Density of Cottonseed Oil and Biodiesel - Journal of Chemical

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Density of Cottonseed Oil and Biodiesel Nieves M. C. Talavera-Prieto,†,‡ Abel G. M. Ferreira,*,† António Alberto Portugal,† and Paula Egas† †

CIEPQPF, Department of Chemical Engineering, University of Coimbra, Polo II, Rua Silvio Lima, 3030-970 Coimbra, Portugal CECOAL-CONICET-UNNE, Ruta 5 Km 2.5, 3400 Corrientes, Argentina

‡

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 09/01/18. For personal use only.

S Supporting Information *

ABSTRACT: The cottonseed oil (CSO) extraction and processing areas including biodiesel (CSB) production created the need for density availability over wide ranges of temperature and pressure. In this work, densities of CSO and CSB were measured. The measurement of CSO density under pressure has never been reported in the literature. To address this limitation, this work reports new experimental data of densities of CSO measured at temperatures from 278 to 358 K and pressures from atmospheric up to 30 MPa using a vibrating tube densimeter. The measured densities of CSO were correlated with the Goharshadi−Morsali−Abbaspour equation of state (GMA EoS) with an absolute average relative deviation of 0.02%. The coefficients of GMA EoS for CSO and CSB were used to calculate the thermal expansivity and isothermal compressibility which influence power and fuel injection and they are rarely presented for vegetable oils and biodiesel, especially at high pressures. The group contribution method GCVOL, Halvorsen model, and Zong fragmentbased approach were used to evaluate the predictive abilities of CSO density data. Good predictions of oil densities were achieved with Halvorsen model for which absolute deviations are in the range of uncertainty of the measurements.

1. INTRODUCTION Cottonseed oil (CSO) is extracted from the seeds of the cottonplant after the removal the cotton lint. CSO contains significant amounts of saturated fatty acids, palmitic acid (22−26%), stearic acid (2−5%), and traces of myristic, arachidic, and behenic acids, monounsaturated fatty acids, being the major species, oleic acid (15−20%) accompanied by traces of palmitoleic acid, diunsaturated linoleic acid (49−58%), and only traces of linolenic acid. Most of the physical and chemical properties of CSO resemble those of the major vegetable oils.1 CSO is used in many instances namely in areas as food processing, new chemical developing, and biodiesel production. The use of triglyceride oils in synthesis of alkyd resins has been widely studied in recent times. Alkyd resins are conventional binders used in the production of paints, varnishes, and other coating products. Among other oils, that contain carbon− carbon double bonds, cottonseed oil is widely used in synthesis and characterization of alkyd resins.2−5 The use of edible vegetable oils and animal fats for biodiesel production has recently been of great concern because of the competition with food materials. The demand for vegetable oils for food has increased tremendously in recent years, and thus it is impossible to justify the use of these oils for fuel use purposes such as biodiesel production. Moreover, these oils could be more expensive to use than fuel. CSO is very often partially or fully hydrogenated and there is a growing consensus that in hydrogenated form these oils are very unhealthy. On the other hand, it has also been suggested that cottonseed oil may be highly contaminated with pesticide residues but insufficient testing has been done. Furthermore, crude cottonseed oil © XXXX American Chemical Society

contains gossypol, a polyphenolic compound, in which consumption causes extreme health conditions. The presence of this toxic substance imposes important limitations on consumption of nonrefined cottonseed oil and must be removed before being eaten by animals. One clever solution can be the use of milled cottonseed treated with methanol in excess for in situ transesterification to obtain biodiesel and an almost free gossypol cottonseed meal.6 In this way cottonseed, could be a significant choice to be used as a raw material for producing biodiesel. Cottonseed biodiesel can be considered a second generation biofuel, because it has not been used in the human food chain. In recent years, there exists many active researches on biodiesel production from CSO which involves studies on CSB production,7 CSB as fuel for engines,8,9 CSB production from enzyme catalyzed transesterification where refined cottonseed oil reacted with short-chain primary and secondary alcohols,10 from solid acid catalysts11 and CSB production assisted by microwave irradiation or ultrasonic methods.12,13 In all the aforementioned areas, the knowledge of density of CSO and CSB plays an important role in the development, performance, and behavior analysis in the applications. The density of CSO was measured at atmospheric pressure by Menzies et al.,14 Magne et al.,15 Arnold et al.,16 Demirbas,17 Macovei,18 and by Eryilmaz et al.19 Nogueira et al.20 and Alptekin and Canakci21 made measurements for CSB. To the best of our knowledge, inclusion of pressure in density of CSO Received: April 18, 2018 Accepted: August 15, 2018

A

DOI: 10.1021/acs.jced.8b00313 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Fatty Acid Composition and Properties of CSO. Material cottonseed oil

Supplier

Cas no

sample purity (wt%)a

propertiesb

Acros Organics

17711

fatty acid composition: MeC14:0 and lower about 1.5%; MeC16:0 about 25%; MeC18:0 about 3%; MeC18:1, 16 to 24%; MeC18:2, 50 to 55%; MeC18:3 and higher

AV ≤ 0.5 mg KOH·g−1 SV = 185 −198 mg KOH·g−1 IV = 95 to 115 g I/100g UM < 1.5% n = 1.4720 to 1.4730 (20 °C, 589 nm)

a

The terminology (MeCm:n) was used for FAMEs, where m is the number of carbon atoms and n the number of double bonds of the related fatty acid: methyl palmitate (MeC16:0), methyl stearate (MeC18:0), methyl oleate (MeC18:1), methyl linoleate (MeC18:2), methyl linolenate (MeC18:3). bAV = acid value; SV = saponification value; IV = iodine value; UM = unsaponifiable matter; n = refractive index.

