CALCULATION OF PHYSICAL AND PHASE
EQUILIBRIUM PROPERTIES FOR BIOFUELS
PROCESSES
Aruma Christopher Okechukwu
24 September 2010
Supervised by: Professor Sandro Macchietto
Professor George Jackson
A thesis submitted to Imperial College London in partial fulfillment of the
requirements for the degree of Master of Science in Advanced Chemical
Engineering with Process Systems Engineering and for the Diploma of Imperial
College
Department of Chemical Engineering and Chemical Technology
Imperial College London
London SW7 2AZ, United Kingdom
i
Table of Contents
TABLE OF CONTENTS ....................................................................................................................................... II
ABSTRACT ................................................................................................................................................. IV
ACKNOWLEDGEMENT ............................................................................................................................... V
LIST OF SYMBOLS / ABBREVIATIONS ......................................................................................................... VI
Superscripts ......................................................................................................................................... vii
LIST OF FIGURES ....................................................................................................................................... VIII
LIST OF TABLES ...........................................................................................................................................IX
CHAPTER 1 ............................................................................................................................................... 1
INTRODUCTION ......................................................................................................................................... 1
1.1
NATURE OF THE BIODIESEL COMPOUNDS ........................................................................ 2
1.2 AIMS OF PROJECT ............................................................................................................................ 3
1.3 STRUCTURE OF THE THESIS ......................................................................................................... 3
CHAPTER 2 ............................................................................................................................................... 5
BIOFUELS: FEEDSTOCKS AND PRODUCTION PROCESSES. .......................................................................... 5
2.1
FEEDSTOCK FOR BIODIESEL .................................................................................................................. 6
2.2
BASIC CHEMISTRY OF TRANSESTERIFICATION REACTION ............................................................................ 7
2.2.1
Base Catalyzed Transesterification .................................................................................... 12
2.2.2 Acid Catalyzed Transesterification Reaction .......................................................................... 12
2.2.3 Conversion of Oil to its Fatty Acids and then to Biodiesel ...................................................... 12
2.2.4 Non-Catalyzed Transesterification of Oil and Fats ................................................................. 13
2.3
BIOETHANOL .................................................................................................................................. 13
2.4
BIOMETHANOL ................................................................................................................................ 14
2.5
BIOGAS.......................................................................................................................................... 15
2.6
PROPERTIES REQUIRED FOR BIODIESEL PROCESSES................................................................................. 15
SUMMARY................................................................................................................................................... 17
CHAPTER 3 ............................................................................................................................................. 18
3.1
STATISTICAL ASSOCIATING FLUID THEORY (SAFT) ...................................................................... 18
3.1.1 IDEAL CONTRIBUTION ................................................................................................................. 20
3.1.2 HARD SPHERE ............................................................................................................................. 20
3.1.3 THE DISPERSION CONTRIBUTION ............................................................................................... 20
3.1.4 CHAIN CONTRIBUTION................................................................................................................ 21
3.1.5 ASSOCIATION CONTRIBUTION .................................................................................................... 21
3.2
SAFT-GAMMA GROUP CONTRIBUTION METHOD ......................................................................... 23
HETERONUCLEAR VS HOMONUCLEAR SEGMENT.................................................................................................. 24
TANGENTIAL VS FUSED SEGMENT..................................................................................................................... 24
3.2
GROUP CONTRIBUTION IN SAFT-GAMMA ............................................................................................ 25
3.3
GROUPS NEEDED IN BIODIESEL SYSTEM................................................................................................. 31
3.5
CONCLUSION .................................................................................................................................. 31
CHAPTER 4 ............................................................................................................................................. 33
METHODOLOGY ....................................................................................................................................... 33
4.1
GROUP IDENTIFICATION AND PARAMETER ESTIMATION ........................................................... 34
ii
4.2
4.3
SELECTION OF EXPERIMENTAL DATA .......................................................................................... 34
PARAMETER OPTIMIZATION ....................................................................................................... 34
CHAPTER 5 ............................................................................................................................................. 36
RESULT AND DISCUSSION ........................................................................................................................ 36
5.1
PURE COMPONENTS ................................................................................................................... 36
5.1.1 Carboxylic Acids ...................................................................................................................... 36
5.1.2 GLYCEROL ............................................................................................................................... 39
5.1.3 ESTERS .................................................................................................................................... 40
5.2
MIXTURES ................................................................................................................................... 47
5.2.1 Carboxylic Acids/Alkane ......................................................................................................... 47
5.2.2 Esters/Alkane ......................................................................................................................... 49
CHAPTER 6 ............................................................................................................................................. 52
6.1
6.2
CONCLUSION .............................................................................................................................. 52
RECOMMENDATION/FUTURE WORK ......................................................................................... 53
APPENDIX .............................................................................................................................................. 54
REFERENCES ..................................................................................................................................... 61
iii
ABSTRACT
Recent policies around the world regarding global warming and the regular volatile oil
price suggest that there will be increased demand for Biofuels. Biofuels are produced
from renewable sources and emit less contaminant to the atmosphere. However, current
high cost of Biofuels when compared to fossil fuel is still a hindrance to their uses. One
of the ways to reduce the cost is through efficient design of the production process. This
requires, very limitedly available, physical and phase equilibrium properties of the
compounds used in the production.
In this work, a group contribution statistical associating fluid theory; SAFT-gamma is
applied for the prediction of the pure components and mixture phase behaviour of
compounds found in biodiesel production. The SAFT-gamma parameters for the groups
used to describe the compounds (esters and glycerol) were obtained by fitting to
experimental data. The performance of SAFT-gamma EoS was evaluated for the
prediction of pure component saturated vapour pressure and liquid density using the
fitted parameter. The results obtained show accurate prediction of the saturated liquid
density for all components considered with an overall %AAD of 0.72%. Also, vapourliquid equilibrium behaviour of ester + alkane; and carboxylic acid + alkane was
predicted using only pure component parameters. The phase equilibrium predictions for
the mixture of esters + alkane and carboxylic acid + alkane show good agreement with
experimental values.
iv
ACKNOWLEDGEMENT
I deeply appreciate the guidance and support I enjoyed from my supervisors; Prof
George Jackson and Prof. Sandro Macchietto. Special thanks to Vasileios Papaioannou
for his patience, understanding and advices.
I am most grateful to the People and Government of the Federal Republic of Nigeria for
providing the funding for my study at imperial College through the Petroleum
Technology Development Fund.
v
LIST OF SYMBOLS / ABBREVIATIONS
C = number of carbons
η = Bartlett correction
A = Helmholtz free energy
T = temperature
Ns = number of spherical segments
N = number of molecules
ρs = molecular density
Λ = thermal de Broglie wavelength
U = intermolecular potential
k = Boltzmann constant
ms = number of segment
V = volume
εkk = square well energy
λkk =Range
Sk = Shape factor
σ = diameter of spherical segment
n = experimental data number
y1 = composition of component 1 in the gas phase
x1 = composition of component 1 in the liquid phase
Ps = saturated vapour pressure
vi
ρl = saturated liquid density
Abbreviations
SAFT = Statistical Association Fluid Theory
FAME = Fatty Acid Methyl Esters
AAD = Average Absolute Deviation
OBJ = objective function
EoS = equation of State
Superscripts
exp = experiment value
calc = calculated value
sat = saturated property
mono = contribution from monomer system
chain = contribution from chain formation
association = contribution due to association
ideal = contribution from ideal state
HS = hard sphere property.
vii
LIST OF FIGURES
Figure 2.1: Transesterification reaction of triglyceride with Methanol to form FAME and
Glycerol........................................................................................................................................... 7
Figure 2.2: Reaction of f Triglyceride with Water to form Diglyceride and Fatty Acid................. 8
Figure 3.1: Cartoon of (a) alcohol molecule within SAFT formalism. ......................................... 18
Figure 3.2: Different representation of Propane............................................................................ 24
Figure 3.3: (a) Spherical tangentially bonded united-atoms of a Propane model. (b) Fused
segment, United-atom model. ....................................................................................................... 24
Figure 3.4: Predicted vapor-liquid equilibria diagrams for binary mixtures of ethanol and 1butanol with the SAFT-gammagroup contribution approach using the parameters obtained from
the pure component data. .............................................................................................................. 30
Figure 3.5: Predicted vapour–liquid equilibrium for binary mixtures of n-heptane + pentanoic
acid with the SAFT-gammagroup contribution approach using the parameters obtained from the
pure component data.. ................................................................................................................... 30
Figure 5.1: Temperature vs. Liquid and vapour density of glycerol. ............................................ 40
Figure 5.2: Pressure vs. Temperature plot for glycerol. ................................................................ 40
Figure 5.3: Pressure-temperature plots of vapour pressure of ethyl esters.................................... 42
Figure 5.4: Temperature vs. saturated liquid density plots for ethyl esters in table 5.8.. .............. 43
Figure 5.5: Pressure-temperature plots of vapour pressure of biodiesel.. ...................................... 46
Figure 5.6: Predicted vapour-liquid equilibrium for n-heptane (component 1) and pentanoic acid
(component 2), at different temperatures using SAFT-gammaMethod. ....................................... 49
Figure 5.7: Vapour-Liquid equilibrium of a mixture of heptane (component 1) and propyl
butanoate. ...................................................................................................................................... 50
Figure 5.8: Vapour-Liquid equilibrium of a mixture of nonane and propyl ethanoate (comp. 1). 50
Figure 5.9: Vapour-Liquid equilibrium of a mixture of heptane (comp.1) and propyl propanoate.
....................................................................................................................................................... 51
Figure 5.10: Vapour-Liquid equilibrium of a mixture of nonane and propyl butanoate (comp. 1).
....................................................................................................................................................... 51
viii
LIST OF TABLES
Table 1.1: Projected Production Cost of Biodiesel compared to petroleum diesel (Dollars per
Gallon) _____________________________________________________________________ 2
Table 2.1: Chemical Structures of common Fatty Acids _______________________________ 9
Table 2.2: Fatty Acids of Non Edible Oils. _________________________________________ 10
Table 2.3:Fatty Acid composition of Oils __________________________________________ 11
Table 2.4: Properties Required For Biodiesel Processes_______________________________ 16
Table 3.1: Individual Group Parameters for the SAFT-gammaEquation of State ___________ 27
Table 3.2: Cross group energy parameters (εkl/kB)/K for the SAFT-gammaequation of state __ 28
Table 3.3: Self- and cross-association energies, for the SAFT-gammaequation of state in units of
K _________________________________________________________________________ 27
Table 3.4: Average absolute deviations (%AAD) of vapor pressures Ps and saturated liquid
densities ρl of the SAFT-gammapredictions compared to experiment.____________________ 29
Table 3.5: Groups needed for modelling biodiesel compounds _____________________ 32
Table 5.1 : Parameter values for Different Models of carboxylic acid functional group ______ 36
Table 5.2: Average Absolute Deviations (%AAD) of predicted saturated liquid density compared
to experimental data [19] for carboxylic acid _______________________________________ 37
Table 5.3: Average Absolute Deviations (%AAD) of predicted saturated vapour pressure
compared to experimental data [19] for carboxylic acids ______________________________ 38
Table 5.4: Average Absolute Deviations (%AAD) of predicted saturated vapour pressure and
liquid density compared to experimental data [19] for fatty acids _______________________ 38
Table 5.5: Parameters for Glycerol modeled as 3 identical segments with 9 associating sites __ 39
Table 5.6: Average Absolute Deviations between predicted and experimental vapor pressure and
liquid density [19]. ___________________________________________________________ 39
Table 5.7: Parameter for Ester Functional group and Cross interaction energy with alkyl groups
___________________________________________________________________________ 41
Table 5.8: Average Absolute Deviations between predicted and experimental vapor pressure and
liquid density [19] of components used in regression _________________________________ 44
Table 5.9: Average Absolute Deviations between predicted and experimental vapor pressure and
liquid density [19] for components not included in regression __________________________ 45
Table 5.10: Average Absolute Deviations between predicted and experimental vapor pressure
and liquid density [19] for some biodiesel. _________________________________________ 46
ix
Table A 1: Experimental data and predicted values by SAFT-gamma method for a binary mixture
of heptane and pentanoic acid at 323.15K using different acid groups____________________54
Table A 2: Experimental data and predicted values by SAFT-gamma method for a binary mixture
of heptane and pentanoic acid at 348.15K using different _____________________________54
Table A 3: Experimental data and predicted values by SAFT-gamma method for a binary mixture
of heptane and pentanoic acid at 373.15K using different acid groups____________________55
Table A4: Experimental data and predicted values by SAFT-gamma Method for a binary mixture
of heptanes and propyl butanoate for a given composition of heptane in the liquid phase____ 56
Table A5: Experimental data and predicted values by SAFT-gamma Method for a binary mixture
of heptane and propyl propanoate for a given composition of heptane in the liquid phase____57
Table A6: Experimental data and predicted values by SAFT-gamma Method for a binary mixture
of nonane and propyl ethanoate for a given ester composition in the liquid phase__________58
Table A7: Experimental data and predicted values by SAFT-gamma Method for a binary mixture
of nonane and propyl butanoate for a given ester composition in the liquid phase__________59
x
_________________________________________________________________________________________________ 1. Introduction
Chapter 1
INTRODUCTION
The current high cost of Biofuels can be reduced through improve design of their
production processes. Biofuels include both gaseous and liquid fuels that are produced
from biomass. This includes biodiesel, bio-alcohols, bio-synthetic gases and biohydrogen. At present, Biodiesel costs over twice the price of petroleum diesel. This is
largely due to cost of feedstock which account for 70-80% of the total cost while the
processing cost is between 20 – 30%. Table 1.1 gives the price of biodiesel produced
from soybeans and grease compared to petroleum diesel. The high cost is militating
against the increased use of biofuels despite their many advantages of using Biofuels.
