Estimation of Physical Constants of Biodiesel-Related Fatty Acid Alkyl

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Thermodynamics, Transport, and Fluid Mechanics

Estimation of Physical Constants of Biodiesel-Related Fatty Acid Alkyl Esters: Normal Boiling Point, Critical Temperature, Critical Pressure, and Acentric Factor Nathan Sombra Evangelista, Frederico Ribeiro do Carmo, and Hosiberto Batista de Sant Ana Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b01310 • Publication Date (Web): 04 Jun 2018 Downloaded from http://pubs.acs.org on June 5, 2018

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Industrial & Engineering Chemistry Research

Estimation of Physical Constants of BiodieselRelated Fatty Acid Alkyl Esters: Normal Boiling Point, Critical Temperature, Critical Pressure, and Acentric Factor Nathan S. Evangelista1,2,*, Frederico R. do Carmo2, Hosiberto B. de Sant’Ana2,3 1

Instituto Federal de Educação, Ciência e Tecnologia do Ceará, Campus Iguatu. 63500-000 Iguatu – CE, Brazil.

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Grupo de Pesquisa em Modelagem Termodinâmica, Departamento de Engenharia e Tecnologia,

Universidade Federal Rural do Semi-Árido, Campus Leste – Centro de Engenharias. 59625-900 Mossoró – RN, Brazil. 3

Grupo de Pesquisa em Termofluidodinâmica Aplicada, Departamento de Engenharia Química, Universidade Federal do Ceará, Campus do Pici. 60455-760 Fortaleza – CE, Brazil.

*Corresponding author: Nathan S. Evangelista, Instituto Federal de Educação, Ciência e Tecnologia do Ceará, Estrada Iguatu-Várzea Alegre, km 5, Vila Cajazeiras. 63500-000 Iguatu – CE, Brazil; e-mail: [email protected]; Tel: +55-85-999155721

ACS Paragon Plus Environment

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ABSTRACT

A comprehensive study regarding the estimation of normal boiling points, critical temperatures, critical pressures, and acentric factors of biodiesel-related esters is presented. Such properties are crucial for simulations of chemical processes involving biodiesel. Although reliable experimental data are available for some esters, their determination for all the existing biodiesel components is an expensive and cumbersome task. In view of that, this work aimed to investigate the performance of group contribution and corresponding states models in the calculation of these properties. The estimation models were tested in terms of accuracy and of the plausibility of combining experimental and calculated values without violating the expected physical behavior for corresponding pairs of esters and for esters belonging to the same homologous series. The main outcome of this work is a recommendation of the most feasible models for engineering applications.


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INTRODUCTION Biodiesel is a mixture of long chain fatty acid alkyl esters (FAAEs) obtained from renewable sources, such as vegetable oils or animal fats.1 It presents technical and environmentally friendly characteristics that have encouraged its use either as an alternative fuel or as a blending component of conventional diesel in vehicle engines.2 To design and optimize processes involving these fuels, the knowledge of a variety of chemical and physical properties of biodiesel components is required.3 The normal boiling point (Tb) indicates the volatility of a substance and, for this reason, it is of great importance for environmental and safety concerns.4,5 This property is often necessary as entry data for the application of models capable of estimating volumetric, transport, and thermodynamic properties of FAAEs (e.g., density, viscosity, thermal conductivity, surface tension, vapor pressure, enthalpy of vaporization, critical properties, and acentric factor). Therefore, reliable values are essential to accurately simulate biodiesel processes, such as spray, atomization, and combustion in diesel engines.6 Moreover, Tb values can be used as initial guess in steps of vapor-liquid equilibrium calculations.3 Critical properties are the pure component constants of greatest interest. The critical pressure (Pc) and the critical temperature (Tc) are commonly used as coordinates of a substance’s critical point.7 Along with acentric factors (ω), these properties are input parameters for many equations of state, which justifies their importance in the description of pure components and mixtures phase behavior.8 Furthermore, Tc, Pc, and ω are used in many correlations for the estimation of other relevant properties, especially those based on the Corresponding States Principle (CSP).9 Although experimental data of the aforementioned properties are readily accessible for common industrial substances,7,9–12 there is a lack of values for fatty acid methyl esters (FAMEs)


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and fatty acid ethyl esters (FAEEs). This scarcity of data may be related to the difficulty in obtaining the esters in pure forms and in carrying out the experiments, because these substances could degrade at severe conditions, especially near their critical points. To the best of our knowledge, the available data do not cover the entire variety of components occurring in biodiesel. Hence, the application of thermodynamic models becomes essential. In the past decades, Group Contribution (GC) methods have been proposed for critical pressures,13–28 critical temperatures,13,14,16–33 and normal boiling points5,13,14,21,22,34–39 estimations. Besides the GC approach,40–42 the CSP has been used for acentric factors calculations as well.7,9,10,43,44 Both these methodologies are predictive, that is, reliable estimates can be obtained without the need for component-specific correlated parameters; instead, only on a small amount of a substance’s information is required.45 Although there is a large number of methods in the literature, each of them has built-in assumptions and practical limits that should apply. Therefore, selecting the most appropriate models is extremely important to achieve realistic results in a process simulation.46 In the last years, a few works regarding the estimation of Tb, Tc, Pc, and ω of fatty esters have been reported. Since this paper presents another contribution to this particular field, we decided to carry out a short survey of the publications related to this topic. Sales-Cruz et al.47 estimated Pc and Tc of FAMEs using GC methods.13,14,21 Experimental data of methyl caprate and methyl laurate were used to validate the models. As a conclusion, they suggested the application of Constantinou and Gani’s14 method for both properties. Anand et al.48 tested correlative and predictive models for the estimation of Tb,13,14,49 Tc,13,14,23,24,30 and Pc13,14,23,49 of FAMEs. By comparing experimental and estimated values, the authors observed that the models of Constantinou and Gani,14 Joback and Reid,13 and Lydersen23 were the most accurate for the previous respective properties. Wallek et al.50 evaluated CSP51 and


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GC5,13,14,21,22,35–37 models implemented in the ARTIST software package52 for Tb estimations. The experimental data used for comparisons comprised ten FAMEs and were taken from the DDB52 and Beilstein/Reaxys53 databases. The reported results favor the methods of Stein and Brown35 and Nannoolal et al.37 Cunico et al.54 analyzed GC methods for the estimation of Tb13,21 (FAMEs and FAEEs), Tc,13,21,30,31 (FAMEs) and Pc13,21 (FAMEs). For Tb, the models of Joback and Reid13 and Marrero and Gani21 output the best results for FAMEs and FAEEs, respectively. The latter model was also the most accurate for Tc and Pc. An et al.6 applied the correlation of Yuan et al.55 and the model of Joback and Reid13 to predict Tb of five FAMEs. The predicted values were compared to the experimental data reported by Rochaya,56 and the authors concluded that none of the models was enough accurate. For Tc and Pc, the authors tested other GC methods as well.15,30,33 Comparisons with experimental data for methyl oleate showed that Ambrose’s model15,33 yielded the smallest deviations for both properties. An indirect evaluation procedure was adopted by García et al.57 They created three packages comprising estimation models for Tb,14,22,55 Tc,14,22,33 Pc,15,26 Vc,13,14,22 and ω7. Calculated values of these properties were inserted into the Rackett-Soave58,59 equation for density estimations. To test the packages, a databank containing experimental density data of FAMEs, FAEEs, and biodiesel was compiled. In a subsequent publication,60 the authors rectified some misleading aspects of the original work. Their final results suggest the application of the following models for pure FAMEs: Yuan et al.55 (Tb), Ambrose15,33 (Pc, Tc), Joback and Reid13 (Vc), and Lee and Kesler7 (ω); for pure FAEEs, the use of Marrero and Pardillo’s22 (Tb, Tc, Vc), Wilson and Jasperson’s26 (Pc), and Lee and Kesler’s7 (ω) methods is suggested. A methodology similar to that of García et al.57,60 had been employed by us in a more recent publication.3 To select the best method for Tb, direct comparisons between experimental and


