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Correlating the Cloud Point of Biodiesel to the Concentration and Melting Properties of the Component Fatty Acid Methyl Esters (FAME) Robert O. Dunn Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b02935 • Publication Date (Web): 11 Dec 2017 Downloaded from http://pubs.acs.org on December 30, 2017

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Energy & Fuels

Correlating the Cloud Point of Biodiesel to the Concentration and Melting Properties of the Component Fatty Acid Methyl Esters (FAME) Robert O. Dunn* Bio-Oils Research, United States Department of Agriculture, Agricultural Research Service, National Center for Agricultural Utilization Research, 1815 N. University St., Peoria, Illinois 61604, United States *Chemical Engineer; Voice: 309-681-6101; Fax: 309-681-6524; E-mail: [email protected]. Mention of trade names or commercial products in this publication is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the U.S. Department of Agriculture. USDA is an equal opportunity provider and employer. The author declares no competing financial interest.

KEYWORDS: Cold Flow Properties, Enthalpy of Fusion, Melting Point, Solid-Liquid Equilibrium Properties of neat biodiesel fuels, six empirical cloud point correlation models from the literature, validation tests for Dunn (1997) and Davis models, melting properties of fatty acid methyl esters, example calculation of solid-liquid equilibrium transition temperature of palm oilfatty acid methyl ester biodiesel and melting properties of free fatty acids in canola oil- and palm oil-fatty acid methyl esters supplied as Supplemental Information.

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ABSTRACT: Biodiesel is a renewable alternative diesel fuel made from plant oils and animal

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fats. In the form of fatty acid methyl esters (FAME), it is usually obtained by transesterification

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of plant oil or animal fat with methanol in the presence of catalyst. Most of the fuel properties of

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biodiesel compare well with conventional diesel fuel (petrodiesel). One major disadvantage of

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biodiesel is its relatively poor cold flow properties which must be monitored during cold weather

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in moderate temperature climates. Two correlation models were developed to accurately

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calculate the cloud point (CP) of biodiesel. Both models were developed using measured CP

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data from binary admixtures of biodiesel fuels made from canola, palm and soybean oils and

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yellow grease (CaME, PME, SME and YGME). One model was based on solid-liquid

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equilibrium (SLE) thermodynamics in organic mixtures. This model required fatty acid

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concentrations (FA Profile) and melting point (MP) and enthalpy of fusion (∆Hfus) data for each

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FAME species in the mixture. A high degree of correlation (R² = 0.949) was found between CP

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and the calculated mixture SLE transition temperature (TSLE). Regression analysis yielded an

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equation for calculating the CP of FAME mixtures. The MODified Empirical Correlation

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(MODEC) model (R² = 0.893) was derived from (1/CP) versus ln(yC16) data where yC16 was the

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mass fraction of methyl palmitate (MeC16) in the mixture. The performances of both models in

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predicting the CP of multicomponent FAME mixtures (biodiesel) were compared against results

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from six empirical correlation models from the literature. The SLE model performed best by

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having close to a 1:1 correlation between calculated (CP-calc) and measured CP data and the

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highest accuracy with respect to average deviations. Although the MODEC model did not

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exhibit a 1:1 correlation, it performed nearly as well as the SLE model in accurately calculating

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the CP of biodiesel. The main benefit of the MODEC model is that it requires only a measured

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yC16 value vis-à-vis complete analysis of the FA Profile in order to apply the SLE model.

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1. INTRODUCTION

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Biodiesel is an alternative diesel fuel made from renewable plant oils and animal fats. Biodiesel

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in the form of fatty acid methyl esters (FAME) is obtained by transesterification of the feedstock

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lipid with methanol in the presence of catalyst.1 It has properties that compare well with

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conventional diesel fuel (petrodiesel) and may be used in blends, or as a neat (100 %; ‘B100’)

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fuel, to power compression-ignition engines. In the US, 10.6 billion L (2.8 billion gal) of

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biodiesel and renewable diesel fuels was produced in 2016.2

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Biodiesel has many advantages that make it attractive for use as an alternative fuel in

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modern compression-ignition (diesel) engines. It is safe to store and handle because it is

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environmentally innocuous and has a high flash point, low toxicity and a rapid biodegradation

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rate.3-5 Blending with biodiesel enhances the ignition quality, lubricity and anti-wear properties

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of petrodiesel.6 Combustion of fuels containing biodiesel reduces hydrocarbons, carbon

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monoxide, sulfur dioxide, polyaromatic hydrocarbons and particulate matter in exhaust

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emissions.3-5,7 Soybean oil-FAME (SME) biodiesel has an energy output/fossil fuel input ratio

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of 4.568 and reduces net greenhouse gas emissions by 66 %.9

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Among the disadvantages of biodiesel are its poor cold flow properties. Biodiesel has a

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high cloud point (CP; defined as the temperature where a haziness is detected in a cooled

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sample10) that may compromise its deployment and performance in cold weather. Throughout

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much of the world, biodiesel must conform to fuel property specifications such as the ASTM D

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6751 or CEN EN 14214 standards. Both of these standards have guidelines and/or requirements

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for cold flow properties of biodiesel.


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Soybean oil biodiesel (SME) develops operability issues when ambient overnight

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temperatures approach 0 to 2 °C.10 These temperatures are generally within the range of CP data

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for SME (−2 to 3 °C). Similarly, palm oil-FAME (PME) has CP in the range 10 to 18 °C and

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may become problematic when ambient temperatures are slightly below room temperature.

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Long-chain saturated-FAME (SFAME) have higher melting points (MP) than unsaturated-

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FAME (UFAME) with the same chain length. Since PME typically has four times the

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concentration of methyl palmitate (MeC16) than SME, it has a higher CP.