The use of biofuels as a transport fuel could result to an average GHG emission
reduction of about 57% compared to the emissions that would have occurred from the
production and use of equivalent quantities of petroleum fuels (Global Renewable Fuels
Alliance, 2009). With the regular unstable oil price, recent policies on the reduction of
carbon emission, concern over security of oil supply and issue of renewability of fossil
fuel, many nations look up to biofuels as a good source of renewable and clean energy.
Other than emission reduction, biodiesel has other advantages over petroleum diesel.
Biodiesel has higher cetane number 45.8 to 56.9 as compared to 40 to 52 of petroleum
diesel. This means that biodiesel ignites more quickly than petroleum diesel; an
important feature of diesel fuel. Biodiesel has superior lubricity and is sometimes
blended with petroleum diesel for increased lubricity. Biodiesel and other biofuels are
derived from domestic and renewable sources and, therefore, can protect non petroleum
producing nations from fluctuating oil price. Biofuels are equally biodegradable and
nontoxic.
Recent policies around the world regarding global warming suggest that there will be
increased demand for biofuels. In March 2007, the European Union agreed to meet a
10% target of biofuels for transportation fuel needs by 2020 (EU Energy Policy2 2010).
The united states target a production of 36 billion gallons of renewable fuel by 2022. It is
1
_________________________________________________________________________________________________ 1. Introduction
believed that Biofuels are the main near-term alternative for insulating consumers against
oil price and lowering the transportation sector’s carbon footprint (Jim Lane 2010).
This work will focus on biodiesel and other types of biofuels are discussed here for
completeness.
Two ways have been proposed for reducing the cost of biodiesel – the use of cheaper
feedstock and the efficient design of the separation processes involved in the production.
The efficient design of the separation processes requires accurate knowledge of various
physical properties and the phase behaviour of the compounds present in the system. One
could have used one of the many equations of state or other simple methods for
calculating the properties but these compounds belong to a peculiar class of fluids.
Table 1.1: Projected Production Cost of Biodiesel compared to petroleum diesel (Dollars
per Gallon)
Marketing Year
Soybean oil
Yellow Grease
Petroleum
2009/2010
2.57
1.42
0.75
2010/2011
2.67
1.47
0.76
2011/2012
2.73
1.51
0.76
2012/2013
2.80
1.55
0.75
Source: Anthony, R. (2002)
1.1
NATURE OF THE BIODIESEL COMPOUNDS
The biodiesel system consists of water, long-chain carboxylic acids and fatty acid methyl
esters, glycerol and methanol. Such systems include both polar and associating
compounds. These features make them exhibit highly non-ideal behaviour and hence
their property prediction more challenging. Thus, classic equations of state and other
method for simple molecules are of very limited application.
2
_________________________________________________________________________________________________ 1. Introduction
Various methods have been proposed for calculation of the properties of systems of this
type taking into account the association and polar nature of the compounds. All of the
methods require as input molecular parameters that have to be based on experimental
data. However, there are very limited experimental data on the compounds and mixtures
of interest here. Providing required data through experiments can also be very expensive
and time consuming.
Statistical Associating Fluid Theory (SAFT) proposed by Chapman et al (1990) accounts
explicitly for hydrogen interaction and has a strong statistical mechanical basis. Different
versions of SAFT have been successfully used to model complex systems including
aqueous system and polymers. A version of SAFT- SAFT-gamma by Lymperiadis et al,
2007- combines the accuracy in modelling of thermodynamic properties of SAFT – type
methods with the predictive capabilities of a group contribution method. SAFT-gamma
has been successfully used in predicting pure component and mixture vapour-liquid
behaviour of associating compounds including carboxylic acids and alcohols. SAFTgamma will be used in this work.
1.2 AIMS OF PROJECT
This work is aimed at evaluating the suitability of SAFT-gamma methods in the
calculation of the phase equilibrium properties of both the pure components and mixtures
common in biodiesel production. This will include extending the SAFT-gamma
parameters table to include functional groups present in biodiesel compounds. The fitted
parameters will be used to predict the physical and phase equilibrium behaviour of some
pure compounds and mixtures of compound involved in biodiesel processing.
1.3 STRUCTURE OF THE THESIS
This work is organized in the following chapters:
Chapter 1 is an introduction to the work. A summary of the aim and methodology is also
presented in this chapter.
3
_________________________________________________________________________________________________ 1. Introduction
Chapter 2 will provide an overview of the feedstock used in the production of Biofuels,
the production processes and the different compounds and groups present in the
production processes.
Chapter 3 will discuss the theory of Statistic Associating Fluid Theory (SAFT) and also
give an overview of the principle of SAFT-gamma equation of State.
Chapter 4 will describe the methodology used in obtaining the parameters for different
groups in the system.
Chapter 5 presents the results and discussion.
Chapter 6 will give the conclusions and areas of further research.
4
Chapter 2
BIOFUELS: FEEDSTOCKS AND PRODUCTION PROCESSES.
Biofuels are of three classes; biogas, bio-alcohol and biodiesel. Biodiesel is composed of
mono-alkyl esters of long chain fatty acids- typically of chain length C14-C22 derived
from vegetable oil and animal fats. These oils are made up of triglycerides which when
reacted with alcohol, form fatty acids methyl esters (FAMEs) and glycerol. Proposed
alcohols for use as biofuels include methanol, ethanol, propanol and butanol. Only
methanol and ethanol have been used in commercial quantity. Biogas is made up of
methane and carbon dioxide. Biofuels are primarily for use in the automotive engines.
(Demirbas, 2009). Biodiesel is used as diesel fuel. Bio-alcohol is either blended in
gasoline to increase the latter's octane rating or used as a substitute for gasoline.
Biofuels are biodegradable and emit less toxic pollutants than petroleum diesel.
Biodiesel is considered better than petroleum-based diesel in terms of sulfur content,
flash point, aromatic content and functions well in the current diesel fuel engines.
Therefore, it will not be required to build new distribution network for Biodiesels.
(Demirbas, 2009).
Although, biofuels do as well as fossil fuel, the latter is preferred because it is far
cheaper than biofuels. Biodiesel costs over twice the price of petroleum diesel at present.
This is largely due to cost of feedstock which account for 70 – 80% of the total cost
while the processing cost is between 20 – 30%. As the world’s petroleum reserve gets
depleted, and environmental and political concerns arise, biofuels are at the forefront of
replacing fossil fuel. Some countries- United States and some members of the European
Union - have legislation for the compulsory blend of an increasing amount of biodiesel
with diesel fuel. Biofuels are produced from renewable sources and every country with
good agricultural base can produce their diesel. Since it is environmentally friendly, less
tax will be paid for environmental pollution.
The following sections will provide the summary of the feedstock and production
processes involved in the producing of the three classes of biofuels. Biogas and bioalcohol are discussed here only for completeness and will not be treated further in this
5
work. Finally, the thermophysical properties of interest, based on the needs of the
production processes, will be highlighted setting in that way targets for the
thermodynamic modelling of these systems.
2.1
Feedstock for Biodiesel
Biodiesel is mainly produced from vegetable oils, animal fats and recycled grease.
Vegetable oils contain triglycerides also known as triacylglycerol, free fatty acids (FFA),
phospholipid and other minute contaminants. Animal tallow has much higher level of
free fatty acids but is a viable feedstock for biodiesel because it is cheaper. Different
sources of vegetable oil are listed in Table 2 and 3. The fatty acid attached to the glycerol
backbone can be of different chain lengths. The percentages of individual fatty acids
present in different vegetable oil sources are shown in Table 2 and 3 show. The free fatty
acids and phospholipids in vegetable oil are usually removed through refining and
degumming respectively. While it is necessary to degum the oil, the free fatty acids can
be converted to biodiesel using appropriate catalyst. Recycled grease is usually a
combination of both animal fats and vegetable oil and other impurities associated with
household waste.
The use of these edible oils in biodiesel production has contributed immensely to
biodiesel high cost. This is due to the competing demand for food and other commercial
uses. Azam et al (2005) investigated the potentials of using non-edible oils from trees,
shrubs and herbs commonly found in India. It is shown that some of these oils have
enormous potential as feed-stocks for biodiesel production. There has been recent
research in the use of other non edible oil sources. (Akbar et al., 2009; Chakraborty et al.,
2009; Zang et al., 2003). Veljković et al. (2006) studied the potential production of
biodiesel from crude tobacco seed oil. Rashid (2008) investigated the suitability of
Moringa Oleifera oil. Also, the used of oil from rubber was studied. (Ikwuagwu et al.,
2000; Ramadhas et al., 2005). Some of the fatty acid compositions for non edible oil
sources are given in Table 3
Researchers have shown that some algae contain natural oil which can be converted to
esters for use as biodiesel. (Sheehan et al., 1998). Algae are made up of carbohydrates,
protein and natural oil. The natural oil and carbohydrate are possible biofuel feedstock.
6
Algae can be gasified to produce biogas, fermented to bioethanol or transesterified to
biodiesel. Sheehan et al (1998) studied the possible use of different species of algae for
biofuel production. However, the cost of microalgae production is still a drawback to
their use. Researchers are studying the possible genetic modifications of oil containing
algae for increased oil yield.
2.2
Basic Chemistry of Transesterification Reaction
Transesterification is the reaction of triglycerides of a fat and oil with an alcohol to form
ester and glycerol. The triglycerides are almost insoluble in alcohol, and as result, a
catalyst is usually added. Recently, the use of co-solvent and supercritical methanol has
been proposed. (Cao et al., 2005) The reaction is a reversible reaction and excess alcohol
is normally used to increase the yield of biodiesel. The general reaction scheme is shown
below.