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estimated data had been performed. Given the scarcity of experimental values for Tc, Pc, and ω at the year of the publication, we had had to rely on the indirect procedure that uses the RackettSoave equation for density estimations. Despite the efforts put in that work, especially to ensure its completeness in terms of database and investigated models, we have recently realized that some of its conclusions must be revised for the following reasons: 1) a few Tb values should not have been used, either because they were not obtained at pressures close to 760 mmHg,61 or because they are not sufficiently reliable; 2) after the recent publications by Nikitin and Popov62– 65

and by us,66 enough Pc, Tc, and ω data is available to perform a direct evaluation of the

available models. Wallek et al.67 have recently published a study regarding the estimation of Tb, Tc and Pc of FAEEs. They compared various methods for Tb,5,13,14,22,23,35–37,68–73 Tc,13,14,16,18–20,22–24,26,30,31,33,74 and Pc13–16,18–20,22–24,26 calculations. To verify the accuracy of each model, the authors compiled a database containing experimental53,75–77 and estimated data. These calculated values were necessary to guarantee the smoothness of the curves of each property against the molar masses of the esters. For Tb, the reported results show that the lowest mean deviations (%AARD, see equation 3) for saturated and unsaturated compounds were generated by the models of Champion71 and Cordes and Rarey5, respectively. For Tc, the best results for saturated and unsaturated substances were obtained from the models of Marrero and Pardillo22 (simple groups) and Nannolal et al.19 Marrero and Pardillo’s model22 (group interactions) was recommended to estimate the critical pressures of saturated FAEEs, whereas Ambrose’s model15 was suggested for unsaturated compounds. Despite these results, we believe that some %AARD values reported by Wallek et al.67 should be reviewed. In our opinion, the authors should have considered only the number of data points that was really used to test the models in the calculation of the mean


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deviations for unsaturated compounds. Following this criterion, the %AARD values obtained from the methods of Cordes and Rarey5 and Nannoolal et al.37 in Tb calculations would be by 5.2% and 6.4%, respectively; in the critical temperature results, the reported %AARD for the models of Ambrose33 and Nannoolal et al.19 should be replaced by 7.6% and 6.1%, respectively. These modifications might affect the authors’ recommendations for unsaturated esters. In this work, we propose a thorough comparative review of how GC and CSP models perform in computing Tb, Tc, Pc, and ω of fatty acid esters. The goal of this article is to outline the appropriate models when experimental data are missing. It should be emphasized some differential aspects of the present investigation in comparison to the papers previously published in the literature: •

A wide variety of compounds, covering FAMEs and FAEEs with diversified chain lengths, including mono- and poly-unsaturated species, have been considered.

•

Unlike in Wallek et al.’s work,67 vapor pressure models68,71–73 and group vector space methods70 have not been used to calculate normal boiling points. Despite that, to the best of our knowledge, we investigated the greatest diversity of GC methods originally proposed for Tb, Tc and Pc estimations.

•

To test the accuracy of the models available for Tb, Tc, and Pc estimations, we have considered only experimental data. Besides the accuracy examinations, the profiles of all properties were checked for consistency in view of empirical constraints explained in the following sections.

METHODOLOGY Experimental databank


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Given the well-known importance of selecting proper data to validate the models,78 we took special attention in identifying reliable values among those reported in the literature. The experimental data were compiled into a databank and the accepted values of Tb, Tc, Pc, and ω are summarized in Table 1. For some esters, the normal boiling temperatures were determined by averaging values reported by different authors. Despite that, none of the points considered in the averages showed large scattering in comparison with others: considering all substances, the highest coefficient of variation was 0.5%, as presented in the Supporting Information. Although Tb is, by definition, the temperature at which a liquid boils under a pressure (P) of 760 mmHg, most of the data we have considered was measured in a slightly extended interval (755 mmHg ≤ P ≤ 765 mmHg). An exception was made for methyl palmitate’s data, which was measured at 747 mmHg, as reported by Krop et al.79 As shown in Figure 1, these authors’ value correlates better with the other data in comparison to that reported by Graboski and McCormick.80 For “ME-C18:2” and “ME-C18:3”, we used the data published by Krop et al.,79 who reported an increase in Tb with an increase in the number of double bonds. They reported the same value of Tb for “ME-C22:0” and “ME-C22:1”. As we did not find other values in the literature, their dataset was adopted in this case as well. Critical property data were obtained from Nikitin and Popov’s works,62–65 whereas the acentric factors were calculated using Pitzer’s definition81 in conjunction with vapor pressure correlations proposed in our previous work.66

Evaluation of predictive methods


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General information about the applied methods are presented in Tables 2 to 5. All parameters for the NRRC, NRR, and MRR models were taken from revised tables provided by the authors.82 To select the best models for each property, the following evaluation procedure was adopted: 1)

Accuracy analysis 1.1)

Direct comparisons between experimental and estimated values were

performed based on the following statistical parameters:

%ARD = 100

%AARD (FAME) =

(1) !" %$%&

!" ∑'

(2) %AARD (FAEE) =

"" %$%&

"" ∑'

(3) )*+

where X

and X ,-., denote experimental and calculated properties,

respectively. The results of each model were divided into two categories: “FAMEs” and “FAEEs”. As their names suggest, they consider only 2$34 2$44 experimental data of FAMEs (N0-1) and FAEEs (N0-1), respectively.

1.2)

For each property, “n × n” packages of models were created, where “n” is

the number of analyzed methods. Each package (i − j) is a combination of two models: one FAMEs (i) and another for FAEEs (j). The formulation of these packages was related to our observations that the most accurate methods for FAMEs and FAEEs were not necessarily the same. The overall accuracy of each package was calculated as follows:


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%AARD (i − j) =

!" = = + : ; ' =

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"" = =

∑>'

=

@

(4) 2$34 2$44 Where N0-1- = N0-1+ N0-1. The packages were ranked in a decreasing

order of accuracy and sent to the next step of the evaluation procedure.

