Evaluation of Optimal Methods for Critical Properties and Acentric

Article pubs.acs.org/jced

Evaluation of Optimal Methods for Critical Properties and Acentric Factor of Biodiesel Compounds with Their Application on Soave− Redlich−Kwong and Peng−Robinson Equations of State Frederico R. do Carmo,*,†,‡ Nathan S. Evangelista,‡ Fabiano A. N. Fernandes,§ and Hosiberto B. de Sant’Ana‡ Departamento de Ciências Exatas, Tecnológicas e Humanas, Universidade Federal Rural do Semi-Á rido, Rua Gamaliel Martins Bezerra, 587, Alto da Alegria, Campus de Angicos, 59515-000 Angicos, RN Brazil ‡ Grupo de Pesquisa em Termofluidodinâmica Aplicada, and §Laboratório de Análise e Desenvolvimento de Processos, Departamento de Engenharia Química, Universidade Federal do Ceará, Campus do Pici, Bloco 709, 60455-760 Fortaleza, CE Brazil †

S Supporting Information *

ABSTRACT: In this work, different methods capable of estimating some properties of fatty acid methyl esters (FAMES) and fatty acid ethyl esters (FAEES) have been evaluated. The results for Tb indicated that the methods of Constantinou and Gani and Marrero and Gani should be applied for FAMES and FAEES, respectively. The evaluation of the methods for critical properties and acentric factor was performed by comparisons between the experimental values and output values by the Racket−Soave equation. The results indicated that different packages should be applied for FAMES, FAEES, and hydroxy-esters. For critical volume estimations, the method of Marrero and Pardillo should be used for any alkyl ester present in biodiesel. Three versions of the group contribution (GCVOL) method as well as the Rackett−Soave equation were employed to estimate pure alkyl esters and biodiesel density. All these methods showed good results in moderate temperatures, but only Rackett−Soave is indicated for high temperatures. A final validation of the chosen packages for critical properties and acentric factor was performed by applying the estimated values of these properties on Peng−Robinson and Soave−Redlich− Kwong equations of state. Additionally, a fully predictive translated volume methodology has been proposed and presented good accuracy.

■

common acronyms. Hence, the first number denotes the number of carbon atoms in the fatty acid chain and the second number indicates the number of double bonds. The letters indicate the type of alkyl ester (“ME” for methyl ester and “EE” for ethyl ester). Therefore, [ME-C16:1] is a methyl ester that has 16 carbon atoms in the fatty acid chain and one double bond. The high production cost of biodiesel, 1.5 to 3 times higher than petrodiesel, is the major handicap to its large-scale commercialization.2 The cost of fresh vegetable oil feedstock is the main cause of this problem.4 Feedstock can represent up to 75 % of the final cost of biodiesel.1 Any produced biodiesel must fulfill the standards normalized specifications to be commercialized. These specifications depend on the region of the world. In the European Union biodiesel is normalized by EN 1414:2008 + A1:2009, in the United States by ASTM 675107, and in Brazil by ANP Resolution no. 45 of 8/26/2014.

INTRODUCTION Biodiesel is a potential alternative fuel to petroleum diesel due to its environmental and technical characteristics. The main advantages of biodiesel use in diesel engines is that it does not require major modifications and small decreases in its performances have been reported.1 Biodiesel is also a good lubricant, therefore its use as a blending component of diesel fuel is receiving increasing attention worldwide.2 Furthermore, biodiesel can offer other benefits such as regional development and social inclusion, especially in developing countries.3 This alternative fuel is a mixture of alkyl esters of long chain fatty acids. Commercial production of biodiesel often employs a transesterification reaction, but this fuel can also be obtained by other methods such as pyrolysis, dilution, and microemulsion.1 In the transesterification reaction, oil (from vegetal or animal source) reacts with a short-chain alcohol (generally methanol or ethanol). The final product of this reaction is a mixture of fatty acid methyl esters (FAMES) or fatty acid ethyl esters (FAEES) when either methanol or ethanol is used as reactant, respectively, in addition to small quantities of nonreacted alcohol, nonreacted oil, and glycerol (a byproduct). In this paper, the pure alkyl esters have been identified by their © XXXX American Chemical Society

Received: July 23, 2015 Accepted: September 30, 2015

A

DOI: 10.1021/acs.jced.5b00638 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

values of the critical properties (and casually of the normal boiling temperature) as input parameters. Some researchers have evaluated GC and CSP methods for predictions of critical properties and acentric factor of FAMES and FAEES. These authors usually apply an indirect procedure to calculate Tc, Pc, Vc, and ω: values of these properties are calculated by using models based on the corresponding states principle5,13,33 or by cubic equations of state.8,11,34 Further, this estimated value is compared to the experimental data of a well-known property. Anand et al.33 evaluated three models for Tb (Meissner,35 Joback and Reid18 and Constantinou and Gani36), five models for Tc (Fedors,37 Joback and Reid, Klincewicz and Reid38 and Constantinou and Gani), four models for Pc (Lydersen,19 Joback and Reid, Eduljee35 and Constantinou and Gani), and five models for ω (Edminster,25 Reid,39 Constantinou et al.,40 Ambrose and Walton,41 and Lee and Kesler42). The authors compared the predicted values of Tc and Pc with experimental data of only three FAMES with short fatty acid chain. After the choice of the models, they used these properties (Tb, Tc, Pc, and ω) as input parameters for CSP and GC models applied in the estimation of vapor pressure42 (Psat), enthalpy of vaporization27,43 (ΔHvl), specific heat capacity18,44 (Cp), and thermal conductivity27 (λ). For biodiesel, Anand and coauthors used the Kay’s mixing rules.45 Finally, they suggested the use of the following calculation methods: Constantinou and Gani for Tb, Lydersen or Joback and Reid for Tc, Lydersen for Pc and Lee and Kesler for ω. Garciá et al.5 claimed that “the selection of the correct package (permutation of different models for different properties) is a key step to ensure a minimum error in the subsequent calculations”. Therewith, these authors evaluated three different combinations of Tb, Tc, Pc, Vc and ω as input parameters for the Rackett−Soave46,47 equation. The results that were output by this equation have been compared to the experimental density data of FAMES, FAEES, and its biodiesel at 288.15 K. They considered biodiesel as a pseudocomponent and its properties were calculated by Lee and Kesler42 mixing rules. All packages tested by these authors are shown in Table 1. Meng et al.48 pointed out some drawbacks found on the

Accurate prediction of physical properties of biodiesel compounds could be an interesting way to study the viability of new feedstock and optimized blends of biodiesel/biodiesel and biodiesel/diesel blends.5−7 Moreover, the knowledge of physical properties of compounds present in biodiesel is also important for the following: a. equipment designing related to biodiesel production: heat exchanger, chemical reactors, distillation columns, pumps etc b. modeling and simulation of new production and purification processes c. modeling and simulation of fuel injection in engines d. modeling and simulation of fuel combustion e. a guide for the production of genetically modified vegetable oils with better characteristics for a specific use To attest the accuracy obtained from calculations of mixtures (such as biodiesel) properties, it is essential to know physical values for its pure components properties. However, there are no experimental data available in the literature5,7,8 for some properties of FAMES and FAEES (e.g., the critical properties). On the other hand, some experimental data for other FAMES and FAEES physical properties, such as the normal freezing temperature (Tf) and the normal boiling temperature (Tb), can be found in the literature. Considering that biodiesel is usually constituted by a wide variety of esters, which may present generally from 6 up to 26 carbons in its molecular structure and with no or up to four double bonds7,9,10, the use of predictive methods to estimate physical properties is essential. The knowledge of normal freezing temperature (Tf) of FAMES and FAEES is important because this property is an input parameter for cloud point (CP) calculations. The cloud point is characterized when crystallization of heavier esters begins to occur. This phenomena should be avoided, since the presence of crystals in a fuel affects its properties such as viscosity, volatility, fluidity, and filterability.11 In the petroleum industry, normal boiling temperature (Tb) is an important parameter for diesel quality control. For this reason, it is also important to know this property for biodiesel.12 It is also an essential parameter for modeling and simulation of biodiesel production process,7 fuel combustion and spray atomization.13−16 Normal boiling temperature is also an input parameter for many models that require the knowledge of critical properties,17−20 vapor pressure, enthalpy vaporization,21−23 and acentric factor.21,24,25 Additionally, this property is useful for vapor−liquid equilibrium calculation procedures. More specifically, its value is used as initial guess for flash calculations and saturation points.26,27 Critical constants (critical temperature, Tc; critical pressure, Pc; critical volume, Vc) and acentric factor (ω) are essential properties necessary for the understanding of pure component and mixtures phase behavior.27 These properties are also input parameters for models based on the corresponding states principle (CSP).13−15,27 Furthermore, Tc, Pc, and ω are needed when cubic equations of state (CEOS) are used to predict properties and to perform phase equilibria calculations.11,28−32 When experimental data are not available, prediction methods can be used. The most widely used methods are based on the group contribution (GC) concept. The main reason for this refers to the fact that the application of these models is simple because only structural molecular and basic properties of component are needed in the calculations. Other consolidated methods are based on the CSP that requires

Table 1. Package of Models Evaluated by Garciá et al.5 property Tb Tc Pc Vc ω

package 1 Constantinou and Gani Constantinou and Gani Wilson and Jasperson95 Constantinou and Gani Lee and Kesler

package 2

package 3 Yuan et al.16

Marrero and Pardillo20 Marrero and Pardillo

Ambrose17,51

Wilson and Jasperson

Ambrose

Marrero and Pardillo

Joback and Reid

Lee and Kesler

Lee and Kesler

Garciá́ s paper. Posteriorly, Garciá et al.49 published a ratification showing that package number 2 was the best. However, the authors claimed that more experimental data for ethylic biodiesel are needed for a better conclusion. An et al.13 tested the methods of Joback and Reid and the correlation proposed by Yuan et al.50 to calculate Tb; the methods of Joback and Reid and Ambrose17,51 to calculate critical properties (Tc, Pc and Vc); the method of Fedors to calculate Tc, and the models of Lee and Kesler and Ambrose for acentric factor calculations. These authors used methyl oleate (ME-C18:1)52 data, as reference, to evaluate critical properties B



Article

and acentric factor models. These values were applied as input parameters for models based on the CSP (vapor pressure,41,42 density,46 enthalpy of vaporization,27,39 and others). These predicted properties have compared to calculated values obtained by DIPPR correlations for five methyl esters (MEC16:0, ME-C18:0, ME-C18:1, ME-C18:2, and ME-C18:3). As a conclusion, the authors suggested the method of Ambrose to calculate the critical temperature and the critical pressure and the method of Joback and Reid to calculate the critical volume of these referred compounds. We believe that the methodology applied by Garciá et al.5 is a good way to validate the methods capable of estimating critical properties and acentric factor, because Rackett-type equations46,47,53,54 present reasonable accuracy for nonpolar and polar compounds. Furthermore, several density data of FAMES, FAEES, and biodiesel are available in the literature at various temperatures and pressures. We claim that the methodologies that use cubic equations of state (such as Soave−Redlich− Kwong, SRK55 and Peng−Robinson, PR56) must be not safe for the evaluation of critical properties and acentric factor, because these equations do not present good results for polar, associating, and/or large molecules. In this paper, an evaluation of the most consolidated methods (based on the GC concept and on the CSP) available in the literature was performed. For the evaluation of Tf and Tb, experimental data of some FAMES and FAEES are available in the literature and have been used for comparisons. In the case of critical properties and acentric factor, density experimental data were used and compared to the values obtained by using the Rackett−Soave equation. A total of 1040 packages for Tc− Pc−ω was tested by employing a methodology similar to that proposed by Garciá et al.5 Further, density values from the Rackett−Soave equation have been compared to the results from three versions of the GCVOL method.57−59 Finally, to evaluate the application of the chosen methods in other models, density calculations at wide ranges of temperature and pressure have been performed by using SRK and PR equations. In addition, volume-translated parameters were proposed for both equations.

Table 2. Evaluated Methods for Normal Freezing Temperature (Tf) Calculations method

abbreviation

Joback and Reid

JR

Constantinou and Gani Marrero and Gani96

CG

Ponce et al.97

LZ

MG

concepts group contribution group contribution group contribution group contribution

input parameters molecular structure molecular structure molecular structure molecular structure

Table 3. Evaluated Methods for Normal Boiling Temperature (Tb) Calculations method

abbreviation

concepts

Joback and Reid

JR

group contribution

Stein and Brown98 Constantinou and Gani Marrero and Pardillo20 Cordes and Rarey99 Marrero and Gani Nannolal et al.100

SB

group contribution

CG

group contribution

MP

group interaction

CR

group contribution

MG

group contribution

NL

group contribution and group interaction

input parameters molecular structure molecular structure molecular structure molecular structure molecular structure molecular structure molecular structure

For our knowledge, critical properties and acentric factor data for FAMES and FAEES are not available in the literature. Therewith, an indirect evaluation of all the studied methods for these properties was performed by the use of density data. Tables 4 and 5 present the methods tested for the prediction of critical properties and acentric factor, respectively. First, densities of pure methyl and ethyl esters have been calculated using the Spencer and Danner53 modified Rackett46 equation (eq 1) in combination with the Soave47 equation (eq 2). In this paper, we refer to the combination of these equations as the Rackett−Soave equation. Further, these estimated values have been compared to experimental data63,64 for 15 methyl esters and 10 ethyl esters. As mentioned before, a permutation of the studied methods for Tc, Pc, and ω (Tables 4 and 5) resulted in 1040 packages of models. Fragmentation of all molecules using functional groups of each method applied on this step can be found in details in the spreadsheet provided in Supporting Information.

■

METHODOLOGY Experimental Data Bank. For the present study, a data bank containing experimental data (obtained from literature) of some properties was developed. Data for the following properties are present in the data bank: normal freezing temperature, normal boiling temperature, density of pure alkyl esters at various temperatures and pressures, methylic and ethylic biodiesel fatty acid profiles (FAMES and FAEES), and biodiesel density at various temperatures and various pressures. A total of 2929 density data of 33 alkyl esters and 2251 densities data of 153 biodiesel from different sources are present in the database. Details of the developed databank are present in Tables S1−S5 in the Supporting Information (SI). Evaluation of Optimal Methods for Tf, Tb, Tc, Pc, Vc and ω of FAMES and FAEES. The evaluated methods for Tf and Tb are present in Tables 2 and 3, respectively. Since experimental data for normal freezing temperature and normal boiling temperature of some alkyl esters are available in the literature,60−62 the evaluation of the studied methods related to these properties was performed directly. It is important to mention that an updated table27 of parameters was used for the methods of JR and CG.

ρ=

MW RTc [1 + (1 − T / Tc)2/7 ] Z Pc RA

(1)

Z RA = 0.2908 − 0.099ω + 0.04ω 2

(2)

where R is the universal gas constant; MW denotes the molecular weight; Tc denotes the critical temperature; Pc denotes the critical pressure; T denotes temperature, and ω denotes the acentric factor. Although different versions of Rackett compressibility factor (ZRA) equation are described in the literature, for example, Yamada and Gunn65 and Vetere,66 the equation suggested by Soave (eq 2) was applied since it is more accurate for large compounds. C



Article

Table 4. Evaluated Methods for Critical Properties (Tc, Pc, and Vc) calculations method

abbreviation

Riedel101 Lydersen19 Ambrose17,51 Fedors37 Joback and Reid Klincewicz and Reid38 Somayajulu102 Constantinou and Gani Tu103 Wilson and Jasperson95 Marrero and Pardillo Marrero and Gani Nannoolal et al.104

RD LD AB FD JR KR SJ CG TU WJ MP MG NL

concepts group group group group group group group group group group group group group

abbreviation

Edminster25 Rudkin

ED

105

corresponding states principle corresponding states principle corresponding states principle corresponding states principle group contribution

RK

Lee and Kesler

LK

Ambrose and Walton41 Han and Peng106 Chen et al.24

AW

Constantinou et al.40 Shouzhi et al.107

CG

concepts

HP CH

corresponding states principle group contribution

SH

group contribution and corresponding states principle

input parameters

Tcm =

Tb and Tc Tb, Tc, and Pc

ϕi =

Tb, Tc, and Pc

molecular structure molecular structure and Tb

(

R

Z RAm =

∑ xiZ RAi

)Z

(3)

[1 + (1 − T / Tcm)]2/7 RAm

(4)

n i=1

and Tb and Tb and Tb

Pc

Vc

X X

X X

X X X X

X X X X

X X X X

X

(6)

(7)

8(Vc, iVc, j)1/2 1/3 3 (Vc,1/3 i + Vc, j )

(8)

Tcij = (1 − kij)(Tc, iTc, j)1/2

(9)

In summary, our procedure consisted of the following steps: a. evaluation of optimal models for Tf and Tb of FAMES and FAEES through comparisons between experimental and predicted values b. calculation of critical properties and acentric factor of alkyl esters using the previously determined optimal model for Tb c. evaluation of optimal package of models (Tc−Pc−ω) through comparisons between experimental densities63,64 and predicted densities from the Rackett−Soave equations (eqs 1 and 2) in a wide temperature range at atmospheric pressure d. evaluation of the best model for the calculation of critical volume of FAMES and FAEES using the Rackett46 equation modified by Spencer and Danner.53 It is important to notice that the optimal package chosen on step “c” was applied in this step e. comparison between biodiesel experimental density data with predicted values calculated by eqs 4 to 9 using the previously chosen properties A computer tool developed in Visual Basic for Applications (VBA), involving MS-Access and MS-Excel, was employed to manipulate the great variety of data present in our databank. Furthermore, a code designed in Fortran 90 was used to perform the calculations. GCVOL Method. As previously mentioned, the prediction capability of Rackett−Soave equation was contrasted and compared to density values obtained from the use of three versions of the group contribution (GCVOL) method.57−59 These methods are based on the GC concept and the original