Table 2. Mass Fractions (wi) and Molar Fractions (xi) of CSO and CSB. CSO

CSB

a

b

component

wi (w/w) %

xi

wi (w/w) %

xi

myristic C14:0 palmitic C16:0 stearic C18:0 oleic acid C18:1 linoleic acid C18:2 Linolenic acid C18:3

1.45 24.15 2.90 19.32 50.72 1.45

0.0174 0.2579 0.0279 0.1873 0.4952 0.0143

0.93 ± 0.28 26.76 ± 1.56 2.81 ± 0.29 17.89 ± 1.71 51.61 ± 2.99

0.0110 0.2845 0.0271 0.1735 0.5039

a Values considering the weight fraction of free fatty acids (FFA) reported in table S1. The mean values of weight fractions of oleic and linoleic acids were considered in the calculations and normalization procedure was realized. bFrom gas chromatography.20

Institute of Standards and Technology (NIST)28 and showed relative deviations in the range 0.03−0.07%, except at 358.15 K where deviations reached 0.15%. The influence of viscosity on density uncertainty (damping effects on the vibrating tube) for liquids with viscosities less than 100 mPa·s can be important. An approximate value of such uncertainty was obtained using the method proposed by Anton Parr and discussed by Fandiño29 for the DMA 512P densimeter. From densities and viscosities presented by Nogueira et al.20 for babassu, soybean, and cottonseed biodiesels, the obtained uncertainty was 0.03 kg·m−3 thus contributing with a negligible value to the combined standard uncertainty. The expanded uncertainties, U, were calculated with confidence level 95% (with coverage factor k = 2) for temperature, pressure, and density. The expanded uncertainties in temperature and pressure were U(T) = ±0.02 K and U(p) = ±0.02 MPa, respectively. The combined standard uncertainty of the density measurements, estimated taking into account the influence of uncertainties associated with calibration equation,27 temperature, pressure, period of oscillations (six-digit frequency counter), viscosity, and density data of calibrating fluids was estimated as uc = ±0.81 kg·m−3 corresponding to an expanded uncertainty of U(ρ) = 1.6 kg·m−3.

was never made and CSB density under pressure was reported in our previous work in the range 288−358 K at pressures from atmospheric up to 30 MPa.22 To address this limitation, in this work the densities of CSO were measured in the range 278−358 K and pressures of 0.1−30 MPa. A comparison of CSO and CSB density with experimental data available in literature is performed. Correlation of the new experimental data of CSO with temperature and pressure with the Goharshadi− Morsali−Abbaspour equation of state (GMA EoS)23 was made and reported. The results for CSB and their treatment with GMA EoS presented in this work are an adapted version of the paper published by us.22 The group contribution method (GCVOL) revised by Pratas et al.,24 the Halvorsen et al. method,25 and that of Zong26 were evaluated for density of the oil. The methods GCVOL and predictive GMA (4PGMA) developed by us22 were tested for prediction of densities of CSB.

2. EXPERIMENTAL SECTION 2.1. Materials. The detailed specifications of CSO from supplier used in density measurements are summarized in Table 1. The details of transesterification of CSO to produce the biodiesel and its characterization were given in our previous paper.22 The mass and molar compositions of CSO and CSB are presented in Table 2. 2.2. Density Measurement. Cottonseed oil densities were determined using an Anton Paar DMA 60 digital vibrating tube densimeter with a DMA 512P measuring cell. The temperature in the vibrating tube cell was measured with a platinum resistance probe (PT100). A Julabo F12-ED thermostatic bath with ethylene glycol was used as circulating fluid in the thermostat circuit of the measuring cell and the temperature was held constant to ±0.01 K. The required pressure was generated and controlled using a Pressure Generator model 50-6-15, High Pressure Equipment Co., with acetone as hydraulic fluid. The measuring setup, the calibration, and performance of the vibrating tube densimeter were described with detail in a previous paper.27 The measured densities of water were compared with reference data from United States National

3. MODELS 3.1. Density. In the following sections, the models used in the correlation and prediction of density data of CSO and CSB are presented. 3.1.1. Goharshadi−Morsali−Abbaspour Equation of State. In the present work, the GMA EoS was used to correlate density with temperature and pressure of CSO. The GMA EoS is conveniently given by23 (2z − 1)Vm3 = A(T ) + B(T )ρm

(1)

where z, Vm, ρm, and T are the compressibility factor, molar volume, molar density, and absolute temperature, respectively. The temperature-dependent parameters A(T) and B(T) are given by the following equations23 A (T ) = A 0 − B

2A1 2A 2 ln T + RT R

(2) DOI: 10.1021/acs.jced.8b00313 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data B(T ) = B0 −

Article

2B1 2B ln T + 2 RT R

Tr =

(3)

where, A0−A2 and B0−B2 are the fitting parameters, and R is the gas constant. Density at different temperatures and pressures was calculated from B(T )ρm5 + A(T )ρm4 + ρm −

(4)

M Vm(T )(1 + Ap)

Δvi = Ai + B i T + CiT 2

(7)

1 = ρoil

where, Ai, Bi, and Ci are the group contribution parameters given by Pratas et al.24 For the contributions relative to −CH3, −CH2, and −COO groups the original version was considered and for −CH the revised version was used because this set of contributions give best prediction of density.24 The mean molar mass is

∑ xiMi

∑ wi i

1 ρi

where, (T) is the liquid molar volume contribution of fragment A at temperature T (K) and Nfrag,A is the number of fragment A in triglyceride i. The temperature dependency of liquid molar volume, VAL, is26 VA L =

