Fatty Acid Ethyl Esters - ACS Publications - American Chemical Society

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Estimation of Pure-Component Properties of Biodiesel-Related Components: Fatty Acid Ethyl Esters Thomas Wallek,*,† Klaus Knöbelreiter,† and Jürgen Rarey‡,§,∥ †

Institute of Chemical Engineering and Environmental Technology, Graz University of Technology, NAWI Graz, Inffeldgasse 25/C, 8010 Graz, Austria ‡ DDBST GmbH, Marie-Curie-Straße 10, 26129 Oldenburg, Germany § University of KwaZulu-Natal, King George V Avenue, Durban 4041, South Africa ∥ Carl von Ossietzky University of Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26129 Oldenburg, Germany S Supporting Information *

ABSTRACT: Common, nonspecialized group-contribution and corresponding-state models for the estimation of normal boiling point, critical data, vapor pressure, liquid density, dynamic viscosity, and surface tension are reviewed in view of their application to fatty acid ethyl esters to provide guidelines for practical application of these models in process engineering. As a result, these properties can be estimated in a satisfactory manner when choosing an appropriate model, showing minimum average absolute mean deviations of the normal boiling point below 5 K (3.4 K for saturated and 4.2 K for unsaturated components), those of the critical temperature below 3 K (2.3 K for saturated and 1.2 K for unsaturated components), those of the critical pressure in the region of 50 kPa (54 kPa for saturated and 2.1 kPa for unsaturated components), and minimum relative mean deviations of saturation pressures from 2% around the normal boiling point to 15% at extremely low pressures, those of liquid density below 1%, those of viscosity at a maximum of 7%, and those of surface tension around 2.4%.

1. INTRODUCTION Growing interest in biobased value chains increases the need for fluid phase property data, notably pure-component properties, of biogenic chemicals. In this context, biodieselrelated components like triglycerides and fatty acid esters represent a substance class of considerable importance because of their usage as fuels and in the pharmaceutical industry. From the various possibilities for transesterification, fatty acid methyl (FAME), and ethyl (FAEE) esters have emerged as the two predominant esters in terms of industrial relevance. While triglycerides and FAME were covered in a previous publication,1 this paper focuses on FAEE to complement the picture. Although FAEE can in many respects be considered as a technically equal alternative to FAME, they are of less industrial relevance, compared to FAME, in Europe and North America. One reason is the fact that methanol, the basis for transesterification of FAME, is a byproduct of organic-synthesis industry and produced in industrial quantities at accordingly low prices. However, ethanol, the basis for FAEE transesterification, is to an increasing degree obtained from renewable sources and can be considered a more environment-friendly product. Yet, its utilization is limited by its price and other disadvantages like higher efforts in phase separation in the course of the biodiesel purification process. One reason for this is that solubilities in ethanol systems are different © XXXX American Chemical Society

compared to those with methanol (i.e., miscible regions in case of FAEE are slightly smaller compared to FAME).2−5 This effect may be attributed to a smaller polarity difference between FAEE and ethanol, compared to FAME and methanol. On the other hand, there are approaches toward cost reduction to make FAEE more competitive, including the use of inexpensive raw materials6 and/or novel production methods. One example for the latter is the evolving genetic development of microorganisms producing bioethanol in industrial quantities, or FAEE directly, omitting the transesterification process.7,8 Another one is the improvement of the transesterification process itself by introducing novel technologies.9 Despite the molecular similarity of FAME and FAEE, it is important to account for differences in their pure-component properties, especially when applying rigorous process simulation which requires pure-component properties along with binary interaction parameters. These differences are particularly apparent for the speed of sound,10 for melting points, viscosity, and heat of combustion to mention fuel-related physical properties11−21 but, beyond that, also for engine-related characteristics in the fields of spray formation, engine Received: September 13, 2017 Revised: January 31, 2018 Accepted: February 7, 2018

A

DOI: 10.1021/acs.iecr.7b03794 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research Table 1. Survey of FAEE Investigated in This Papera component ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl ethyl

acetate propionate butyrate valerate hexanoate heptanoate octanoate nonanoate decanoate undecanoate laurate myristate palmitate 3-butenoate 4-pentenoate oleate linoleate linolenate

formula

Cx:y

Ctot:db

CAS

DDB

M (g/mol)

Pmax (kPa)

C4H8O2 C5H10O2 C6H12O2 C7H14O2 C8H16O2 C9H18O2 C10H20O2 C11H22O2 C12H24O2 C13H26O2 C14H28O2 C16H32O2 C18H36O2 C6H10O2 C7H12O2 C20H38O2 C20H36O2 C20H34O2

C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 C4:1 C5:1 C18:1 C18:2 C18:3


141−78−6 105−37−3 105−54−4 539−82−2 123−66−0 106−30−9 106−32−1 123−29−5 110−38−3 627−90−7 106−33−2 124−06−1 628−97−7 1617−18−1 1968−40−7 111−62−6 544−35−4 1191−41−9

21 205 371 897 2185 2472 1762 2473 4680 7173 3053 3312 3313 6239 9528 3505 6470 30276

88.1 102.1 116.2 130.2 144.2 158.2 172.3 186.3 200.3 214.3 228.4 256.4 284.5 114.1 128.2 310.5 308.5 306.5

3839.690 280.000 280.000 187.590 174.601 101.858 101.325 101.325 101.325 101.325 101.858 101.325 101.325 101.525 101.325 101.325 101.325 101.325

a

Cx:y, number of carbons x and number of double bonds y in the fatty acid chain (not including O2C2H5 of the ester group); Ctot:db, total number of carbon atoms:number of double bonds; CAS, Chemical Abstracts Service number; DDB, Dortmund Data Bank number; M, molar mass; and Pmax, maximum experimental pressure.

combustion, performance, and emissions.22−34 However, in addition to dedicated fuel-related applications, process engineering calculations in general require basic purecomponent data specifically for FAEE like normal boiling point, critical data, saturation pressure, liquid density, and surface tension to model the production and subsequent processing of fatty acid esters as well as the characterization of surrogates.18,35,36 Model comparisons for FAEE often focus on FAEE mixtures derived from one typical fatty acid source (e.g., Canola biodiesel, Jatropha biodiesel, etc.) instead of pure FAEE components,37,38 or binary interaction parameters of gE models for FAEE mixtures which are relevant for separation processes.39 Chang et al. published recommendations for pure-component property estimation in the course of biodiesel production processes.40 Covarrubias-Cervantes et al. analyzed saturated vapor pressure trends depending on the molecular structure of selected ethyl esters.41 Garciá Santander et al. measured boiling points of triglycerides and ethyl esters and compared them to the group-contribution methods of Joback and Constantiou and Gani as implemented in the commercial simulation software Aspen Plus.42 Ceriani et al. lately improved their group-contribution (GC) method for the estimation of vapor pressures and enthalpies of vaporization of edible fat/oil and biofuel components.43 Bolonio et al. derived correlations for the estimation of cold flow properties of FAEE as functions of the percentage of unsaturated compounds.21 Sajjadi et al. presented a comprehensive review on properties of prediction models for biodiesel-related components including density, viscosity, flash point, and a number of fuel-related properties, to some extent distinguishing between FAEE and FAME.44 Wang et al. proposed a new group-contribution method based on the Riedel equation for vapor pressures of fatty acid methyl, ethyl, propyl, and butyl esters with a special ester group to distinguish between the esters.45 Saxena et al. compared, among others, a specialized GC approach, the Peng−Robinson equation of state and corresponding-state approaches for vapor pressure prediction based on a set of 55 FAEE data points.46 Evangelista

