H-LW -V equilibrium for systems formed with
binary gas mixtures
Hallvard Bruusgaard
Department of Chemical Engineering
McGill University, Montreal
March, 2011
A thesis submitted to McGill University in partial fulfillment of the requirements of the
degree of Doctor of Philosophy
©Hallvard Bruusgaard 2011
Abstract
Hydrate-liquid-vapor phase equilibria for systems with binary gas hydrate form-
ers was investigated. The Gibbs phase rule was applied to establish the number of
variables needed to specify the systems of interest as well as one additional intensive
variable to justify the equilibrium. A novel method was used to map the equilib-
rium planes for nitrogen+carbon dioxide+water and methane+ethane+water under
hydrate-liquid-vapor equilibrium. For the nitrogen+carbon dioxide+water system it
was found that along any given isotherm the equilibrium pressure increases with an
increased mole fraction of nitrogen in the vapor phase. The methane+ethane+water
system forms both structure I and structure II hydrates and hence consists of two
phase planes. The transition from structure I to structure II takes place around a 3
to 1 ratio of methane to ethane in the vapor phase. A 3D phase diagram of the sys-
tem is presented, containing both the structure I and a structure II sections. Along
any given isotherm and isobar in the structure I and II regions, it was found that the
equilibrium pressure increased and the equilibrium temperature decreased respec-
tively, with increasing mole fraction of methane in the gas phase. The equilibrium
pressure of structure I is found to be less sensitive to temperature and composition
changes than structure II.
The solubility of methane and carbon dioxide in the methane+carbon diox-
ide+water system under hydrate-liquid-vapor equilibrium was determined. The
solubility of methane increases with increasing pressures and decreasing tempera-
tures and the solubility of carbon dioxide increases with decreasing pressures and
increasing temperatures. Equilibrium vapor phase compositions were also mea-
sured and found to agree with other reported literature data. The system was also
completely modelled using a flash based technique where equilibrium pressures and
respective phase compositions were determined at various isotherms. The predic-
tive model is based on the Trebble-Bishnoi equation of state and the van der Waals
& Platteeuw and Holder models. The predictions were found to fit the data well
and all model parameters were independently optimized. This is the first time that
the solubility of hydrate formers in a binary hydrate forming system under hydrate
equilibrium conditions have been experimentally measured and compared to pre-
dicted values. The equilibrium data is an essential component in the expansion
of a hydrate growth model from single to multiple gas hydrate formers. A kinetic
growth model for systems with mixtures of gas hydrate formers was developed and
is proposed.
Resume
Les equilibres de phase hydrate-liquide-vapeur pour les systemes a gaz binaires
formant des hydrates ont ete etudies. La regle des phases de Gibbs a ete appliquee
pour etablir le nombre de variables necessaires pour preciser les systemes d’interet
ainsi qu’une variable supplementaire intensive pour justifier l’equilibre. Une nouvelle
methode a ete utilisee pour cartographier les plans d’equilibre pour l’azote+dioxyde
de carbone+eau et du methane+ethane+eau sous l’equilibre entre hydrate-liquide-
vapeur. Pour le systeme d’azote+dioxyde de carbone+eau, il a ete constate que
peu importe l’isotherme, la pression d’equilibre augmente avec la fraction molaire
d’azote dans la phase vapeur. Le systeme de methane+ethane+eau forme a la fois les
hydrates de structure I et II, composant ainsi deux plans de phase. La transition de
la structure I a la structure II a lieu autour d’un ratio de 3 a 1 de methane a l’ethane
en phase vapeur. Un diagramme 3D du systeme est presente, contenant a la fois les
sections de la structure I et II. Pour toute donnee d’isotherme et d’isobare dans les
regions de structure I et II, il a ete constate que la pression d’equilibre a augmente
et la temperature d’equilibre a diminue, respectivement, avec l’augmentation de
la fraction molaire d’ethane dans la phase gazeuse. La pression d’equilibre de la
structure I se trouve a etre moins sensible aux changements de temperature et de
composition que la structure II.
La solubilite du methane et du dioxyde de carbone dans le systeme de methane+
dioxyde de carbone+eau en equilibre sous hydrate-liquide-vapeur a ete determinee.
La solubilite du methane augmente avec la pression et diminue avec la temperature.
La solubilite du dioxyde de carbone montre un comportement inverse : elle augmente
avec la diminution de pression et l’augmentation de la temperature. Les composi-
tions d’equilibre en phase vapeur ont egalement ete mesurees et sont en accordance
avec les donnees de litterature disponibles. Le systeme a ete completement modelise
en utilisant une technique de base qui calcule la vaporisation instantanee, ou les
pressions d’equilibre et les compositions de phase respectives ont ete determinees a
des isothermes differentes. Le modele predictif est base sur l’equation d’etat Trebble-
Bishnoi, ainsi que les modeles van der Waals & Platteeuw et Holder. Les predictions
conformes aux donnees et tous les parametres modeles ont ete independamment
optimises. C’est la premiere fois que la solubilite des formateurs d’hydrates est
mesuree et comparee aux valeurs prevues dans un systeme binaire de formation
d’hydrates et dans des conditions d’equilibre d’hydrates. Les donnees d’equilibre
dans le developpement une composante essentielle dans representent d’un modele
de croissance d’hydrates, des formateurs d’hydrates de gaz simples aux formateurs
multiples. Un modele cinetique de croissance pour des systemes avec des melanges
de formateurs d’hydrates de gaz a ete developpe et propose.
Acknowledgements
First of all I would like to express my gratitude to my supervisor, Dr. Phillip
Servio, for his assistance, guidance, patience and trust in me during my graduate
studies. Thank you for your challenging and constructive discussions and for your
inspiration and friendship.
Chemical Engineering at McGill University has been a great learning experience.
I would like to thank my current and former research colleagues, in particular Dany
Posteraro, Anthony Carbone, Yeshai Mishal, Andre Breton and Juan Beltran for
their assistance, humour and fruitful debates. A special thanks also goes out to Mr.
Frank Caporuscio whose technical assistance helped me over many hurdles.
Julie Chamoun, you have always been there for me. During my highs and lows
there has always been a small but strong pillar keeping me up and running. Thank
you for being such a source of strength and endurance and for never losing faith.
Finally I would like to thank my family for all their love and support: my
dad for his never-ending enthusiasm and interest in my studies, my mom for her
understanding and consideration and my siblings who have kept me in the loop as
one of the crazy Bruusgaard six.
I would like to dedicate this thesis to all these people who have meant a lot to
me in various ways during my studies.
Contents
1 Introduction 1
2 Background 3
2.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Clathrate Hydrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Structure I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Structure II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.3 Structure H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Various Aspects of Hydrates . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Pipeline Blockage . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 In Situ Hydrates . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.3 Environmental Concerns . . . . . . . . . . . . . . . . . . . . . . 9
2.3.4 Carbon Dioxide Sequestration . . . . . . . . . . . . . . . . . . . 10
2.3.5 Gas Transportation . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Phase Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 Partial Phase Diagram for Simple Hydrates . . . . . . . . . . 14
2.4.2 Gibbs’ phase rule for non-reacting systems . . . . . . . . . . . 14
2.4.3 Solubility of gases in water in the presence of hydrates . . . . 16
2.5 Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.1 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.2 Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
i
CONTENTS ii
3 N2+CO2+H2O Equilibrium 24
3.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 CH4+C2H6+H2O Equilibrium 34
4.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.4 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.5 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5 CH4+CO2+H2O Solubilities 46
5.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.4 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.5 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6 CH4+CO2+H2O Solubility Predictions 58
6.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
CONTENTS iii
6.4 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.5 System Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.6.1 Vapor Phase Predictions . . . . . . . . . . . . . . . . . . . . . . 68
6.6.2 Liquid Phase Predictions . . . . . . . . . . . . . . . . . . . . . . 68
6.6.3 Pressure Predictions . . . . . . . . . . . . . . . . . . . . . . . . 68
6.6.4 Predictions trends . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7 Kinetic Model for Multicomponents 73
7.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.4 Growth model for simple hydrates . . . . . . . . . . . . . . . . . . . . 75
7.5 Proposed growth model for mixed hydrates . . . . . . . . . . . . . . . 76
7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8 Conclusion and Future Recommendations 80
8.1 Comprehensive Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 80
8.2 Future Work Recommendations . . . . . . . . . . . . . . . . . . . . . . 83
8.3 Other Significant Contributions . . . . . . . . . . . . . . . . . . . . . . 84
Bibliography 96
List of Figures
2.1 Structure I water cavities . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Comparison of Required Gas Storage Conditions . . . . . . . . . . . . 11
2.3 Comparison of Storage Potential of in hydrate structures . . . . . . . 12
2.4 Partial Phase Diagram for a simple hydrate system . . . . . . . . . . 15
2.5 Solubility of CH4 for the system CH4+H2O under H-Lw-V equilibrium 18
2.6 Solubility of CO2 for the system CO2+H2O under H-Lw-V equilibrium 18
2.7 Solubility of CH4 for the system CH4+H2O under H-Lw-V equilibrium 19
2.8 Solubility of CO2 for the system CO2+H2O under H-Lw-V equilibrium 19
2.9 Driving Force for Hydrate Growth . . . . . . . . . . . . . . . . . . . . 22
3.1 Jefri - DBR Phase Behaviour System . . . . . . . . . . . . . . . . . . . 28
3.2 Isotherms for the N2+CO2+H2O system under H-LW -V equilibrium 32
4.1 Isotherms for the CH4+C2H6+H2O system under H-LW -V equilibrium 40
4.2 Constant gas phase composition for the CH4+C2H6+H2O system un-
der H-LW -V equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 3D planes representation of the CH4+C2H6+H2O system under H-
LW -V equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.1 Apparatus used for H-LW -V solubility measurements of the CH4+CO2+H2O
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 Vapor phase mole fraction of CO2 under H-LW -V equilibrium for the
CH4+CO2+H2O system . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
iv
LIST OF FIGURES v
5.3 Liquid phase mole fraction of CH4 under H-LW -V equilibrium for the
CH4+CO2+H2O system . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.4 Liquid phase mole fraction of CO2 under H-LW -V equilibrium for the
CH4+CO2+H2O system . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.1 Predicted vs experimental liquid phase mole fraction of CH4 in the
CH4+CO2+H2O system . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2 Predicted vs experimental liquid phase mole fraction of CO2 in the
CH4+CO2+H2O system . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.3 Predicted vs experimental vapor phase mole fraction of CO2 in the
CH4+CO2+H2O system . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.4 Predicted hydrate phase mole fraction of CH4 in the CH4+CO2+H2O
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.5 Predicted hydrate phase mole fraction of CO2 in the CH4+CO2+H2O
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.1 Driving force - Gas Mixture . . . . . . . . . . . . . . . . . . . . . . . . 77
7.2 Interfacial Resistances - Gas Mixture . . . . . . . . . . . . . . . . . . . 78
List of Tables
3.1 H-LW -V equilibrium data for the N2+CO2+H2O system . . . . . . . 30
4.1 H-LW -V equilibrium data for the CH4+C2H6+H2O system . . . . . . 41
5.1 H-LW -V solubility data for the CH4+CO2+H2O system . . . . . . . 53
6.1 Mixing rule parameters for the Trebble-Bishnoi EOS (Trebble and
Bishnoi, 1988a) for binary systems. a(Hashemi et al., 2006), b(Trebble
and Bishnoi, 1988a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
vi
Contributions of Authors
The following dissertation is a manuscript-based document containing three pub-
lished peer-reviewed articles, as well as one accepted peer-reviewed article. The
author of the present dissertation is the first author for all the publications and was
responsible for the experimental work, the data analysis, as well as the writing of
each article. Co-author Beltran contributed in the editing and reviewing process
and co-author Carbone performed supervised replicates as part of equipment train-
ing.
– Bruusgaard, H., Beltran, J. & Servio, P., V-Lw-H Equilibrium Data for the
system N2+CO2+H2O , Journal of Chemical and Engineering Data, 53, 2594-
2597, 2008
– Bruusgaard, H., Carbone, A. & Servio, P., H-Lw-V equilibrium measurements
for the CH4+C2H6+H2O hydrate forming system, Journal of Chemical and
Engineering Data, 55 (9), 3680-3683, 2010
– Bruusgaard, H., Beltran, J. & Servio, P., Solubility measurements for the
CH4+CO2+H2O system under hydrate-liquid-vapor equilibrium, Fluid Phase
Equilibria, 296, 106-109, 2010
– Bruusgaard, H. & Servio, P., Prediction of methane and carbon dioxide solu-
bilities for the CH4+CO2+H2O system under hydrate-liquid-vapor equilibrium,
Fluid Phase Equilibria, Accepted Manuscript, February 2011
vii
Original Contributions
The following is a list of the original contributions from the thesis:
– Development of an alternative method to the isobaric and isothermal search
methods to determine H-Lw-V equilibria for binary gas hydrate former sys-
tems.
– Demonstrating that in addition to satisfying the phase rule, an additional
intensive variable must be reported to justify that the equilibrium has been
achieved.
– Mapping of the H-Lw-V equilibrium planes for the CH4+CO2+H2O and the
CH4+C2H6+H2O systems.
– Development of a method to determine the solubilities for binary gas hydrate
forming systems.
– Determination of solubilities for CH4 and CO2 in the liquid phase for the
CH4+CO2+H2O system under H-Lw-V equilibrium. This is the first reported
work to determine solubilities for binary gas hydrate forming systems in the
presence of hydrates.
– Modelling of the solubility data for CH4 and CO2 in the liquid phase for the
system CH4+CO2+H2O under H-Lw-V equilibrium. This is the first reported
work to predict solubilities for binary gas hydrate forming systems in the pres-
ence of hydrates.
– Proposing a kinetic growth model for systems with mixed hydrate formers.
viii
Chapter 1
Introduction
Hydrates are crystalline structures formed from water and a hydrate forming
substance such as gases and volatile liquids. Currently the most important reason
for hydrate research is flow assurance in gas and oil pipelines. Crystalline structures
will form due to the natural occurrence of gas and water in these environments.
The resulting clogged pipelines lead to large economical losses. A recent example
of such an event and the economical consequences can be seen in the first attempt
made by British Petroleum to seal the oil well in the Gulf of Mexico. Due to
improper considerations the initial plan to seal the well failed as a consequence of
the formation of hydrates. The well remained fully open for an additional month
before it was successfully capped. The month almost ended up sealing the fate
for British Petroleum, a company with a market cap of 287 billion USD. The need
to further understand hydrates will keep growing as oil and gas exploitation takes
place at more and more extreme ocean depths.
The second important, but still somewhat premature reason for hydrate interest
is the extraction of energy from large amount of natural hydrates on earth. The
amount of methane stored in hydrates is estimated to be equivalent to twice that
of fossil fuels in the world (Suess et al., 1999). Although some pilot projects have
been employed in permafrost regions, the vast majority of these in situ hydrates
are located in the ocean floor sediments and the extraction of this energy source is
1
CHAPTER 1. INTRODUCTION 2
still not currently commercially feasible.