MWm n xT ∑i = 1 Pi c,i c, i

j

∑j xjVc, j

1 − kij =

molecular structure Tb, Tc, and Pc

The last step of this evaluation was to perform a comparison between biodiesel experimental data present in our databank and biodiesel densities (ρm) predicted using the equations proposed by Spencer and Danner,54 as follows: ρm =

and Tb and Tb

X X X X X X X X X X X X X

xiVc, i

Tb, Tc, and Pc

MW [(1 − T / Tc)2/7 ] VcZ RA

structure structure structure structure structure structure structure structure structure structure structure structure structure

T ∑ ∑ ϕϕ i j cij i

After the selection of the optimal package of models for FAMES and FAEES, nine methods for critical volume (Table 4) were evaluated by using the Rackett equation modified by Spencer and Danner53 (eq 3). The results from this equation have been compared to the same experimental data employed in the previous procedure. ρ=

molecular molecular molecular molecular molecular molecular molecular molecular molecular molecular molecular molecular molecular

Spencer and Danner54 suggested the mixing rules proposed by Chuen and Prausnitz67 for critical temperature of mixture (biodiesel) (Tcm) calculations:

Table 5. Evaluated Methods for Acentic Factor (ω) Calculations method

Tc

input parameters

contribution contribution contribution interaction contribution contribution contribution contribution contribution contribution interaction interaction contribution and group interaction

(5)

where xi is the molar composition for each alkyl ester (FAME or FAEE); MWm is the molecular weight of biodiesel and ZRam is the Rackett compressibility factor of biodiesel. D



Article

version was proposed by Elbro et al.57 For pure compounds (as alkyl esters) the method is MW MW = ∑i niΔvi V

ρ=

and Mead.71 The following objective function (Fobj) was minimized: Fobj =

(10)

where MW denotes the molecular weight (g/mol) and V is the molar volume (cm3/mol). The contributions of all group volume increments Δvi must be added for the calculation of the molar volume, and ni denotes the number of groups i present in the molecular structure of the compound. The temperature influence in the molar group volume is calculated using the following equation: Δvi = Ai + Bi T + CiT 2

whereby the units are K, cm /mol, cm /(mol·K) and cm3/ (mol·K2) for the temperature (T) and for the parameters Ai, Bi and Ci, respectively. It is important to mention that the only difference between all three versions of GCVOL method studied refers to the values of each group parameter. These versions were named here as GCVOL-Elbro (proposed by Elbro et al.57), GCVOLIhmels (proposed by Ihmels et al.58) and GCVOL-Pratas (proposed by Pratas et al.59). The groups and each contribution (Δvi) used to draw alkyl esters are shown in the spreadsheet provided in the SI. To calculate biodiesel density the Kay’s mixing rules45 was used:

ρm =

3

∑ xiρi

P=

where xi and ρi denote the molar fraction and the density (calculated by GCVOL method) of the alkyl ester i present in biodiesel, respectively. Extension to High-Pressures. For some applications, it may be necessary to know accurate values of biodiesel density at high pressures. For this purpose, the Rackett−Soave equation was extended here using a similar approach used by Schedemann et al.68 for biodiesel and Evangelista et al.69 for ionic liquids. The proposed method is based on the following Tait-type equation: ρ0 (T , P0) ρ= ⎡B+P⎤ 1 − C ln⎣⎢ B + P ⎦⎥ 0

i=1

a ·α(Tr , ω) RT − c V−b V (V + b)

b = 0.08664

(18)

RTc Pc

(19) (20)

m = 0.480 + 1.574ω − 0.176ω 2

(21)

56

Peng and Robinson proposed a modification in the attractive and in the covolume terms of the SRK equation. The PR equation is presented below: P=

ac ·α(Tr , ω) RT − V−b V (V + b) + b(V − b)

2

B = b0 + b1·(T /E) + b2 ·(T /E) + b3·(T /E) + b4 ·(T /E) C = c0 + c1·(T /E)

(17)

α(Tr , ω) = [1 + m(1 − Tr0.5)]2

(13)

4

(16)

(RTc)2 Pc

ac = 0.42747

where

3

ρ(T , P)exp − ρ(T , P)calc ρ(T , P)exp

where V is the molar volume; R is the universal gas constant; P denotes pressure; T denotes temperature; Tr is the reduced temperature. The parameters ac and α(Tr,ω) represent the attractive term and b is called covolume. These parameters were calculated using the following equations:

(12)

i

Nexp

∑

where ρ(T,P)calc denotes the density calculated using eq 13 and ρ(T,P)exp denotes the experimental density value. The summation extends to all the experimental data (Nexp) considered in the estimation. Cubic Equation of State. It is important to apply the values produced by the chosen models (that is, the models that compose the best package) in other equations that require values of critical properties and acentric factor as input parameters. This procedure is essential to ensure the validity of the chosen package. For this purpose, we performed calculations of alkyl esters and biodiesel density at wide temperature and pressure ranges by using the most popular cubic equations of state (CEOS): Soave−Redlich−Kwong55 (SRK) and Peng−Robison56 (PR). The modification in Redlich−Kwong72 CEOS proposed by Soave55 popularly known as SRK CEOS is shown below:

(11) 3

1 Nexp

(RTc)2 Pc

(23)

RTc Pc

(24)

ac = 0.45724

(14) (15)

b = 0.07780

whereby the units are MPa for coefficient B and b0; all other coefficients are dimensionless; E is a constant with a value of 100 K; P0 is the reference pressure (atmospheric pressure −0.1 MPa) and ρ0(T,P0) is the density at reference pressure (calculated by the Rackett−Soave equation). It is important to notice that these parameters are universal for all alkyl esters. This consideration is in accordance to the fact that the influence of pressure on similar liquid volumes is virtually the same.69,70 The estimation of the parameters of Tait-type equation was performed by using the Simplex method proposed by Nelder

(22)

α(Tr , ω) = [1 + m(1 − Tr0.5)]2

(25)

m = 0.37464 + 1.54226ω − 0.26992ω 2

(26)

To improve liquid density predictions of pure alkyl esters, a pure component volume translation parameter was calculated. This concept was first suggested by Martin73 and further developed by Peneloux et al.,74 it is defined as c pure = vCEOS − vexp(Tr = 0.7) E

(27) DOI: 10.1021/acs.jced.5b00638 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

JR

417.98 463.74 509.50 555.26 601.02 646.78 692.54 696.70 700.86 440.86 486.62 532.38 669.66 719.58 723.74 811.32

experimental

423.1562 466.2062 497.2062 531.5161 568.9562 611.2062 625.2062 622.2062 639.2062 441.0075 480.0075 518.0075 585.8361 608.3661 595.9261 620.9261

alkyl ester

ME-C6:0 ME-C8:0 ME-C10:0 ME-C12:0 ME-C14:0 ME-C16:0 ME-C18:0 ME-C18:1 ME-C18:2 EE-C6:0 EE-C8:0 EE-C10:0 EE-C16:0 EE-C18:1 EE-C18:2 EE-C18:1.OH FAMES FAEES overall

CG 423.46 466.15 501.44 531.53 557.75 580.99 601.85 598.78 597.22 445.91 484.55 517.04 591.68 608.61 607.12 631.76

MP 425.54 468.41 507.75 544.37 578.83 611.52 642.70 644.40 646.11 443.21 484.48 522.61 624.03 656.33 658.00 702.66

Tb/K 421.55 464.01 502.84 538.07 569.67 597.66 622.16 625.73 629.30 443.23 483.88 520.91 610.30 637.33 640.91 670.04

SB 427.43 469.71 505.23 535.85 562.76 586.77 608.44 608.79 609.91 449.57 488.18 521.07 597.87 618.86 619.93 643.18

MG 432.21 473.35 509.51 541.90 571.34 598.40 623.48 625.29 627.09 453.50 478.11 513.36 600.68 627.21 628.97 656.73

CD 425.24 467.23 504.30 537.63 568.02 596.01 622.01 621.67 621.33 435.00 475.37 511.26 600.84 626.05 625.72 659.72

NL

Table 6. Experimental and Predicted Values of Normal Boiling Temperatures (FAMES and FAEES) JR 1.22 0.53 2.47 4.47 5.64 5.82 10.77 11.97 9.65 0.03 1.38 2.78 14.31 18.28 21.45 30.66 5.84 12.70 8.84

CG 0.07 0.01 0.85 0.00 1.97 4.94 3.74 3.76 6.57 1.11 0.95 0.19 1.00 0.04 1.88 1.75 2.44 0.99 1.80

0.56 0.47 2.12 2.42 1.74 0.05 2.80 3.57 1.08 0.50 0.93 0.89 6.52 7.88 10.42 13.16 0.91 5.76 2.15

MP 0.38 0.47 1.14 1.23 0.13 2.22 0.49 0.57 1.55 0.51 0.81 0.56 4.18 4.76 7.55 7.91 1.65 3.75 3.45

SB

%AARD MG 1.01 0.75 1.62 0.82 1.09 4.00 2.68 2.16 4.58 1.94 1.70 0.59 2.05 1.73 4.03 3.59 2.08 2.23 2.15

CR 2.14 1.53 2.48 1.96 0.42 2.09 0.28 0.50 1.89 2.84 0.39 0.90 2.53 3.10 5.55 5.77 1.48 3.01 2.15

NL 0.49 0.22 1.43 1.15 0.16 2.49 0.51 0.09 2.80 1.36 0.96 1.30 2.56 2.91 5.00 6.25 1.04 2.91 1.86

Journal of Chemical & Engineering Data Article

F



Article

where cpure is the volume translation parameter; vCEOS is the molar volume calculated by CEOS and vexp(Tr = 0.7) is the experimental molar volume at Tr = 0.7. For mixtures (biodiesel), the classical mixing rules proposed by van der Waals were applied: n

a=

n

∑ ∑ xixjaij i

(28)

j

n

b=

∑ xibi

(29)

i n

c=

∑ xici

(30)

i

aij =

aiaj (1 − kij)

(31)

where x, a, b, and c are the molar fraction, the attractive term, the covolume term, and the volume translation parameter of alkyl ester i, respectively. The interaction parameter, kij, is usually calculated by regression analysis of experimental phase equilibrium data. In this work, all kij were considered equal to zero.

Figure 1. Relative deviation ΔTb/Tb = {Tb(expt) − Tb(calc)}/ Tb(expt) of the experimental normal boiling temperature Tb(expt) from those calculated with all studied methods for normal boiling temperature of some alkyl esters.

■

RESULTS AND DISCUSSION To determine the accuracy of the performed predictions, two statistical parameters have been used: relative deviation (% RD) and absolute average relative deviation (% AARD): %RD =

X exp − X calc X exp

%AARD = calc

1 Nexp

Nexp

∑ i=1

(32)

X exp − X calc X exp

(33) exp

where X denotes the calculated property and X denotes the experimental property value. The summation goes over all of the experimental data (Nexp) considered in the estimation. Results for Normal Boiling Temperature and Normal Freezing Temperature. Experimental data of nine FAMES and seven FAEES taken from open literature61,62,75 were compared to the values produced by the methods presented in Table 3. Table 6 presents the available experimental data for Tb of alkyl esters and summarizes all predicted values and %AARD obtained by each predictive method employed for this property. Figure 1 illustrates the deviations obtained for each method. On the basis of only the analysis of Table 6 and Figure 1, one would intuitively affirm that the best methods able to calculate Tb for FAME and FAEES would be SB and CG, respectively. However, an attentive analysis of Figure 2 revealed that the combination of these methods generates an inconsistent physical behavior for fatty acid chains containing more than 15 carbon atoms. At this point, values for Tb of FAMES (calculated by SB) become higher than the values of FAEES (calculated by CG). For this reason, a deep analysis for data shown in Table 6 has been performed in order to avoid this inconsistency. As a conclusion, we suggest the methods of CG and MG to calculate this property for FAMES and FAEEs, respectively. It is important to mention that the chosen method that should be applied for estimations of FAMES normal boiling temperature is in accordance to the results of Garciá et al.5 and Su et al.7 Figure 3 depicts the predicted values of this

Figure 2. Normal boiling temperature of saturated FAMES (squares) and FAEES (circles) calculated by Stein−Brown and Constantinou− Gani methods, respectively.

property for saturated alkyl esters using the chosen methods. Unsaturated alkyl esters have also presented a consistent predicted behavior of this property by using these methods. For a more detailed view of the calculations obtained at this point, readers are referred to the spreadsheet provided in the Supporting Information. Experimental Tf data60 for FAMES and FAEES were compared to the values produced by the methods presented in Table 2. Calculated values and %AARD obtained by each method are present in Tables 7 and 8 for FAMES and FAEES, respectively. As it can be observed in these tables, the best results were produced by the method of CG for saturated FAMES (%AARD = 3.48%) and for saturated FAEES (%AARD = 1.29%). As it can be seen in Table 6, none of the methods studied presented reliable results for unsaturated alkyl esters. For this reason and given the availability of experimental data in literature,60 we proposed correlations to calculate this property of FAMES and FAEES (including the saturated). These G



Article

Tf /K = −0.2846nca 2 + 14.842nca + 137.90

(34)

b. For saturated FAMES with even nca Tf /K = −0.2987nca 2 + 15.665nca + 123.25

(35)

c. For saturated FAEES with odd nca Tf /K = −0.3041nca 2 + 16.301nca + 109.27

(36)

d. For saturated FAEES with even nca Tf /K = −0.1636nca 2 + 10.681nca + 158.44

(37)

e. For monounsaturated FAMES Tf /K = 0.0001nca + 0.4205 Tb/K

Figure 3. Normal boiling temperature of saturated FAMES (squares) and FAEES (circles) calculated by Constantinou−Gani and Marrero− Gani methods, respectively.

(38)

f. For monounsaturated FAEES Tf /K = 0.0038nca + 0.3353 Tb/K

correlations were proposed based on the work of Yalkowsky et al.76 and are a function of the number of carbon atoms in the fatty acid chain (namely nca): a. For saturated FAMES with odd nca

(39)

g. For polyunsaturated FAMES and FAEES

Table 7. Experimental and Predicted Values of Normal Freezing Temperatures (FAMES) Tf/K

%AARD

FAME

experimental

JR

CG

MG

LZ

JR

CG

MG

LZ

ME-C8:0 ME-C9:0 ME-C10:0 ME-C11:0 ME-C12:0 ME-C13:0 ME-C14:0 ME-C14:1 ME-C15:0 ME-C15:1 ME-C16:0 ME-C16:1 ME-C17:0 ME-C17:1 ME-C18:0 ME-C18:1 ME-C18:1.OH ME-C18:2 ME-C19:0 ME-C19:1 ME-C20:0 ME-C20:1 ME-C21:0 ME-C22:0 ME-C22:1 ME-C23:0 ME-C24:0 ME-C24:1 saturated unsaturated overall

235.72 238.16 259.67 260.98 277.45 278.32 291.24 220.89 291.62 239.05 301.63 270.16 301.73 257.13 310.81 252.94 268.07 230.06 311.18 270.82 319.58 265.36 320.73 326.37 270.10 326.53 331.76 282.64

233.02 244.29 255.56 266.83 278.10 289.37 300.64 295.56 311.91 306.83 323.18 318.10 334.45 329.37 345.72 340.64 386.46 335.56 356.99 351.91 368.26 363.18 379.53 390.80 385.72 402.07 413.34 408.26

226.27 236.18 245.21 253.50 261.18 268.32 274.99 264.78 281.26 271.68 287.17 278.15 292.75 284.23 298.04 289.97 303.95 285.00 303.08 295.41 307.87 300.57 312.46 316.84 310.17 321.05 325.09 318.95

214.42 222.84 230.80 238.35 245.54 252.39 258.94 264.63 265.21 270.66 271.23 276.46 277.00 282.04 282.56 287.42 321.32 294.30 287.92 292.61 293.09 297.62 298.09 302.92 307.16 307.60 312.13 316.12

225.70 233.07 240.44 247.82 255.19 262.57 269.94 310.65 277.31 318.02 284.69 325.39 292.06 332.77 299.44 340.14 349.08 380.85 306.81 347.52 314.18 354.89 321.56 328.93 369.64 336.31 343.68 384.39

1.15 2.57 1.58 2.24 0.23 3.97 3.23 33.80 6.96 28.35 7.14 17.75 10.84 28.09 11.23 34.67 44.16 45.86 14.72 29.94 15.23 36.86 18.33 19.74 42.81 23.13 24.59 44.45 9.82 33.28 28.51

4.01 0.83 5.57 2.86 5.86 3.59 5.58 19.87 3.55 13.65 4.80 2.96 2.98 10.54 4.11 14.64 13.39 23.88 2.60 9.08 3.66 13.27 2.58 2.92 14.84 1.68 2.01 12.85 3.48 13.47 7.43