et al. reviewed GC and corresponding-state approaches for vapor pressures and enthalpies of evaporation, distinguishing between FAME and FAEE.47,48 Caldeira et al. reviewed prediction models for biodiesel-related components, comprising viscosity, density, and fuel-related properties in view of quantifying the range of variation of model results when considering the uncertainty in the fatty acid composition.49 Finally, Alavianmehr et al. proposed a perturbed hard trimer chain (PHTC) equation of state with the trimer expression derived from the statistical associating fluid theory-trimer (SAFT-T) and applied it to several biomaterials, including FAEE, to predict densities and related thermodynamic properties.50 The goal of this paper is to use broadly available experimental information from data banks to verify the applicability of established, mostly nonspecialized models for the estimation of normal boiling point, critical data, saturation pressure, liquid density, dynamic viscosity, and surface tension to FAEE. It is intended to be complementary to recent model evaluations in this field. Because a sharp distinction between data used for model development and data used for model assessment, which would be desirable from the mathematical point of view, is not possible, the comparisons in this paper are intended as guidelines for the practicing engineer which model to use for engineering purposes, rather than statistically rigorous comparisons. Data for model comparison were retrieved from the Dortmund Data Bank (DDB),51,52 Reaxys,53 Springer Materials,54 and the National Institute of Standards and Technology (NIST).55 The limited availability of FAEE pure-component data is, on the one hand, a consequence of the abovementioned lower technical pertinence of FAEE compared to FAME and, on the other hand, due to few measurements for pure esters, compared to mixtures of typical fatty acid profiles related to their main fatty acid source.56−61 A structural search for saturated and unsaturated ethyl ethers in the data banks, not necessarily derived from fatty acids, resulted in a list of 100 possible candidates in total. This list is part of the Supporting B


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Industrial & Engineering Chemistry Research Information. Of these, for 74 substances experimental data were found. Of the latter, for 13 saturated and 5 unsaturated FAEE, a minimum data basis for a meaningful model comparison could be retrieved. It was obvious to also consider ethyl acetate, although not a fatty acid ester, in the comparisons due to its molecular similarity. Data for ethyl acetate were taken from Reaxys, Springer Materials, NIST and DDB. 2516 Data points were actually used for model evaluation, approximately 500 further data points were available but not used because they were distributed over substances for which no sufficient amount of other data was available. 47% Of all data were contributed by the DDB, 34% by Springer Materials (mainly ethyl acetate data), 17% by Reaxys, and 2% by NIST. This distribution also reflects the contributions for saturated FAEE. Unsaturated components make up only 5% of total data, of which 56% originated from the DDB, 43% from Reaxys, and 1% from NIST. The distribution by property shows that clearly more than half of all data are saturation pressures, one-quarter liquid densities, and one-quarter normal boiling point and transport properties. While saturation pressures are found in equal parts in the DDB, Springer Materials, and Reaxys, half of normal boiling points came from Reaxys and roughly two-thirds of liquid density and transport properties were found in the DDB. Table 1 summarizes all 18 FAEE investigated in this paper, comprising 13 unsaturated and 5 saturated components. Throughout this paper, the nomenclature Cx:y is used to characterize a substance by the number of carbons x and the number of double bonds y in the fatty acid chain, not including O2C2H5 of the ester group.

Table 2. Survey of Normal Boiling Points, Critical Data, and Acentric Factors, Used in This Paper for Model Evaluationsa component Cx:y

Tb (K)

Tc (K)

Pc (kPa)

ω [1]


350.4 372.4 394.6 416. 8 438.7 460.2 481.0 500.9 519.7 537.0 552.8* 578.8* 595.7* 398. 5 418.3 616.4* 628.7* 633.7*

522.0 546.3 571.0 594.0 615.2 635.0 653.9 671.3 687.1 701.7 715.0 738.7 759.3 577.0* 596.1* 783.2* 788.7* 794.5*

3852 3362 2978 2750 2531 2357 2159 1925 1696* 1530* 1412* 1267* 1151* 3248* 2906* 1226* 1247* 1268*

0.3713 0.3895 0.4101 0.4523 0.4960 0.5497 0.5915 0.6211 0.6556 0.6834 0.7137 0.7664 0.7735 0.4372 0.4703 0.8255 0.8489 0.8758

a

Nomenclature Cx:y according to Table 1; Tb, normal boiling point temperature; Tc, critical temperature; Pc, critical pressure, and ω, acentric factor. Asterisked values are estimated data as explained in the text.

2. BASIC INPUT DATA FOR PURE-COMPONENT ESTIMATION MODELS In the following, prior to model comparisons, the normal boiling points, critical data, and acentric factors used in this paper are critically assessed because their plausibility and consistency is an essential prerequisite for the application of most estimation models in terms of a consistent set of input data. From the authors’ experience, it is essential to regard these data in the context of related homologous series of substances, in this particular case along with those of FAME and n-alkanes. Table 2 gives a summary of these data. 2.1. Normal Boiling Points. Figure 1 illustrates the FAEE normal boiling points used in this paper as a function of molar mass along with those of FAME and n-alkanes, showing a smooth curvature as expected from other homologous series62 which can also be observed for further pure-component properties of FAEE, like flash point, and enthalpy of vaporization.63,64 Figure 1 suggests a nearly linear trend for normal boiling points of the rather short-chained components, C2:0−C6:0, whereas in the case of FAME linearity is more significantly observed in the region C10:0−C14:0.1 Concerning the influence of double bonds on normal boiling points, literature reports an increase of the normal boiling point with increasing number of double bonds for the similar substance class of FAME.1,65 This behavior is confirmed for FAEE as can be seen from Figure 1, concerning C4:0/C4:1 and C5:0/C5:1. Although for the long-chained saturated components, C12:0, C14:0, and C16:0, single experimental data were available,42,66 these data showed considerable scattering in relation to the neighboring esters which seemed unrealistic, keeping in mind that only the chain length changes but functional groups stay the same. Therefore, it was decided to rely on averaged values from the normal point estimation methods listed in Table 3

