A new UNIFAC parameterization for the prediction of liquid-liquid equilibrium of biodiesel systems

Accepted Manuscript A new UNIFAC parameterization for the prediction of liquid-liquid equilibrium of biodiesel systems Larissa C.B.A. Bessa, Marcela C. Ferreira, Charlles R.A. Abreu, Eduardo A.C. Batista, Antonio J.A. Meirelles PII:

S0378-3812(16)30245-X

DOI:

10.1016/j.fluid.2016.05.020

Reference:

FLUID 11105

To appear in:

Fluid Phase Equilibria

Received Date: 24 March 2016 Revised Date:

11 May 2016

Accepted Date: 14 May 2016

Please cite this article as: L.C.B.A. Bessa, M.C. Ferreira, C.R.A. Abreu, E.A.C. Batista, A.J.A. Meirelles, A new UNIFAC parameterization for the prediction of liquid-liquid equilibrium of biodiesel systems, Fluid Phase Equilibria (2016), doi: 10.1016/j.fluid.2016.05.020. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT 1

A new UNIFAC parameterization for the prediction of liquid-liquid equilibrium of

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biodiesel systems

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Larissa C. B. A. Bessaa, Marcela C. Ferreiraa, Charlles R. A. Abreub, Eduardo A. C.

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Batistaa, Antonio J. A. Meirellesa,*

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a

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Food Engineering, Faculty of Food Engineering, University of Campinas, Campinas,

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São Paulo, Brazil, 13083–862.

Laboratory of Extraction, Applied Thermodynamics and Equilibrium, Department of

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b

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Janeiro, RJ, Brazil.

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School of Chemistry, Federal University of Rio de Janeiro (UFRJ), 21941-909 Rio de

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*Corresponding author. Tel.: +55 19 3521-4037, Fax.:+55 19 3521-4027

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e-mail

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[email protected]

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(Marcela C. Ferreira), [email protected] (Charlles R. A. Abreu), [email protected]

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(Eduardo A. C. Batista)

[email protected] (Larissa

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addresses:

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(Antonio

Bessa),

J.A.

Meirelles),

[email protected]

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Abstract

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The environmental adversities and the global concern about the conservation of

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non-renewable natural resources have stimulated a search for environmentally friendly

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energy sources. In this context, biodiesel has emerged as an important alternative to

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replace fossil fuels, due to its renewability, non-toxicity and biodegradability.

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Modeling, simulation and design of unit operations involved in the production of edible

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oils and biodiesel require knowledge of phase equilibrium. Several versions of the

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UNIFAC model are frequently used for process design when experimental

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determination of phase equilibrium data is difficult or time-consuming. In this work, the

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original UNIFAC model parameters are first checked for their predictive capability and

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then modified in terms of new readjusted binary interaction parameters. It was noted

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that the UNIFAC model without any changes in its parameters results in inadequate

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predictions. Thus, in order to obtain a good predictive tool, a comprehensive liquid-

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liquid equilibrium data bank of systems present in biodiesel production was organized

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and new UNIFAC interaction parameters were adjusted. At first, the molecules were

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divided into UNIFAC traditional structural groups. However, this first approach

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resulted in poor prediction, probably as a consequence of the strongly polar hydroxyl

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groups bonded to the consecutive carbon atoms of glycerol and acylglycerol molecules.

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Thus, a new group (‘OHgly’) was introduced and two matrices of parameters were

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adjusted. In general, satisfactory predictions were obtained and a significant

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improvement in the performance of this group contribution model has been achieved.

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Keywords: Liquid-liquid equilibrium; biodiesel; modeling; UNIFAC; proximity effects.

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1. Introduction

Increasing search for alternatives to petroleum-based fuels has led to the

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development of fuels from various sources, including renewable feedstocks such as fats

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and oils. Several types of fuels can be derived from these triacylglycerol-containing

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feedstocks. One of them is biodiesel, which is defined as the mono-alkyl esters of

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vegetable oils or animal fats [1]. Considering its well-known environmental and

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economic benefits, biodiesel is expected to be a good alternative to petroleum-based

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fuels. It can be used to address the limitations associated with fossil fuels, as the

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continued rise in crude oil prices, scarce fossil energy resources and environmental

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concerns [2]. So far, biodiesel has mainly been produced by transesterification of

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triacylglycerols (TAGs) and/or esterification of free fatty acids (FFAs) using

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homogeneous basic or acid catalysts [3, 4]. The transesterification reaction is a three-

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stage reaction, which produces two intermediate products (diacylglycerols and

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monoacylglycerols). Stoichiometrically, the reaction requires a molar ratio alcohol:oil

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of 3:1, but excess alcohol (methanol being the most commonly used alcohol) is usually

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added to shift the reaction towards the products [4, 5]. In Brazil, however, the use of

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ethanol is advantageous because of its large scale production, apart from allowing

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obtaining biodiesel through a totally renewable process. On the other hand, one

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disadvantage related to the use of ethanol is that the phase separation can be more

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difficult when compared with methanol [6]. In this sense, a better understanding and

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prediction of phase equilibrium of the biodiesel related systems are required for the

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proper design, operation and optimization of the reactor and separation units [4].