A vast majority of the research on gas hydrates has been performed on simple
systems, containing only a single hydrate former. The main advantage of study-
ing simple rather than mixed systems is the number of variables that need to be
considered. In simple systems it is easier to isolate and determine fundamental in-
trinsic variable(s) of interest for the specific system. The information that cannot
be obtained through such studies on simple systems is the effect hydrate forming
mixtures and their ratios have on the hydrate structures and properties. Most hy-
drates found, whether in industry or nature, will exist as mixed hydrates and hence
multicomponent hydrate properties need to be understood and considered.
In order to develop a better understanding of these more complex systems,
ranging from equilibrium properties to growth models, I have chosen to focus on
binary gas hydrate systems. Understanding such mixtures and their properties is
essential in various aspects such as: hydrate formations, hydrate transportation,
sequestration of flue gas using hydrate and the extraction of methane in natural
hydrates through selective replacement by carbon dioxide. The obtained equilibrium
properties and presented model predictions also serve as an essential component to
determine the driving force for hydrate kinetics.
Chapter 2
Background
Hydrates or gas hydrates are nonstochiometric crystalline compounds that be-
long to the group of inclusion compounds known as clathrates (Huang et al., 1965).
The hydrate structure is made up of water molecules that form a cavity through
hydrogen bonding. The empty hydrate lattice is thermodynamically unstable. The
lattice is stabilized through the presence of a gas or a volatile liquid inside the lattice
(Englezos, 1993). There is no chemical bonding between the lattice and the guest
molecule, only physical bonding via weak van der Waal’s forces.
2.1 History
The discovery of hydrates in 1810 is accredited to Sir Humpry Davy (Davy,
1811). Davy discovered that an aqueous solution of chlorine would crystallize at
temperatures below 9.0○ C. Hydrates remained a purely academic interest for the
next century. Research was focused on discovering the species capable of hydrate
formation along with respective partial pressure-temperature phase diagrams. A
new milestone in hydrate history was reached after the discovery of hydrates in
gas-pipelines in the 1930s. Hydrates were found to clog pipelines, becoming a ma-
jor concern to the rapidly growing gas and oil industry (Hammerschmidt, 1934).
Since then, large amounts of industrial resources were used in the development of
3
CHAPTER 2. BACKGROUND 4
inhibitors along with determining various thermodynamic properties of hydrates
(Sloan and Koh, 2008). The last major step in hydrate history occurred in the
1960s with the discovery of in situ hydrates in the Siberian permafrost by Mako-
gon(Makogon, 1965). For the first time hydrates were considered a potential en-
ergy source. The reason being that naturally occurring hydrate is formed mainly
from methane, the main component of natural gas. Hydrates were later discovered
in large amounts in seafloor sediments. More recent estimates predict the total
amount of energy stored as hydrates to be equivalent to twice that of all fossil fuels
combined (Suess et al., 1999).
2.2 Clathrate Hydrates
Clathrate compounds usually consist of two molecular species. They arrange
themselves in space in such a way that one of the species forms lattices (host)
that physically entrap the other species (guest). Clathrates are further categorized
based on whether the lattice is made up of water molecules or not. The water
based clathrates are called clathrate hydrates, but they are commonly known as gas
hydrates or simply hydrates (Englezos, 1993).
In the hydrate lattice, water molecules form cages via hydrogen bonding. The
resulting structure is thermodynamically unstable without the presence of a guest
molecule inside the cavity. The guest molecule interacts with the hydrate lattice
through weak attractive van der Waal’s forces that stabilize the crystal structure.
There is no physical bonding in the hydrate structure. Hydrates consist of approx-
imately 85 % water on a molecular basis (Sloan and Koh, 2008). The type or types
of guest molecules determines the resulting hydrate structure. The structure must
contain cages with a suitable size ratio to the guest molecules. A guest to cage size
ratio is approximately 0.9 for stable hydrate structures. Multiple occupancies in
the large cages have been reported, but only under extreme pressures (Chazallon
and Kuhs, 2002). The three most common hydrate structures are structure I (sI),
structure II (sII) and structure H (sH). All three structures have been identified
CHAPTER 2. BACKGROUND 5
in nature in the form of pure and coexisting structures (Hester and Brewer, 2009).
Molecules that interfere with the hydrogen bonding of water molecules in the lattice
(Jeffrey, 1984) as well as molecules of insufficient diameter to stabilize the smallest
cages cannot stabilize a hydrate structure(Sloan and Koh, 2008).
2.2.1 Structure I
A structure I hydrate is created from water molecules that arrange themselves
in space to form twelve linked pentagonal faces called a pentagonal dodecahendron
(512). When the pentagonal dodecahendrons cavities link together through their
vertices, a polyhedron cavity with twelve pentagonal and two hexagonal faces called
tetrakaidecahedron (51262) is created (Englezos, 1993). A sI unit cell consists of two
512 and six 51262 cavities which consist of a total of 46 water molecules (Sloan and
Koh, 2008). The cavity structure and arrangement is illustrated in figure 2.1.
sI hydrates form from molecules with diameters in the range of 420-580 pm
(Tse et al., 1986). Common sI hydrate forming gases is pure methane, ethane and
carbon dioxide (Sloan, 2003). Some mixtures of these sI forming guest molecules,
like methane and ethane mixture, can yield sII at certain ratios (Subramanian et al.,
2000b).
2.2.2 Structure II
Structure II hydrate is formed when the pentagonal dodecahendron (512) cavities
link together through face sharing. The arrangement gives rise to a hexakaidecahe-
dron cavity, being a polyhedron with twelve pentagonal and four hexagonal faces
(51264) (Englezos, 1993). A sII unit cell consists of sixteen 512 and eight 51262 cavi-
ties which consist of a total of 136 water molecules. The large cavity in sII is slightly
larger than the large sI cavity and the small cavity in sII is slightly smaller than
the small sI cavity (Sloan and Koh, 2008). The cavity structure and arrangement
is illustrated in figure 2.1.
sII hydrates form from molecules with diameters between 600 and 700 pm and
CHAPTER 2. BACKGROUND 6
Figure 2.1: Water cavities present in Structure I, Structure II and Structure Hhydrate (adapted from Hester and Brewer (2009)).
CHAPTER 2. BACKGROUND 7
smaller than 400 pm. Common sII hydrate forming gases are propane and iso-
butane, which occupy the large cavity (Sloan, 2003). The smallest hydrate forming
gas molecules like argon and krypton will also form sII due to the small size of the
512 cavity (Holder and Manganiello, 1982; Davidson et al., 1984).
2.2.3 Structure H
The structure H hydrate was discovered in 1987 by Ripmeester (Ripmeester
et al., 1987). Unlike sI and sII, the sH hydrate cannot form simple hydrates. The
structure contains the basic (512) cage found in sI and sII. It also contains 435663
cage which has three square, six pentagonal and three hexagonal faces and a large
51268 cage with twelve pentagonal and eight hexagonal faces. A sH unit cell consists
of three 512, two 435663 and one 51268 cavities for a total of 34 water molecules (Sloan
and Koh, 2008). In order to form a stable structure two hydrate forming molecules
of different sizes are required. The cavity structure and arrangement is illustrated
in figure 2.1.
sH hydrates form from large molecules with diameters between 800 and 900
pm that can occupy the larger cage in a mixture with smaller molecules such as
methane and carbon dioxide (Sloan, 2003). Common large sH forming molecules
are adamantane and neohexane.
2.3 Various Aspects of Hydrates
Hydrates crystals are important in many different ways. In addition to being
a concern to the oil and gas industry, these ice-like crystals contain the largest
natural source of methane on earth. The unique properties of hydrates also make
them applicable to a wide range of applications.
CHAPTER 2. BACKGROUND 8
2.3.1 Pipeline Blockage
Hydrates have long been known to block oil and gas transmission lines (Hammer-
schmidt, 1934). The presence of these non-flowing crystalline structures in pipelines
halts the flow and can result in production stoppage for up to several months while
the hydrates dissociate (Sloan, 2003). The dissociation process is also a concern
with respect to safety and property damage (Chatti et al., 2005). When heated, a
hydrate plug is likely to detach from the wall. If a large pressure gradient is present
in the pipe, the result could be a high velocity solid hydrate projectile shooting
through the pipe. Speeds of such projectiles have been measured at 300 km/h
with the possibility of pipeline blowouts and erupted pipe walls. Local heating of
a hydrate plug is also dangerous due to a substantial local pressure build-up from
dissociated hydrates (Sloan, 2003).
The presence of water and hydrate forming hydrocarbons in oil as gas wells
combined with the demand for a continuous process operating under hydrate form-
ing conditions has made hydrate inhibition an important research field. Hydrate
inhibitors are classified as thermodynamic, kinetic or antiagglomerants. Thermo-
dynamic inhibitors alter the conditions under which hydrate form, while kinetic
and antiagglomerants retard hydrate formation and growth times to exceed the
residence time of the gas within the hydrate-prone section of a pipeline. Thermody-
namic inhibitors such as methanol and glycols are frequently used in industry, but
large quantities of up to 60 wt% are required (Koh et al., 2002) and the alcohols are
difficult to recycle (Sloan and Koh, 2008). Consequently recent research has been
devoted into the development of cost efficient and environmentally friendly poly-
mers (Karaaslan and Parlaktuna, 2002) and dispersants (Koh et al., 2002) proven
to be efficient at quantities of less than 1 wt%.
2.3.2 In Situ Hydrates
The discovery of large quantities of in situ hydrates by Cherskii and Makogon
made hydrates considered a potential future energy source (Makogon, 1965; Cher-
CHAPTER 2. BACKGROUND 9
skii and Makogon, 1970). The majority of natural hydrates have been uncovered in
the ocean floor sediments, but large quantities have also been found in permafrost
regions. Natural hydrates mainly consist of methane, the main component of nat-
ural gas. The estimated quantities of organic carbon found as in situ hydrates
exceed more than twice that in current fossil fuel reserves (Suess et al., 1999). Con-
sequently, the development of methods to extract the energy is being researched,
but has yet to become economically viable. The discovery of vast methane deposits
has also resulted in studies being conducted to evaluate the threats related to global
decomposition of natural gas hydrates in both the permafrost and in the less ac-
cessible oceanic regions. Methane-hydrates exist in sufficiently large quantities to
significantly alter the earth’s climate if the crystals were to become unstable and
decompose (Englezos, 1993).
2.3.3 Environmental Concerns
Methane, the most abundant natural hydrate former, has a global warming
potential 21 times greater than carbon dioxide (Taylor, 1991). If the earth’s tem-
perature keeps rising, large quantities of natural hydrates are likely to become ther-
modynamically unstable and decompose. The released methane will enhance the
global warming process as continuously increasing amounts of methane are being
released into the atmosphere owing to the acceleration of hydrate decomposition.
This scenario is often referred to as the ”runaway” greenhouse effect (Englezos,
1993). Hydrates have resulted in disasters throughout history. Scientists suspect
an unstable hydrates field to have caused one of history’s most impressive releases
of methane 8000 years ago, known as the Storrega submarine landslide. Scientific
evidence shows that 5600 km3 of sediments slid 800 km in the Norwegian Sea. The
result of such movements were devastating tsunamis and horrific swells along the
coastline of Norway. (Suess et al., 1999).
CHAPTER 2. BACKGROUND 10
2.3.4 Carbon Dioxide Sequestration
With carbon dioxide accounting for an estimated 2/3 of the increase in global
warming (Bryant, 1997), another important benefit to hydrate research is the po-
tential development of technology to capture and store carbon dioxide in the ocean
(Chatti et al., 2005). The ocean was suggested as a way of disposing carbon dioxide
produced from fossil fuels since 1977 (Marchetti, 1977). The potentially beneficial
environmental aspect of successful carbon dioxide sub-sea sequestration has led to
further research within the area (Holder et al., 1995; Brewer et al., 1999; Brewer,
2000). Despite the fact that marine carbon dioxide sequestration currently remains
at the experimental phase (Chatti et al., 2005), the ocean already serves as the
world’s most powerful buffer against global warming through its natural uptake of
carbon dioxide (Brewer et al., 1999).
2.3.5 Gas Transportation
The use of hydrate for storage and transportation of natural gas (NG) has
long been investigated because hydrates store large quantities of gas (Sloan and
Koh, 2008). Although the gas density is not as high as that of liquefied natural
gas (LNG), and that of compressed natural gas (CNG) the temperature and pres-
sure requirements are much closer to standard temperature and pressure conditions
(STP)(Sloan and Koh, 2008). This is illustrated in figure 2.2. The storage capac-
ity for a specific gas is known to vary depending on the hydrate structure. The
maximum storage potential of methane in the small cage has been compared and
found to be in ratio of 1:3:4 for sI, sII and sH respectively (Khokhar et al., 2000).
This is illustrated in figure 2.3 where the maximum energy density of CH4 in the
small cavities of sI, sII and sH is shown and compared to the energy density of
LNG. The energy density is defined as the energy of methane entrapped per unit
volume. In a feasibility study by Børrehaug and Gudmundsson a 24 % reduction
in cost was estimated when comparing transportation of NG in the form of hydrate
to that of LNG (Khokhar et al., 1998). In addition to be potentially economically
CHAPTER 2. BACKGROUND 11
NG 160 m3 @ STP
1m3
1m3
1m3
Increasing Temperatures
Decreasing Pressures
LNG -‐160°C 1 bar
HYDRATE -‐15 to 15°C 1 to 25 bar
CNG 25°C 200 bar
Figure 2.2: Conditions required to compress 160 m3 of natural gas (NG) into 1 m3
of liquified natural gas (LNG), hydrate and compressed natural gas (CNG).
beneficial, crystallizing gas is regarded as a safer way of storing toxic and explosive
gases (Englezos, 1993).
2.4 Phase Equilibria
Since the discovery of hydrates, the greater part of hydrate equilibria studies
have focused on gathering incipient hydrate formation data for hydrates as well
as to develop predictive methods for the calculation of phase equilibria. Incipient
hydrate formation conditions describe an infinitesimal amount of hydrate crystal in
equilibrium with the fluid phases. Knowledge and predictive models of the required
conditions for hydrate formations are essential for designing efficient and economical
CHAPTER 2. BACKGROUND 12
0.0E+00
2.0E+06
4.0E+06
6.0E+06
S I S II S H LNG
Energy Den
sity [K
cal/m
3 ]
Figure 2.3: Maximum energy density of CH4 in the small cavities of sI, sII and sHcompared to the energy density of LNG. The values are obtained from the work ofKhokhar et al. (Khokhar et al., 1998).