9.04 6.43 11.12 8.67 11.50 9.32 11.09 19.80 9.06 13.22 10.08 2.33 8.19 9.69 9.09 13.63 19.86 27.92 7.47 8.05 8.29 12.16 7.06 7.19 13.72 5.80 5.92 11.84 8.55 14.07 10.63

4.25 2.14 7.40 5.04 8.02 5.66 7.31 40.63 4.91 33.03 5.62 20.44 3.20 29.42 3.66 34.47 30.22 65.54 1.40 28.32 1.69 33.74 0.26 0.78 36.85 2.99 3.59 36.00 4.00 35.09 16.31

H



Article

Table 8. Experimental60 and Predicted Values of Normal Freezing Temperatures (FAEES) Tf/K

%AARD

FAEE

experimental

JR

CG

MG

LZ

JR

CG

MG

LZ

EE-C8:0 EE-C9:0 EE-C10:0 EE-C11:0 EE-C12:0 EE-C13:0 EE-C14:0 EE-C14:1 EE-C15:0 EE-C16:0 EE-C16:1 EE-C17:0 EE-C17:1 EE-C18:0 EE-C18:1 EE-C18:1.OH EE-C18:2 EE-C18:3 EE-C19:0 EE-C19:1 EE-C20:0 EE-C20:1 EE-C21:0 EE-C22:0 EE-C22:1 EE-C23:0 EE-C23:1 EE-C24:0 EE-C24:1 saturated unsaturated overall

172.26 186.29 200.32 214.34 228.37 242.40 256.42 254.41 256.42 284.48 282.46 284.48 282.46 312.53 310.51 326.51 308.50 306.48 312.53 310.51 340.58 338.56 354.61 368.64 366.62 382.66 380.65 396.69 394.67

228.41 229.59 252.71 253.72 271.37 271.08 285.67 207.80 284.96 296.38 236.50 297.85 253.13 306.13 252.83 255.99 216.43 211.44 308.43 265.64 314.48 264.35 316.81 321.79 262.61 324.37 286.72 329.07 274.36

244.29 255.56 266.83 278.10 289.37 300.64 311.91 306.83 323.18 334.45 329.37 345.72 340.64 356.99 351.91 397.73 346.83 341.75 368.26 363.18 379.53 374.45 390.80 402.07 396.99 413.34 408.26 424.61 419.53

236.18 245.21 253.50 261.18 268.32 274.99 281.26 271.68 287.17 292.75 284.23 298.04 289.97 303.08 295.41 308.71 290.70 285.76 307.87 300.57 312.46 305.48 316.84 321.05 314.66 325.09 318.95 328.98 323.07

222.84 230.80 238.35 245.54 252.39 258.94 265.21 270.66 271.23 277.00 282.04 282.56 287.42 287.92 292.61 325.46 299.25 305.61 293.09 297.62 298.09 302.47 302.92 307.60 311.71 312.13 316.12 316.53 320.40

6.95 11.31 5.59 9.61 6.63 10.90 9.19 47.66 13.41 12.84 39.27 16.07 34.57 16.61 39.19 55.37 60.25 61.63 19.40 36.72 20.68 41.65 23.35 24.95 51.17 27.43 42.39 29.03 52.91 29.03 61.63 19.77

3.40 6.80 0.31 2.94 1.12 1.44 1.54 30.74 0.77 1.23 20.18 0.06 14.55 1.00 16.84 20.59 34.31 35.15 0.18 13.15 0.64 15.56 0.01 0.23 19.82 0.22 11.24 0.03 17.76 1.29 20.82 9.37

2.44 0.53 5.68 3.22 6.99 4.48 7.16 30.25 4.82 6.54 19.26 5.13 13.55 5.95 15.73 27.14 38.27 44.54 4.97 12.04 5.21 14.42 4.38 4.41 18.70 3.77 10.25 3.81 16.78 4.68 21.74 11.74

2.04 4.73 1.94 0.58 3.24 0.42 2.93 53.04 0.10 1.46 40.70 0.53 34.37 0.22 37.45 39.25 79.37 102.86 1.87 33.60 2.25 37.04 3.83 4.51 43.56 5.95 34.06 6.68 42.79 2.55 48.18 21.43

Tf /K = 0.35453 Tb/K

unsaturated), FAEES (saturated and unsaturated), and hydroxy-esters. Figure 4 presents %AARD distribution for all the evaluated packages. The number of experimental data employed at this point were FAMES (218 for 15 compounds), FAEES (155 for 10 compounds), and hydroxy-esters (16 for methyl ricinoleate). “Experimental” data of methyl ricinoleate was indirectly obtained by using experimental data of castor oil biodiesel collected by Cavalcante.78 From Figure 4, it can be observed that an incorrect choice of the package may result in very unreliable density predictions. Of all the evaluated packages, 38 (for FAMES), 22 (for FAEES), and 50 (for hydroxy-esters) presented %AARD higher than 50 %. For these respective classes of esters, a correct choice of the packages led to very accurate density predictions (%AARD below 1 %). It is important to notice that the higher deviations probably were not related to the Rackett−Soave equation applied in this work, since some authors27,53,54,65,79 have shown that this equation predicts density accurately for many classes of compounds, including esters. The following methods capable of estimating Tc were present in the packages that produced %AARD values lower than 2%: CG, FD, MG, MP, NL, and TU (for FAMES) and CG, FD, MG, AB, NL, RL, and TU (for FAEES). For critical pressure, AB, SJ, and LD for FAMES, and AB, LD, MP, and SJ for FAEES were present in the packages that produced good

(40)

h. For hydroxy FAMES and FAEES Tf /K = 0.4212 Tb/K

(41)

For classes a−d, the correlations were developed based only on nca, because some authors reported satisfactory results for this kind of correlation.11,77 Otherwise, correlations e−h are also functions of Tb. Given the obtained low values for the % AARD (Table 9), we concluded that these correlations can be accurately used for calculations of normal freezing temperature FAMES and FAEES. Critical Properties and Acentric Factor. First, the packages for critical temperature (Tc), critical pressure (Pc) and acentric factor (ω) were evaluated. For methods of Tc and ω that use Tb as input parameter, predicted values of this property (obtained with the CG and MG methods) were used in the cases of unavailability of experimental data. These estimated values as well as the packages tested can be seen in the Supporting Information spreadsheet. To obtain a more accurate choice of the packages, the studied compounds have been divided into three groups: FAMES (saturated and I



Article

Table 9. %AARD for the Normal Freezing Temperatures (FAMES and FAEES)

Table 10. %AARD for the 10 Best Packages (FAMES) methods

FAME

%AARD

FAEE

%AARD

Tc

Pc

ω

%AARD

ME-C8:0 ME-C9:0 ME-C10:0 ME-C11:0 ME-C12:0 ME-C13:0 ME-C14:0 ME-C14:1 ME-C15:0 ME-C15:1 ME-C16:0 ME-C16:1 ME-C17:0 ME-C17:1 ME-C18:0 ME-C20:1 ME-C18:1.OH ME-C18:2 ME-C19:0 ME-C19:1 ME-C20:0 ME-C21:0 ME-C22:0 ME-C23:0 ME-C24:1 FAMES overall

2.66 4.31 3.71 2.20 3.33 1.59 2.48 5.80 1.67 0.06 1.39 9.78 2.07 3.38 0.76 1.61 2.11 1.50 1.92 5.07 0.79 1.04 0.94 0.67 2.49 2.51

EE-C8:0 EE-C9:0 EE-C10:0 EE-C11:0 EE-C12:0 EE-C13:0 EE-C14:1 EE-C15:0 EE-C16:0 EE-C16:1 EE-C17:0 EE-C17:1 EE-C18:0 EE-C18:1 EE-C18:1,OH EE-C19:1 EE-C20:0 EE-C20:1 EE-C21:0 EE-C22:0 EE-C22:1 EE-C23:0 EE-C23:1 EE-C24:0

2.20 0.77 1.51 0.76 3.06 0.48 7.59 0.14 3.01 0.19 0.22 3.82 2.75 2.86 2.16 3.59 2.49 0.77 0.21 2.34 4.50 0.32 2.20 2.58

FD TU FD FD TU TU TU FD MG CG

SJ SJ LD LD LD AB LD AB SJ LD

SH SH CG HP CG SH HP SH SH SH

0.62 0.69 0.74 0.82 0.84 0.99 0.99 1.02 1.20 1.23

FAEES 2.40

2.29

Table 11. %AARD for the 10 Best Packages (FAEES) methods Tc

Pc

ω

%AARD

FD NL TU FD NL FD TU TU FD FD

SJ SJ SJ LD AB AB LD AB LD LD

SH SH SH CG SH SH CG SH SH HP

0.89 1.09 1.11 1.15 1.19 1.23 1.33 1.33 1.34 1.37

Table 12. %AARD for the 10 Best Packages (Methyl Ricinoleate) methods Tc

Pc

ω

%AARD

WJ MP CG MP NL MG WJ AB WJ MG

JR NL JR JR NL NL JR JR JR NL

PO RE HP CG HP HP CH LK RE CG

0,10 0.10 0.14 0.19 0.21 0.22 0.29 0.29 0.34 0.37

After choosing the best methods for Tc, Pc, and ω calculations, the evaluation of all methods able to estimate Vc (Table 4) was performed. %AARD values of FAMES and FAEES for all the studied methods are shown in Table 14. Given the lowest %AARD values obtained by the method of MP and the capability of isomer differentiation provided by this method, we suggest the use of it for FAMES, FAEES, and hydroxy-esters. Figures illustrating the behavior of normal boiling temperature, critical properties, and acentric factor as a function of number of carbon in fatty acid chain are shown in the spreadsheet provided in the Supporting Information. Biodiesel Density PredictionsComparison with GCVOL Methods. In this step, experimental data of esters and biodiesel were compared to the results produced by the previously mentioned equations. The data were divided into three groups: (a) FAMES and FAEES at atmospheric pressure,

Figure 4. %AARD distribution for all the studied packages of models.

results (%AARD below to 2 %). Our results indicated that all the packages of models that presented %AARD lower than 2 % included group contribution methods (CG, SH, HP) for the estimation of the studied esters acentric factors. Tables 10, 11, and 12 present values of %AARD for the 10 best packages evaluated for FAMES, FAEES, and methyl ricinoleate, respectively. Figures 5 and 6 show in detail the % AARD distribution produced by these packages for FAMES and FAEES, respectively. From these figures, it can be seen that none of these packages presented %AARD values higher than 4 % for FAMES and higher than 4.5 % for FAEES. After evaluating the physical consistency for all methods, the use of the methods described in Table 13 is proposed. J



Article

and FAEES has been used. Table 15 presents the values of % AARD and of maximum relative deviation (%MRD) for each method. From this table, it can be observed that GCVOL-OL60 presented the best results. Although the Rackett−Soave method produced the highest value for %AARD between predicted and experimental densities (%AARD = 1.03 %), this method can still be considered accurate, given the fact that the value obtained for this parameter was very low and is within acceptable limits for engineering calculations. An analysis of the influence of temperature on density behavior of methyl linoleate63,80,81 is illustrated in Figure 7. From this chart, it can be seen that none of the GCVOL model versions presented a physically consistent behavior for the density at higher temperatures. This fact was expected since the authors57,58 did not employ density data at temperatures higher than the normal boiling temperatures of the compounds considered in the methods development. We emphasize that the Racket−Soave equation generates a consistent behavior and hence should be used at these conditions. Biodiesel at Atmospheric Pressure. A total of 1075 experimental density data of biodiesel derived from different sources, such as soybean, castor, babassu, beef tallow, fish oil, and others were used. The data have been collected by different authors in a wide range of temperatures (273.15 K to 523.15 K) and atmospheric pressure. For more details about these biodiesel samples, see Tables S4 and S5 of the Supporting Information file. Density values produced by the Racket−Soave equation (using critical properties and acentric factor values outputted by the models that comprise the previously chosen packages) were applied in the Lee and Kesler21 mixing rules (eqs 6 to 9). These mixing rules were previously used by various researchers.82−86 Different than the results observed for pure alkyl esters, the best prediction of biodiesel density was obtained from the GCVOL-Pratas model. Table 16 presents the statistical parameters for all biodiesel samples considered in this procedure. The highest %RD values observed were 14.30 %, 14.14 %, and 13.95 % for the following methods: original GCVOL, GCVOL−Pratas and GCVOL−OL-60, respectively. These values were obtained for castor biodiesel.5 Experimental density and the predicted behaviors for another castor biodiesel78 are shown in Figure 8. This chart illustrates the superiority of the behavior from the method suggested in this work in comparison to the others analyzed. Despite the highest value produced by the Racket−Soave equation for the overall %AARD, this method generated the lowest value among the maximum absolute relative deviations calculated. This specific deviation was observed in the density prediction of a blend composed by soybean biodiesel and babassu biodiesel at 373 K. The experimental data used were reported by Nogueira et al.84 An analysis of the density prediction capability of each model at high temperatures has been performed. To illustrate the results obtained, Figure 9 presents the experimental and the predicted density behavior of a soybean biodiesel studied by Pratas.59 The same behavior was observed by Meng et al.86 for a canola biodiesel studied by these authors. FAMES FAEES and Biodiesel at High Pressures. The estimation of the generalized parameters of eqs 13−15 was performed by using experimental data of only three FAMES (C14:0,81,87 C18:1,63,87−90 and C18:263,68,87−90). The obtained values of these parameters were: b0 = 8.35115 MPa, b1 =

Figure 5. %AARD distribution for the 10 best package of models (FAMES).

Figure 6. %AARD distribution for the 10 best package of models (FAEES).

Table 13. %AARD for the Chosen Packages method esters class

Tc

Pc

ω

FAMES FAEES methyl ricinoleate

TU FD NL

AB SJ NL

SH SH HP

Table 14. %AARD for All the Studied Methods Used in Critical Volume Calculations %AARD method

FAMES

FAEES

MP KR JR MG CG AB LD SJ FD

7.41 8.27 8.26 8.31 8.30 9.56 9.74 10.19 13.71

8.06 9.86 9.88 9.98 9.99 11.18 11.36 11.81 15.38

(b) biodiesel at atmospheric pressure, and (c) FAMES, FAEES, and biodiesel at high pressures. FAMES and FAEES at Atmospheric Pressure. In this group, a databank constituted of 883 experimental data of 33 FAMES K



Article

Table 15. Statistical Parameters for All the Studied Models Used in Density Calculations at Atmospheric Pressure (FAMES and FAEES) original GCVOL

GCVOL-OL-60

GCVOL-Pratas

%RD

%RD

%RD

T/K

Rackett-Soave %RD

alkyl ester

min

max

%AARD

max

min

%AARD

max

min

%AARD

max

min

%AARD

max

min

ME-C6:0 ME-C7:0 ME-C8:0 ME-C9:0 ME-C10:0 ME-C11:0 ME-C12:0 ME-C13:0 ME-C14:0 ME-C15:0 ME-C16:0 ME-C16:1 ME-C17:0 ME-C18:0 ME-C18:1 ME-C18:2 ME-C18:3 ME-C19:0 ME-C20:0 ME-C20:1 ME-C22:0 ME-C22:1 ME-C24:0 EE-C8:0 EE-C10:0 EE-C12:0 EE-C14:0 EE-C16:0 EE-C18:0 EE-C18:1 EE-C18:2 EE-C18:3 EE-C20:0 FAMES FAEES overall

293.15 293.15 283.15 293.15 278.15 293.15 283.15 293.15 293.15 293.15 303.15 278.15 313.15 313.15 283.15 278.15 278.15 313.15 313.15 278.15 333.15 278.15 338.15 278.15 283.15 283.15 283.15 303.15 313.15 278.15 278.15 278.15 318.15

313.15 313.15 353.15 313.15 363.15 313.15 353.15 313.15 393.15 313.15 393.15 363.15 313.15 363.15 393.15 393.15 363.15 313.15 373.15 373.15 373.15 363.15 373.15 363.15 353.15 353.15 393.15 363.15 363.15 363.15 363.15 373.15 373.15

0.27 0.43 0.37 0.62 0.47 0.68 0.54 0.74 0.61 0.74 0.34 0.84 0.66 0.40 0.46 1.02 1.87 0.64 0.24 0.52 0.18 0.41 0.16 1.33 1.31 1.27 1.15 0.99 0.91 0.49 0.69 1.30 0.73 0.63 1.12 0.83

−0.17 −0.33 0.12 −0.50 0.17 −0.58 −0.02 −0.64 −0.05 −0.64 0.03 −0.02 −0.66 0.00 1.39 2.67 −0.17 −0.33 0.25 −0.50 0.53 −0.58 0.10 −0.64 1.11 −0.64 0.65 1.64 0.66 0.65 1.39 2.67 3.48 3.48 2.86 3.48

−0.37 −0.54 −0.84 −0.73 −0.98 −0.78 −0.94 −0.85 −1.57 −0.85 −0.68 0.02 0.66 0.00 0.03 0.01 0.38 0.64 0.00 0.00 0.02 0.05 0.01 0.23 0.34 0.18 0.42 0.62 0.62 0.03 0.00 0.03 0.43 −1.57 0.00 −1.57