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Modeling of the reaction and separation processes required to produce higher

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purity biodiesel involves determining the liquid–liquid equilibrium and thus, a reliable

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thermodynamic model is essential [7]. However, because of the size of the molecules

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and the strong molecular interactions involved in the transesterification, the

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thermodynamic modeling is particularly challenging [8].

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Considering that the biodiesel production process basically involves fatty acid

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esters, alcohol and glycerol, and that the various kinds of esters have many physical-

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chemical similarities among them, such systems are generally treated as a pseudoternary

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one, consisting of an equivalent alkyl ester of fatty acid + alcohol + glycerol. Based on

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this assumption, equilibrium data for a wide variety of alkyl esters may be correlated

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using models such as UNIQUAC (Universal Quasi Chemical) and NRTL (Non-random,

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two liquid) with very good results [7, 9-12]. An alternative to the usually applied

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activity coefficient models to predict systems with polar compounds with strong

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associative interactions found at the biodiesel production and purification processes is

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the use of association equations of state. Among these associating equations are the

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statistical associating fluid theory (SAFT) [13] and the Cubic-Plus-Association (CPA)

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equations of state [14]. Recently, both equations have been used to describe these

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systems [15-20], presenting encouraging results, although their predictive character is

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still limited to simpler fatty compounds.

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ACCEPTED MANUSCRIPT Nevertheless, this approach does not take into account the different behaviors of

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triacylglycerols, fatty acids and specific esters and does not permit reliable prediction of

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equilibrium data for different types of biodiesel/oil systems (different compositions in

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terms of esters/triacylglycerols) with the parameters adjusted using those models.

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Furthermore, the number of components involved is usually large and the experimental

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information is scarce, so that it is particularly interesting to use a group contribution

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method.

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The UNIFAC group contribution method [21] has proven to be a fast and in

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many cases a reliable tool for the prediction of liquid-phase activity coefficients.

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Extensive tables with revised and updated interaction parameters have been published

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[22-27]. However, the current methods and corresponding set of available parameters

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provide improperly description of the liquid-liquid equilibrium (LLE) of systems

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containing vegetable oils, partial acylglycerols, free fatty acids, alcohol and/or biodiesel

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[9-11, 28-30].

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For this reason, the purpose of this article is to present a UNIFAC parameter

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matrix especially suited for the prediction of LLE of biodiesel systems. The original

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UNIFAC model was first checked using two different sets of parameters available in the

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literature to assess their predictive capability and then improved in terms of new

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regressed binary interaction parameters. It was used an approach to readjust the

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interaction parameters for UNIFAC model based on experimental data for real

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multicomponent systems. A similar analysis has been previously performed by the

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research group for the adjustment of UNIFAC interaction parameters for systems

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present in the deacidification of vegetable oils, i.e., systems composed of (vegetable oil

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+ fatty acids + ethanol + water) [31]. The database collected in that previous work has

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been updated and was also used in the present adjustment procedure. Thus, it was

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intended to obtain a matrix of parameters appropriate for the representation of fatty

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systems from the oil deacidification up to the biodiesel production.

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With the correct representation of the phase equilibrium involved in the entire

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sequence of biodiesel production, the corresponding process can be investigated and

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optimized with confidence. A good-quality predictive tool contributes to an

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improvement of industrial investment both in equipment design as in process

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optimization.

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2. Thermodynamic modeling

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In the context of the ever increasing importance of the liquid-liquid equilibrium

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in the processing of oils and fats, especially during the oil deacidification and biodiesel

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production, the readjustment of a new set of interaction parameters of interest for these

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types of systems is necessary to improve the predictive capacity of the UNIFAC method

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when applied to fatty systems. In the present work, the adjustment of new interaction

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parameters was based on experimental data for real fatty systems already available in

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the literature. In fact, experimental equilibrium data for systems containing pure fatty

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compounds are very rare and do not provide a data basis sufficiently comprehensive for

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readjusting parameters of existing groups.

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In order to obtain a suitable predictive tool, it is required to work with an

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experimental liquid-liquid equilibrium database as comprehensive as possible. It has

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been collected, from the literature, 218 systems containing biodiesel/esters, partial

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acylglycerols (mono and diacylglycerol), alcohol (methanol or ethanol), glycerol and

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water, summing up a total of 1145 tie lines, at temperatures ranging from T/K = 293.15

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to 393.15. Table 1 shows a summary of the equilibrium systems used in the

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readjustment procedure. For each group of data, table 1 gives the original oil, the

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number of systems, the number of tie lines, the temperature range and the corresponding

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reference. It should be considered that a larger set of liquid-liquid equilibrium data

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involving compounds of interest for this study is available in the literature, apart from

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the data shown in table 1. However, all those data whose error in the sum of mass

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fractions at each phase was greater than or equal to 0.001 were not considered in the

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parameter readjustment procedure, since these data could incorporate errors in the

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deviations values not derived from the equilibrium calculations.

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TABLE 1.

Summary of the data bank.