CHAPTER 2. BACKGROUND 13
processes in hydrate related industries (Englezos, 1993). Traditionally an isochoric
reactor equipped with viewing windows is used to determine the hydrate equilib-
rium temperature and pressure conditions. Equilibrium conditions are determined
either by the frequently used isothermal pressure-search method or by the isobaric
temperature-search method. Either method works by stepwise shifting the system
towards hydrate dissociation conditions by the adjustment of only one state param-
eter while visually monitoring the presence of a hydrate phase. A large collection
of hydrate-liquid-vapor (H-LW -V) equilibrium data for various systems is provided
by Sloan (Sloan and Koh, 2008).
With the growing amount of equilibrium data available, research effort was in-
vested into computation of phase equilibrium for hydrate systems. van der Waals
and Platteeuw proposed a model for the chemical potential of water in the hydrate
phase and computed incipient formation pressures for various gases (van der Waals
and Platteeuw, 1959). The theory was later combined with classical thermodynam-
ics by Kobayashi and co-workers to predict incipient hydrate formation conditions
(Saito et al., 1964; Nagata and Kobayashi, 1966). The van der Waals and Platteeuw
model also served as the basis for the algorithm by Parrish and Prausnitz to predict
equilibria in multicomponent mixtures (Parrish and Prausnitz, 1972). Later, other
models that considered hydrate formation conditions from electrolyte and polymer
solutions were presented by Englezos (Englezos, 1992a,b).
A hydrate forming system at equilibrium can be completely solved using a flash
calculation. The calculation solves mass balances and equilibrium equations for all
phases simultaneously (Englezos, 1993). A suitable equation of state (EOS), such
as the Trebble-Bishnoi EOS (Trebble and Bishnoi, 1987) can be used to describe
the vapor and liquid phases, while the hydrate phase is commonly described with
models based on the van der Waals and Platteteeuw theory. Complete system
calculations and prediction were first performed by Bishnoi et al. (Bishnoi et al.,
1989) and Gupta et al. (Gupta et al., 1991). The calculations were based on an
algorithm that simultaneously solves phase equilibria and stability equations for
multicomponent systems.
CHAPTER 2. BACKGROUND 14
2.4.1 Partial Phase Diagram for Simple Hydrates
Hydrates formed from a single hydrate former and water, i.e. simple hydrates,
have been the subject of the most commonly studied hydrate systems. They have
been the primary interest of hydrate researchers since the work done by Deaton and
Frost over 60 years ago (Deaton and Frost, 1946). A typical partial phase diagram
for the regions of interest is shown in figure 2.4
The primary region of interest is found at temperatures and pressures above
the lower quadruple point (Q1) and can be observed in the graph as the region
above the H-Lw-V equilibrium line. Gases such as methane and nitrogen which are
supercritical at the lower quadruple point will not have a defined upper limit for
H-Lw-V equilibrium conditions. Gases such as carbon dioxide and propane that are
not supercritical at Q1 will have an upper quadruple point (Q2). The presence of
a vapor pressure line above Q1 results in upper limiting conditions (temperature
and pressure) at which H-Lw-V equilibrium can occur (Q2) and is also important
to consider in hydrate kinetic as it limits the potential driving force for hydrate
growth.
2.4.2 Gibbs’ phase rule for non-reacting systems
The formation of hydrate crystals is a non-chemical process in which water
molecules link together through hydrogen bonding which forms a lattice that in-
teracts with the guest molecule through weak van der Waal’s forces. As a result,
the degrees of freedom associated with hydrate systems are defined by Gibbs’ phase
rule for non-reacting systems as follows:
F = N − π + 2 (2.1)
where F is the degrees of freedom, N is the number of components and π is
the number of phases. The degrees of freedom of a system define the number of
variables needed to specify the intensive state of a system. To ensure that the system
has achieved equilibrium the measurement of an unspecified intensive variable is
CHAPTER 2. BACKGROUND 15
I-‐H-‐V
H-‐L-‐V
H-‐Lw
-‐L
Lw-‐L-‐V
Q1
Q2
Log (Pressure)
Temperature
Figure 2.4: Partial Phase Diagram for simple hydrate former systems. The H-L-V and the Lw-L-V lines are dotted as their appearance depends on the state ofthe hydrate former. Q1 represents the lower quadruple point(I-Lw-H-V) and Q2represents a possible upper quadruple point(H-Lw-L-V).
CHAPTER 2. BACKGROUND 16
required. To completely define a specific system an extensive property must also be
reported. For a simple hydrate system under H-Lw-V equilibria the system has one
degree of freedom. With the specification of one variable, temperature or pressure in
the case of simple hydrates, the system is completely specified. However, to justify
that the system has reached equilibrium an additional intensive variable must be
reported.
For a binary hydrate forming system with two degrees of freedom two intensive
variables must be specified and an additional variable reported. Due to the difficulty
of holding the fraction of a specific component constant in a given phase, the phase
rule is typically satisfied by controlling the temperature and pressure. To justify or
verify that the system has achieved equilibrium, a phase composition analysis must
be performed.
For more complex systems where the number of hydrate formers exceeds two, it
would be necessary to form the hydrate in an environment where the gas phase is
present in such excess that the formation of hydrates would not significantly alter
the gas phase composition. With such a “locked“ gas phase composition, the system
can be analyzed and treated as a single hydrate former.
2.4.3 Solubility of gases in water in the presence of hydrates
The solubility of hydrate former systems under V-Lw equilibrium has been ex-
tensively studied over the years. On the contrary, only a limited number of studies
have considered the solubility of typical hydrate formers under H-Lw equilibrium.
The methane-water and carbon dioxide-water systems account for almost all the
studies within this field, due to the potential applications associated with these
simple hydrates systems. The solubility of other systems in the presence of hy-
drates, such as ethane-water (Kim et al., 2003) and propane-water (Gaudette and
Servio, 2007), has also been reported. High pressure systems, such as nitrogen-
water will require the development of new procedures and/or techniques in order
to overcome the pressure limitation of the current measurement techniques. The
experimental data along with theoretical and semi-empirical models have been used
CHAPTER 2. BACKGROUND 17
to establish the effect of pressure and temperature on the solubility of gas in water
under H-Lw equilibrium.
The effect of temperature on the solubility of the hydrate formers under V-
Lw and H-Lw equilibria is well known from experimental data and correspond-
ing model predictions. Servio and Englezos performed solubility measurements
on the methane+water and carbon dioxide+water systems in the presence of hy-
drates (Servio and Englezos, 2001, 2002). The solubility data was later modelled by
Hashemi et al. The model uses the Trebble Bishnoi’s equation of state along with
the models by van der Waal & Platteeuw and the Holder (Hashemi et al., 2006) to
predict the solubility of the hydrate formers in the liquid phase under H-Lw equi-
librium. Plots of the experimental data and corresponding model predictions for
the solubility of methane and carbon dioxide in the methane+water and the carbon
dioxide+water systems under Lw-V, H-Lw-V and H-V are shown in figure 2.5, 2.6.
In the H-Lw region, both systems have positive trends with increasing solubility of
the hydrate former with increasing temperatures along the isobars. In the Lw-V
region the trends reverse for both systems and solubilities decrease with increasing
temperatures along the isobars. The results and trends agree with the findings of
other researchers such as Yang et al. (Yang et al., 2000, 2001), Kim et al. (Kim
et al., 2003) and Gaudette and Servio (Gaudette and Servio, 2007).
The effect of pressure on solubility of the hydrate former under H-Lw equilibria is
not as evident as that of temperature (Servio and Englezos, 2002) and has therefore
been more difficult to establish. Early on, Handa derived a model based on the
work of van der Waal and Platteauw which predicted that the solubility of methane
decreases at increasing pressures in the H-Lw region (Handa, 1990). The following
experimental results of Yang et al. (Yang et al., 2000, 2001), Servio and Englezos
(Servio and Englezos, 2001, 2002) and Kim et al. (Kim et al., 2003) bore evidence
of a weak pressure dependency of the solubility of methane under H-Lw equilibrate,
however, no exact trends were inferred. Handa’s predictions were experimentally
confirmed by Seo et al. (Seo et al., 2002). More recently Lu et al. reached the
same conclusion with the use of Raman spectroscopy to determine the solubility of
CHAPTER 2. BACKGROUND 18
Figure 2.5: Solubility of CH4 along iso-bars for the system CH4+H2O under H-Lw-V equilibrium. Figure is adaptedfrom Hashemi et al. (Hashemi et al.,2006).
Figure 2.6: Solubility of CO2 along iso-bars for the system CO2+H2O under H-Lw-V equilibrium. Figure is adaptedfrom Hashemi et al. (Hashemi et al.,2006).
methane in the H-Lw region (Lu et al., 2008). Very limited conclusive data exist
regarding the effect of pressure on carbon dioxide under H-Lw equilibra. Someya et
al. performed experiments where carbon dioxide solubility was found to increase at
increasing pressures in the H-Lw region for isotherms greater than 277 K (Someya
et al., 2005).
The effect of pressure on the solubility of the methane (see figure 2.7 ) and
the carbon dioxide (see figure 2.8) under H-Lw has recently been derived and pre-
dicted from first principles using fundamental thermodynamics by Bergeron et al.
(Bergeron et al., 2009). The results were found to be in agreement with recent
experimental results (Someya et al., 2005) and semi-empirical predictions (Hashemi
et al., 2006).
CHAPTER 2. BACKGROUND 19
Figure 2.7: Solubility of CH4 alongisotherms for the system CH4+H2O un-der H-Lw-V equilibrium. Figure isadapted from Bergeron et al. (Bergeronet al., 2009).
Figure 2.8: Solubility of CO2 alongisotherms for the system CO2+H2O un-der H-Lw-V equilibrium. Figure isadapted from Bergeron et al. (Bergeronet al., 2009).
2.5 Kinetics
The formation of hydrates is a process analogous to the crystallization process
(Makogon, 1981; Bishnoi and Natarajan, 1996). The phase transformation can be
divided into a nucleation and a growth phase (Natarajan et al., 1994). The hydrate
nucleation phase is initialized with a supersaturation of the liquid phase in which
hydrate nuclei form and dissolve (Englezos et al., 1987a). The phase continues until
a nuclei of critical size is formed and the growth phase commences (Sloan and Koh,
2008), a point often referred to as the turbidity point (Englezos et al., 1987a)
2.5.1 Nucleation
The formation of hydrate nuclei is based on the natural occurrence of clusters
of molecules of the dissolved substance that form as a result of local concentration
gradients. For each supersaturated solution there exists a critical cluster. A critical
cluster is defined as a cluster of the size required to stay in equilibrium with the
supersaturated solution and is often referred to as a critical nucleus ((Natarajan
CHAPTER 2. BACKGROUND 20
et al., 1994). Critical clusters are stable and further growth immediately leads to
the formation of crystal hydrates. Clusters of a size less than the critical size are
unstable and may grow or break in the aqueous solution (Bishnoi and Natarajan,
1996). The time required to form a hydrate nuclei of critical size and induce hydrate
growth is known as the induction time and was first described by Hammerschmidt
in the 1930s (Hammerschmidt, 1934).
The duration or time of the nucleation phenomena is stochastic in nature and
cannot be predicted, but it can be influenced by certain factors in addition to
temperature and pressure. The level of supersaturation has been related to the
induction time by Bishnoi (Bishnoi and Natarajan, 1996) and is found to have
an inverse relationship. This finding can be seen in connection with reportedly
reduced induction times at higher stir rates (Englezos et al., 1987a). The history
of water has also been proven a factor for induction time by repeatedly more rapid
formation of hydrates from previously crystallized water compared to distilled water
(Vysniauskas and Bishnoi, 1983). In addition, it has been suggested that the ratio
of hydrate former diameter to cavity size affects induction times (Sloan and Koh,
2008). Specific system properties such as the heterogeneties of the reactor wall and
stirrer along with impurities are also factors known to affect the induction time
(Natarajan et al., 1994).
2.5.2 Growth
Hydrate growth commences with the formation of a nuclei of critical size which
grows spontaneously to form hydrate crystals. The growth period is characterized
by an exothermic process that incorporates large amounts of saturated gas into
the formation of a hydrate phase (Sloan and Koh, 2008). The rate of growth of a
hydrate phase is therefore governed by the heat and mass transfer rates along with
(or as part of) the previously discussed factors affecting induction time.
The foundation for modern hydrate growth models which is based on Mako-
gon’s view of hydrate formation as a crystallization process (Makogon, 1981), was
developed by Vysniauskas and Bishnoi in the 1980’s. They concluded that formation
CHAPTER 2. BACKGROUND 21
kinetics is dependent on the vapor-liquid interfacial area, pressure, temperature and
degree of supercooling (Vysniauskas and Bishnoi, 1983). A semi-empirical model
was also presented.
By further developing the work of Vysniauskas & Bishnoi, Englezos et al. de-
veloped a mechanistic model with the reaction rate constant as the only adjustable
parameter (Englezos et al., 1987a). The model was the first hydrate growth model
based on kinetics of crystallization. The rate of hydrate formation was found to be
proportional to the difference in the fugacity of the dissolved gas at the experimental
conditions and fugacity of the dissolved gas at the three-phase equilibrium curve at
the experimental temperature and corresponding pressure. The work was expanded
to model gas mixtures based on the same theory and driving force (Englezos et al.,
1987b).
In 1994 Skovborg and Rasmussen redirected the idea of the driving force for hy-
drate growth from being a thermodynamic property to being a mass-transfer gradi-
ent (Skovborg and Rasmussen, 1994). This was followed up by a similar conclusion
by Mork and Gudmundsson, who also found hydrate growth to be solely governed
by mass transfer. They defined the driving force as the difference in concentration
between the hydrate former at the gas-liquid interface under H-Lw equilibrium and
the hydrate former at the crystal surface at a system pressure and the corresponding
H-Lw-V temperature (Mork and Gudmundsson, 2002).
The basis for the most recent driving force definition was presented by Hashemi
(Hashemi et al., 2007) and was based on her previous solubility work (Hashemi
et al., 2006). The driving force is mass transfer based and defined as the difference in
concentration of the hydrate former in liquid under hydrate liquid water equilibrium
and the hypothetical liquid-vapor equilibrium at a given temperature and pressure.
The driving force is illustrated in figure 2.9.
The driving force gave rise to the most recent approach for hydrate kinetic
growth model by Bergeron and Servio (Bergeron and Servio, 2008a). The model
is based on Englezos’ model (Englezos et al., 1987a) combined with a simplified
version of the driving force definition proposed by Hashemi et al. (Hashemi et al.,
CHAPTER 2. BACKGROUND 22
Temperature
Mole frac/o
n of hydrate fo
rmer
Lw-‐V
H-‐Lw-‐V
DF
Figure 2.9: Illustration of driving force (DF) for hydrate growth as described byHashemi et al. (Hashemi et al., 2007). The Lw-V and the H-Lw curves represent thesolubilities for the hydrate former at a function of temperature at a given pressure.’Lw-V’ represents hypothetical Lw-V solubilities under H-Lw conditions.
CHAPTER 2. BACKGROUND 23
2007). The development of a kinetic modelling for multiple hydrate fomers follow
in Chapter 7.
