EXPERIMENT ON BIO-DIESEL:

DETERMINING VISCOSITY-

TEMPERATURE DEPENDENCY

OF BIO-DIESEL THROUGH

FATTY ACID PROFILE

Erond Perez & Luke Asgill

Acknowledgements

We would like to express our deepest gratitude to the people and institution which helped us and

guided us through the course of this project. This project was successful thanks to Professor Richard

Brown for his input and advice, particularly on deriving the predictive model, and to Professor

Dennis De Pellegrin for helping us during experimentation and sharing his extensive knowledge in

the field of Tribology. Extra gratitude must be made to research student Jahirul Islam for his

extensive support, advice and guidance during the course of the project and for providing the test

samples. Thank you very much for the time and effort you have given to us, for the project would

not have been a success without the help you gave us.

We would also like to give our thanks to Nathaniel Raup, who assisted us in the laboratory, for

setting up the Rheometer and for providing support whenever he could. Our thanks also goes to

QUT and David Kabelele for giving us this wonderful opportunity to work on this project.

Abstract

The ever increasing awareness of climate change is driving sectors of governments to pursue cleaner

sources of fuel. One of the most feasible alternatives is biodiesel fuels. Biodiesels are a sustainable

and renewable source of energy, derived from vegetable oils, a variety of fats and other organic

sources. These organic diesel fuels are produced through a transesterification process and due to

the process, possess features similar with the chemical composition of petrodiesel, but without any

sulphur, aromatic hydrocarbons and metals. However, other than being a sustainable, renewable

and relatively clean source of energy, the performance characteristic of biofuels must also be taken

into account. This report examined the viscosity of four different biofuels and nine different

manufactured methyl esters at different temperatures. From this experiment and knowledge of the

fatty acid composition of each sample, a mathematical model was developed in order to predict the

viscosity of any biodiesel at any temperature of interest. The predictive model attained in this report

showed a percentage error ranging from 0 to 8.1% when compared with the experimental results.

The importance of such a prediction is that if viscosity can be predicted accurately, there may be no

need for expensive testing in order to determine the performance of a particular fuel in an engine,

let alone determining the viscosity experimentally.

Table of Contents

List of Figures ........................................................................................................................................... i

List of Tables ............................................................................................................................................ i

List of Equations ....................................................................................................................................... i

1. Introduction .................................................................................................................................... 1

1.1. Biodiesel production ............................................................................................................... 1

1.2. Biodiesel Quality Standards .................................................................................................... 2

2. Viscosity .......................................................................................................................................... 3

2.1. Modelling ................................................................................................................................ 3

2.2. Fuel Sample Fatty Acid Profiles ............................................................................................... 4

3. Experimental Machinery & Methodology ...................................................................................... 6

3.1. Methodology ........................................................................................................................... 6

4. Results and Data analysis ................................................................................................................ 8

5. Discussion ...................................................................................................................................... 13

6. Conclusion ..................................................................................................................................... 14

7. Reference List ................................................................................................................................ 15

Appendices ............................................................................................................................................ 16

Appendix i – Biodiesel Quality Standards ......................................................................................... 16

Appendix ii – Linear Trend Lines for the Relationship between the Logarithm of Viscosity to

Temperature ..................................................................................................................................... 18

Appendix iii – Derivation for the General Equation Relating Temperature, Fatty Acid Composition

and Viscosity ..................................................................................................................................... 26

Appendix iv – MatLab Procedure to Derive the Relationship between Gradient Values and Fatty

Acid Composition .............................................................................................................................. 27

i

List of Figures

Figure 1 - The transesterification reaction. R is a mixture of various carbon chains. Methanol is the

most commonly employed alcohol (R = CH3) ......................................................................................... 2

Figure 2 - Measured viscosity and calculated viscosity using the modified Grunberg-Nissan equation

(Equation 2). ............................................................................................................................................ 4

Figure 3 - The Brookfield DV-III rheometer and temperature bath set-up............................................. 7

Figure 4 - User interface of the accompanying software for the Brookfield rheometer. ....................... 7

Figure 5 - Standard and Logarithmic Relationship between Viscosity and Temperature. ................... 10