2)

Consistency analysis 2.1)

A comprehensive variety of FAAEs that may occur in biodiesel was

compiled in a literature survey. These esters were collected from scientific papers, structures databases83 and catalogs of chemical companies.84,85 At total, 40 pairs of corresponding FAMEs/FAEEs ranging from 6 to 26 carbon atoms in the fatty acid chain, including mono- and poly-unsaturated esters, have been found. 2.2)

Our objective was to obtain a set of values for Tb, Tc, Pc, and ω covering

all the registered FAAEs. Considering that reliable experimental data were already available for the esters presented in Table 1, we had to identify which package of models would be the most appropriate to fill the gaps of values for the other compounds. In view of that, we combined experimental data with estimated values output by the models in each package. The consistency of the final set of values was checked in view of empirical trends expected for: 2.2.1) members of a corresponding “ME/EE” pair:


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TB(44C*:E) > TB(34C*:E) (5) T,(44C*:E) > T,(34C*:E) (6) P,(44C*:E) < P,(34C*:E) (7) ω(44C*:E) > ω(34C*:E) (8) where ME − Cx: y and EE − Cx: y are methyl and ethyl esters containing equal fatty-acid derived chains. In Cx:y, x and y denote the number of carbons and double bonds in the fatty acid chain, respectively. 2.2.2) adjacent members of a homologous series: TB(M) > TB() (9) T,(M) > T,() (10) P,(M) < P,() (11) ω(M) > ω() (12)


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where X M and X denote adjacent members of a homologous series. Five homologous

series

were investigated:

saturated,

mono-

unsaturated, di-unsaturated, tri-unsaturated and tetra-unsaturated. Detailed information of the registered esters as well as the analyzed packages can be found in the Supporting Information. This file also contains flowcharts presenting step-by-step details of the evaluation procedure. From Tables 2 to 5, one should notice that Tb may be required for Tc estimation (TB → T, ) but the reciprocal is not true (T, ↛ TB ). Similarly, T, → P, but P, ↛ T, ; P, → ω but ω ↛ P,. Considering that the final profile of each property would be input to the subsequent evaluation, the following validation order was adopted: 1) models for Tb; 2) models for Tc; 3) models for Pc; 4) models for ω.

RESULTS Normal boiling point The performances of the studied models are presented in Table 6. More details about these results, including the calculated values of Tb, are presented in the Supporting Information. Although none of the methods was originally proposed for biodiesel components, most of them output accurate results for both classes of esters. With a few exceptions (SCB(ME/EE), JR(ME)/(EE), CG(ME), and MP(ME)), the %ARD values were randomly distributed with respect to the size of the fatty acid chain. For the three latter models, the accuracy of at least 70% of the estimations decreased as the chain lengths increased. We investigated two hypotheses to account for this behavior: 1) uncertainties within the “-CH2-” group parameters, which would propagate and reduce the quality of prediction for longer compounds; 2) similarities in the assumptions of the JR, CG and MP models. The former hypothesis was rejected because there


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were exceptions to these trends; the latter was discarded after analyzing the equations of the models. In addition to that, the results of similar methods (e.g., MG ↔ CG, SB ↔ JR) did not present such evident trends. The accuracy of the SCB model clearly improved for longer substances. The several assumptions behind this method hindered us from understanding this fact. Considering the results for FAMEs, the most accurate models followed the order: SB (0.69%) > EVE (0.71%) > CR (1.07%) > GM (1.20%) > MG (1.40%) > EWOR2 (1.77%) > EWOR1 (1.83%) > CG (2.08%) > MP (2.60%) > NRRC (3.64%) > JR (7.86%) > SCB (8.14%). For FAEEs, the order was considerably different: EVE (0.21%) > GM (0.45%) > EWOR1 (0.49%) > EWOR2 (0.55%) > CR (0.63%) > SB (0.77%) > CG (0.88%) > MP (1.18%) > MG (1.23%) > NRRC (2.94%) > JR (3.01%) > SCB (9.55%). Further, the models were combined into 144 packages. The consistency of all Tb profiles obtained from the combination of experimental (Table 1) and estimated data (generated by the methods in each package) were tested in view of empirical restrictions presented in equations (5) and (9). As shown in Table 7, only 13 pairs of models passed this test. Considering its highest overall accuracy, we suggest the package 47, which comprises the SB (for FAMEs) and EVE (for FAEEs) methods. The recommended normal boiling temperatures for saturated compounds are illustrated in Figure 2. To check the values for the other esters, readers can consult the Supporting Information, which also contains detailed results of the consistency test.

Critical temperature A summary of the deviations obtained by each model is presented in Tables 8 and 9. To check the calculated values of Tc, readers should consult the Supporting Information. Excepting the AV


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method, which was originally developed for biomolecules, all models were proposed to cover a broad variety of organic compounds. Despite that, most of them generated very accurate results, which confirms their capability to calculate the critical temperatures of fatty esters. Although the accuracy of the JR (EE), R (ME/EE), L (EE), JDB (EE), DSG (EE), WQ1/WQ2 (EE), and LXX (EE) models tended to decrease for longer compounds, most of the results were randomly distributed. Like in the previous section, we did not obtain a reasonable explanation for this behavior. A rather general hypothesis is that these trends are simply mathematical errors, possibly resulting from various reasons (e.g., characteristics of the database used in the regressions of each group’s parameters, combined uncertainties from different parameters etc.). However, the lack of information necessary to verify this hypothesis limited us from proceeding. On the other hand, the poor results obtained from the DSG model for “ME-C18:2” and “MEC18:3” are certainly related to an approximation adopted in their fragmentations: none of the groups proposed in the original paper could be used to represent the methylene groups (-CH2-) occurring between conjugated double bonds. For this reason, we used the “C-(H)2(Cd)(C)” group, which symbolizes a “-CH2-” simultaneously attached to a sp2 and sp3 carbon atoms. Although the same assumption was adopted when dividing these compounds into the groups of the JDB model, the deviation for “ME-C18:3” was lower than that for “ME-C18:2”. Considering the FAMEs database, the accuracy of the models decreased as follows: WQ2 (0.67%) > AV (0.69%) > A (0.70%) > S (0.70%) > MG (0.72%) > WJ (0.80%) > NRR (0.81%) > CG (1.07%) > MP (1.09%) > JR (1.12%) > L (1.39%) > T (1.45%) > KR (1.68%) > F (1.81%) > WQ1 (1.98%) > LXX (3.50%) > JDB (4.71%) > R (7.33%) > DSG (15.40%). The ranking obtained for FAEEs was: AV (0.29%) > WJ (0.35%) > NRR (0.43%) > A (0.46%) > S (0.47%) > CG (0.66%) > WQ1 (0.67%) > MP (0.72%) > WQ2 (0.79%) > MG (1.01%) > JR (1.04%) > L


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(1.21%) > KR (1.61%) > LXX (2.00%) > JDB (2.47%) > T (2.52%) > F (2.90%) > DSG (3.37%) > R (5.24%). At total, 361 pairs were generated with the analyzed models. Then, we verified which of them could be combined with experimental data (Table 1) to generate critical temperature profiles obeying the restrictions from equations (6) and (10). The packages approved in the consistency test, along with their accuracies, are presented in Table 10. For outputting the lowest overall deviation, we recommend the MG and A models for FAMEs and FAEEs, respectively. It is important to mention that Ambrose’s model33 (A) requires normal boiling points as input parameters. To obtain the reported accuracy and consistency, one must use the previously suggested Tb values. The recommended critical temperatures for saturated FAMEs and FAEEs are illustrated in Figures 3 and 4, respectively. To check the values for the other esters, readers can consult the Supporting Information, which also contains additional details about the consistency test.

