Viscosities and viscosity deviations of binary mixtures of biodiesel + petrodiesel (or n-hexadecane) at different temperatures

Abstract

Viscosities of four binaries mixtures [soybean biodiesel + diesel oil (or n-hexadecane) and coconut biodiesel + diesel oil (or n-hexadecane)] have been determined at T = (293.15, 313.15, 333.15, 353.15, 373.15) K and atmospheric pressure over the entire composition range. Experimental data were fitted to the Andrade equation and the adjustable parameters and the standard deviations between experimental and calculated values were estimated. From the experimental data, the viscosity deviations, <img src="/img/revistas/bjce/v29n3/21e02.jpg" alt="" align="absmiddle" />, were calculated by using the Redlich - Kister polynomial equation. The comparison between experimental data determined in this work and four predictive methods used for the estimation of viscosities of biodiesel fuels (based on their fatty acid composition) is discussed.

Viscosity; Binary Mixtures; Biodiesel; Petrodiesel

THERMODYNAMICS

Viscosities and viscosity deviations of binary mixtures of biodiesel + petrodiesel (or n-hexadecane) at different temperatures

F. M. R. Mesquita^I; F. X. Feitosa^II; F. R. do Carmo^III; R. S. de Santiago-Aguiar^IV; H. B. de Sant'AnaV, ^*

^IGrupo de Pesquisa em Termofluidodinâmica Aplicada, Departamento de Engenharia Química, Centro de Tecnologia, Phone: + (55) (85) 3366-9611, Fax: + (55) (85) 3366-9610, Universidade Federal do Ceará,Campus do Pici, Bloco 709, CEP: 60455-760, Fortaleza - CE, Brazil. E-mail: [e-mail]

^IIGrupo de Pesquisa em Termofluidodinâmica Aplicada, Departamento de Engenharia Química, Centro de Tecnologia, Phone: + (55) (85) 3366-9611, Fax: + (55) (85) 3366-9610, Universidade Federal do Ceará,Campus do Pici, Bloco 709, CEP: 60455-760, Fortaleza - CE, Brazil. E-mail: [e-mail]

^IIIGrupo de Pesquisa em Termofluidodinâmica Aplicada, Departamento de Engenharia Química, Centro de Tecnologia, Phone: + (55) (85) 3366-9611, Fax: + (55) (85) 3366-9610, Universidade Federal do Ceará,Campus do Pici, Bloco 709, CEP: 60455-760, Fortaleza - CE, Brazil. E-mail: [e-mail]

^IVGrupo de Pesquisa em Termofluidodinâmica Aplicada, Departamento de Engenharia Química, Centro de Tecnologia, Phone: + (55) (85) 3366-9611, Fax: + (55) (85) 3366-9610, Universidade Federal do Ceará,Campus do Pici, Bloco 709, CEP: 60455-760, Fortaleza - CE, Brazil. E-mail: [e-mail]

^VGrupo de Pesquisa em Termofluidodinâmica Aplicada, Departamento de Engenharia Química, Centro de Tecnologia, Phone: + (55) (85) 3366-9611, Fax: + (55) (85) 3366-9610, Universidade Federal do Ceará,Campus do Pici, Bloco 709, CEP: 60455-760, Fortaleza - CE, Brazil. E-mail: [e-mail]

ABSTRACT

Viscosities of four binaries mixtures [soybean biodiesel + diesel oil (or n-hexadecane) and coconut biodiesel + diesel oil (or n-hexadecane)] have been determined at T = (293.15, 313.15, 333.15, 353.15, 373.15) K and atmospheric pressure over the entire composition range. Experimental data were fitted to the Andrade equation and the adjustable parameters and the standard deviations between experimental and calculated values were estimated. From the experimental data, the viscosity deviations,

, were calculated by using the Redlich - Kister polynomial equation. The comparison between experimental data determined in this work and four predictive methods used for the estimation of viscosities of biodiesel fuels (based on their fatty acid composition) is discussed.

Keywords: Viscosity; Binary Mixtures; Biodiesel; Petrodiesel.

INTRODUCTION

In recent years, the decreasing oil supply, associated with the objective of a clean energy economy, has become a major issue in the search for alternative energy sources. The search for alternative energy sources has led to the development of different technologies for fuel production from biomass, such as biodiesel.

Among the raw materials used in the production of biodiesel, vegetable oils from soybean seeds, palm trees and cotton seeds are widely used. Soybean seeds and coconut are the most commonly used raw materials for the production of biodiesel in Brazil (Boletim Mensal do Biodiesel/ANP, 2011). Biodiesel presents advantages related to its use to replace a proportion of petroleum diesel in compression ignition engines in order to achieve a significant emission reduction. In Brazil, since January 2010, 5% of biodiesel is used in commercial diesel oil (B5).

