethanol produced from renewable agricultural resources is worthy of consideration in light of its relative independence from petroleum-based sources. Ethanol is also more miscible with oils than methanol, which adds to its appeal.14 © 2014 American Chemical Society

Received: Revised: Accepted: Published: 7209

May 7, 2013 April 1, 2014 April 8, 2014 April 8, 2014 dx.doi.org/10.1021/ie402811n | Ind. Eng. Chem. Res. 2014, 53, 7209−7216

Industrial & Engineering Chemistry Research

Article

Table 1. Calculated Critical Temperatures and Pressures for Triolein by Various Methods methods parameter

literature data

Tc, K

947.1

27

cal. % error cal. % error

0.468227

Pc, MPa

Lydersen

Joback

GANI

3439.8 263.19 0.4700 0.38

2663.3 181.21 0.2359 −49.62

926.6 −2.16 0.3259 −30.39

Table 2. Critical Parameters, Boiling Temperature and Acentric Factor of Compounds Used for Calculations compound

formula

formula weight

Tc, K

pc, MPa

Tb, K

ω

T D M MeOL EtOL IpOL G MeOH EtOH IPA

C57H104O6 C39H72O5 C21H40O4 C19H36O2 C20H38O2 C21H40O2 C3H8O3 CH4O C2H6O C3H8O

885.4 621.0 356.5 296.5 310.5 324.5 92.1 32.0 46.1 60.1

926.6, 946.028 870.4, 870.028 804.8, 800.028 734.5 732.5 737.7 850.025 512.525 514.025 508.325

0.47, 0.4628 0.68, 0.8728 1.24, 1.2928 1.15, 1.1328 1.23,1.1020 1.18, 1.0120 7.525 8.125 6.125 5.225

819.6, 85428 759.4, 75728 676.0, 66028 595.9 605.9 610.6 563.225 337.925 351.425 355.425

0.982, 0.8323 1.499, 1.6828 1.962 1.840 1.864 1.841 1.32025 0.56625 0.63725 0.66925

were calculated using the Ambrose method with an average relative error of approximately 4.6%, which is higher than the results by the methods of Lydersen and Joback. Therefore, the GANI method for Tc and the Lydersen method for Pc were chosen to estimate the critical values for all of the system’s reactants. In a similar manner, the normal boiling point and the acentric factor of the reaction materials were predicted using the GANI method and the CSGC-AF method, respectively. Compared with the literature data, the obtained data (shown in Table 2) show little deviation, indicating that the calculation methods are accurate and feasible. Those critical parameters have enriched the thermodynamic database of biodiesel production and are valuable to estimate the transesterification experiments conditions with supercritical alcohols in further research.

transesterification reaction varies with the number of carbon atoms in alcohols. Triolein, which is the major constituent of triglycerides containing similar fatty acid residues, was chosen for the threestepwise transesterification reactions with three alcohols (methanol, ethanol and isopropanol) in the supercritical state. In this condition, di- and monoolein are formed as intermediates.24 The three reaction systems can be generally represented by eq 1: step 1: T + A ⇌ D + E step 2: D + A ⇌ M + E step 3: M + A ⇌ G + E

(1)

where A denotes methanol, ethanol, or isopropanol, respectively; and E denotes MeOL, EtOL, or IpOL, respectively.

3. CALCULATION OF STANDARD FORMATION ENTHALPY, ENTROPY AND THE HEAT CAPACITY VALUES BASED ON TEMPERATURE Most of the published studies have shown that the reaction temperature is the foremost parameter to influence the extent of the transesterification reaction for biodiesel production, especially in the region above the critical temperature of methanol (514.0 K),29 while the influence of pressure is not as significant as that of temperature. Fang et al.15 reported the phase equilibrium data for the mixtures of supercritical methanol + C18 methyl esters and observed that the binary system became homogeneous at pressures a little higher than the critical pressure of methanol (8.09 MPa). The analogous conclusion was obtained from the vapor−liquid equilibria data for methanol + methyl laurate and methanol + methyl myristate systems.30 The particular phase behavior indicates that, at the supercritical state, pressure has little influence on the improvement of the fatty acid methyl esters yield. Therefore, in this study, the thermodynamic properties are calculated based upon the most relevant factor for analysis, temperature. 3.1. Calculation of Standard Values of the Formation Enthalpy and Entropy in the Gas State. To obtain the chemical equilibrium constant for any chemical reaction, it is necessary to calculate the values of the three required