Critical pressure The accuracy obtained from all models is presented in Tables 11 and 12. The estimated critical pressures are available in the Supporting Information. In comparison with Tc results, the methods output considerably higher deviations for critical pressures, which attests their lower capability to calculate the referred property. This inferior quality in Pc predictions had already been observed by Poling et al.,9 who applied the JR, CG, WJ and MP models to calculate the critical pressures of a wide variety of organic compounds. Despite the worse estimates, some models output results within the uncertainty inherent to the experimental data for various substances. We


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did not observe any obvious patterns in the deviations: the %ARD can be either higher or lower regardless of the size chain or degree of unsaturation. For FAMEs, a decreasing ranking of accuracy was observed: JR (4.99%) > MP (5.95%) > CG (6.00%) > WJ (6.02%) > NRR (6.03%) > WQ (6.10%) > JDB (7.01%) > LXX (7.40%) > A (7.99%) > S (8.08%) > L (8.28%) > MG (9.63%) > > AV (12.75 %) > KR (16.40%). For FAEEs, a quite similar order was observed: MP (3.89%) > JR (4.02%) > CG (4.38%) > WQ (4.72%) > WJ (6.68%) > NRR (7.00%) > JDB (7.94%) > LXX (8.44%) > S (8.89%) > A (8.89%) > L (9.15%) > MG (9.95%) > AV (14.14%) > KR (16.46%). In the further evaluation step, the models were combined into 196 pairs. Differently from what had been observed for Tb and Tc, none of the packages was approved in the consistency test, which indicates that all the analyzed Pc profiles violated either one or both the restrictions presented in equations (7) and (11). In a deeper analysis of these results, we noticed that a few packages failed in the same specific points of the saturated and monounsaturated homologous series. Specifically, for the JR/MP pair, which was the most accurate, an interesting fact was observed: if we consider the uncertainty inherent to the experimental data, the failure points will disappear, as shown in Table 13. In view of that, we recommend the JR and MP model for FAMEs and FAEEs, respectively. The suggested critical pressures for all the studied esters are available in the Supporting Information. The Pc profiles for saturated compounds are illustrated in Figure 5. According to Lydersen,23 the quantity (MW/Pc)0.5, where MW denotes the molecular weight, should be a linear function of the number of repeating units in a molecule for a given homologous series. Nikitin and Popov63 pointed out that several investigations have confirmed this rule. The trendlines plotted in Figures 6 and 7 indicate that the suggested profiles for saturated compounds are in accordance with Lydersen’s23 observation.


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Acentric factor The performances of the studied models are presented in Table 14. With exception to the WMJS (because this model was fully developed considering Tc data generated by Marrero and Gani’s21 model), the input parameters of all methods were taken from the profiles recommended in the previous sections. No patterns were observed in the deviations, except that all models output lower %AARD for FAEEs, which is probably related to the absence of unsaturated compounds in ethylic esters comparisons. According to Gmehling et al.,12 when a vapor pressure model is coupled with Pitzer’s81 definition, the acentric factor estimation tends to be more realistic. In fact, considering the deviations per compound, the good accuracy obtained from the MRR method emphasizes that. For FAMEs, the models’ accuracies decreased according to the order: MRR (2.78%) > CDJ (6.37%) > LK (6.41%) > AW (7.15%) > WMJS (7.78%) > SYP (7.84%) > CG (7.86%) > R (8.18%) > E (9.62%) > HP (9.91%). For FAEEs, a different ranking was observed: SYP (2.23%) > MRR (2.61%) > LK (5.46%) > CDJ (5.55%) > AW (6.51%) > CG (6.62%) > R (7.45%) > WMJS (7.47%) > HP (8.91%) > E (9.05%). Despite having generated the best results for ethylic esters, the SYP model predicted unrealistic acentric factors for hydroxy esters, which might indicate an error in the “-OH” group parameter. For “ME-C18:1,OH” and “EE-C18:1,OH”, the calculated values were: ωSYP = 0.272 and ωSYP = 0.240, respectively. The methods were further combined into 100 pairs, and we verified which acentric factor profiles would obey the constraints from equations (8) and (12). Like for Pc, none of the packages has passed the consistency test. In this case, we observed several failure points in the results of all packages. In addition to that, the fact that the values of ω (Table 1) carry


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uncertainties related to the critical pressures62–65 and to the vapor pressure correlations,66 hindered us from eliminating the failure points. As an alternative test, the acentric factors presented in Table 1 were temporarily ignored and the consistency of the ω profiles (containing only data generated by the methods in each package) was verified. The packages approved in this further analysis are presented in Table 15. Considering these results, two options arise when acentric factors of FAMEs and FAEEs are needed: 1) to use only the data from Table 1; 2) to use only estimated values. If the second option will be selected, we recommend the CG method for both classes of esters, given the issues regarding the application of the SYP method for hydroxy esters. In addition to that, the CG/CG combination generates ω profiles with equivalent behavior, as illustrated in Figure 8.

CONCLUSIONS In this work, we have investigated how different estimation methods perform in computing relevant physical constants of fatty acid esters. For that, a database containing experimental (Tb, Tc, and Pc) and calculated values (ω) was developed. The experimental data were extracted from different literature sources, whereas the acentric factors were obtained using Pitzer’s definition in conjunction with vapor pressure correlations. The models were tested in terms of accuracy and of the plausibility of combining experimental and estimated values without violating empirical trends for corresponding pairs of esters and for esters belonging to the same homologous series. This procedure was adopted to avoid inconsistencies if experimental and estimated data points will be combined. For Tb, Tc, and Pc, experimental values should be used when they are available. In other cases, we suggest the application of the SB, MG, and JR models to calculate these respective properties for FAMEs; for FAEEs, we recommend the EVE, A and MP models,


18

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respectively. For acentric factors, one must choose between using only the values obtained from vapor pressure correlations or only estimated points. If the second option will be selected, the application of the CG model is suggested for FAMEs and FAEEs.

Supporting Information. MS-Excel spreadsheet containing complete information about the studied compounds, along with the recommended values for their physical constants; details about the evaluation procedure, including flowcharts of the adopted methodology, and results output by all models. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *Tel: +55-85-999155721. E-mail: [email protected] Funding Sources Funding for this research was provided by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil). Notes The authors declare no competing financial interest. All calculations were carried out using the OCTOPUS v1.0 computational tool. It is available for free at https://github.com/thegibbsproject/octopus. ACKNOWLEDGMENT


19


Page 20 of 54

The authors thank the financial support provided by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil). ABBREVIATIONS Roman Letters %AARD = Absolute average relative deviation. CSP = Corresponding states principle. FAAE = Fatty acid alkyl ester. FAEE = Fatty acid ethyl ester. FAME = Fatty acid methyl ester. GC = Group contribution. MW = Molecular weight. nca = Number of carbon atoms in the fatty acid chain. 2$34 = Number of experimental data of FAMEs. N0-12$44 N0-1= Number of experimental data of FAEEs.

N0-1- = Total number of experimental data. P = Pressure. Pc = Critical pressure. Tb = Normal boiling temperature. Tc = Critical temperature. Vc = Critical volume. Vvdw = van der Waals volume.

Greek Letters ω = Acentric factor.


20

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Superscripts calc = calculated. exp = experimental.