Figure 1. Normal boiling points of FAEE from Table 2 as a function of molar mass, along with those of saturated FAME1 and n-alkanes.55

instead, because these more smoothly continue the trend of the Tb-curve over molar mass, reflecting the nature of group contribution approaches to homogeneously account for chain lengths. Lacking experimental data, the three long-chained unsaturated components were also estimated, using the Cordes/Rarey model for C18:3, the Rarey/Nannoolal model for C18:2, and a smooth curve regression for C18:1, considering the influence of double bonds on the normal boiling point as discussed before. 2.2. Critical Temperatures. Figure 2 illustrates the critical temperatures of FAEE used in this paper as a function of molar mass along with those of FAME and n-alkanes, showing a practically linear shape from C2:0−C4:0 and a smooth curvature from C4:0-C16:0. Whenever multiple experimental data for one component were available, it was decided to take those which were closest to the smooth curvature of Figure 2, C


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Industrial & Engineering Chemistry Research Table 3. Survey of Models Used for Normal Point Estimationa model

abbreviation

method

Pailhes (Psat method) Ericksen/Rowley

PP ER

GC GC

Cordes/Rarey

CR

GC

Rarey/Nannoolal

RN

GC

Moller/Rarey/ Ramjugernath (Psat method) Rarey/Nannoolal (Psat method) Lydersen

MRRP

input data

Table 4. Survey of Group-Contribution Models Used for Critical Temperature Estimationa reference

62

GC

{Psat, Tsat} molecular structure, UNIQUAC r molecular structure molecular structure {Psat, Tsat}

RNP

GC

{Psat, Tsat}

71

LY

GC

72

Stein/Brown

SB

GC

Devotta/Rao

DR

GC

Joback/Reid

JR

GC

Wen/Qiang (group vector space method) Gani/Constantinou

GVS

GC

GC

GC

Marrero/Pardillo

MP

GC

Marrero/Pardillo (simple groups) Marrero/Pardillo (simple groups + simple method) Champion/Rarey/ Ramjugernath (Psat method)

MPG

GC

MPGM

GC

molecular structure, Tc molecular structure molecular structure molecular structure molecular structure molecular structure molecular structure molecular structure molecular structure

CRRP

GC

molecular structure

model

67 68

69 70

73

abbreviation

Fedors Alvarez/Valderrama

FE AV

Wilson/Jasperson

WJ

Wen/Quiang Wen/Quiang (Tb)

WQ WQT

Ambrose

AM

Rarey/Nannoolal (estim. Tb) Rarey/Nannoolal (given Tb)

RNET RNGT

Chein-Hsiun Tu Daubert

CHT DA

Lydersen

LY

Klincewicz/Reid

KR

Somayajulu

SO

Joback

JO

Gani/Constantinou Marrero/Pardillo

GC MP

Marrero/Pardillo (simple groups)

MPG

74 75 76 77 78 78 78

a

79

input data

reference

molecular structure molecular structure, Tb molecular structure, Tb molecular structure molecular structure, Tb molecular structure, Tb molecular structure

81 82

molecular structure, Tb molecular structure molecular structure, Tb molecular structure, Tb molecular structure, Tb molecular structure, Tb molecular structure, Tb molecular structure molecular structure, Tb molecular structure, Tb

86

83 84 84 85 86

87 88 72 89 90 75 77 78 78

Tb, normal boiling point temperature.

2.3. Critical Pressures. Figure 3 illustrates the FAEE critical pressures as a function of molar mass along with those

a

GC, group-contribution; {Psat, Tsat}, a point on the saturation pressure curve; and Tc, critical temperature.

Figure 3. Critical pressures of FAEE from Table 2 as a function of molar mass, along with those of saturated FAME1 and n-alkanes.55

Figure 2. Critical temperatures of FAEE from Table 2 as a function of molar mass, along with those of saturated FAME1 and n-alkanes.55

of FAME and n-alkanes. Generally, the critical pressures used in this paper are mostly taken from one recent publication.80 However, as in the case of normal boiling points and critical temperatures, in the interest of a smooth curvature, the value for C3:0 was taken from another source,91 and for C4:0 a mean value of two experimental points was preferred.92,93 In the longchained region, values for C10:0, C14:0, and C16:0 were adapted within experimental uncertainty, and for C11:0 and

following the arguments concerning smoothness as discussed in Figure 1. The critical temperatures for C12:0−C16:0 were slightly adapted in terms of the smooth shape of the curve but within the experimental uncertainty of the measured values.80 Critical temperatures of the unsaturated FAEE were estimated, using approaches from Table 4, in particular RNET for C4:1, C18:1, C18:2, C18:3, and Ambrose for C5:1. D


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Industrial & Engineering Chemistry Research C12:0 accordingly higher values were taken, slightly beyond this uncertainty. Critical pressures of the unsaturated esters were consistently estimated with the Lydersen approach, cf. Table 5, which plausibly reflects the relative position of the unsaturated esters to the respective saturated compounds. Table 5. Survey of Group-Contribution Models Used for Critical Pressure Estimationa model

abbreviation

input data

reference 82 83

89 90

Alvarez/Valderrama Wilson/Jasperson

AV WJ

Wen/Quiang Ambrose

WQ AM

Rarey/Nannoolal Lydersen Joback Gani/Constantinou Marrero/Pardillo Marrero/Pardillo (simple groups) Klincewicz/Reid Somayajulu

RN LY JO GC MP MPG

molecular structure molecular structure, Tc molecular structure molecular structure, Tb molecular structure molecular structure molecular structure molecular structure molecular structure molecular structure

KR SO

molecular structure molecular structure

a

84 85 86 72 75 77 78 78

Figure 4. Acentric factors of FAEE from Table 2 as a function of molar mass, along with those of saturated FAME1 and n-alkanes.55

3. ESTIMATION OF PURE-COMPONENT PROPERTIES 3.1. Normal Boiling Point. The normal boiling points listed in Table 2 were compared to estimations by the groupcontribution methods of Table 3. Three of these models require experimental reference points on the saturation pressure curve as additional input. In the interest of comparability, these reference points were taken from the pressure range 2−11 kPa because only in this range reference points were available for nearly all substances, as discussed later. Comparisons in terms of absolute deviations and average absolute mean deviations (AMD) are compiled in Table 7, using the definition

Tb, normal boiling point temperature; and Tc, critical temperature.

2.4. Acentric Factors. The acentric factors of FAEE were calculated via their definition94 ⎛ P sat ⎞ ω = −log10⎜ i ⎟ −1 ⎝ Pc ⎠0.7·T

(1)

c

sat

AMD =

where Pi designates the saturation pressure, Pc the critical pressure, and Tc the critical temperature. Because in the temperature region around 0.7Tc not enough experimental data were available, most of the saturation pressures were estimated using the models listed in Table 6, representing those approaches of Table 11 showing the best representation of the normal boiling point region for each respective substance. Figure 4 illustrates the resulting acentric factors for FAEE as a function of molar mass, showing a reasonably smooth curvature in the context of the acentric factors of n-alkanes and FAME. In the following, based on Tb, Tc, Pc, and ω of Table 2 as basic input data for pure-component property models, comparisons for normal boiling point, critical data, saturation pressure, liquid density, dynamic viscosity, and surface tension were conducted. For better orientation, complete tables of the estimated values of the respective estimation models are listed in the Supporting Information.