Chapter 3
Vapor + Liquid Water + Hydrate
Equilibrium Data for the System
N2+CO2+H2O1
3.1 Preface
Phase equilibria for simple hydrate system have been extensively studied since
the discovery of hydrates in natural gas pipelines. However, both in industry and in
nature, hydrates are often formed from a mixture of gases rather than from a single
hydrate former. Previous work has been done on several binary hydrate forming
systems, but many of the reported studies have treated the loading composition as
an equilibrium composition and consequently the system is inadequately described.
With the exception of a few data points, no previous complete equilibrium data
existed for the N2+CO2+H2O system under H-LW -V equilibrium. Due to the im-
portance of the mixture in relation to flue gas sequestration the system was studied
to properly map and describe its H-LW -V equilibrium plane.
1. Reproduced in part with permission from Bruusgaard, H., Beltran, J. & Servio, P., V-Lw-HEquilibrium Data for the system N2+CO2+H2O , Journal of Chemical and Engineering Data, 53,2594-2597, 2008. Copyright 2011 American Chemical Society. DOI: 10.1021/je800445x
24
CHAPTER 3. N2+CO2+H2O EQUILIBRIUM 25
3.2 Abstract
Three phase equilibrium conditions for the N2+CO2+H2O system in H-LW -V
equilibrium were determined. The temperature and pressure conditions studied
were in the range of 275 to 283 K and 2.0 to 22.4 MPa, respectively. As the system
has 2 degrees of freedom, pressure and temperature were fixed and gas composition
was measured when equilibrium was achieved. The collected data represents points
on an equilibrium plane. It was found that along any given isotherm on the plane,
the hydrate equilibrium pressure increases with increasing mole fraction of nitrogen
in the gas phase.
3.3 Introduction
Gas hydrates are non-stoichiometric crystalline solids that form when molecules
from a gas or volatile liquid, suitable for hydrate formation, are enclosed in a cage
consisting of water molecules (Englezos, 1993). Hydrates were first discovered in
the 1810 by Sir Humphry Davy (Davy, 1811). During the following 100 years
the interest in these ice-like structures was purely academic. Research was put into
discovering the different compounds capable of hydrate formation and the respective
temperature-pressure conditions at which these hydrates formed. The interest in
hydrates accelerated after the discovery of hydrates in gas-pipelines in the 1930s
when hydrates were found to clog the pipelines, becoming a major concern to the
rapidly growing gas and oil industry (Hammerschmidt, 1934). Since then, large
amount of industrial resources have been used in the development of inhibitors as
well as in finding the thermodynamic properties of hydrate formation (Servio, 2002).
Natural gas hydrates are found in large amount at the bottom of the ocean as well as
in permafrost regions (Sloan, 2000). It is currently estimated that the hydrocarbon
reserves found in hydrates exceed more than twice of all other hydrocarbon sources
combined (Kvenvolden, 2002). The use of hydrates in storage of carbon dioxide on
the bottom of the ocean has been suggested as a way of reducing greenhouse gas
emissions into the atmosphere (Brewer, 2000).
CHAPTER 3. N2+CO2+H2O EQUILIBRIUM 26
CO2 and N2 are known to form S I and S II respectively (Sloan, 1998). Davison
et al. suggested that nitrogen occupied and stabilized both the small and large cages
of structure II (Davidson et al., 1986). In the case of a gas mixture, the resulting
hydrate structure is reported to differ according to the gas ratios. For the N2+CO2
system, 85 mol % of N2 has been reported as the boundary of coexisting S I and S II
hydrate (Diamond, 1994). Seo et al. later performed studies using X-ray diffraction
and NMR and he confirmed that the N2+CO2 hydrate does form structure I at
from a loading composition of 10 and 20 mol % of CO2 (Seo and Lee, 2004). The
equilibrium values for the nitrogen+carbon dioxide + water (N2+CO2+H2O) sys-
tem in hydrate-liquid water-vapor (H-LW -V) equilibrium have also been previously
studied. Fan et al were amongst the first to study the mixture at low concentrations
of nitrogen (Shuan-Shi and Tian-Min, 1999). Kang et al. followed this study by
reporting equilibrium points for the entire range of gas mixture ratios (Kang et al.,
2001). In both cases, equilibrium temperature and pressure values are reported
along with the loading compositions of gas. In the data presented, the equilibrium
vapor phase is assumed constant with changing pressure and temperature. Kang
et al. also modeled H-V equilibrium for the N2+CO2+H2O system and reports the
hydrate-vapor composition. In a more recent study, Linga et al. studied the kinetics
of the N2+CO2+H2O system and reported a few equilibrium points were reported
in the study at 273.7K (Linga et al., 2007b). This paper presents equilibrium values
for the system N2+CO2+H2O under H-LW -V equilibrium; temperature, pressure
and vapor phase composition equilibrium values are reported. The work illustrates
the vast difference between loading and equilibrium composition of the gas phase
of a mixture. Unless a third variable is measured and reported, then there is an
infinite number of potential equilibrium points at the given temperature and pres-
sure. The work is inspired by previous work by Beltran et al. performed on a
different system (Beltran and Servio, 2008b). This work acquires the equilibrium
points through the use of a new technique, justified by the phase rule applied to bi-
nary gas-phase mixtures under H-LW -V equilibrium. The procedure is described in
detail in the experimental section and the application of the phase rule is explained
CHAPTER 3. N2+CO2+H2O EQUILIBRIUM 27
in the discussion section.
3.4 Experimental Apparatus
Experiments were carried in a Jefri-DBR Phase Behavior System (Oilphase-
DBR- Schlumberger) Figure 3.1. The heart of the system was a high-pressure
PVT cell consisting of a glass cylinder (20 cm in height and total void volume 150
cm3), secured between two full-length sight glass windows, inside a stainless steel
frame. This design allowed for unimpaired visibility of the entire contents of the cell.
Pressure was regulated through an automated, high-pressure, positive displacement
pump (Oilphase-DBR- Schlumberger). The hydraulic fluid inside the pump was
connected to a floating isolation piston located inside the PVT cell. The piston
isolated the hydraulic fluid from the process side of the PVT cell. Controlled dis-
placement of the isolation piston allowed for volume changes in the process chamber,
thus providing and effective way to control pressure. The PVT cell was mounted
inside a temperature controlled air bath by means of a bracket, attached to a hor-
izontal shaft. An electric motor powered the shaft, which oscillated through sixty
degrees about its center of gravity at forty cycles per minute. Temperature and
pressure inside the PVT cell were monitored with a platinum RTD probe, and a
pressure transducer (both supplied with the Phase Behavior system). Using a cov-
erage factor of k = 2 and assuming the corresponding standard uncertainty had a
normal distribution, each expanded uncertainty was estimated to be UT = 0.2 K and
Up = 14 kPa, for temperature and pressure respectively. Vapor phase samples were
taken using a previously evacuated sample bomb, and analyzed with a gas chro-
matograph (Varian CP3800) equipped with a gas sampling, injection valve. After
injection, separation of the gas mixture was achieved by passing the sample through
an arrangement consisting of a 0.5 m x 1/8" pre-column, packed with 80-100 mesh
Hayesep T (Varian Inc.), and a 2.6 m x 1/8" column, packed with 80-100 mesh
Hayesep R (Varian Inc). The effluent was monitored with a thermal conductivity
detector.
CHAPTER 3. N2+CO2+H2O EQUILIBRIUM 28
Figure 3.1: Jefri - DBR Phase Behaviour System
CHAPTER 3. N2+CO2+H2O EQUILIBRIUM 29
3.5 Experimental Procedure
The process side of the pre-vacuumed pressure cell was filled with 10 cm3 of
deionized distilled water followed the addition of a gas mixture. The pressure cell
was sealed and the refrigeration unit was started and the desired temperature de-
fined. The electrical motor was then switched on to cause the liquid to move in
order to reduce the concentration gradients within the system. The system was
pressurized to a value within the hydrate formation region and left over night to
equilibrate and saturate. To form hydrates it was often found necessary increase
the pressure of the system followed by a rapid drop in pressure. After achieving
hydrate formation it was necessary to force the hydrate from the interface into the
bulk. The pressure was lowered temporarily to ensure that all the hydrates on the
interface would start decomposing and start dropping into the liquid phase. When
all the interfacial hydrates had dropped into the liquid, the system pressure was
increased to a value where hydrates would not form on the interface. This step was
repeated until a pressure was found where the hydrate appeared as stable crystal
in the bulk. The system was then left to equilibrate and pressure, temperature
and system volume as well as the presence of hydrates in the bulk were monitored.
When all parameters reached steady state values a gas sample was taken of the
gas phase and analyzed in the GC. The estimated standard uncertainties were as
follows: for temperature uT = 0.3 K, for pressure up = 0.03 MPa, and for vapor
phase mole fraction uy1 = 0.02. With a coverage factor of k = 2 and assuming
the corresponding standard uncertainty had a normal distribution, each expanded
uncertainty was estimated to be UT = 0.6 K, Up = 0.06 MPa, and Uy1 = 0.04.
3.6 Results and Discussion
To confirm the accuracy of the system used, pure nitrogen and pure carbon
dioxide equilibrium points were determined using the classical isothermal pressure
method (Beltran and Servio, 2008b). The obtained data was found to agree with
literature data (Deaton and Frost, 1946; van Cleeff and Diepen, 1960). The ob-
CHAPTER 3. N2+CO2+H2O EQUILIBRIUM 30
Table 3.1: Hydrate-liquid-vapor equilibrium. Temperature T, Pressure p, vapor-phase mole fraction of nitrogen y1 and loading composition of nitrogen y1L for thesystem N2+CO2+H2O under H-LW -V equilibrium.
T /K p/MPa y1 y1L
275.3 1.6 0.0 0.0275.3 2.0 23.7 20.0275.3 2.2 29.6 20.0275.3 3.4 55.7 50.0275.3 3.4 55.2 50.0275.3 3.4 55.5 50.0275.3 3.5 56.4 50.0275.4 3.6 58.2 50.0275.3 3.8 60.5 50.0275.2 4.0 63.5 50.0275.3 7.3 83.0 79.0275.4 7.7 83.8 79.0275.6 20.1 100.0 100.0277.4 2.7 25.5 20.0277.2 5.1 63.9 50.0277.4 9.9 83.0 79.0279.4 3.6 28.9 20.0279.0 6.1 60.7 50.0279.3 12.1 81.5 79.0281.0 4.0 21.3 20.0281.1 7.8 58.4 50.0281.1 16.0 81.7 79.0281.1 16.7 81.7 79.0282.9 5.5 22.0 20.0283.1 11.7 51.7 50.0283.0 22.4 81.1 79.0
CHAPTER 3. N2+CO2+H2O EQUILIBRIUM 31
tained data points had a pressure difference of less than 4% at a given temperature
for the two systems when compared to known values. For binary gas systems un-
der H-LW -V equilibrium, the phase rule states that the degree of freedom (DF)
for the system is 2. By setting the system temperature and pressure, the compo-
sition of the various phases will have to adjust accordingly to achieve equilibrium.
This means that regardless of the composition of the initial mixture used, the same
equilibrium (temperature, pressure and vapor phase compositions) will have to be
achieved. This is valid at any given temperature and pressure which resides between
the equilibrium values for the pure components. The result of a system with two
degrees of freedom is an equilibrium plane rather than equilibrium lines. Unlike
the search methods used on systems containing pure gases to determine equilibrium
(isotherm and isobar search method), gas mixture equilibrium can be achieved by
fixing temperature and pressure as well as monitoring the internal volume of the
system (Englezos and Hall, 1994). When the system volume no longer requires ad-
justments to maintain constant pressure at a constant temperature, the system has
reached equilibrium. Gas sampling was conducted several times up to 10 hrs after
the system was at equilibrium to confirm that the gas phase composition was no
longer changing. Figure 3.2 presents the obtained data for N2+CO2+H2O system
in H-LW -V equilibrium, where mol fraction of nitrogen is plotted vs. pressure at
various isotherms ranging from 2 to 10 ○C. The isotherms represent lines on the
H-LW -V equilibrium plane. The data obtained is also listed in Table 3.1. It can be
seen from the graph that along any given isotherm the hydrate equilibrium pressure
increases with increasing mole fraction of nitrogen in the gas phase. The data pre-
sented in Table 3.1 also illustrate the importance of differentiating between loading
and equilibrium composition. Loading composition is irrelevant from a thermody-
namic point of view. With all components present, any equilibrium point on the
equilibrium plane should be possible to achieve from one specific loading composi-
tion. However, it is expected that loading composition will affect the kinetics. As
most previous data only reported loading composition, the only data points possible
to compare to literature values are those for the pure mixtures, as well as the data
CHAPTER 3. N2+CO2+H2O EQUILIBRIUM 32
points provided by Linga (Linga et al., 2007b). Lingas data does not cover a wide
enough range of concentrations to confirm any trends observed in the current data,
however its worth noticing that the few points reported are located on or very close
to the equilibrium plane modeled from the obtained data.
Figure 3.2: Hydrate-liquidaq-vapor equilibrium isotherms for the system containingnitrogen + carbon dioxide + water. Equilibrium, vapor-phase mole fraction of N2,y1. △, this work at 283 K; ◆, this work at 281 K; #, this work at 279 K; ▲ ,thiswork at 277 K; 3,this work at 275 K; , Linga’s data at 273.7 K (Linga et al.,2007b); ◻ , CO2 data adapted from Deaton (Deaton and Frost, 1946); ∎, N2 dataadapted from van Cleeff (van Cleeff and Diepen, 1960).
3.7 Conclusion
Equilibrium conditions for the N2+CO2+H2O system in H-LW -V equilibrium
were determined, and temperatures, pressures and vapor phase compositions were
reported. Experimental isotherms of the system were presented. It was found that
CHAPTER 3. N2+CO2+H2O EQUILIBRIUM 33
along any given isotherm the hydrate equilibrium pressure increases with increasing
mole fraction of nitrogen in the gas phase. Due to the lack of current literature
values no data or trend comparison was possible.
Chapter 4
H-LW -V equilibrium
measurements for the
CH4+C2H6+H2O hydrate forming
system 1
4.1 Preface
To further enhance the knowledge of binary hydrate forming systems another
mixture of importance, CH4+C2H6+H2O, with limited H-LW -V equilibrium data
available was investigated. The key temperature region in hydrate formation for
the system (from 273 to 279 K) had not yet been described. The system is unique
as it forms both structure I and structure II. The structural transition region is
reported to be at around 75 mol % of CH4 in the vapor phase. As the location
of the phase split had been described in literature, structure I and structure II 3D
planes could be constructed. The relationship between temperature, pressure and
1. Reproduced in part with permission from Bruusgaard, H., Carbone, A. & Servio, P., H-Lw-Vequilibrium measurements for the CH4+C2H6+H2O hydrate forming system, Journal of Chemicaland Engineering Data, 55 (9), 3680-3683, 2010. Copyright 2011 American Chemical Society. DOI:10.1021/je100213e
34
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 35
vapor fractions for the system could then be established.