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TABLES Table 1. Selected properties of FAMEs and FAEEsa

compound

propertyc

acronymb Tb/K

Tc/K

Pc/bar

ω

methyl caproate

ME-C6:0

423.3086–93

612.00

28.80

0.4043

methyl enanthate

ME-C7:0

445.2986–88,91,92,94

626.00

25.30

0.4885

methyl caprylate

ME-C8:0

465.9180,87,88,91,95

646.00

23.40

0.5332

methyl pelargonate

ME-C9:0

486.7588,91,95

665.00

20.60

0.5550

methyl caprate

ME-C10:0

498.9479,80,87,91,96

675.00

19.30

0.6524

methyl undecanoate

ME-C11:0

523.3986

694.00

17.50

-

methyl laurate

ME-C12:0

535.1580

709.00

15.20

0.6607

methyl myristate

ME-C14:0

568.1580

730.00

13.20

0.7765

methyl palmitate

ME-C16:0

595.1579

760.00

11.70

0.7982

methyl stearate

ME-C18:0

625.1580

785.00

10.80

0.8529

methyl oleate

ME-C18:1

620.6579,80

777.00

12.10

0.9068

methyl linoleate

ME-C18:2

619.1579

778.00

12.40

0.9220

methyl linolenate

ME-C18:3

620.1579

779.00

14.40

0.9699

methyl arachidate

ME-C20:0

642.1579

-

-

-

methyl behenate

ME-C22:0

666.1579

-

-

-

methyl erucate

ME-C22:1

666.1579

817.00

9.60

-

ethyl caproate

EE-C6:0

440.3888,89,91,97–100

615.20

25.30

0.5154


34

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compound

acronym

propertyc

b

Tb/K

Tc/K

Pc/bar

ω

ethyl enanthate

EE-C7:0

460.6487,88,92,97

635.00

23.60

-

ethyl caprylate

EE-C8:0

479.7688,97,99,101

655.00

21.60

0.5916

ethyl pelargonate

EE-C9:0

499.7597,101–104

-

-

-

ethyl caprate

EE-C10:0

515.9587,97,103

687.00

17.40

0.6529

ethyl undecanoate

EE-C11:0

534.1597

701.00

15.20

-

ethyl laurate

EE-C12:0

547.4879,87,99

718.00

13.70

0.6783

ethyl myristate

EE-C14:0

581.9599

740.00

12.70

0.7897

ethyl palmitate

EE-C16:0

-

767.00

11.50

0.8641

a

Empty fields indicate that the values have not been found.

b

ME, methyl ester; EE, ethyl ester; in Cx:y, x and y denote the number of carbons and double bonds in the fatty acid chain, respectively. c

Tb, normal boiling temperature; Tc, critical temperature; Pc, critical pressure; ω, acentric factor.


35


Page 36 of 54

Table 2. Group contribution models applied in normal boiling point estimations required compound informationa method

acronym molecular structure

MW

Vvdw

Joback/Reid13

JR

X

Constantinou/Gani14

CG

X

Marrero/Gani21

MG

X

Stein/Brown35

SB

X

Marrero/Pardillo22

MP

X

Cordes/Rarey5

CR

X

Ericksen et al.36

EWOR1b

X

X

X

Ericksen et al.36

EWOR2c

X

X

X

Nannoolal et al.37

NRRC

X

Ghasemitabar/Movagharnejad38 GM

X

Emami et al.39

EVE

X

Scilipoti et al.34

SCB

X

a

X

X

MW, molecular weight; Vvdw, van der Waals volume.

b c

X

Vvdw values were estimated considering UNIFAC group volume parameters.105

Vvdw values were estimated by using Zhao et al.’s model.106


36

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Table 3. Group contribution models applied in critical temperature estimations required compound informationa method


MW

Tb

Joback/Reid13

JR

X

Constantinou/Gani14

CG

X

Marrero/Gani21

MG

X

Marrero/Pardillo22

MP

X

X

Riedel29

R

X

X

Lydersen23

L

X

X

Fedors30

F

X

Klincewicz/Reid24,25

KR

X

Tu31

T

X

Wilson/Jasperson26

WJ

X

X

Jalowka et al.27,28

JDB

X

X

Dalmazzone et al.32

DSG

X

Ambrose33

A

X

Wen/Qiang16

WQ1

X

Wen/Qiang16

WQ2

X

X

Li et al.17

LXX

X

X

Somayajulu18

S

X

X

Nannoolal et al.19

NRR

X

X

Álvarez/Valderrama20

AV

X

X

X

X

X

X


37


a

Page 38 of 54

MW, molecular weight; Tb, normal boiling temperature.

Table 4. Group contribution models applied in critical pressure estimations required compound informationa method


MW

Joback/Reid13

JR

X

Constantinou/Gani14

CG

X

Marrero/Gani21

MG

X

Marrero/Pardillo22

MP

X

Lydersen23

L

X

X

Klincewicz/Reid24,25

KR

X

X

Wilson/Jasperson26

WJ

X

Jalowka et al.27,28

JDB

X

Ambrose15

A

X

Wen/Qiang16

WQ

X

Li et al.17

LXX

X

X

Somayajulu18

S

X

X

Nannoolal et al.19

NRR

X

X

Álvarez/Valderrama20

AV

X

X

a

Tb Tc

X X X

X

X

MW, molecular weight; Tb, normal boiling temperature; Tc, critical temperature.


38

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Table 5. Models applied in acentric factor estimations required compound informationa method

acronym

conceptual basisb

molecular structure

MW

Tb Tc P c

Constantinou/Gani40 CG

GC

X

Han/Peng41

HP

GC

X

Shouzhi et al.42

SYP

GC

X

Ambrose/Walton9

AW

CSP

X

X

X

Lee/Kesler7

LK

CSP

X

X

X

Edmister10

E

CSP

X

X

X

Rudkin44

R

CSP

X

X

X

Chen et al.43

CDJ

CSP

X

X

X

Wang et al.107

WMJSc

GC

X

X

X

Moller et al.73

MRRd

GC

X

X

X

X

X X

a

MW, molecular weight; Tb, normal boiling temperature; Tc, critical temperature; Pc, critical pressure. b

GC, Group Contribution; CSP, Corresponding States Principle.

c

This method considers Pitzer’s definition81 coupled with Wang et al.’s vapor pressure model.107 d

This method considers Pitzer’s definition81 coupled with Moller et al.’s vapor pressure model.73


39


Page 40 of 54

Table 6. Results of normal boiling point estimations %ARD when calculated by the method of compound JR