Original oil / Ester

Brazil nut Canola Canola + partial acylglycerols Castor Coconut Commercial biodiesel Corn Corn + partial acylglycerols

T/K Systems Tie lines 303.15 - 323.15 2 10 293.15 - 313.15 7 31 303.15 - 318.15 4 22 298.15 - 333.15 28 136 293.15 - 323.15 4 23 293.15 1 7 293.15 - 313.15 5 27 303.15 - 318.15 4 22

Reference [32] [33-35] [11] [36-38] [39, 40] [41] [40, 42] [11]

ACCEPTED MANUSCRIPT [12] [43, 44] [29, 45] [18, 46] [17, 18] [46] [17, 18] [17, 18, 47] [6] [29] [42] [10] [48] [9, 29] [49, 50] [49, 51-53] [54] [55, 56] [28] [12] [4, 37, 40, 56-62] [12, 63] [63] [34, 35, 57]

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11 36 24 30 20 19 19 51 19 6 15 23 102 11 50 83 7 44 4 11 220 23 12 27

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2 6 4 5 3 3 3 8 2 1 3 4 23 2 8 13 1 7 1 2 50 4 2 6

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303.15 - 318.15 293.15 - 333.15 298.15 - 338.15 298.15 - 353.15 313.15 - 353.15 298.15 - 333.15 298.15 - 353.15 298.15 - 353.15 313.15 - 323.15 298.15 293.15 - 313.15 303.15 - 318.15 298.15 - 333.15 298.15 298.15 - 318.15 293.15 - 393.15 333.15 293.15 - 313.15 318.15 303.15 - 318.15 293.15 - 343.15 303.15 - 318.15 303.15 - 318.15 293.15 - 323.15

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Cottonseed + partial acylglycerols Cottonseed Crambe Ethyl laurate Ethyl linoleate Ethyl myristate Ethyl oleate Ethyl palmitate Ethyl stearate Fodder radish Frying oil High-oleic sunflower + partial acylglycerols Jatropha curcas Macauba Methyl linoleate Methyl oleate Methyl palmitate Palm Palm + partial acylglycerols Rice bran + partial acylglycerols Soybean Soybean + partial acylglycerols Soybean + ethyl oleate Sunflower

In addition, the data collected by Hirata et al. [31], which involve systems

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composed of (vegetable oil + fatty acids + ethanol + water), were updated and also

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considered, applying the same tolerance in the mass balance deviation adopted for

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biodiesel systems. For this type of systems, the final database comprises 105 systems

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summing up a total of 937 tie lines. Thus, it was intended to obtain a matrix of

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parameters that is appropriate for the representation of systems from the oil

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deacidification up to the biodiesel production.

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The software used for adjusting the interaction parameters was developed in

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Fortran and was formulated in a previous work [31]. It is worth mentioning that the

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parameters obtained by Hirata et al. [31] presented a great improvement in the

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prediction of the systems studied by the authors. However, these parameters do not

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represent precisely systems containing biodiesel [10, 11].

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The modeling developed in this work is based on the original UNIFAC model

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[21]. The parameters adjustment is based on the minimization of the composition

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objective function, given by Eq. 1, using the simplex method [64].

ACCEPTED MANUSCRIPT D

N P −1

[(

FI , exp FI , calc S = ∑∑∑ winm − winm m =1 n =1 i =1

) + (w 2

FII , exp inm

FII , calc − winm

)] 2

(1)

where D is the total number of data banks, N is the total number of tie lines, P is the

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total number of pseudocomponents in each data bank; i, n, and m stand for component,

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tie line and data group, respectively; FI and FII refer to phases I and II, respectively;

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exp and calc stand for experimental and calculated mass fractions (w), respectively.

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Each system was analyzed considering all its main components (i.e., several

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esters, tri-, di- and monoacylglycerols) in phase equilibrium calculations, so that the

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system can be considered in all its complexity. However, to make it possible to compare

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the calculated values and the experimental data, in the objective function (Eq. 1), which

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evaluates the difference between the calculated values and the experimental

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compositions, the different classes of components, such as esters, tri-, di- and

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monoacylglycerols, are grouped into pseudocomponents, in the way the experimental

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data are usually presented in the literature.

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The deviations between experimental and calculated compositions in both

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phases were calculated using the root mean square deviation (∆w/%), which is given by

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the following equation:

∑∑ [(w

∆w = 100 178

P

n =1 i =1

FI , exp i, n

− wiFI, n, calc

) + (w 2

FII , exp i, n

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, calc − wiFII ,n

)] 2

(2)

2 NP

Unfortunately, in the literature, the biodiesel used in the phase equilibrium was

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not always expressed in terms of its ester composition. On the other hand, the

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composition of the oil that originated that biodiesel, in terms of fatty acids, was always

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available in the selected references. Thus, for the references that do not contain that first

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information, the esters composition was assumed to be the same as that of its original

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oil, in terms of fatty acids.

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First, the liquid-liquid equilibrium of systems present in the database was

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calculated through the original UNIFAC model [21] using two sets of interaction

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parameters already available in the literature: (i) UNIFAC-LLE proposed by Magnussen

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et al. [27] and (ii) UNIFAC-HIR, adjusted by Hirata et al. [31]. The UNIFAC area and

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volume parameters were assumed to be the same as those presented by Magnussen et al.