O
O
CH2 – O – C – R1
O
CH2 – O – C – R2
+
3 CH3OH
Catalyst
O
CH2 – O – C – R2
O
+
CH – OH
O
CH2 – O – C – R3
Triglyceride
CH2 – OH
CH2 – O – C – R1
CH2 – O – C – R3
Fatty Acid Methyl Esters
Methanol
CH2 – OH
Glycerol
(Triacylglycerol)
Figure 2.1: Transesterification reaction of triglyceride with Methanol to form FAME
and Glycerol
Fats and oils usually contain free fatty acids and water in addition to triglycerides. Other
side reaction included the hydrolysis of the triglyceride in the presence of water to form
diglyceride and fatty acid. The reaction scheme is given in figure 2.2
7
O
CH3 – OH
CH2 – O – C – R1
O
CH2 – O – C – R2
+
H2O
CH2 – O – C – R2
O
+
HO – C – R1
O
CH2 – O – C – R3
Triglyceride
O
O
CH2 – O – C – R3
Diglyceride
Water
Fatty acid
Figure 2.2: Reaction of f Triglyceride with Water to form Diglyceride and Fatty Acid
Catalysts in use include alkaline, mineral acids and enzymes. The use of enzyme in
commercial quantity is limited to Japan. (Gerpen et al., 2004). The presence of free fatty
acids determines the choice of catalyst used.
Many primary alcohols have been used for biodiesel production. These include
methanol, ethanol, isopropanol and butanol (Gerpen et al., 2004). The choice of which
alcohol to use is determined by its cost, water content, ease of recovery for recycle and
the quantity required. For instance, ethanol can be used but forms azeotropic mixture
with water which makes it recovery more expensive. High water content can lead to poor
esterification reaction resulting in high yield of free fatty acids and soap. Methanol is
widely used because it is cheaper and easier to recover. The alcohol is usually added in
excess of the oils (6:1) to drive the reaction as close to completion as possible. The
excess alcohol is recovered and recycled back into the process to minimize operating
cost.
8
Table 2.1: Chemical Structures of common Fatty Acids
Fatty
C: Double Chemical Structure
acids
Bond
Myristic
14:0
CH3(CH2)12COOH
Palmitic
16:0
CH3(CH2)14COOH
Stearic
18:0
CH3(CH2)16COOH
Oleic
18:1
CH3(CH2)7 CH=CH(CH2)7 COOH
Linoleic
18:2
CH3(CH2)4 CH=CHCH2CH=CH(CH2)7 COOH
Linolenic
18:3
CH3CH2 CH=CHCH2CH=CHCH2 CH=CH(CH2)7 COOH
Arachidic
20:0
CH3(CH2)18 COOH
Behenic
22:0
CH3(CH2)20 COOH
Erucic
22:1
CH3(CH2)7 CH=CH(CH2)11 COOH
In the next sections, the four major biodiesel routes are described. The routes are
classified based on the catalyst used namely: base catalyzed, Direct Acid-catalyzed,
Conversion of oil first to fatty acid and then to biodiesel and Non-catalytic
transesterification.
9
Table 2.2: Fatty Acids of Non Edible Oils.
Oil / fat
Myristic
Palmitic
Palmoleic
Stearic
Oleic
Linoleic
Linolenic
Arachidic
Behenic
14:0
16:0
16:1
18:0
18:1
18:2
18:3
20:0
22:0
-
6.5
-
6
72.2
1
-
4
Jatropha curcas
0.1
14.2
0.7
7.0
44.7
32.8
0.2
Terminalia
-
32.2
0.5
6.4
31.3
28.8
Rubber seed
-
10.2
-
8.7
24.6
Yellow grease
2.43
23.24
3.79
12.96
44.32
Moringa
others
Ref.
7.1
3.2
(49)
0.2
-
-
(1)
-
0.3
-
-
(8)
39.6
16.3
-
-
-
(48)
6.97
0.67
-
-
-
(29)
Oleifera
10
Table 2.3: Fatty Acid composition of Oils
Oil or fat
Myristic
Palmitic
Palmoleic
Stearic
Recinoleic
oleic
Linoleic
linolenic
14:0
16:0
16:1
18:0
8.1
18:1
18:2
18:3
Arachidic
Erucic
others
20:0
22:1
0–2
20 – 25
-
1–2
23 – 35
40 – 50
-
-
-
Soybean
-
6 – 12
-
2–5
20 – 30
50 – 60
5 – 11
-
-
Rapeseed
-
3.5
-
0.9
64.1
22.3
8.2
-
-
Sunflower
-
6.4
0.1
2.9
17.7
72.9
-
-
-
-
4–7
-
2–4
25 – 40
35 – 40
25 – 60
-
-
11.4
0
2.4
48.3
32.0
0.9
4.0
Cottonseed
Ref
(23)
-
(23)
(15)
..
(15)
seed
Linseed
Peanut kernel
(23)
(15)
11
Poppyseed
-
12.6
0.1
4.0
22.3
60.2
0.5
-
-
(15)
Safflower
-
7.3
-
1.9
13.6
77.2
-
-
-
(15)
-
13.1
-
3.9
52.8
30.2
-
-
-
(15)
1.1
44.1
0.2
4.4
-
39.0
10.6
0.3
0.2
0.2
Olive
-
9 – 10
-
2–3
-
73 - 84
10 – 12
-
-
-
Peanut
-
8–9
-
2–3
50 – 65
20 – 30
-
-
-
Castor oil
-
1.1
-
3.1
4.9
1.3
-
Bay laurel leaf
-
25.9
0.3
3.1
10.8
11.3
17.6
31.0
-
-
(15)
Hazelnut kernel
-
4.9
0.2
2.6
83.6
8.5
0.2
-
-
-
(15)
Walnut kernel
-
7.2
0.2
1.9
18.5
56.0
16.2
-
-
-
(15)
Olive kernel
-
5.0
0.3
1.6
74.7
17.6
-
0.8
-
-
(15)
3-6
24 – 32
-
20 – 25
37 – 43
2 -3
-
-
-
1–2
28 – 30
-
12 – 18
40 – 50
7 – 13
0–1
-
-
seed
Sesame
seed
Palm oil
Tallow
Lard
89.6
-
(29)
(23)
-
(23)
(15)
(23)
-
(23)
___________________________________________________________________2. Biofuels: feedstock and production processes
2.2.1 Base Catalyzed Transesterification
Sodium hydroxide and Potassium hydroxide are the most commonly used base catalysts.
Sodium hydroxide is preferred because it is cheaper and has a high product yield (Demirbas,
2009) Base catalyst is generally faster than acid-catalysts. However, the base reacts with any
containing fatty acid to form soap. It is therefore necessary to first reduce the free fatty acid
in the oils by refining process. Alternatively a high free acid content feed-stock is usually
reacted in acid catalyzed system first.
The base catalyst is dissolved in excess methanol and then reacted with the oil in a reactor.
After the reaction, two liquid phases are produced – one rich in FAME and the other rich in
glycerol. Acidified water is added to the reactor content to neutralize the base and also wash
both the esters and glycerol. The acid also converts any soap present to fatty acid. The two
liquid phases are separated by settling. The excess methanol is distributed between the esters
and glycerol phases.
2.2.2 Acid Catalyzed Transesterification Reaction
When the feedstock contains very high level of free fatty acids and water, acid catalyzed
transesterification is preferred to the use of base catalysts (Gerpen et al., 2004, Demirbas,
2009). This is to avoid the formation of soaps which will interfere with the reaction rate.
Acids in used include sulphuric acid and phosphoric acid. The methanol reacts with free
fatty acids to form ester and water. A base is then added to neutralize the acid catalyst. The
resulting mixture consists of ester and triglycerides and can be used directly in a
conventional base-catalyzed system described in above.
2.2.3 Conversion of Oil to its Fatty Acids and then to Biodiesel
This is an alternative process for converting oils and Fats with high level of free fatty acid
and water. The triglycerides in the oil and fats are first hydrolyzed to free acid and glycerol
using steam and sulphuric acids. The free fatty acid is separated from glycerol and the acid
convert to esters.
12
___________________________________________________________________2. Biofuels: feedstock and production processes
2.2.4 Non-Catalyzed Transesterification of Oil and Fats
Saka et al. (Saka & Kusdiana, 2001) and Demirbas, (Demirbaş, 2003) proposed the use of
supercritical methanol for the transesterification of oil and fats. With a combination of
selected reaction conditions, excess supercritical methanol (350 -400oC, and pressure greater
than 80 atm), can convert vegetable oils and fats to ester and glycerol without a catalyst. The
resulting product is a mixture of esters, methanol and glycerol. This makes the separation of
products easier than in other transesterification processes. This reduces both production cost
and energy consumption. While the above may be interesting, the scale up to commercial
process is difficult (Gerpen et al., 2004).
Another non-catalytic system is the BIOX process developed in Canada. This uses a
cosolvent -tetrahydrofuran- to overcome the low solubility of methanol in oils and fats. The
boiling point of the cosolvent is very close to that of methanol making it possible to recover
the two in a single step for recycling. Note that there is no need to separate methanol from
the cosolvent. The ester and glycerol is the separated. The process is very close to
commercial use (Gerpen et al). Cao et al. (2005) proposed the use of propane and CO2 as
cosolvents, they achieved high conversion with low reaction time operating at 540 K and
pressures around 12 MPa.
2.3
Bioethanol
Bioethanol simply means ethanol produced from biomass. Years ago, a German inventor
known as Nikolaus August Otto conceived his invention of running the combustion engine
using ethanol.
Bioethanol is at present, the most widely used biofuel with America and Brazil as the
highest producers and users. Today, ethanol is mainly used as a blend with gasoline fuel.
The use of ethanol can reduce particulate emissions and increase the octane number of the
fuel. Bioethanol is produced from three basic raw material types; sugar, starch and
lignocellulosic material.
13
___________________________________________________________________2. Biofuels: feedstock and production processes
The sugar containing raw materials includes sugarcane and sugar beets. Brazil uses
sugarcane for ethanol production. These materials are easier to ferment as they contain
disaccharide and do not require any pre-treatment. The sugar, mainly sucrose, is first
hydrolyzed to glucose and fructose and then fermented to ethanol.
Starchy feedstocks include all plant materials containing carbohydrate. The mostly used is
corn by the United States of America. Other feed stocks in this category include potatoes
and cassava. Starch is converted by fermentation into ethanol. Fermentation is an anaerobic
process in which enzymes usually yeast converts sugar to ethanol. For details of the
chemistry of sugar fermentation see Ashok (2009). The ethanol usually has high amount of
water. The bioreactor effluent is fed to an evaporator to separate the ethanol/water mixture
from the solid part. The mixture is taken for distillation. Note that ethanol forms azeotropic
mixture above 95% concentration. (Demirbas, 2009).
As a result of competing demand for food materials, bioethanol researchers are focusing on
producing ethanol from lignocelluloses materials such corn stock, wheat straw, pulpwood,
algae and municipal waste. These materials composed of cellulose; hemicelluloses and
lignin are very cheap feedstock compared to others. Cellulose and hemicelluloses are
polysaccharides which can be enzyme or acid-hydrolyzed to monosaccharide and eventually
fermented to ethanol. However, there two major drawbacks to their use. In their molecule,
there is a cross linking between the cellulose, hemicelluloses and lignin which makes it
difficult to extract the sugar. Furthermore, high percentage of hemicelluloses is Pentose
which is difficult to ferment.
2.4
Biomethanol
Methanol can be used as alternative liquid fuel, which can be used directly for powering
Otto engines. Methanol is less used as motor fuel than ethanol but it is hoped that its use in
the future will increase. It is currently blended with gasoline (Chmielniak & Sciazko, 2003).
Biomethanol are produced from biogas, pyrolysis of wood and gasification of biomass. The
14
___________________________________________________________________2. Biofuels: feedstock and production processes
use of energy crops for biogas/ methanol production is been studies by researchers. It could
be possible to use special fast growing grasses and trees as feedstock in future.
2.5
Biogas
All biomass can be gasified to form biogas also called synthetic gas. Biogas is made up
mainly methane and carbon dioxide with small traces of hydrogen, hydrogen sulphide and
carbon monoxide. Biogas is formed when anaerobic bacteria breakdown organic materials in
the absence of oxygen. Animal dung, sewage sludge, waste water, agricultural residues and
municipal waste is common feedstock for biogas production. The materials are fed in a
bioreactor with anaerobic bacteria. The gas formed is collected at the top of the reactor exit.
Biogas is mainly used for electricity generation and heating. With the removal of impurities,
biogas is very important route to the production of methanol (George et al., 2006).