2. CALCULATION OF THERMODYNAMIC PARAMETERS FOR INDIVIDUAL COMPOUNDS To conduct the thermodynamic analysis of the designated reactions, the basic thermodynamic parameters of each component involved in the transesterification must be estimated using an appropriate method. The thermodynamic data for methanol, ethanol, isopropanol, and glycerol are available.25 However, the parameters for the other six components were absent from the literature and need to be calculated using the proper methods. To select the suitable method, the critical temperatures and pressures for triolein were calculated and compared using different group methods, including the Lydersen, Joback, and GANI methods.26 The results are listed in Table 1. The critical temperature, Tc, was calculated by the GANI method which provides both a first-order approximation and a more accurate second-order prediction with the smallest average relative error (0.85%). The critical pressure, Pc, was calculated by the Lydersen method (one of the earliest successful methods to estimate the critical parameters with an average error lower than 2%). These two methods obtained the closest values to those reported in literature. The reported data 7210

dx.doi.org/10.1021/ie402811n | Ind. Eng. Chem. Res. 2014, 53, 7209−7216


Article

Table 3. Calculated Standard Enthalpy and Entropy of the Formation for All Compounds component

ΔHθf 298.15(g) (kJ mol−1)

ΔHθv (kJ·mol−1)

ΔHθf 298.15 (l) (kJ·mol−1)

Sθ298.15 (g) (J·mol−1 K−1)

Sθv (J·mol−1·K−1)

Sθ298.15(l) (J·mol−1·K−1)


−1843.30 −1420.00 −995.45 −649.9025 −658.10 −697.10 −582.8025 −201.5025 −234.0025 −272.4025

285.77 222.69 151.86 84.625 65.44 66.83 85.8025 37.6025 42.7025 45.3025

−2129.07 −1651.79 −1147.31 −734.5025 −721.68 −761.30 −688.5225 −239.1025 −276.9825 −317.8625

2548.80 1832.80 1122.60 955.67 996.67 1027.80 400.90 239.8825 280.6425 309.2025

142.99 138.84 132.50 125.63 126.54 126.96 196.43 112.64 119.60 128.62

2405.81 1693.96 990.10 830.04 870.13 900.84 204.4725 127.2425 161.0425 180.5825

thermodynamic properties: the formation enthalpy, entropy, and Gibbs free energy. As few researchers have shown interest in the subject reaction systems, the related thermodynamic parameters have not been reported in literature, with the exception of alcohols, glycerol and methyl oleate. In this work, the Benson’s Group Method31 was employed to estimate the standard values of the Formation Enthalpy and Entropy at 298.15 K: θ Δf H298.15 (g) =

∑

θ niΔf H298.15, i

i θ S298.15 (g ) =

∑

θ niS298.15, i − R ln σ + R ln η

i

Table 4. Calculated Coefficients in the Temperature Dependence of the Constant-Pressure Heat Capacity: CpL = A + BT + CT2/(J·mol−1·K−1)

(2)

(3)

The calculated values of standard enthalpy and entropy of the formation for the ten substances of interest are listed in Table 3. 3.2. Calculation of Standard Values of the Formation Enthalpy and Entropy in the Liquid State. To calculate the standard values of the formation enthalpy and entropy in the liquid state, the standard values of the vaporization entropy were first evaluated using Zhao’s empirical formula,32 as shown in eq 4, where the empirical constants a and b are 125.4 J mol−1·K−1 and −222.376 J·mol−1·K−1, respectively. The standard values of the vaporization enthalpy were calculated using the GANI method. After that, the standard values of the formation enthalpy and entropy in liquid state were obtained by eqs 5 and 6 below. The final results are shown in Table 3. ΔSvθ = a lgTb + b(J·mol−1·K−1)

(4)

ΔH θf (l) = ΔH θf (g ) − ΔHvθ

(5)

θ θ S298.15 (l) = S298.15 (g ) − Svθ

(6)

component

A

B

C × 103


1475.0791 1105.3142 735.5490 509.4171 521.5520 549.5995 365.7840 7.2703 6.3610 3.7702