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[27], showed in Table 2.

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TABLE 2.

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UNIFAC group volume (Rk) and area (Qk) parametersa.

Sub group

Rk

Qk

CH2

CH3

0.9011

0.848

C=C OH

CH2 CH CH=CH OH

0.6744 0.4469 1.1167 1.0000

0.540 0.228 0.867 1.200

H2 O COOH

H2 O COOH

0.9200 1.3013

1.400 1.224

1.6764

1.420

COOC CH2COO Magnussen et al. [27].

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Main group

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Then, the adjustment of new parameters of interaction between groups was

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carried out in order to achieve a better description of the experimental data. For the

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parameters adjustment, both UNIFAC-LLE and UNIFAC-HIR parameters were tested

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as initial estimate for the first attempt to minimize the objective function. The

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adjustment strategy was to use the resulting parameters of a prior minimization to the

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next one, until the parameters are not altered anymore. The compounds used in this

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study were divided, in a first approach, into structural groups characteristic of the

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original UNIFAC (‘‘CH3’’, ‘‘CH2’’, ‘‘CH’’, ‘‘CH=CH’’, ‘‘CH2COO’’, “COOH” e

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‘‘OH’’).

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In order to validate the results of the proposed modeling procedure, the systems

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composed by sunflower oil + commercial mixture of mono- and diacylglycerols (+ ethyl

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linoleate) + ethanol, at T/K = 303.15 and 318.15, presented in a previous work [10]

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were used. They are representative systems of the transesterification step in the

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biodiesel production and they were chosen in order to reveal the great improvement in

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the behavior description of the minor components on phase equilibrium, since that was

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one of the main difficulties presented when using the parameters available in the

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literature. It is important to mention that these systems were not considered in the

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database for the parameters adjustment.

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3. Results and discussion

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Initially, an attempt was made to describe the molecules of the compounds

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studied with the elementary groups originally proposed by Fredenslund et al. [21].

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experimental data. In addition, regarding the partial acylglycerols distribution, the

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slopes of the calculated tie lines exhibit an inverse behavior in comparison to the

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experimental ones, estimating the preferred phase of diacylglycerols wrongly, as can be

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seen in figure 1.

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FIGURE 1. Liquid-liquid equilibrium for the system high-oleic sunflower oil(1) +

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diacylglycerol(2) + monoacylglycerol(3) + ethanol(4) at 318.15 K, DAG distribution: ●,

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experimental data [10]; - - -, calculated values using UNIFAC-LLE; ······, calculated

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values using UNIFAC-HIR; ̵ ̵ ̵ ̵ ̵ ̵, calculated values using the first attempt of UNIFAC

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parameters readjustment.

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Furthermore, the use of the UNIFAC model without any changes in their

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functional groups underestimates the mass fraction of monoacylglycerols in the oil

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phase and overestimates the mass fraction of these components in the alcoholic phase.

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This is observed by the more accentuated slope of the calculated tie lines in relation to

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the experimental ones, as shown in figure 2. This behavior was observed for whatever

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the matrix of parameters used.

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FIGURE 2. Liquid-liquid equilibrium for the system high-oleic sunflower oil(1) +

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diacylglycerol(2) + monoacylglycerol(3) + ethanol(4) at 318.15 K, MAG distribution:

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●, experimental data [10]; - - -, calculated values using UNIFAC-LLE; ······, calculated

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values using UNIFAC-HIR; ̵ ̵ ̵ ̵ ̵ ̵, calculated values using the first attempt of UNIFAC

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parameters readjustment.

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In the UNIFAC model, polar groups, whether bonded to consecutive atoms or

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not, are treated the same way. Such a simple parameterization requires a small number

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of structural groups, but cannot represent interactions between adjacent atoms in a

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molecule [65]. The UNIFAC model does not take into account, for example, proximity

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effects that occur when two or more strongly polar groups are bonded to the same or

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adjacent carbon atoms [66]. One way to overcome this limitation is to define specific

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functional groups for certain classes of compounds.

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Since the predictions using this first attempt of parameters adjustment were not

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good, and taking advantage of the fact that the UNIFAC model is quite flexible,

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allowing the addition of new groups to better describe a system, the ‘OH’ group

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attached to the carbon chain of the glycerol (present, thus, in the mono- and

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diacylglycerols molecules, besides glycerol) was considered as a different functional

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group (‘OHgly’). It was considered that this group behaves differently than the

256

traditional ‘OH’ group of alcohol molecules due to the effect of strongly polar hydroxyl

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groups bonded to consecutive carbon atoms in the glycerol and acylglycerol molecules.

ACCEPTED MANUSCRIPT This proximity effect may force this 'OH' group to present specific interactions,

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different from those of the usual alcohol group. Proximity effects on predictions of

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UNIFAC model have been discussed previously in the literature [67, 68]. The adoption

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of specific functional groups for certain classes of compounds due to proximity effects

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has already been proposed by Peng et al. [69] for dicarboxylic and hydroxycarboxylic

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acids, by Ninni et al. [70] for poly(ethylene glycol), by Ozdemir and Sadikoglu [71] and

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Marcolli and Peter [65] for the polyol/water systems, among others. In addition,

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modified parameterizations for other UNIFAC model [72] have also been used for

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systems containing polyols [73] and sugars [74].

