Thermochemical properties estimation for biodiesel related mixtures

Daniela de Freitas Borghi1, Charlles Rubber de Almeida Abreu

2, Reginaldo Guirardello

3

1,3 LSOPQ Department of Chemical Process, School of Chemical Engineering, State University of

Campinas, UNICAMP 13083-970, Campinas SP, Brazil email address: dani_borghi@yahoo.com.br 2 Chemical School, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

Currently, biodiesel production has been studied in several countries due to the imminent

exhaust of oil resources and because of the characteristics of biodiesel, which is a fuel with environmental

advantages regarding the emission of pollutant gases. Brazil is a large producer of soybeans and ethanol,

which gives the country a great potential to become reference as a producer of ethylic soybean biodiesel.

However, data on thermochemical properties of compounds present in the biodiesel production process

are rarely available. Within this context, the present work aimed to obtain standard enthalpies of

formation at 298.15 K (fH0

298.15K(g)), ideal gas heat capacities (Cp), entropies (S) and sigma profiles of

biodiesel-related compounds.To obtain the gas phase properties, a methodology described in the literature

(Osmont et al., 2007) was applied, in which the ab initio method B3LYP/6-31G (d, p) and the Gaussian

03 software were employed. In addition, the software MOPAC was used to generate the sigma profiles

for these molecules to be used directly in the COSMO-SAC model. In the method used, the correlation

between experimental standard enthalpies of formation at 298.15 K and those calculated by the

methodology employed here has been very good. Therefore, the thermochemical data obtained in this

study may be useful for carrying out phase equilibrium calculations with application to the biodiesel

production process. The compounds considered in the present work were glycerol, dodecanoic acid,

palmitic acid, stearic acid, oleic acid, linoleic acid, linolenic acid, oleic acid monoester, oleic acid diester,

oleic acid triester, and methyl oleate.

Keywords: biodiesel, thermochemical properties, Gaussian 03, sigma profile, COSMO-SAC

1. Introduction

Brazil consumes 40 billion liters of diesel annually and needs to import a large portion of this amount

(Suarez and Meneghetti, 2007). As the country was unable to fill the growing demand for diesel in recent

years, the search for new fuels to replace petroleum diesel has been explored (Meher et al., 2006).

Biodiesel is one of the leading alternatives to fossil fuels and one of its advantages is the release of 78%

less carbon dioxide than diesel (Jamrz et al., 2007). The country, as a large producer of soybeans and

ethanol, has great potential to become a reference as ethylic soybean biodiesel producer (Ferrari et al.,

2005).

Biodiesel made from vegetable oils has been extensively studied in recent years, but despite the progress

already achieved in the research and development of biodiesel production processes, thermochemical data

of the related compounds are still rarely available in the literature.

With the advances in computational chemistry, a priori predictions of phase equilibrium of mixtures

without any experimental data are becoming possible. While classical group contribution estimation

methods may provide robust predictions, the quantum mechanical methods present a viable, although less

reliable, alternative to estimate the phase behaviour with no requirements on extensive experimental data

(Wang et al., 2009).

The conductor-like screening model for real solvent (COSMO-RS), first proposed by Klampt and co-

workers (1993), utilize the results of quantum mechanical solvation calculations and satisfactorily

describes the phase equilibrium of a mixture without any experimental data (Yang et al. 2010). Later, Lin

and Sandler (2002) developed a COSMO segment activity coefficient model (COSMO-SAC), a variant of

COSMO-RS method. In COSMO-based models, the activity coefficient of a component in liquid mixture

is determined by considering the molecular surface interactions which are assumed to be dominated by

local electrostatic interactions. Klamt proposed that the electrostatic energy of contacting surfaces was

approximated using the screening charges on the molecule surface when the molecule is in a perfect

conductor (the calculations to generate sigma-profiles) (Wang, et al., 2009).