List of Tables

Table 1 - The fatty acid composition of the test fluids. Note that on the table, pure 810, pure 1214

and pure 1875A are 100%. 810-1214, 810-1875A, 1214-1875A are 50-50 mixes. Main 1875A, Main

810 and Main 1214 are 2⁄3-1⁄6-1⁄6 mix where the 2⁄3 component is as indicated .............................. 5

Table 2 - Averaged viscosity results for the 13 different fluids. The viscosity is measured in mPas. ..... 9

Table 3 - Comparison of the calculated gradients, as determined from the relationship derived, to

the experimentally calculated gradients. ............................................................................................. 12

List of Equations

Equation 1 - General Grunberg-Nissan Equation. ................................................................................... 3

Equation 2 - Simplified Grunber-Nissan Equation. ................................................................................. 3

Equation 3 - General relationship between viscosity and temperature. ................................................ 8

Equation 4 - Relationship between viscosity and temperature with reference to the viscosity at 40 oC.

................................................................................................................................................................ 8

Equation 5 - Revised Grunberg-Nissan equation involving dependence on temperature. .................... 8

Equation 6 - General relationship between rate of change of the logarithm of viscosity and fatty acid

composition. ........................................................................................................................................... 9

Equation 7 - Relationship between the rate of change of the logarithm of viscosity and fatty acid

composition. ......................................................................................................................................... 12

1

1. Introduction

The primary issue with traditional petroleum based diesel (petrodiesel) is that it is not renewable.

According to statistics released by British Petroleum, global oil supplies will be exhausted in the next

40 years [1] or much sooner as the models used for the predictions cannot accurately account for

the increasing use of oil in developing countries [2]. As the oil supply decreases, it will reach a point

where the energy required, to find and extract one barrel worth of oil will be substantially greater

than the energy contained in one barrel of oil itself [2].

Aside from peak oil issues, concerns for the climate are also a problem due to petrodiesel’s high

emissions. The ever increasing awareness of the current, rapid climate change is driving sectors of

government to pursue cleaner sources of fuel to aid in mitigating our net effect on our local and thus

global climate. Biodiesels, organically based diesel fuels, are becoming one of the most feasible

alternatives to current technologies. Biodiesels are sustainable, renewable and typically have a lower

emissions profile than petrodiesel. Furthermore, biodiesel feedstocks operate on a closed carbon

cycle; that is, just as much or less carbon is emitted when burning the biodiesel fuels as the organic

feedstocks consume. It must be deliberated that these mentioned advantages of biodiesels are not

the only consideration to be taken into account. Performance characteristics and thus the actual

useability of different biodiesel fuels must also be considered. This report examines the viscosity, a

primary tribological property in fuel standards, of four different biodiesel fuels and nine different

manufactured fuels. The four biodiesel fuels tested are all considered as potential replacements or

supplements for traditional petrodiesel. Connections and a predictive model in relation to the fatty

acid composition and temperature on viscosity will also be made.

1.1. Biodiesel production

Biodiesels are derived from vegetable oils, a variety of fats and other organic sources and consists of

alkyl esters, primarily methyl esters. Biodiesels possess features common with the chemical

composition of petrodiesel. Since biodiesels are made entirely from organic sources, unlike

petrodiesel, it does not contain any sulphur, aromatic hydrocarbons, metals or crude oil residue [3].

The raw material (the oils from organic sources) has a significantly higher viscosity then traditional

petrodiesel. There are four methods to reduce the viscosity of the raw oils to enable their use in

common diesel engines without operational problems. These methods are:

1) Blending with petrodiesel

2) Pyrolysis

3) Microemulsification (co-solvent blending)

4) Transesterification.

Transesterification is the most common method, as this method leads to the production of alkyl

esters and what is known as a biodiesel. This process is a chemical reaction between the

triacylglycerol compounds of the raw oils and alcohol molecules. This process separates the

triacylglycerol into an alkyl ester and a glycerol compound. This reaction can be seen schematically

in Figure 1 below [4].