1 n

n exp ∑ |Tbcalc , i − Tb , i |

(2)

i=1

calc

where Tb,i designates the calculated normal boiling point temperature, Tb,iexp the respective experimental value, and n the number of data points. Generally, estimations for saturated FAEE are better than that for unsaturated components. For saturated FAEE, the Cordes/Rarey and Champion/Rarey/Ramjugernath (Psat method) approaches can equally be recommended, for unsaturated components the Cordes/Rarey approach shows the lowest deviations. For C18:3, the Ericksen/Rowley model is not applicable due to missing parameters. Furthermore, it can be seen that both Joback/Reid and the derived method of Devotta/Rao seem to overestimate the influence of chain length in their models. Among the Marrero/Pardillo approaches, the MP variant should be preferred. While Stein/ Brown and Marrero/Pardillo mostly overestimate normal boiling points, the models of Rarey/Nannoolal, Rarey/

Table 6. Vapor Pressure Models Used for the Estimation of Vapor Pressures at 0.7Tc for Application of eq 1 to Calculate Acentric Factorsa component Cx:y

a

C2:0

C3:0

C4:0

C5:0

C6:0

C7:0

C8:0

C9:0

method component

exp C11:0

RM C12:0

MY C14:0

RNET C16:0

RNGT C4:1

CRRP C5:1

GNT C18:1

GNT C18:2

C10:0 MI C18:3

method

MI

MI

RNET

RNGT

RI

CRRP

RM

GNT

RNET

Nomenclature Cx:y according to Table 1; model abbreviations according to Table 11. E


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Table 7. Experimental Boiling Points, Tbexp, along with Absolute Deviations and Average Absolute Mean Deviations (AMD) of Estimated Normal Boiling Points, Tbcalca Tbcalc − Tbexp (K) component Cx:y C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 AMD C4:1 C5:1 C18:1 C18:2 C18:3 AMD

Tbexp

(K)

350.4 372.4 394.6 416.8 438.7 460.2 481.0 500.9 519.7 537.0 552.8* 578.8* 595.7* 398.5 418.3 616.4* 628.7* 633.7*

PP

ER

CR

5.4 3.4 1.6 −1.4 4.7 3.8 2.3 3.6 1.3 −4.2 0.5 2.3 16.3 3.9 1.6 4.0 13.7 −2.2 1.8 4.7

−1.3 −1.8 −0.3 −0.1 −0.9 −2.2 −3.7 −5.1 −6.0 −6.1 −5.3 0.6 13.9 3.6 17.4 −4.3 26.3 15.1 N.A. 15.8

−7.7 −1.0 2.7 4.2 4.1 3.0 1.3 −0.7 −2.5 −3.7 −4.2 −1.4 8.1 3.4 −1.4 2.4 13.8 3.3 − 4.2

RN

Tbcalc component Cx:y C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 AMD C4:1 C5:1 C18:1 C18:2 C18:3 AMD

Tbexp

(K)

350.4 372.4 394.6 416.8 438.7 460.2 481.0 500.9 519.7 537.0 552.8* 578.8* 595.7* 398.5 418.3 616.4* 628.7* 633.7*

−11.4 −4.9 −1.1 0.5 0.7 −0.2 −1.6 −3.2 −4.7 −5.6 −5.7 −2.1 8.2 3.8 −5.7 −1.7 12.6 − −5.4 5.1 − Tbexp (K)

MRRP

RNP

LY

SB

1.4 0.1 −3.2 −6.6 −0.6 −2.4 −2.6 −3.5 −3.2 −10.8 −2.9 −0.7 12.6 3.9 −1.9 −0.1 9.3 −6.1 −6.6 4.8

1.3 0.1 −3.3 −6.6 −0.4 −2.1 −2.3 −3.0 −2.9 −10.5 −2.7 −0.8 12.3 3.7 −3.7 −4.3 −5.2 −4.4 −7.8 5.1

−3.7 −1.9 −0.8 2.8 3.6 4.1 −9.5 −1.0 7.7 7.9 12.6 11.2 19.7 6.6 14.7 1.0 33.5 21.8 9.7 16.1

0.7 3.1 4.4 4.8 4.5 3.8 2.9 1.9 1.3 1.0 1.5 5.3 14.6 3.8 −4.8 −1.8 17.3 5.1 0.0 5.8

DR

JR

GVS

GC

MP

MPG

MPGM

CRRP

−1.2 −0.4 0.3 1.0 1.9 3.3 5.4 8.4 12.5 18.0 25.1 44.9 73.7 15.1 −6.9 −3.8 102.9 94.9 94.0 60.5

−1.0 −0.2 0.5 1.2 2.1 3.5 5.6 8.6 12.7 18.2 25.3 45.1 73.9 15.2 −6.7 −3.6 103.1 95.1 94.2 60.5

−8.6 −3.0 1.4 3.9 5.0 5.1 4.8 4.4 4.4 4.9 6.5 13.6 28.0 7.2 −9.1 −2.7 44.5 38.7 −134.5 45.9

−3.9 −3.0 3.6 6.7 7.2 5.9 3.5 0.5 −2.6 −5.5 −7.8 −9.1 −4.0 4.9 −5.2 0.7 −6.4 −20.1 −26.6 11.8

−1.0 0.4 3.1 4.3 4.5 4.1 3.5 3.0 3.0 3.7 5.4 13.2 28.3 6.0 −3.7 0.0 39.9 29.3 26.0 19.8

−5.2 −1.0 1.3 2.4 2.7 2.5 2.3 2.2 2.7 4.0 6.4 15.5 32.1 6.2 −7.1 −3.4 43.9 31.9 27.0 22.7

−5.9 −5.0 −4.3 −3.6 −2.7 −1.3 0.8 3.9 8.0 13.5 20.6 40.5 69.3 13.8 −11.9 −8.9 104.1 101.6 106.3 66.6

−1.5 −1.2 −2.6 −3.0 −3.3 −4.1 −3.1 −5.2 −3.1 −5.2 −2.4 −2.5 −3.6 3.4 −3.4 −4.1 −7.1 −7.5 −14.4 7.3

a Nomenclature Cx:y according to Table 1; model abbreviations according to Table 3. Asterisked values are estimated data as explained in the text. N.A. not applicable for this substance.