1 + B2,A T B1,A

i

(16)

where, B1,A and B2,A are the temperature dependency parameters of fragment A, which values were given by Zong et al.26 Using eqs 14−16, Freitas et al.30 fitted eq 5 to pVT data of oils and they found A = −2.80 × 10−4 MPa−1. The acronym GCVOL/ZONG is used in this work for eq 5 combined with Zong equations. 3.2. Model Evaluation. The predictive ability analysis of the aforementioned models was evaluated in terms of the following statistical measures: the relative percentage deviation (%RD), the average absolute relative deviation (AARD), the average absolute deviation (AAD), and the root-mean-square deviation (RMSD). The AAD and AARD quantify the magnitude of data scatter, while RMSD is a measure of model accuracy. They are defined as follows %RD = 100 ×

(∑ xiZRA ) {

(15)

VAL

ρoil (T , p = 1 atm) [(1 + (1 − Tr )2/7 ]

(14)

Vi L = ΣNfrag,AVA L(T )

where xi and Mi are the molar fraction and the molar mass of specie i. For oils, the molar fractions xi, the molar mass, Mi, the number ni of group i and respective contributions, Δvi, are relative to fatty acids and for methylic biodiesel correspond to the FAMEs. The value A = −5.7 × 10−4 MPa−1 was obtained and used by Pratas et al.24 for estimation of densities of biodiesel fuels. We have recalculated the value of parameter A by fitting densities of methyl palmitate, methyl oleate, and methyl linoleate since they are abundant FAMEs in the biodiesels.22 The value A = −5.46 × 10−4 ± 4.35 × 10−6 MPa−1 was obtained and applied to the prediction of the 19 biodiesels.22 Freitas et al.30 fitted eq 5 to pressure, volume, temperature data (pVT) of palm, soybean, and Jatropha curcas oils available in the ranges 283.15−363.15 K and 0.1−45.0 MPa, founding A = −5.99 × 10−4 MPa−1. This value was used in the model described by eq 5 and labeled here as GCVOL. 3.1.3. Halvorsen. One of the most used models for the calculation of oil densities is due to Halvorsen et al.25 It combines the fatty acid critical properties and the composition of oil (fatty acids content) to predict the density using the modified Rackett equation

xiTci y zz pci z

(13)

where, ρoil is the oil density, ρi and wi are the density and mass fraction of triglyceride i, respectively. This approach requires the knowledge of representative triglyceride molecules. The density of each triglyceride molecule (ViL) is estimated from its molar volume using

(8)

i

(12)

The values of critical temperature and pressure, Tci and pci, and ZRAi of the fatty acids present in CSO are given in Table S1 (cf. Supporting Information). Using eq 9 for calculation of Vm,oil (T) with Moil calculated from eq 13, Freitas et al.30 fitted eq 5 to pVT data of vegetable oils founding A = −4.29 × 10−4 M Pa−1. The combination of eqs 5 and 9 is labeled as GCVOL/HAL. 3.1.4. Zong. Zong et al.26 developed a model to estimate thermophysical properties of triglyceride mixtures. They divided each triglyceride (TG) molecule into four parts, one glycerol fragment and three fatty-acid fragments. Then they correlated experimental data to obtain the contribution of each fragment to the overall property. The density of oil can be calculated using26

where, ni is the number of group i in the substance and Δvi is a temperature dependent group molar volume given by

i R jjj∑i k

(11)

Moil = 3 ∑ xiMi + 38.0488

(6)

i

∑i xiMi

i

where molar mass of oil, Moil, is calculated from

(5)

∑ niΔvi

=

∑ xiTc

Fc = 0.0236 + k|875 − Moil|

2p =0 RT

where, ρ is the density in g·cm , p is the absolute pressure (MPa), Vm(T) is the molar volume (cm3·mol−1), and M is the molar mass (g·mol−1). The molar volume was calculated as

M=

(10)

i

−3

Vm =

Tc,mix

Tc,mix =

3.1.2. Group Contribution Method. The details of GCVOL for the prediction of liquid densities as a function of temperature and pressure were given by us previously.22 The GCVOL was presented by Pratas et al.24 ρ ( T , p) =

T

+ Fc

%AARD = (9) C

Xcalc − X X

100 × N

N

∑ i=1

(17)

Xcalc − X X

(18)



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Table 3. Experimental Values of Density Data (ρ) for CSO as a Function of Temperature (T) and Pressure (p)a ρ/(kg·m−3) at T/K p/MPa

278.15

283.15

288.15

293.15

298.15

308.15

318.15

328.15

338.15

348.15

358.15

0.1 0.1 1.0 2.0 2.0 3.0 4.0 4.0 5.0 6.0 6.0 7.0 8.0 8.0 9.0 10.0 10.0 15.0 15.0 20.0 20.0 25.0 25.0 30.0 30.0

927.8 927.8 928.2 928.7

924.3 924.0 924.5 924.8

920.8 920.4 920.9 921.1

917.3 917.0 917.3 917.8

907.3

900.9

894.7

888.7

883.0

877.4

907.9 908.4

901.6 902.1

895.4 895.9

889.4 890.0

883.6 884.2

877.8 878.6

929.1 929.6

925.4 925.8

921.8 922.2

918.3 918.9

909.0 909.6

902.8 903.4

896.7 897.3

890.7 891.4

884.9 885.6

879.2 879.9

930.1 930.5

926.4 926.7

922.8 923.2

919.3 919.9

910.2 910.8

904.0 904.6

897.9 898.6

892.0 892.7

886.3 886.9

880.7 881.2

931.0 931.3

927.5 927.6

923.9 924.1

920.3 920.9

911.3 911.8

905.1 905.7

899.1 899.7

893.3 893.9

887.5 888.2

881.9 882.6

931.8 932.3

928.1 928.5

924.7 925.0

921.3 921.8

912.4 912.9

906.4 906.8

900.4 900.9

894.4 895.1

888.4 889.4

882.4 883.9

934.4

930.8

927.4

924.3

915.5

909.5

903.7

898.0

892.5

887.1

936.4

933.0

929.7

926.7

918.1

912.2

906.5

900.9

895.5

890.2

938.5

935.1

931.9

928.9

920.6

914.8

909.2

903.7

898.4

893.3

940.6

937.2

934.1

931.2

913.9 913.7 914.3 914.8 914.8 915.4 915.9 915.9 916.5 917.0 916.7 917.5 918.0 917.9 918.4 919.0 918.9 921.7 921.4 924.1 923.8 926.5 926.2 928.9 928.6