1.69 1.26 1.13 0.68 0.70 0.32 0.40 0.16 0.33 0.17 0.32 0.83 0.13 0.23 0.21 0.25 0.78 0.21 0.30 0.30 0.27 0.30 0.22 0.24 0.31 0.45 0.51 0.41 0.41 0.43 0.14 0.17 0.31 0.44 0.34 0.40

1.83 1.41 1.60 0.84 1.37 0.47 1.02 0.20 1.73 0.03 0.66 1.34 0.13 0.57 0.55 0.43 0.99 0.21 0.64 0.57 0.54 0.83 0.45 3.59 0.81 1.02 1.10 0.85 0.75 1.00 0.56 0.57 0.69 1.83 3.59 3.59

1.55 1.11 0.39 0.51 −0.09 0.16 −0.20 −0.12 −0.94 −0.30 −0.11 0.62 0.13 0.00 0.02 0.03 0.33 0.21 0.03 0.03 0.01 0.02 0.03 0.02 0.00 0.01 0.07 0.01 0.09 0.14 0.00 0.00 0.01 −0.94 0.00 −0.94

0.23 0.04 0.19 0.24 0.37 0.36 0.39 0.46 0.67 0.49 0.54 1.35 0.50 0.49 0.46 0.21 0.45 0.49 0.43 0.26 0.42 0.46 0.43 1.26 1.22 1.19 1.16 1.08 1.04 0.79 0.44 0.35 0.94 0.50 0.99 0.70

0.29 0.05 −0.08 −0.24 −0.29 −0.36 −0.34 −0.44 −0.39 −0.46 −0.31 −1.29 −0.50 −0.42 −0.38 −0.06 0.29 0.05 −0.08 −0.24 −0.29 −0.36 −0.34 −0.44 1.46 −0.46 1.12 1.54 0.50 0.50 0.79 0.66 0.53 1.54 2.54 2.54

0.17 −0.02 −0.66 −0.24 −1.14 −0.36 −0.57 −0.47 −1.65 −0.52 −0.66 1.29 0.50 0.01 0.38 0.06 0.07 0.49 0.41 0.21 0.41 0.40 0.42 0.03 0.12 0.49 0.40 1.05 1.02 0.75 0.40 0.24 0.92 −1.65 0.03 −1.65

0.62 0.25 0.11 0.27 0.50 0.58 0.72 0.73 1.13 0.64 0.96 0.50 0.47 0.86 0.48 1.55 3.36 0.28 0.26 0.80 0.41 1.26 1.23 1.12 1.42 1.52 1.44 1.15 0.71 0.54 0.43 0.61 0.16 1.03 1.03 1.03

0.68 0.31 1.23 0.33 2.61 0.67 2.20 0.83 2.98 0.74 2.19 0.93 0.47 1.05 1.16 2.27 3.79 0.28 0.45 1.32 0.60 1.78 1.40 2.61 3.13 2.79 2.72 1.42 0.97 1.01 0.84 1.07 0.31 3.79 2.61 3.79

0.57 0.20 0.00 0.20 0.01 0.49 0.45 0.63 0.04 0.53 0.42 0.00 0.47 0.04 0.00 0.00 2.85 0.28 0.01 0.42 0.24 0.82 1.07 0.06 0.04 1.01 0.29 0.83 0.42 0.01 0.03 0.02 0.01 0.00 0.01 0.00

A %AARD value of 1.25 % was produced by the application of this Rackett−Soave−Tait methodology in the prediction of density of pure alkyl at high pressures. Figure 10 shows the % AARD distribution for each studied alkyl ester. It is important to mention that all 2125 experimental density data (at high pressures) of pure alkyl esters available in the developed data bank were used to analyze the accuracy of the methodology proposed here. A value of 0.55 % for this same statistical parameter was obtained between the estimated and the experimental values of biodiesel density. A distribution of relative deviation (%RD) versus pressure is presented in Figure 11. From this figure, it can concluded that this methodology also presented good results at high pressures (%AARD lower than 3.2 %). A total of 1147 experimental biodiesel density data at high pressures were employed. We claim that, for specific cases, it might be necessary to perform a new estimation of the parameters related to the Taittype equation applied here. For this purpose, more experimental data of biodiesel or pure alkyl esters would be

Figure 7. Effect of temperature on the density behavior of methyl linoleate.

11.34895 MPa, b2 = −2.24592 MPa, c0 = 0.039388, and c1 = 5.4591·10−5. By applying this methodology, the universality of these parameters could be attested. L



Article

Table 16. Statistical Parameters for All the Studied Models Used in Density Calculations at Atmospheric Pressure (Biodiesel)

biodiesel no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

ID soybean rapeseed palm soybean+rapeseed rapeseed+palm soybean+palm soybean+rapeseed +palm sunflower GP soya algae babassu beef tallow borage camelina oil canola oil castor white grease coconut 2 coconut 3 coffee corn evening primrose hemp hepar high IV hepar low IV jatropha linseed moringa oleifera neem palm perilla seed poultry fat rice bran soybean sunflower used cooking oil yellow grease coconut colza soybean coconut+colza (w1 = 0.0962) coconut+colza (w1 = 0.1967) coconut+colza (w1 = 0.2989) coconut+colza (w1 = 0.3970) coconut+colza (w1 = 0.4974) coconut+colza (w1 = 0.5977) coconut+colza (w1 = 0.6952) coconut+colza (w1 = 0.8039) coconut+colza (w1 = 0.9017) coconut+soybean (w1 = 0.0983)

% AARD

original GCVOL

GCVOL-OL-60

GCVOL-Pratas

Rackett-Soave

%RD

%RD

%RD

%RD

max

min

% AARD

max

min

% AARD

max

min

% AARD

max

min

0.72 0.70 0.68 0.72 0.55 0.53 0.58

1.84 1.78 1.83 1.73 1.38 1.36 1.46

−0.81 −0.58 −0.37 −0.30 −0.32 −0.36 −0.39

0.43 0.50 0.79 0.49 0.52 0.42 0.46

0.69 0.89 2.03 0.88 0.89 0.77 0.79

−0.66 −0.41 −0.08 −0.13 −0.11 −0.15 −0.20

0.21 0.24 0.40 0.11 0.11 0.09 0.07

0.12 0.26 1.41 0.36 0.21 0.19 0.25

−0.67 −0.40 −0.15 −0.05 −0.04 −0.16 −0.12

1.31 1.31 0.81 1.41 0.99 0.96 1.12

1.86 1.82 2.11 1.87 1.35 1.45 1.58

0,62 0,72 0,13 1,01 0,61 0,59 0,72

0.83 0.66 0.61 0.66 0.53 0.72 0.32 0.20 0.43 14.30 0.61 0.81 0.60 0.37 0.71 0.49 0.99 0.67 0.68 0.73 0.77 0.87 0.95 0.97 0.66 0.84 0.92 1.02 1.11 1.27 2.36 0.02 0.03 0.37 0.36

1.87 1.56 1.38 −0.66 −0.53 −0.72 −0.32 −0.20 −0.43 −14.30 −0.61 −0.81 0.60 0.52 1.46 0.93 1.92 1.24 1.27 1.39 1.50 1.64 1.80 1.86 1.26 1.54 1.68 1.81 1.91 2.18 7.37 −0.02 −0.03 0.37 −0.36

−0.25 −0.44 −0.24 −0.66 −0.53 −0.72 −0.32 −0.20 −0.43 −14.30 −0.61 −0.81 0.60 −0.65 −0.12 −0.63 0.03 0.05 0.06 0.06 0.04 0.04 0.07 0.08 0.09 0.16 0.17 0.23 0.26 0.33 0.35 −0.02 −0.03 0.37 −0.36

0.47 0.35 0.43 0.46 0.08 0.44 0.23 0.13 0.28 13.95 0.37 0.57 0.64 0.54 0.74 0.12 0.61 1.09 1.07 1.02 0.88 0.79 0.75 0.68 1.12 1.07 1.04 1.02 0.99 0.92 1.91 0.12 0.10 0.61 0.07

0.69 0.55 0.70 −0.46 0.08 −0.44 −0.23 −0.13 −0.28 −13.95 −0.37 −0.57 0.64 0.96 1.05 0.03 0.81 1.42 1.40 1.35 1.15 1.03 0.97 0.87 1.51 1.40 1.33 1.27 1.23 1.11 6.12 0.12 0.10 0.61 −0.07

−0.09 −0.27 −0.06 −0.46 0.08 −0.44 −0.23 −0.13 −0.28 −13.95 −0.37 −0.57 0.64 −0.03 0.26 −0.37 0.20 0.56 0.55 0.51 0.42 0.33 0.32 0.29 0.61 0.59 0.56 0.57 0.55 0.52 0.50 0.12 0.10 0.61 −0.07

0.07 0.11 0.04 0.53 0.18 0.50 0.33 0.22 0.35 14.14 0.44 0.64 0.51 0.37 0.07 0.71 0.09 0.30 0.29 0.27 0.20 0.17 0.17 0.13 0.31 0.34 0.34 0.36 0.37 0.37 1.41 0.03 0.01 0.54 0.15

0.11 −0.06 0.05 −0.53 −0.18 −0.50 −0.33 −0.22 −0.35 −14.14 −0.44 −0.64 0.51 −0.29 0.11 −0.58 0.16 0.39 0.38 0.34 0.27 0.26 0.24 0.19 0.41 0.41 0.42 0.44 0.46 0.44 5.45 0.03 0.01 0.54 −0.15

−0.01 −0.19 −0.07 −0.53 −0.18 −0.50 −0.33 −0.22 −0.35 −14.14 −0.44 −0.64 0.51 −0.53 −0.03 −0.94 −0.01 0.10 0.10 0.12 0.05 0.02 0.06 0.04 0.16 0.21 0.22 0.24 0.22 0.26 0.33 0.03 0.01 0.54 −0.15

1.45 1.16 1.16 0.82 0.50 0.33 1.75 2.05 1.27 2.88 0.66 0.50 3.00 0.30 1.24 0.65 1.11 0.88 0.90 0.97 1.04 1.12 1.16 1.15 0.86 1.13 1.25 1.36 1.46 1.59 2.67 1.75 1.74 1.65 0.72

1.87 1.59 1.50 0.82 0.50 0.33 1.75 2.05 1.27 −2.88 0.66 0.50 3.00 0.57 1.51 1.07 1.41 1.17 1.20 1.27 1.35 1.41 1.46 1.47 1.18 1.44 1.54 1.66 1.75 1.89 6.48 1.75 1.74 1.65 0.72

1,14 0,84 0,88 0,82 0,50 0,33 1,75 2,05 1,27 −2,88 0,66 0,50 3,00 0,08 1,03 0,27 0,82 0,57 0,60 0,70 0,76 0,80 0,88 0,86 0,59 0,88 1,00 1,11 1,16 1,31 1,51 1,75 1,74 1,65 0,72

0.14

−0.14

−0.14

0.02

−0.02

−0.02

0.23

−0.23

−0.23

1.17

1.17

1,17

0.84

−0.84

−0.84

0.71

−0.71

−0.71

0.79

−0.79

−0.79

0.94

0.94

0,94

1.05

−1.05

−1.05

0.88

−0.88

−0.88

0.95

−0.95

−0.95

0.54

0.54

0,54

0.66

−0.66

−0.66

0.41

−0.41

−0.41

0.47

−0.47

−0.47

0.55

0.55

0,55

0.11

0.11

0.11

0.29

0.29

0.29

0.14

0.14

0.14

1.43

1.43

1,43

0.19

0.38

−0.05

0.32

0.49

0.14

0.11

0.16

0.06

1.33

1.42

1,23

1.32

2.32

0.32

0.78

0.95

0.43

0.30

0.36

0.23

1.58

1.91

1,31

1.28

2.29

0.25

0.74

0.90

0.36

0.25

0.28

0.17

1.54

1.85

1,27

1.33

2.22

0.38

0.96

1.15

0.53

0.46

0.54

0.35

1.56

1.87

M

1.25



Article

Table 16. continued

biodiesel no. 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95

ID coconut+soybean (w1 = 0.1979) coconut+soybean (w1 = 0.3060) coconut+soybean (w1 = 0.4016) coconut+soybean (w1 = 0.6002) coconut+soybean (w1 = 0.8041) coconut+soybean (w1 = 0.9057) babassu soybean cotton seed cotton seed+babassu (w1 = 0.166) cotton seed+babassu (w1 = 0.196) cotton seed+babassu (w1 = 0.299) cotton seed+babassu (w1 = 0.490) cotton seed+babassu (w1 = 0.684) cotton seed+babassu (w1 = 0.805) cotton seed+babassu (w1 = 0.900) soybean+babassu (w1 = 0.099) soybean+babassu (w1 = 0.297) soybean+babassu (w1 = 0.404) soybean+babassu (w1 = 0.501) soybean+babassu (w1 = 0.605) soybean+babassu (w1 = 0.804) soybean+babassu (w1 = 0.901) soy b sunflower rapessed palm fish sunflower palm jatropha curcas rapeseed oil used cooking oil canola linseed rapeseed sunflower jatropha palm soybean code 1 code 2 code 3 code 4

% AARD

original GCVOL

GCVOL-OL-60

GCVOL-Pratas

Rackett-Soave

%RD

%RD

%RD

%RD

max

min

% AARD

max

min

% AARD

max

% AARD

min

max

min

0.87

1.35

0.35

0.93

1.22

0.53

0.66

0.73

0.52

1.98

2.11

1.81

0.32

0.68

−0.50

0.30

0.58

−0.21

0.29

−0.25

−0.36

0.19

0.47

−0.07

0.42

0.93

−0.34

0.24

0.37

−0.15

0.28

−0.23

−0.39

0.64

0.97

0.29

0.34

0.46

−0.73

0.23

0.37

−0.49

0.47

−0.44

−0.52

0.36

0.07

−0.72

0.58

1.34

−0.30

0.24

0.38

−0.18

0.21

−0.18

−0.28

0.24

0.29

−0.51

0.57

1.30

−0.27

0.35

0.59

−0.14

0.09

−0.06

−0.16

0.20

0.45

−0.27

0.58 0.60 0.46 0.50

1.32 1.43 0.82 0.77

−0.46 −0.27 −0.85 −0.99

0.22 0.36 0.29 0.46

0.30 0.65 −0.10 −0.29

−0.36 −0.13 −0.73 −0.88

0.29 0.09 0.67 0.84

−0.24 −0.03 −0.62 −0.79

−0.40 −0.18 −0.78 −0.97

0.26 0.19 0.54 0.76

0.11 0.37 −0.05 −0.27

−0.58 −0.26 −0.99 −1.21

0.75

−0.23

−1.28

0.63

−0.37

−1.03

1.14

−1.09

−1.26

1.02

−0.60

−1.43

4.26

4.26

4.26

4.39

4.39

4.39

4.28

4.28

4.28

4.73

4.73

4.73

0.45

0.51

−1.03

0.50

−0.18

−1.01

0.79

−0.70

−0.87

0.42

0.92

−0.05

0.48

1.09

−0.54

0.26

0.43

−0.37

0.19

−0.15

−0.30

1.26

1.57

0.98

0.45

1.19

−0.27

0.42

0.84

−0.01

0.09

0.00

−0.15

0.57

1.00

0.31

0.72

1.84

−0.81

0.43

0.69

−0.66

0.21

0.12

−0.67

1.31

1.86

0.62

0.70

1.78

−0.58

0.50

0.89

−0.41

0.24

0.26

−0.40

1.31

1.82

0.72

0.68

1.83

−0.37

0.79

2.03

−0.08

0.40

1.41

−0.15

0.81

2.11

0.13

0.72

1.73

−0.30

0.49

0.88

−0.13

0.11

0.36

−0.05

1.41

1.87

1.01

0.55

1.38

−0.32

0.52

0.89

−0.11

0.11

0.21

−0.04

0.99

1.35

0.61

0.53

1.36

−0.36

0.42

0.77

−0.15

0.09

0.19

−0.16

0.96

1.45

0.59

0.58

1.46

−0.39

0.46

0.79

−0.20

0.07

0.25

−0.12

1.12

1.58

0.72

0.83

1.87

−0.25

0.47

0.69

−0.09

0.07

0.11

−0.01

1.45

1.87

1.14

0.66 0.61 0.66 0.53 0.72 0.32 0.20 0.43 14.30 0.61 0.81 0.60 0.37 0.71 0.49 0.99 0.67 0.68 0.73 0.77 0.87

1.56 1.38 −0.66 −0.53 −0.72 −0.32 −0.20 −0.43 −14.30 −0.61 −0.81 0.60 0.52 1.46 0.93 1.92 1.24 1.27 1.39 1.50 1.64

−0.44 −0.24 −0.66 −0.53 −0.72 −0.32 −0.20 −0.43 −14.30 −0.61 −0.81 0.60 −0.65 −0.12 −0.63 0.03 0.05 0.06 0.06 0.04 0.04

0.35 0.43 0.46 0.08 0.44 0.23 0.13 0.28 13.95 0.37 0.57 0.64 0.54 0.74 0.12 0.61 1.09 1.07 1.02 0.88 0.79

0.55 0.70 −0.46 0.08 −0.44 −0.23 −0.13 −0.28 −13.95 −0.37 −0.57 0.64 0.96 1.05 0.03 0.81 1.42 1.40 1.35 1.15 1.03