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The objective of the present study is to develop an accurate correlation for calculating the

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CP of biodiesel based on two factors: 1) its fatty acid concentration profile, referred to as the ‘FA

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Profile’ and defined as the identity and concentration of each FAME species present; and 2) the

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MP and enthalpy of fusion (∆Hfus) of each FAME species. Several studies11-20 examined

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biodiesel admixtures (blends of two or more biodiesel fuels derived from different feedstocks)

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with the goal of mitigating deficiencies associated with poor cold flow properties or oxidative

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stability, or high kinematic viscosity (ν) in unblended biodiesel fuels. Some of these studies

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reported correlations for estimating CP (or cold filter plugging point) only as functions of FA

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Profile concentrations with little or no attention paid to the melting properties of FAME species.

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This work investigates FAME made from four feedstocks: canola (CaME), palm (PME)

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and soybean (SME) oils and yellow grease (YGME). Four binary admixtures were prepared for

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each of the six admixture systems in varying mass fractions (y1). The preparation of admixtures

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was intended primarily to diversify the number of FAME mixtures (28) from a starting point of

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four neat biodiesel fuels. The FA Profiles of the admixtures were calculated from analyses

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performed on the component biodiesel fuels. The CP of each mixture was measured directly in

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the course of the present work.


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Six mathematical models from the scientific literature17,21-24 were tested for validation by

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applying them to FA Profile data obtained for the mixtures and comparing results for calculated

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and measured CP data. Two new correlations for calculating the CP of biodiesel were also

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developed. First, the solid-liquid equilibrium (SLE) transition temperature (TSLE) of the mixtures

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were calculated from melting properties of the pure FAME species and correlated with

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corresponding measured CP data. The second correlation, termed the MODified Empirical

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Correlation (MODEC) model, was based on thermodynamic theory for the SLE in mixtures of

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compounds. This model correlated CP as a function of the mass fraction of MeC16 (yC16) in the

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mixtures.

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2. EXPERIMENTAL SECTION 2.1. Materials. The biodiesel (FAME) samples were acquired as finished products:

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CaME was from Archer-Daniels-Midland (Decatur, IL); PME produced by Sime Darby

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Biodiesel Sdn. Bhd. (Selangor, Malaysia) was obtained courtesy of the Malaysian Palm Oil

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Board (Washington, DC); SME was an experimental sample obtained via the National Biodiesel

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Board (NBB; Jefferson City, MO); and YGME was from Superior Process Technologies

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(Minneapolis, MN). Biodiesel samples were tested for fuel quality by analysis of acid value

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(AV), oxidation induction period (IP) at 110 °C, ν at 40 °C, water content, free and total

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glycerides and total monoacylglycerols (MAG) using standard test methods. Experimental

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methods, instruments and a summary of the data are presented in the supplemental information.

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2.2. Methods. Fatty acid concentration profiles (FA Profiles) were determined for the

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four neat biodiesel fuels. Concentration (mass fraction) data were from analyses performed on a

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Varian (Walnut Creek, CA) model 8400 gas chromatograph (GC) with a flame-ionization


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detector (FID) and a Supelco (Bellefonte, PA) SP2380 GC column. The carrier gas was helium

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and FAME species were identified by retention times and quantified by peak areas.

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Concentration data for the admixtures were calculated by applying mass balances to each FAME

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species based on GC-analysis of the FA Profiles of the two component biodiesel fuels.

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In the present work, the term ‘admixture’ refers to binary mixtures of two component

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biodiesel fuels (24 mixtures); ‘neat biodiesel’ refers to the biodiesel fuel components (4

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mixtures); and ‘mixture’ refers collectively to all admixtures and neat biodiesel fuels (28

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mixtures). Each admixture was prepared by weighing the appropriate masses of the neat

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biodiesel components and mixing in a laboratory flask. Admixtures with mass fractions (y1) =

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0.2, 0.4, 0.6 and 0.8 were prepared for each system (the subscript ‘1’ refers to the biodiesel fuel

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designated with the heading ‘Biodiesel 1’). Admixture samples were sealed in vials and stored

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in a dark refrigerator when not in use. None of the comparison models were developed

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considering the melting properties (MP and ∆Hfus) of the individual FAME components.

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Cloud point (CP) data of the biodiesel and biodiesel admixtures were measured with a

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model PSA-70S automatic analyzer from Phase Technology (Richmond, BC, Canada). Data

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were measured according to ASTM test method D 5773.25

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2.3. Correlations. Six empirical correlation models from the literature were found for

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calculating the CP of biodiesel based on FA Profile concentration factors. These correlations are

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outlined in eqs S1-S6 in the supplemental information. Three correlations were linear functions

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based on the mass concentration of total-SFAME (ΣSFAME), total-UFAME (ΣUFAME) or

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MeC16.17,23 One correlation was a non-linear function of ΣUFAME mass concentration.24 The

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remaining two are multivariate expressions based on 1) weighted average number of C-atoms in

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the fatty acid chain (NC) plus the ΣUFAME molar concentration21; and 2) the mass fractions (yi)


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of five FAME, MeC16, methyl stearate (MeC18), methyl oleate (MeC18:1), methyl linoleate

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(MeC18:2) and methyl linolenate (MeC18:3).22

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Solid-liquid equilibrium transition temperatures (TSLE) were used to develop a correlation

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for calculating the CP of biodiesel fuels based on thermodynamic theory. The TSLE data were

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calculated using the equation reported in Imahara et al.26:

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=

−

∆

(1)

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where MP (K) and ∆Hfus (J/mol) are melting properties of the pure FAME species, xi is the mole

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fraction of the FAME and Rg is the gas constant. The transition temperature of FAME species ‘i’

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in the admixture is Tf. This equation assumes an ideal solution in the liquid phase and

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independent crystallization of FAME species into the solid phase (that is, no solid solutions).

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Equation 1 was used to calculate Tf values for each FAME species present and the mixture TSLE

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value was taken as the maximum Tf value. The mixture TSLE was determined from the maximum

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of the calculated Tf values and its associated FAME defined as the “controlling” species in the

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mixture. In the present work, MP and ∆Hfus data were acquired from the scientific literature for

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use in eq 1. Measured CP data were then matched in data pairs with the corresponding mixture

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TSLE data for all admixtures, including the four neat biodiesels, and subjected to linear regression

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analysis to establish the SLE correlation.