The aim of this paper is to obtain thermochemical properties of biodiesel-related compounds by means of

methods described in the literature, using the Gaussian 03 software to obtain ideal-gas properties and to

generate the sigma profiles, needed in COSMO-based models, for the molecules of glycerol, dodecanoic

acid, palmitic acid, stearic acid, oleic acid, linoleic acid, linolenic acid, oleic acid monoester, oleic acid

diester, oleic acid triester, and methyl oleate.

2. Method

The standard enthalpies of formation at 298.15 K, heat capacities and entropies of the gas-phase can be

obtained by an Ab initio B3LYP/6-31G (d, p) method, using an atomization approach, developed by

Osmont et al. (2007), using the quantum chemistry package Gaussian 03. The model used includes zero-

point energy and atomic number corrections.

Three atomic corrections are derived for atomic molecules: one for hydrogen atoms, one for carbon

atoms, and one for oxygen atoms. In this method, there is no distinction between oxygen atoms. The

corrections to be applied to an oxygen atom in a carbonyl group, in a hydroxyl group, or in an ether bond

are the same. The same holds for carbon atoms involved in single bonds or in double bonds.

The atomic corrections c*i are given in Table 1.

Table 1.Atomic corrections c*i used in this study

Atom c*i (hartree tom-1)

H 0.581896

C 38.115345

O 75.150410

Osmont et al. (2007)

The gas-phase standard enthalpy of formation of molecule j at 298.15K can be determined by:

(1)

where i is the number of atoms of type i in molecule j and c*i the atomic correction for an atom of type i.

Ej and ZPEj denote, respectively, the electronic energy and the zero-point energy, both calculated using

the Gaussian 03 software. fH0

298.15K(g) is in kcal mol-1.

Prior to the energy calculations, it is necessary to perform the molecule geometry optimization, also using

the Gaussian 03 software.

Typically, a model based on COSMO methods requires data on the charge distribution on the surface of a

molecule immersed in a perfect conductor, known as the sigma profile. In this work, we used the

Gaussian 03 to optimize the structure of some molecules of the biodiesel production process and the

standalone program provided by the Virginia Tech group (at http://www.design.che.vt.edu/VT-

Databases.html) free on the web is used to generate the sigma profile from the output of MOPAC

calculation for these molecules. The output file of MOPAC calculation contains the 3D coordinates,

segment charge, segment area and charge/area of the molecule. These profiles are intended to be used

directly in the COSMO-SAC model. The results were compared to the VT sigma profile database

(Mullins, et al., 2006) when available.

3. Results and Discussion

Gaussian jobs are normally very time-consuming and they often need to run for weeks and consume hundreds of CPU hours. Molecular geometry optimization was the

calculation that spent more computational time in this work since the calculations were performed several times, once for each possible molecule structure. For instance, the

total CPU time spent for the geometry optimization of oleic acid, adding up all the tested possibilities, was 3312900 seconds (38 days, 8 hours, and 15 minutes).

Table 2 shows the CPU time spent in the calculations of fH0298.15K(g), Cp and S in Gaussian 03.

Table 2. CPU time (in seconds) of fH0

298.15K(g), Cp and S calculations.

Temperature (K)

Compounds 298.15 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Glycerol 2759 861 838 845 840 837 836 839 862 839 839 839 837

Dodecanoic Acid 51256 48168 9366 10737 9185 9310 9138 9343 9225 8975 10775 9214 8975

Palmitic Acid 20825 20802 20595 20293 20351 20826 20537 20394 20566 20548 20447 20493 20753

Linolenic Acid 19738 23538 19191 19785 20142 20335 19980 19690 19641 20073 20433 19679 20223

Linoleic Acid 20750 20787 20928 21287 21021 20861 20838 21105 21066 20569 20465 20912 21074

Oleic Acid 29869 29775 30192 30004 31976 29923 30549 30504 29969 29875 30036 30792 30323

Stearic Acid 38530 30177 30208 29691 30245 30308 29939 30582 30087 24581 26516 23326 23988

Methyl Oleate 72640 71002 70765 71913 72638 72411 71305 71814 73606 73057 73036 73473 74432

Oleic Acid Monoester 45508 45771 45673 46028 45549 46466 46955 46215 46033 46471 47470 46558 46755

Oleic Acid Diester 141683 158178 165637 165950 160826 138109 138196 143060 135603 147777 140101 142337 138341

Figure 1 presents an example of part of Gaussian 03 output file showing the Cv, S and sum of electronic

and thermal enthalpies (represented in equation (1) by ).