−0.27 −0.06 −0.46 0.08 −0.44 −0.23 −0.13 −0.28 −13.95 −0.37 −0.57 0.64 −0.03 0.26 −0.37 0.20 0.56 0.55 0.51 0.42 0.33

0.11 0.04 0.53 0.18 0.50 0.33 0.22 0.35 14.14 0.44 0.64 0.51 0.37 0.07 0.71 0.09 0.30 0.29 0.27 0.20 0.17

−0.06 0.05 −0.53 −0.18 −0.50 −0.33 −0.22 −0.35 −14.14 −0.44 −0.64 0.51 −0.29 0.11 −0.58 0.16 0.39 0.38 0.34 0.27 0.26

−0.19 −0.07 −0.53 −0.18 −0.50 −0.33 −0.22 −0.35 −14.14 −0.44 −0.64 0.51 −0.53 −0.03 −0.94 −0.01 0.10 0.10 0.12 0.05 0.02

1.16 1.16 0.82 0.50 0.33 1.75 2.05 1.27 2.88 0.66 0.50 3.00 0.30 1.24 0.65 1.11 0.88 0.90 0.97 1.04 1.12

1.59 1.50 0.82 0.50 0.33 1.75 2.05 1.27 −2.88 0.66 0.50 3.00 0.57 1.51 1.07 1.41 1.17 1.20 1.27 1.35 1.41

0.84 0.88 0.82 0.50 0.33 1.75 2.05 1.27 −2.88 0.66 0.50 3.00 0.08 1.03 0.27 0.82 0.57 0.60 0.70 0.76 0.80

N



Article

Table 16. continued

biodiesel no. 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 FAMES

ID code 5 code 6 code 7 code 8 code 9 code 10 code 11 code 12 code 13 code 14 code 15 code 16 code 17 code 18 code 19 code 20 code 21 jatropha sample 1 jatropha sample 2 soybean commercial A soybean commercial B palm jatropha soybean jatropha soybean soybean rapeseed frying oil biodiesel palm fame jatropha fame palm soybean canola corn ricebran canola soybean palm corn oil crambe oil fodder radish oil coconut oil macauba pulp oil palm FAEE jatropha FAEE castor soybean animal fat commercial biodiesel castor palm beef tallow cotton seed soybean chicken fat coconut soybean biodiesel

original GCVOL

GCVOL-OL-60

GCVOL-Pratas

Rackett-Soave

%RD

%RD

%RD

%RD

% AARD

max

min

% AARD

max

min

% AARD

max

min

% AARD

max

0.95 0.97 0.66 0.84 0.92 1.02 1.11 1.27 2.36 0.02 0.03 0.37 0.36 0.14 0.84 1.05 0.66 0.11 0.19 1.32 1.28 1.33 0.87 0.32 0.42 0.34 0.58 0.57 0.58 0.60 0.46 0.50 0.75 4.26 0.45 0.48 0.45 0.72 0.70 0.68 0.72 0.55 0.53 0.58 0.83 0.66 0.61 0.66 0.53 0.72 0.32 0.20 0.43 14.30 0.61 0.81 0.60 0.37 0.88

1.80 1.86 1.26 1.54 1.68 1.81 1.91 2.18 7.37 −0.02 −0.03 0.37 −0.36 −0.14 −0.84 −1.05 −0.66 0.11 0.38 2.32 2.29 2.22 1.35 0.68 0.93 0.46 1.34 1.30 1.32 1.43 0.82 0.77 −0.23 4.26 0.51 1.09 1.19 1.84 1.78 1.83 1.73 1.38 1.36 1.46 1.87 1.56 1.38 −0.66 −0.53 −0.72 −0.32 −0.20 −0.43 −14.30 −0.61 −0.81 0.60 0.52 7.37

0.07 0.08 0.09 0.16 0.17 0.23 0.26 0.33 0.35 −0.02 −0.03 0.37 −0.36 −0.14 −0.84 −1.05 −0.66 0.11 −0.05 0.32 0.25 0.38 0.35 −0.50 −0.34 −0.73 −0.30 −0.27 −0.46 −0.27 −0.85 −0.99 −1.28 4.26 −1.03 −0.54 −0.27 −0.81 −0.58 −0.37 −0.30 −0.32 −0.36 −0.39 −0.25 −0.44 −0.24 −0.66 −0.53 −0.72 −0.32 −0.20 −0.43 −14.30 −0.61 −0.81 0.60 −0.65 −14.30

0.75 0.68 1.12 1.07 1.04 1.02 0.99 0.92 1.91 0.12 0.10 0.61 0.07 0.02 0.71 0.88 0.41 0.29 0.32 0.78 0.74 0.96 0.93 0.30 0.24 0.23 0.24 0.35 0.22 0.36 0.29 0.46 0.63 4.39 0.50 0.26 0.42 0.43 0.50 0.79 0.49 0.52 0.42 0.46 0.47 0.35 0.43 0.46 0.08 0.44 0.23 0.13 0.28 13.95 0.37 0.57 0.64 0.54 0.78

0.97 0.87 1.51 1.40 1.33 1.27 1.23 1.11 6.12 0.12 0.10 0.61 −0.07 −0.02 −0.71 −0.88 −0.41 0.29 0.49 0.95 0.90 1.15 1.22 0.58 0.37 0.37 0.38 0.59 0.30 0.65 −0.10 −0.29 −0.37 4.39 −0.18 0.43 0.84 0.69 0.89 2.03 0.88 0.89 0.77 0.79 0.69 0.55 0.70 −0.46 0.08 −0.44 −0.23 −0.13 −0.28 −13.95 −0.37 −0.57 0.64 0.96 6.12

0.32 0.29 0.61 0.59 0.56 0.57 0.55 0.52 0.50 0.12 0.10 0.61 −0.07 −0.02 −0.71 −0.88 −0.41 0.29 0.14 0.43 0.36 0.53 0.53 −0.21 −0.15 −0.49 −0.18 −0.14 −0.36 −0.13 −0.73 −0.88 −1.03 4.39 −1.01 −0.37 −0.01 −0.66 −0.41 −0.08 −0.13 −0.11 −0.15 −0.20 −0.09 −0.27 −0.06 −0.46 0.08 −0.44 −0.23 −0.13 −0.28 −13.95 −0.37 −0.57 0.64 −0.03 −13.95

0.17 0.13 0.31 0.34 0.34 0.36 0.37 0.37 1.41 0.03 0.01 0.54 0.15 0.23 0.79 0.95 0.47 0.14 0.11 0.30 0.25 0.46 0.66 0.29 0.28 0.47 0.21 0.09 0.29 0.09 0.67 0.84 1.14 4.28 0.79 0.19 0.09 0.21 0.24 0.40 0.11 0.11 0.09 0.07 0.07 0.11 0.04 0.53 0.18 0.50 0.33 0.22 0.35 14.14 0.44 0.64 0.51 0.37 0.52

0.24 0.19 0.41 0.41 0.42 0.44 0.46 0.44 5.45 0.03 0.01 0.54 −0.15 −0.23 −0.79 −0.95 −0.47 0.14 0.16 0.36 0.28 0.54 0.73 −0.25 −0.23 −0.44 −0.18 −0.06 −0.24 −0.03 −0.62 −0.79 −1.09 4.28 −0.70 −0.15 0.00 0.12 0.26 1.41 0.36 0.21 0.19 0.25 0.11 −0.06 0.05 −0.53 −0.18 −0.50 −0.33 −0.22 −0.35 −14.14 −0.44 −0.64 0.51 −0.29 5.45

0.06 0.04 0.16 0.21 0.22 0.24 0.22 0.26 0.33 0.03 0.01 0.54 −0.15 −0.23 −0.79 −0.95 −0.47 0.14 0.06 0.23 0.17 0.35 0.52 −0.36 −0.39 −0.52 −0.28 −0.16 −0.40 −0.18 −0.78 −0.97 −1.26 4.28 −0.87 −0.30 −0.15 −0.67 −0.40 −0.15 −0.05 −0.04 −0.16 −0.12 −0.01 −0.19 −0.07 −0.53 −0.18 −0.50 −0.33 −0.22 −0.35 −14.14 −0.44 −0.64 0.51 −0.53 −14.14

1.16 1.15 0.86 1.13 1.25 1.36 1.46 1.59 2.67 1.75 1.74 1.65 0.72 1.17 0.94 0.54 0.55 1.43 1.33 1.58 1.54 1.56 1.98 0.19 0.64 0.36 0.24 0.20 0.26 0.19 0.54 0.76 1.02 4.73 0.42 1.26 0.57 1.31 1.31 0.81 1.41 0.99 0.96 1.12 1.45 1.16 1.16 0.82 0.50 0.33 1.75 2.05 1.27 2.88 0.66 0.50 3.00 0.30 0.99

1.46 1.47 1.18 1.44 1.54 1.66 1.75 1.89 6.48 1.75 1.74 1.65 0.72 1.17 0.94 0.54 0.55 1.43 1.42 1.91 1.85 1.87 2.11 0.47 0.97 0.07 0.29 0.45 0.11 0.37 −0.05 −0.27 −0.60 4.73 0.92 1.57 1.00 1.86 1.82 2.11 1.87 1.35 1.45 1.58 1.87 1.59 1.50 0.82 0.50 0.33 1.75 2.05 1.27 −2.88 0.66 0.50 3.00 0.57 6.48

O

min 0.88 0.86 0.59 0.88 1.00 1.11 1.16 1.31 1.51 1.75 1.74 1.65 0.72 1.17 0.94 0.54 0.55 1.43 1.23 1.31 1.27 1.25 1.81 −0.07 0.29 −0.72 −0.51 −0.27 −0.58 −0.26 −0.99 −1.21 −1.43 4.73 −0.05 0.98 0.31 0.62 0.72 0.13 1.01 0.61 0.59 0.72 1.14 0.84 0.88 0.82 0.50 0.33 1.75 2.05 1.27 −2.88 0.66 0.50 3.00 0.08 −2.88



Article

Table 16. continued

biodiesel no. FAEES biodiesel overall

ID

% AARD 0.59 0.83

original GCVOL

GCVOL-OL-60

GCVOL-Pratas

Rackett-Soave

%RD

%RD

%RD

%RD

max 4.26 7.37

min

% AARD

−1.70 −14.30

0.46 0.72

max 4.39 6.12

min

% AARD

−1.53 −13.95

0.60 0.53

max 4.28 5.45

min

% AARD

−1.98 −14.14

0.49 0.90

max

min

4.73 6.48

−2.16 −2.88

Figure 10. %AARD distribution for pure alkyl esters at high pressures. Figure 8. Effect of temperature on the relative deviations (eq 32) calculated between the experimental (castor biodiesel sample78) and the estimated density: original-GCVOL (red circles), GCVOL−OL-60 (blue up triangles), GCVOL−Pratas (orange down triangles), and the Rackett−Soave equation (green squares).

Figure 11. Effect of pressure on the relative deviations (eq 32) between the experimental and the estimated biodiesel density (obtained from the Rackett−Soave−Tait equation). This chart includes all the data present in the databank.

Furthermore, the values obtained for the %AARD by SRK and PR without volume translation are within the order of magnitude.27 Experimental data at Tr = 0.7 for many esters are not available. For this, the “experimental value” referred on eq 27 was calculated using the Rackett−Soave equation for all alkyl esters. The values were calculated at T = 298.15 K, because most alkyl esters are in the liquid phase at this temperature. Pure component volume translation parameters calculated for all alkyl esters are presented in the Supporting Information spreadsheet. Some authors68,91−93 calculated pure alkyl ester densities using different equations of state (EOS). Pratas et al.92 used CPA EOS for densities calculation of three methyl esters. The %AARD obtained by these authors were 0.59 %, 0.99 %, and

Figure 9. Effect of temperature on the density behavior of soybean biodiesel.

needed. However, we conclude that the proposed methodology could accurately predict density of esters and of biodiesel at high pressures. Hence, the universality of the parameters has been confirmed. Prediction Using Cubic Equation of State. Table 17 shows all the statistical parameters obtained by SRK and PR calculations. It is important to mention that density data at high pressures were also considered in this validation step. All values of %AARD observed in Table 17 are in accordance with the expected results. For most of the data considered, PR CEOS presented better results than SRK CEOS for liquid densities.27 P



Article

Table 17. Statistical Parameters Obtained from SRK and PR Density Predictions with and without Translation Parameters (FAMES and FAEES) PR without translation

SRK without translation

%RD

PR with translation

%RD

SRK with translation

%RD

%RD

alkyl ester

%AARD

max

min

%AARD

max

min

%AARD

max

min

%AARD

max

min

ME-C6:0 ME-C7:0 ME-C8:0 ME-C9:0 ME-C10:0 ME-C11:0 ME-C12:0 ME-C13:0 ME-C14:0 ME-C15:0 ME-C16:0 ME-C16:1 ME-C17:0 ME-C18:0 ME-C18:1 ME-C18:2 ME-C18:3 ME-C19:0 ME-C20:0 ME-C20:1 ME-C22:0 ME-C22:1 ME-C24:0 EE-C8:0 EE-C10:0 EE-C12:0 EE-C14:0 EE-C16:0 EE-C18:0 EE-C18:1 EE-C18:2 EE-C18:3 EE-C20:0 FAMES FAEES overall

7.48 8.75 10.34 11.19 12.45 13.41 14.65 15.37 15.70 17.16 16.94 16.60 18.30 18.46 18.40 19.35 19.71 19.50 18.89 19.88 19.83 21.25 20.88 10.98 13.46 15.13 16.45 17.10 18.37 18.51 17.94 16.94 19.47 16.69 14.59 16.06

7.84 9.12 12.27 11.58 16.00 13.83 16.69 15.80 18.33 17.58 19.72 18.42 18.30 20.10 21.95 23.19 21.28 19.50 20.17 21.84 20.63 22.95 21.58 14.08 18.47 17.53 19.00 18.37 19.43 20.33 19.73 18.93 20.62 23.19 20.62 23.19

7.13 8.37 7.90 10.79 9.03 12.99 12.12 14.95 12.11 16.73 14.08 14.83 18.30 16.75 13.36 13.71 18.05 19.50 17.79 18.04 19.04 19.48 20.20 8.25 9.20 12.75 12.96 15.86 17.32 16.73 16.22 15.05 18.33 7.13 8.25 7.13

17.62 18.68 19.81 20.75 21.51 22.66 23.59 24.35 24.47 25.90 25.56 25.43 26.90 27.04 26.89 27.69 28.20 27.94 27.43 28.31 28.26 29.49 29.19 20.39 22.41 24.01 25.11 25.86 26.97 27.08 26.59 25.72 27.94 25.35 23.49 24.80

17.90 18.98 21.22 21.07 24.50 23.01 25.17 24.71 26.95 26.26 27.90 26.98 26.90 28.46 29.89 30.98 29.54 27.94 28.52 29.99 28.95 30.97 29.78 23.30 26.72 25.92 27.22 26.94 27.88 28.64 28.13 27.42 28.92 30.98 28.92 30.98

17.34 18.38 18.09 20.43 18.72 22.31 21.63 24.00 21.47 25.54 23.24 23.94 26.90 25.58 22.46 22.75 26.80 27.94 26.50 26.73 27.58 27.97 28.60 18.33 18.95 22.12 22.25 24.81 26.07 25.56 25.12 24.12 26.96 17.34 18.33 17.34

0.63 0.35 0.74 0.37 1.19 0.58 0.84 0.73 1.64 0.63 1.95 1.26 0.81 1.36 1.58 1.93 2.93 0.62 1.63 1.04 1.22 1.12 0.55 1.06 1.66 1.34 1.76 2.14 1.87 1.31 1.22 1.48 1.41 1.54 1.55 1.54

0.96 0.61 2.00 0.64 3.73 0.99 2.85 1.15 5.11 1.07 4.60 2.82 0.81 3.02 5.79 5.22 4.56 0.62 2.73 2.15 2.03 2.60 1.18 3.14 4.88 3.47 5.05 3.38 2.94 2.93 2.72 3.21 2.59 5.22 4.45 5.22

0.30 −0.09 −1.91 −0.64 −3.73 −0.99 −2.85 −1.15 −5.11 −1.07 −4.60 −2.82 −0.81 −3.02 −5.79 −4.61 1.28 −0.62 −2.73 −1.80 −2.03 −1.10 −1.18 −3.14 −4.88 −3.47 −5.05 −3.38 −2.94 −2.93 −2.72 −3.21 −2.59 −5.79 −5.05 −5.79

0.71 0.33 0.43 0.25 1.39 0.52 0.92 0.68 1.93 0.59 2.10 1.01 0.69 1.14 1.37 1.52 3.08 0.51 1.26 0.86 0.82 1.07 0.34 1.16 1.80 1.48 2.03 1.84 1.55 1.09 0.99 1.21 1.06 1.44 1.67 1.51

0.89 0.54 0.99 0.46 4.02 0.82 2.14 1.01 5.13 0.94 4.50 2.20 0.69 2.46 5.70 4.58 4.42 0.51 2.13 2.01 1.46 2.48 0.65 2.85 4.87 2.89 4.96 2.80 2.40 2.39 2.17 2.55 2.01 4.42 2.99 4.42

0.52 0.12 −0.99 −0.46 −4.02 −0.82 −2.14 −1.01 −5.13 −0.94 −4.50 −2.20 −0.69 −2.46 −5.70 −4.58 1.84 −0.51 −2.13 −1.19 −1.46 −0.62 −0.65 −2.26 −4.87 −2.89 −4.96 −2.80 −2.40 −2.39 −2.17 −2.55 −2.01 −5.70 −4.96 −5.70

0.84 % for methyl laurate, methyl myristate, and methyl oleate, respectively. These authors used the Wilson and Jasperson method for critical temperature prediction. Hosseini et al.93 used Yukawa hard-core chain EOS and obtained, for each respective FAME studied by Pratas et al.,92 %AARD values of 0.53 %, 0.33 %, and 0.35 %. Oliveira et al.94 used soft-SAFT EOS in the volumetric behavior prediction of ethyl laurate. These authors obtained %AARD values of 0.49 % for 15 different FAMES and %AARD of 1.8 % for ethyl laurate. As it can be observed in Table 17 results obtained by the application of PR and SRK using a constant volume translation parameter are within similar orders of magnitude. SRK CEOS with volume translation presented the best results for FAMES (% AARD = 1.44 %), while for FAEES PR CEOS with volume translation produced the lowest overall deviation (%AARD = 1.55 %). The statistical parameters calculated using the predicted density values produced by PR and SRK CEOS for all different biodiesels studied are shown in Table 18. As expected, PR without translation presented better results than SRK without

translation. Although these translated EOS presented similar deviation results, density values predicted by SRK CEOS are slightly better than the values obtained from PR CEOS. The highest absolute relative deviations produced by the translated versions of PR CEOS and SRK CEOS were 5.95 % and 4.87 % for FAMES biodiesel; 4.84 % and 4.81 % for FAEES biodiesel. The results observed in Table 18 are similar in order of magnitude and in some cases better than those obtained by others researchers.68,92−94 However, it is important to mention that, unlike all these authors that used experimental density data to make regressions of specific parameters of the equations they employed, we propose a fully predictive method to calculate density of FAME, FAEES, and biodiesel.