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The MODEC equation was developed by rearranging and modifying eq 1 as follows:

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= + !

(2)

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where CP (K) is the measured CP of the mixture, yC16 is the mass fraction of MeC16 and A and B

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are constants determined from linear regression of (1/CP) versus ln(yC16) data. Once constants A

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and B were inferred, the correlation for calculating CP (°C) was obtained by rearranging eq 2:

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"# = $1(&

+ !') − 273.15

(3)

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Note this model assumes MeC16 is the SLE controlling FAME in the mixtures. All mathematical operations used to calculate mean values, perform regression and

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statistical analysis of experimental results, and validation testing of calculated CP data (CP-calc)

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against measured CP data were conducted using Microsoft (Redmond, WA) Excel® 2013

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spreadsheets.

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3. RESULTS AND DISCUSSION 3.1. Neat Biodiesel Fuel Properties. Results from analysis of AV, IP, ν, water content,

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free and total glycerols and total MAG content are summarized in Table S1 in the supplemental

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information. Based on these properties, the overall quality of the neat biodiesel samples used in

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the study was very good. Free and total glycerols and total MAG concentrations were very low

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indicating the fuels were well refined. Viscosities (ν) were in a narrow range, 4.09-4.622 mm²/s,

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and water contents were within maximum limits in ASTM standard D 6751.27

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Three of the property data points were outside the specified limits. The AV of both

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CaME and PME exceeded the maximum limit (0.50 mg KOH/g).27 These results indicated

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relatively low free fatty acid (FFA) concentrations (0.27 and 0.44 mass%) and were not expected

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to influence the outcome of the present study. The IP of SME was very low as a result of this 8 ACS Paragon Plus Environment

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biodiesel having the highest polyunsaturated-FAME concentration among the four neat

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biodiesels and no added oxidation inhibitors.

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3.2. FA Profiles of Admixtures. Results from GC/FID analysis of the four neat biodiesel

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fuels are summarized in Table 1. The most abundant species present in the neat biodiesel fuels

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were MeC16, MeC18, MeC18:1, MeC18:2 and MeC18:3. The neat fuels had diverse ranges in

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FA Profile with respect to yC16 = 0.0413-0.448, yC18:1 = 0.1970-0.6490 and ΣSFAME = 0.0688-

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0.504 (or ΣUFAME = 0.496-0.9312). PME had the highest ΣSFAME content mainly due to its

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yC16 = 0.448. Although CaME had the highest ΣUFAME content (0.9312), SME had the highest

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concentration in total polyunsaturated-FAME (ΣPUFAME = 0.6634). The high ΣPUFAME

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content of SME likely caused it to fail the IP specification in ASTM standard D 6751 as

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discussed earlier. YGME had the highest yC18 (0.0655), possibly the result of partial

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hydrogenation of oleic acid moieties in the parent oil during its use as a cooking oil.

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Table 1. Fatty Acid Concentration Profiles (FA Profile) of Biodiesel Derived from Canola, Palm and Soybean Oils and Yellow Grease (CaME, PME, SME and YGME).a Mass fractions (yi) are mean values from n = 3 analyses. FAME CaME PME SME YGME yi SD yi SD yi SD yi SD MeC14 0.000515 8×10−6 0.0099 1×10−4 ND Traceb MeC16 0.0413 2×10−4 0.448 2×10−3 0.1101 6×10−4 0.1375 7×10−4 −6 b MeC16:1 0.000242 8×10 Trace ND 0.0088 2×10−4 −5 −4 −4 MeC18 0.02038 2×10 0.0418 2×10 0.0395 2×10 0.0655 4×10−4 −4 −3 −4 MeC18:1 0.6490 3×10 0.407 1×10 0.1970 4×10 0.406 3×10−3 −5 −4 −4 MeC18:2 0.18709 5×10 0.0887 6×10 0.5746 5×10 0.340 1×10−3 −5 b −4 MeC18:3 0.08199 7×10 Trace 0.0788 4×10 0.0349 3×10−4 −5 −5 b MeC20 0.00659 7×10 0.00374 3×10 Trace 0.00765 8×10−5 −5 b b MeC20:1 0.01286 9×10 Trace ND Trace Total 1.0000 1.000 1.0000 1.000 CaME contained traceb of methyl erucate (MeC22:1). PME contained tracesb of methyl laurate (MeC12); YGME contained traces of methyl docosanoate (MeC22) and MeC22:1. a FAME = Fatty acid methyl esters; SD = standard deviation; MeC14 = methyl myristate; MeC16 = methyl palmitate; MeC16:1 = methyl palmitoleate; MeC18 = methyl stearate; MeC18:1 = methyl oleate; MeC18:2 = methyl linoleate; MeC18:3 = methyl linolenate; MeC20 = methyl arachidate; MeC20:1 = methyl eicosenoate; ND = not detected. b yi < 0.0001 (ignored).


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Many empirical models developed to estimate the cold flow properties of biodiesel were

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based on FAME compositional factors. This is common despite the more fundamental approach

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of using molar concentrations to directly correlate with the molecular structures of the

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components. Shown in Figure 1 is a plot of concentration data from FA Profiles of the

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admixtures prepared for study. These profiles were calculated from the concentration data in

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Table 1. The graph shows the mole fraction (xi) plotted against mass fraction (yi) corresponding

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to 196 FAME concentrations in the admixtures. Regression analysis yielded a straight line with

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slope = 1.006 (standard error [SE] = 0.0026), intercept = −7×10−4 (5.3×10−4), adjusted

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correlation coefficient (R²) = 0.9987 and standard error of the y-estimate (σy) = 0.0059. This line

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matched the 1:1 correlation xi = yi for yi = 0.0-0.6. The likely explanation for the high degree of

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correlation resides in the studied biodiesel fuels being composed of 98+ mass% FAME species

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with C16 or C18 tailgroup chain lengths. The data in Figure 1 suggest that using mass

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concentrations instead of molar concentrations to derive composition-based correlations for

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predicting the properties of biodiesel introduces little error in the results.