CG

MG

SB

MP

CR

EWOR1

EWOR2

NRRC

GM

EVE

SCB

ME-C6:0

1.26%

0.04%

0.98%

0.41%

0.53%

2.10%

0.86%

0.78%

3.58%

0.99%

1.28%

15.54%

ME-C7:0

0.99%

0.14%

0.96%

0.46%

0.49%

1.84%

0.63%

0.56%

3.54%

0.36%

1.14%

13.95%

ME-C8:0

0.47%

0.05%

0.82%

0.41%

0.54%

1.60%

0.50%

0.44%

3.49%

0.88%

1.00%

12.62%

ME-C9:0

0.03%

0.45%

0.29%

0.59%

0.35%

1.07%

0.17%

0.10%

3.13%

0.78%

1.16%

11.75%

ME-C10:0

2.12%

0.50%

1.26%

0.78%

1.77%

2.12%

1.43%

1.37%

4.37%

1.78%

0.19%

9.67%

ME-C11:0

1.72%

1.21%

0.44%

0.47%

0.57%

0.52%

0.10%

0.04%

2.90%

0.42%

1.08%

10.08%

ME-C12:0

3.76%

0.68%

0.13%

0.54%

1.72%

1.26%

1.12%

1.06%

3.81%

1.55%

0.08%

8.53%

ME-C14:0

5.79%

1.83%

0.95%

0.27%

1.88%

0.56%

1.03%

0.97%

3.36%

1.26%

0.30%

7.67%

ME-C16:0

8.68%

2.38%

1.41%

0.42%

2.75%

0.55%

1.65%

1.60%

3.59%

1.32%

0.07%

6.51%

ME-C18:0

10.78%

3.73%

2.67%

0.48%

2.81%

0.27%

1.48%

1.43%

2.98%

0.46%

0.44%

6.33%

ME-C18:1

12.25%

3.28%

1.79%

0.82%

3.83%

0.75%

2.92%

2.85%

3.67%

0.37%

0.47%

5.32%

ME-C18:2

13.20%

3.29%

1.37%

1.64%

4.35%

1.28%

3.33%

3.24%

3.86%

1.70%

0.89%

4.76%

ME-C18:3

13.69%

3.70%

1.35%

2.05%

4.46%

1.41%

3.32%

3.21%

3.63%

3.45%

0.91%

4.58%

ME-C20:0

14.97%

3.33%

2.18%

0.50%

4.74%

0.74%

3.16%

3.11%

4.22%

1.65%

0.81%

4.63%

ME-C22:0

17.70%

4.21%

2.98%

0.36%

5.29%

0.41%

3.48%

3.43%

4.07%

0.59%

0.67%

4.34%

ME-C22:1

18.32%

4.40%

2.84%

0.90%

5.53%

0.66%

4.17%

4.10%

4.02%

1.64%

0.82%

4.01%

EE-C6:0

0.11%

1.26%

2.09%

0.65%

0.64%

0.48%

0.58%

0.65%

2.90%

0.27%

0.04%

12.99%

EE-C7:0

0.67%

1.20%

1.97%

0.73%

0.79%

0.39%

0.57%

0.64%

3.03%

0.73%

0.13%

11.62%

EE-C8:0

1.43%

1.00%

1.75%

0.86%

0.98%

0.34%

0.51%

0.58%

3.13%

0.87%

0.27%

10.47%

EE-C9:0

1.95%

0.34%

1.10%

0.62%

0.83%

0.70%

0.79%

0.85%

2.82%

0.17%

0.03%

9.82%


40

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%ARD when calculated by the method of compound JR

CG

MG

SB

MP

CR

EWOR1

EWOR2

NRRC

GM

EVE

SCB

EE-C10:0

3.18%

0.21%

0.99%

0.96%

1.29%

0.50%

0.44%

0.51%

3.09%

0.35%

0.35%

8.78%

EE-C11:0

3.95%

0.49%

0.32%

0.73%

1.23%

0.85%

0.61%

0.67%

2.80%

0.15%

0.11%

8.35%

EE-C12:0

5.60%

0.44%

0.41%

1.25%

1.97%

0.44%

0.01%

0.05%

3.29%

0.62%

0.63%

7.31%

EE-C14:0

7.21%

2.11%

1.18%

0.37%

1.72%

1.36%

0.43%

0.49%

2.47%

0.47%

0.11%

7.06%

AARD (FAME)

7.86%

2.08%

1.40%

0.69%

2.60%

1.07%

1.83%

1.77%

3.64%

1.20%

0.71%

8.14%

AARD (FAEE)

3.01%

0.88%

1.23%

0.77%

1.18%

0.63%

0.49%

0.55%

2.94%

0.45%

0.21%

9.55%

Table 7. Packages approved in the consistency test (Tb) %AARD

package no.

model 'i' (FAME)

model 'j' (FAEE)

FAME

FAEE

i-j

47

SB

EVE

0.69%

0.21%

0.53%

131

EVE

EVE

0.71%

0.21%

0.54%

40

SB

SB

0.69%

0.77%

0.72%

124

EVE

SB

0.71%

0.77%

0.73%

71

CR

EVE

1.07%

0.21%

0.78%

41

SB

MP

0.69%

1.18%

0.86%

125

EVE

MP

0.71%

1.18%

0.87%

66

CR

CR

1.07%

0.63%

0.93%

64

CR

SB

1.07%

0.77%

0.97%

65

CR

MP

1.07%

1.18%

1.11%

45

SB

NRRC

0.69%

2.94%

1.44%

129

EVE

NRRC

0.71%

2.94%

1.45%

69

CR

NRRC

1.07%

2.94%

1.69%


41


Page 42 of 54

Table 8. Results of critical temperature estimations %ARD when calculated by the method of compound JR

CG

MG

MP

R

L

F

KR

T

WJ

ME-C6:0

2.24%

1.76%

1.77%

2.07%

2.45%

2.05%

0.89%

0.87%

0.28%

1.74%

ME-C7:0

1.16%

0.51%

0.48%

1.00%

1.89%

1.07%

1.97%

0.69%

1.43%

0.52%

ME-C8:0

1.35%

0.61%

0.47%

1.19%

2.67%

1.36%

1.78%

0.91%

1.31%

0.59%

ME-C9:0

1.33%

0.84%

0.55%

1.15%

3.31%

1.42%

1.53%

1.31%

1.11%

0.47%

ME-C10:0

1.68%

0.05%

0.49%

1.46%

4.38%

1.84%

2.46%

1.06%

2.08%

0.76%

ME-C11:0

0.91%

0.59%

0.02%

0.63%

4.42%

1.12%

1.87%

2.25%

1.52%

0.05%

ME-C12:0

1.93%

0.79%

0.00%

1.59%

6.24%

2.18%

1.74%

1.18%

1.42%

0.99%

ME-C14:0

0.81%

0.31%

0.83%

0.27%

7.01%

1.12%

2.43%

2.42%

2.12%

0.01%

ME-C16:0

1.71%

1.42%

0.04%

0.93%

9.89%

2.03%

1.50%

1.13%

1.20%

1.27%

ME-C18:0

1.20%

2.12%

0.35%

0.09%

11.61%

1.48%

1.00%

1.17%

0.68%

1.31%

ME-C18:1

0.57%

1.16%

1.11%

0.63%

11.15%

1.09%

2.16%

2.40%

1.87%

0.69%

ME-C18:2

0.58%

1.33%

1.41%

0.81%

11.28%

1.36%

2.15%

3.05%

1.90%

0.72%

ME-C18:3

0.15%

1.51%

1.70%

1.54%

11.05%

1.23%

2.13%

4.20%

1.92%

0.35%

ME-C22:1

0.02%

1.93%

0.81%

1.83%

15.33%

0.17%

1.77%

0.90%

1.39%

1.72%

EE-C6:0

0.53%

1.23%

1.27%

0.47%

1.26%

0.44%

3.76%

1.23%

3.21%

0.11%

EE-C7:0

0.77%

1.11%

1.25%

0.70%

2.10%

0.78%

3.54%

1.37%

3.06%

0.01%

EE-C8:0

1.26%

0.68%

0.96%

1.16%

3.24%

1.35%

3.08%

1.20%

2.66%

0.40%

EE-C10:0

1.32%

0.42%

1.04%

1.11%

4.81%

1.53%

2.90%

1.61%

2.56%

0.37%


42

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EE-C11:0

0.99%

0.34%

1.14%

0.71%

5.34%

1.25%

2.90%

2.12%

2.58%

0.05%

EE-C12:0

1.93%

0.28%

0.69%

1.55%

7.12%

2.21%

2.35%

1.12%

2.04%

1.04%

EE-C14:0

0.58%

0.17%

1.15%

0.04%

7.81%

0.90%

2.68%

2.51%

2.38%

0.06%

EE-C16:0

0.93%

1.04%

0.59%

0.00%

10.24%

1.23%

2.01%

1.70%

1.69%

0.73%

AARD (FAME)

1.12%

1.07%

0.72%

1.09%

7.33%

1.39%

1.81%

1.68%

1.45%

0.80%

AARD (FAEE)

1.04%

0.66%

1.01%

0.72%

5.24%

1.21%

2.90%

1.61%

2.52%

0.35%

Table 9. Results of critical temperature estimations (continuation) %ARD when calculated by the method of compound JDB