■

CONCLUSIONS In this work, many prediction methods able to calculate essential properties of alkyl esters present in biodiesel were evaluated. The following properties were studied: normal freezing temperature (Tf), normal boiling temperature (Tb), critical temperature (Tc), critical pressure (Pc), critical volume Q



Article

Table 18. Statistical Parameters Obtained from SRK and PR Density Predictions with and without Translation Parameters (Biodiesel) PR without translation


%RD biodiesel no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

ID soybean rapeseed palm soybean+rapeseed rapeseed+palm soybean+palm soybean+rapeseed+palm sunflower GP soyA algae babassu beef tallow borage camelina oil canola oil castor white grease coconut 2 coconut 3 coffee corn evening primrose hemp hepar high IV hepar low IV jatropha linseed moringa oleifera neem palm perilla seed poultry fat rice bran soybean sunflower used cooking oil yellow grease coconut colza soybean coconut+colza (w1 = 0.0962) coconut+colza (w1 = 0.1967) coconut+colza (w1 = 0.2989) coconut+colza (w1 = 0.3970) coconut+colza (w1 = 0.4974) coconut+colza (w1 = 0.5977) coconut+colza (w1 = 0.6952) coconut+colza (w1 = 0.8039) coconut+colza (w1 = 0.9017) coconut+soybean (w1 = 0.0983) coconut+soybean (w1 = 0.1979) coconut+soybean (w1 = 0.3060)

PR with translation

%RD


%RD

%RD

% AARD

max

min

% AARD

max

min

% AARD

max

min

% AARD

max

min

19.13 19.43 19.85 19.72 19.42 19.37 19.52 19.02 18.83 18.89 19.87 16.83 19.54 20.10 20.41 20.09 20.07 19.65 16.93 16.89 20.18 20.08 20.11 20.15 19.51 19.57 19.73 20.26 20.18 20.53 19.46 20.69 19.82 20.33 19.90 19.98 17.31 20.00 15.10 18.87 18.57 18.51 18.16 17.78 17.43 17.07 16.68 16.34 15.90 15.51 17.00

20.70 21.03 21.65 21.37 21.11 21.06 21.21 20.74 20.56 20.30 19.87 16.83 19.54 20.10 20.41 20.09 20.07 19.65 16.93 16.89 20.18 20.08 20.11 20.15 19.51 19.57 19.73 20.26 20.18 20.53 19.46 20.69 19.82 20.33 19.90 19.98 17.31 20.00 16.69 20.42 20.12 20.06 19.72 19.33 18.99 18.63 18.24 17.92 17.49 17.11 18.76

17.33 17.54 16.66 17.35 17.10 16.99 17.13 17.40 17.19 17.53 19.87 16.83 19.54 20.10 20.41 20.09 20.07 19.65 16.93 16.89 20.18 20.08 20.11 20.15 19.51 19.57 19.73 20.26 20.18 20.53 19.46 20.69 19.82 20.33 19.90 19.98 17.31 20.00 13.56 17.37 17.06 17.01 16.65 16.28 15.92 15.57 15.17 14.81 14.37 13.98 15.26

27.56 27.82 28.20 28.09 27.82 27.78 27.91 27.57 27.39 27.45 28.26 25.62 27.97 28.48 28.75 28.46 28.31 28.07 25.70 25.66 28.55 28.47 28.50 28.53 27.95 28.00 28.15 28.63 28.54 28.86 27.90 29.01 28.22 28.68 28.30 28.36 25.99 28.39 24.16 27.45 27.19 27.14 26.83 26.50 26.20 25.88 25.54 25.24 24.86 24.52 25.79

28.98 29.16 29.67 29.42 29.19 29.14 29.28 29.04 28.87 28.65 28.26 25.62 27.97 28.48 28.75 28.46 28.31 28.07 25.70 25.66 28.55 28.47 28.50 28.53 27.95 28.00 28.15 28.63 28.54 28.86 27.90 29.01 28.22 28.68 28.30 28.36 25.99 28.39 25.49 28.77 28.50 28.45 28.15 27.81 27.52 27.20 26.86 26.58 26.20 25.86 27.29

26.13 26.31 25.54 26.14 25.92 25.83 25.95 26.19 26.01 26.29 28.26 25.62 27.97 28.48 28.75 28.46 28.31 28.07 25.70 25.66 28.55 28.47 28.50 28.53 27.95 28.00 28.15 28.63 28.54 28.86 27.90 29.01 28.22 28.68 28.30 28.36 25.99 28.39 22.88 26.18 25.92 25.87 25.56 25.24 24.93 24.62 24.28 23.96 23.58 23.24 24.32

0.87 0.91 1.55 1.36 0.96 1.00 1.10 1.04 0.95 0.84 1.14 0.40 0.63 2.02 2.28 1.58 2.54 0.97 0.32 0.31 1.53 1.80 2.13 2.18 0.80 0.78 1.21 2.63 1.17 1.84 0.81 3.31 1.33 1.91 1.68 1.35 1.58 1.56 1.49 1.00 1.00 0.96 0.93 0.93 0.97 0.99 1.04 1.09 1.24 1.35 1.48

2.49 2.45 3.13 2.91 2.44 2.49 2.64 2.51 2.22 1.98 1.14 0.40 0.63 2.02 2.28 1.58 −2.54 0.97 0.32 0.31 1.53 1.80 2.13 2.18 0.80 0.78 1.21 2.63 1.17 1.84 0.81 3.31 1.33 1.91 1.68 1.35 −1.58 1.56 0.11 2.04 2.01 1.85 1.68 1.47 1.31 1.13 0.92 0.79 0.56 0.35 0.57

−0.92 −0.97 −1.97 −1.03 −1.47 −1.49 −1.35 −0.90 −1.22 −0.86 1.14 0.40 0.63 2.02 2.28 1.58 −2.54 0.97 0.32 0.31 1.53 1.80 2.13 2.18 0.80 0.78 1.21 2.63 1.17 1.84 0.81 3.31 1.33 1.91 1.68 1.35 −1.58 1.56 −2.90 −1.02 −1.05 −1.20 −1.36 −1.55 −1.71 −1.86 −2.07 −2.25 −2.48 −2.68 −3.01

0.73 0.76 1.32 1.15 0.77 0.80 0.91 0.99 0.84 0.79 1.06 0.32 0.56 1.95 2.21 1.50 2.61 0.89 0.24 0.23 1.45 1.72 2.06 2.11 0.73 0.71 1.14 2.55 1.10 1.77 0.74 3.23 1.25 1.84 1.60 1.28 1.65 1.48 1.11 0.91 0.89 0.80 0.78 0.72 0.69 0.70 0.74 0.78 0.87 0.98 1.15

2.35 2.31 2.47 2.24 1.84 1.80 1.95 2.37 2.08 1.87 1.06 0.32 0.56 1.95 2.21 1.50 −2.61 0.89 0.24 0.23 1.45 1.72 2.06 2.11 0.73 0.71 1.14 2.55 1.10 1.77 0.74 3.23 1.25 1.84 1.60 1.28 −1.65 1.48 0.07 2.00 1.97 1.81 1.65 1.44 1.28 1.10 0.89 0.76 0.53 0.32 0.53

−0.75 −0.65 −1.40 −0.47 −0.90 −0.92 −0.79 −0.34 −0.65 −0.39 1.06 0.32 0.56 1.95 2.21 1.50 −2.61 0.89 0.24 0.23 1.45 1.72 2.06 2.11 0.73 0.71 1.14 2.55 1.10 1.77 0.74 3.23 1.25 1.84 1.60 1.28 −1.65 1.48 −2.10 −0.37 −0.39 −0.53 −0.68 −0.84 −0.99 −1.13 −1.33 −1.49 −1.70 −1.89 −2.32

17.03

18.70

15.31

25.83

27.25

24.37

1.27

0.72

−2.72

0.94

0.68

−2.01

16.96

18.63

15.32

25.77

27.19

24.39

1.17

0.87

−2.44

0.89

0.84

−1.72

R



Article

Table 18. continued PR without translation


%RD biodiesel no. 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

ID coconut+soybean (w1 = 0.4016) coconut+soybean (w1 = 0.6002) coconut+soybean (w1 = 0.8041) coconut+soybean (w1 = 0.9057) babassu soybean cotton seed cotton seed+babassu (w1 = 0.166) cotton seed+babassu (w1 = 0.196) cotton seed+babassu (w1 = 0.299) cotton seed+babassu (w1 = 0.490) cotton seed+babassu (w1 = 0.684) cotton seed+babassu (w1 = 0.805) cotton seed+babassu (w1 = 0.900) soybean+babassu (w1 = 0.099) soybean+babassu (w1 = 0.297) soybean+babassu (w1 = 0.404) soybean+babassu (w1 = 0.501) soybean+babassu (w1 = 0.605) soybean+babassu (w1 = 0.804) soybean+babassu (w1 = 0.901) soy B sunflower rapessed palm fish sunflower palm jatropha curcas rapeseed oil used cooking oil canola linseed rapeseed sunflower jatropha palm soybean code 1 code 2 code 3 code 4 code 5 code 6 code 7 code 8 code 9 code 10 code 11

% AARD

max

16.95

18.57

16.88

PR with translation

%RD


%RD

%RD

min

% AARD

max

min

% AARD

min

% AARD

15.38

25.77

27.14

24.45

1.08

1.02

−2.15

0.79

0.99

−1.42

18.42

15.40

25.73

27.02

24.49

0.93

1.28

−1.65

0.65

1.25

−0.90

16.76

18.25

15.45

25.62

26.88

24.55

0.89

1.54

−1.12

0.72

1.50

−0.35

16.77

18.14

15.47

25.64

26.78

24.57

0.81

1.64

−0.86

0.72

1.60

−0.08

16.10 18.68 18.26 16.48

17.69 20.21 19.81 18.06

14.54 17.19 16.73 14.88

25.03 27.29 26.92 25.37

26.38 28.59 28.23 26.70

23.73 26.03 25.62 24.03

1.12 1.01 0.93 1.06

0.75 2.07 1.57 0.91

−2.32 −0.96 −1.51 −2.21

0.78 0.94 0.77 0.76

0.72 2.03 1.53 0.87

−1.54 −0.29 −0.84 −1.45

16.54

18.13

14.95

25.42

26.76

24.09

1.07

0.94

−2.18

0.77

0.90

−1.43

16.78

18.36

15.21

25.62

26.96

24.32

1.04

1.03

−2.06

0.74

1.00

−1.31

17.17

18.76

15.61

25.97

27.31

24.65

1.03

1.18

−1.93

0.73

1.14

−1.21

17.60

19.16

16.03

26.34

27.66

25.02

0.98

1.33

−1.78

0.72

1.29

−1.08

17.88

19.44

16.34

26.59

27.91

25.29

0.95

1.46

−1.63

0.74

1.43

−0.93

18.07

19.65

16.54

26.75

28.09

25.46

0.95

1.55

−1.56

0.76

1.51

−0.88

16.35 16.90 17.18 17.45 17.73 18.24 19.34 20.26 20.31 20.35 19.63 17.90 18.43 17.98 19.79 18.96 19.04 19.70 19.87 21.44 20.04 20.20 19.62 20.31 19.67 19.27 19.42 19.54 19.54 19.60 19.72 19.52 19.30 19.61 19.20

17.96 18.49 18.75 19.02 19.28 19.78 21.27 20.26 20.31 20.35 19.63 19.46 20.02 19.47 20.20 20.94 20.63 19.70 19.87 21.44 20.04 20.20 19.62 20.31 19.67 19.27 19.42 19.54 19.54 19.60 19.72 19.52 19.30 19.61 19.20

14.79 15.36 15.65 15.92 16.17 16.71 17.72 20.26 20.31 20.35 19.63 16.33 16.91 16.50 19.39 17.02 17.52 19.70 19.87 21.44 20.04 20.20 19.62 20.31 19.67 19.27 19.42 19.54 19.54 19.60 19.72 19.52 19.30 19.61 19.20

25.25 25.73 25.98 26.21 26.46 26.90 27.88 28.63 28.66 28.70 28.06 26.59 27.06 26.64 28.22 27.51 27.61 28.13 28.30 29.66 28.44 28.58 28.07 28.68 28.10 27.73 27.87 27.97 27.97 28.03 28.13 27.95 27.77 28.04 27.67

26.62 27.07 27.30 27.54 27.77 28.21 29.68 28.63 28.66 28.70 28.06 27.92 28.41 27.91 28.56 29.21 28.95 28.13 28.30 29.66 28.44 28.58 28.07 28.68 28.10 27.73 27.87 27.97 27.97 28.03 28.13 27.95 27.77 28.04 27.67

23.95 24.44 24.70 24.93 25.14 25.61 26.47 28.63 28.66 28.70 28.06 25.27 25.78 25.39 27.87 25.87 26.32 28.13 28.30 29.66 28.44 28.58 28.07 28.68 28.10 27.73 27.87 27.97 27.97 28.03 28.13 27.95 27.77 28.04 27.67

1.09 1.02 0.97 0.95 0.93 0.98 1.62 2.06 2.05 1.96 1.03 1.02 0.97 0.95 1.32 1.08 1.12 1.16 2.38 2.06 1.84 1.79 1.09 2.19 1.25 0.35 0.75 0.90 0.80 1.07 0.92 0.86 0.90 1.01 0.68

0.91 1.19 1.32 1.48 1.62 1.88 4.19 2.06 2.05 1.96 1.03 1.16 1.76 0.81 1.74 2.57 2.62 1.16 2.38 2.06 1.84 1.79 1.09 2.19 1.25 0.35 0.75 0.90 0.80 1.07 0.92 0.86 0.90 1.01 0.68

−2.20 −1.88 −1.72 −1.58 −1.47 −1.19 −0.31 2.06 2.05 1.96 1.03 −1.96 −1.37 −2.19 0.90 −1.42 −0.47 1.16 2.38 2.06 1.84 1.79 1.09 2.19 1.25 0.35 0.75 0.90 0.80 1.07 0.92 0.86 0.90 1.01 0.68

0.78 0.72 0.70 0.74 0.77 0.83 1.80 1.99 1.98 1.88 0.95 0.75 0.81 0.72 1.32 0.98 1.30 1.16 2.38 2.06 1.84 1.79 1.10 2.19 1.18 0.28 0.67 0.82 0.72 1.00 0.85 0.79 0.82 0.93 0.61

0.87 1.16 1.29 1.45 1.58 1.84 4.83 1.99 1.98 1.88 0.95 1.13 1.72 0.73 1.67 2.40 2.55 1.16 2.38 2.06 1.84 1.79 1.10 2.19 1.18 0.28 0.67 0.82 0.72 1.00 0.85 0.79 0.82 0.93 0.61

−1.43 −1.14 −0.99 −0.86 −0.76 −0.50 0.16 1.99 1.98 1.88 0.95 −1.28 −0.71 −1.62 0.98 −0.76 0.19 1.16 2.38 2.06 1.84 1.79 1.10 2.19 1.18 0.28 0.67 0.82 0.72 1.00 0.85 0.79 0.82 0.93 0.61

S

max

max

min



Article

Table 18. continued PR without translation


%RD biodiesel no.