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Another common feature of empirical correlations is the use of the MeC16 concentration

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as a surrogate for ΣSFAME concentration in the biodiesel fuel. This assumption may be

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intuitively based on the relative abundance of palmitic acid in many feedstock oils and fats

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including camelina, canola, corn, cottonseed, jatropha, linseed, low-erucic acid rapeseed

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(LEAR), olive, palm, peanut, sesame, soybean and sunflowerseed oils plus lard and tallow.28,29

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The results in Figure 2 show that ΣSFAME increases linearly as yC16 increases for the 28 FAME

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mixtures. Regression analysis yielded slope = 1.04 (SE = 0.020), intercept = 0.041 (0.0042), R²

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= 0.991 and σy = 0.012. Nearly identical results were obtained from analysis of mole fraction

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data (slope = 1.04 [0.018], intercept = 0.039 [0.0041], R² = 0.992 and σy = 0.011). These results


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showed that for the correlations tested in the present study, variations in the ΣSFAME

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concentration were highly correlated to variations in the MeC16 concentration in FAME

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mixtures.

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Figure 1. Comparison of mass and mole fractions (yi and xi) of fatty acid methyl ester (FAME) species present in binary biodiesel admixtures.

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Figure 2. Comparison of total saturated-FAME (ΣSFAME) and methyl palmitate (yC16) mass fractions in multicomponent FAME mixtures. See Figure 1 for abbreviations.


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3.3. CP of Neat Biodiesel Fuels. Data from CP measurements conducted on the four neat

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biodiesel fuels are presented in Table 2. In general, the results compared well with results in the

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literature for CaME, PME, SME and YGME. CaME had CP = −2.3 °C which agreed with

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results in four studies.30-33 Canola oil is similar in FA Profile to LEAR oil29 and results for

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CaME in the present work compared well with data reported for LEAR-FAME.30,34 Data in

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Table 2 agreed with results in three studies30,35,36 on PME and compared well with data in two

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studies37,38 on SME. The CP values for CaME, PME and SME were within temperature ranges

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reported in a recent review article.10

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Table 2. Measured Cloud Point (CP) Data and Calculated Mixture Solid-Liquid Equilibrium (SLE) Temperatures.a CP data are mean values from n = 3 measurements. Biodiesel 1 Biodiesel 2 y1 CP TSLE FAME xi °C SD °C CaME None 1.000000 −2.3 0.1 −0.73 MeC20 0.00595 PME None 1.000000 13.1 0.7 20.28 MeC16 0.470 SME None 1.000000 −2.8 0.4 4.75 MeC16 0.1188 YGME None 1.000000 2.8 0.2 8.44 MeC18 0.0640 SME PME 0.200171 11.1 0.5 18.41 MeC16 0.402 0.399814 8.0 0.4 16.19 MeC16 0.332 0.599748 5.5 0.5 13.47 MeC16 0.262 0.798622 2.57 0.06 9.93 MeC16 0.191 SME YGME 0.200661 1.8 0.2 7.62 MeC18 0.0589 0.399936 0.5 0.1 6.74 MeC18 0.0539 0.599850 −0.5 0.3 5.77 MeC18 0.0488 0.797861 −2.0 0.2 5.27 MeC16 0.1248 CaME PME 0.200004 10.7 0.3 18.00 MeC16 0.388 0.400049 5.7 0.6 15.18 MeC16 0.304 0.599914 2.8 0.1 11.46 MeC16 0.219 0.799717 −2.0 0.1 5.95 MeC16 0.133 CaME YGME 0.200463 0.5 0.1 7.00 MeC18 0.0553 0.400044 −1.07 0.06 5.32 MeC18 0.0465 0.600012 −2.07 0.06 3.31 MeC18 0.0378 0.799926 −2.6 0.1 0.79 MeC18 0.0290 CaME SME 0.200043 −3.1 0.2 3.35 MeC16 0.1042 0.400280 −4.8 0.0b 1.75 MeC16 0.0895 0.596710 −4.8 0.0b 0.34 MeC18 0.0277 0.799914 −4.1 0.0b −1.03 MeC18 0.0239 PME YGME 0.200191 4.2 0.3 11.20 MeC16 0.214 0.399940 6.8 0.4 14.20 MeC16 0.279 0.599861 9.23 0.06 16.59 MeC16 0.344 0.800095 11.3 0.3 18.58 MeC16 0.407 a y1 = Mass fraction of Biodiesel 1 in admixture; TSLE = SLE transition temperature; xi = mole fraction of controlling FAME species. See Table 1 for abbreviations.


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b

Same result after three replicate measurements (SD = 0).

Comparison of the CP value for YGME with values reported in the literature was

266

performed keeping in mind there is a large variety in yellow greases characterized by industry.

267

Yellow grease is obtained as a waste material from food processing and interchangeably referred

268

to as used cooking or used frying oil (note: brown grease, another waste oil from food

269

processing, is generally lower in quality). Nevertheless, the measured CP value for YGME in

270

Table 2 agreed well with data reported for used cooking/frying oil-FAME12,39 and other

271

YGME.40,41 Based on the fuel properties (including CP) and FA Profile data, the YGME used in

272

the present study appears to have been well processed with no measurable “trans” type UFAME

273

content.

274

3.4. CP of Admixtures. Measured CP data for the 24 admixtures are summarized in

275

Table 2. Each data point is matched with y1 = mass fraction of ‘Biodiesel 1’ in the

276

corresponding binary admixture. CP data for the SME/PME, CaME/PME and CaME/SME

277

systems were compared with data for these admixtures reported in another study.18 Similarly,

278

CP data from the CaME/YGME admixture system were compared with results reported in a

279

study on LEAR-FAME/used cooking oil-FAME due to the similarities in the respective FA

280

Profiles of the component biodiesel fuels.12

281

Comparison of the measured CP data for these four admixture systems is made in the

282

four graphs shown in Figure 3 where the data are plotted as a function of y1. All four admixture

283

systems exhibit consistent trends in the data-curves for the present study and comparison data.