2

Figure 1 - The transesterification reaction. R is a mixture of various carbon chains. Methanol is the most commonly employed alcohol (R = CH3)

1.2. Biodiesel Quality Standards

The primary criterion for biodiesel quality is adherence to the appropriate standard. Even when used

in low-level blends with petrodiesel fuel, biodiesels are expected to meet the standard before

blending. When specifications are met, the biodiesel can be used in most engines without

modifications, while also maintaining the engine’s durability and reliability [4]. The purpose of

quality standards is to ensure appropriate, sustainable use of current technologies. Presented below

are the ASTM standards for biodiesels. Furthermore, both the European and Australian standards

can be found in Appendix i.

3

2. Viscosity

Viscosity is defined as the measure of resistance to flow of a liquid due to internal friction of one

part of a fluid moving over another. Viscosity affects the atomization of a fuel upon injection into the

combustion chamber and as the viscosity becomes higher, the tendency for incomplete combustion

and in consequence, coking becomes greater. For this reason, viscosity is an important consideration

for biodiesels which generally possess higher viscosities. There are two different measurements of

viscosity, dynamic and kinematic. Dynamic or absolute viscosity is the measurement of resistance to

shear flow, whereas kinematic viscosity is the ratio of the dynamic viscosity to the density of the

fluid; kinematic viscosity is equal to dynamic viscosity divided by density, which results in a quantity

that does not depend on the force applied. Kinematic viscosity is one of the primary specifications in

biodiesel standards [5].

2.1. Modelling

There are numerous pieces of literature regarding the prediction of viscosity from fatty acid

compositions. The importance of such an investigation is that if the viscosity of any given biodiesel

fuel can be predicted from its chemical composition, there may be no need for expensive testing in

order to determine the performance of the fuel in an engine, let alone determining the viscosity

experimentally [6].

A paper presented by C.A.W. Allen et.al. presents one such method for predicting the viscosity of

biodiesel fuels from the knowledge of their fatty acid composition. This model uses a logarithmic

relationship between the components of the fluid to determine the dynamic viscosity. The

Grunberg-Nissan equation (shown in equation 1)

Equation 1 - General Grunberg-Nissan Equation.

ln 𝜇𝑚 = ∑𝑥𝑖 𝑙𝑛 𝜇𝑖 + ∑∑𝑥𝑖 𝑥𝑗 𝐺𝑖𝑗

𝑛

𝑖≠𝑗

𝑛

𝑖

where 𝜇𝑚 is the mean viscosity of mixture (Pa s), 𝜇 is the viscosity of pure 𝑖th component (Pa s), 𝑥𝑖 and 𝑥𝑗 is the mole

fractions of the 𝑖th and 𝑗th components, 𝐺𝑖𝑗 is the interaction parameter (Pa s), 𝑛is the number of components.

has been identified to be the most accurate equation for computing the viscosity of liquid mixtures.

This equation was developed for binary mixtures and works best with non-associate liquids.

Biodiesel fuels are non-associated liquids that are comprised of mixtures of fatty acids with similar

chemical structures and due to this, the components in such a mixture do not interact with one

another. With this reasoning, the second term which comprises the interaction parameter can be

neglected. Mass fraction is used in preference of mole fraction as well, thus yielding equation 2

which C.A.W. Allen et.al used to predict viscosity, based on the fatty acid composition.

Equation 2 - Simplified Grunber-Nissan Equation.

ln 𝜇𝑚 = ∑𝑦𝑖 𝑙𝑛 𝜇𝑖

𝑛

𝑖=1

4

where 𝑦𝑖 is the mass fraction.

Some results of their investigation are presented in Figure 2 below. As seen from their results and as

discussed in the original paper, viscosity increases with the methyl ester chain length (number of

carbon atoms), as well as with an increasing degree of saturation (number of double or triple bonds

between the carbon atoms). This also holds for the alcohol moiety because the viscosity of ethyl

esters is slightly higher than that of methyl esters. Factors such as double-bond configurations, also

influence viscosity, where cis double-bond configurations give a lower viscosity than trans

configurations; however, the double-bond position has a lesser effect on viscosity, while branching

in the ester moiety has little or no influence on viscosity (unpublished results) [5][6].

It should be noted that both the model presented and those presented in other papers do not

incorporate the effect of temperature upon viscosity as well as the fatty acid composition.