Nannoolal (Psat method), and Champion/Rarey/Ramjugernath (Psat method) tend to underestimate the data. 3.2. Critical Temperature. The critical temperatures listed in Table 2 were compared to estimations by the groupcontribution methods of Table 4 which mostly require the normal boiling point as a reference point. Comparisons in terms of absolute deviations and average absolute mean deviations (AMD) are compiled in Table 8, yielding the Marrero/Pardillo (MPG variant) approach as the best choice for saturated esters and RNET for the unsaturated components. While the Fedorov model tends to significantly overestimate critical temperatures, these are considerably underestimated by

the Daubert approach. The Wen/Quiang and Wen/Quiang (Tb) approaches are of limited applicability for unsaturated FAEE due to missing double bond contributions. 3.3. Critical Pressure. The critical pressures listed in Table 2 were compared to estimations by the group-contribution methods of Table 5. Only two of these require a characteristic temperature as reference point [i.e., the normal point temperature (AM) or the critical temperature (WJ), respectively]. Table 9 shows the resulting comparisons in terms of absolute deviations and average absolute mean deviations (AMD). While the Marrero/Pardillo can be recommended for the saturated FAEE, for unsaturated F


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Table 8. Experimental Critical Temperatures, Tcexp, along with Absolute Deviations and Average Absolute Mean Deviations (AMD) of Estimated Critical Temperatures, Tccalca Tccalc − Tcexp (K) component Cx:y C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 AMD C4:1 C5:1 C18:1 C18:2 C18:3 AMD

Tcexp

(K)

522.0 546.3 571.0 594.0 615.2 635.0 653.9 671.3 687.1 701.7 715.0 738.7 759.3 577.0* 596.1* 783.2* 788.7* 794.5*

FE

AV

WJ

18.5 22.8 23.5 23.5 23.1 22.5 21.2 20.3 19.8 19.7 19.9 21.1 23.1 21.5 25.3 28.4 28.9 32.2 35.0 30.0

8.8 7.2 5.1 4.2 4.6 5.5 6.1 7.1 8.0 8.4 8.2 4.0 −7.2 6.5 10.0 9.5 −16.7 −8.4 −9.1 10.8

4.6 2.0 −0.8 −1.9 −1.6 −0.7 0.1 1.2 2.3 2.8 2.5 −2.3 −14.8 2.9 3.0 2.1 −23.1 −11.0 −8.0 9.4

WQ

Tccalc component Cx:y C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 AMD C4:1 C5:1 C18:1 C18:2 C18:3 AMD a

Tcexp

(K)

522.0 546.3 571.0 594.0 615.2 635.0 653.9 671.3 687.1 701.7 715.0 738.7 759.3 577.0* 596.1* 783.2* 788.7* 794.5*

−0.7 −1.2 −1.2 −1.3 −1.1 −0.7 −0.4 0.5 2.0 4.1 6.8 13.3 21.0 4.2 N.A. N.A. 29.6 29.9 29.9 29.8 − Tcexp (K)

WQT

AM

RNET

RNGT

3.0 1.1 −1.7 −3.1 −3.2 −2.7 −2.4 −1.8 −1.3 −1.1 −1.8 −6.9 −19.5 3.8 N.A. N.A. −26.6 −13.7 −9.6 16.7

4.8 1.4 −2.0 −3.6 −3.6 −2.8 −2.0 −0.7 0.7 1.7 2.1 −1.0 −11.5 2.9 1.6 − −18.0 −6.5 −4.1 6.1

−14.4 −5.5 −1.5 0.8 2.1 2.5 1.9 1.3 0.7 0.3 0.0 −0.1 0.1 2.4 − 6.1 − − − 1.2

2.7 1.6 0.2 19.7 1.2 2.8 4.1 5.6 6.9 7.7 7.4 2.6 −10.2 5.6 8.4 8.6 −15.6 0.0 6.8 7.9

CHT

DA

LY

KR

SO

JO

GC

MP

MPG

13.2 18.0 19.3 −29.5 19.8 19.4 18.5 17.8 17.4 17.4 17.7 18.9 20.7 19.0 9.8 14.4 18.2 13.8 9.2 13.1

−19.3 −23.3 −26.6 −3.8 −32.2 −33.2 −33.3 −35.9 −37.9 −39.7 −45.7 −62.4 −92.4 37.4 −22.1 −25.3 −115.0 −95.9 −90.0 69.7

6.8 3.0 −1.1 2.6 −5.0 −5.6 −6.1 −6.0 −5.8 −5.7 −6.0 −9.4 −18.6 6.3 0.8 −1.4 −23.2 −13.0 −11.9 10.1

3.0 2.4 1.7 −3.6 5.0 8.0 10.9 13.9 16.7 18.7 19.3 15.0 −0.3 9.1 8.1 9.3 −4.5 17.3 27.8 13.4

4.7 7.2 −2.1 −4.9 −3.7 −2.9 −2.0 −0.7 0.6 1.7 2.0 −1.0 −11.6 3.5 1.9 0.5 −17.9 −6.2 −3.5 6.0

3.4 0.4 −3.0 7.2 −5.5 −5.5 −5.5 −5.0 −4.3 −3.9 −4.0 −7.0 −16.3 5.5 1.8 0.1 −19.7 −7.7 −4.5 6.8

−0.8 2.2 5.8 −4.5 7.6 7.0 5.5 4.1 2.8 1.8 1.0 0.1 −0.3 3.3 −5.4 0.6 −6.3 −12.2 −18.3 8.6

6.9 1.2 −2.4 −2.8 −5.2 −5.0 −4.8 −4.0 −2.9 −1.8 −1.2 −2.5 −9.4 3.9 4.7 2.7 −9.7 3.4 8.5 5.8

3.4 1.1 −1.6 −2.8 −2.7 −1.9 −1.2 0.0 1.3 2.5 3.0 1.1 −7.1 2.3 4.7 3.7 −10.1 1.4 4.0 4.8

Nomenclature Cx:y according to Table 1; model abbreviations according to Table 4. N.A., not applicable for this substance.

components the well-established Ambrose approach shows a remarkable accuracy. The Lydersen model was not considered for the unsaturated compounds because this model was used for their estimation. Just as for the critical temperature, the Wen/Quiang approach was not applicable to the short-chained unsaturated FAEE. 3.4. Vapor Pressure. Table 10 subdivides the 1423 vapor pressure data points into five pressure regions. Most experimental data were available for the short-chained esters (C2:0−C6:0), and half of data points are found in pressure regions IV and V (10−100 kPa) around the normal boiling point. The long-chained respectively unsaturated components, on the other hand, are mainly represented in the low-pressure

regions I and II, probably mainly determined in the course of vacuum purification processes. Pressure region II (1−10 kPa), however, is more or less homogeneously populated by all kinds of FAEE. Table 10 is also visualized by a heatmap in the Supporting Information. Table 11 lists the vapor pressure estimation models used for comparison, comprising six group-contribution and five corresponding-state approaches. Out of the latter, only the CGL model is specialized on biogenic components and was taken into account, outside formal competition, as a frequently cited, nongeneral approach. It is the only group-contribution model in this comparison that only relies on the molecular structure as input. All other GC models additionally need a G