ID

103 code 12 104 code 13 105 code 14 106 code 15 107 code 16 108 code 17 109 code 18 110 code 19 111 code 20 112 code 21 113 jatropha sample 1 114 jatropha sample 2 115 soybean commercial A 116 soybean commercial B 117 palm 118 jatropha 119 soybean 120 jatropha 121 soybean 122 soybean 123 rapeseed 124 frying oil biodiesel 125 palm FAME 126 jatropha FAME 127 palm 128 soybean 129 canola 130 corn 131 ricebran 132 canola 133 soybean 134 palm 135 corn oil 136 crambe oil 137 fodder radish oil 138 coconut oil 139 macauba pulp oil 140 palm FAEE 141 jatropha FAEE 142 castor 143 soybean 144 animal fat 145 commercial biodiesel 146 castor 147 palm 148 beef tallow 149 cotton seed 150 soybean 151 chicken fat 152 coconut 153 soybean FAMES biodiesel FAEES biodiesel overall

% AARD

max

19.75 19.83 19.58 19.59 19.58 19.78 19.62 19.41 19.98 19.34 19.99 19.60 19.38 19.43 18.57 18.39 18.68 19.79 18.70 19.61 19.93 20.07 17.95 18.35 18.07 18.11 18.53 18.04 18.28 17.96 17.63 17.42 23.00 19.85 18.34 16.00 17.28 18.03 18.07 25.02 19.12 18.79 19.21 20.82 17.99 17.34 19.36 18.55 18.24 15.22 17.80 19.07 18.01 18.98

19.75 19.83 19.58 19.59 19.58 19.78 19.62 19.41 19.98 19.34 19.99 19.60 20.62 20.66 18.57 19.89 20.19 20.20 20.26 23.41 24.28 20.82 19.27 19.68 19.65 19.69 20.08 19.54 19.81 19.66 19.34 18.94 23.00 21.54 20.04 17.49 19.18 19.41 19.47 25.11 20.43 20.00 22.64 22.37 19.51 18.87 20.83 20.05 19.82 16.68 19.36 25.11 23.00 25.11

PR with translation

%RD min

% AARD

max

19.75 19.83 19.58 19.59 19.58 19.78 19.62 19.41 19.98 19.34 19.99 19.60 18.07 18.11 18.57 16.90 17.18 19.39 17.20 16.38 16.58 19.28 16.67 17.00 16.53 16.59 17.04 16.53 16.85 16.28 15.96 15.93 23.00 18.23 16.66 14.49 15.39 16.70 16.67 24.93 17.84 17.60 15.75 19.27 16.52 15.85 17.93 17.09 16.85 13.83 16.27 13.56 14.49 14.49

28.16 28.24 28.01 28.02 28.01 28.19 28.05 27.86 28.36 27.80 28.39 28.04 27.87 27.90 27.13 27.00 27.28 28.22 27.31 27.84 28.13 28.47 26.62 26.97 26.70 26.74 27.11 26.68 26.90 26.60 26.31 26.13 31.07 28.26 26.93 24.92 25.99 26.67 26.71 32.75 27.64 27.34 27.48 29.02 26.66 26.08 27.88 27.15 26.87 24.27 26.46 27.50 26.65 27.43

28.16 28.24 28.01 28.02 28.01 28.19 28.05 27.86 28.36 27.80 28.39 28.04 28.93 28.97 27.13 28.29 28.57 28.56 28.63 31.16 31.95 29.12 27.74 28.11 28.06 28.10 28.44 27.96 28.21 28.06 27.78 27.43 31.07 29.72 28.40 26.18 27.63 27.85 27.90 32.84 28.76 28.38 30.48 30.38 27.95 27.39 29.13 28.43 28.23 25.49 27.80 32.84 31.07 32.84

(Vc), and acentric factor (ω). All the analyzed methods of Tf presented unsatisfactory results. Therewith, to calculate this


%RD min

% AARD

max

28.16 28.24 28.01 28.02 28.01 28.19 28.05 27.86 28.36 27.80 28.39 28.04 26.74 26.77 27.13 25.75 26.02 27.87 26.03 25.18 25.36 27.80 25.53 25.82 25.39 25.45 25.84 25.40 25.68 25.17 24.88 24.86 31.07 26.87 25.49 23.66 24.37 25.53 25.50 32.67 26.55 26.33 24.65 27.67 25.41 24.82 26.67 25.91 25.70 23.12 25.16 22.88 23.66 23.66

0.99 1.18 0.83 0.85 0.84 1.08 0.84 0.61 1.22 0.49 1.58 1.06 1.15 1.10 0.13 0.79 1.01 1.32 1.01 1.58 1.68 1.81 0.91 0.77 1.33 1.18 1.06 1.21 1.08 1.45 1.62 2.04 4.84 1.02 1.43 1.21 2.32 1.34 1.31 3.79 0.97 0.68 1.42 1.22 0.93 1.18 1.08 0.81 0.87 0.84 1.41 1.20 1.40 1.22

0.99 1.18 0.83 0.85 0.84 1.08 0.84 0.61 1.22 0.49 1.58 1.06 2.35 2.27 −0.13 1.32 2.03 1.74 2.05 5.20 5.95 2.59 0.62 1.12 0.40 0.61 0.78 0.43 0.69 0.43 0.21 −0.46 4.84 1.27 0.46 0.33 −0.29 0.11 0.18 3.92 2.22 1.48 4.08 0.60 0.95 0.50 2.48 1.38 1.30 0.89 0.26 5.95 4.84 5.95

%RD min

% AARD

max

min

0.99 1.18 0.83 0.85 0.84 1.08 0.84 0.61 1.22 0.49 1.58 1.06 −0.37 −0.45 −0.13 −1.71 −0.98 0.90 −1.03 −2.06 −2.09 1.00 −2.01 −1.64 −2.83 −2.58 −2.36 −2.65 −2.33 −3.08 −3.30 −3.57 4.84 −2.23 −3.08 −2.60 −4.30 −2.69 −2.74 3.65 −0.45 −0.99 −3.00 −2.74 −2.07 −2.56 −0.45 −1.62 −1.71 −1.84 −2.94 −3.01 −4.30 −4.30

0.91 1.11 0.76 0.78 0.76 1.00 0.76 0.54 1.14 0.41 1.54 1.03 1.14 1.09 0.13 0.61 0.92 1.32 0.91 1.24 1.33 1.85 0.68 0.59 1.09 0.94 0.83 0.97 0.85 1.23 1.39 1.79 4.81 0.83 1.20 0.94 2.11 1.11 1.08 3.74 0.97 0.58 1.25 1.05 0.69 0.92 1.21 0.63 0.65 0.56 1.17 1.01 1.17 1.02

0.91 1.11 0.76 0.78 0.76 1.00 0.76 0.54 1.14 0.41 1.54 1.03 2.20 2.13 −0.13 1.25 1.99 1.66 2.01 4.11 4.87 2.48 0.58 1.08 0.32 0.54 0.71 0.36 0.62 0.33 0.11 −0.50 4.81 1.18 0.36 0.21 −0.40 0.07 0.15 3.88 2.07 1.37 3.08 0.53 0.88 0.42 2.41 1.31 1.22 0.80 0.19 4.87 4.81 4.87

0.91 1.11 0.76 0.78 0.76 1.00 0.76 0.54 1.14 0.41 1.54 1.03 −0.08 −0.16 −0.13 −1.15 −0.31 0.98 −0.36 −2.14 −2.19 1.20 −1.48 −1.12 −2.27 −2.04 −1.82 −2.10 −1.79 −2.53 −2.75 −3.01 4.81 −1.73 −2.54 −1.94 −3.74 −2.18 −2.24 3.59 −0.07 −0.61 −3.02 −2.33 −1.49 −1.98 0.11 −1.05 −1.13 −1.14 −2.38 −3.02 −3.74 −3.74

property, we proposed eight correlations. For Tb, CG and MG methods should be used for FAMES and FAEES, respectively. T



Article

V/cm3·mol−1 = volume ρ/g·cm−3 = density c/cm3·mol−1 = volume translation parameter MW/g·mol−1 = molecular weight CEOS = cubic equation of state CSP = corresponding state principle GC = group contribution SRK = Soave−Redlich−Kwong PR = Peng−Robinson R = universal gas constant ZRA = compressibility factor ω = acentric factor x = molar fraction kij = binary interaction parameter

We concluded that the packages (Tc, Pc, ω) TU-AB-SH (% AARD = 0.99 %) for FAMES, FD-SJ-SH (%AARD = 0.89 %) for FAEES, and NL-NL-HP (%AARD = 0.21 %) for hydroxyesters should be used. For all the studied alkyl esters, the MP method should be used for Vc. Additionally, the Rackett−Soave equation and three versions of the GCVOL method were compared in density predictions of pure alkyl esters and of biodiesel. Only the Rackett−Soave equation was able to predict a physically consistent volumetric behavior at severe temperatures for all the studied compounds. The Rackett−Soave−Tait equation was also applied to predict density in high-pressure conditions and presented good accuracy. A final validation of the chosen packages for critical properties and acentric factor was performed by applying the estimated values on PR and SRK CEOS for density prediction. The obtained results were inaccurate, as expected. To improve the results, pure component volume translation parameters were calculated for various alkyl esters. These parameters were calculated by the Rackett−Soave equation at 298.15 K. The values of %AARD obtained by PR CEOS with volume translation were 1.54 % and 1.55 % for FAMES and FAEES, respectively. Using SRK CEOS with volume translation these values were 1.44 % and 1.67 %, respectively. For biodiesel, % AARD values obtained by PR CEOS with volume translation were 1.20 % and 1.40 % for methilic and ethylic biodiesel, respectively, while for SRK CEOS with volume translation, these values were 1.01 % and 1.17 %. All these low values indicate that the models related to the chosen packages can be applied to estimate the input properties of equations of state. Finally, we emphasize that we used a fully predictive methodology to obtain the volume translation parameters, unlike what is seen in the literature.

■

Subscript

■

REFERENCES

(1) Atabani, a. E.; Silitonga, a. S.; Badruddin, I. A.; Mahlia, T. M. I.; Masjuki, H. H.; Mekhilef, S. A Comprehensive Review on Biodiesel as an Alternative Energy Resource and Its Characteristics. Renewable Sustainable Energy Rev. 2012, 16, 2070−2093. (2) Demirbas, A. Progress and Recent Trends in Biodiesel Fuels. Energy Convers. Manage. 2009, 50, 14−34. (3) Demirbas, A. H.; Demirbas, I. Importance of Rural Bioenergy for Developing Countries. Energy Convers. Manage. 2007, 48, 2386−2398. (4) Canakci, M.; Gerpen, J. Van. Biodiesel Production from Oils and Fats with High Free Fatty Acids. Trans. ASAE 2001, 44, 1429−1436. (5) García, M.; Alba, J.-J.; Gonzalo, A.; Sánchez, J. L.; Arauzo, J. Comparison of Methods for Estimating Critical Properties of Alkyl Esters and Its Mixtures. J. Chem. Eng. Data 2012, 57, 208−218. (6) Silveira, M. B.; do Carmo, F. R.; Santiago-Aguiar, R. S.; de Sant’Ana, H. B. Ab−diesel: Liquid−liquid Equilibrium and Volumetric Transport Properties. Fuel 2014, 119, 292−300. (7) Su, Y.-C.; Liu, Y. a.; Diaz Tovar, C. A.; Gani, R. Selection of Prediction Methods for Thermophysical Properties for Process Modeling and Product Design of Biodiesel Manufacturing. Ind. Eng. Chem. Res. 2011, 50, 6809−6836. (8) Arvelos, S.; Rade, L. L.; Watanabe, E. O.; Hori, C. E.; Romanielo, L. L. Evaluation of Different Contribution Methods over the Performance of Peng−Robinson and CPA Equation of State in the Correlation of VLE of Triglycerides, Fatty Esters and glycerol+CO2 and Alcohol. Fluid Phase Equilib. 2014, 362, 136−146. (9) Chang, A.-F.; Liu, Y. a. Integrated Process Modeling and Product Design of Biodiesel Manufacturing. Ind. Eng. Chem. Res. 2010, 49, 1197−1213. (10) Hoekman, S. K.; Broch, A.; Robbins, C.; Ceniceros, E.; Natarajan, M. Review of Biodiesel Composition, Properties, and Specifications. Renewable Sustainable Energy Rev. 2012, 16, 143−169. (11) Lopes, J. C. A.; Boros, L.; Meirelles, A. J. A.; Daridon, J. L.; Pauly, J.; Marrucho, I. M.; Coutinho, J. A. P. Prediction of Cloud Points of Biodiesel. Energy Fuels 2008, 5, 747−752. (12) Goodrum, J. Volatility and Boiling Points of Biodiesel from Vegetable Oils and Tallow. Biomass Bioenergy 2002, 22, 205−211. (13) An, H.; Yang, W. M.; Maghbouli, A.; Chou, S. K.; Chua, K. J. Detailed Physical Properties Prediction of Pure Methyl Esters for Biodiesel Combustion Modeling. Appl. Energy 2013, 102, 647−656.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00638. Additional details of the evaluated packages; details of developed data bank of pure alkyl esters and biodiesel (PDF) MS-Excel spreadsheet containing the structural groups specifications (of FAMES and FAEES) using all the studied methods (XLSX)

■

b = normal boiling f = normal freezing c = critical exp = experimental calc = calculated r = reduced m = relative to mixture (biodiesel) i = component i RA = Rackett

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +55-85999998649. Fax: + 55-84-33178503. Funding

The authors acknowledge the financial support provided by ́ CAPES (Coordenaçaõ de Aperfeiçoamento de Pessoal de Nivel Superior, Brazil) Notes

The authors declare no competing financial interest.

■

NOMENCLATURE FAMES = fatty acid methyl esters FAEES = fatty acid ethyl esters ME = methyl ester EE = ethyl ester T/K = temperature P/bar = pressure U



Article

(14) Anand, K.; Sharma, R. P.; Mehta, P. S. A Comprehensive Approach for Estimating Thermo-Physical Properties of Biodiesel Fuels. Appl. Therm. Eng. 2011, 31, 235−242. (15) Mohd Yasin, M. F.; Cant, R. S.; Chong, C. T.; Hochgreb, S. Discrete Multicomponent Model for Biodiesel Spray Combustion Simulation. Fuel 2014, 126, 44−54. (16) Yuan, W.; Hansen, a C.; Zhang, Q. Vapor Pressure and Normal Boiling Point Predictions for Pure Methyl Esters and Biodiesel Fuels. Fuel 2005, 84, 943−950. (17) Ambrose, D. Correlation and Estimation of Vapour−Liquid Critical Properties. I Critical Temperatures of Organic Compounds; National Physical Laboratory: Teddington, 1978. (18) Joback, K. G.; Reid, R. C. Estimation of Pure-Component Properties from Group-Contributions. Chem. Eng. Commun. 1987, 57, 233−243. (19) Lydersen, A. L. Estimation of Critical Properties of Organic Compounds; University of Wisconsin College Engineering: Eng. Exp. Stn. Rep. 3, Madison, 1955. (20) Marrero-morejon, J.; Pardillo-Fontdevila, E. Estimation of Pure Compound Properties Using Group-Interaction Contributions. AIChE J. 1999, 45, 615−621. (21) Lee, B. I.; Kesler, M. G. A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States. AIChE J. 1975, 21, 510−527. (22) Moller, B.; Rarey, J.; Ramjugernath, D. Estimation of the Vapour Pressure of Non-Electrolyte Organic Compounds via Group Contributions and Group Interactions. J. Mol. Liq. 2008, 143, 52−63. (23) Nannoolal, Y.; Rarey, J.; Ramjugernath, D. Estimation of Pure Component Properties Part 3. Estimation of the Vapor Pressure of Non-Electrolyte Organic Compounds via Group Contributions and Group Interactions. Fluid Phase Equilib. 2008, 269, 117−133. (24) Chen, D. H.; Dinivahi, M. V.; Jeng, C. Y. New Acentric Factor Correlation Based on the Antoine Equation. Ind. Eng. Chem. Res. 1993, 32, 241−244. (25) Edminster, W. C. Applied Hydrocarbon Thermodynamics Part 4. Compressibility Factors and Equations of State. Pet. Refin. 1958, 37, 173−179. (26) Kontogeorgis, G. M.; Folas, G. K. Thermodynamic Models for Industrial Applications: From Classical and Advanced Mixing Rules to Association Theories; John Wiley & Sons, Ltd: Chichester, 2010. (27) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill Education: New York, 2001. (28) Oliveira, M. B.; Ribeiro, V.; Queimada, A. J.; Coutinho, J. A. P. Modeling Phase Equilibria Relevant to Biodiesel Production: A Comparison of G E Models, Cubic EoS, EoS-G E and Association EoS. Ind. Eng. Chem. Res. 2011, 50, 2348−2358. (29) Valderrama, J. O. The State of the Cubic Equations of State. Ind. Eng. Chem. Res. 2003, 42, 1603−1618. (30) Tamouza, S.; Passarello, J.-P.; Tobaly, P.; de Hemptinne, J.-C. Application to Binary Mixtures of a Group Contribution SAFT EOS (GC-SAFT). Fluid Phase Equilib. 2005, 228−229, 409−419. (31) Jaubert, J.-N.; Coniglio, L.; Denet, F. From the Correlation of Binary Systems Involving Supercritical CO 2 and Fatty Acid Esters to the Prediction of (CO 2 − Fish Oils) Phase Behavior. Ind. Eng. Chem. Res. 1999, 38, 3162−3171. (32) Jaubert, J.-N.; Coniglio, L. The Group Contribution Concept: A Useful Tool To Correlate Binary Systems and To Predict the Phase Behavior of Multicomponent Systems Involving Supercritical CO 2 and Fatty Acids. Ind. Eng. Chem. Res. 1999, 38, 5011−5018. (33) Anand, K.; Sharma, R. P.; Mehta, P. S. A Comprehensive Approach for Estimating Thermo-Physical Properties of Biodiesel Fuels. Appl. Therm. Eng. 2011, 31, 235−242. (34) Díaz, O. C.; Schoeggl, F.; Yarranton, H. W.; Satyro, M. A.; Lovestead, T. M.; Bruno, T. J. Modeling the Vapor Pressure of Biodiesel Fuels. Int. J. Appl. Sci., Eng. Technol. 2012, 6, 839−849. (35) Windholz, M.; Green, D. W. Perry’s Chemical Engineering Handbook, 6th ed.; McGraw Hill Inc.: New York, 1984.