Figure 2 - Measured viscosity and calculated viscosity using the modified Grunberg-Nissan equation (Equation 2).

2.2. Fuel Sample Fatty Acid Profiles

Table 1, seen on the ensuing page, contains the fatty acid compositions of the thirteen different

fluids tested. As can be seen, the varying mixtures of the manufactured methyl esters provide a

comprehensive range of fatty acid profiles.

5

Table 1 - The fatty acid composition of the test fluids. Note that on the table, pure 810, pure 1214 and pure 1875A are 100%. 810-1214, 810-1875A, 1214-1875A are 50-50 mixes. Main 1875A, Main 810 and Main 1214 are 2⁄3-1⁄6-1⁄6 mix where the 2⁄3 component is as indicated

Fatty acid content

C6 C8 C10 C12 C14 C16 C16:1 C18 C18:1 C18:2 C18:3 C20 C20:1

Pure 810 0.043 0.541 0.406 0.01 0 0 0 0 0 0 0 0 0

Pure 1214 0 0.003 0.006 0.7 0.236 0.05 0 0.005 0 0 0 0 0

Pure 1875A 0 0 0 0.002 0.01 0.21 0 0.77 0 0 0 0.008 0

810-1214 0.021 0.272 0.206 0.355 0.118 0.025 0 0.003 0 0 0 0 0

810-1875A 0.021 0.271 0.203 0.006 0.005 0.105 0 0.385 0 0 0 0.004 0

1214-1875A 0 0.001 0.003 0.351 0.123 0.13 0 0.388 0 0 0 0.004 0

Main 1875A 0.007 0.09 0.069 0.12 0.046 0.148 0 0.515 0 0 0 0.005 0

Main 810 0.029 0.361 0.272 0.124 0.041 0.043 0 0.129 0 0 0 0.001 0

Main 1214 0.007 0.092 0.072 0.469 0.159 0.068 0 0.132 0 0 0 0.001 0

Canola 0 0 0 0 0 0.037 0 0.017 0.594 0.235 0.102 0.015 0

Cottonseed 0 0 0 0 0.008 0.2445 0.007 0.0235 0.171 0.542 0.0035 0.0005 0

Tallow 0 0 0 0 0.02 0.305 0.03 0.215 0.39 0.03 0.01 0 0

Cooking oil 0 0 0 0 0 0.096 0.012 0.035 0.58 0.179 0.063 0.008 0.027

The fatty acid compositions of the pure esters were obtained from the supplier while for the ester mixtures, the presented values were calculated according

to their mixing proportions. It should be noted that all the fatty acid compositions obtained from the ester supplier and pieces of literature consist of a

range of values and were thus averaged to yield a single value as presented in Table 1. The full range of fatty acid compositions for each of the fluids can be

found in Appendix i.

6

3. Experimental Machinery & Methodology

Determining the viscosity of biodiesels is an essential part in identifying and understanding how it

will perform in engines. In the experiment conducted, a Brookfield DV-III Programmable Rheometer

was used to measure the viscosity of biodiesel samples and observe the change in viscosity in

relation to changes in temperature.

The principle of operation of the DV-III is to drive a spindle (which is immersed in the test fluid)

through a calibrated spring. The viscous drag of the fluid against the spindle is measured by the

spring deflection. The resulting deflection is measured with a rotary transducer. The temperature of

the test sample is controlled externally by an oil bath connected to the device [7].

3.1. Methodology

The tests were conducted according to ASTM D445, however, the starting temperature for the

sample was at room temperature (about 25-27 °C). The procedure carried out is listed below. The

Brookfield rheometer was controlled externally via accompanying software on a computer. The CP-

41 spindle was used since it provided the most accurate measurements for low viscosity fluids.

Preparation:

1. The cup and spindle were removed from the rheometer and cleaned with acetone. During

this time, the rheometer was calibrated by zeroing the machine.

2. The CP-41 spindle was reattached to the rheometer. Gloves were worn to avoid

contamination from the hands.

3. The cup was attached and the distance between the cup and spindle was set; the rheometer

set-up during this step is displayed in Figure 3. This was done by turning the flicker switch at

the front which sends a current through the cup and spindle. When the two parts come into

contact the light flicks to red. The correct spacing is one unit away from the point of contact.