4.2 Abstract
Three phase equilibrium conditions for the CH4(1)+C2H6(2)+H2O(3) system in
H-LW -V equilibrium were determined to ascertain the effects of pressure, tempera-
ture and gas phase composition in the temperature region above the freezing point
of water as well as to construct a 3D phase diagram. The obtained equilibrium
temperature, pressure and gas phase compositions were in the range of (275 to 281)
K, (0.7 to 2.7) MPa and y1 = (0.30 to 0.85) respectively. Along any given isotherm
and isobar, the equilibrium pressure increased and the equilibrium temperature de-
creased respectively with increasing mole fraction of methane in the gas phase both
for structure I and structure II hydrates. At constant gas phase compositions the
system followed the exponential trend seen for pure gases, with equilibrium pres-
sures close to that of simple ethane hydrates even at high concentrations of methane
in the system. A 3D representation of the phase diagram was constructed of the
system. The diagram consists of two planes due to the presence of both structure I
and structure II. The structure change is seen by the intersection of the two planes
and there is no significant discontinuity in the phase plane diagram.
4.3 Introduction
Clathrate hydrates are non-stoichiometric crystalline solids. Hydrates form when
water molecules link together through hydrogen bonding and form cages that en-
trap gases and volatile liquids suitable for hydrate formation (Englezos, 1993). Sir
Humphry Davy was the first to describe these crystalline structures in 1810 (Davy,
1811). Over 100 years later, hydrates were recognized to plug gas pipelines (Ham-
merschmidt, 1934). The implication of this discovery was an exponential allocation
of resources towards the hydrate field, in particular to map the phase equilibrium
curves and towards finding suitable hydrate inhibitors (Englezos, 1993).
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 36
More recently, other reasons to research hydrates have surfaced. Hydrates
formed from natural gas have been discovered in situ (Makogon, 1965). Large
deposits of natural gas hydrates have been located in the ocean and permafrost
regions (Sloan, 2000). Conservative estimates suggest the corresponding amount of
energy to exceed that found in all other hydrocarbon sources combined (Kvenvolden,
2002). These natural hydrates could pose a global threat as the vast amounts of
methane stored in the form of hydrate could lead to an acceleration of the global
warming process if decomposed due to the high greenhouse gas potential of methane
(Englezos, 1993; Taylor, 1991). On the contrary, carbon dioxide sequestration us-
ing hydrates technology has been suggested as a way to mitigate global warming
(Brewer, 2000). Another field of growing interest is that of hydrate formation from
multiple gas hydrate formers. The combination and ratios of mixed hydrate form-
ers can alter the resulting structure and hence also the equilibrium conditions of a
system significantly (Sloan, 1998). Understanding mixed systems is essential when
applying hydrate technology to gas sequestration and separation.
CH4 and C2H6 are known to form S I as simple hydrates (Sloan, 1998). H-
LW -V equilibrium for these systems (CH4+H2O and C2H6+H2O) were investigated
by Deaton and Frost in the 1940’s. Deaton and Frost also performed H-LW -V
equilibrium experiments for the CH4(1)+C2H6(2)+H2O(3) system, but only over
a limited gas phase composition range (Deaton and Frost, 1946). In 1980 Holder
and Grigoriou performed additional experiments investigated this binary gas system
(Holder and Grigoriou, 1980). Holder and Hand also modeled the system as a S I
but found disagreements between the proposed model and the data at certain gas
phase compositions (Holder and Hand, 1982). Hendriks et al. later investigated
binary gas mixture systems, including the CH4(1)+C2H6(2)+H2O(3) system, from
a thermodynamic point of view. They conjectured that over a given gas phase
composition range the S II hydrate is formed despite the simple hydrates in the
mixture being S I.
The structural dependency of hydrates on gas phase composition for the CH4(1)+
C2H6(2)+H2O(3) system was experimentally proven by Subramanian et al. Using
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 37
Raman and NMR spectroscopic techniques they determined a change in hydrate
structure from S I to S II between 0.722 and 0.750 mole fraction of methane in the
vapor phase at 274 K (Subramanian et al., 2000b). Subramanian et al. also demon-
strated that the system will return to S I with methane vapor phase mole fraction
y1 > 0.992 (Subramanian et al., 2000a). X-ray experiments were performed on the
system of interest at 263 K by Takeya et al. and demonstrated that for methane
gas phase compositions between y1 = 0.79 to 0.98, S II is present (Takeya et al.,
2003). Spectroscopy analysis of the system has also been performed under very high
pressures by Hirai et al. (Hirai et al., 2008). Hashimoto et al. presented isother-
mal phase equilibria for the CH4(1)+C2H6(2)+H2O(3) system at three separate
isotherms and combined the results with Raman spectroscopic analysis (Hashimoto
et al., 2008). The effect of inhibitors on S I and S II have been studied by Ohno et
al. by altering the gas phase composition of the system. (Ohno et al., 2009)
Up to this point no reliable data (only loading composition reported, not equi-
librium) has been presented in literature for the CH4(1)+C2H6(2)+H2O(3) sys-
tem below 279 K. In the present work equilibrium data has been obtained for the
CH4(1)+C2H6(2)+H2O(3) system at temperatures near and above the freezing point
of water. These results are combined with existing data in order to elicit the effect
of composition on equilibrium pressure at given isotherms along with the effect of
temperature on equilibrium pressure at set compositions. A 3D representation of
the data for the CH4(1)+C2H6(2)+H2O(3) system is also presented. Due to the
presence of a structure change a large number of equilibrium data is required in
order to properly describe the resulting equilibrium planes for the given mixture.
The equilibrium data determined in this work has been obtained using a technique
that satisfies the phase rule and that previously has been used to describe a binary
a gas mixture system (Bruusgaard et al., 2008).
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 38
4.4 Experimental Apparatus
Experiments were carried in a Jefri-DBR Phase Behavior System (Oilphase-
DBR- Schlumberger) described in detail in a previous work (Bruusgaard et al.,
2008). The system consists of a refrigerated PVT cell with pressure regulated by
an automated, high-pressure, positive displacement pump (Oilphase-DBR- Schlum-
berger). The hydraulic fluid inside the pump is connected to a floating isolation
piston located inside the PVT cell. The piston isolates the hydraulic fluid from the
process side of the PVT cell.
Temperature and pressure inside the PVT cell were monitored with a platinum
RTD probe, and a pressure transducer (both supplied with the Phase Behavior
system). Using a coverage factor of k = 2 and assuming the corresponding standard
uncertainty had a normal distribution, each expanded uncertainty were estimated
to be UT = 0.2 K and Up = 14 kPa, for temperature and pressure respectively.
Vapor phase samples were taken using a previously evacuated sample bomb
with a volume of 2 cm3, and analyzed with a gas chromatograph (Varian CP3800)
equipped with a gas sampling injection valve. After injection, separation of the
gas mixture was achieved by passing the sample through an arrangement consisting
of a 0.5 m x 1/8" pre-column, packed with 80-100 mesh Hayesep® T (porous
polymer from Varian Inc.), and a 2.6 m x 1/8" column, packed with 80-100 mesh
Hayesep® R (porous polymer from Varian Inc). The effluent was monitored with
a thermal conductivity detector.
4.5 Experimental Procedure
UHP (99.95%) CH4+C2H6 gas mixtures provided by MEGS was added to the
system which then was pressurized to a value within the hydrate formation region
and left over night to equilibrate and saturate. Once hydrates were observed formed
the system was allowed to equilibrate and pressure, temperature and system volume
as well as the presence of hydrates in the bulk were monitored. When all parameters
reached steady state values a gas sample was taken out of the gas phase and analyzed
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 39
in the GC. A more detailed procedure can be found in a previous work (Bruusgaard
et al., 2008). The estimated standard uncertainties were as follows: for temperature
uT = 0.2 K, for pressure up = 0.03 MPa, and for vapor phase mole fraction uy1 =
0.015. With a coverage factor of k = 2 and assuming the corresponding standard
uncertainty had a normal distribution, each expanded uncertainty was estimated to
be UT = 0.4 K, Up = 0.06 MPa, and Uy1 = 0.03.
4.6 Results and Discussion
The accuracy of the system was confirmed through a comparison of the data
presented in Table 4.1 with equilibrium data obtained by Hashimoto at the 279
K isotherm both for SI and S II hydrates (Hashimoto et al., 2008). Hashimoto’s
data was within the experimental uncertainty of the presented work at the com-
mon isotherm as demonstrated in Figure 4.1. No uncertainties were reported by
Hashimoto, but one replicate exist in the reported data showing a relative difference
in vapor fraction of 5.4 % for identical operating conditions. Aside from the data
presented by Hishimoto no other equilibrium data have been found for the system
with equilibrium (not loading) composition reported. An equilibrium composition
is required to justify an equilibrium point at a given temperature and pressure in
a system containing a binary gas mixture due to the resulting 2 degrees of freedom
(Bruusgaard et al., 2008).
The effect of pressure changes on the CH4(1)+C2H6(2)+H2O(3) system in H-
LW -V equilibrium with a constant gas phase composition was studied and the results
are graphed in Figure 4.2. Interpolated values extracted from the data of Hashimoto
were also included to allow for trend observation over a larger temperature range
(Hashimoto et al., 2008). Equilibrium values for pure ethane and methane from
Deaton and Frost were also included to illustrate the boundaries of the system
(Deaton and Frost, 1946). Along any given isotherm maintaining a constant gas
phase composition the three phase equilibrium pressures exhibit much the same
type of trend behaviour as that of pure methane and ethane. The equilibrium
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 40
Figure 4.1: Hydrate-liquidaq-vapor equilibrium isotherms for the methane(1) +ethane(1) + water system(1). y1, equilibrium vapor-phase mole fraction of CH4;◆, this work at 275 K; ∎, this work at 277 K; ▲, this work at 279 K; ,this work at281 K; △, Equilibrium data at 279 K – S I (Hashimoto et al., 2008) ; 3, Equilibriumdata at 279 K – S II (Hashimoto et al., 2008) ; ◻, Equilibrium data at 283 K – S I(Hashimoto et al., 2008) ; #, Equilibrium data at 283 K – S II. (Hashimoto et al.,2008)
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 41
Table 4.1: Hydrate-liquid-vapor equilibrium. Temperature T, Pressure p, vapor-phase mole fraction of methane y1 and loading composition of methane y1L for thesystem CH4(1)+C2H6(2)+H2O(3) under H-LW -V equilibrium.
T /K p/MPa y1 y1L
275.1 0.69 0.309 0.300275.2 1.03 0.612 0.600275.3 1.41 0.838 0.850277.1 0.92 0.307 0.300277.1 1.25 0.603 0.600277.2 1.23 0.601 0.600277.2 1.76 0.839 0.850278.2 1.90 0.837 0.850279.1 2.14 0.837 0.850279.1 1.17 0.307 0.300279.2 1.52 0.608 0.600279.3 1.52 0.609 0.600281.1 1.92 0.605 0.600281.1 2.65 0.838 0.850281.2 1.90 0.611 0.600281.2 1.45 0.303 0.300
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 42
Figure 4.2: Hydrate-liquidaq-vapor equilibrium for constant gas phase compositionsfor the methane(1) + ethane(2) + water system(3). , this work y1 = 0.31 ; ∎, thiswork y1 = 0.61 ; ▲, this work y1 = 0.84 ; #, y1 = 0.31 (Hashimoto et al., 2008) ;◻, y1 = 0.61 (Hashimoto et al., 2008) ; △ y1 = 0.84 (Hashimoto et al., 2008) ; 3, SI – S II transition composition (Hashimoto et al., 2008; Subramanian et al., 2000b); +, y2 = 1.00 (Deaton and Frost, 1946) ; x, y1 = 1.00 .(Deaton and Frost, 1946)
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 43
pressure increases exponentially with increasing temperature. This is the case for
both structure I (y1 = 0.31 and 0.61) and structure II (y1 = 0.84) hydrates. All
equilibrium data is found to be within the boundaries formed by the pure systems
being structure I hydrates. The equilibrium values are much closer to those of pure
ethane than those of pure methane even at gas phase compositions close to y1 =
0.85.
Figure 4.3 present a 3D representation of the S I and S II equilibrium planes.
Mole fraction of methane in the gas phase, temperature and pressure is represented
by the x and y and z axis respectively. The planes represent all available data for the
CH4(1)+C2H6(2)+H2O(3) system in H-LW -V equilibrium. Spectroscopy data ob-
tained from literature (Subramanian et al., 2000b,a; Takeya et al., 2003; Hashimoto
et al., 2008) was used to define the structural transition region from SI to S II, indi-
cated by the red transition line, and the plane borders (both SI) are represented by
the equilibrium conditions for pure methane and pure ethane acquired by Deaton
and Frost, Reamer et al. and Holder and Hand (Deaton and Frost, 1946; Sloan,
1998). The gas phase composition at which the structure changes between S I and S
II is dependent on temperature and pressure. The structure change region appears
in the 0.60 to 0.75 mole fraction of methane in the gas phase for the examined
temperature and pressure range. The region defining the line bordering the two
structures is likely to contain both structures simultaneously. The structure change
is illustrated by the red line intersection of two planes as demonstrated in 4.3 where
the entire mixture composition range is shown. There is no discontinuity appear-
ing in the 3D model of the equilibrium planes due to the structure change for the
CH4(1)+C2H6(2)+H2O(3) system. In the structure I section of 4.3, the equilibrium
plane is very flat, and as a result, has an equilibrium pressure very insensitive to
gas phase composition changes. In the structure II section of 4.3, the equilibrium
plane is very curved and shows that equilibrium pressure is very sensitive to both
temperature and gas phase composition changes. For both structure I and struc-
ture II, it was observed that along any given isotherm and isobar on the plane, the
hydrate equilibrium pressure increases and the equilibrium temperature decreased
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 44
Figure 4.3: Structure I and structure II 3D planes representation of the hydrate-liquidaq-vapor equilibrium for the methane(1) + ethane(2) + water system(3). y1,equilibrium vapor-phase mole fraction of methane; red –, quadruple line, HSI-HSII-Laq-V equilibrium (Subramanian et al., 2000b; Hashimoto et al., 2008); *, puremethane (Deaton and Frost, 1946) (SI); #, pure ethane (Sloan, 1998) (SI).
CHAPTER 4. CH4+C2H6+H2O EQUILIBRIUM 45
respectively with increasing mole fraction of methane in the gas phase.
4.7 Conclusion
Three phase equilibrium conditions for the CH4(1)+C2H6(2)+H2O(3) system in
H-LW -V equilibrium were determined to ascertain the effects of pressure, tempera-
ture and gas phase composition. A 3D phase diagram of the system is presented.