284

The results exhibit some separation between CP data in the present study and data from the

285

literature. The separations were most likely caused by small deviations in the CP of the

286

component biodiesel fuels. Nevertheless, deviations between curves were generally small, 2.513 ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

287

3.8 °C for SME/PME, 2-3.9 °C for CaME/PME, 2.5-4.8 °C for CaME/SME and 0.2-0.5 °C for

288

CaME/YGME.

289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306

Figure 3. Cloud point (CP)-composition charts of admixture systems: (a) soybean oil-FAME (SME)/palm oilFAME (PME; (b) canola oil-FAME (CaME)/PME; (c) CaME/SME; and (d) CaME/yellow grease-FAME (YGME). Results from ‘This study’ are compared with superimposed data from references.12,18 Measured CP data are average values from three replicates (standard deviations ≤ 0.66). See Figure 1 for abbreviations.

307

The SME/PME, CaME/PME and CaME/YGME admixture systems showed steady

308

decreases in CP as y1 increases. The CaME/PME curve [Figure 3(b)] exhibited concave upward

309

behavior where CP decreased steadily at y1 = 0-0.8 before nearly leveling off at y1 > 0.8. This

310

trend is repeated in the data from the comparison study.18 Similar behavior was observed for the

311

CaME/YGME system [Figure 3(d)] where CP leveled off at y1 ~ 0.7-0.8.


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Energy & Fuels

312

The phase behavior observed in Figure 3(c) for the CaME/SME system was the result of

313

narrow deviations in measured CP data for the component biodiesel fuels (0.5 °C for the present

314

study; 1 °C for the comparison study18). In the comparison study, CP decreased from 1 °C at y1

315

= 0.0 to 0 °C at all other mass fractions. In contrast, the results for the present work show a

316

slight decrease from −2.8 to −3.1 °C at y1 = 0.0-0.2, a sharp decrease from −3.2 to −4.8 °C at y1

317

= 0.2-0.4 and a steady increase back to −2.5 °C at y1 = 0.4-1.0.

318

3.5. Testing the Six Literature Correlations. Six correlation models taken from the

319

literature were tested for validation against measured CP data for the 28 FAME mixtures studied

320

herein. Presented in Table 3 is a summary of the model names (Dunn, Davis, Sarin #1, Sarin #2,

321

Su and Clements) and compositional and structural factors inferred from FA Profile data in Table

322

1. These factors were used in the associated models to calculate CP data (CP-calc) for

323

comparison with measured CP data in Table 2. Measured CP and CP-calc data for the 28

324

mixtures were organized into data pairs, one set for each model, and tested for validation by

325

regression analysis. Results are summarized in Table 4.

326 327

328 329 330 331

Table 3. Correlation Factors of Neat Biodiesel Fuels Calculated from FA Profile Data in Table 1.a Correlation Factor CaME PME SME YGME Dunn (1997) ΣSFAME, mass% 6.8788 50.4 14.96 21.06 Sarin #2; Clements ΣUFAME, mass% 93.12 49.6 85.04 78.9 Sarin #1 YC16, mass% 4.13 44.8 11.01 13.75 Davis yC16 0.0413 0.448 0.1101 0.1375 Davis yC18 0.02038 0.04183 0.0395 0.0655 Davis yC18:1 0.6490 0.407 0.1970 0.406 Davis yC18:2 0.18709 0.0887 0.5746 0.340 Davis yC18:3 0.08199 N/A 0.0788 0.0349 Su NC 18.94 18.0 18.76 18.7 Su ΣUFAME, mol% 92.82 47.5 84.25 78.1 a ΣSFAME = Total saturated-fatty acid methyl ester (FAME) concentration; ΣUFAME = total unsaturated-FAME concentration; YC16 = mass fraction of MeC16; yCm:n = mass fraction of FAME ‘MeCm:n’; N/A = not applicable; NC = weighted-average number of C-atoms in ester chain. See Table 1 for abbreviations.

332 15 ACS Paragon Plus Environment

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333 334

335 336 337 338 339 340 341 342 343 344 345

Table 4. Results from Regression Analysis of Calculated CP (CP-calc) versus Measured CP Data for the Six Literature Empirical Correlations and the SLE and MODEC Models.a Model Slope SE Intercept SE σy F R² Dunn (1997)b 3.2 0.11 1.4 0.65 0.968 3.2 816 Davisc 3.9 0.36 13 2.1 0.810 10 116 Sarin #1d 1.10 0.050 2.2 0.29 0.947 1.4 486 Sarin #2d 1.28 0.045 1.1 0.26 0.968 1.3 816 Sue 0.98 0.031 2.3 0.18 0.974 0.9 995 Clementsf 0.86 0.053 3.0 0.31 0.907 1.5 266 SLE (eq 4) 0.95 0.042 0.1 0.25 0.949 1.2 507 MODEC (eq 6) 0.89 0.059 0.3 0.34 0.893 1.7 227 MODEC (modified eq 6)g 0.93 0.049 0.2 0.29 0.932 1.4 357 a MODEC = MODified Empirical correlation; SE = Standard error of slope or intercept; R² = adjusted correlation coefficient; σy = standard error of the y-estimate; F = variance ratio (model/residuals). See Table 2 for abbreviations. b Ref. 23. c Ref. 22. d Ref. 17. e Ref. 21. f Ref. 24. g Omitting data for neat CaME.