4. The cup was removed once again and 2 mL of an oil sample was placed in the cup. The cup

was then reattached to the rheometer.

7

Figure 3 - The Brookfield DV-III rheometer and temperature bath set-up.

Test:

1. On the dashboard of the accompanying software (see below), the shear rate was set to 20

per second, the temperature of the cup at room temperature was recorded and the test was

engaged by pressing the icon. After a few moments the spindle would reach the

designated shear rate and the viscosity measurement would settle.

2. The shear rate was increased by 20 per second four times, recording the result each time.

3. The temperature was then increased using the oil bath. Steps 5 and 6 were repeated once

the temperature of the cup reached the desired level (temperature of the cup was

measured with a thermocouple and displayed on the accompanying software). The

temperature was set to 30, 35, 40, 45, 50, 60, 70, 80 and 90 oC. At 60 oC, the shear rate was

initially set to 100 per second (instead of 20 per second) to increase the sensitivity and

hence limit noise and variation in results.

Figure 4 - User interface of the accompanying software for the Brookfield rheometer.

8

4. Results and Data analysis

Table 2, shown on the following page, consists the averaged results obtained through viscosity

measurements of the four biodiesels, three pure methyl esters and six mixed methyl esters. From

Table 2 the relationship between chain length and degree of saturation outlined in Section 2.1 in

clearly evident. Methyl Octanoate and Decanoate (810) has a significantly lower viscosity than

Methyl Stearate (1875A) due to its much shorter chain lengths. Evidence of the effect of saturation

can be seen by comparing Methyl Stearate (1875A) to Canola biodiesel. Both methyl esters comprise

primarily of chain lengths of 18 carbon atoms, however Canola has a large degree of saturation

whereas Methyl Stearate is entirely un-saturated. Consequently, Canola biodiesel has a higher

viscosity.

Below, Figure 5 graphically illustrates the relationship between viscosity and temperature. As seen,

there is a clear, logarithmic relationship between the viscosity and temperature. Due to this, the y-

axis has been made logarithmic in second graph of Figure 5 to generate a linear relationship of the

form:

Equation 3 - General relationship between viscosity and temperature.

ln 𝜇 = 𝑚𝑇 + 𝑐

As the Grunberg-Nissan equation models the viscosity at the reference temperature of 40 oC, a

relationship between the viscosity at any temperature, relative to the same reference temperature

can be seen below.

Equation 4 - Relationship between viscosity and temperature with reference to the viscosity at 40 oC.

𝜇𝑥 = 𝜇𝑟 ∙ 𝑒𝑚(𝑇𝑥− 𝑇𝑟)

Where µx is the viscosity at any temperature, µr is the viscosity at the reference temperature and Tx and Tr are

the temperature at the desired point and at the reference point, respectively.

Equation 4 was then integrated with the Grunberg-Nissan equation to yield Equation 5 below. This

model is capable of predicting the viscosity at any temperature, with the knowledge of the fatty acid

composition. The derivation for reaching this model can be seen in Appendix iii.

Equation 5 - Revised Grunberg-Nissan equation involving dependence on temperature.

ln 𝜇𝑥 = ∑𝑦𝑖 ln 𝜇𝑖

𝑛

𝑖=1

+ 𝑚(𝑇𝑥 − 𝑇𝑟)

Thus, as can be seen from the above equation, the only variable unknown is ‘m’. The ‘m’ value

depicts the slope of the relationship seen in Equation 3. As seen by the trend lines in Appendix ii and

Figure 5 below, there is a direct correlation between the slope of the line and the fatty acid

composition. As such, this correlation was modeled as seen below.

9

Equation 6 - General relationship between rate of change of the logarithm of viscosity and fatty acid composition.

𝑚 = 𝐴[%𝐶6] + 𝐵[%𝐶8] + 𝐶[%𝐶10] + 𝐷[%𝐶12] + 𝐸[%𝐶14] + 𝐹[%𝐶16] + 𝐺[%𝐶16: 1]

+ 𝐻[%𝐶18] + 𝐼[%𝐶18: 1] + 𝐽[%𝐶18: 2] + 𝐾[%𝐶18: 3] + 𝐿[%𝐶20] + 𝑀[%𝐶20: 1]

Where 𝐴 − 𝑀 are coefficients to be calculated.