The data of this work agrees well with data in the literature at 279 K. Along any
given isotherm and isobar, the equilibrium pressure increased and the equilibrium
temperature decreased respectively with increasing mole fraction of methane in the
gas phase both for structure I and structure II hydrates. At constant gas phase
composition the system followed the exponential trend seen for pure gases, with
equilibrium pressures close to that of simple ethane hydrates even at high concen-
trations of methane in the system. The equilibrium pressure of structure I is found
to be less sensitive to temperature and composition changes than structure II.
Chapter 5
Solubility measurements for the
CH4+CO2+H2O system under
hydrate-liquid-vapor equilibrium 1
5.1 Preface
With the understanding of equilibrium for certain binary gas hydrate formers
well established, the focus is now shifted towards the composition of the liquid
phase. For simple hydrate systems the driving force for hydrate growth has been
defined by the difference between bulk and equilibrium liquid fraction of the hydrate
formers. No such work has been attempted for binary gas hydrate forming systems.
The CH4+CO2+H2O system under H-LW -V equilibrium has been mapped, with
the vapor fraction as the justifying variable, but no reports have been made on
the liquid fractions. The CH4+CO2+H2O system was selected as the system forms
structure I, regardless of the ratio of the hydrate formers. The solubilities results for
the liquid phase are a major milestone when developing a kinetic model to describe
1. Reprinted from: Bruusgaard, H., Beltran, J. & Servio, P., Solubility measurements for theCH4+CO2+H2O system under hydrate-liquid-vapor equilibrium, Fluid Phase Equilibria, 296, 106-109, 2010, Copyright 2011, with permission from Elsevier
46
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 47
hydrate growth from binary gas hydrate forming mixtures. As for simple hydrate
systems, the difference between H-Lw-V equilibrium liquid mole fraction and the
bulk mole fraction will define the driving force for crystal growth.
5.2 Abstract
Phase equilibria for the CH4+CO2+H2O system have been investigated in the
past, but mole fraction of methane and carbon dioxide in the bulk liquid phase
has not been measured under hydrate-liquid-vapor equilibrium. Equilibrium liquid
composition is very important as it defines the driving force for hydrate growth.
This study presents the solubility of methane and carbon dioxide under H-Lw-
V equilibrium. Emphasis is made on the effect of pressure along the respective
isotherms on the equilibrium mole fraction of the individual hydrate formers in the
liquid.
5.3 Introduction
Gas Hydrates, or clathrate hydrates, are non-stoichiometric crystalline com-
pounds in which guest molecules of suitable size and shape are trapped inside a
network of hydrogen-bonded water molecules. The water network is stabilized by
weak van der Waals forces between the host and the guest molecules. Clathrate hy-
drates occur naturally in permafrost regions and in sub-sea sediment where existing
pressures and temperatures allow for thermodynamic stability of the hydrate (Sloan
and Koh, 2008). Hydrates crystals were discovered in the 1800’s and were investi-
gated strictly from an academic point of view until a major discovery in the 1930’s
(Englezos, 1993). It was then recognized, that plugging of natural gas pipelines
was due to the formation of natural gas hydrates and not to ice (Hammerschmidt,
1934). The latter transformed hydrate research from a small academic field into a
highly applied field with wide interest particularly to the oil and gas industry.
Various other motives for hydrate research have surfaced more recently. Hy-
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 48
drates of natural gas have been discovered in situ (Makogon, 1965). Most of these
natural gas hydrates are found in the ocean bottom; however, there is a consider-
able amount of hydrates found in permafrost regions (Sloan, 2003). Conservative
estimates suggest that the energy stored in the form of hydrates exceeds all other hy-
drocarbon sources combined (Suess et al., 1999). In addition to being a potentially
vast energy source for the future, the enormous quantities of methane stored as hy-
drates also pose an environmental concern due to the high global warming potential
of methane (Taylor, 1991). Hydrates have also been suggested as an economically
advantageous alternative to liquefied natural gas (LNG) for transportation and stor-
age of gas (Thomas and Dawe, 2003). Carbon dioxide is also an important hydrate
former both because of its negative greenhouse properties (Taylor, 1991) as well as
its presence as a contaminant in natural gas (Golombok et al., 2009). The use of
hydrate technology to sequester CO2 from mixed streams containing either N2/CO2,
H2/CO2 or CH4/CO2 mixtures is currently being explored (Linga et al., 2007a; van
Dereren et al., 2009).
Based on the combination and ratio of hydrate formers the crystalline and ther-
modynamic properties can vary significantly from that of hydrate formed from pure
guests (Sloan and Koh, 2008). By taking advantage of these particular mixture
properties it has been experimentally proven that it is possible to selectively re-
place enclathrated methane using carbon dioxide gas under the appropriate ther-
modynamic conditions (Ohgaki et al., 1996). More recently it has been shown that
gas hydrates can be used to reduce the carbon dioxide content in methane/carbon
dioxide mixtures containing 25% CO2 (van Dereren et al., 2009).
A better understanding of mixed hydrate systems phase equilibria is required
in order to exploit the potential applications of hydrate formation in the presence
of gas mixtures. Previously, bulk liquid phase solubility experiments have been
performed for pure methane and carbon dioxide in water in presence of hydrates
(Servio and Englezos, 2002, 2001). Phase equilibria for the system CH4+CO2+H2O
have been investigated in the past (Ohgaki et al., 1996; Unruh and Katz, 1949;
Berecz and Balla-Achs, 1983; Adisasmito et al., 1991; Dholabhai and Bishnoi, 1994;
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 49
Seo and Lee, 2001; Beltran and Servio, 2008a), but to the best of our knowledge
the equilibrium mole fraction of methane and carbon dioxide in the bulk liquid
phase has not been measured under hydrate-liquid-vapor equilibrium for this mixed
system. Equilibrium liquid composition is very important as it defines the driving
force for hydrate growth (Bergeron and Servio, 2008a; Bergeron et al., 2010). The
present study addresses this gap in the understanding of the phase equilibrium for
the system CH4+CO2+H2O by presenting the solubility of methane and carbon
dioxide under H-Lw-V equilibrium. Emphasis is made on the effect of pressure
along the respective isotherms on the equilibrium mole fraction of the individual
hydrate formers in the liquid.
5.4 Experimental Apparatus
A simplified diagram of the setup is illustrated in Figure 5.1. The crystallizer
is made of 316 stainless steel with a pressure rating of 20 MPa. It is equipped
with a MM-D06 magnetic stirrer from Pressure Product Industries and has two
polycarbonate windows to allow for visual inspections. The crystallizer is connected
to a reservoir using a Baumann 51000 control valve which makes it possible to
maintain constant pressure during liquid sampling. Reactor and reservoir biases
are also in place to increase the accuracy of the pressure readings in the system.
The entire system is immersed in a temperature controlled bath consisting of a
20% ethylene-glycol/water mixture. The pressure is monitored using Rosemount
pressure transducers configured to a span of 0-14 MPa and differential pressure
transducers configured to a span of 0-2 MPa, with an accuracy of ± 0.065% of the
given span. The system temperatures are monitored using high accuracy (± 0.1 K)
RTD probes from Omega. All readings were automatically recorded using a National
Instruments data acquisition system. The liquid sample ports are equipped with a
Norman 4200 in-line filters which retain particles greater than 200 nm in diameter.
The filters prevent the collection of unwanted hydrate particles with the liquid
samples. A digital gasometer from Chandler Engineering is used to measure the
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 50
amount of gas flashing out of the liquid when the sample is left to equilibrate at
room temperature and atmospheric pressure. A gas chromatograph (Varian CP-
3800) equipped with a sampling valve and a TCD detector is used to obtain vapor
phase compositions.
Figure 5.1: Schematic of the apparatus. 1-Gas Source, 2-Reservoir, 3-Reservoir bias,4-Crystallizer Bias, 5-Liquid Port (low), 6-Liquid Port (high), 7-Magnetic Stirrer,8-Crystallizer, 9-Gas port, 10-Stirrer, 11-Chiller. CV-Control valve, P-PressureTransducer, DP-Differential Pressure Transducer
5.5 Experimental Procedure
Hydrate-Liquid-Vapor (H-Lw-V) solubility experiments for the system CH4+CO2
+H2O were performed using previously reported knowledge of multicomponent gas
hydrate phase equilibria (Beltran and Servio, 2008a; Bruusgaard et al., 2008) com-
bined with a flash technique used for solubility measurements applied in the past
to single hydrate formers systems (Servio and Englezos, 2002, 2001). To begin an
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 51
experiment, the crystallizer was filled with 300 mL of distilled deionized water. The
gas phase was then flushed three times using a high purity gas mixture of CH4+CO2
(MEGS) by pressurizing the crystallizer to 1000 kPa and then purging the gas phase
to remove any air left in the reactor. The system was then pressurized with the
same mixture of CH4+CO2 to allow saturation and hydrate formation at constant
temperature. Subsequently, the system was left to equilibrate while the tempera-
ture was kept constant. Gas was not supplied to the system during the equilibrating
stage of the experiment. When the pressure reached a constant value (unchanged
for 5 hours) a vapor-phase sample and a hydrate-free, liquid sample were collected
into separate, evacuated sample bombs for further analysis. The composition of the
vapor phase was analyzed directly in the gas chromatograph, and the resulting mole
fraction was compared with the corresponding literature values (Ohgaki et al., 1996;
Adisasmito et al., 1991; Dholabhai and Bishnoi, 1994; Seo and Lee, 2001; Beltran
and Servio, 2008a) in order to guarantee the system had reached equilibrium. The
liquid samples were flashed prior to further analysis. The latter involved bringing
the liquid sample bomb to room temperature and atmospheric pressure by expan-
sion of the sample into the gasometer. When gas stopped evolving from the liquid,
the sample bomb was heated to 353 K to ensure the remaining gas present in the
liquid phase flowed into the gasometer. The sample bomb was then disconnected
from the gasometer, and the remaining gas in the gasometer chamber was allowed
to equilibrate to room temperature.
The number of moles of CH4 and CO2 in the gasometer is given by Equation
5.1.
nGi = yGi (p − pH2O)V
ZRT(5.1)
where p, pH2O, V, yGi , R, T, Z are atmospheric pressure, vapor pressure of
water at room temperature, volume of the vapor phase in the gasometer, mole
fraction of the respective component in the vapor phase, universal gas constant,
room temperature, and the compressibility factor for the given gas mixture. The
compressibility factors were obtained from the Trebble-Bishnoi equation of state
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 52
(Trebble and Bishnoi, 1987, 1988b,a). By knowing the weight of the sample bomb,
as well as by analyzing the vapor evolved from the liquid phase sample, the mole
fraction of the respective hydrate formers could be calculated. xEQi represents the
equilibrium mole fraction of component i in the liquid phase of a gas mixture at the
experimental temperature and pressure as given by Equation 5.2 where nGi is the
number of moles of component i in the liquid sample and nTOT is the total number
of moles in the liquid sample.
xEQi = nGinTOT
(5.2)
Using the method described above to determine the equilibrium conditions, it
was estimated that the standard uncertainties were as follows: for temperature uT
= 0.1 K, for pressure up = 0.015 MPa, for the vapor-phase mole fraction of CO2
uyCO2= 0.02, for the solubility of methane uxCH4
= 0.000040, and for solubility of
carbon dioxide uxCO2= 0.00027. With a coverage factor of k = 2 and assuming
the corresponding standard uncertainty had a normal distribution, each expanded
uncertainty was estimated to be UT = 0.2 K, Up = 0.03 MPa, UyCO2= 0.04, UxCH4
= 0.000080, and UxCO2= 0.00054.
5.6 Results and Discussion
Solubility experiments were conducted under hydrate-liquid-vapor equilibrium.
Experimental conditions ranged from 274 to 280 K and 1.4 to 5 MPa. The data are
tabulated in Table 5.1 and are also plotted in Figure 5.3 for methane and Figure 5.4
for carbon dioxide respectively. Mixtures of carbon dioxide and methane form cubic
structure I hydrates only, like pure methane and CO2 hydrates (Uchida et al., 2005).
Considering this, and applying Gibbs phase rule two degrees of freedom result under
hydrate-liquid-vapor equilibrium. In order to satisfy this requirement two intensive
variables must be controlled, and a third one reported in order to guarantee that the
system is indeed at equilibrium (Beltran and Servio, 2008a; Bruusgaard et al., 2008).
Here, temperature and pressure were controlled while the vapor phase compositions
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 53
Table 5.1: Hydrate-liquid-vapor equilibrium: Temperature T, Pressure p, liquid-phase mole fraction of methane xCH4 and carbon dioxide xCO2 , and vapor-phasemole fraction of carbon dioxide yCO2 for the system methane + carbon dioxide +water.
T /K p/MPa xCH4 xCO2 yCO2 Phases Present274.0 1.66 0.000235 0.01076 0.612 H-Lw-V274.1 1.88 0.000468 0.00860 0.440 H-Lw-V274.1 2.30 0.000776 0.00468 0.203 H-Lw-V276.2 2.14 0.000309 0.01176 0.588 H-Lw-V276.2 2.38 0.000508 0.00959 0.420 H-Lw-V276.3 2.81 0.000827 0.00594 0.229 H-Lw-V278.0 2.53 0.000293 0.01410 0.659 H-Lw-V278.2 3.01 0.000638 0.01019 0.400 H-Lw-V278.2 3.33 0.000832 0.00754 0.270 H-Lw-V280.1 3.26 0.000330 0.01620 0.668 H-Lw-V280.1 3.66 0.000641 0.01174 0.432 H-Lw-V280.1 4.03 0.000911 0.00858 0.283 H-Lw-V
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 54
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5p /MPa
y CO
2
This work, T = 274.2 K
This work, T = 276.2 K
This work, T = 278.2 K
This work, T = 280.2 K
Beltran, 2008, T = 275.2 K
Beltran, 2008, T = 277.2 K
Beltran, 2008, T = 279.2 K
Seo, 2001, T = 274.2 K
Seo, 2001, T = 277.2 K
Ohgaki, 1996, T = 280.3 K
Adisasmito, 1991, T = 275.7 K
Adisasmito, 1991, T= 277.8 K
Figure 5.2: Equilibrium, vapor-phase mole fraction of carbon dioxide under hydrate-liquid-vapor equilibrium for the system methane + carbon dioxide + water , yCO2 .Solid markers, this work. Literature data is also shown (Ohgaki et al., 1996; Adis-asmito et al., 1991; Dholabhai and Bishnoi, 1994; Seo and Lee, 2001; Beltran andServio, 2008a).
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 55
were used to verify the system had reached equilibrium by comparison with the data
available in the literature (Ohgaki et al., 1996; Adisasmito et al., 1991; Dholabhai
and Bishnoi, 1994; Seo and Lee, 2001; Beltran and Servio, 2008a). The reported
vapor phase mole fractions were found to agree with the references above within
experimental uncertainties (Figure 5.2).