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For this second approach, values for group volume and surface area parameters

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Rk and Qk for the new group were considered equal to the alcohol group ‘OH’ (Table 2).

269

For the adjustment of the parameters of the ‘OHgly’ group, the interaction parameters

270

for the traditional ‘OH’ group were used as initial estimate. In this case, it was first used

271

a reduced database, containing only the systems that comprise the components that

272

contain the ‘OHgly’ group (i.e., glycerol, mono- and diacylglycerols) and interaction

273

parameters were readjusted only for this group. Then, the other systems were added to

274

the database and all the parameters were readjusted. Again, the matrix of parameters of

275

a resulting minimization was used to the next until the parameters are not altered

276

anymore. Table 3 shows the resulting matrix of parameters of this adjustment

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procedure.

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TABLE 3.

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Matrix of readjusted UNIFAC interaction parameters. CH C=C 0.00 239.32 470.13 0.00 73.52 212.36 230.67 207.51 445.72 508.21 -462.69 1040.51 414.99 1274.10

AC C

CH C=C OH H2O COOH COOC OHgly

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OH H2O COOH COOC OHgly 714.56 2045.36 14.88 560.42 1092.77 954.33 328.14 4709.13 49.03 69.93 0.00 19.65 -417.57 172.62 0.00 -90.08 0.00 30.79 -11.22 23.26 24.00 -63.41 0.00 6289.17 4.39 243.03 616.17 306.77 0.00 -25.02 0.00 57.25 -952.41 -146.14 0.00

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This new set of parameters was used to predict the LLE of each system present

283

in the database. Table 4 shows the overall average deviations for each type of system

284

using the three matrices of parameters studied, and the overall average deviation

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considering all systems. The average deviations for all systems can be found in the

286

Supplementary material.

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TABLE 4.

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Overall average deviations. System Deacidification Biodiesel Partial acylglycerols Global

∆w/% UNIFAC-LLE UNIFAC-HIR 5.72 1.84 4.27 6.50 7.31 2.64 5.03 4.32

This work 2.59 3.66 1.81 3.13

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It can be seen that for the deacidification systems, the UNIFAC-HIR matrix of

292

parameters resulted in the lowest value of average deviation. This result was, in a

293

certain way, expected, since the authors who proposed those parameters studied

294

specifically the systems containing (vegetable oil + fatty acids + solvent), characteristic

295

of the deacidification process of vegetable oils. However, values of deviations obtained

296

with the parameters readjusted in this study were also low, especially when compared to

297

the original UNIFAC-LLE parameters. Figure 3 shows that for the deacidification

298

system, the UNIFAC-HIR parameters result in better prediction, but the parameters

299

readjusted in this work also yielded values close to the experimental data. One can also

300

observe that the slopes of the tie lines obtained using the original UNIFAC-LLE

301

parameters exhibit an inverse behavior in relation to the experimental ones, estimating

302

partition coefficients erroneously.

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FIGURE 3. Liquid-liquid equilibrium for the system soybean oil(1) + commercial linoleic acid(2) + anhydrous ethanol(3) at 298.15 K: ●, experimental data [75]; - - -, calculated values using UNIFAC-LLE; ······, calculated values using UNIFACHIR; ̵ ̵ ̵ ̵ ̵ ̵, calculated values using the new readjusted parameters.

309

In contrast, for the other systems, it was noted that, in general, the prediction of

310

equilibrium data was significantly improved when readjusted parameters were used.

311

Regarding the systems present in the transesterification of vegetable oils, with special

312

emphasis on partial acylglycerols, an analysis can be performed by the validation

313

system. It is worth noting that the low global average deviation value for systems

314

containing partial acylglycerols using the UNIFAC-HIR parameters (2.64 %) can cause

315

an improper perception that the use of these parameters would be better for predicting

316

the LLE of this type of system. However, more important than evaluate only the

317

numerical value of the deviation, it is essential to analyze the behavior of the

318

components in the system. Figures 4 to 9 show the equilibrium diagrams for the

319

validation system, including both experimental and calculated data, using the UNIFAC-

320

LLE parameters, the UNIFAC-HIR and the readjusted ones. It is worth remembering

321

that these data were not included in the database for the readjustment procedure. In

322

figures 6 and 9, in order to have a better interpretation of the five-component phase

323

equilibrium data, the experimental and calculated results were represented in a

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simplified form, showing only the ethyl linoleate and ethanol compositions in a explicit

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ACCEPTED MANUSCRIPT way and grouping the acylglycerols as a third pseudocomponent, which consists of

326

TAG-DAG-MAG.

327 328 329 330 331 332

FIGURE 4. Liquid-liquid equilibrium for the system sunflower oil(1) + diacylglycerol(2) + monoacylglycerol(3) + ethanol(5) at 303.15 K, DAG distribution: ●, experimental data [10]; - - -, calculated values using UNIFAC-LLE; ······, calculated values using UNIFAC-HIR; ̵ ̵ ̵ ̵ ̵ ̵, calculated values using the new readjusted parameters.