2.6
Properties Required For Biodiesel Processes
The production process for biodiesel involves the separation of various products whose
purity is critical to the cost of the produced biodiesel and the economic viability of the
whole process. For instance, the recovery of high quality of glycerol is primary option to be
considered to lower the cost of biodiesel. (Demirbas, 2009). The high grade glycerol can be
used as raw material for other products such as pharmaceuticals and possibly in hydrogen
production.(Wen et al., 2008). It is predicted that in the biofuel industry, the processing
technologies will play a key role in determining industry leaders and maximizing
profitability (Ashok, 2009).
The composition of the reaction mixture generally depends on the type of transesterification
used. Typically, the system is made up of methanol, glycerol, water, fatty acid methyl esters,
free fatty acid and unreacted triglyceride. Sometimes, diglyceride and monoglyceride can
also be present. When supercritical methanol is used, the reaction mixture consists of
methanol, FAMEs and glycerol. If co-solvents like tetrahydrofuran or hexane is used, the
solvent and methanol are considered as a single component – pseudocomponent... The
15
___________________________________________________________________2. Biofuels: feedstock and production processes
solvent is not separated from methanol before recycling. After the reaction, two liquid
phases are formed. One phase is rich in glycerol and the other in FAMEs. The two liquid
phases are separated by settling. Each of the phases contains, in addition to the major
component, methanol, fatty acids, water and unreacted triglyceride. The two liquid phases
are purified in separate distillation columns.
From the description above, three separation sections are involved in the production of
biodiesel namely the separation of the two liquid phases in the reactor and the two
distillation columns for the purification of glycerol and FAMEs. The design of these
separators requires both the physical and phase behaviour of the different compounds in the
system. Both the liquid – liquid and vapour – liquid equilibria data are need. See table 2.4.
Table 2.4: Properties Required For Biodiesel Processes
Pure Components
Mixtures

Saturated density

Heat capacity

Vapour pressure

Kinematic Viscosity

Thermal conductivity

Methyl ester + methanol + glycerol

Boiling point

Methyl esters + methanol

Methyl ester + glycerol

Methyl ester + methanol + glycerol + hexane

Methanol + glycerol
Liquid-liquid equilibrium

Methyl esters and glycerol
Vapour-liquid equilibrium
This work will be focusing on the pure component saturated density, vapour pressure and
vapour-liquid equilibria of mixtures.
16
___________________________________________________________________2. Biofuels: feedstock and production processes
Summary
This chapter discussed three classes of Biofuels – biodiesel, bio-alcohol and biogas. The
various sources of raw materials for the production of Biofuels are also highlighted. These
fuels can do as well as those produced from fossil fuel. Among other advantages, biofuel
fuels are produced from renewable sources and produce fewer emissions than fossil fuel.
However, their used is hindered by their high cost. The two ways to reduce the cost of
Biofuels are through using cheaper raw materials and efficient design of the production
processes. Efficient design and optimization of the process can reduce production cost by
providing highly purified products and through energy savings. The production process of
biodiesel involves liquid – liquid and vapour – liquid separation. This requires the
knowledge of the physical and phase equilibrium of the compounds present in the mixture
including methanol, glycerol, water, fatty acids, triglycerides and fatty acid methyl esters
(biodiesel).
The next chapter will discuss the various methods that have been applied for the calculation
of properties and phase equilibrium of compounds that are present in biodiesel processing
system.
17
______________________________________________________________________________________________ 3. Theory of SAFT EoS
Chapter 3
3.1
STATISTICAL ASSOCIATING FLUID THEORY (SAFT)
Statistical Associating Fluid Theory (SAFT) (Chapman et al., 1989; Chapman et al., 1990) is
based on Wertheim’s Thermodynamic Perturbation Theory for associating and chain fluids.
In SAFT, molecules are represented as chains of tangentially bonded spherical segments
interacting through a potential. Short range sites are placed in the segments to account for
hydrogen bonds through which different segments can bond together.
i
1
m
...
3
m
...
3
j
2
(a)
2
1
(b)
Figure 3.1: Cartoon of (a) alcohol molecule within SAFT formalism. The molecule is made
up of m tangentially bonded segments representing the aliphatic chain and two associating
sites i and j accounting for the proton and electron pair, respectively of oxygen in the –OH
radical. (b) n-alkane (no associating site)
18
______________________________________________________________________________________________ 3. Theory of SAFT EoS
Figure 4.1 shows a simple model of alcohol molecule. The molecule is made up of m equal
sphere (segment) representing the aliphatic chain. The segment may represent CH3, CH2,
OH or any combination of the three and is taken as a united atom group. Two associating
sites i and j, for instance, is placed in the OH radical to account for its hydrogen bond. In the
case of n-alkanes, there is no associating site due to absence of hydrogen bonding. In the
original SAFT by Chapman et al, all the segments/spheres are considered to be of the same
size.
The EOS of a fluid is given in terms of the residual Helmholtz energy which is the
difference between the total molar Helmholtz energy and that of the ideal gas at the same
molar density and temperature.
Aresidual(T,ρ) = A(T,ρ) – Aideal(T,ρ)
3.1
The residual Helmholtz energy is further expressed as a sum of a series of term that
represent the contributions of different intermolecular effects to the intermolecular potential
of the molecule. These contributions include that from segment repulsion-dispersion, from
chain formation and from association between different segments.
Aresidual a = Aseg + Achain + Aassoc
3.2
The superscripts refer to contribution from segment interactions, chain formation and
association between segments. The segment contribution is made up of the hard sphere and
contribution due to attraction/dispersion between the spheres. From equations 4.1 and 4.2,
and dividing by NkT, the reduced Helmholtz energy is given by
=
3.3
where N is the number of molecules, T the temperature, ρ the molar density and k the
Boltzmann constant. The superscripts HS and disp denote hard sphere and dispersion
19
______________________________________________________________________________________________ 3. Theory of SAFT EoS
(attraction) contribution respectively. The different contributions are briefly described
below.
3.1.1 IDEAL CONTRIBUTION
The Helmholtz energy of N molecules of ideal gas is given by
3.4
where
is the total number density. V is the volume occupied by the gas at a
temperature T and
is the energy contribution for the non translational degree of
freedom.
3.1.2 HARD SPHERE
The commonly used hard sphere term is the Carnahan-Starling expression given below.
3.5
where
is the packing fraction (reduced density) and m is the number of
segments per molecule.
3.1.3 THE DISPERSION CONTRIBUTION
In the pioneer work of Chapman et al, 1990, an expression proposed by Cotterman et al is
used.
3.6
where
20
______________________________________________________________________________________________ 3. Theory of SAFT EoS
3.1.4 CHAIN CONTRIBUTION
This is the free energy contribution to the system due to chain formation. The expression
depends on the nature of the original unassociated fluid and involves only its structural
properties (Chapman et al., 1990)
3.7
where m is the number of segment per molecule and
is the monomer-monomer
background function evaluated at a contact. For a fluid of hard sphere as in the original
SAFT,
can be approximated as below.
3.8
Where
3.9
3.1.5 ASSOCIATION CONTRIBUTION
The Helmholtz energy contribution due to association between sites on different segments is
obtained from Wertheim theory according to the expression below.
3.10
where is the number of sites and
is obtained from the solution of the simplified mass
action equation for site A:
A = 1, 2 ..., s
The association strength
is
21
3.11
______________________________________________________________________________________________ 3. Theory of SAFT EoS
3.12
where the radial distribution function of monomers
associated reference system
can be replaced with un-
.
In the SAFT method, there are many ways one could model individual segment making it
adaptable to several specific systems. Consequently, over the years, there have been many
proposed version of SAFT. The difference between the versions is mainly the intermolecular
potential models and modification of some of the contributions to the Helmholtz energy.
Some of the mostly used models include Lennard-Jones, square-well, the Sutherland,
Yukawa and Mie potentials.
SAFT accounts explicitly for hydrogen interaction and have a strong statistical mechanical
base. Different versions of SAFT have been used to successfully model complex systems
including aqueous system and polymers. A review of SAFT can be found in Muller &
Gubbins, (2001). Economou, (2002). Tan et al., (2008). A modified SAFT ((Huang &
Radosz, 1990) has been used to model fluids containing esters, carboxylic acids, alcohol and
water. A good agreement with experimental data was recorded. Nguyen et al (2005 & 2008)
used three different versions of SAFT to model vapour–liquid phase equilibrium of various
ester containing binary mixtures including: ester + ester, ester + alkane, ester + cyclohexane,
ester + alkyl-benzene, ester + xylene and ester + alcohols. A polar term with multipolar
segment approach was incorporated in the model to account for dipole and quadrupole
interactions. It is interesting to note that binary interaction parameters were not used in their
model for mixtures. It was noted that polar SAFT-VR gave a better correlation for heavy
esters than GC SAFT and original SAFT. Perturbed Chain SAFT has also been applied with
success to polar compounds (Dominik et al., 2005.;Gross & Sadowski, 2001b).
Coupling of SAFT with a group-contribution approach has been presented. These versions
of SAFT include simplified PC-SAFT, GC-SAFT and SAFT-gamma. This makes them
22
______________________________________________________________________________________________ 3. Theory of SAFT EoS
predictive. Most of them apply group contribution approach to obtain molecular parameters
(Tamouza et al.2004) while others distinguish between functional groups on molecular level.
(Lymperiadis et al., 2007; Peng et al., 2009).
It was generally observed that SAFT gave more reliable predictions when compared to other
methods.(Economou, 2002). A good advantage of using group contribution SAFT approach
is that it can be used to predict pure component properties unlike other methods that rely on
separate methods for pure component properties. The version of SAFT used in this work is
discussed in the next section.
3.2
SAFT-gamma GROUP CONTRIBUTION METHOD
SAFT-gamma (Lymperiadis et al., 2007 & 2008) couples a group contribution approach in
the earlier version of SAFT - SAFT-VR (Gil-Villegas et al., 1997). SAFT-gamma is a
heteronuclear generalization of the standard models used in SAFT in which the functional
groups are modelled as fused heteronuclear united-atom spherical segments. The repulsive
and attractive interaction potential between segments is described in terms of a simple
square-well model of variable range. The interactions between a spherical segment (group or
atom) of type k with another segment of type l is described in the square-well form as
3.13
where r denotes the distance between the centers of the two segments, σ
denotes the contact distance between the segments, and λ
23
λ σ
λ σ
σ
σ
σ
σ
______________________________________________________________________________________________ 3. Theory of SAFT EoS
denotes the range of the attractive interaction of well depth ε . The key features of SAFTgamma are summarised below.
Heteronuclear vs Homonuclear Segment
In SAFT-gamma, molecules are represented as heteronuclear model. This means that
different segments have different size. This is in contrast to most other versions of SAFT
which model molecules as comprising of identical segments. Figure 3.1 shows the two
representation of propane.
(a)
(b)
Figure 3.2: Different representation of Propane. (a) Homonuclear: all segments are
identical. (b) Heteronuclear: segments are of different sizes
Tangential vs Fused Segment
In most of the other versions of SAFT, molecules are represented as a collection of
tangential bonded segment. In SAFT-gamma, molecules are represented as fused segments.
(a)
(b)
Figure 3.3: (a) Spherical tangentially bonded united-atoms of a Propane model. (b) Fused
segment, United-atom model.
24
______________________________________________________________________________________________ 3. Theory of SAFT EoS
3.2
Group Contribution in SAFT-gamma
In SAFT-gamma, the segments represent the functional groups that are in the molecules.
Each segment is characterised by a set of parameters which used in transferable manner
regardless of the molecules that contain the segment. In other words, the parameters are
characteristics of the functional groups and not the molecules. This is in contrast to group
contribution method used in GC-SAFT where the contribution of each functional group to
the molecular parameters is obtained from the average of the parameters for the groups. Also
GC-SAFT uses a homonuclear representation of the molecules.
A functional group, represented by a fused-united-atom model is characterised by the shape
factor Sk (accounting for non-sphericity of the segment), a hard-sphere diameter σkk, a
square-well energy εkk, and a range λkk. Hydrogen bonding groups also have the number of
site of each type and the corresponding association energy
and range
parameters for the interaction between one group and other (εkl, λkl.