Table 2 - Averaged viscosity results for the 13 different fluids. The viscosity is measured in mPas.

10

0

1

2

3

4

5

6

7

8

9

0 10 20 30 40 50 60 70 80 90 100

Vis

cosi

ty (

mP

as)

Temperature (oC)

Relationship Between Viscosity and Temperature

Pure 810

Pure 1214

Pure 1875A

810|1214

810|1875A

1214|1875A

Main 810

Main 1214

Main 1875A

Canola

Cotton Seed

Beef Tallow

Cooking Oil

Figure 5 - Relationship between Viscosity and Temperature.

11

-0.5

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80 90 100

Log

of

Vis

cosi

ty (

mP

as)

Temperature (oC)

Logarithm of Viscosity Against Temperature

Pure 810

Pure 1214

Pure 1875-A

810|1214

810|1875-A

1214|1875-A

Main 810

Main 1214

Main 1875-A

Canola Biodiesel

Cotton Seed

Beef Tallow

Cooking Oil

Figure 6 - Logarithm of Viscosity plotted against temperature.

12

MATLAB was used to solve the equation based on the known fatty acid compositions and the

equations of the trend lines in Appendix ii. The input codes for this procedure are shown in Appendix

iv. The derived equation can be seen below. The gradient values attained with Equation 6 are shown

below, in Table 3 and are compared to those determined experimentally. As can be seen, there is

little error in the model and the errors present can be accounted for by the range of composition

values and the usage of averaged values to derive the equation.

Equation 7 - Relationship between the rate of change of the logarithm of viscosity and fatty acid composition.

𝑚 = −13.9[%𝐶6] + 2.86[%𝐶8] − 2.38[%𝐶10] + 0.79[%𝐶12] − 2.45[%𝐶14] + 0.005[%𝐶16]

− 1.03[%𝐶16: 1] + 0.2[%𝐶18] − 0.014[%𝐶18: 1] + 0.004[%𝐶18: 2]

+ 2.41[%𝐶18: 3] − 17.41[%𝐶20] − 0.69[%𝐶20: 1]

The above equation can be used in unison with Equation 3 to determine the viscosity at any

temperature. As the viscosity of pure saturated methyl esters as well as for chain lengths greater

than 18 are not known, the above equation cannot be used to model the methyl esters tested.

Table 3 - Comparison of the calculated gradients, as determined from the relationship derived, to the experimentally calculated gradients.

Sample Fluid Actual Gradients Calculated Gradients Error (%)

pure 810 -0.011 -0.0116 5.454545

pure 1214 -0.0147 -0.0145 -1.36054

pure 1875 -0.0185 -0.0188 1.621622

810|1214 -0.0118 -0.0117 -0.84746

810|1875 -0.0148 -0.0136 -8.10811

1214|1875 -0.0166 -0.0172 3.614458

main 810 -0.012 -0.0121 0.833333

main 1214 -0.0157 -0.0156 -0.63694

main 1875 -0.0163 -0.0163 0

canola -0.0192 -0.0192 0

cotton seed -0.0118 -0.0118 0

beef tallow -0.0169 -0.0169 0

cooking oil -0.0184 -0.0184 0

13

5. Discussion

The results produced clearly reinforce previous findings on viscous behavior, particularly the

correlation between fatty acid composition and degree of saturation. The study has also identified a

direct correlation between the logarithmic decrease in viscosity with an increase in temperature and

the fatty acid composition.

From the results section, a predictive model, based off the Grunberg-Nissan equation was derived.

This model can be used to predict the viscosity of fluids at any temperature with knowledge of the

fluid’s fatty acid composition. This equation however, has a maximum error of approximately 8%.

This error margin is likely due to lack of information upon the exact fatty acid composition of the

different fluids tested. Furthermore, the equation does not take into account the configuration of

saturated carbon chains which have also been noted to affect the viscosity.