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
1 1.5 2 2.5 3 3.5 4 4.5 5
p /MPa
xC
H 4 H-L-V at T = 274 KH-L-V at T = 276 KH-L-V at T = 278 KH-L-V at T = 280 KH-L at T = 274 KH-L at T = 276 KH-L at T = 278 KH-L at T = 280 K
Figure 5.3: Liquid-phase mole fraction of methane under hydrate-liquid-vapor equi-librium for the system methane + carbon dioxide + water, black markers. Liquid-phase mole fraction of carbon dioxide under hydrate-liquid equilibrium (emptymarkers) for pure methane hydrate (Ref. Servio and Englezos (2002)) and forpure carbon dioxide hydrate (Ref. Servio and Englezos (2001)) are also included toillustrate the upper and lower boundaries of the mixed system.
The solubility of the hydrate formers in the CH4+CO2+H2O system is bound
by the individual H-Lw-V equilibrium curves of the simple hydrate formers of inter-
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 56
0
0.005
0.01
0.015
0.02
0.025
1 1.5 2 2.5 3 3.5 4 4.5 5
p /MPa
XC
O2 H-L-V at T = 274 K
H-L-V at T = 276 KH-L-V at T = 278 KH-L-V at T = 280 KH-L at T = 274 KH-L at T = 276 KH-L at T = 278 KH-L at T = 280 K
Figure 5.4: Liquid-phase mole fraction of carbon dioxide under hydrate-liquid-vapor equilibrium for the system methane + carbon dioxide + water, black mark-ers. Liquid-phase mole fraction of carbon dioxide under hydrate-liquid equilibrium(empty markers) for pure methane hydrate (Ref. Servio and Englezos (2002)) andfor pure carbon dioxide hydrate (Ref. Servio and Englezos (2001)) are also includedto illustrate the upper and lower boundaries of the mixed system.
CHAPTER 5. CH4+CO2+H2O SOLUBILITIES 57
est, CH4 and CO2. As experimental conditions approach one of these boundaries,
the solubility and gas phase composition also approach that of the respective pure
system. This behavior can be more explicitly demonstrated when plotting the H-
Lw equilibrium data obtained by (Servio and Englezos, 2002, 2001) for the pure
components together with the binary mixture equilibrium data as seen in Figures
5.3 and 5.4. The solubility of methane under H-Lw-V equilibrium was found to
increase with increasing pressures and decreasing temperatures, i.e. as conditions
approach equilibrium conditions of pure methane (Figure 5.3). On the other hand,
the solubility of carbon dioxide under H-Lw-V equilibrium was found to increase
with decreasing pressures and increasing temperatures i.e. as conditions approach
equilibrium conditions of pure carbon dioxide (Figure 5.4). Such a pressure trend
along the isotherm represents a reversal of the trend predicted for pure methane
(Handa, 1990) and pure carbon dioxide (Bergeron et al., 2009) as simple hydrate
guests under H-Lw equilibrium.
5.7 Conclusion
The mole fraction of CH4 and CO2 in the liquid phase for the system CH4+CO2
+H2O was measured under hydrate-liquid-vapor equilibrium. Temperatures varied
from 274 to 280 K and the corresponding equilibrium pressures ranged from 1.4
to 5 MPa. Results showed that solubility of methane increases with increasing
pressure and decreasing temperatures and the solubility of carbon dioxide increases
with decreasing pressures and increasing temperatures. The trend is opposite to
the solubility trend for CH4 and CO2 as simple gas hydrate formers under H-Lw
equilibrium. Equilibrium vapor phase compositions were also measured and found
to agree within experimental uncertainties with previously reported literature data.
Chapter 6
Prediction of methane and carbon
dioxide solubilities for the
CH4+CO2+H2O system under
hydrate-liquid-vapor equilibrium 1
6.1 Preface
The natural step following the previous chapter was to model the obtained H-
LW -V equilibrium data. The CH4+CO2+H2O system was predicted through a
flash type procedure based on the Trebble-Bishnoi equation of state along with the
models by van der Waals & Platteeuw and Holder. The predictions were shown to
fit the data very well, especially considering that all parameters were independently
optimized. In view of the success of the predictive model, it is likely that it can be
applied in the prediction of equilibrium pressure and to determine the respective
phase compositions for other binary gas hydrate forming systems, given that the
1. Reprinted from: Bruusgaard, H. & Servio, P., Prediction of methane and carbon dioxidesolubilities for the CH4+CO2+H2O system under hydrate-liquid-vapor equilibrium, Fluid PhaseEquilibria, 305 (2), 97-100, 2011, Copyright 2011, with permission from Elsevier
58
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 59
binary interaction parameters have been obtained.
6.2 Abstract
Three phase, hydrate-liquid water-vapor (H-Lw-V) equilibrium conditions for
the CH4+CO2+H2O system have been predicted. The modelling is based on the
Trebble-Bishnoi equation of state along with the models by van der Waals & Plat-
teeuw and Holder. The predictions are demonstrated for the temperature region
between 274 to 280 K and the pressure region between 1.4 to 5 MPa. The predicted
vapor mole fraction of carbon dioxide have an AARE of 10.2 % and the predicted
solubilities for methane and carbon dioxide in the liquid phase have an AARE of
9.0 % and 3.2 %, respectively. This is the first study to predict the solubility of
methane and carbon dioxide in the liquid phase for the CH4+CO2+H2O system
under H-Lw-V equilibrium.
6.3 Introduction
Gas Hydrates, or clathrate hydrates, are non-stoichiometric crystalline com-
pounds in which guest molecules of suitable size and shape are trapped inside a
network of hydrogen-bonded water molecules. The water network is stabilized by
weak van der Waals forces between the host and the guest molecules. Clathrate
hydrates occur naturally in permafrost regions and in sub-sea sediment where ex-
isting pressures and temperatures allow for thermodynamic stability of the hydrate
(Sloan and Koh, 2008). Hydrates crystals were discovered in the 1800’s and were
researched from an academic point of view only until the 1930’s (Englezos, 1993). It
was then recognized that plugging of natural gas pipelines was the result of forma-
tion of natural gas hydrates (Hammerschmidt, 1934). The discovery transformed
hydrate research from a small academic field into a highly applied field with wide
interest particularly to the oil and gas industry.
Hydrates of natural gas have been discovered in situ (Makogon, 1965) and con-
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 60
servative estimates suggest that the energy stored in the form of hydrates exceeds
all other hydrocarbon sources combined (Suess et al., 1999). The enormous quan-
tities of methane stored as hydrates also pose an environmental concern due to
the high global warming potential of methane (Taylor, 1991). The use of hydrates
in industry have also been suggested as an economically advantageous alternative
to liquefied natural gas (LNG) for transportation and storage of gas (Thomas and
Dawe, 2003).
While large numbers of equilibrium studies have been conducted on hydrate
forming systems, there is only a limited number of studies performed on the solubil-
ity of typical hydrate formers under H-Lw or H-Lw-V equilibrium. The methane-
water and carbon dioxide water systems account for almost all the studies within
the field (Handa, 1990; Yang et al., 2000, 2001; Servio and Englezos, 2001, 2002;
Kim et al., 2003). A few other systems have also been studied (Kim et al., 2003;
Gaudette and Servio, 2007). The solubility of simple hydrate systems has been mod-
elled from a thermodynamic point of view (Hashemi et al., 2006; Sun and Duan,
2007; Mohammadi and Richon, 2007). The effect of temperature and pressure on
the solubility for simple hydrate systems have also been modelled (Bergeron et al.,
2007, 2009).
The combination and ratio of hydrate formers can cause the crystalline and
thermodynamic properties to vary significantly from that of hydrate formed from
pure guests (Sloan and Koh, 2008). By taking advantage of these particular mix-
ture properties it has been experimentally proven that it is possible to selectively
replace enclathrated methane using carbon dioxide gas under the appropriate ther-
modynamic conditions (Ohgaki et al., 1996). More recently it has been shown that
gas hydrates can be used to reduce the carbon dioxide content in methane/carbon
dioxide mixtures containing 25% CO2 (van Dereren et al., 2009).
Phase equilibria for the system CH4+CO2+H2O under H-Lw-V equilibria have
been investigated in the past (Ohgaki et al., 1996; Unruh and Katz, 1949; Berecz
and Balla-Achs, 1983; Adisasmito et al., 1991; Dholabhai and Bishnoi, 1994; Seo and
Lee, 2001; Beltran and Servio, 2008a),but the only work found to have measured the
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 61
solubility of methane and carbon dioxide in the liquid phase for the given system
is the work of Bruusgaard et al. (Bruusgaard et al., 2010). The system’s vapor
phase have been modelled under H-Lw-V equilibrium (Seo and Lee, 2001; Herri
et al., 2010), but no model predictions exist for the liquid phase composition. The
hydrate former equilibrium liquid composition is essential as it defines the driving
force for hydrate growth (Bergeron and Servio, 2008a; Bergeron et al., 2010). This
study presents phase equilibrium predictions for the CH4+CO2+H2O system under
H-Lw-V equilibrium which includes the solubility of the hydrate formers in the
liquid phase. The predictions were evaluated based on available experimental data.
The equilibrium calculations are based on the Trebble Bishnoi equation of state
(EOS) along with the models by van der Waals & Platteeauw (van der Waals and
Platteeuw, 1959) and Holder (Holder et al., 1980).
6.4 Theory
Three phase hydrate-liquid-vapor equilibrium is defined by the following chem-
ical potentials:
µVi = µLi (i = 1,N) (6.1)
µLi = µHi (i = 1,N) (6.2)
where N is the total number of components in the system. In three phase hydrate-
liquid-vapor equilibrium calculations, Equations 6.1 and 6.2 are solved simultane-
ously. The chemical potential of the components in the vapor and liquid phases are
calculated using an appropriate equation of state. In this study the Trebble-Bishnoi
equation of state is used. The chemical potential of water in the hydrate phase was
calculated using the model of van der Waals and Platteeuw (van der Waals and
Platteeuw, 1959):
µHw = µMTw +RT∑
m
νmln⎛⎝
1 −∑m
θmj⎞⎠
(6.3)
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 62
where µMTw represents the chemical potential of water in the hydrate lattice, νm is
the number of cavities type m per water molecule for a given hydrate structure and
θmj is the fraction of cavities type m occupied by hydrate former j. The fractional
occupancy is defined by the following expression (Parrish and Prausnitz, 1972):
θmj =Cmjfj
1 +∑k
Ckjfj(6.4)
where C represents the Langmuir constant and f is the fugacity. The Langmuir
constant are temperature depended and are determined using an empirical correla-
tion given by Parrish and Prausnitz (Parrish and Prausnitz, 1972) which is valid in
the range 260−300 K.
The equilibrium relation for water between the hydrate and the liquid phase is
defined by Equation 6.2 as:
µLw = µHw (6.5)
The chemical potential difference between water in the empty hydrate lattice and
that in the pure liquid state at the system temperature and pressure is:
µMTw − µLo
w = ∆µMT−Low (6.6)
The right hand side of Equation 6.6 is commonly represented by Holder et al.
(Holder et al., 1980) as:
∆µMT−Low
RT=
∆µMT−Lo
w,To
RTo+ ∫
p
po
∆νMT−Low
RTdp − ∫
T
To
∆hMT−Low
RT 2dT (6.7)
An expression for the chemical potential of water in the empty hydrate lattice can
be obtained by combining Equations 6.6 and 6.7:
µMTw
RT=
∆µMT−Lo
w,To
RTo+ ∫
p
po
∆νMT−Low
RTdp − ∫
T
To
∆hMT−Low
RT 2dT + µ
Low
RT(6.8)
Equations 6.3 and 6.8 can be used to obtain an expression for the chemical potential
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 63
of water in the hydrate phase:
µHwRT
=∆µMT−Lo
w,To
RTo+∫
p
po
∆νMT−Low
RTdp−∫
T
To
∆hMT−Low
RT 2dT + µ
Low
RT+RT∑
m
νmln⎛⎝
1−∑m
θmj⎞⎠
(6.9)
where
∆hMT−Low = ∆hMT−Lo
w,To+ ∫
T
To
∆CpMT−Lo
w dT (6.10)
The required parameters were all obtained from the work of Holder et al. (Holder
et al., 1980), except a re-optimized value of ∆hMT−Lo
w,Towhich obtained from the work
of Hashemi et al. (Hashemi et al., 2006). The chemical potential of water in the
liquid phase is given in terms of the activity by:
µLw = µLow +RT lnaw (6.11)
where a is the activity. Substituting Equations 6.5 and 6.11 into Equation 6.9 gives
the following expression:
∆µMT−Lo
w,To
RTo+ ∫
p
po
∆νMT−Low
RTdp − ∫
T
To
∆hMT−Low
RT 2dT + lnaw = −RT∑
m
νmln⎛⎝
1 −∑m
θmj⎞⎠
(6.12)
Isofugacity and the minimization of Gibbs energy are the equilibrium criteria.
All components must be distributed amongst the system phases such that the Gibbs
energy is at a minimum. Gibbs energy of the system is obtained by the following
equation:
G =∑π∑i
Xπi µ
πi (6.13)
where Xπi is the molar composition of component i in phase π.
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 64
6.5 System Predictions
The system was predicted by the minimization of energy using a flash technique.
The vapor and liquid properties were evaluated using the Trebble-Bishnoi equation
of state (EOS) (Trebble and Bishnoi, 1987, 1988a) which is a four parameter cubic
equation of state. The interaction parameters used in the calculations are listed in
Table 6.1:
Table 6.1: Mixing rule parameters for the Trebble-Bishnoi EOS (Trebble and Bish-noi, 1988a) for binary systems. a(Hashemi et al., 2006), b(Trebble and Bishnoi,1988a)
Binary pair Ka Kb Kc Kd T Range (K)CO2−H2O a 0.9688 0.5181 0.3757 0.1647 273.2−353.1CH4−CO2
b 0.8760 0.0275 0.0000 0.0000 199.8−271.5CH4−H2O a,b 0.4199 -0.1727 -0.0001 -1.2274 274.2−444.3
The EOS related parameters were obtained from the work of Trebble and Bishnoi
except the value for the binary interaction parameters for CO2−H2O which has
been re-optimized by Hashemi et al. (Hashemi et al., 2006). The CH4−CO2 mixing
parameters were optimized by Trebble and Bishnoi based on data in the temperature
range 199.8−271.5 K and they were assumed valid for temperatures up to 280 K.
The value of ∆µMT−Lo
w,Toused in the present study is the re-optimized value of 1256
J/mol (Hashemi et al., 2006) and the value of ∆hMT−Lo
w,Tois -4860 J/mol (Parrish
and Prausnitz, 1972). The hydrate properties were predicted using the models of
van der Waals & Platteeauw (van der Waals and Platteeuw, 1959) and Holder et
al. (Holder et al., 1980).