(36) Constantinou, L.; Gani, R. New Group Contribution Method for Estimating Properties of Pure Compounds. AIChE J. 1994, 40, 1697−1710. (37) Fedors, R. F. A Relationship between Chemical Structure and the Critical Properties. Chem. Eng. Commun. 1982, 16, 149−151. (38) Klincewicz, K. M.; Reid, R. C. Estimation of Critical Properties with Group Contribution Methods. AIChE J. 1984, 30, 137−142. (39) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases & Liquids, 4th ed.; McGraw Hill Inc.: New York, 1987. (40) Constantinou, L.; Gani, R.; O’Connell, J. P. Estimation of the Acentric Factor and the Liquid Molar Volume at 298 K Using a New Group Contribution Method. Fluid Phase Equilib. 1995, 103, 11−22. (41) Ambrose, D.; Walton, J. Vapour Pressures up to Their Critical Temperatures of Normal Alkanes and 1-Alkanols. Pure Appl. Chem. 1989, 61, 1395−1403. (42) Lee, B. I.; Kesler, M. G. A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding. AIChE J. 1975, 21, 510−527. (43) Pitzer, K. S.; Lippmann, D. Z.; Curl, R. F., Jr; Huggins, C. M.; Petersen, D. E. The Volumetric and Thermodynamic Properties of Fluids. II. Compressibility Factor, Vapor Pressure and Entropy of Vaporization. J. Am. Chem. Soc. 1955, 77, 3433−3440. (44) Bondi, A. Estimation of Heat Capacity of Liquids. Ind. Eng. Chem. Fundam. 1966, 5, 442−449. (45) Kay, W. B. Density of Hydrocarbon. Ind. Eng. Chem. 1936, 28, 1014−1019. (46) Rackett, H. G. Equation of State for Saturated Liquids. J. Chem. Eng. Data 1970, 15, 514−517. (47) Soave, G. S. A Noncubic Equation of State for the Treatment of Hydrocarbon Fluids at Reservoir Conditions. Ind. Eng. Chem. Res. 1995, 34, 3981−3994. (48) Meng, X.; Jia, M.; Wang, T. Comment on “ Comparison of Methods for Estimating Critical Properties of Alkyl Esters and Its Mixtures ” - Support Information. J. Chem. Eng. Data 2013, 58, 2687− 2688. (49) García, M.; Alba, J.-J.; Gonzalo, A.; Sánchez, J. L.; Arauzo, J. Reply to Comment on “Comparison of Methods for Estimating Critical Properties of Alkyl Esters and Its Mixtures. J. Chem. Eng. Data 2013, 58, 2689−2694. (50) Yuan, W.; Hansen, a. C.; Zhang, Q. Vapor Pressure and Normal Boiling Point Predictions for Pure Methyl Esters and Biodiesel Fuels. Fuel 2005, 84, 943−950. (51) Ambrose, D. Correlation and Estimation of Vapour-Liquid Critical Properties. II Critical Pressures and Vol.s of Organic Compounds; National Physical Laboratory: Teddington, 1979. (52) Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation; Taylor & Francis: Washington, DC, 1989. (53) Spencer, C. F.; Danner, R. P. Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data 1972, 17, 236−241. (54) Spencer, C. F.; Danner, R. P. Prediction of Bubble-Point Density of Mixtures. J. Chem. Eng. Data 1973, 18, 230−234. (55) Soave, G. Equilibrium Constants from a Modified RedlichKwong Equation of State. Chem. Eng. Sci. 1972, 27, 1197−1203. (56) Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (57) Elbro, H. S.; Fredenslund, A.; Rasmussen, P. Group Contribution Method for the Prediction of Liquid Densities as a Function of Temperature for Solvents, Oligomers, and Polymers. Ind. Eng. Chem. Res. 1991, 30, 2576−2582. (58) Ihmels, E. C.; Gmehling, J. Extension and Revision of the Group Contribution Method GCVOL for the Prediction of Pure Compound Liquid Densities. Ind. Eng. Chem. Res. 2003, 42, 408−412. (59) Pratas, M. J.; Freitas, S. V. D.; Oliveira, M. B.; Monteiro, S. C.; Lima, A. S.; Coutinho, J. a. P. Biodiesel Density: Experimental Measurements and Prediction Models. Energy Fuels 2011, 25, 2333− 2340. V



Article

(60) Knothe, G.; Dunn, R. O. A Comprehensive Evaluation of the Melting Points of Fatty Acids and Esters Determined by Differential Scanning Calorimetry. J. Am. Oil Chem. Soc. 2009, 86, 843−856. (61) García Santander, C. M.; Gómez Rueda, S. M.; de Lima da Silva, N.; de Camargo, C. L.; Kieckbusch, T. G.; Wolf Maciel, M. R. Measurements of Normal Boiling Points of Fatty Acid Ethyl Esters and Triacylglycerols by Thermogravimetric Analysis. Fuel 2012, 92, 158− 161. (62) Graboski, M. S.; McCormick, R. L. Combustion of Fat and Vegetable Oil Derived Fuels in Diesel Engines. Prog. Energy Combust. Sci. 1998, 24, 125−164. (63) Pratas, M. J.; Freitas, S.; Oliveira, M. B.; Monteiro, S. C.; Lima, A. S.; Coutinho, J. a. P. Densities and Viscosities of Fatty Acid Methyl and Ethyl Esters. J. Chem. Eng. Data 2010, 55, 3983−3990. (64) Pratas, M. J.; Freitas, S.; Oliveira, M. B.; Monteiro, S. C.; Lima, A. S.; Coutinho, J. a. P. Densities and Viscosities of Minority Fatty Acid Methyl and Ethyl Esters Present in Biodiesel. J. Chem. Eng. Data 2011, 56, 2175−2180. (65) Yamada, T.; Gunn, R. D. Saturated Liquid Molar Volumes. The Rackett Equation. J. Chem. Eng. Data 1973, 18, 234−236. (66) Vetere, A. Methods to Predict the Critical Constants of Organic Compounds. Fluid Phase Equilib. 1995, 109, 17−27. (67) Chueh, P. L.; Prausnitz, J. M. Vapor-Liquid Equilibria at High Pressures: Calculation of Partial Molar Volumes in Nonpolar Liquid Mixtures. AIChE J. 1967, 13, 1099−1107. (68) Schedemann, A.; Wallek, T.; Zeymer, M.; Maly, M.; Gmehling, J. Measurement and Correlation of Biodiesel Densities at Pressures up to 130 MPa. Fuel 2013, 107, 483−492. (69) Evangelista, N. S.; do Carmo, F. R.; de Santiago-Aguiar, R. S.; de Sant’Ana, H. B. Development of a New Group Contribution Method Based on GCVOL Model for the Estimation of Pure Ionic Liquid Density over a Wide Range of Temperature and Pressure. Ind. Eng. Chem. Res. 2014, 53, 9506−9512. (70) Paduszynski, K.; Domanska, U. A New Group Contribution Method For Prediction of Density of Pure Ionic Liquids over a Wide Range of Temperature and Pressure. Ind. Eng. Chem. Res. 2012, 51, 591−604. (71) Nelder, J. A.; Mead, R. A Simplex Method for Function Minimization. Comput. J. 1965, 7, 308−313. (72) Redlich, O.; Kwong, J. N. S. On the Thermodynamics of Solutions; an Equation of State; Fugacities of Gaseous Solutions. Chem. Rev. 1949, 44, 233−244. (73) Martin, J. J. Cubic Equations of State-Which? Ind. Eng. Chem. Fundam. 1979, 18, 81−97. (74) Péneloux, A.; Rauzy, E.; Fréze, R. A Consistent Correction for Redlich-Kwong-Soave Volumes. Fluid Phase Equilib. 1982, 8, 7−23. (75) Sanghvi, R.; Yalkowsky, S. H. Estimation of the Normal Boiling Point of Organic Compounds. Ind. Eng. Chem. Res. 2006, 45, 2856− 2861. (76) Yalkowsky, S. H.; Krzyzaniak, J. F.; Myrdal, P. B. Relationships between Melting Point and Boiling Point of Organic Compounds. Ind. Eng. Chem. Res. 1994, 33, 1872−1877. (77) van Bommel, M. J.; Oonk, H. A. J.; van Miltenburg, J. C. Heat Capacity Measurements of 13 Methyl Esters of N -Carboxylic Acids from Methyl Octanoate to Methyl Eicosanoate between 5 and 350 K. J. Chem. Eng. Data 2004, 49, 1036−1042. (78) Cavalcante, R. M. Prediçaõ da Densidade de Biodiesel Proveniente de Diferentes Matérias-Primas. Master Thesis, Federal University of Rio de Janeiro, Rio de Janeiro, 2010 (in portuguese); http://www.eq.ufrj. br/prh13/download/?prh13-predicao-da-densidade-de-biodiesel.pdf (accessed May 7, 2015). (79) Mulero, A.; Cachadiña, I.; Parra, M. I. Liquid Saturation Density from Predictive Correlations Based on the Corresponding States Principle. Part 1: Results for 30 Families of Fluids. Ind. Eng. Chem. Res. 2006, 45, 1840−1848. (80) Gouw, T. H.; Vlugter, J. C. Physical Properties of Fatty Acid Methyl Esters. I. Density and Molar Volume. J. Am. Oil Chem. Soc. 1964, 41, 142−145.

(81) Ndiaye, E. H. I.; Habrioux, M.; Coutinho, J. A. P.; Paredes, M. L. L.; Daridon, J. L. Speed of Sound, Density, and Derivative Properties of Methyl Oleate and Methyl Linoleate under High Pressure. J. Chem. Eng. Data 2013, 58, 2345−2354. (82) Baroutian, S.; Aroua, M. K.; Raman, A. A. A.; Sulaiman, N. M. N.; Ester, E.; Transesterification, P. Densities of Ethyl Esters Produced from Different Vegetable Oils. J. Chem. Eng. Data 2008, 53, 2222− 2225. (83) Do Carmo, F. R.; Sousa, P. M.; Santiago-Aguiar, R. S.; de Sant’Ana, H. B. Development of a New Model for Biodiesel Viscosity Prediction Based on the Principle of Corresponding State. Fuel 2012, 92, 250−257. (84) Nogueira, C. a.; Feitosa, F. X.; Fernandes, F. a. N.; Santiago, R. S.; de Sant’Ana, H. B. Densities and Viscosities of Binary Mixtures of Babassu Biodiesel + Cotton Seed or Soybean Biodiesel at Different Temperatures. J. Chem. Eng. Data 2010, 55, 5305−5310. (85) Feitosa, F. X.; Rodrigues, M. D. L.; Veloso, C. B.; Cavalcante, C. L.; Albuquerque, M. C. G.; de Sant’Ana, H. B. Viscosities and Densities of Binary Mixtures of Coconut + Colza and Coconut + Soybean Biodiesel at Various Temperatures. J. Chem. Eng. Data 2010, 55, 3909−3914. (86) Meng, X.; Jia, M.; Wang, T. Predicting Biodiesel Densities over a Wide Temperature Range up to 523K. Fuel 2013, 111, 216−222. (87) Pratas, M. J.; Oliveira, M. B.; Pastoriza-Gallego, M. J.; Queimada, A. J.; Piñeiro, M. M.; Coutinho, J. A. P. High-Pressure Biodiesel Density: Experimental Measurements, Correlation, and Cubic-Plus-Association Equation of State (CPA EoS) Modeling. Energy Fuels 2011, 25, 3806−3814. (88) Ndiaye, E. H. I.; Habrioux, M.; Coutinho, J. A. P.; Paredes, M. L. L.; Daridon, J. L. Speed of Sound, Density, and Derivative Properties of Ethyl Myristate, Methyl Myristate, and Methyl Palmitate under High Pressure. J. Chem. Eng. Data 2013, 58, 1371−1377. (89) Outcalt, S. L. Compressed-Liquid Density Measurements of Methyl Oleate and Methyl Linoleate. J. Chem. Eng. Data 2011, 56, 4239−4243. (90) Ott, L. S.; Huber, M. L.; Bruno, T. J. Density and Speed of Sound Measurements on Five Fatty Acid Methyl Esters at 83 kPa and Temperatures from (278.15 to 338.15) K. J. Chem. Eng. Data 2008, 53, 2412−2416. (91) Oliveira, M. B.; Freitas, S. V.D.; Llovell, F.; Vega, L. F.; Coutinho, J. a. P. Development of Simple and Transferable Molecular Models for Biodiesel Production with the Soft-SAFT Equation of State. Chem. Eng. Res. Des. 2014, 92, 2898−2911. (92) Pratas, M. J.; Oliveira, M. B.; Pastoriza-Gallego, M. J.; Queimada, A. J.; Piñeiro, M. M.; Coutinho, J. A. P. High-Pressure Biodiesel Density: Experimental Measurements, Correlation, and Cubic-Plus-Association Equation of State (CPA EoS) Modeling. Energy Fuels 2011, 25, 3806−3814. (93) Hosseini, S. M.; Alavianmehr, M. M.; Moghadasi, J. Prediction of Volumetric Properties of Some Fatty Acid Methyl Esters, Biodiesel Fuels and Their Blends Using Perturbed Yukawa Hard-Core Chain Equation of State. Fluid Phase Equilib. 2014, 372, 105−112. (94) Oliveira, M. B.; Freitas, S. V. D.; Llovell, F.; Vega, L. F.; Coutinho, J. a P. Development of Simple and Transferable Molecular Models for Biodiesel Production with the Soft-SAFT Equation of State. Chem. Eng. Res. Des. 2014, 92, 2898−2911. (95) Wilson, G. M.; Jasperson, L. V. Critical Constants Tc, Pc Estimation Based on Zero, First, Second-Order Methods. In AIChE Meeting; New Orleans, LA, 1996. (96) Marrero, J.; Gani, R. Group-Contribution Based Estimation of Pure Component Properties. Fluid Phase Equilib. 2001, 183−184, 183−208. (97) Pérez Ponce, A. A.; Salfate, I.; Pulgar-Villarroel, G.; PalmaChilla, L.; Lazzús, J. A. New Group Contribution Method for the Prediction of Normal Melting Points. J. Eng. Thermophys. (Novosibirsk, Russ. Fed.) 2013, 22, 226−235. (98) Stein, S. E.; Brown, R. L. Estimation of Normal Boiling Points from Group Contributions. J. Chem. Inf. Model. 1994, 34, 581−587. W



Article

(99) Cordes, W.; Rarey, J. A New Method for the Estimation of the Normal Boiling Point of Non-Electrolyte Organic Compounds. Fluid Phase Equilib. 2002, 201, 409−433. (100) Nannoolal, Y.; Rarey, J.; Ramjugernath, D.; Cordes, W. Estimation of Pure Component Properties Part 1. Estimation of the Normal Boiling Point of Non-Electrolyte Organic Compounds via Group Contributions and Group Interactions. Fluid Phase Equilib. 2004, 226, 45−63. (101) Riedel, L. Estimation of Unknown Critical Pressures of Organic Compounds. Z. Elektrochem. 1949, 53, 222−228. (102) Somayajulu, G. R. Estimation Procedures for Critical Constants. J. Chem. Eng. Data 1989, 34, 106−120. (103) Chein-Hsiun, Tu. Group-Contribution Estimation of Critical Temperature with Only Chemical Structure. Chem. Eng. Sci. 1995, 50, 3515−3520. (104) Nannoolal, Y.; Rarey, J.; Ramjugernath, D. Estimation of Pure Component Properties Part 2. Estimation of Critical Property Data by Group Contribution. Fluid Phase Equilib. 2007, 252, 1−27. (105) Valderrama, J. O.; Robles, P. A. Critical Properties, Normal Boiling Temperatures, and Acentric Factors of Fifty Ionic Liquids. Ind. Eng. Chem. Res. 2007, 46, 1338−1344. (106) Han, B.; Peng, D. A Group-Contribution Correlation for Predicting the Acentric Factors of Organic Compounds. Can. J. Chem. Eng. 1993, 71, 332−334. (107) Shouzhi, Y.; Yuanyuan, J.; Peisheng, M. Estimation of Acentric Factor of Organic Compounds with Corresponding States Group Contribution Method. Chin. J. Chem. Eng. 2005, 13, 709−712.

X


Evaluation of Optimal Methods for Critical Properties and Acentric

Recommend Documents