. The cross
,
) are also
required. The number of segments in each functional group should also be specified.
As in other versions of SAFT method, the Helmholtz free energy of the mixture is given as
the sum of different contributions per molecule.
A
A IDEAL A MONO ACHAIN A ASSOC




Nk BT Nk BT
Nk BT
Nk BT
Nk BT
3.16
Where A IDEAL = free energy of an ideal gas of the molecules. A MONO = Residual free energy
contribution due to hard-sphere repulsion and dispersive interactions btw groups. ACHAIN =
free energy contribution due to the formation of chains of heteronuclear groups.
25
______________________________________________________________________________________________ 3. Theory of SAFT EoS
A ASSOC = free energy contribution due to intermolecular association between sites on
association groups. N = the total number of molecules in the mixture and kB is the
Boltzmann constant. The expansion of each of the above can found in the original work of
Lymperiadis et al, 2007 & 2008)
The different group parameters are fitted to pure component vapour pressure and saturated
liquid densities of homologous families, e.g. n-alkanes, branched alkanes, n – alkyl
benzenes, mono and disaturated alkenes and 1-alkanols. The groups used to describe the
above components include CH3, CH2, CH3CH, ACH, ACCH2, CH2=, CH=, and OH. The
existing parameters table is presented in Table 3.1. It is important to note that the theory
allows for the determination of binary (cross group) interaction parameters based on pure
component experimental data alone. This allows for the method to be applied (in some
cases) in a fully predictive manner to the study of the phase behaviour of mixtures. The
different unlike interaction parameters are summarised in Table 3.2. The association energy
and range for the groups regressed are shown in Table 3.3.
The properties of pure components from different chemical families (table 3.4); including
alcohol and carboxylic acid were predicted with percentage absolute average deviation in
saturated vapour pressure of 8.18% and liquid density of 0.75%. SAFT-gamma parameters
were also used to predict liquid–liquid (LLE) and vapour-liquid equilibria of n-hexane +
propan-2-one binary mixture and also the VLE and LLE of some selected systems including
a polymer-solvent system. Good descriptions of these systems were obtained even at high
pressures. Figures 3.5 and 3.6 show the VLE of a mixture ethanol and 1-butanol; and nheptane and pentanoic acid.
26
______________________________________________________________________________________________ 3. Theory of SAFT EoS
Table 3.1: Individual Group Parameters for the SAFT-gamma Equation of State
Group
Sk
NSTk
nk,a
nk,b
CH3
1
3.810
1.413
252.601
0.667
0
-
-
CH2
1
4.027
1.661
240.482
0.3330
0
-
-
CH3CH
1
4.518
1.643
243.723
0.487
0
-
-
ACH
1
3.241
1.765
240.600
0.390
0
-
-
ACCH2
1
4.159
1.772
273.274
0.644
0
-
-
CH2=
1
3.628
1.469
190.917
0.670
0
-
-
CH=
1
3.558
1.697
315.343
0.370
0
-
-
C=O
2
2.787
1.782
386.833
0.482
1
2
0
COOH
3
2.806
1.538
269.285
0.644
2
2
1
NH2
1
3.908
1.527
398.872
0.472
2
1
2
OH
1
4.723
1.740
336.839
0.223
2
2
1
is the number of identical segments in group k,  kk is the diameter of each segment
In table 3.1,
in group k, kk the range of the dispersive interactions between two segments of group k,  kk the
strength of hose interactions. NSTk The number of association site type in group k, nk ,a or ( nk ,b ) the
number of association site of type a or b in group k (Source: Lymperiadis et al, 2008)
Table 3.2: Self- and cross-association energies,
state in units of K
C=O
a
C=O
COOH
COOH
NH2
NH2
OH
OH
A
A
B
A
B
A
B
for the SAFT-gamma equation of
COOH
a
NH2
b
0
-
a
OH
b
a
b
0
0
0
3594.295
0
953.630
953.630
0
0
2583.781
2583.781
0
(Source: Lymperiadis et al, 2008) Empty cells (...) indicate energy yet to be determined.
27
Table 3.3: Cross group energy parameters
for the SAFT-gamma equation of state
28
Groups
CH3
CH2
CH3CH
ACH
ACCH
CH2=
CH=
C=O
COOH
NH2
CH3
252.601
261.520
279.720
139.763
195.618
244.301
232.335
294.070
257.515
283.840 378.901
CH2
261.520
240.482
244.718
244.400
156.222
233.444
221.117
207.512
283.497
308.722 306.818
CH3CH
279.720
244.718
243.723
-
-
-
-
-
-
-
-
ACH
139.763
244.400
-
240.600
238.038
-
-
-
-
-
-
ACCH
195.618
156.222
-
238.038
273.274
-
-
-
-
-
-
CH2=
244.301
233.444
-
-
-
190.917
230.720
-
-
-
-
CH=
232.335
221.117
-
-
-
230.720
315.343
-
-
-
-
C=O
294.070
207.512
-
-
-
-
-
386.833
-
-
-
COOH
257.515
283.497
-
-
-
-
-
-
269.285
-
-
NH2
283.840
308.722
-
-
-
-
-
-
-
398.872 -
OH
378.901
306.818
-
-
-
-
-
-
-
-
(-) indicate cross energy yet to be determined.
OH
336.839
______________________________________________________________________________________________ 3. Theory of SAFT EoS
Table 3.2: Average absolute deviations (%AAD) of vapor pressures Ps and saturated liquid
densities ρl of the SAFT-gamma predictions compared to experiment (where n is the number
of data points) for the components not included in the parameter estimation database.
Compound
n-Pentadecane
n-Octadecane
n-Tetracosane
T range(K)
283-633
301-671
293-723
n
76
75
87
%AADPs
8.26
12.48
19.51
T range(K)
283-633
301-671
293-723
n
76
75
87
&AADρl
0.52
2.207
0.42
2-methyltetradecane
2-methylhexadecane
2-Methyloctadecane
403-537
428-568
451–595
9
9
9
3.53
4.84
8.12
283-598
293-643
293–653
11
11
10
0.36
0.38
0.39
n-Dodecylbenzene
n-Tridecylbenzene
n-Tetradecylbenzene
599–663
343–463
298–627
20
13
3
7.97
3.74
15.31
293–698
283–375
10
10
1.35
1.05
1-Dodecene
1-Tetradecene
396–487
431–524
19
10
4.34
5.24
263–578
253–613
11
10
0.62
1.08
Tridecan-2-one
424–546
15
2.94
-
-
-
Dodecanoic acid
Tetradecanoic acid
Hexadecanoic acid
403–572
385–465
440–577
11
17
9
7.35
12.08
18.64
333–573
333–573
353–573
13
13
12
0.97
0.77
0.62
Dodecan-1-amine
Tetradecan-1-amine
Hexadecan-1-amine
354–532
382–564
405–596
11
11
11
5.91
4.14
5.75
313–573
333–573
14
13
0.67
0.68
1-Dodecanol
1-Tetradecanol
1-Octadecanol
425–549
424–569
435–518
24
12
27
5.03
6.84
15.87
308–549
313–573
353–573
39
14
12
0.65
0.94
0.74
Average %AAD
-
-
8.18
-
-
0.75
29
______________________________________________________________________________________________ 3. Theory of SAFT EoS
Figure 3.4: Predicted vapor-liquid equilibria diagrams for binary mixtures of ethanol and 1butanol with the SAFT-gamma group contribution approach using the parameters obtained
from the pure component data. The symbols represent the experimental data and the
continuous curves correspond to the SAFT-gamma predictions.
Figure 3.5: Predicted vapour–liquid equilibrium for binary mixtures of n-heptane +
pentanoic acid with the SAFT-gamma group contribution approach using the parameters
obtained from the pure component data. where x1 is the mole fraction of n-heptane. The
symbols represent the experimental data and the continuous curves correspond to the
SAFT-gamma predictions.
30
______________________________________________________________________________________________ 3. Theory of SAFT EoS
3.3
Groups needed in biodiesel system
In group contribution, the identification of groups making up a compound is usually done by
empirical method. Table 3.8 gives the possible groups that can be used to describe various
compounds making up the biodiesel system. The symbol (*) indicates group not yet present
in the SAFT-gamma parameter table (Table 3.1-3) while (√) shows the groups already fitted.
In addition to the individual group parameters, the cross energy parameter between the
groups is needed. The existing SAFT-gamma parameter table has parameters for carboxylic
acid group, alkenes and alcohol series. Although the deviations in vapour pressure and
liquid density for carboxylic acid are low, the description of the phase behaviour of the
binary mixture (figure 3.6) needs be improved.
3.5
Conclusion
This chapter reviewed the theory of SAFT equation of state. The original SAFT and all
versions of SAFT take in account association and chain formation in details. SAFT equation
of state has been successfully applied to strong associating mixtures including aqueous
system. SAFT- γ incorporates group contribution in the SAFT method and treats compounds
at the level of their representative functional groups instead of molecules used by other
versions of SAFT. This makes SAFT- γ fully predictive. To predict biodiesel system, some
of the groups, not in the present SAFT- γ table, need to be determined. These include esters,
glycerol and methanol functional groups as well as their cross interaction parameters. The
next
section
will
discuss
the
methodology
31
used
in
this
work.
Table 3.3: Groups needed for modelling biodiesel compounds
32
CH3
CH2
CH=CH
OH
C3H8O3
COOH
COO-
CH2COO
CH2COOH
CH3OH
CH
Ref.
CH3OH
√
-
-
√
-
-
-
-
-
-
-
[39]
Methanol
CH3OH
-
-
-
-
-
-
-
-
-
*
-
[59]
Carboxylic
acid
CH3(CH2)n(CH=CH)nCOOH
√
√
√
-
-
√
-
-
-
-
-
Carboxylic
acid
CH3(CH2)n(CH=CH)nCOOH
√
√
√
-
-
-
-
-
*
-
-
Fatty
methyl ester
CH3(CH2)n(CH=CH)nCOOCH3
√
√
√
-
-
-
*
-
-
-
-
[31]
Fatty
methyl ester
CH3(CH2)n(CH=CH)nCOOCH3
√
√
√
-
-
-
-
*
-
-
-
[2][35]
glycerol
(CH2OH)2CHOH
-
-
-
-
*
-
-
-
-
-
-
[2]
glycerol
(CH2OH)2CHOH
-
√
-
√
-
-
-
-
-
-
*
[39]
Compounds
Structure
Methanol
The symbol (*) indicates group not yet present in the SAFT-gamma parameter table (Table 3.1-3) while (√) shows the groups already
fitted.
_________________________________________________________________________________________________ 4. Methodology
Chapter 4
METHODOLOGY
As noted earlier, in SAFT-gamma method, four parameters are used to describe non
associating group k. These include the hard sphere diameter σkk, the square well energy
ϵkk and the range λkk, and the shape factor Sk. There is also a cross energy parameter ϵkl
between any two groups k and l. Associating groups have, in addition to the above, the
site-site energy ϵHS and the cut-off distance rkk between site type a and b. The problems
in this work include modelling and fitting the SAFT-gamma parameters for glycerol,
esters and the cross interaction parameters of these groups with the alkanes groups- CH3
and CH2 and other groups fitted in the existing parameter table. These are required for
the prediction of the pure component and mixture properties. The procedure followed in
this work is listed as follows
i.
Description of the compounds in terms of the appropriate functional groups
that characterise them. The presence of hydrogen bonding in any group need
also be identified and the number of segment specified.
ii.
Selection of experimental data. The experimental data used here are the
saturated vapour pressure and liquid density.
iii.
Fitting SAFT –γ parameters for each functional group to experimental data.
iv.
The optimised parameters are then used to predict both component and
mixture properties of compounds containing the functional groups and the
prediction compared the experimental data. The experimental data used for
comparison are normally different from those used in fitting the parameters.
The procedure is iterative as the choice of the component groups, the number of
segments per each group are adjusted to provide the best prediction. Details of the steps
are given in the next sections.