Article


Table 9. Experimental Critical Pressures, Pcexp, along with Absolute Deviations and Average Absolute Mean Deviations (AMD) of Estimated Critical Pressures, Pccalca Pccalc − Pcexp (kPa) component Cx:y

Pcexp

C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 AMD C4:1 C5:1 C18:1 C18:2 C18:3 AMD

[kPa]

3852 3362 2978 2750 2531 2357 2159 1925 1696* 1530* 1412* 1267* 1151* 3248* 2906* 1226* 1247* 1268*

AV

WJ

WQ

AM

RN

LY

1561.3 1233.1 1013.5 777.8 629.3 505.6 456.6 483.3 534.9 548.6 533.3 457.4 397.0 702.4 1086.4 888.6 205.0 212.2 219.8 522.4

193.9 147.6 135.5 48.3 7.3 −36.3 −23.7 48.4 133.8 172.3 175.3 122.2 73.5 101.4 27.6 5.7 −112.2 −104.3 −95.8 69.1

−71.9 −2.1 50.5 −6.3 −33.9 −74.2 −64.6 3.9 85.8 121.6 122.7 68.6 21.3 56.0 N.A. N.A. −161.7 −153.9 −145.5 153.7 − Pcexp (kPa)

132.6 118.6 111.6 27.4 −8.7 −46.4 −27.9 53.0 148.9 199.3 214.8 187.8 164.1 110.8 2.2 0.4 −3.0 0.6 4.4 2.1

−23.4 74.7 126.4 69.5 41.7 0.9 9.6 76.8 157.2 191.2 190.3 131.8 80.0 90.3 55.6 86.5 −96.5 −76.6 −55.2 74.1

163.8 144.2 133.3 46.1 7.7 −31.8 −14.8 64.9 159.8 209.3 224.2 195.9 171.3 120.5 − − − − − −

Pccalc component Cx:y C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 AMD C4:1 C5:1 C18:1 C18:2 C18:3 AMD a

Pc

exp

(kPa)

3852 3362 2978 2750 2531 2357 2159 1925 1696* 1530* 1412* 1267* 1151* 3248* 2906* 1226* 1247* 1268*

JO

GC

MP

MPG

KR

SO

68.9 126.9 146.5 64.3 16.9 −38.8 −41.4 17.4 91.7 121.4 117.7 56.7 5.1 70.3 28.5 38.1 −173.0 −156.9 −139.6 107.2

205.9 138.7 145.8 56.7 6.4 −49.5 −50.6 11.1 88.9 122.7 123.4 71.4 28.8 84.6 −61.0 −45.7 −177.1 −199.1 −221.7 140.9

−32.2 −24.6 21.2 −40.2 −70.8 −112.9 −104.3 −36.2 45.7 81.9 83.6 31.1 −14.3 53.8 −168.5 −127.2 −194.5 −185.9 −176.6 170.5

20.3 86.0 111.9 34.7 −8.6 −61.0 −60.8 0.4 76.7 108.1 105.8 47.1 −2.7 55.7 −30.8 −12.4 −185.2 −175.4 −164.9 113.7

17.8 102.7 156.9 111.5 100.2 78.5 107.1 194.0 293.4 345.3 361.1 331.9 304.3 192.7 209.7 219.9 158.4 190.3 224.8 200.6

132.2 118.3 111.3 27.2 −8.9 −46.5 −28.0 52.9 148.8 199.2 214.8 187.7 164.1 110.8 91.8 71.7 9.4 26.4 44.8 48.8

Nomenclature Cx:y according to Table 1; model abbreviations according to Table 5. N.A., not applicable for this substance.

Table 12 summarizes the model comparisons for the five pressure regions of Table 10, using the relative mean deviation (RMD) which is defined as follows:

reference point. Except for the Rarey/Nannoolal (estimated Tb) approach which relies on an intrinsic Tb-estimation, for all other methods, the normal boiling points of Table 2 were chosen as reference points. On the other hand, the corresponding-state models usually use two reference points on the saturation pressure curve. To be concrete, the Riedel, Miller, and Gomez-Nieto/Thodos approaches, which are based on a Riedel-type equation, use critical point and normal boiling point. However, Ambrose/ Walton, based on a Wagner-type equation, and Lee/Kessler, also a Riedel derivate, use the acentric factor instead of the normal boiling point.

RMD =

xicalc

1 n

n

∑ i=1

xicalc − xiexp 100% xiexp

(3)

xiexp

where represents a calculated quantity, the respective experimental value, and n the number of data points. The overall impression is that all approaches work better around the normal boiling point, in regions IV and V, compared to the low pressure regions, except for the Rarey/Nannoolal (estim. Tb) approach which is beyond 20% deviation in all regions. The Rarey/Moller approach shows a universal applicability with the H


Article


Table 10. Available Vapor Pressure Data (Number of Data Points) Subdivided into Pressure Regions along with Temperature Ranges of Experimental Data, Tmin and Tmax; Nomenclature Cx:y According to Table 1 pressure region (kPa) component Cx:y

I (100)

total

Tmin (K) Tmax (K) C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 C4:1 C5:1 C18:1 C18:2 C18:3 total

253.41 452.99 0 0 0 0 20 0 18 9 29 8 20 27 13 0 0 2 0 3 149 10.5%

255.40 536.83 59 0 9 12 22 5 19 3 12 3 28 23 17 1 8 9 5 2 237 16.6%

313.51 462.37 174 13 49 24 21 0 10 0 6 0 0 0 0 0 0 0 0 0 297 20.9%

330.13 568.20 198 32 104 20 16 2 3 1 1 0 0 1 0 3 0 0 0 0 381 26.8%

349.50 546.15 187 40 104 11 8 1 1 1 1 0 2 0 0 2 1 0 0 0 359 25.2%

618 85 266 67 87 8 51 14 49 11 50 51 30 6 9 11 5 5 1423 100.0%

Table 11. Survey of Vapor Pressure Modelsa

a

model

abbreviation

method

input data

Ceriani/Gani/Liu Myrdal/Yalkowski Rarey/Moller Rarey/Nannoolal (estim. Tb) Rarey/Nannoolal (given Tb) Gomez-Nieto/Thodos Riedel Miller Ambrose/Walton Lee/Kessler Champion/Rarey/Ramjugernath (Psat method)

CGL MY RM RNET RNGT GNT RI MI AW LK CRRP

GC, specialized on biogenic components GC GC GC GC corresponding-state corresponding-state corresponding-state corresponding-state corresponding-state GC

molecular structure, molecular structure, molecular structure, molecular structure, molecular structure, Tc, Pc, Tb, T Tc, Pc, Tb, T Tc, Pc, Tb, T Tc, Pc, ω, T Tc, Pc, ω, T molecular structure,

reference T Tb, T Tb, T T Tb, T

43 95 70 69 71 96 97 98 99 100 79

T

GC, group-contribution. T, temperature; Tc, critical temperature; Pc, critical pressure; ω, acentric factor; and Tb, normal boiling point.