Biodiesel can be obtained by the transesterification reaction of vegetable oils or other materials largely composed of triacylglycerols, such as animal fats or used frying oils, with monohydric alcohols to give the corresponding mono-alkyl esters (Knothe and van Gerpen, 2009).

Because biodiesel is completely miscible with diesel oil, the blending of both fuels in any proportion is possible and recommended in order to improve fuel qualities. However, the differences in the chemical nature of biodiesel and diesel oil may cause differences in the physicochemical properties of the blend, affecting engine performance and pollutant emissions (Benjumea et al., 2008; Jha et al., 2008). For this reason, the major concerns when dealing with biodiesel + diesel oil mixtures are the knowledge of thermodynamics and transport properties, such as viscosity and its dependence on composition and temperature. It should also be mentioned that viscosity influences the atomization quality, the size of the fuel drops and the quality of combustion (Encinar et al., 2005; Tate et al., 2006).

In this context, the aim of this study is to investigate the viscosity behavior of four binary mixtures [soybean biodiesel + diesel oil (or n-hexadecane) and coconut biodiesel + diesel oil (or n-hexadecane)] at T = (293.15, 313.15, 333.15, 353.15, 373.15) K and atmospheric pressure. It is important to notice that, although hexadecane is a slightly larger molecule than the average for diesel oil, it is commonly used as a reference molecule for modeling diesel oil thermodynamic properties and usually used as a reference molecule in lumping procedures. For this reason, the viscosity of biodiesel (+ diesel oil or + n-hexadecane) mixtures was experimentally determined as previously done for density (Mesquita et al., 2011). From the experimental data, the viscosity deviations, , were derived. The models proposed by Yuan (Yuan et al., 2009), and Revised Yuan (Pratas et al., 2010) and do Carmo (do Carmo et al., 2012) were used in order to predict the viscosity data.

EXPERIMENTAL SECTION

Chemicals

N-Hexadecane obtained from Merck was used without further purification. Its mass fraction purity was greater than 99%, as confirmed by chromatographic analysis.

Diesel oil was kindly furnished by Lubrificantes e Derivados de Petróleo do Nordeste - LUBNOR, Petrobras S/A. This sample was characterized by determining its density, flash point, kinematic viscosity, distillation temperatures, and molecular weight. Diesel oil used in this study was distilled following the procedure established in ASTM D868. The diesel oil properties are presented in Table 1.

Biodiesel

In this study, commercial grade edible soybean and coconut oils were used for biodiesel production. Due to their low acidity number (less than 0.5 mg KOH g^-1), no pretreatment was needed. The biodiesel samples were obtained by alkaline-catalyzed (potassium methoxide, mass fraction (w) = 0.008) transesterification of soybean oil and coconut oil, respectively, using methanol (supplied from J.T. Baker) as the transesterification alcohol. Methanol in excess, volume fraction (φ) = 100%, was used in those reactions at a methanol/oil ratio of 1/6. The resulting phases of glycerine and esters were separated after 12 h of settling and the resulting ester phase was washed in three steps, as described in earlier works (Feitosa et al., 2010; Mesquita et al., 2011; Nogueira et al., 2010; Santos et al., 2009). The conversion of oil into biodiesel using this technique was greater than 98.2 ± 1.2%, for both biodiesels.

The basic properties of coconut biodiesel, soybean biodiesel and diesel oil are presented in Table 1. It is worth mentioning that the properties of the biodiesels are within the limits regulated by the USA (ASTM D 6751), European Union (EN 14214), and Brazil (ANP 42), in Standard Resolution No. 7 (Brazilian Regulatory Agency/ANP, 2011).

The chemical compositions of the oils, given as the equivalent fatty acid methyl esters (FAME) composition in terms of mass fraction (w), are presented in Table 2. This analysis was obtained by gas chromatography and it revealed that soybean biodiesel is mainly composed of linoleic (w = 0.5494), oleic (w = 0.2387), and palmitic (w = 0.1132) acids. Coconut biodiesel presented lauric acid (w = 0.3535), myristic acid (w = 0.1984), and oleic acid (w = 0.1430) as the constituents of highest concentration.

Biodiesel Characterization

The biodiesel samples were characterized according to the procedures and standards dictated by Standard Resolution No. 7 (Brazilian Regulatory Agency/ANP, 2011). The ester content was assayed using a Varian CP-3800 gas chromatography system with a FID (flame ionization detector). The detector temperature was set at 523.15 K and the injector temperature was set at 473.15 K. The separation column was CP WAX 52CB 30 m x 0.25 mm x 0.05 μm DB. The temperature was set at 483.15 K.