33
_________________________________________________________________________________________________ 4. Methodology
4.1
GROUP IDENTIFICATION AND PARAMETER ESTIMATION
In group contribution methods, the description of compound by their functional groups is
by empirical methods. Similar groups found in the literature for other group contribution
methods such as UNIFAC are used in the group construction of the various compounds.
4.2
SELECTION OF EXPERIMENTAL DATA
Dertherm database is the main source for the experimental values of the saturated vapour
pressure and liquid density used in this work. The liquid densities used are for pure
components at a pressure of 1 atm. The range of temperature for all data is usually
chosen far from the critical points. This is to avoid distortion due to fluctuations around
the critical conditions. In this work, data are selected in the range between 0.3Tc and
0.9Tc; where Tc is the critical temperature. This range of temperature is far from the
triple and critical temperature.
4.3
PARAMETER OPTIMIZATION
As noted earlier, in SAFT-gamma method, four parameters are used to describe non
associating group k. These include the hard sphere diameter σkk, the square well energy
ϵkk and the range λkk, and the shape factor Sk. There is also a cross energy parameter ϵkl
between a group k and l. Associating groups have in addition to the above, the site-site
energy ϵHS and the cut-off distance rkk between site type a and b. The interaction energy
between any two groups needs also be determined. Usually, the parameters were
determined by fitting to experimental saturated vapour pressure and liquid density.
The estimation of parameter is done through the minimization of a relative least squares
function
4.1
Where the first sum is over the number of species NC, the second over the number of
measured variable NVi of species, and the third is over the number of data points DPij of
34
_________________________________________________________________________________________________ 4. Methodology
the variable j(saturated pressure and liquid density) of the species i.
experimental value of the variable j of species i and
is the kth
is the kth value of the variable j
of species i calculated with the SAFT-gamma method. And θ is a set of the parameters to
be estimated. This is implemented through gPROMS parameter estimation program. It is
to be noted that this is non-linear optimization problem and thus several local optimum
exist. The initial guesses are adjusted to give an optimum with the smallest deviation in
the estimated variables.
The predictions from SAFT-gamma method is compared to the experimental values
through the percentage Absolute Average Deviation (%AAD) for each variable
(saturated vapour pressure and liquid density) given by
4.2
Where n is the number of points,
the experimental value of the variable and
the predicted value of the same variable.
35
is
_______________________________________________________________________________________5. Results and Discussion
Chapter 5
RESULT AND DISCUSSION
In this chapter, the parameters fitted for new groups and predictions for some of the pure
component and mixture properties are presented and discussed.
5.1
PURE COMPONENTS
5.1.1 Carboxylic Acids
In the existing SAFT-gamma, carboxylic acid is modelled in terms of CH3, CH2 and a
carbonyl group COOH comprising three identical segments and one active associating
site. The parameters for the groups were obtained by regression to vapour-liquid data of
eight members of the carboxylic acid homologous family-from pentanoic to decanoic
acid. The percentage Absolute Average Deviation (%AAD) in saturated vapour pressure
for the eight acids is 3.6 and in saturated liquid density is 1.36.
Table 5.1 : Parameter values for different models of carboxylic acid functional group
Parameters
σ kk
λ kk
COOH
2.806
CH2COOH
3.055
1.538
1.625
269.285
Sk
275.106
0.644
0.727
Cross energy with CH3 (
) 257.515
212.411
Cross energy with CH3 (
) 283.497
265.856
/kb
3594.295
2.244
3778.915
2.175
.
(Both COOH and CH2COOH are made up of three identical segments each)
As noted earlier, the predictions of phase behaviour of mixture using COOH group need
to be improved. The use of an alternative group; CH2COOH is observed to improve the
36
_______________________________________________________________________________________5. Results and Discussion
prediction of saturated vapour pressure and vapour-liquid equilibrium as will be
discussed in mixture section. The CH2COOH group is similarly made up three identical
segments with one active associating site. The parameters for the CH2COOH and COOH
are given in Table 5.1
As expected, the diameter of CH2COOH is larger than that of COOH due to inclusion of
CH2 in the group. The %AAD in saturated liquid density and vapour pressure for the
same experimental data [19] used by Lymperiadis et al (2008) are shown in tables 5.2
and 5.3 respectively.
Table 5.2: Average Absolute Deviations (%AAD) of predicted saturated liquid density
compared to experimental data [19] for carboxylic acid
Compounds
Propanoic acid
Butanoic acid
Pentanoic acid
Hexanoic acid
Heptanoic acid
Octanoic acid
Nonanoic acid
Decanoic acid
T
range(K)
237-490
343-563
233-553
273-588
263-583
293-573
288-323
313-573
n
33
21
26
27
16
22
7
14
Average %ADD
COOH
model
2.90
0.73
0.78
1.19
1.44
1.31
1.56
0.97
CH2COOH
model
2.98
0.72
0.8
1.21
1.48
1.33
1.67
0.94
1.36
1.39
Although there is a slight increase in the deviation in saturated liquid density from 1.36
to 1.39, the prediction of saturated vapour pressure improve with %AAD reducing from
3.6 to 3.49
37
_______________________________________________________________________________________5. Results and Discussion
Table 5.3: Average Absolute Deviations (%AAD) of predicted saturated vapour pressure
compared to experimental data [19] for carboxylic acids
T range(K)
n
COOH model
CH2COOH Model
Propanoic acid
328-438
35
6.20
6.15
Butanoic acid
343-452
34
4.72
5.23
Pentanoic acid
Hexanoic acid
Heptanoic acid
303-465
355-478
348-494
19
38
40
2.47
3.75
3.24
2.15
3.25
3.13
Octanoic acid
403-513
35
2.52
2.44
Nonanoic acid
Decanoic acid
Average %ADD
372-529
350-543
11
13
1.43
4.45
3.60
1.16
4.39
3.49
.
In table 5.4, predicted values for palmitic and stearic acid are compared to experimental
saturated vapour pressure [19]. The large deviation in vapour pressure can be attributed
to uncertainty in the experimental measurement and typical low pressure of the
compounds.
Table 5.4: Average Absolute Deviations (%AAD) of predicted saturated vapour pressure
and liquid density compared to experimental data [19] for fatty acids
Compounds
T range(K)
n
%AAD Ps
T range(K)
n
%AAD ρl
Palmitic acid
339 – 405
19
12.91
353 – 573
12
0.66
Stearic acid
349 – 421
21
15.41
353 – 573
12
0.72
38
_______________________________________________________________________________________5. Results and Discussion
5.1.2 GLYCEROL
Glycerol is modelled as consisting of three identical groups - CH2OH. Two associating
models were considered; the nine and six-site model. For the nine site model, CH2OH
has two sites of type a and one site of type b while for the six sites, the group has two
sites each of type a and b. Both models gave similar prediction of both saturated vapour
pressure and liquid density with the nine site model slightly better. The group parameters
were estimated from pure component experimental saturated liquid density and vapour
pressure and given in table 5.5.
Table 5.5: Parameters for Glycerol modeled as 3 identical segments with 9 associating
sites
Parameters
σ kk
λ kk
Sk
CH2OH
4.180
1.610
397.294
(
0.553
)
2217.449
2.421
Excellent prediction of the saturated liquid density can be seen from Table 5.6 with
%AAD of 0.469. However, there is considerable large deviation in the saturated vapour
pressure. In figure 5.1 and 5.2 are shown the vapour-liquid coexistence curve and the
Pressure-Temperature plot respectively. Again, a good agreement with the experimental
values of the saturated liquid density is seen in figure 5.1.
Table 5.6: Average Absolute Deviations between predicted and experimental vapor
pressure and liquid density [19].
Glycerol
T,
Range(K)
n
P,
range(kPa)
%AAD Ps
391 - 536
52
0.03 - 53
16.99
39
288- 573
n
%AAD ρl
27
0.476
_______________________________________________________________________________________5. Results and Discussion
900
800
T/K
700
600
500
400
300
0
0.005
0.01
0.015
ρg & ρl(mol/cm^3)
P/kPa
Figure 5.1: Temperature vs. Liquid and vapour density of glycerol. Open symbols
represent the experimental data [19] and solid lines predictions using the SAFT-gamma
method
200
180
160
140
120
100
80
60
40
20
0
200
300
400
500
600
T/K
Figure 5.2: Pressure vs. Temperature plot. Open symbols represent the experimental
data [19] and solid lines predictions using the SAFT-gamma method
5.1.3 ESTERS
As mentioned in the methodology section, the first step is the description of the
compounds in terms of the representative groups. The esters in biodiesel system is made
40
_______________________________________________________________________________________5. Results and Discussion
up CH3,CH2, CH= and the ester functional group. The existing SAFT-gamma parameter
table includes the parameters for CH3, CH2, and CH= as well as their cross energy
interactions. These parameters for the alkyl groups are transferred to the ester chain
without modification. A new group representing the ester functional group is modelled as
CH2COO. This is similar to the model used by Kuramochi et al (2009) in their work
using UNIFAC method. CH2COO group is made up of three identical segments. Pure
esters are non self associating and the parameters required include the hard sphere
diameter σkk, the square well energy ϵkk and the range λkk and the shape factor Sk of the
ester functional group and also the cross energy interactions with the three alkyl groups.
The parameters for CH2COO as well as the unlike energy interaction with CH3 and CH2
were obtained from regression to pure component experimental data (saturated liquid
density and vapour pressure, Dertherm database[19]) of saturated ethyl ester chemical
family starting from ethyl ethanoate to ethyl undecanoate. The ester functional group
parameter was regressed to pure components experimental in the temperature range of
0.3Tc – 0.9Tc, where Tc is the critical temperature. This range of temperature is believed
to be far from the triple and critical temperature so as to avoid distortion due to
fluctuations around the critical condition. The parameters that gave the best fitting are
given in Table 5.7
The esters considered in biodiesel also include a double bond and thus the cross energy
interaction between C= and CH2COO is required. This was determined using LorentzBerthelot combining rule where the cross interaction energy between two groups is taken
as the geometric mean of the group’s individual square well energy ϵkk.
Table 5.7: Parameter for Ester Functional group and Cross interaction energy with alkyl
groups
Parameters
CH2COO
σ kk
λ kk
Sk
CH3&CH2COO
2.828 1.775 161.677 0.685
247.881
CH2&CH2COO
170.740
CH=&CH2COO
245.859
It can be seen that the diameter is smaller than that of CH3 (3.80) and CH2 (4.027).
However, it should be noted that CH2COO is made up of three segments while the alkyl
41
_______________________________________________________________________________________5. Results and Discussion
groups are made up of one segment each. The cross energy parameters of ester functional
group CH2COOH with CH3 and CH2 lie in-between the individual like energy.
The quality of the prediction was evaluated in terms of the percentage Absolute Average
Deviation (%AAD). This is shown in tables 5.8 and 5.9. Accurate prediction of the pure
component saturated liquid density can be seen in table 5.8 with %AAD in saturated
liquid density, for components used for regression, of 0.398. Also in table 5.9, %AAD of
0.555 in liquid density for compounds not included in the regression (pure prediction
from group parameters) is recorded. The overall average %AAD saturated vapour
pressure is 6.540 for component used in regression and 6.98 for those not included.
Large deviation in the vapour pressure is observed for long-chain molecules. However, it
is noted that these compounds have low vapour pressure (as can be seen in their pressure
range in tables 5.8 & 5.9) and small error leads to large %AAD. Also, there is
uncertainty in the experimental measurements.
350
1
300
2
250
4
200
P/kPa
3
5
150
6
100
7
8
50
0
150
200
250
300
350
400
450
500
550
T/K
Figure 5.3: Pressure-temperature plots of vapour pressure of ethyl esters. The circles
represent the experimental data [19] while the continuous curves correspond to the
predicted values with SAFT-gamma parameter. The numbers represents the serial
numbers in table 5.8
42
_______________________________________________________________________________________5. Results and Discussion
It is to be noted that this method does not distinguish between the isomers; for example
methyl butanoate (CH3CH2CH2COOCH3) and ethyl propanoate (CH3CH2COOCH2CH3).