Table 12. Resulting RMD for Vapor Pressure Estimation Using the Models of Table 11 model Ceriani/Gani/Liu Myrdal/Yalkowski Rarey/Moller Rarey/Nannoolal (estim. Tb) Rarey/Nannoolal (given Tb) Gomez-Nieto/Thodos Riedel Miller Ambrose/Walton Lee/Kessler Champion/Rarey/Ramjugernath (Psat method)

pressure region (kPa) I (100)

24.1 28.4 14.6 20.4 14.9 93.6 37.7 28.7 18.4 31.0 16.4

20.3 25.7 12.3 28.0 11.7 31.0 20.2 15.9 12.6 12.7 15.1

18.0 8.3 3.5 37.0 3.5 3.7 2.9 2.4 2.8 3.3 6.3

11.3 2.5 2.0 27.2 2.0 1.6 2.0 1.8 2.1 2.3 1.9

9.1 7.1 1.6 24.5 1.6 2.0 1.7 1.9 2.9 2.0 3.0

CGL MY RM RNET RNGT GNT RI MI AW LK CRRP

Rarey/Ramjugernath Psat method. The older models of GomezNieto/Thodos and Riedel cannot be recommended for pressure region I. In the regions III−V, deviations of most

least deviations at extremely low pressures and also a good performance in the other regions, closely followed by the GC methods of Rarey/Nannoolal (given Tb) and the Champion/ I


Article

Industrial & Engineering Chemistry Research Table 13. Available Experimental Density Data (No. Data Points) and Temperature Regionsa

a

component Cx:y

Tmin (K)

Tmax (K)

no. data points

C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 C4:1 C18:1 C18:2 C18:3

273.15 273.15 298.15 273.15 273.15 273.15 273.15 273.15 273.15 273.95 283.15 283.15 295.15 290.25 278.15 288.65 278.15

363.15 463.15 553.70 422.84 442.80 452.79 428.45 453.15 373.15 359.55 407.35 368.15 573.15 360.35 363.15 343.15 373.15

55 57 22 38 50 47 36 10 24 10 22 16 32 8 18 12 20

Table 15. Resulting RMD for Density Estimation Using the Models of Table 14a RMD (%) component Cx:y

CT

GCVOL and GCVOL 60O

ext. GCVOL

GCVOL 60C

C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 C4:1 C18:1 C18:2 C18:3 averaged RMD

0.1 0.2 3.5 3.3 6.1 10.1 10.4 6.4 0.5 3.3 4.5 4.0 8.4 3.6 7.4 16.1 16.4 6.1

1.6 0.8 0.7 1.3 1.2 1.3 1.2 1.4 1.2 1.1 1.8 1.2 0.8 0.9 0.5 0.4 0.7 1.1

1.6 0.8 0.7 1.3 1.2 1.3 1.2 1.4 1.2 1.1 1.8 1.2 0.8 2.6 0.5 0.4 0.7 1.2

2.2 1.9 2.4 0.5 0.4 0.3 0.3 0.5 0.3 0.5 1.0 0.5 0.5 1.6 0.4 0.3 0.1 0.8

Nomenclature Cx:y according to Table 1.

models are below 5%, with the exceptions of Ceriani/Gani/Liu, Myrdal/Yalkowski, and Rarey/Nannoolal (estim. Tb). Furthermore, Table 12 illustrates generally similar deviations for the Rarey/Moller and Rarey/Nannoolaal (given Tb) approaches. Another recent model comparison reports comparable deviations of 14.84% (CGL), 6.73% (RM), 9.11% (RNGT), 64.57% (GNT), 26.12% (RI), 6.96% (AW), and 21.64% (LK), whereby these numbers do not distinguish between the five pressure regions.47 Concerning the Ceriani/Gani/Liu approach, the authors of the original work report deviations of 12.9% for saturated and 8.1% for unsaturated components, referring to the whole pressure range up to 1 atm, which suggests that these authors mainly used data from pressure regions III−IV.43 Other authors, applying the same model to a relatively small FAEE database, report deviations between 16.35% and 26.42%, depending on chain lengths.45 Another paper states 48.19% deviation for this approach, using mainly low-pressure data in the regions I−III.46 3.5. Liquid Density. Table 13 summarizes the 477 experimental data points along with temperature ranges used for comparison of the density estimation models listed in Table 14, comprising four group-contribution methods and one corresponding-state approach. Results in terms of RMD, eq 3, are summarized in Table 15. All GCVOL variants show deviations around one percent, favoring GCVOL 60 (completely new) with 0.8% averaged RMD. This approach also shows least deviations for the long-

a


Table 16. Available Experimental Viscosity Data (No. Data Points) and Temperature Regions between Tmin and Tmaxa

a

component Cx:y

Tmin (K)

Tmax (K)

no. data points

C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C12:0 C14:0 C16:0 C18:1 C18:2 C18:3

273.15 273.54 288.15 273.15 288.15 273.15 288.15 288.15 283.15 283.15 283.15 298.15 273.15 278.15 278.15

473.15 543.15 501.41 373.15 368.15 373.15 368.15 373.15 368.15 368.15 368.15 513.15 373.15 363.15 373.15

44 25 20 10 13 10 13 6 17 16 16 20 21 18 20


chained components. GCVOL and GCVOL 60O deliver the same results because they rely on the same functional groups for the components investigated. The same is true for ext. GCVOL with the exception of the shortest unsaturated ester. The strengths of the Campbell/Thodos corresponding-state

Table 14. Survey of Models Used for Density Estimationa

a

model

abbreviation

method

Campbell/Thodos Elbro/Fredenslund/Rasmussen Tsibanogiannis/Kalospiros/Tassios Ihmels/Gmehling GCVOL 60 (original plus new) Ihmels/Gmehling GCVOL 60 (completely new)

CT GCVOL ext. GCVOL GCVOL 60O GCVOL 60C

corresponding-state GC GC GC GC

input data M, Tc, Pc, molecular molecular molecular molecular

Tb, μ, T structure, T structure + T structure, T structure, T

reference 101 102 103 104 104

M, molar mass; T, temperature; Tc, critical temperature; Pc, critical pressure; Tb, normal boiling point; and μ, dipole moment. J


Article

Industrial & Engineering Chemistry Research Table 17. Survey of Models Used for Viscosity Estimationa

a

model

abbreviation

method

Ceriani/Goncalves/Coutinho Ceriani/Goncalves/Rabelo et al. Rarey/Nannoolal (given Tb) Orrick/Erbar van Velzen Joback Souders Thomas

CGC CGR RNGT ORER VAVE JOBA SOU THOM

GC, specialized on biogenic components GC, specialized on biogenic components GC GC GC GC viscosity-density-constant GC

input data molecular structure, molecular structure, molecular structure, molecular structure, molecular structure, molecular structure, liquid density molecular structure,

reference

T T Tb, T liquid density at 25 °C, T T T Tc, liquid density

105 106 107 108 109 75 110 111

T, temperature; Tb, normal boiling point; and Tc, critical temperature.