333 334 335 336

FIGURE 5. Liquid-liquid equilibrium for the system sunflower oil(1) + diacylglycerol(2) + monoacylglycerol(3) + ethanol(5) at 303.15 K, MAG distribution: ●, experimental data [10]; - - -, calculated values using UNIFAC-LLE; ······, calculated

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325

ACCEPTED MANUSCRIPT values using UNIFAC-HIR; parameters.

̵ ̵ ̵ ̵ ̵ ̵, calculated values using the new readjusted

339 340 341 342 343 344

FIGURE 6. Liquid-liquid equilibrium for the system sunflower oil(1) + diacylglycerol(2) + monoacylglycerol(3) + ethyl linoleate (4) + ethanol(5) at 303.15 K: ●, experimental data [10]; - - -, calculated values using UNIFAC-LLE; ······, calculated values using UNIFAC-HIR; ̵ ̵ ̵ ̵ ̵ ̵, calculated values using the new readjusted parameters.

345 346 347 348

FIGURE 7. Liquid-liquid equilibrium for the system sunflower oil(1) + diacylglycerol(2) + monoacylglycerol(3) + ethanol(5) at 318.15 K, DAG distribution: ●, experimental data [10]; - - -, calculated values using UNIFAC-LLE; ······, calculated

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337 338

ACCEPTED MANUSCRIPT values using UNIFAC-HIR; parameters.

̵ ̵ ̵ ̵ ̵ ̵, calculated values using the new readjusted

351 352 353 354 355 356 357

FIGURE 8. Liquid-liquid equilibrium for the system sunflower oil(1) + diacylglycerol(2) + monoacylglycerol(3) + ethanol(5) at 318.15 K, MAG distribution: ●, experimental data [10]; - - -, calculated values using UNIFAC-LLE; ······, calculated values using UNIFAC-HIR; ̵ ̵ ̵ ̵ ̵ ̵, calculated values using the new readjusted parameters.

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349 350

358 359 360 361

FIGURE 9. Liquid-liquid equilibrium for the system sunflower oil(1) + diacylglycerol(2) + monoacylglycerol(3) + ethyl linoleate (4) + ethanol(5) at 318.15 K: ●, experimental data [10]; - - -, calculated values using UNIFAC-LLE; ······, calculated

ACCEPTED MANUSCRIPT 362 363 364

values using UNIFAC-HIR; parameters.

̵ ̵ ̵ ̵ ̵ ̵, calculated values using the new readjusted

From figures 4 to 9, it can be seen that the equilibrium data predictions were

366

significantly improved by using the parameters readjusted in this work when compared

367

to the use of the original UNIFAC-LLE and the UNIFAC-HIR parameters. This can

368

also be proven by the deviation values between experimental and calculated data,

369

presented in table 5, and by the average distribution coefficients (ki, given by the ratio

370

between the content of the component i in the alcoholic phase and the content of this

371

component in the oil phase), shown in figure 10 and whose values are of interest in

372

order to observe the behavior of the minor components in the system. One can see that

373

the average distribution coefficients calculated using the parameters readjusted in this

374

work are quite similar to the experimental ones, different from the other parameters

375

matrices from literature. 10

8

ki

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0

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4

2

MAG

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DAG

376

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303.15

Linoleate

DAG

Temperature (K)

MAG

Linoleate

318.15

377

FIGURE 10. Average distribution coefficient (ki): ◊, experimental data [10];

378

, calculated values using UNIFAC-LLE; ∆, calculated values using UNIFAC-HIR; ○,

379

calculated values using the new readjusted parameters.

380 381

For the system at 303.15 K, one can see in Table 5 that a significant

382

improvement of the phase equilibrium predictions is achieved, both numerically and

383

graphically. As for the system at 318.15 K, graphically, it can be noted very satisfactory

384

predictions of the LLE. However, numerically, it is observed that when using the

ACCEPTED MANUSCRIPT UNIFAC-HIR parameters, the calculated deviations values are the lowest. Again, this

386

low deviation value may lead to an improper conclusion that, by using these parameters,

387

the liquid-liquid equilibrium involved is properly predicted. This may be true when

388

analyzing the esters partition in the phases, as shown in figures 6 and 9. Through these

389

figures, it is observed that both the UNIFAC-HIR parameters and the new parameters

390

adjusted in this work have correctly predicted the equilibrium data, both much better

391

than the prediction using the original UNIFAC-LLE parameters, and presenting

392

between them only a small difference in the biphasic region size.

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TABLE 5.