Shown in Figure 4 are CP-calc results for four correlation models versus measured CP

346

data in the present work. Two models were omitted because they deviated significantly from the

347

desired 1:1 correlation between CP-calc and measured CP data (results are presented in the

348

supplemental information). For the Dunn (1997) model, correlation between CP-calc and

349

measured data was second highest for the six correlations tested, based on R² = 0.968 and σy =

350

3.2. The performance of this model was likely affected by 11 admixtures plus neat PME and

351

YGME having ΣSFAME concentrations outside the range (0.06-0.20) of correlation.23 The

352

Davis model yielded the highest slope, intercept and σy values and the lowest R² from the

353

validation tests. This model probably failed because it accounted only for five FAME species

354

present in the admixtures and ignored the remaining FAME species.22

355

The Su model demonstrated the best validation results among the six literature models

356

with slope = 0.98, intercept = 2.3 and the lowest σy = 0.9. The second-best model was Sarin #1

357

with slope = 1.10, intercept = 2.2 and σy = 1.4. Although it had a lower intercept and σy than

358

Sarin #1, the slope (1.28) of the Sarin #2 model caused it to fail validation. These three models 16 ACS Paragon Plus Environment

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Energy & Fuels

359

demonstrated a nearly linear correlation (R² = 0.947-0.974) between CP-calc and measured CP

360

data. The Clements model yielded a low slope = 0.86, a high intercept = 3.0 and σy = 1.2.

361

Results for this correlation were clearly non-linear (R² = 0.91) showing a concave upward pattern

362

in Figure 4(d).

363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380

Figure 4. Validation graphs showing calculated CP (CP-calc) versus measured CP results for literature correlations: (a) Sarin #1; (b) Sarin #2; (c) Su; and (d) Clements. Dashed lines = 1:1 correlation between calculated and measured data. See Figure 3 for abbreviations.

Summarized in Table 5 are results from direct comparison of CP-calc and measured CP

381

data for the six literature correlation models. The Dunn (1997) and Davis models had very high

382

maximum absolute deviations (ADmax) of 34.66 and 48.57. The remaining four models had

383

lower ranges in absolute deviation (AD) = 0.02-6.56; however, each of these models yielded


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

384

positive deviations (CP-calc > CP) for 24+ of the mixtures tested. The lowest average absolute

385

deviation (AAD) = 2.1 was observed for the Sarin #2 model which correlated the CP of biodiesel

386

with MeC16 mass% (YC16).17 The Su model yielded the lowest root-mean-squared deviation

387

(RMSD) = 2.4 and had the lowest range in AD = 0.45-3.93.

388 389 390

391 392 393 394 395 396 397 398 399

Table 5. Deviations between Measured CP and CP-Calc from the Six Literature Empirical Correlations and the SLE and MODEC Models.a Model Deviations ADmin ADmax AAD RMSD Dunn (1997)b 0.34 34.66 9.9 14 Davisc 1.05 49.31 21 27 Sarin #1d 0.18 5.47 2.5 2.8 Sarin #2d 0.02 6.56 2.1 2.6 Sue 0.45 3.93 2.2 2.4 Clementsf 0.52 5.91 2.7 3.2 SLE (eq 4) 0.05 3.06 0.94 1.2 MODEC (eq 6) 0.03 4.96 1.4 1.7 MODEC (modified eq 6)g 0.01 2.93 1.2 1.4 a ADmin = Minimum absolute deviation; ADmax = minimum absolute deviation; AAD = average absolute deviation; RMSD = root-mean-squared deviation. See Tables 1, 2 and 4 for abbreviations. b Ref. 23. c Ref. 22. d Ref. 17. e Ref. 21. f Ref. 24. g Omitting CP data for neat CaME.

400

3.6. Mixture TSLE Data. Equation 1 was applied to determine the Tf of each FAME

401

species present in the 28 FAME mixtures. FA Profile data were from Table 1 and MP and ∆Hfus

402

data were from the literature (Table S2 in the supplemental information). An example showing

403

how TSLE = 20.28 °C was inferred from Tf data for neat PME is given in Table S3 in the

404

supplemental information. The data in the last three columns of Table 2 are a summary of the

405

mixture TSLE values, identity and mole fraction (xi) of the controlling FAME species in the 28

406

mixtures. These results were determined in accordance with SLE thermodynamic theory for

407

ideal solutions in the liquid phase and independent crystallization of FAME species.


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Energy & Fuels

408

Fifteen admixtures and two neat biodiesel fuels had MeC16 identified as the TSLE-

409

controlling FAME. YGME had MeC18 as the controlling FAME leading to three SME/YGME

410

and four CaME/YGME admixtures having the same controlling FAME. The same was true for

411

two CaME/SME admixtures despite neither component biodiesel having MeC18 as the

412

controlling FAME. Although neat CaME had a small concentration of MeC20 (yC20 = 0.00659

413

[xC20 = 0.00595]), this species was the controlling FAME according to SLE theory. Thus, small

414

concentrations of higher-MP species can have a disproportionate effect on the TSLE of FAME

415

mixtures. These results also showed that neither MeC14 nor any of the UFAME species present

416

in the FAME mixtures had an impact on the SLE phase transitions.

417

Two admixture systems had two different controlling FAME species depending on the

418

composition (y1). The SME/YGME system had MeC18 at y1 ≤ 0.600 and MeC16 at y1 > 0.600.

419

At y1 = 0.600, calculated Tf values were nearly identical (5.77 and 5.76 °C) for MeC18 and

420

MeC16 indicating that the SLE curves for these two FAME intersect near this composition.

421

Increasing SME content decreased xC16 and xC18 in the admixtures causing the Tf values for both

422

FAME to decrease. The intersection of the SLE curves was due to the Tf of MeC18 decreasing

423

in larger increments than MeC16.

424

The second admixture system demonstrating an intersection in SLE curves was

425

CaME/SME where the controlling FAME changed from MeC16 to MeC18 at 0.400 < y1 < 0.598.