923.0

917.3

911.8

906.4

901.2

896.1

Expanded uncertainties, U: U(ρ) = 1.6 kg·m−3, U(T) = 0.02 K, U(p) = 0.02 MPa. Bold values are relative to the most recent measurements.

a

AAD =

1 × N

N

∑ |Xcalc − X | i=1

N

RMSD =

∑ i=1

(Xcalc − X )2 N

(19)

(20)

In eqs 17−20, the summations go over N selected data points, Xcalc is the calculated value of density and X is the reported experimental value at the same temperature and pressure.

4. RESULTS AND DISCUSSION 4.1. Density. Cottonseed oil pVT data measured in our laboratory is reported in Table 3. To our knowledge, these are the first measurements for CSO under pressure. From Table 3, it can be seen that the oil density behaves as expected, meaning that density decreases as temperature increases and pressure drops. The density of CSO were measured at atmospheric pressure by Menzies et al.14 at 293−503 K, Magne et al.15 at 273−374 K, Arnold et al.16 at 298−343 K, Demirbas17 at T = 311.15 K, Macovey18 in range of 254 K, and Eryilmaz et al.19 at 298−373 K. These measurements were compared with determinations of this study in Figure 1. Taking linear representations of density data obtained in this work at atmospheric pressure, maximum relative deviation of about 0.3% is obtained from the values measured by Menzies et al.14 up to 313 K and deviations decrease up to zero at 358 K. For temperatures higher than 358 K, the measurements made by Menzies et al. almost follow our ones with the increase of temperature. Relative deviations ranging between 0.01% and 0.25% are obtained by comparing values of this work with the

Figure 1. Comparison between the densities of this work for CSO with values from the literature. Δ, this work; ×, Menzies et al.;14 red circle, Magne et al.;15 red triangle down solid, Arnold et al.;16 red square solid, Demirbas;17 red + symbol, Macovei;18 blue × symbol, Eryilmaz et al.19

measurements made by Magne et al.,15 Macovei,18 and Eryilmaz et al.19 and 1.8% for the values of Arnold et al.16 Cottonseed biodiesel pVT data were measured and reported in our previous work22 for temperatures between 288 to 358 K and pressures up to 30.0 MPa. In Figure 2 the density of CSO and CSB are compared as a function of pressure and temperature in a three-dimensional plot. From this figure, it can be concluded that the PVT planes D



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The calculation of molar volume and molar density in GMA EoS involves the molar mass, M. Some procedures of calculation of this quantity are available for vegetable oils and biodiesel. For oils, eq 13 was proposed by Halvorsen et al.25 From the fatty acid profile of CSO (cf. Table 2), eq 13 gives Moil = 859.4 g.mol−1, which was used in this work. This value is close to 849.4 g·mol−1 estimated by Ceriani and Meirelles.31 From eq 8 and Table 2, the mean molar mass of CSB is M = 287.5 g·mol−1. The coefficients A0−A2 and B0−B2 of the GMA EoS obtained by fitting eqs 1, 2, and 3 to the pVT data through least-squares with confidence limits of 95% are given in Table 4 for CSO and CSB. Table 4. Fitting Parameters of GMA EoS Applied to the Correlation of Experimental pVT Data of CSO and CSB with 95% Confidence Limitsa parameter A0b A1c A2d B0e B1f B2g h

Figure 2. The 3D density plot for CSO and CSB as function of pressure and temperature. Symbols correspond to the experimental data for the oil (black) and biodiesel (red): ☆, 278.15 K; triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K. The lines represent GMA EoS. The CSB results were reported in a previous work.22

σ σρi r2 Np %AARD

relative to CSO and CSB lie almost parallel in space. For a more detailed and quantitative view of the results, the twodimensional plot of densities of CSO and CSB as function of temperature and pressure are presented in Figure 3. It can be

oil

biodiesel20

−9757.00018 ± 3151.7994 468.5901 ± 616.2269 6.5798 ± 1.9377 12520.5111 ± 2976.0709 414.2958 ± 579.9925 −8.1256 ± 1.8309 0.2558 0.211 0.9990 165 0.018

93.75307 ± 27.1477 45.51811 ± 5.4239 −0.051795 ± 0.01662 −25.7089 ± 8.9420 −12.9335 ± 1.7818 0.014473 ± 0.005479 0.001458 0.10 0.9998 120 0.007

a

The standard deviation (σ), coefficient of determination (r2), number of data points (Np), standard deviation in density (σρ), and the average relative deviation in density (%AARD) are given. b A 0 /(dm 9 ·mol −3 ). c A 1 /(MPa·dm 12 ·mol −4 ). d A 2 /(MPa·dm 12 · mol − 4 ·K − 1 ). e B 0 /(dm 1 2 ·mol − 4 ). f B 1 /(MPa·dm 1 5 ·mol − 5 ). g B2/(MPa·dm15·mol−5·K−1) . hσ/(dm9·mol−3). iσρ/(kg·m−3).