−0.7072 −1.2734 −1.8397 −0.3055 −0.1836 −0.3010 −2.4060 0.1328 0.2278 0.3287

5.8483 6.1244 6.4005 2.0693 1.8436 2.2179 6.6766 −0.0610 −0.1154 −0.1730

θ Δr H298.15 = θ Δr S298.15 =

∑ ∑

θ vBΔf H298.15 θ vBS298.15

(7) (8)

The standard Gibbs free energy change in every chemical reaction is defined by eq 9, and the equilibrium constant for each reaction step is calculated directly by eq 10: θ θ θ Δr G298.15 = Δr H298.15 − T Δr S298.15

K θ(T ) = exp[−Δr G θ (T )/RT ]

(9) (10)

The changes in enthalpy, entropy, Gibbs free energy and the corresponding values of the equilibrium constant for each step of the triolein transesterification with three different alcohols are shown in Table 5. As shown in Table 5, for the triolein and methanol reaction system, the enthalpy changes of the first and third steps of the transesterification are −18.12 kJ·mol−1 and −36.61 kJ·mol−1, respectively, indicating that these reactions are slightly exothermic. The enthalpy change of the second step of the transesterification is low and positive, indicating a slightly endothermic reaction. The changes in Gibbs free energy for the three reaction steps are similar to the enthalpy changes. Although in the first and third reaction steps, ΔG < 0, the equilibrium position of the reaction corresponds to the presence of more product than reactants at equilibrium. The chemical equilibrium constant for each reaction step is so low that significantly energetic conditions are required to promote the reaction, as illustrated by the spontaneity and the extent of triolein transesterification with methanol at 298.15 K. For the other two reaction systems, the enthalpy change of each reaction step is greater than zero but less than 60 kJ·mol−1, indicating that each reaction step is slightly endothermic. The

3.3. Calculation Coefficients of the Constant-Pressure Heat Capacity in the Liquid State. In these systems, because the process pressure is constant and the main reaction phase is liquid, the constant-pressure heat capacity CpL in dependence on temperature were calculated by RozickaDomalski method33 and are shown in Table 4.

4. CALCULATION OF GIBBS FREE ENERGY AND CHEMICAL EQUILIBRIUM CONSTANT 4.1. Calculation of Standard Values of Gibbs free energy and Chemical Equilibrium Constant for Each Reaction Step at 298.15 K. The enthalpy and entropy change of each reaction step can be evaluated using the standard values of the formation enthalpy and entropy at 298.15 K in the familiar expression: 7211



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Table 5. Changes in Enthalpy, Entropy, Gibbs free energy and the Corresponding Values of the Equilibrium Constant for Each Individual Step of Triolein Transesterification Reaction at 298.15 K reaction

ΔrHθ298.15 (kJ·mol−1)

ΔrSθ298.15 (J·mol−1 K−1)

ΔrGθ298.15 (kJ·mol−1)

M1 M2 M3 E1 E2 E3 I1 I2 I3

−18.12 9.08 −36.61 32.58 59.78 14.09 33.84 61.04 15.35

−9.05 −1.06 −82.83 −2.76 5.23 −76.54 8.41 16.40 −65.37

−15.42 9.40 −11.91 33.40 58.22 36.91 31.33 56.15 34.84

K 5.03 2.26 1.22 1.41 6.30 3.41 3.24 1.45 7.87

× × × × × × × × ×

composition of equilibrium mixture 102 10−2 102 10−6 10−11 10−7 10−6 10−10 10−7

products dominate reactants dominate products dominate negligible products

Table 6. Changes in Enthalpy, Entropy, Gibbs Free Energy and the Corresponding Values of the Equilibrium Constant for Each Overall Triolein Transesterification System at 298.15 K reaction system

ΔrHθ298.15 (kJ·mol−1)

ΔrSθ298.15 (J·mol−1·K−1)

ΔrGθ298.15 (kJ·mol−1)

