Predicting the surface tension of mixtures of fatty acid ethyl esters and biodiesel fuels using UNIFAC activity coefficients

Abstract

This work presents the use of a formal thermodynamic model together with UNIFAC activity coefficients model, without any further adjustable parameter, to predict the surface tension of biodiesel fuels based on the equality of chemical potentials between the vapor-liquid interface and liquid bulk. The biodiesel samples included in this work were reported previously in the open literature. They were produced from vegetable oils such as: canola, coconut, corn, cottonseed, hazelnut, lard, palm, peanut, rapeseed, safflower, soybean, sunflower, and Walnut. Surface tension values for 18 samples of binary, ternary and quaternary mixtures of fatty acid ethyl esters (FAEEs) at T = 298.15 were predicted with an average absolute relative deviation (AARD) = 1.39%. Surface tension values for 31 biodiesel samples composed by fatty acid methyl esters (FAMEs) were also predicted at temperatures from 303.15 K to 353.15 K. The AARD value obtained for the 78 experimental points of biodiesel samples was 1.86% which shows a very good agreement with experimental measurements. In the UNIFAC method, predictions of surface tension values for the mixtures are based on the knowledge of the values of the surface tension for the pure components; these values were obtained from different sources. Also, two simple mixing rules on mass and mole fraction basis were used to predict the surface tension of biodiesel fuels. The AARD value obtained from the comparison between experimental and calculated values were: 2.77% and 2.91% for mixing rules on mass and mole fractions, respectively.

Introduction

The country's energy problems are deep and complex. The increase on the consumption of fossil fuels cause an increase of greenhouse gases concentration in the atmosphere and that effect leads to an increase in global temperatures [1,2]. In this regard, several agreements have been internationally signed to reduce the greenhouse gas emissions from the combustion of fuels [3]. The validity and enforceability of the various agreements with the intention of controlling and reducing pollutant emissions are some reasons for the development and use of renewable and environmentally friendly energy resources.

Biodiesel is a renewable bio-fuel and eco-friendly alternative fuel commonly produced from vegetable oils or animal fats by the transesterification reaction [4,5]. It is a mixture of fatty acid alkyl esters. Vegetable oils or animal fats are transesterified catalitically with an alcohol such as methanol or ethanol. A catalyst is usually included to improve the reaction rate and also yield of biodiesel [[6], [7], [8]]. Biodiesel has sulfur at low concentrations, which makes it a non-toxic and clean burning fuel [9]. It is a biodegradable fuel that doesn't have negative impact on our environment. In other words, it is an environmentally a friendly alternative to fossil fuels [[10], [11], [12]]. It reduces greenhouse gas emissions [13]. Biodiesel fuel can also help increase engine life because it has excellent lubricity. It can be used mixed with fossil diesel or alone in diesel engines [14]. Currently, production costs of biodiesel are rather high compared to fossil diesel. Also lower energy content, lower oxidation stability, higher viscosity, higher cloud point and higher pour point are disadvantages of biodiesel in comparison with petroleum based diesel [15].