The standard deviations in the individual coefficients are given as well as the goodness of fit and the standard deviation for density (σρ). The standard deviation for density (σρ) is ÄÅ N É ÅÅ p (ρ − ρ)2 ÑÑÑ1/2 ÅÅ i Ñ cal ÑÑ σρ = ÅÅÅ∑ Ñ ÅÅ i = 1 (N − k) ÑÑÑ (21) ÅÇ ÑÖ where, ρcal and ρ are the densities calculated from eq 4 and the experimental for the measurement i, respectively, and k (= 6) is the number of fitted parameters. The statistical indicators allowed one to conclude that GMA EoS gives an excellent pVT data correlation for CSO and CSB, because the standard deviations in density are low (lower than the combined uncertainty) and extremely lower AARDs were obtained. From Table 4, it can be seen that some variances are high when they are compared with the corresponding parameters themselves, but always we must keep in mind that the standard deviations of the coefficients indicate the range over which a parameter value could extend without affecting model fit too adversely for a given confidence level. We have found that with the same set of data (T, p, (2z − 1)V3m), different values for parameters Ai and Bi can be obtained with the same standard deviation. Under isothermal conditions, the quantity (2z − 1)V3m must have a linear behavior with the molar density as it is expected by inspection of eq 1. The isotherms of (2z − 1)V3m versus molar density ρm, are presented in Figure 4 for CSO and CSB.

Figure 3. Density for CSO and CSB as function of pressure and temperature. Symbols correspond to the experimental data for the oil (black) and biodiesel (red): ☆, 278.15 K; triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K. The lines represent GMA EoS. The CSB results were reported in a previous work.22

seen that for each isotherm the density of oil runs almost parallel with density of biodiesel according to what could be observed in Figure 2. The differences Δρ = (ρoil − ρBd) between the densities of the oil and biodiesel corresponding at the same (T,p) coordinates are comprised between 34.4 kg·m3 at (288.15 K, 30.0 MPa) and 40.2 kg·m3 at (358.15 K, 0.1 MPa). E



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Figure 4. Isotherms of (2z − 1)Vm3 versus the molar density (ρm) for CSO (a) and CSB (b) from GMA EoS. Experimental: ☆, 278.15 K; triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K. The lines represent GMA EoS. The CSB results were reported in a previous work.22

Figure 5. Relative density deviations between the calculated values with GMA EoS (ρcal) and the experimental values (ρ) for the oil (a) and biodiesel (b): ☆, 278.15 K; triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K. The CSB results were reported in a previous work.22

The linearity holds well for all isotherms. The linearity is very important for safe extrapolation of density at high temperatures and pressures as it was verified in a previous work.22 The relative deviations between experimental and calculated values with GMA EoS were evaluated and presented in Figure 5 as function of temperature and pressure. The relative deviations are very small, usually in the range ± 0.04% (less than ± 0.4 kg.m−3) for CSO and ± 0.02% (less than ± 0.2 kg.m−3) for CSB. The densities reported in the literature for CSO at atmospheric pressure and different temperatures by the authors before mentioned are compared with values obtained from GMA EoS in Figure 6 where the RDs are plotted as a function of temperature. The densities calculated from GMA EoS deviated less than 0.3% (less than 1 kg·m−3) from data reported by Menzies et al. in the range 293−433 K. For this reason, it can be said that the GMA EoS should have excellent extrapolation ability outside the temperature domain used in its establishment (between 273 and 358 K). This behavior was also found and discussed for CSB.22 Data reported by Magne et al.15 are also in excellent agreement with GMA EoS results especially at temperatures up to 333 K (RD less than 0.1%). The densities reported by Macovey18 and Eryilmaz et al.19 are also in very good agreement with densities derived from GMA EoS. Data reported by Macovey18 is in excellent agreement at 253 and 273 K proving the ability of GMA EoS for low temperature extrapolation. The values reported by Arnold et al.16 and Dermibas17 deviate 1% or more from GMA EoS. 4.2. Density Prediction. The experimental density data for CSO were compared with the values obtained from predictive models presented in Section 3. For the application of eq 14

Figure 6. Relative density deviations between the calculated values with GMA EoS (ρcal) and the experimental values (ρ) from the literature for CSO, at atmospheric pressure. Δ, this work; ×, Menzies et al.;14 red circle open, Magne et al.;15 red triangle down solid, Arnold et al.;16 red square solid, Demirbas;17 red + symbol, Macovei;18 blue × symbol, Eryilmaz et al.19

relative to Zongs method, the composition of oil and the densities of individual triglyceride molecules must be available. Oils are complex mixtures of triglycerides (TGs) (90−98%), very small amounts diglycerides (DGs), monoglycerides (MGs), and free fatty acids (FFAs) (1−5%).32 The studies in the literature presenting oil properties and the corresponding oil composition in terms of TGs, DGs, MGs, and FFAs are scarce and the feed oil analysis is represented usually by the FFA composition. Chang and Liu33 proposed three approaches to characterize feed oils: the mixed−TG (MTGA) where detailed TG composition is considered, the simple−TG (STGA), and the pseudo−TG (PTGA), where FFA composition is used. F



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Table 5. Statistical Results Obtained from the Application of the Predictive Models for the Calculation of CSO and CSB Densitiesa model

AARD (%)

GCVOL GCVOL/HALV GCVOL/ZONG(MTGA) GCVOL/ZONG(STGA)

2.24 0.16 0.74 0.89

GCVOL 4PGMA

0.56 0.13

AAD/kg·m−3

RMSD/kg·m−3

20.46 1.42 6.79 8.15

20.83 2.18 7.23 8.58

4.84 1.11

5.36 1.46

CSO

CSB

a

The results are relative to the studied ranges of temperature and pressure.