DSG

A

WQ1

WQ2

LXX

S

NRR

AV

ME-C6:0

2.00%

3.61%

2.01%

1.48%

1.07%

1.41%

2.03%

0.61%

1.76%

ME-C7:0

1.03%

3.12%

0.84%

0.35%

0.04%

0.22%

0.85%

0.70%

0.50%

ME-C8:0

1.42%

3.81%

0.93%

0.38%

0.15%

0.45%

0.94%

0.68%

0.56%

ME-C9:0

1.57%

4.53%

0.79%

0.42%

0.15%

0.60%

0.80%

0.82%

0.43%

ME-C10:0

2.72%

4.15%

1.04%

0.75%

0.55%

1.20%

1.05%

0.54%

0.72%

ME-C11:0

1.89%

5.20%

0.18%

0.44%

0.17%

0.88%

0.19%

1.35%

0.11%

ME-C12:0

3.78%

5.83%

1.14%

0.62%

0.96%

2.40%

1.15%

0.28%

0.91%

ME-C14:0

3.85%

6.28%

0.04%

1.95%

0.11%

2.72%

0.03%

1.22%

0.18%

ME-C16:0

6.47%

8.26%

0.97%

1.71%

1.45%

5.45%

0.98%

0.14%

0.87%

ME-C18:0

7.63%

9.90%

0.73%

1.92%

1.51%

7.23%

0.73%

0.27%

0.59%

ME-C18:1

7.37%

0.49%

0.18%

3.74%

0.75%

5.96%

0.16%

0.81%

0.47%

ME-C18:2

7.49%

40.80%

0.30%

4.36%

0.63%

5.33%

0.25%

1.24%

1.01%

ME-C18:3

7.03%

116.89%

0.01%

4.98%

0.10%

4.33%

0.06%

2.12%

1.15%

ME-C22:1

11.61%

2.67%

0.58%

4.67%

1.73%

10.86%

0.56%

0.49%

0.34%

EE-C6:0

0.08%

1.01%

0.21%

0.17%

0.15%

0.44%

0.22%

0.57%

0.13%

EE-C7:0

0.42%

1.46%

0.35%

0.10%

0.34%

0.16%

0.36%

0.54%

0.02%

EE-C8:0

1.23%

2.17%

0.72%

0.23%

0.79%

0.49%

0.74%

0.21%

0.37%

EE-C10:0

2.12%

3.00%

0.59%

0.31%

0.88%

1.25%

0.60%

0.31%

0.31%


43


Page 44 of 54

EE-C11:0

2.23%

3.39%

0.20%

0.68%

0.60%

1.47%

0.21%

0.64%

0.04%

EE-C12:0

3.96%

4.32%

1.10%

0.53%

1.63%

3.03%

1.10%

0.36%

0.91%

EE-C14:0

3.79%

4.96%

0.23%

1.63%

0.57%

3.38%

0.23%

0.73%

0.35%

EE-C16:0

5.95%

6.65%

0.29%

1.74%

1.36%

5.78%

0.30%

0.12%

0.19%

AARD (FAME)

4.71%

15.40%

0.70%

1.98%

0.67%

3.50%

0.70%

0.81%

0.69%

AARD (FAEE)

2.47%

3.37%

0.46%

0.67%

0.79%

2.00%

0.47%

0.43%

0.29%

Table 10. Packages approved in the consistency test (Tc) %AARD

package no.

model 'i' (FAME)

model 'j' (FAEE)

FAME

FAEE

i-j

51

MG

A

0.72%

0.46%

0.62%

55

MG

S

0.72%

0.47%

0.63%

356

AV

WQ1

0.69%

0.67%

0.68%

346

AV

MP

0.69%

0.72%

0.70%

52

MG

WQ1

0.72%

0.67%

0.70%

42

MG

MP

0.72%

0.72%

0.72%

41

MG

MG

0.72%

1.01%

0.82%


44

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Table 11. Results of critical pressure estimations %ARD when calculated by the method of compound JR

CG

MG

MP

L

KR

WJ

ME-C6:0

2.28%

2.63%

3.30%

0.15%

2.91%

0.64%

0.11%

ME-C7:0

0.72%

0.18%

0.08%

3.20%

0.35%

4.01%

2.10%

ME-C8:0

0.94%

1.54%

0.82%

1.49%

0.64%

4.08%

0.89%

ME-C9:0

2.80%

2.18%

3.99%

5.31%

4.10%

10.02%

5.42%

ME-C10:0

0.64%

0.11%

3.12%

3.08%

3.10%

9.79%

2.82%

ME-C11:0

2.16%

1.78%

6.25%

4.63%

6.05%

13.69%

5.62%

ME-C12:0

8.63%

8.45%

14.89%

11.23%

14.41%

23.36%

13.15%

ME-C14:0

7.63%

8.11%

18.29%

10.19%

16.99%

27.36%

12.77%

ME-C16:0

5.60%

6.92%

21.18%

8.09%

18.70%

30.22%

12.95%

ME-C18:0

0.39%

2.65%

20.74%

2.74%

16.83%

28.98%

8.98%

ME-C18:1

7.25%

8.50%

8.80%

5.61%

6.07%

19.56%

1.92%

ME-C18:2

6.25%

10.83%

7.20%

5.16%

5.31%

21.28%

2.36%

ME-C18:3

16.33%

23.31%

6.78%

15.87%

7.71%

8.67%

14.21%

ME-C22:1

8.22%

6.87%

19.36%

6.57%

12.72%

27.88%

1.04%

EE-C6:0

0.72%

0.18%

0.08%

2.75%

0.35%

4.01%

0.34%

EE-C7:0

1.78%

2.38%

1.66%

4.92%

1.48%

3.20%

1.67%

EE-C8:0

1.95%

2.55%

0.82%

4.87%

0.72%

4.92%

0.97%

EE-C10:0

2.75%

2.36%

6.86%

0.11%

6.66%

14.34%

5.15%


45


Page 46 of 54

EE-C11:0

8.63%

8.45%

14.89%

6.03%

14.41%

23.36%

11.87%

EE-C12:0

11.64%

11.76%

20.27%

9.15%

19.41%

29.40%

16.33%

EE-C14:0

4.19%

5.05%

16.95%

2.18%

15.15%

25.87%

9.55%

EE-C16:0

0.53%

2.27%

18.06%

1.15%

14.98%

26.55%

7.56%

AARD (FAME)

4.99%

6.00%

9.63%

5.95%

8.28%

16.40%

6.02%

AARD (FAEE)

4.02%

4.38%

9.95%

3.89%

9.15%

16.46%

6.68%

Table 12. Results of critical pressure estimations (continuation) %ARD when calculated by the method of compound JDB