Figure 1: example of part of Gaussian 03 output file.

Table 3 shows the standard enthalpies of formation at 298.15K obtained in the present work.

Table 3. Calculated standard enthalpies of formation at 298.15K.

Compound Name

C3H8O3 Glycerol -132.1

C12H24O2 Dodecanoic acid -151.3

C16H32O2 Palmitic acid -170.1

C18H30O2 Linolenic acid -93.6

C18H32O2 Linoleic acid -122.3

C18H34O2 Oleic acid -150.1

C18H36O2 Stearic acid -179.5

C19H36O2 Methyl Oleate -148.8

C21H40O4 Oleic Acid Monoester -101.2

C39H72O5 Oleic Acid Diester -328.6

Values of

are in kcal mol-1

.

As showed by Osmont et al. (2007), the correlation between the experimental standard enthalpies of

formation at 298.15 K and the values they calculated using their methodology was very good (mean

average deviation of 1.8 kcal mol-1).

The method described by Osmont et al. (2007) is general, since it incorporates only three atomic

corrections and can be applied to any molecule containing C, H, and O.

The calculated heat capacities (Cp) and entropies (S) data of the compounds are shown in Tables 4 and 5, respectively, in a wide temperature range from 298.15 to 1400K. No

experimental data are available to be compared with the calculated data.

Table 4. Calculated Cp (cal mol-1 K-1)in the temperature range from 298.15 to1400K.

Temperature (K)

Compounds 298.15 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Glycerol 27.4 27.5 34.1 40.1 45.0 49.2 52.6 55.6 58.1 60.3 62.2 63.9 65.4

Dodecanoic Acid 64.7 65.0 84.1 102.0 117.3 130.3 141.3 150.7 158.8 165.8 171.9 177.1 181.7

Palmitic Acid 84.0 84.5 109.9 133.6 154.0 171.3 186.0 198.6 209.4 218.7 226.8 233.8 239.8

Linolenic Acid 89.3 89.8 115.6 139.2 159.2 176.0 190.3 202.4 212.8 221.8 229.5 236.2 242.0

Linoleic Acid 90.9 91.4 118.0 142.7 163.7 181.4 196.4 209.2 220.2 229.6 237.8 244.9 251.0

Oleic Acid 92.2 92.7 120.4 146.0 168.0 186.6 202.4 215.8 227.4 237.4 246.0 253.5 260.0

Stearic Acid 93.7 94.2 122.7 149.4 172.3 191.8 208.3 222.5 234.7 245.2 254.2 262.1 270.0

Methyl Oleate 97.6 98.1 126.8 153.7 177.0 196.7 213.4 227.7 240.0 250.6 259.7 267.7 274.6

Oleic Acid Monoester 78.9 79.5 113.0 143.1 168.0 188.5 205.6 220.2 232.8 243.8 253.3 261.8 269.1

Oleic Acid Diester 201.3 202.4 262.6 318.3 366.0 406.2 440.2 469.3 494.1 515.6 534.0 550.0 564.0

Table 5.Calculated S (cal mol-1 K-1)in the temperature range from 298.15 to 1400 K.