For MTGA, one needs the TG composition of cottonseed oil. Ceriani et al.31 reported the TG profile of a CSO given in Table S2, cf. Supporting Information. The calculations allow one to obtain an FFA profile close to that presented by CSO from ACROS: MeC14:0 and lower, 1.0% (ACROS, about 1.5%); MeC16:0, 26.4% (ACROS, about 25%); MeC18:0, 2.1% (ACROS, about 3%); MeC18:1, 18.0% (ACROS, 16−24%); MeC18:2, 50.0% (ACROS, 50−55%); MeC18:3, 0.4% (ACROS, < 1.5%). Therefore, we have considered the TG profile from Ceriani et al.31 for MTGA. For STGA only the FFA composition is required. The oil is represented by a mixture of simple TGs, that means each TG is composed by the same FFA fragments and it is present with the corresponding FFA fraction. The PTGA represents the oil as a simple−TG molecule with the same mass-averaged number of CH2 groups (n) in the FFA chain and the same mass-averaged number of CHCH groups (m) as the original oil mixture. These are calculated with the equations

Figure 7. RDs between predicted (ρcal) and experimental densities (ρ) as a function of the pressure for CSO and GCVOL model: ☆, 278.15 K; triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K.

of RDs is observed again with maximum deviation −1.0% at 358.15 K and 30 MPa and a minimum close to zero at 278.15 K and pressures lower than 10 MPa. From Figure 10, it can be concluded that deviations at atmospheric pressure are in the range ±0.2%. From Figure 9, where the RDs for the method GCVOL/ ZONG are represented as a function of temperature and the pressure, it can be seen that MTGA predicts density with a reasonable level with AARD = 0.74% and accuracy of 7.23 kg·m−3. The maximum deviation of 1.1% at 288.15 K and 0.1 MPa and a minimum of −0.01 at 328.15 K and 30.0 MPa are observed for the RDs. Deviations ranging between 0.9 and 1% (AARD = 1.03%) are observed at atmospheric pressure, cf. Figure 10. The results with STGA used in GCVOL/ZONG

N

n=

∑ xini i

(22)

N

m=

∑ ximi i

(23)

where N is the number of fatty acids present in the feed oil, xi is the mole fraction of each fatty acid, and ni and mi indicate the total numbers of CH2 groups and CHCH groups, respectively, in each simple−TG component. Table S3 (cf. Supporting Information) lists the ni and mi values and FFA composition which give n = 38.9 and m = 3.7. The predicted densities of CSO obtained from the application of the models in terms of the statistical indicators are given in Table 5, relative to the studied ranges of temperature and pressure of this work. The RDs between calculated and experimental data are provided in Figures 7−9. From Figure 7, it can be seen that the RDs resulting from the application of GCVOL model are temperature-dependent with a maximum of 3% at 278.15 K and 30 MPa and a minimum of 1.4% at 358.15 K at the same pressure. The AARD is 2.24%, which correspond to the very high RMSD in Table 5. The predicted values of densities show always very high positive deviations. The relative deviations at atmospheric pressure are displayed in Figure 10. Despite the high RDs obtained, the big advantage of this method is the simplicity and straightforward density estimation. For GCVOL/HALV, the densities are predicted with a very good level with overall AARD = 0.16% and RMSD = 2.2 kg·m−3, corresponding to an accuracy close to the uncertainty of the measurements. From Figure 8, a temperature-dependence

Figure 8. RDs between predicted (ρcal) and experimental densities (ρ) as a function of the pressure for CSO and GCVOL/HALV: ☆, 278.15 K; triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K. G



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methodology is that it allows the prediction of density with the FFA oil profile which is much easier to access and it is usually supplied with the analysis of the oils. In our previous work,22 we have reported experimental pVT data for CSB and we have applied suitable predictive models, in particular GCVOL and predictive GMA (4PGMA). The RDs as a function of pressure and temperature for these models are presented in Figure 11. It can be seen that GCVOL underpredicts

Figure 9. RDs between predicted (ρcal) and experimental densities (ρ) as a function of the pressure for CSO with the GCVOL/ZONG(MTGA) (black) and GCVOL/ZONG(STGA) (red) methods: ☆, 278.15 K; triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K.

Figure 11. RDs between the predicted (ρcal) and the experimental values (ρ) as function of pressure and temperature for CSB. Black and red symbols correspond to GCVOL and 4PGMA, respectively: triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K.

the density by more than 0.5% (about 4 kg·m−3) for temperatures higher than 318 K and pressures above 10 MPa. For 4PGMA, the RDs are uniform with pressure, allowing an excellent prediction of densities with RDs within ±0.3% corresponding to AARD = 0.13% and RMSD = 1.46 kg·m−3, close to the experimental expanded uncertainty. 4.3. Mechanical Coefficients. Some important thermomechanical properties, like the thermal expansivity, αp = −(1/ρ)(∂ρ/∂T) p , and isothermal compressibility k T = (1/ρ)(∂ρ/∂p)T, can be derived from the GMA equation of state as follows34

Figure 10. RDs between the predicted (ρcal) and the experimental values (ρ) of CSO at atmospheric pressure using GCVOL EoS and the GCVOL extension of Halvorsen and Zong models. ▲, GCVOL; ▼, GCVOL/HALV; ●, GCVOL/ZANG(MTGA); ■, GCVOL/ZANG(STGA).

method are also displayed in Figure 9. They are similar to those obtained with MTGA, cf. Table 5. The predictions from PTGA method are not provided because they are similar to those obtained from MTGA. The advantage of using PTGA αp =