395

Deviation values between experimental and calculated data for the validation system

396

(sunflower oil + commercial mixture of mono- and diacylglycerols + ethyl linoleate +

397

ethanol). Temperature/K 303.15 318.15

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∆w/% UNIFAC-LLE UNIFAC-HIR 9.07 4.90 7.40 2.30

398

This work 2.26 2.45

Nevertheless, when observing the partition of partial acylglycerols (DAGs and

400

MAGs), it is found that the predictions using both the original UNIFAC-LLE and the

401

UNIFAC-HIR parameters were not adequate. In the case of diacylglycerols (figures 4

402

and 7), it is observed that using the parameters from literature the slopes of the

403

calculated tie lines were inverted when compared to experimental ones, which

404

reinforces the poor quality of the systems composition predictions, estimating a

405

diacylglycerol preference for the alcoholic phase, which is not consistent with the

406

experimental observation. Figure 10 also shows the error in the prediction of the

407

distribution of DAG when using the UNIFAC-HIR parameters. The experimental

408

distribution coefficient (ki) of DAGs is smaller than unity, indicating their preference for

409

the oil phase. On the other hand, the average distribution coefficients calculated using

410

UNIFAC-HIR are greater than unity, indicating an opposite distribution.

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411

In relation to the monoacylglycerols (figures 5 and 8), it can be seen that by

412

using both sets of interaction parameters from literature, the slopes of the calculated tie

413

lines are more accentuated than those of the experimental ones, indicating that the mass

414

fraction of MAG is underestimated in the oil phase and overestimated in the alcoholic

415

phase. This effect is greatest when the UNIFAC-LLE parameters were used, justifying

ACCEPTED MANUSCRIPT the larger deviation values. When the newly readjusted parameters are used, there is a

417

very significant improvement in the description of tie lines. The slope of the tie lines for

418

both DAGs and MAGs are in agreement with the experimental ones and much closer to

419

the experimental data, showing the improvement in the prediction of equilibrium data.

420

Thus, more important than assessing only the numerical value of the calculated

421

deviations, the analysis of the components behavior in the system is essential to ensure

422

the quality of the equilibrium prediction.

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In general, it can be concluded that when proximity effects are considered, the

424

newly defined functional groups are clearly superior to the groups currently used. The

425

adoption of a new group ‘OHgly’ led to an improvement in the agreement with the

426

experimental data without losing the simplicity of the group contribution approach.

427

Kang et al. [76] also observed that using the UNIFAC model for mixtures containing

428

components with multiple hydroxyl groups attached to adjacent carbon atoms shows

429

insufficient predictive capabilities. According to the authors, the main reason for such

430

behavior is the reduction in hydrogen bonding interaction due to steric hindrances.

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In addition to satisfactorily describe ternary systems, it is important that the

432

obtained UNIFAC parameters are also able to predict the phase behavior of the

433

corresponding binary sub-systems. Thus, some binary mixtures reported in the literature

434

were also used to validate the parameters. Table 6 gives the system analyzed, the

435

temperature range, the corresponding reference and the calculated deviations (∆w).

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TABLE 6.

438

Deviation values between experimental and calculated data for binary sub-systems.

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System

Temperature (K)

Glycerol + methyl oleate 323.15 - 383.15 Triolein + glycerol 323.15 - 383.15 FAME_castora + water 303.15 - 333.15 a FAME_castor + glycerol 303.15 - 333.15 FAEE_castorb + water 303.15 - 333.15 b FAEE_castor + glycerol 303.15 - 333.15 a Fatty acid methyl ester from castor oil b Fatty acid ethyl ester from castor oil

∆w/%

Reference

1.76 3.46 1.41 1.94 1.07 1.66

[20] [20] [38] [38] [38] [38]

439 440

Turning back to table 4, the average deviation value obtained for biodiesel

441

systems when using the new parameters readjusted in this study indicates that there was

442

an improvement in the equilibrium prediction for this type of system, presenting a

ACCEPTED MANUSCRIPT reduction in the deviation value of, approximately, 14.3% compared to UNIFAC-LLE

444

parameters and 43.7% when compared to the UNIFAC-HIR parameters. However, the

445

obtained deviation value (3.66%) is still relatively high, indicating a difficulty in

446

predicting the equilibrium of this type of system using the UNIFAC model. This can be

447

demonstrated by the analysis of figure 11. This figure shows that there is indeed an

448

improvement in the equilibrium prediction, especially regarding biodiesel-rich phase.

449

However, the new parameters yielded results that are not yet fully adequate.

450

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FIGURE 11. Liquid-liquid equilibrium for the system ethylic biodiesel of palm oil(1) +

452

ethanol(2) + glycerol(3) at 323.15 K: ●, experimental data [55]; - - -, calculated values

453

using UNIFAC-LLE; ······, calculated values using UNIFAC-HIR; ̵ ̵ ̵ ̵ ̵ ̵, calculated

454

values using the new readjusted parameters.

456

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According to Kang et al. [76], certain strong interactions, present in diols or

457

glycerol, for example, cannot be described by the UNIFAC additivity concept.

458

According to them, it is unlikely that defining new subgroups can resolve this problem.