The good agreement between predicted and experimental data can be seen in Figure 5.3
(the Pressure-temperature plots of experimental data and values predicted with the
parameters in table 5.6). Also Figure 5.4 shows the Temperature vs saturated liquid
density plots for the esters.
800
700
600
T/K
500
400
300
8 7 6 5
200
4
3
2
1
100
0
0
0.002
0.004
0.006
0.008
0.01
0.012
ρl/(mol/cm^3
Figure 5.4: Temperature vs. saturated liquid density plots for ethyl esters in table 5.8.
The circles represent the experimental data [19] while the continuous curves correspond
to the predicted values with SAFT-gamma parameter.
43
Table 5.8: Average Absolute Deviations between predicted and experimental vapor pressure and liquid density [19] of components
used in regression
44
S/N
Compound
Temp. Range
Pressure Range
n
%AAD p
Temp. Range
n
%AAD
ρl
1
Ethyl ethanoate
273 – 373
3.32 – 203.70
36
2.834
273 – 503
29
0.513
2
Ethyl propanoate
263 – 363
0.498 – 70.637
12
4.972
289 – 333
8
0.0140
3
Ethyl butanoate
318 – 338
6.133 – 119.19
25
8.601
273 – 353
17
0.522
4
Ethyl hexanoate
279 – 309
0.052 – 0.427
8
2.987
238 – 442
30
0.201
5
Ethyl octanoate
237 – 318
0.0211 – 0.105
8
5.762
273 – 368
16
0.300
6
Ethyl nonanoate
307 – 333
0.0189 – 0.126
10
1.736
273 – 303
3
0.757
7
Ethyl decanoate
323 – 359
0.023 – 0.126
11
6.696
273 – 359
12
0.465
8
Ethyl undecanoate
289 – 341
0.006 – 0.0393
7
18.781
289 – 359
9
0.409
Average
6.54
0.398
Table 5.9: Average Absolute Deviations between predicted and experimental vapor pressure and liquid density [19] for components not
included in regression
45
Compound
Temp.
Range/K
Pressure
range/kPa
n
%AAD p
Ref.
Temp. Range
n
%AAD ρl
Ref.
Methyl Propanoate
330 – 364
48 - 151
34
7.835
[46]
373 – 528
26
1.095
[62]
Ethyl propanoate
263 – 546
0.54 – 3361
33
6.925
[61]
289 – 333
8
0.014
[57]
Methyl butanoate
317 – 360
11 – 63
9
10.656
[13]
276 – 360
13
0.960
[57][34]
Propyl butanoate
389 – 434
45 – 161
86
3.990
[44]
289 – 360
9
0.401
[57]
Propyl hexanoate
316 – 393
0.27 – 13
12
1.982
[6]
273 – 372
6
0.455
[30][6]
Butyl decanoate
409 – 492
1.60 – 24
8
10.496
[36]
292 – 360
9
0.408
[57]
Average
6.98
0.555
_______________________________________________________________________________________5. Results and Discussion
Pure component saturated vapour pressure and liquid density some fatty acid methyl
esters (biodiesels) were also predicted. The result is shown in table 5.10 and figure 5.5.
Accurate prediction of the saturated liquid density with overall %AAD of 0.452 can be
observed. The deviation of the vapour pressure is equally reasonable considering the low
pressure range. No experimental data is reported for methyl erucate (erucic acid methyl
ester).
Table 5.10: Average Absolute Deviations between predicted and experimental vapor
pressure and liquid density [19] for some biodiesel.
n
T, range.
K
P range. kPa
%AADP
T range.
K
n
%AADρl
Methyl palmitate
9
344- 361
0.001-0.005
11.37
303-353
6
0.622
Methyl stearate
10
335-359
0.0001-.001
10.92
313-353
9
0.328
Methyl oleate
14
428-485
0.14-2.00
9.59
288-363
6
0.705
palmitate
8
oleate
erucate
4
0
300
350
400
450
500
550
600
Figure 5.5: Pressure-temperature plots of vapour pressure of biodiesel. The circles
represent the experimental data [19] while the continuous curves correspond to the
predicted values with SAFT-gamma parameter.
46
_______________________________________________________________________________________5. Results and Discussion
Generally, SAFT-gamma method gives accurate prediction of the pure component
saturated liquid density for all the components considered in this work. Also a very
reasonable prediction of vapour pressure is achieved considering the characteristic low
pressure of the compounds under investigation.
5.2
MIXTURES
5.2.1 Carboxylic Acids/Alkane
In Figures 5.5a –c are shown the phase behaviour of a mixture of pentanoic acid and npentane at different temperatures. The accuracy of the predicted values was tested through the
relative error of the equilibrium pressure given by %AAD = (1/n
and the absolute error of the vapour mole fraction y, define by AAD = (1/n
.
It can be seen from figures 5.5a-c, that the new group gives an improved prediction of
the phase behaviour. The use of the new group CH2OOH resulted in the reduction of
overall relative error in equilibrium pressure from 14.60% for COOH group to 7.85%.
Also, the description of the vapour composition (absolute error in mole fraction)
improved from an AAD of 0.92 to 0.56. The predicted and experimental data is attached
in the appendix (Tables A1- A3).
47
_______________________________________________________________________________________5. Results and Discussion
120
T = 373.15 K
100
P/kPa
80
60
40
20
0
0
0.2
0.4
0.6
0.8
1
x1
(a)
50
T = 348.15 K
45
40
P/kPa
35
30
25
20
15
10
5
0
0
0.2
0.4
x1
0.6
(b)
48
0.8
1
_______________________________________________________________________________________5. Results and Discussion
20
18
323.15 K
16
P/kPa
14
12
10
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1
x1
(c)
Figure 5.6: Predicted vapour-liquid equilibrium for n-heptane (component 1) and
pentanoic acid (component 2), at different temperatures using SAFT-gamma Method.
The open circles represent the experimental data [19], while the continuous line,
prediction for CH2COOH model and the dash line for COOH model.
5.2.2 Esters/Alkane
The parameters determined above for esters groups were used to make pure predictions
of the vapour-liquid equilibrium of a mixture of alkane with long chain esters. The
predictions by SAFT-gamma approach were compared to the data taken from Dertherm
data base [45]. The isobaric (101.3kPa) VLE of a mixture of alkane and esters are shown
in Figure 5.6-9. The agreement between prediction and experimental measurement
appears satisfactory with the overall AAD in the vapour composition for the four
mixtures of 1.37% and the relative error in the equilibrium temperature of 0.004. The
predicted and experimental data is attached in appendix (Table A4- A7).
49
_______________________________________________________________________________________5. Results and Discussion
420
415
heptane / propyl butanoate
410
405
400
T /K
395
390
385
380
375
370
365
0
0.2
0.4
0.6
0.8
1
x1, y1
Figure 5.7: Vapour-Liquid equilibrium of a mixture of heptane (component 1) and
propyl butanoate. The symbol represents experimental data [45] while the continuous
line represents prediction by SAFT-gamma
430
420
T/K
410
400
390
380
370
360
0
0.2
0.4
0.6
0.8
1
x1, y1
Figure 5.8: Vapour-Liquid equilibrium of a mixture of nonane and propyl ethanoate
(comp. 1). The symbol represents experimental data [45] while the continuous line
represents prediction by SAFT-gamma
50
_______________________________________________________________________________________5. Results and Discussion
400
395
heptane/propyl propanoate
T,K
390
385
380
375
370
365
0
0.2
0.4
0.6
0.8
1
x1, y1
Figure 5.9: Vapour-Liquid equilibrium of a mixture of heptane (comp.1) and propyl
propanoate. The symbol represents experimental data [45] while the continuous line
represents prediction by SAFT-gamma
426
nonane/propyl butanoate
424
T/K
422
420
418
416
414
412
0
0.2
0.4
0.6
0.8
1
x1, y1
Figure 5.10: Vapour-Liquid equilibrium of a mixture of nonane and propyl butanoate
(comp. 1). The symbol represents experimental data [45] while the continuous line
represents prediction by SAFT-gamma
51
________________________________________________________________________________________________________ Appendix
Chapter 6
6.1
CONCLUSION
Biodiesel is seen as a good replacement of petroleum diesel in the transport sector as it is
more environmentally friendly and renewable. There is a need, however, to make the
cost of biodiesel competitive compare to diesel from fossil fuel. One of the ways of
reducing the cost is through a more efficient process design of the production processes.
This requires extremely limited available, physical and phase equilibrium properties of
the biodiesel system.
The biodiesel system consists of associating and polar molecules which make them
unique. Different methods applied in the literature for calculating their properties involve
using an input from experimental data, which is not readily available.
The objective of this work was to calculate the physical and phase equilibrium properties
of compound common to biodiesel system using a group contribution SAFT-gamma
method. SAFT-gamma method, like other group contribution method, is fully predictive,
and properties of the fluids can be calculated from their molecular structure. In this work,
•
The SAFT-gamma group parameters were extended to ester and glycerol
functional groups. The ester was modelled by means of CH3, CH2, C= and CH2COOH
and glycerol as comprising three identical group-CH2OH
•
The performance of SAFT-gamma EoS was evaluated for the prediction of pure
component saturated vapour pressure and liquid density. The phase equilibria of straightchain alkane with carboxylic acids and esters were also predicted by the SAFT-gamma
approach. Prediction using the obtained parameters gave a reasonable description of the
saturated liquid density, vapour pressure as well as the phase description of the mixtures
tested.
52
________________________________________________________________________________________________________ Appendix
6.2
RECOMMENDATION/FUTURE WORK
The three identical segments for glycerol seem to give large deviation in saturated
vapour pressure. There is need to used a different model or groups to improve the
prediction.
Other compound in the biodiesel system, such as mono/diglycerides and methanol need
to be modelled and the parameter for the groups fitted. The parameter for the cross
energy between any pair of carboxylic acid, glycerol, methanol, esters and glycerides
also need to be determined.
In addition to the saturated liquid density and vapour pressure, the group parameters
could be simultaneously fitted to the phase equilibrium of mixture. This will improve the
accuracy of the SAFT-gamma predictions.
53
________________________________________________________________________________________________________ Appendix
APPENDIX
Table A 1: Experimental data and predicted values by SAFT-gamma method for a
binary mixture of heptane and pentanoic acid at 323.15K using different acid groups.
Experimental
P/kPa
x_heptane
y_heptan
e
COOH group prediction
CH2COOH prediction
P/kPa
P/kPa
x_heptane
y_heptane
x_heptane
y_heptane
12.039
0.365
0.988 10.2405
0.365
0.9870
13.5545
0.365
0.9891
13.479
0.453
0.989 11.7622
0.453
0.9897
14.3269
0.453
0.9901
14.079
0.497
0.988 12.4390
0.497
0.9908
14.6342
0.497
0.9905
15.105
0.567
0.993 13.4202
0.567
0.9922
15.0682
0.567
0.9910
16.799
0.767
0.987 15.7527
0.767
0.9952
16.2568
0.767
0.9929
Table A 2: Experimental data and predicted values by SAFT-gamma method for a
binary mixture of heptane and pentanoic acid at 348.15K using different acid groups.
Experimental
P/kPa
x_heptane
COOH group prediction
y_heptane
P/kPa
x_heptane
y_heptane
CH2COOH prediction
P/kPa
x_heptane
y_heptane
16.852
0.126
0.952 11.9026
0.126
0.9297
20.3991
0.126
0.9588
15.692
0.128
0.924 12.0550
0.128
0.9307
20.6040
0.128
0.9593
17.332
0.136
0.937 12.6586
0.136
0.9345
21.3999
0.136
0.9610
22.158
0.201
0.959 17.2218
0.201
0.9548
26.6689
0.201
0.9701
28.851
0.287
0.978 22.4304
0.287
0.9682
31.2919
0.287
0.9757
28.958
0.308
0.977 23.5768
0.308
0.9704
32.1449
0.308
0.9766
34.13
0.408
0.983 28.4635
0.408
0.9779
35.2733
0.408
0.9798
35.024
0.464
0.983 30.8431
0.464
0.9809
36.5787
0.464
0.9810
37.077
0.534
0.985 33.5223
0.534
0.9838
37.9645
0.534
0.9824
39.637
0.6
0.987 35.7980
0.6
0.9861
39.1370
0.6
0.9836
40.197
0.652
0.986 37.4502
0.652
0.9877
40.0249
0.652
0.9846
43.103
0.758
0.984 40.5243
0.758
0.9906
41.8626
0.758
0.9868
43.943
0.778
0.991 41.0701
0.778
0.9912
42.2247
0.778
0.9873
43.583
0.789
0.984 41.3668
0.789
0.9914
42.4269
0.789
0.9876
54
________________________________________________________________________________________________________ Appendix
Table A 3: Experimental data and predicted values by SAFT-gamma method for a
binary mixture of heptane and pentanoic acid at 373.15K using different acid groups.