(2B1 + 2B2 T )ρm5 + (2A1 + 2A 2 T )ρm 4 + 2p 5ρm5 (RT 2B0 − 2B1T + 2B2 T 2 ln T ) + 4ρm4 (RT 2A 0 − 2A1T + 2A 2T 2 ln T ) + RT 2ρm

kT =

ρm RT +

5ρm5 (RTB0

2 − 2B1 + 2B2 T ln T ) + 4ρm4 (RTA 0 − 2A1 + 2A 2T ln T )

The calculated mechanical coefficients from GMA EoS, αp and kT, are presented in Table S4 for CSO (cf. Supporting Information). Results for CSB can be found in our previous work.22 In Figure 12, the thermal expansivity along isotherms, (αp, p)T, is provided for CSO and CSB. In the (T,p) ranges covered in this study, αp of CSO decreases with the increase of pressure at isothermal conditions as expected but it decreases

(24)

(25)

with temperature at isobaric conditions which is unusual. The αp of CSO behaves abnormally with the temperature decreasing with the increase of the temperature until temperatures near 338 K. At this temperature, the behavior inversion occurs at 4 MPa and αp increases with the temperature as expected. As far as we know, this behavior was not reported for vegetable oils H



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For kT, the observed variations with temperature and pressure of CSO and CSB are in accordance to the expected as illustrated in the (kT, p)T plots given in Figure 13. Some parabolic bends are observed in kT as the temperature increases, particularly at low pressure. The value of kT at standard conditions for CSO and CSB are 0.57 and 0.67 GPa−1, respectively, indicating that biodiesel is more compressible than the oil. This should be explained by the difference in molecular structure of the liquids being FAMEs molecules more flexible than TGs ones. The value of kT of CSB is close to the mean ⟨kT⟩ = 0.68 ± 0.01 GPa−1 found in our previous work22 taking into consideration 19 biodiesels. For Diesel D-2 the value 0.73 GPa−1 was calculated from the density data measured by Tat and Van Gerpen37 meaning that biodiesel has compressibility close to that for Diesel which is advantageous in terms of the compression of diesel blends with biodiesel to be used in the injection.

perhaps due to the scarcity of pVT measurements for these liquid substances.

Figure 12. Thermal expansivity (αp) as function of pressure and temperature for CSO (a) and CSB (b) predicted from GMA EoS: ☆, 278.15 K; triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K. The CSB results were reported in a previous work.22

For biodiesel the expected beahavior is observed (cf. Figure 12b). In a previous study22 for biodiesels, we have found that the values of αp, behaved normally, that is, increasing as temperature rises at isobaric conditions particularly at low pressures. However, at 65 MPa isotherms (αp,p)T intersect and after a small decrease of αp with temperature was observed for pressures higher than 65 MPa. At the intersection point (dαp/dT) p = 0, that is, αp is independent of temperature at that pressure. The intersection of the αp isotherms was first described by Bridgman35 and some recent studies revealed that this behavior seems to be general and that such intersections are common to occur at pressures below 200 MPa.36 The values of αp at standard conditions (T = 298.15 K, p = 0.1 MPa) for CSO and CSB are similar, 7.16 × 10−4 and 7.38 × 10−4 K−1, respectively. The value of αp at those standard conditions for CSB is lower than the mean ⟨αp⟩ = (8.237 ± 0.249) × 10−4 K−1 calculated over 19 biodiesels in our previous work22 and also lower than the value of Diesel D-2 (8.20 ± 0.16) × 10−4 K−1 calculated from the density data measured by Tat and Van Gerpen37 and Santos et al.38 The thermal expansivity is related to the engine power loss due to the fuel heating.39 The higher the thermal expansivity the greater the power loss. Thus, from the results obtained for CSB and for diesel some performance differences in power due to corresponding differences in αp should be expected.

Figure 13. Isothermal compressibility (kT) as function of pressure and temperature for CSO (a) and CSB (b) predicted from GMA EoS: ☆, 278.15 K; triangle with cross, 288.15 K; Δ, 298.15 K; ∇, 308.15 K; ○, 318.15 K; □, 328.15 K; ◊, 338.15 K; ×, 348.15 K; +, 358.15 K. The CSB results were reported in a previous work.22

5. CONCLUSIONS The experimental densities of cottonseed oil were measured in the range T = 278.15−358.15 K and pressures p = 0.1−30.0 MPa. The measured data correlated well with the Goharshadi− Morsali−Abbaspour equation of state with AARD = 0.018%. For the correlation of data measured for cottonseed biodiesel with the same equation of state. we have obtained AARD = 0.007%.22 For CSO, the predictive group contribution method GCVOL combined with Halvorsen model gives an excellent temperature and pressure dependencies of experimental data I