459

In fact, other approaches have been adopted in this work as attempts to further improve

460

the LLE prediction of these systems, such as to consider the entire carbon chain of the

461

glycerol molecule as an independent structural group, to consider the whole methanol

462

molecule as a single group, to differentiate the groups ‘OH primary’ from ‘OH

463

secondary’ and to differentiate the ester group (‘CH2COO’) of acylglycerol molecules

464

from those of alkyl esters. However, none of these strategies generated better results,

ACCEPTED MANUSCRIPT 465

indicating that the deviations observed in this work must be associated with a limitation

466

of the UNIFAC model itself, and not only the interaction parameters used. As a last alternative to improve the prediction of liquid-liquid equilibrium

468

involving compounds of the biodiesel production, it was opted to adjust new parameters

469

considering only these systems in the database. For this, the interaction parameters

470

shown in table 3 were used as initial estimate for the readjustment of new parameters. It

471

is worth noting that in this case, the structural group ‘COOH’, specific for acid

472

molecules, was ignored since it does not appear in any molecule of this new reduced

473

database. Again, the matrix of parameters of a resulting minimization was used for the

474

next until there were no further changes in the parameters. The new matrix of

475

parameters resulting from this readjustment procedure is presented in table 7.

SC

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476

TABLE 7.

478

UNIFAC interaction parameters readjusted specifically for biodiesel systems.

479

CH C=C OH H2O COOC OHgly 0.000 380.420 394.210 2577.210 1127.950 1170.100 2037.300 0.000 1192.650 74.650 -12.050 91.750 134.050 266.610 0.000 14.680 202.160 0.000 129.970 351.070 -78.610 0.000 -7.200 85.320 -446.430 4.763 555.530 326.490 0.000 -21.650 375.350 1720.100 0.000 -8.415 -23.250 0.000

TE D

CH C=C OH H2O COOC OHgly

M AN U

477

In general, the new readjustment procedure showed a significant improvement in

481

the prediction of the equilibrium data, which is evidenced by the low overall mean

482

deviation value (2.69%). This can also be seen from figure 12, where one can observe

483

the great improvement in the system description.

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FIGURE 12. Liquid-liquid equilibrium for the system ethylic biodiesel of palm oil(1) +

486

ethanol(2) + glycerol(3) at 298.15 K: ●, experimental data [55]; - - -, calculated values

487

using UNIFAC-LLE; ······, calculated values using UNIFAC-HIR; ̵ ̵ ̵ ̵ ̵ ̵, calculated

488

values using the parameters readjusted specifically for biodiesel systems.

489

The significant improvement in the prediction of equilibrium data is due mainly

491

to the use of a specific database. Furthermore, the removal of the group ‘COOH’

492

reduced the number of interaction parameters to be readjusted (from 42 to 30), which

493

facilitates the computational work. It is worth noting that this new matrix should be

494

used only to systems present in the purification steps of biodiesel, i.e. systems

495

composed of biodiesel/esters, ethanol or methanol, water and/or glycerol. For systems

496

containing fatty acids and acylglycerols, these parameters are not recommended.

497

Indeed, the equilibrium data for the deacidification and transesterification systems were

498

calculated, using the parameters listed in table 7, and the overall average deviations

499

obtained were 4.48 and 3.31%, respectively.

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500

Thus, one can conclude that when it is of interest, or if it is necessary, using a

501

single matrix of parameters from the oil deacidification up to the biodiesel production,

502

the use of the matrix shown in table 3 is suggested. However, when the system to be

503

studied comprises exclusively compounds involved in the biodiesel purification, the

504

matrix of table 7 is the most recommended. As for the case where only compounds

ACCEPTED MANUSCRIPT 505

present in vegetable oils deacidification are involved, both the parameters of table 3,

506

and those presented by Hirata et al. [31] can be used with confidence.

507 508

4. Conclusions

509

The results presented in this study contribute to a more precise description of the

511

actual behavior of the transesterification systems involved in the biodiesel production.

512

In addition, the results confirm that the UNIFAC model without any changes in their

513

parameters may give unsatisfactory predictions. Therefore, it should be used with

514

caution or modified to obtain better estimations. A first attempt was made to describe

515

the molecules of the compounds studied with the traditional groups originally proposed

516

by the model, but poor predictions were obtained, generating improper deviations from

517

experimental data. A new group ‘OHgly’ was then introduced due to proximity effects,

518

and two matrices of new parameters have been readjusted. In general, adequate

519

predictions were obtained and significant improvement of the performance of this group

520

contribution method was achieved in comparison with the results using UNIFAC

521

parameters available in the literature. This modified UNIFAC model resulted in an

522

important improvement in the agreement between calculated and experimental data

523

without losing the simplicity of the group contribution approach.

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Acknowledgements

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The authors wish to acknowledge CAPES for the scholarship and FAPESP

528

(08/56258-8 and 09/54137-1), FAEPEX/UNICAMP and CNPq (483340/2012-0,

529

406856/2013-3, 305870/2014-9 and 309780/2014-4) for their financial support.

530 531 532 533 534 535 536 537 538

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ACCEPTED MANUSCRIPT Highlights •

The actual behavior of the transesterification systems involved in the biodiesel production was more accurately described.

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UNIFAC model without any changes in their parameters may give unsatisfactory predictions for biodiesel systems. A new structural group was introduced due to proximity effects.

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A noteworthy improvement in the predictions was observed without losing the

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simplicity of the group contribution method.

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