Experimental
COOH group prediction
CH2COOH prediction
23.678
0.062
0.863
16.0046
0.062
0.7842
26.8464
0.062
0.8690
26.745
0.077
0.86
18.7791
0.077
0.8186
31.3369
0.077
0.8891
40.37
0.138
0.926
29.2693
0.138
0.8901
46.2229
0.138
0.9281
48.689
0.183
0.936
36.2577
0.183
0.9150
54.4803
0.183
0.9408
58.222
0.264
0.943
47.4300
0.264
0.9340
63.2890
0.264
0.9510
60.755
0.291
0.952
50.7948
0.291
0.9454
68.1452
0.291
0.9557
72.554
0.411
0.963
63.9204
0.411
0.9618
77.4202
0.411
0.9636
77.194
0.483
0.966
70.5927
0.483
0.9681
81.4496
0.483
0.9668
82.953
0.557
0.975
76.7059
0.557
0.9731
84.9781
0.557
0.9696
88.659
0.657
0.98
84.0245
0.657
0.9788
89.2940
0.657
0.9733
91.646
0.701
0.966
86.9768
0.701
0.9810
91.1475
0.701
0.9750
55
________________________________________________________________________________________________________ Appendix
Table A4: Experimental data and predicted values by SAFT-gamma Method for a binary
mixture of heptanes and propyl butanoate for a given composition of heptane in the
liquid phase.
T/K
415.39
414.57
413.35
411.74
410
407.82
404.36
401.76
398.78
395.82
393.86
392.28
389.93
388.53
387.45
386.33
385.17
384.37
383.58
382.76
381.73
381.1
380.4
379.26
378.82
378.18
377.12
376.05
374.58
373.52
372.55
372.02
371.59
Experimental data
X_heptane
y_heptane
0.0076
0.0304
0.0158
0.0617
0.0279
0.1027
0.0443
0.1547
0.0621
0.2058
0.0858
0.2681
0.1281
0.3623
0.1633
0.4325
0.2073
0.5024
0.2553
0.5701
0.2913
0.6113
0.3227
0.6419
0.3653
0.685
0.3966
0.7099
0.4248
0.7308
0.4511
0.7497
0.4789
0.77
0.5033
0.7843
0.5269
0.7975
0.5523
0.8104
0.5803
0.8267
0.5987
0.8369
0.6234
0.8483
0.6566
0.8653
0.6736
0.8728
0.6916
0.882
0.7312
0.8978
0.7701
0.9142
0.8296
0.9372
0.8842
0.9557
0.9262
0.9707
0.9588
0.9818
0.9844
0.9901
Prediction by SAFT-gamma
T/K
X_heptane
y_heptane
414.1972
0.0076
0.02831
413.4138
0.0158
0.05766
412.2871
0.0279
0.09886
410.8138
0.0443
0.15092
409.2818
0.0621
0.20297
407.3441
0.0858
0.26586
404.1517
0.1281
0.36261
401.7283
0.1633
0.43068
398.9603
0.2073
0.50313
396.2285
0.2553
0.56946
394.351
0.2913
0.61227
392.8186
0.3227
0.64562
390.8789
0.3653
0.68592
389.5448
0.3966
0.71247
388.4019
0.4248
0.73448
387.382
0.4511
0.75359
386.3481
0.4789
0.77247
385.4748
0.5033
0.78805
384.6583
0.5269
0.80232
383.8085
0.5523
0.81690
382.903
0.5803
0.83211
382.3245
0.5987
0.84167
381.5672
0.6234
0.85401
380.5814
0.6566
0.86979
380.0897
0.6736
0.87755
379.5779
0.6916
0.88554
378.4818
0.7312
0.90242
377.4408
0.7701
0.91817
375.9067
0.8296
0.94092
374.5504
0.8842
0.96067
373.5344
0.9262
0.97527
372.7595
0.9588
0.98632
372.1582
0.9844
0.99485
56
________________________________________________________________________________________________________ Appendix
Table A5: Experimental data and predicted values by SAFT-gamma Method for a binary
mixture of heptane and propyl propanoate for a given composition of heptane in the
liquid phase.
T/K
394.57
394
393.55
392.62
391.81
391.12
390.17
389.22
388.28
387.35
386.55
385.8
384.85
384.16
383.49
382.83
382.1
381.01
380.5
379.73
378.61
377.27
376.75
376.36
375.19
374.55
374.18
373.19
372.41
371.4
371.16
371.03
Experimental data
X_heptane
y_heptane
0.0182
0.054
0.0265
0.0723
0.0329
0.0892
0.0489
0.1235
0.0605
0.1442
0.0742
0.1723
0.0943
0.2085
0.1152
0.2451
0.137
0.2783
0.1567
0.3133
0.1787
0.3422
0.1902
0.3571
0.2253
0.4055
0.243
0.4275
0.2599
0.4492
0.2852
0.4762
0.3088
0.4998
0.3405
0.5329
0.3601
0.5527
0.3938
0.5812
0.4319
0.6182
0.4938
0.6633
0.5213
0.6852
0.5367
0.6952
0.6057
0.7474
0.6635
0.7823
0.7003
0.8025
0.7808
0.8506
0.8605
0.8984
0.948
0.9555
0.979
0.9807
0.998
0.998
Prediction by SAFT-gamma
T/K
X_heptane
y_heptane
392.4569
0.0182
0.0483
391.9999
0.0265
0.0691
391.6559
0.0329
0.0845
390.8272
0.0489
0.1214
390.2529
0.0605
0.1466
389.6015
0.0742
0.1749
388.6953
0.0943
0.2136
387.8107
0.1152
0.2509
386.9455
0.137
0.2868
386.2095
0.1567
0.3171
385.4349
0.1787
0.3486
385.0486
0.1902
0.3642
383.9406
0.2253
0.4086
383.4192
0.243
0.4294
382.9426
0.2599
0.4484
382.265
0.2852
0.4753
381.6686
0.3088
0.4990
380.9164
0.3405
0.5290
380.4766
0.3601
0.5466
379.7613
0.3938
0.5755
379.0084
0.4319
0.6062
377.8933
0.4938
0.6530
377.435
0.5213
0.6727
377.1873
0.5367
0.6836
376.1476
0.6057
0.7307
375.3543
0.6635
0.7690
374.8813
0.7003
0.7932
373.9297
0.7808
0.8457
373.0715
0.8605
0.8996
372.2385
0.948
0.9612
371.9691
0.979
0.9841
371.8109
0.998
0.9985
57
________________________________________________________________________________________________________ Appendix
Table A6: Experimental data and predicted values by SAFT-gamma Method for a binary
mixture of nonane and propyl ethanoate for a given ester composition in the liquid phase.
T/K
421.15
418
415.19
412.27
409.05
405.23
400.84
399.51
395.82
395.05
393.28
391.72
389.85
388.67
387.27
385.35
384.1
382.7
381.35
380.55
379.35
378.5
377.55
376.86
376.23
375.79
375.47
375.12
374.79
Experimental data
X_ester
y_ester
0.0081
0.0539
0.0241
0.1439
0.0436
0.2224
0.0696
0.3035
0.098
0.3713
0.1464
0.4632
0.2037
0.5567
0.223
0.5791
0.2793
0.6413
0.2958
0.6559
0.3254
0.6842
0.3562
0.7111
0.4061
0.7425
0.4272
0.7597
0.4707
0.7827
0.5256
0.8118
0.5685
0.8313
0.6104
0.8519
0.6829
0.8735
0.7051
0.8832
0.7628
0.9032
0.7907
0.9154
0.8357
0.931
0.861
0.9414
0.9033
0.9572
0.9311
0.9666
0.9451
0.972
0.9711
0.984
0.9836
0.9901
Prediction by SAFT-gamma
T/K
X_ester
y_ester
422.1145
0.0081
0.0514
418.958
0.0241
0.1420
415.4396
0.0436
0.2362
411.2453
0.0696
0.3382
407.2254
0.098
0.4274
401.4798
0.1464
0.5408
396.074
0.2037
0.6339
394.5229
0.223
0.6585
390.6137
0.2793
0.7164
389.6171
0.2958
0.7303
387.9725
0.3254
0.7527
386.4347
0.3562
0.7729
384.2617
0.4061
0.8006
383.4447
0.4272
0.8108
381.9224
0.4707
0.8295
380.2638
0.5256
0.8498
379.134
0.5685
0.8637
378.1446
0.6104
0.8761
376.6402
0.6829
0.8958
376.2209
0.7051
0.9016
375.1976
0.7628
0.9166
374.7296
0.7907
0.9241
374.0002
0.8357
0.9367
373.6003
0.861
0.9442
372.9428
0.9033
0.9582
372.5164
0.9311
0.9684
372.3035
0.9451
0.9741
371.9117
0.9711
0.9855
371.7256
0.9836
0.9915
58
________________________________________________________________________________________________________ Appendix
Table A7: Experimental data and predicted values by SAFT-gamma Method for a binary
mixture of nonane and propyl butanoate for a given ester composition in the liquid phase.
T/K
422.7
422.17
421.65
420.47
420
419.47
418.87
417.5
416.51
416.24
415.76
415.39
415.21
414.9
414.8
414.65
414.47
414.35
414.4
414.45
414.55
414.65
414.76
414.95
415.06
415.26
415.35
415.64
415.69
415.89
416
Experimental data
X_ester
y_ester
0.0159
0.041
0.0315
0.0657
0.0501
0.0916
0.101
0.1581
0.1249
0.1871
0.1514
0.2175
0.1826
0.2505
0.2748
0.3435
0.3558
0.4186
0.3887
0.4472
0.4308
0.4802
0.4716
0.5162
0.5045
0.5416
0.5388
0.5707
0.5567
0.5808
0.5967
0.6185
0.6423
0.6568
0.6885
0.6929
0.7257
0.726
0.7705
0.7645
0.8023
0.7921
0.8234
0.8113
0.857
0.8421
0.8812
0.8648
0.9039
0.8884
0.9266
0.9123
0.9448
0.9311
0.9614
0.9509
0.9701
0.9614
0.9868
0.9807
0.9926
0.9891
Prediction by SAFT-gamma
T/K
X_ester
y_ester
423.34
0.0159
0.0279
422.90
0.0315
0.0542
422.39
0.0501
0.0842
421.13
0.101
0.1598
420.60
0.1249
0.1924
420.05
0.1514
0.2266
419.44
0.1826
0.2647
417.92
0.2748
0.3652
416.86
0.3558
0.4425
416.49
0.3887
0.4717
416.07
0.4308
0.5076
415.71
0.4716
0.5412
415.46
0.5045
0.5676
415.22
0.5388
0.5946
415.10
0.5567
0.6085
414.88
0.5967
0.6395
414.67
0.6423
0.6747
414.50
0.6885
0.7106
414.41
0.7257
0.7400
414.34
0.7705
0.7764
414.32
0.8023
0.8031
414.32
0.8234
0.8213
414.36
0.857
0.8513
414.40
0.8812
0.8738
414.46
0.9039
0.8958
414.54
0.9266
0.9186
414.62
0.9448
0.9376
414.70
0.9614
0.9556
414.75
0.9701
0.9653
414.85
0.9868
0.9844
414.89
0.9926
0.9912
59
______________________________________________________________________________________________________ References
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