426

Increasing the CaME content decreased both xC16 and xC18 causing Tf for both FAME to decrease

427

in a fashion similar to the SME/YGME admixture data. The calculated point of intersection

428

between the SLE curves for MeC16 and MeC18 was at y1 = 0.475 and Tf = 2.81 °C for

429

CaME/SME.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

430

At 0.800 < y1 < 1.000, the CaME/SME system exhibited a second intersection between

431

SLE curves for MeC18 and MeC20. This occurs because MeC20 was identified as the

432

controlling FAME in neat CaME. This admixture system appears to undergo a eutectic-like

433

phase transition because Tf values for MeC20 trended upward with increasing CaME content

434

(that is, xC20) in the admixtures. The calculated intersection of SLE curves for MeC18 and

435

MeC20 occurred at y1 = 0.8865 and Tf = ‒1.67 °C, corresponding to a mole ratio (xC18/xC20) =

436

4.22. Such transitions have been observed for binary mixtures of pure MeC16/MeC1826,42,43 and

437

MeC16/MeC20.43,44 The behavior discussed earlier for experimental data in Figure 3(c) may

438

have been affected by intersecting SLE curves for controlling FAME in this admixture system.

439

When calculating the TSLE data (Table 2), it was observed that for the nine admixtures

440

with MeC18 as the controlling FAME, Tf values calculated for MeC16 were within −1.9 °C of

441

TSLE of those mixtures. Neat YGME also had MeC18 as the controlling FAME and the Tf value

442

for MeC16 in this biodiesel fuel deviated by −1.3 °C from the mixture TSLE. These narrow

443

deviations, combined with MeC16 being identified as the controlling FAME for 15 admixtures

444

plus neat PME and SME, may explain the high correlation observed earlier between ΣSFAME

445

and yC16 (Figure 2). Apparently, MeC16 has a Tf value that allows the assumption that it is the

446

SLE-determining FAME species in the FAME mixtures being studied. The lone exception was

447

neat CaME where MeC20 was identified as the controlling FAME with the corresponding

448

mixture TSLE = −0.79 °C, compared to Tf = −5.25 °C for MeC16 in the mixture.

449

Equation 1 was used to check the assumption made earlier that elevated AV (FFA) of

450

CaME and PME did not affect the SLE in mixtures composed of these two biodiesels. Melting

451

properties (MP and ∆Hfus data) were used in the equation to calculate Tf values of fatty acids that

452

may have been present in these biodiesel fuels. Mole fractions of fatty acids were assumed to be


Page 20 of 37

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Energy & Fuels

453

equal in proportion to the corresponding FAME concentrations. Results presented in Table S4 in

454

the supplemental information demonstrated that all fatty acids had calculated Tf values below the

455

mixture TSLE values of the neat biodiesel fuels (Table 2). These results appear to confirm that the

456

elevated AV did not impact the SLE phase transition results in the present study.

457

3.7. SLE Model for CP. Comparing the data in Table 2 shows that TSLE > CP for each

458

FAME mixture studied. Deviations (CP − TSLE) ranged from −1.8 to −9.4 °C. The TSLE is

459

defined as the SLE transition temperature of a mixture at equilibrium. Since the CP of biodiesel

460

is measured under non-equilibrium conditions (rapid cooling, no agitation), it does not represent

461

an equilibrium transition temperature.45,46 Instead, it is likely that the effects of supercooling

462

caused CP < TSLE in the multicomponent FAME mixtures. Supercooling is the phenomenon

463

where substances remain in a liquid phase at temperatures below the normal freezing point

464

unless a seed crystal or nucleus is present.47,48 Such effects have been observed when comparing

465

cooling and heating differential scanning calorimetry (DSC) analyses performed on FAME

466

mixtures38,47,49-51 and petrodiesel and jet fuels.52,53

467

The development of the SLE model began with statistical analysis and linear regression

468

of 28 (CP, TSLE) data pairs for corresponding FAME mixtures. A paired two sample t-test of the

469

mean values yielded a Pearson coefficient (PC) = 0.975 favoring correlation between CP and

470

TSLE data. Linear regression analysis resulted in the following equation:

471 472

"# = 0.82 123 − 5.0

(4)

473 474

where CP and TSLE are in °C, R² = 0.949, σy = 1.2 and variance ratio (F = model/residuals) = 507.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

475

These regression results supported two main conclusions from the present study. First,

476

eq 4 has a high probability of predicting CP within 1.2 °C. Second, although CP itself is not an

477

equilibrium transition temperature, it demonstrates a nearly linear correlation with the TSLE of

478

multicomponent FAME mixtures (biodiesel) determined from SLE thermodynamic theory.

479

Given these considerations, eq 4 was applied to calculate a separate set of CP-calc data from TSLE

480

data in Table 2 and the results tested against the measured CP data.

481

Figure 5 is a graph showing CP-calc versus measured CP for the SLE model. Regression

482

analysis (results summarized in Table 4) yielded close to a 1:1 correlation with the slope (0.95)

483

being closer to unity than all literature models except Su. The SLE model also had a smaller

484

intercept coefficient (0.1) than any of the literature models tested. Deviations between CP and

485

CP-calc from the SLE model (Table 5) were in the range AD = 0.05-3.06. Lastly, results from

486

the SLE model had the lowest AAD (0.94) and RMSD (1.2) among the correlations compared.

487

Overall, these results suggested that the SLE model was the most accurate model for calculating

488

the CP of the multicomponent FAME mixtures studied in this work.

489

490 491 492

Figure 5. Comparison of CP-calc versus measured CP data for the solid-liquid equilibrium (SLE) model for FAME mixtures (eq 4).


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Energy & Fuels

493 494 495

Dashed line = 1:1 correlation. See Figures 1, 3 and 4 for abbreviations.

496

3.8. MODEC Model for CP. Performing a paired two sample t-test on 28 (CP, yC16) data

497

pairs for corresponding FAME mixtures yielded PC = 0.974. The data plotted as (1/CP) versus

498

ln(yC16) [eq 2] are shown in Figure 6(a). Linear regression analysis of the data yielded the

499

equation:

500 501

= −1.02 × 105 ln − 3.44 × 10:

(5)

502 503

where CP is in K, R² = 0.887, σy = 2.4×10‒5 and F = 212. The low R² for this equation was

504

mainly the result of scatter.