K

overall-1 overall-2 overall-3

−45.65 106.45 110.23

−92.94 −74.07 −40.56

−17.94 128.53 122.32

1.39 × 103 3.03 × 10−23 3.71 × 10−22

⎡ Δ r H θ (T ) = ⎢ ⎣

results verified the fact that the reaction heat of transesterification is small at room temperature. The Gibbs free energy of each reaction step is positive, and the chemical equilibrium constant is so minimal that it can be neglected. 4.2. Calculating Standard Values of Gibbs free energy and Chemical Equilibrium Constant for the overall reaction at 298.15 K. To verify the validity and compare with the stepwise transesterification results with different alcohols, the standard values of Gibbs free energy and chemical equilibrium constants for the overall reaction were calculated at 298.15 K. As well-known, the three-step transesterification reaction expressed by eq 1 can be integrated into a one-step reaction. Thus, the three reaction systems with different alcohols can be represented as follows:

T

⎤

θ ∫298.15K ∑ vBCpL ,B⎥⎦dT + Δr H298.15 K

(12)

The Gibbs free energy at temperature T can be derived from the Gibbs−Helmholtz equation (eq 13). Similarly, ln K at temperature T can be derived from the Van’t Hoff Isochore (eq 14). ⎡ ∂(ΔG θ /T ) ⎤ ΔH θ ⎥ =− 2 ⎢ ∂T T ⎦ ⎣

(13)

⎡ ∂ln K ⎤ ΔH θ ⎢⎣ ⎥⎦ = ∂T P RT 2

(14)

P

overall − 1: T + 3MeOH ⇌ 3E + G

5. RESULTS AND DISCUSSION The relationships of ΔH−T, ΔG−T, and ln K−T for each reaction step were calculated and are depicted in Figures 1, 2, and 3, respectively. From 300 to 700 K, the enthalpy appears to increase. For T&SCE and T&SCI, the enthalpy of each transesterification step is positive. However, for T&SCM, the enthalpy for each transesterification step became positive for T > 545.31 K (in the supercritical methanol region). At high temperatures, the reaction equilibrium is displaced in the direction of higher concentrations of esters. Thus, an increase in temperature over the supercritical alcohol region leads to a rise in the ester yield. It can be seen from Figure 2 that, for T > 563.37 K, the Gibbs free energy of each transesterification step for T&SCM is negative, so each reaction step can proceed spontaneously. Unfortunately, for the other two reaction systems, i.e., T&SCE and T&SCI, the Gibbs free energy is positive in each reaction step. Consequently, it is necessary to provide additional external energy for these systems to make them function. The systems’ comparison based on the thermodynamic considerations illustrates that only supercritical methanol can react with triolein to form methyl esters under favorable reaction conditions, making it more attractive to industrial scale-up. In the integrated form of eq 14 (assumes that ΔH is independent of temperature),

overall − 2: T + 3EtOH ⇌ 3E + G overall − 3: T + 3IPA ⇌ 3E + G

(11)

The changes in enthalpy, entropy, Gibbs free energy, and the equilibrium constant for the three overall reaction systems under the standard conditions are shown in Table 6. From the results of the three overall reaction systems, it is obvious that the changes in enthalpy and Gibbs free energy for triolein transesterification with methanol is negative, whereas the other two reaction systems are both positive. The results indicate that only the transesterification between triolein and methanol is exothermic and can proceed spontaneously at 298.15 K. The equilibrium constant for each overall reaction system shows the similar tendency as the stepwise reaction calculation. As the overall reaction calculation results have a high coherence with the stepwise ones, they indicate that ethanol and isopropanol are not commonly used in making biodiesel due to the lower reactivity in comparison to methanol. Therefore, methanol is clearly demonstrated as the most suitable alcohol for biodiesel production via transesterification. 4.3. Calculating the Standard Values of Gibbs Free Energy and Chemical Equilibrium Constant dependence on Temperature. According to the data in Table 4, the enthalpy of each reaction step at temperature T can be related to the values at 298.15 K by integration of eq 12 to obtain, 7212



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Figure 1. Temperature dependences of the enthalpy for each transesterification step corresponding to the number of the reactions from set (1).

ln

Δ H θ (T − T1) K2 = r m· 2 K1 R TT 1 2

Figure 2. Temperature dependences on the Gibbs free energy of each transesterification step corresponding to the number of the reactions from set (1).