A

WQ

LXX

S

NRR

AV

ME-C6:0

2.44%

3.56%

0.38%

3.33%

3.57%

0.91%

0.30%

ME-C7:0

1.74%

0.29%

3.00%

0.26%

0.30%

2.89%

3.71%

ME-C8:0

0.57%

1.26%

1.60%

1.39%

1.27%

1.89%

3.23%

ME-C9:0

4.83%

3.46%

5.72%

3.18%

3.45%

6.42%

8.63%

ME-C10:0

2.94%

2.48%

3.75%

2.08%

2.48%

4.81%

7.99%

ME-C11:0

4.25%

5.43%

5.55%

4.91%

5.43%

6.98%

11.45%

ME-C12:0

14.36%

13.75%

12.46%

13.08%

13.74%

14.33%

20.58%

ME-C14:0

12.71%

16.34%

11.84%

15.48%

16.33%

14.31%

23.89%

ME-C16:0

17.16%

18.05%

10.07%

17.04%

18.05%

13.00%

26.18%

ME-C18:0

14.82%

16.20%

4.94%

15.10%

16.20%

8.12%

24.57%

ME-C18:1

1.03%

5.82%

3.77%

4.13%

6.94%

0.00%

13.28%

ME-C18:2

0.16%

5.39%

3.49%

3.00%

7.67%

1.18%

12.65%

ME-C18:3

13.06%

7.35%

14.55%

10.07%

4.26%

9.61%

1.12%

ME-C22:1

8.08%

12.41%

4.25%

10.56%

13.42%

0.01%

20.92%

EE-C6:0

0.65%

0.29%

1.29%

0.26%

0.30%

1.70%

3.71%

EE-C7:0

1.39%

2.10%

3.27%

2.23%

2.10%

0.09%

2.35%

EE-C8:0

0.06%

1.33%

3.03%

1.60%

1.33%

0.41%

3.60%

EE-C10:0

6.12%

6.04%

2.41%

5.51%

6.03%

6.52%

12.09%


46

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EE-C11:0

12.39%

13.75%

8.64%

13.08%

13.74%

13.22%

20.58%

EE-C12:0

19.59%

18.73%

12.01%

17.94%

18.72%

16.94%

26.16%

EE-C14:0

11.12%

14.52%

5.13%

13.60%

14.51%

10.11%

22.19%

EE-C16:0

12.22%

14.36%

1.94%

13.32%

14.35%

7.04%

22.42%

AARD (FAME)

7.01%

7.99%

6.10%

7.40%

8.08%

6.03%

12.75%

AARD (FAEE)

7.94%

8.89%

4.72%

8.44%

8.89%

7.00%

14.14%

Table 13. Consistency analysis of the JR/MP package Homologous series: saturated compounds equation (7)b

a

Pc/bar

Adjacent pair Failure point i

i+1

i

i+1

1st scenario

2nd scenario

1

ME-C12:0 ME-C13:0

15.2 ± 0.5

15.29

-0.09

0.41

2

ME-C14:0 ME-C15:0

13.2 ± 0.4

13.23

-0.03

0.37

3

EE-C12:0

13.7 ± 0.4

13.91

-0.21

0.19

EE-C13:0

Homologous series: monounsaturated compounds equation (11)d

c

Pc/bar

Adjacent pair Failure point i 1 a b c

i+1

ME-C17:1 ME-C18:1

i

i+1

1st scenario

11.98

12.1 ± 0.4

-0.12

2nd scenario 0.28

Pc(i): experimental; Pc(i+1): estimated (JR).

Pc(i) values: 1st scenario (15.2, 13.2, and 13.7); 2nd scenario (15.7, 13.6, and 14.1).

Pc(i): estimated (MP); Pc(i+1): experimental.

d

Pc(i+1) values: 1st scenario (12.1); 2nd scenario (11.7).


47


Page 48 of 54

Table 14. Results of acentric factor estimations %ARD when calculated by the method of compound CG

HP

SYP

AW

LK

E

R

CDJ

WMJS

MRR

ME-C6:0

17.98%

23.27%

18.26%

2.11%

2.30%

1.67%

2.13%

2.20%

21.89%

3.09%

ME-C7:0

6.53%

11.05%

5.87%

2.01%

1.75%

2.61%

2.09%

1.90%

5.83%

1.15%

ME-C8:0

5.69%

9.83%

4.24%

2.92%

2.45%

4.02%

3.14%

2.70%

4.91%

1.38%

ME-C9:0

9.24%

13.09%

7.03%

2.73%

2.04%

4.34%

3.12%

2.31%

3.94%

0.16%

ME-C10:0

0.55%

2.53%

3.32%

13.28%

12.53%

15.02%

13.75%

12.79%

5.17%

10.02%

ME-C12:0

10.87%

13.31%

6.42%

14.27%

13.28%

16.52%

14.90%

13.23%

1.94%

6.66%

ME-C14:0

4.91%

6.28%

0.72%

9.42%

8.05%

12.78%

10.78%

8.05%

8.29%

1.96%

ME-C16:0

12.10%

12.62%

4.27%

16.17%

14.83%

19.33%

17.41%

14.45%

2.37%

4.47%

ME-C18:0

14.12%

13.74%

4.00%

11.44%

9.89%

15.28%

13.21%

9.46%

0.77%

0.66%

ME-C18:1

5.77%

7.14%

6.56%

3.73%

2.02%

8.21%

6.06%

2.19%

6.66%

1.92%

ME-C18:2

2.49%

5.55%

12.45%

7.18%

5.57%

11.39%

9.36%

5.75%

13.81%

1.61%

ME-C18:3

4.05%

0.48%

20.96%

0.50%

2.23%

4.27%

2.21%

1.44%

17.82%

0.33%

EE-C6:0

0.97%

5.26%

0.23%

0.44%

0.08%

1.30%

0.58%

0.31%

7.04%

0.08%

EE-C8:0

2.49%

6.10%

0.27%

3.86%

3.17%

5.51%

4.30%

3.53%

5.40%

2.33%

EE-C10:0

5.82%

8.63%

2.20%

6.26%

5.25%

8.67%

7.04%

5.53%

7.59%

2.49%

EE-C12:0

14.08%

16.08%

8.68%

15.53%

14.44%

17.98%

16.22%

14.21%

7.34%

6.40%

EE-C14:0

8.26%

9.22%

1.61%

3.25%

1.68%

7.20%

5.02%

1.73%

9.09%

3.04%


48

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EE-C16:0

8.12%

8.18%

0.42%

9.72%

8.16%

13.64%

11.55%

7.98%

8.35%

1.31%

AARD (FAME)

7.86%

9.91%

7.84%

7.15%

6.41%

9.62%

8.18%

6.37%

7.78%

2.78%

AARD (FAEE)

6.62%

8.91%

2.23%

6.51%

5.46%

9.05%

7.45%

5.55%

7.47%

2.61%

Table 15. Packages approved in the consistency test (ω) %AARD

package no.

model 'i' (FAME)

model 'j' (FAEE)

FAME

FAEE

i-j

21

SYP

CG

7.84%

6.62%

7.44%

1

CG

CG

7.86%

6.62%

7.45%

22

SYP

HP

7.84%

8.91%

8.20%

12

HP

HP

9.91%

8.91%

9.58%


49


Page 50 of 54

GRAPHICAL ABSTRACT


50

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FIGURES

Figure 1. Accepted normal boiling points of methyl esters as a function of the number of carbons in the fatty acid chain (nca). The expected trend for members of the same homologous series favors the value reported by Krop et al.79

Figure 2. Recommended Tb values as functions of the number of carbons in the fatty acid chain (nca): results for saturated compounds.



Figure 3. Recommended Tc values as functions of the number of carbons in the fatty acid chain (nca): results for saturated FAMEs.

Figure 4. Recommended Tc values as functions of the number of carbons in the fatty acid chain (nca): results for saturated FAEEs.


Page 52 of 54

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Figure 5. Recommended Pc values as functions of the number of carbons in the fatty acid chain (nca): results for saturated compounds.

Figure 6. Ratio (MW/Pc)0.5 versus the number of carbon atoms in the fatty acid chain (nca): results for saturated FAMEs.



Figure 7. Ratio (MW/Pc)0.5 versus the number of carbon atoms in the fatty acid chain (nca): results for saturated FAEEs.

Figure 8. Estimated ω values as functions of the number of carbons in the fatty acid chain (nca): results for saturated compounds.


Page 54 of 54

Estimation of Physical Constants of Biodiesel-Related Fatty Acid Alkyl

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