Table 18. Resulting RMD for Viscosity Estimation Using the Models of Table 17a RMD (%)

a

component Cx:y

CGC

CGR

RNGT

ORER

VAVE

JOBA

SOU

THOM

C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C12:0 C14:0 C16:0 C18:1 C18:2 C18:3 averaged RMD

46.2 43.2 5.2 13.6 5.4 12.1 4.0 4.8 2.8 1.5 1.1 1.1 3.7 2.4 3.5 10.0

35.2 130.5 15.0 5.6 4.4 3.4 2.3 3.5 2.3 3.2 6.4 15.0 9.3 7.7 19.9 17.6

6.3 14.9 6.4 4.6 3.7 6.8 6.1 8.6 7.9 8.1 5.4 4.1 4.2 24.1 35.6 9.8

5.6 23.6 7.3 11.2 11.7 12.5 13.2 12.4 11.2 11.7 13.6 16.5 41.7 66.4 86.7 23.0

10.3 22.6 5.6 4.6 3.2 3.9 3.1 2.7 3.9 4.7 4.4 8.3 8.7 10.7 11.5 7.2

6.6 28.0 13.7 19.6 18.9 21.9 18.6 20.5 18.2 18.0 20.0 20.5 28.9 33.2 33.1 21.3

20.5 35.1 8.6 5.0 6.1 15.3 12.2 20.4 14.1 13.0 13.0 11.9 18.1 35.5 49.6 18.6

5.3 16.4 3.9 3.6 5.3 8.6 11.0 16.1 20.2 32.2 48.6 61.1 134.3 183.7 229.1 52.0


listed in Table 17, comprising seven group-contribution methods and one approach based on the viscosity-densityconstant. For estimation of liquid densities as a function of temperature, required by the approaches of Thomas and Souders, the GCVOL 60 (completely new) approach by Ihmels and Gmehling was used. Liquid densities at 25 °C, required by the Orrick/Erbar model, were taken as experimental data from the DDB. Results of the model comparison in terms of RMD, eq 3, are summarized in Table 18. Overall, the van Velzen approach shows the least deviations of 7%, followed by RNGT with roughly 10%. The specialized CGC approach, however, has its strengths when applied to long-chained components starting with C8:0 and to the unsaturated esters, with deviations below 5%. The Souders approach seems to underestimate the influence of chain length, and its relatively significant deviations may also be attributed to estimated densities as input data. The Joback method succeeds for ethyl acetate, C2:0, but shows relatively similar deviations for all other substances, independent of chain length. The Thomas approach shows the most significant deviations with exceptions in the short-chained region. Interestingly, all models show exceptional deviations for propanoic acid ethyl ester, C3:0. 3.7. Surface Tension. Table 19 summarizes the 186 experimental data points along with temperature ranges used for comparison of the surface tension estimation models listed in Table 20, comprising the group-contribution model by

Table 19. Available Experimental Surface Tension Data (No. Data Points) and Temperature Regions between Tmin and Tmaxa

a

component Cx:y

Tmin (K)

Tmax (K)

no. data points

C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 C4:1 C18:1

253.15 288.15 288.15 289.45 273.15 288.15 288.15 288.15 289.25 288.15 293.15 293.15 295.15 290.25 293.15

346.45 333.25 359.95 360.15 359.05 360.15 360.25 453.15 359.75 363.15 361.35 338.15 419.15 360.35 453.15

41 7 13 7 23 9 13 9 5 14 7 6 24 4 4


approach are limited to the two shortest-chained components which may be attributed to the widespread use and broad availability of measured data for these components. 3.6. Dynamic Viscosity. Table 16 summarizes the 269 experimental data points along with temperature ranges used for comparison of the dynamic viscosity estimation models K


Article

Industrial & Engineering Chemistry Research Table 20. Survey of Models Used for Surface Tension Estimationa

a

model

abbreviation

method

input data

reference

Rarey/Olivier Brock

RO BR

GC corresponding-state

molecular structure, Tb, T Tc, Pc, Tb, T

112 113

T, temperature; Tb, normal boiling point; Tc, critical temperature; Pc, critical pressure.

■

Table 21. Resulting RMD for Surface Tension Estimation Using the Models of Table 20a

* Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b03794. Complete list of 100 esters, not necessarily derived from fatty acids, found in the data banks; a visualization (heatmap) of Table 10; and a complete list of the estimated values of the methods applied in this paper (PDF)

RMD (%)

a

component Cx:y

RO

BR

C2:0 C3:0 C4:0 C5:0 C6:0 C7:0 C8:0 C9:0 C10:0 C11:0 C12:0 C14:0 C16:0 C4:1 C18:1 averaged RMD

5.3 3.3 0.5 0.5 1.1 1.8 2.1 1.7 2.1 2.8 2.7 1.1 4.9 1.7 4.3 2.4

2.8 0.9 0.6 1.8 5.8 4.4 3.8 2.1 6.3 9.5 11.8 15.9 25.3 4.5 16.7 7.5

ASSOCIATED CONTENT

S

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Thomas Wallek: 0000-0001-9687-106X Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes


The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The authors thank DDBST GmbH for providing experimental data and gratefully acknowledge support from NAWI Graz.

Rarey/Olivier and the corresponding-state approach by Brock. Evaluations in terms of the RMD are summarized in Table 21. An averaged RMD of 2.4% favors the Rarey/Olivier approach compared to that of Brock, with the exception of the two shortest-chained esters for which the Brock model turns out to be the better choice.

4. SUMMARY

■

On the whole, the pure-component properties of fatty acid ethyl esters can be estimated in a satisfactory manner by common nonspecialized group-contribution and corresponding-state approaches when choosing an appropriate model, depending on chain length, substance, and temperature, or pressure range, respectively: minimum average absolute mean deviations of the normal boiling point are below 5 K (3.4 K for saturated and 4.2 K for unsaturated components), those of the critical temperature below 3 K (2.3 K for saturated and 1.2 K for unsaturated components), those of the critical pressure in the region of 50 kPa (54 kPa for saturated and 2.1 kPa for unsaturated components); minimum relative mean deviations of saturation pressures range from 2% around the normal boiling point to 15% at extremely low pressures, those of liquid density are below 1%, those of viscosity at a maximum of 7% and those of surface tension around 2.4%. Consequently, these estimations, along with their estimated accuracy, provide a useful basis for rigorous process simulation. In addition, the survey of available data given in this paper could be used as a starting point for experimenters to fill in the gaps that are still evident in various regions of interest.

ABBREVIATIONS FAEE = fatty acid ethyl ester FAME = fatty acid methyl ester GC = group contribution method AMD = absolute mean deviation RMD = relative mean deviation REFERENCES

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