In regards to the four biodiesel fuels tested and compared to used petrodiesel fuel, which has a

viscosity between 2-6 mPas around 40 oC, all four fuels possess viscosities fairly similar. The highest

viscosity at 40 oC is 5.448 mPas from Canola biodiesel. The lowest viscosity at this temperature was

achieved by Beef Tallow (4.274 mPas). These values are within the higher part of the range of

petrodiesel quantities. Although, in order to compare these fuels to various standards, the kinematic

viscosities of the fuels must be known, this requires knowledge of their density. The density of these

fuels was found to vary by a significant degree and was thus deemed un-useable. Nevertheless,

considering methyl esters possess similar chemical compositions to petrodiesel the densities of

biodiesel fuels can be expected to also be similar. Based off this consideration, all four biodiesel fuels

tested can be considered as safe to use in standard compression ignition engines.

14

6. Conclusion

The experiment conducted examined the temperature dependence of viscosity of four biodiesel

fuels and nine manufactured methyl esters. The results clearly demonstrate the logarithmic

relationship between viscosity and temperature. Furthermore, the effect of fatty acid chain length as

well as the degree of saturation upon viscosity is also characterized. Pure methyl ester stearate

demonstrated a much higher viscosity than methyl ester octanoate/decanoate. Canola biodiesel, is

around 80-90% saturated and consequently had a higher viscosity than the methyl ester stearate;

both have chain lengths of 18 carbon atoms. From the relationship observed, an equation, based off

the Grunberg-Nissan equation, was derived, modeling the dependence of viscosity on temperature

and fatty acid composition. Subsequently, if the fatty acid composition of potential biodiesel fuels

can be approximated, research and testing can be significantly reduced and viable biodiesel fuels can

be identified efficiently.

From the four biodiesel fuels tested, their dynamic viscosity at 40 oC was compared to that of

traditional ultra-low-sulphur-diesel (ULSD). From this comparison, it was seen that the biodiesel fuels

possess similar viscosities to ULSD.

15

7. Reference List

[1] European Union, “World: Oil Supplies will be Exhausted in 40 Years,” Czech Republic Business Bulletin, Sep-2004.

[2] T. Trainer, “The Death of the Oil Economy,” Earth Island Journal, vol. 12, no. 2, p. 25, 1997.

[3] A. Rashid and et al., “Biodiesel A Renewable Alternate Clean and Environment Friendly Fuel For Petrodiesel Engines: A review,” International Journal of Engineering Science and Technology, vol. 3, no. 10, pp. 7707-7713, 2011.

[4] J. V. Gerpen and G. Knothe, “Biodiesel Production,” in Biodiesel Handbook, 2nd ed., J. V. Gerpen, G. Knothe, and J. Krahl, Eds. Illinois: AOCS Press, 2005.

[5] J. V. Gerpen and G. Knothe, “Fuel Properties,” in Biodiesel Handbook, 2nd ed., J. V. Gerpen, G. Knothe, and J. Khral, Eds. Illinois: AOCS Press, 2005.

[6] C. A. W. Allen, K. C. Watts, R. G. Ackman, and M. J. Pegg, “Predicting the viscosity of biodiesel fuels from thein fatty acid ester composition,” Fuel, vol. 7, no. 8, pp. 1319-1326, 1999.

[7] “Brookfield Digital Rheometer MODEL DV-III Operating Instructions.” .

16

Appendices

Appendix i – Biodiesel Quality Standards

17

18

Appendix ii – Linear Trend Lines for the Relationship between the

Logarithm of Viscosity to Temperature

See next page.

19

20

21

22

23

24

25

26

Appendix iii – Derivation for the General Equation Relating Temperature,

Fatty Acid Composition and Viscosity

ln 𝜇 = 𝑚𝑇 + 𝑐

⇔ 𝜇 = 𝑒𝑚𝑇+𝑐

As the goal is to determine viscosity at any temperature, with reference to the viscosity at 40 oC as

the Grunberg-Nissan equation is referenced at this temperature, the viscosity can be determined as

the reference viscosity multiplied by the ratio between the viscosity at the desired temperature and

the viscosity at the reference temperature

⇒ 𝜇𝑥 = 𝜇𝑟 ∙ (𝜇𝑥

𝜇𝑟)