Temperature (K)

Compounds 298.15 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

Glycerol 82.0 82.2 91.0 99.3 107.1 114.3 121.1 127.5 133.5 139.1 144.5 149.5 154.3

Dodecanoic Acid 142.3 142.7 164.1 184.8 204.8 223.9 242.0 259.2 275.5 291.0 305.7 319.7 333.0

Palmitic Acid 171.5 172.0 199.8 226.9 253.1 278.2 302.0 324.7 346.2 366.6 386.0 404.4 422.0

Linolenic Acid 182.6 183.1 212.5 240.9 268.1 293.9 318.4 341.5 363.4 384.1 403.8 422.4 440.1

Linoleic Acid 185.5 186.0 216.0 245.0 273.0 299.6 324.8 348.7 371.3 392.7 413.1 432.4 450.8

Oleic Acid 186.4 187.0 217.4 247.1 275.7 303.1 329.1 353.7 377.0 399.2 420.2 440.2 459.2

Stearic Acid 186.0 186.6 217.6 247.9 277.2 305.3 332.0 357.4 381.5 404.4 426.1 446.8 437.4

Methyl Oleate 195.1 195.7 277.8 259.1 289.2 318.0 345.4 371.4 396.0 419.4 441.6 462.7 482.8

Oleic Acid Monoester 139.5 140.0 167.5 196.0 224.4 251.9 278.2 303.3 327.1 349.8 371.5 392.1 411.8

Oleic Acid Diester 343.6 344.9 411.3 476.0 538.4 597.9 654.5 708.0 758.8 806.9 852.6 896.0 937.3

In this study, no corrections of Cp and S values using the tables of Pitzer and Gwinn (1942) were performed, as done in the paper of Osmont et al. (2007). For heat capacities,

the neglect of these corrections leads to an underestimation of the Cp from 300 to 500 K and then to an overestimation of Cp. This overestimation increases with the size of

the molecule and with the temperature. According to Osmont, et al. (2007), it ranges from 6 to 12 cal mol-1 K-1, depending on the size of the molecule, at 1000 K and from

about 9 to 19 cal mol-1 K-1, depending on the size of the molecule, at 2000 K. for entropy, the neglect of these corrections leads to an underestimation up to about 1500 K.

Sigma profiles obtained for water, glycerol, methanol, dodecanoic acid, palmitic acid, linolenic acid,

linoleic acid, oleic acid, stearic acid, methyl oleate, oleic acid monoester, oleic acid diester, and oleic acid

triester are shown bellow.

Figure 2. Sigma profiles of water, glycerol, methanol, and dodecanoic acid generated from MOPAC

program compared with the VT database (Mullins, et al., 2006).

Figure 2.(continued)

Figure 3. Sigma profiles of monoester oleic acid, diester oleic acid and triester oleic acid generated from

MOPAC.

Figure 2 shows that there are noticeable differences between sigma profiles generated with the different

methods. However, there is much similarity between them, for example, for methyl oleate, the sigma

profile from MOPAC starts from -0,004 e/2 and ends at 0,010 e/2, and from VT database starts from -

0,007 e/2 and ends at 0,013 e/2, a slight difference. The proximity of the peaks for most compounds is

another similarity between the methods. Wang et al. (2009) have similar results using the

GAMESS/COSMO package. According to the authors, the range of sigma profile is important because it

shows how polarized the molecule is, so similar range indicates that the polarization is similar between

the different sources. The positions and heights of peaks indicate detailed segmentation and are expected

to be different because the strategy of segmentation and the procedure of calculation are different from

one method to another.

Figure 3 shows the sigma profiles of monoester oleic acid, diester oleic acid and triester oleic acid

generated in this study. There is no literature data available of the sigma profile of these molecules to

compare with the results obtained here.

4. Conclusions

The present paper provides standard enthalpies of formation at 298.15 K (fH0298.15K(g)), heat capacities

(Cp), and entropies (S) of compounds normally present in the biodiesel production process using a

methodology described by Osmont et al. (2007). This method is sufficiently accurate and therefore the

thermochemical properties obtained here can be used, for example, to carry out calculations of phase

equilibrium conditions regarding the biodiesel production process.

We find that different methods used to obtain the sigma profile can result in significant differences in its

values. Despite this, the sigma profiles to be used in the COSMO-SAC model, generated in this study,

can be used to predict phase diagrams of mixtures involved in the biodiesel production.

Acknowledgments

The authors gratefully acknowledge the financial support of CAPES (Coordenao de Aperfeioamento

Pessoal de Nvel Superior).

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