505

It was observed earlier that neat CaME was the only mixture where the SLE controlling

506

FAME was MeC20 instead of MeC16 or MeC18. This data point, labeled “C” in Figure 6(a),

507

clearly demonstrates the largest deviation from the regression line drawn through the data.

508

Omitting point “C” from the regression analysis increased the relative correlation to nearly linear

509

(R² = 0.929) while only slightly affecting the slope (1.12×10−4) and intercept (3.42×10−5)

510

coefficients.

511

Results from the regression analysis yielded the following MODEC model equation:

512 513

CP = ;1(& −1.02 × 105 ln

− 3.44 × 10: '< − 273.15

(6)

514 515

where CP is in °C. Equation 6 was subsequently used to calculate a separate set of CP-calc

516

values to be tested against corresponding measured CP data. Results are shown graphically in 23 ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

517

Figure 6(b) and summarized in Table 4. Two sets of data were obtained, one for CP-calc data

518

from eq 6 and the other for data generated from the analysis omitting the neat CaME data.

519 520 521 522 523 524 525 526 527 528 529

Figure 6. Development of the MODified Empirical Correlation (MODEC) model for the CP of FAME mixtures (eq 6): (a) (1/CP) versus ln(yC16), linear trend line (R² = 0.887); (b) comparison of CP-calc versus measured CP data, dashed line = 1:1 correlation. See Figures 1-3 and 4 for abbreviations.

The results in Table 4 for the MODEC model in eq 6 did not indicate a 1:1 correlation

530

with respect to the slope (0.89) of the regression line. The R² = 0.893 indicated non-linear

531

behavior due in part to deviation at point “C” (neat CaME) in Figure 6(b). The results from the

532

analysis omitting neat CaME yielded a nearly linear (R² = 0.932) correlation that was close to a

533

1:1 relationship with respect to slope (0.93) and intercept (0.2) coefficients. Both eq 6 and the

534

modified correlation had σy < 2. Deviation results (Table 5) show that both MODEC equations

535

had AAD and RMSD < 2, values that were lower than all models tested except the SLE model.

536

The MODEC model modified by omitting the CaME data had the lowest ADmax (2.93) among

537

the models tested in this work.

538

This preliminary validation test showed that the MODEC model worked well when

539

multicomponent FAME mixtures (biodiesel) have MeC16 or MeC18 as the SLE controlling

540

FAME species. As observed earlier, neat CaME had MeC20 as the controlling FAME species

541

and did not fit the correlation as well as the other 27 mixtures. Noting that 12 admixtures had


Page 24 of 37

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Energy & Fuels

542

CaME as a component, it was concluded that only the admixtures with higher concentrations (y1

543

> 0.800) of CaME were likely to demonstrate deviations from the pattern. This is remarkable

544

considering that the MODEC model was based on the hypothesis that (1/CP) was correlated to

545

ln(yC16). The results in the present study indicated that despite not yielding a good preliminary

546

validation results for calculating the CP of biodiesel, the MODEC model performed nearly as

547

well as the more theoretically-based SLE model.

548 549

4. CONCLUSIONS

550

This work evaluated six empirical correlations from the literature for accuracy in calculating the

551

cloud point (CP) of biodiesel fuels. Validation tests against measured CP data were conducted

552

for fatty acid methyl esters (FAME) from canola, palm and soybean oil and yellow grease

553

(CaME, PME, SME and YGME) plus 24 binary biodiesel admixtures. Two models, Su and

554

Sarin #1, demonstrated close to a 1:1 correlation.

555

Two new correlation models were developed that out-performed the literature models.

556

The solid-liquid equilibrium (SLE) model yielded a nearly linear correlation (R² = 0.949)

557

between temperatures calculated from thermodynamic theory (TSLE) and CP of the mixtures.

558

Results helped explain why methyl palmitate (MeC16) is often successfully used as a surrogate

559

for total saturated-FAME (ΣSFAME) concentration in physical property correlations for FAME

560

mixtures when concentrations of longer-chain FAME were very low. This model had the lowest

561

absolute average deviation (AAD) and root-mean-squared deviation (RMSD) values among the

562

correlations tested in the present study.

563 564

This work showed that 99.1 % of variations in the ΣSFAME concentration were driven by variations in the MeC16 concentration of the mixtures studied. The MODified Empirical


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

565

Correlation (MODEC) model was a direct relationship between 1/CP and ln(yC16[mass fraction

566

of MeC16]). This model yielded a good correlation (R² = 0.893) between calculated and

567

predicted CP values. Neat CaME contained a small concentration of methyl arachidate (MeC20)

568

and omitting this mixture increased R² to 0.932. The MODEC model had the second lowest

569

AAD and RMSD values.

570

Comparing these two models, the benefit of the MODEC model is that it required only

571

yC16 to calculate the CP of most FAME mixtures. This model becomes less accurate when

572

FAME with alkyl chains of C20+ were able to affect the SLE of the mixtures. The benefit of the

573

more accurate SLE model is that it can predict the CP of all FAME mixtures. For this model to

574

be applied, it is important that the fatty acid concentration profile be known to approximately

575

100 %.

576 577

ACKNOWLEDGEMENTS

578

Kimberly L. Ascherl and Kevin Steidley provided technical assistance for experiments and

579

measurement of fuel properties.

580 581

This work was funded as part of the in-house research of the Agricultural Research Service of

582

the United States Department of Agriculture.

583 584 585 586

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Figure 1 84x62mm (300 x 300 DPI)


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Energy & Fuels



Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3 165x118mm (300 x 300 DPI)


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Figure 4 165x115mm (300 x 300 DPI)


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Energy & Fuels

Figure 6 167x59mm (300 x 300 DPI)


Correlating the Cloud Point of Biodiesel to the ... - ACS Publications

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