Viscosity Determination

Viscosities of the pure liquids and their binary mixtures were measured by using an Anton Paar SVM 3000 digital viscosimeter in a cell containing a tube filled with sample, which rotates at constant speed, as described elsewhere (Feitosa et al., 2010; Nogueira Jr. et al., 2010). The mixtures were prepared by mass using an electronic balance (Tecnal Mark 210 A). All biodiesel blends were prepared in the mass fraction range between w = (0.09 and 0.9), at 298.15 K. The balance has an uncertainty of 0.0001 g. It was ensured that the components were adequately mixed before being transferred to the viscosimeter by stirring the sample tube for about five minutes in a vortex apparatus. Viscosity measurements have an uncertainty of ± 0.35%. The temperature in the cell was regulated to ± 0.01 K. The uncertainty in mass fractions reported in this work is estimated to be lower than ± 1.8 × 10^-3.

Thermodynamic modeling

Viscosity

The Andrade equation was used for predicting n-hexadecane viscosity (Reid et al., 1987):

where A and B, characteristic parameters obtained by regression of experimental data, are: A = -4.643; B = 1700.00.

For biodiesel viscosity prediction, four models have been applied. The first model was the Yuan model (Yuan et al., 2009), with parameters specific for FAMES (Fatty Acid Methyl Esters). The second model used was the Yuan model with parameters revised by Pratas (Pratas et al., 2010). The equation for these models is:

where A, B and T₀ are characteristic parameters for each FAME, T is the temperature in K and is the viscosity in mPa. The parameters are shown in Table 3. These models first calculate the viscosity of FAMES, then calculate the biodiesel viscosity from the following equation:

where is the viscosity, x the mole fraction and the subscript "i" indicates the "ith" FAME in the biodiesel. The parameters used to calculate the viscosity of C6:0 were the same as those of C8:0, because characteristic parameters for C6:0 were not found in the literature.

The other models for calculating the biodiesel viscosity are based on the principle of corresponding states, as proposed by do Carmo et al. (2012) using one- and two-reference fluids, Equations (4) and (5), respectively.

where , (for i=1 or 2) and T_c, P_c and MW are the critical temperature, critical pressure and molecular weight, respectively. The subscript "mix" indicates these properties for the mixture (biodiesel). The subscripts "1" and "2" indicate the properties of reference fluids. The methyl esters used as reference fluids are: C18:1 for the one-reference fluid, and C12:0 and C18:1 for two-reference fluids. It is important to mention that, for viscosity prediction of reference fluids from the do Carmo models, the Yuan model was used, see Table 4.

Andrade's equation (Eq. (1)), as proposed by Reid et al. (1987), was used to represent the dynamic viscosity variation with temperature for biodiesel mixtures.

The viscosity deviation, Δη, was calculated from the experimental viscosity data by the Redlich - Kister polynomial equation (Eq. (6)), as proposed by Redlich and Kister (1987):

where is the viscosity deviation, w₁ is the mass fraction of component 1, k is the degree of the polynomial expansion, and A_j is a parameter.

Critical Properties

Several properties of methyl esters were estimated using the Marrero-Gani Method (Marrero and Gani, 2001): critical temperature (T_c), critical pressure (P_c), critical volume (V_c) and normal boiling temperature (T_nb). The acentric factor (ω) was estimated by the Constantinou-Gani method (Constantinou and Gani, 1994). For the estimation of biodiesel critical properties, the Lee-Kesler mixing rules were used, as recommended by Knapp et al. (1982). The explanation and justification for selecting each method can be seen in detail in do Carmo et al. (2012).

RESULTS AND DISCUSSION

Biodiesels and diesel oil have a multicomponent composition. Nevertheless, it was treated here as a pure pseudocomponent (e.g., the molecular weight of biodiesel was considered to be a weighted average in terms of mass fraction) and the mixtures as pseudobinary mixtures only for the purpose of parameter estimation.

The viscosity of coconut biodiesel was lower than that of diesel oil and other biodiesels, such as colza, soybean, cotton seed, and babassu (Feitosa et al., 2010; Nogueira Jr et al., 2010). According to Nakpong and Wootthikanokkhan (2010), this happens because of the presence of methyl esters of lower molecular weight (C12:0 and C14:0), compared to other biodiesels (see also Table 2).

The parameters (A and B) of Equation (6) and the regression coefficients (R²) are given in Table 5. The regression coefficient (R²) was better than 0.997.