(15)

K decreases inversely with temperature and vice versa for an exothermic reaction. In this work, for T > 563.37 K, the 7213



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Hanh et al.34 investigated the triolein transesterification with various alcohols in an ultrasonic field. The results confirmed that the rate of the ester formation depends upon the type of alcohol used, where the greater the number of carbon atoms in alcohol becomes, the slower the rate of reaction becomes. In addition, it was suggested that the steric hindrance of secondary alcohols, such as isopropanol, isobutanol, and isohexanol strongly affects the transesterification of triolein, leading to minimal ester conversion. Chen et al.35 studied the reaction processes and the mechanism of supercritical transesterification using in situ ATR infrared spectroscopy. The results showed that for T > 498.15 K, the vibrating peaks of hydroxyl group of methanol split, which was not found to be the case with ethanol and propanol. The new vibration form C+...O...H+, which strengthens the electrophilicity and the nucleophilicity of methanol, should be the main reason for accelerating the rate of T&SCM supercritical transesterification. The results obtained in this study agree well with the conclusions reported in literature. Comparison of this work with the published reports shows that the group-contribution analysis method is feasible for analyzing the chemical equilibrium and the feasibility of triolein transesterification with supercritical lower alcohols.

6. CONCLUSIONS A comparative study of three transesterification reaction systems-T&SCM, T&SCE, and T&SCI was conducted using thermodynamic analysis. The related properties of triolein, diolein, monoolein, methanol, ethanol, isopropanol, methyl oleate, ethyl oleate, isopropyl oleate, and glycerol involved in transesterification were calculated. The standard values of enthalpy and entropy for the ten individual compounds were obtained via the Benson’s Group Method. In addition, the constant-pressure heat capacity was calculated using the Rozicka−Domalski method. The satisfactory agreement between the calculated data of this work and those in literature28 proved that the methods employed here are feasible for property estimation. The obtained data further enhance the thermodynamic database of biodiesel production. The chemical equilibria in transesterification of T&SCM, T&SCE, and T&SCI were studied in detail. The diagrams of ΔH-T, ΔG -T, and ln K-T for the reaction systems were constructed in the supercritical temperature range. The results illustrated that only triolein transesterification using supercritical methanol can proceed under the proper reaction conditions and that the transesterification reaction rarely occurs when the alcohol reactant is changed from methanol to either ethanol or isopropanol. This study provided a reliable thermodynamic method for analyzing other related reaction systems in the production of biodiesel fuel.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 0086-2982664375. Fax: 0086-2982255509. E-mail: [email protected].

Figure 3. Temperature dependences on lnK of each transesterification step corresponding to the numbers of the reactions from set (1).

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

chemical equilibrium constant of the transesterification steps for all three systems increases directly with increasing temperature, thus promoting the forward rate of reaction.

Notes

The authors declare no competing financial interest. 7214



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Article

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ACKNOWLEDGMENTS The authors would like to acknowledge the following financial supports: National Natural Science Foundation of China (No. 21376186), the Ministry of Education (Doctoral Special Research Foundation No. 20110201110032), China and the Fundamental Research Funds for the Central Universities (New Teacher Research Support Plan No. 08141002 and International Cooperation Project No. 2011jdhz37 and Integrated Cross Project xjj2014136 in Xi’an Jiaotong University), Natural Science Basic Research Plan in Shaanxi Province of China (No. 2012JM2010), and the Ministry of Human Resources and Social Security of China (Sci. & Tech. Project for Overseas Scholars, No. 19900001).

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ABBREVIATIONS

A = alcohol D = diolein E = esters EtOH = ethanol EtOL = ethyl oleate G = glycerol IPA = isopropanol IpOL = isopropyl oleate M = monoolein MeOH = methanol MeOL = methyl oleate T = triolein

Notations

K1 equilibrium constants at T1 K2 equilibrium constants at T2 R ideal gas constant (J mol−1 K−1) T temperature (K) P pressure (MPa) CpL,B constant-pressure heat capacity of component B (J mol−1 K−1) a i ,b i ,d i contributed values of heat capacity for the corresponding groups ni number of group ι ́ vB stoichiometric coefficient of component B Greek Letters

σ symmetry number η number of optical isomers Superscript

θ standard state Subscript

b boiling point c critical point f formation i structural group r reaction

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REFERENCES

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