= 𝜇𝑟 (𝑒𝑚𝑇𝑥+𝑐

𝑒𝑚𝑇𝑟+𝑐)

= 𝜇𝑟𝑒𝑚(𝑇𝑥−𝑇𝑟)

In order to combine the above result with the Grunberg-Nissan equation, the ‘µr’ term must be

manipulated to yield ‘ln µr’

ln 𝜇𝑥 = ln𝜇𝑟𝑒𝑚(𝑇𝑥−𝑇𝑟)

= ln𝜇𝑟 + ln 𝑒𝑚(𝑇𝑥−𝑇𝑟)

∴ ln 𝜇𝑥 = ∑𝑦𝑖 ln 𝜇𝑖 + 𝑚(𝑇𝑥 − 𝑇𝑟)

𝑛

𝑖=1

27

Appendix iv – MatLab Procedure to Derive the Relationship between

Gradient Values and Fatty Acid Composition

[ 0.043 0.541 0.406

0 0.003 0.0060 0 0

0.010 0 00.700 0.236 0.0500.002 0.010 0.210

0 0 0

0 0.005 00 0.770 0

0 0 0

0 0 00 0 0.008

0

00

0.021 0.272 0.2060.021 0.271 0.203

0 0.001 0.003

0.355 0.118 0.0250.006 0.005 0.1050.351 0.123 0.13

0 0.003 0

0 0.385 00 0.388 0

0 0 00 0 0.0040 0 0.004

0

00

0.007 0.090 0.0690.029 0.361 0.2720.007 0.092 0.072

0.120 0.046 0.1480.124 0.041 0.0430.469 0.159 0.068

0 0.514 0

0 0.129 00 0.132 0

0 0 0.005

0 0 0.0010 0 0.001

0

00

0 0 0 0 0 00 0 0

0 0 0.037

0 0.008 0.2450 0.02 0.305

0 0.017 0.594

0.007 0.024 0.1710.03 0.215 0.39

0.235 0.102 0.0150.542 0.004 0.0010.03 0.01 0

0

00

0 0 0 0 0 0.096 0.012 0.035 0.580 0.179 0.063 0.008 0.027 ]

Matrix A – Fatty acid compositions. Each row is a different fuel and columns are the percentages of C6 to C20:1

[ −0.011−0.014−0.019−0.012−0.013−0.017−0.016−0.012−0.016−0.019−0.013−0.017−0.018]

Matrix B – The experimentally determined gradients

28

The input for matrix A

>> A=[0.043,0.541,0.406,0.01,0,0,0,0,0,0,0,0,0;

0,0.003,0.006,0.70,0.236,0.05,0,0.005,0,0,0,0,0;

0,0,0,0.002,0.01,0.21,0,0.77,0,0,0,0.008,0;

0.021,0.272,0.206,0.355,0.118,0.025,0,0.003,0,0,0,0,0;

0.021,0.271,0.203,0.006,0.005,0.105,0,0.385,0,0,0,0.004,0;

0,0.001,0.003,0.351,0.123,0.13,0,0.388,0,0,0,0.004,0;

0.007,0.09,0.069,0.12,0.046,0.148,0,0.514,0,0,0,0.005,0;

0.029,0.361,0.272,0.124,0.041,0.043,0,0.129,0,0,0,0.001,0;

0.007,0.092,0.072,0.469,0.159,0.068,0,0.132,0,0,0,0.001,0;

0,0,0,0,0,0.037,0,0.017,0.594,0.235,0.102,0.015,0;

0,0,0,0,0.008,0.2445,0.007,0.0235,0.171,0.542,0.0035,0.0005,0;

0,0,0,0,0.02,0.305,0.03,0.215,0.39,0.03,0.01,0,0;

0,0,0,0,0,0.096,0.012,0.035,0.58,0.179,0.063,0.008,0.027];

Input for matrix B

>> m=[-0.011;-0.014;-0.019;-0.012;-0.013;-0.017;-0.016-0.012;-0.016;-0.019;-0.013;-0.017;-0.018];

This command was used to solve for constants A-M for 𝒎

>> x = pinv (A)*m