Viscosity - temperature curves for pure fuels and several blends are shown in Figures 1 - 4. As can be seen from these figures, the viscosity variation with temperature is similar in the case of biodiesel, diesel oil (or n-hexadecane) and their blends.

Tables 6 and 7 present the measured viscosities (η) and the viscosity deviations (Δη) for the binary mixtures [coconut biodiesel + diesel oil (or n-hexadecane) and soybean biodiesel + diesel oil (or n-hexadecane)] at T = (293.15, 313.15, 333.15, 353.15, 373.15) K and atmospheric pressure, over the entire composition range.

The parameters A_j, of the Redlich - Kister polynomial Equation (Eq. (6)), obtained by fitting the equations to the experimental values with a least squares algorithm are given in Table 8, along with the standard deviations σ, defined as follows:

where represents the experimental viscosity deviation, is the calculated viscosity deviation, n is the number of experimental data and p the order of the related polynomial. The regression coefficient (R²) was better than 0.975 for all the studied systems, except for the coconut biodiesel + diesel oil system at T = 373.15 K, where the R² value was 0.826.

Figures 5 to 8 show the viscosity deviations, , calculated by using the Redlich - Kister polynomial equation, as described above. An interesting finding was that, for all systems and temperatures studied, the values presented a negative trend. It was also observed that the viscosity increases with increasing temperature. The negative viscosity deviation for all the studied mixtures could be interpreted as indicating that the attractive forces between molecules are stronger than the repulsion forces.

Table 9 presents the global comparison between the experimental and estimated viscosity using different models for coconut biodiesel, soybean biodiesel and n-hexadecane. While

Table 10 presents the global comparison between experimental and estimated viscosity for the biodiesel/n-hexadecane blends using the Vogel equation for n-hexadecane and the do Carmo model. It can be observed from these tables that the do Carmo model with one reference fluid gives the lowest average relative deviation (ARD) between experimental and calculated values, with 4.48% for biodiesel, followed by the do Carmo two-reference fluids model (5.69%), the Yuan model (6.75%) and the Revised Yuan model (7.15%). The ARD for the Andrade equation for n-hexadecane was 3.63%.

ªOriginal Yuan Model;

^bRevised Yuan Model by Pratas ;

^cCarmo with one reference fluid;

^dCarmo with two reference fluids.

Figure 9 presents a comparative analysis between experimental data for coconut and soybean biodiesel and the estimated viscosity for the do Carmo model with one reference fluid.

Figure 10 presents the experimentally determined viscosity variation with temperature for coconut biodiesel + n-hexadecane mixtures and that predicted using the Vogel equation (for n-hexadecane) and the do Carmo model with one reference fluid (for biodiesel). The use of Andrade's equation (for n-hexadecane) and the do Carmo one-reference fluid model (for biodiesel) with Eq. (5) gives good accuracy for the blends, as shown in Table 10.

CONCLUSIONS

An Anton Paar SVM 3000 digital viscosimeter was used to measure the viscosities of four binary mixtures [soybean biodiesel + diesel oil (or n-hexadecane) and coconut biodiesel + diesel oil (or n-hexadecane)], in the range of 293.15 to 373.15 K and at atmospheric pressure. From these experimental data, it could be observed that important errors are introduced by using n-hexcadecane as the sole molecule representing diesel oil, especially in lumping procedures. For this reason, we warn the readers which respect to its use. Additionally, the experimental viscosity deviations, , were calculated by using the Redlich - Kister polynomial equation. In all cases, negative values of the viscosity deviations were found, indicating that attractive forces among molecules are stronger than the repulsion forces. Of the viscosity prediction models studied, the do Carmo one-reference fluid model presents the best results, with an ARD equal to 4.48%. This model presented good results when used with Andrade's equation (for n-hexadecane) for viscosity prediction calculations of (biodiesel + n-hexadecane) blends.

ACKNOWLEDGEMENTS

The financial support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil), Brazilian National Agency of Petroleum, Natural Gas and Biofuels (Agência Nacional do Petróleo, Gás Natural e Biocombustíveis - ANP), and CTPetro/FINEP (Financiadora de Estudos e Projetos) is gratefully acknowledged.

NOMENCLATURE

Submitted: July 23, 2011

Revised: November 7, 2011

Accepted: January 13, 2012

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To whom correspondence should be addressed

Publication Dates

• Publication in this collection
  25 Oct 2012
• Date of issue
  Sept 2012

History

• Received
  23 July 2011
• Accepted
  13 Jan 2012
• Reviewed
  07 Nov 2011