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(7) Rashid, U.; Anwar, F.; Knothe, G. Evaluation of biodiesel obtained from cottonseed oil. Fuel Process. Technol. 2009, 90, 1157−1163. (8) Altin, R.; Ç etinkaya, S.; Yücesu, H. S. The potential of using vegetable oil fuels as fuel for diesel engines. Energy Convers. Manage. 2001, 42, 529−538. (9) Sarada, S. N.; Shailaja, M.; Raju, A. V. S. R.; Radha, K. K. Optimization of injection pressure for a compression ignition engine with cotton seed oil as an alternate fuel. International Journal of Engineering, Science and Technology 2011, 2, 142−149. (10) Royon, D.; Daz, M.; Ellenrieder; Locatelli, G. S. Enzymatic production of biodiesel from cotton seed oil using t-butanol as a solvent. Bioresour. Technol. 2007, 98, 648−653. (11) Joshi, H. C.; Toler, J.; Walker, T. Optimization of cottonseed oil ethanolysis to produce biodiesel high in gossypol content. J. Am. Oil Chem. Soc. 2008, 85, 357−363. (12) Azcan, N.; Danisman, A. Alkali Catalyzed Transesterification of cottonseed oil by microwave irradiation. Fuel 2007, 86, 2639−2644. (13) Georgogianni, K. G.; Kontominas, M. G.; Pomonis, P. J.; Avlonitis, D.; Gergis, V. Alkaline conventional and in situ transesterification of cottonseed oil for the production of biodiesel. Energy Fuels 2008, 22, 2110−2115. (14) Menzies, A. W. C.; Kleinspehn, W. G.; Lewis, G. Q., Bingham, E. C. Determination of specific heat, density, surface tension, viscosity, and lubricating value of typical oils. Bingham, E. C. Cutting fluids. Technologic Papers of Bureau of Standards, 1922, T 204. https:// archive.org/details/cuttingfluids1922204bing. (accessed April 2018). (15) Magne, F. C.; Hughes, E. J.; Skau, E. L. Density-composition data of cottonseed oil-solvent mixtures. J. Am. Oil Chem. Soc. 1950, 27, 552− 555. (16) Arnold, L. K.; Juhl, W. G.; Arvidson, H. C. Densities and viscosities of trichloroethylene miscellas of cottonseed oil, fish oil, and beef tallow. J. Am. Oil Chem. Soc. 1954, 31, 393−395. (17) Demirbas, A. Relationships derived from physical properties of vegetable oil and biodiesel fuels. Fuel 2008, 87, 1743−1748. (18) Macovei, V. M. Culegere de caracteristici termofizice pentru biotehnologie şi industrie alimentară. Ed. Alma, Galaţi; 2000. (19) Eryilmaz, T.; Yesilyurt, M. K.; Yumak, H.; Arslan, M.; Sahin, S. Determination of the fuel properties of cottonseed oil methyl ester and its blends with diesel fuel. Int. J. Autom. Eng. Technol. 2014, 3, 79−90. (20) Nogueira, C. A.; Feitosa, F. X.; Fernandes, F. A. N.; Santiago, R. S.; de Sant’Ana, H. B. Densities and viscosities of binary mixtures of babassu biodiesel + cotton seed or soybean biodiesel at different temperatures. J. Chem. Eng. Data 2010, 55, 5305−5310. (21) Alptekin, E.; Canakci, M. Characterization of the key fuel properties of methyl ester−diesel fuel blends. Fuel 2009, 88, 75−80. (22) Prieto, N. M. C. T.; Ferreira, A. G. M.; Portugal, A. T. G.; Moreira, R. J.; Santos, J. B. Correlation and prediction of biodiesel density for extended ranges of temperature and pressure. Fuel 2015, 141, 23−38. (23) Goharshadi, E. K.; Morsali, A.; Abbaspour, M. New regularities and an equation of state for liquids. Fluid Phase Equilib. 2005, 230, 170−175. (24) Pratas, M. J.; Freitas, S. V. D.; Oliveira, M. B.; Monteiro, S. C.; Lima, A. S.; Coutinho, J. A. P. Biodiesel density: experimental measurements and prediction models. Energy Fuels 2011, 25, 2333− 2340. (25) Halvorsen, J.; Mammel, J. W.; Clements, L. Density estimation for fatty acids and vegetable oils based on their fatty acid composition. J. Am. Oil Chem. Soc. 1993, 70, 875−880. (26) Zong, L.; Ramanathan, S.; Chen, C. C. Fragment-based approach for estimating thermophysical properties of fats and vegetable oils for modeling biodiesel production processes. Ind. Eng. Chem. Res. 2010, 49, 876−886. (27) Ferreira, C.; Talavera-Prieto, M. C.; Fonseca, I. M. A.; Portugal, A. T. G.; Ferreira, A. G. M. Measurements of pVT, viscosity, and surface tension of trihexyltetradecylphosphonium tris(pentafluoroethyl)trifluorophosphate ionic liquid and modelling with equations of state. J. Chem. Thermodyn. 2012, 47, 183−196.

with AARD = 0.16%. The GCVOL combined with ZONG models using MTGA and STGA give reasonable predictions of density with AARDs of 0.74% and 0.89%, respectively. For CSB, the 4PGMA gives excellent predictions of densities in the studied ranges of temperature and pressure (AARD = 0.13%). Comparing the densities of CSO and CSB as functions of pressure and temperature, it was observed that they run almost parallel one each other for the isotherms with differences between 34 to 40 kg·m−3. The behavior of the thermal expansivity as a function of pressure was predictable, that is, a decrease is observed for increasing pressures at isothermal conditions for oil and biodiesel. However, for the oil the same property decreased with increasing temperature at isobaric conditions which is unusual. This behavior is reversed at 338 K. The isothermal compressibility behaves as expected, that is, the isobaric increase with temperature and the isothermal decrease with pressure are observed for oil and biodiesel.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00313.

■

The data for the molar mass, critical temperature, critical pressure and Rackett parameter for fatty acids of CSO needed for application of Halvorsen method are provided in Table S1. The triglyceride profile for CSO needed for application of Zong method (MTGA) is presented in Table S2. Data for the application of Zong method in the PTGA are provided in Table S3. The detailed information on mechanical coefficients of CSO calculated from GMA EoS is shown in Table S4 (PDF)

AUTHOR INFORMATION

Corresponding Author

*Tel.: +351 239 798 729. Fax: +351 239 798 703. E-mail: abel@ eq.uc.pt. ORCID

Abel G. M. Ferreira: 0000-0002-8316-200X Notes

The authors declare no competing financial interest.

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REFERENCES

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Density of Cottonseed Oil and Biodiesel - Journal of Chemical

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