Due to the global focus on the use of these biofuels and since physicochemical properties for this type of mixtures have important role on its quality and efficacy, it is necessary to be able to determine experimentally or predict their values. For example, one of the physical properties that plays an important role in atomization process is the surface tension [[16], [17], [18], [19]]. The study of surface tension is a key issue in diesel fuels because this property has influence on the economic, social, technical and environmental aspects of the fuel use. Good combustion in diesel engines depends on the formation of small size and fine spray of fuel. Surface tension is an important parameter in the shaping of oil droplets. Higher surface tension opposes the formation of smaller droplets from the liquid fuel. So, with decreasing surface tension, the quality of atomization in a compression ignition engine increases [20]. The surface tension value will change with changes in the source of biodiesels and their compositions. A lot of studies and researches have been carried out to predict the surface tension of fossil fuels and there are many different methods for this reason [[21], [22], [23]]. Also, some studies have been performed for estimating the surface tension of pure fatty acid esters and biodiesels. Phankosol et al. [24] correlated the surface tensions of pure FAME and its mixture to the Gibbs free energies of interfacial interaction. They suggested two equations for prediction of the surface tension of pure FAME and biodiesel. The surface tension of pure FAME was derived from carbon numbers and number of double bonds. For biodiesel, the surface tension was derived from fatty acid composition and the surface tension of the FAME. AARDs were reported at 1.21% for 8 types of FAMEs and 1.84% for 10 types of biodiesels. Thangaraja et al. [25] suggested a methodology for estimating the surface tension values for vegetable oil and biodiesel, doing this for karanja, palmolein and coconut. The deviation of the estimated values with respect to those measured was 7%, at temperature range from 306 to 353 K. An et al. [26] employed the Macleod–Sugden correlation [27,28] and the corresponding-states correlation by Miller [29] for predicting surface tension values of methyl oleate over a large temperature range. They reported that Miller's method was more accurate than the Macleod-Sugden correlation. Wallek et al. [30] applied the group-contribution model by Rarey/Olivier [31] and the corresponding-states correlation by Brock [32] for predicting the surface tension of fatty acid ethyl esters, reporting AARDs of 2.4% and 7.5%, respectively. Melo-Espinosa et al. [33] developed the models based on artificial neural networks (ANN) and multiple linear regressions (MLR) for predicting the surface tension, estimating surface tension values for 15 vegetable oils and a pure fatty acid (oleic) at T = 293.15 K, obtaining good performance for predicting this property; according to the residuals analysis, ANN performed better than MLR. Hajra et al. [34] compared the methods proposed by Macleod-Sugden [27,28], Miller-Thodos-Brock-Bird [29,32], Curl-Pitzer [35], Sastri-Rao [36], and Escobedo-Mansoori [37], to estimate surface tension values, finding that the best predictions for pure FAMEs were achieved using Macleod–Sugden [27,28] with AARD values ≤ 2.6% whereas the best predictions of the surface tension of petrodiesel-biodiesel blends were achieved using Sastri–Rao method [36] with AARD values ≤ 4.5%. Ruan et al. [38] investigated the methods proposed by Miller [29], Curl-Pitzer [35], Sastri-Rao [36] and Zuo-Sternby [39], estimating surface tension values for some waste cooking oil-based biodiesel finding that the Sastri-Rao and Pitzer methods have the higher estimation accuracy with AARD values of 0.48% and 1.35%, respectively. Hosseini et al. [40] proposed the molecular thermodynamic-based model and artificial neural network (ANN) for prediction of surface tension of FAMEs and biodiesels, predicting the surface tension values of 9 FAMEs and 3 biodiesels at temperatures from 283 to 393 K, obtaining AARD values of 1.82% and 0.44%, respectively. Díaz-Tovar et al. [41] predicted the surface tension of edible oils and biodiesels based on the approaches of Ceriani et al. [42] and Marrero et al. [43]. Ferrando et al. [44] predicted the surface tension of oxygenated compounds, esters, and two FAMEs using the AUA force field; they also used two different methods for estimating the surface tension, the Irving−Kirkwood (IK) method [45] based on the mechanical definition of the surface tension and the Test-Area (TA) method [46] based upon a thermodynamic model; for both, the deviations were less than 4%. Oliveira et al. [47] applied the coupling of the gradient theory with the CPA EoS to predict the surface tension of esters in a wide temperature range; the AARD of 1.5% was obtained using a simple correlation for the temperature dependence of the gradient theory influence parameter and an AARD of 5.44% was obtained whenever the influence parameters are considered to be temperature independent.

In the present study, the surface tension of biodiesel fuels has been investigated. Considering the amount of experimental information compiled up to now by us, we carried out the prediction of surface tension values for different mixtures of biodiesel fuels. First, the modelling work has been conducted for estimating the surface tension values of several binary, ternary and quaternary mixtures of fatty acid ethyl esters at 298.15 K with UNIFAC model. The equality of chemical potentials of the components of the system under study in the liquid bulk and the liquid –vapor interface is used to model the surface tension of these systems. The thermodynamic model together with the UNIFAC activity coefficients model used in this work allows to simultaneously predict the surface tension and the average interfacial composition of some complex mixtures of fatty acid methyl ester used as biodiesel fuels at temperatures from 303.15 to 353.15 K. Also, in order to test its performance, two mixing rules have been used to estimate the surface tension of biodiesel fuels from pure component surface tension values, the Dalton's mass-average method on mass fraction basis and the Kay's mixing rule on mole fraction basis. Finally, a comparison was made between experimental data and the results obtained with the mentioned models.