6.6 Results and Discussion
The solubility (or equilibrium mole fraction) of CH4 and CO2 in the liquid
phase was modelled for the CH4+CO2+H2O system under hydrate-liquid-vapor
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 65
equilibrium. The modelled temperatures ranged from 274 to 280 K and the pressures
ranged from 1.4 to 5 MPa. The data used to verify the model is adapted from
Bruusgaard et al. (Bruusgaard et al., 2010) based on 12 available data points.
Methane and carbon dioxide solubility data and models are presented in Figure
6.1 and 6.2 respectively. Data and modelling of the equilibrium vapor fraction of
carbon dioxide is presented in Figure 6.3. The vapor composition data for carbon
dioxide used in the current study for the CH4+CO2+H2O system has previously
been compared to, and found to agree very well with other H-Lw-V equilibrium
data in the literature (Bruusgaard et al., 2010).
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
1000 2000 3000 4000 5000
XC
H4
Pressure [KPa]
274 K -‐ Data[28] 276 K -‐ Data[28] 278 K -‐ Data[28] 280 K -‐ Data[28] 274 K -‐ Model 276 K -‐ Model 278 K -‐ Model 280 K -‐ Model
Figure 6.1: Predicted vs experimental liquid phase mole fraction of CH4 in theCH4+CO2+H2O system under H-Lw-V equilibrium
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 66
0.000
0.005
0.010
0.015
0.020
1000 2000 3000 4000 5000
XC
O2
Pressure [KPa]
274 K -‐ Data[28] 276 K -‐ Data[28] 278 K -‐ Data[28] 280 K -‐ Data[28] 274 K -‐ Model 276 K -‐ Model 278 K -‐ Model 280 K -‐ Model
Figure 6.2: Predicted vs experimental liquid phase mole fraction of CO2 in theCH4+CO2+H2O system under H-Lw-V equilibrium
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 67
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
1000 2000 3000 4000 5000
YC
O2
Pressure [KPa]
274 K -‐ Data[28] 276 K -‐ Data[28] 278 K -‐ Data[28] 280 K -‐ Data[28] 274 K -‐ Model 276 K -‐ Model 278 K -‐ Model 280 K -‐ Model
Figure 6.3: Predicted vs experimental vapor phase mole fraction of CO2 in theCH4+CO2+H2O system under H-Lw-V equilibrium
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 68
6.6.1 Vapor Phase Predictions
Experimental data and vapor phase composition predictions are presented in
Figure 6.3. The amount of water in the vapor phase under H-Lw-V equilibrium is
several orders of magnitudes smaller than that of the hydrate formers. In the ranges
predicted, the fraction of water in the vapor phase was found to vary between 0.025
and 0.038 %. Consequently, methane is assumed to be the balance to carbon dioxide
in the vapor phase. The average absolute relative error (AARE) for the model for
carbon dioxide mole fraction in the vapor phase is found to be 10.2 %.
6.6.2 Liquid Phase Predictions
The amount of hydrate former present in the liquid phase defines the driving
force for hydrate growth (Bergeron and Servio, 2008a; Bergeron et al., 2010). Exper-
imental data and model predictions for the liquid fraction of methane and carbon
dioxide are presented in Figure 6.1 and 6.2, respectively. The model is found to
have an (AARE) of 9.0 % for the solubility of methane, 3.2 % for the solubility
of carbon dioxide. The magnitude of the AARE values based on solubilities are
heavily affected by the sensitivity of solubility towards pressure changes. Figure
6.1, 6.2 and 6.3 all contain large mole fraction gradients with respect to pressure
along the isotherms. This is further demonstrated by comparing the difference in
predicted and experimental pressure at a given solubility or vapor fraction.
6.6.3 Pressure Predictions
The model predictions were evaluated with respect to pressure differences at a
given mol fraction and the resulting AAREs are found to be 2.1 % and 1.2 % for the
solubility of methane and carbon dioxide respectively and and 2.5% for the carbon
dioxide in the vapor phase. The low AARE in terms of pressure demonstrates the
accuracy of the pressure predictions and also emphasizes the effect of the gradient
of mole fraction with respect to pressures along the isotherms in both the vapor and
liquid phases.
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 69
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
1000 2000 3000 4000 5000
ZC
H4
Pressure [KPa]
274 K -‐ Model 276 K -‐ Model 278 K -‐ Model 280 K -‐ Model
Figure 6.4: Predicted hydrate phase mole fraction of CH4 in the CH4+CO2+H2Osystem under H-Lw-V equilibrium
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 70
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
1000 2000 3000 4000 5000
ZC
O2
Pressure [KPa]
274 K -‐ Model 276 K -‐ Model 278 K -‐ Model 280 K -‐ Model
Figure 6.5: Predicted hydrate phase mole fraction of CO2 in the CH4+CO2+H2Osystem under H-Lw-V equilibrium
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 71
6.6.4 Predictions trends
In agreement with the data, the model for solubility of methane in the liquid
phase under H-Lw-V equilibrium predicts an increase in solubility with increasing
pressures and decreasing temperatures, i.e. as conditions approach H-Lw-V equi-
librium conditions of pure methane. The model predicted the hydrate phase mole
fraction of methane to follow the same temperature and pressure trends as the sol-
ubility of methane in the liquid as shown in Figure 6.4. On the contrary, when
conditions approach H-Lw-V equilibrium conditions of pure carbon dioxide (being
the more stable of the two hydrate formers with respect to pressure) the model pre-
dicts solubility of carbon dioxide in the liquid phase under H-Lw-V equilibrium to
increase with decreasing pressures and increasing temperatures. The mole fraction
of carbon dioxide in the hydrate phase is also predicted to follow the same temper-
ature and pressure trends as the solubility of carbon dioxide in the liquid phase, as
seen in Figure 6.5. The fractional occupancy of the hydrate phase was found to be
in the range of 0.91 to 0.96 in the examined region.
6.7 Conclusion
Three phase, hydrate-liquid-vapor (H-Lw-V) equilibrium conditions for the CH4+
CO2+H2O system have been predicted for the temperature region between 274 to
280 K and the pressure region between 1.4 to 5 MPa. When compared to to ex-
perimental data, the vapor mole fraction of carbon dioxide was predicted with an
AARE of 10.2 % and the predicted solubilities for methane and carbon dioxide in
the liquid phase have an AARE of 9.0 % and 3.2 %, respectively. The predicted
mole fractions are found to be very sensitive to the predicted pressure. When the
model predictions are evaluated in terms of pressure the AARE are found to be 2.1
% and 1.2 % for the solubility of methane and carbon dioxide in water respectively
and and 2.5% for the carbon dioxide in the vapor phase. All interactions parameters
used were optimized completely independent of the predicted data. No other known
literature has been found to report the solubility of hydrate formers in the liquid
CHAPTER 6. CH4+CO2+H2O SOLUBILITY PREDICTIONS 72
phase for the CH4+CO2+H2O hydrate forming system.
Chapter 7
Proposed Kinetic Growth Model
for Systems with Mixtures of Gas
Hydrate Formers
7.1 Preface
The successful model predictions of equilibrium mole fraction of hydrate formers
in the liquid phase for binary hydrate forming mixtures represent an important
milestone in the expansion of Bergeron & Servio’s kinetic model for simple hydrate
systems into a kinetic growth model for hydrate mixtures. A proposed kinetic model
for mixed systems is presented in this chapter. The model is based on the kinetic
model for simple hydrate systems by Bergeron and Servio along with the kinetic
growth model for hydrate mixtures by Englezos et al.
7.2 Abstract
A kinetic growth model for systems with mixtures of gas hydrate formers is
proposed. The model is an expansion of the model by Bergeron and Servio which has
successfully been applied to simple hydrate systems. Additional data and analysis
73
CHAPTER 7. KINETIC MODEL FOR MULTICOMPONENTS 74
are required to test the model.
7.3 Introduction
Gas hydrates are non-stoichiometric crystalline solids that form when molecules
from a gas or volatile liquid, suitable for hydrate formation, get entrapped in a
cage formed of water molecules (Englezos, 1993). Hydrates were discovered in the
1810 by Sir Humphry Davy (Davy, 1811). Initially hydrates were researched with an
academic interest by discovering hydrate forming compounds and the mapping of the
temperature and pressure conditions at which the hydrates decompose. The interest
in hydrates intensified with the discovery of hydrate clogs in gas-pipelines in the
1930s (Hammerschmidt, 1934). Since then, large amount of industrial resources have
been used in the development of inhibitors as well as in finding the thermodynamic
properties of hydrate formation (Servio, 2002). Natural gas hydrates are found in
large amount in ocean sediments as well as in permafrost regions (Sloan, 2000).
The amount of methane in the form of natural hydrates have been estimated to
be in the order of 104 Gt (Kvenvolden, 2002). The use of hydrates in storage of
carbon dioxide on the bottom of the ocean has been suggested as a way of limiting
greenhouse gas emissions into the atmosphere (Brewer, 2000).
The formation of hydrates is analogous to a crystallization process (Makogon,
1981; Bishnoi and Natarajan, 1996). The phase transformation can be divided into
a nucleation and a growth phase (Natarajan et al., 1994). The nucleation phase is
stochastic in nature and consequently cannot be well predicted. More success has
been achieved in modelling the growth phase. With the base for the modern hydrate
formation model well established in the work of Vysniauskas & Bishnoi (Vysniauskas
and Bishnoi, 1983), Englezos et al. (Englezos et al., 1987a) and Hashemi et al.
(Hashemi et al., 2007), Bergeron and Servio developed a simplified kinetic model
for simple hydrate systems (Bergeron and Servio, 2008a).
CHAPTER 7. KINETIC MODEL FOR MULTICOMPONENTS 75
7.4 Growth model for simple hydrates
In the model by Bergeron and Servio (Bergeron and Servio, 2008a) the overall
resistance to hydrate growth between the liquid water and the hydrate is given by
Equation 7.1:
R = 1
AP
⎡⎢⎢⎢⎢⎣
1
kH−L+ 1
kr
⎤⎥⎥⎥⎥⎦(7.1)
where kH−L is the mass transfer coefficient in the diffusion layer around the hydrate
particle, kr is the intrinsic reaction rate constant and AP represents the area of
the particle. By assuming kH−L ≫ kr and by using the measured particle size
distribution to determine the area of the hydrate particles, the following kinetic
growth model is obtained:
dn
dt= VLρwMWw
πµ2kr(xL − xH−L) (7.2)
Where VL is the liquid volume in the reactor, ρw is the density of water, MWw is
the molecular weight of water, x is the mol fraction, µj is the jth moment of the
particle size distribution (Kane et al., 1974) and kr is the intrinsic reaction rate
constant.
A more theoretical approach for determining the intrinsic reaction rate constant
is done by estimating the total surface area of the particles using a population
balance which gives the following equation:
dn
dt= VLρwMWw
π(µ00G
2t2 + 2Lcµ00Gt +Lcµ0
0)kr(xL − xH−L) (7.3)
Where G is the growth rate and Lc is the critical hydrate diameter. Based on kinetic
data and particle size analysis, the intrinsic reaction rate constant for methane,
carbon dioxide and propane have been determined by Bergeron and Servio (Bergeron
et al., 2010; Bergeron and Servio, 2008a,b).
CHAPTER 7. KINETIC MODEL FOR MULTICOMPONENTS 76
7.5 Proposed growth model for mixed hydrates
Based on the model of Bergeron and Servio (Bergeron and Servio, 2008a) and
how Englezos et al.(Englezos et al., 1987b) expanded their model to multi-components
systems the following is proposed:
dn
dt= VLρwMWw
πµ2
n
∑i=1
⎡⎢⎢⎢⎢⎣kriφi(xBi − xEqi )
⎤⎥⎥⎥⎥⎦(7.4)
The summation accounts for the individual contribution of each gas hydrate
former. φi is the fractional contribution of component i on the second moment.
The values of φi can be obtained by spectroscopic techniques such as RAMAN or
X-ray diffraction. The value of kr is the intrinsic reaction rate constant for the
individual hydrate formers for a given hydrate structure. xBi is the individual mole
fraction of component i in the bulk which is not a thermodynamic property and is
strongly dependent on the hydrodynamics.
The driving force for a single component hydrate forming system is defined
slightly differently than a multicomponent. This is because for a pure component
system at a specified temperature and pressure, only H-Lw equilibrium is possible.
Therefore, crystals in the liquid will continue to grown until the bulk concentration
of the hydrate former reaches the two phase (H-Lw) solubility.
A binary mixture has an additional degree of freedom and therefore has a H-
Lw-V equilibrium state possible at a given temperature and pressure. In order to
ensure that the system never achieves equilibrium the gas phase composition must
be different than the equilibrium gas phase composition at the same temperature
and pressure. An illustrative example of typical component driving forces in all
fluid phases for binary hydrate forming systems is demonstrated in Figure 7.1.
For a binary vapor phase, one of the components must have a mole fraction that
exceeds its equilibrium value at the given conditions, section A of Figure 7.1, while
the other component will consequently have a vapor phase concentration lower than
its equilibrium value, section B of Figure 7.1. In the liquid phase the mole fractions
of both components must be greater than the solubility at the given temperature
CHAPTER 7. KINETIC MODEL FOR MULTICOMPONENTS 77
Figure 7.1: Illustrative example of the driving force for all fluid phases in a binaryhydrate forming system. The surfaces illustrate the H-Lw-V equilibrium plane in therespective phase and the circle illustrates the compositions during hydrate growth ata given temperature and pressure. The driving force is the horizontal mole fractiondifference between the circle and the plane, illustrated by a vertical line.
CHAPTER 7. KINETIC MODEL FOR MULTICOMPONENTS 78
Liquid Phase Hydrate Vapor Phase
H-‐Lw interface Lw-‐V interface
Hydrate form
er 1, m
ole frac<o
n
Hydrate form
er 2, m
ole frac<o
n
x1B
x1EQ
x2B
x2EQ
y1V
y1EQ
y2V
y2EQ
z1EQ
z2EQ
Figure 7.2: Illustrative example to show a possible mole fraction profile in thehydrate (z), liquid (x) and vapor (y) phase for a binary hydrate forming systemduring hydrate growth. Superscript V refers to the vapor and B refers to the bulkliquid. The thin dotted lines represent the equilibrium mole fraction (EQ) for eachhydrate former in the respective phase.
CHAPTER 7. KINETIC MODEL FOR MULTICOMPONENTS 79
and pressure to allow for hydrate growth to occur, sections C and D of Figure 7.1.
To better understand what is taking place in the system the mole fraction profile
throughout each phase is examined. Since the vapor phase composition is not at
equilibrium, all other phases must have a composition that differs from equilibrium,
Figure 7.2. Thefore , if the composition in the bulk is measured, the driving force can
be evaluated by xBi −xEqi for each hydrate former. The resistance between xBi and xEqi
is then assumed to be only dependent on the intrinsic reaction rate constant. This
is because the mass transfer coefficient in the diffusion layer is much greater than
the intrinsic reaction rate constant under the appropriate hydrodynamic conditions
(i.e. high agitation in the bulk) (Bergeron and Servio, 2008b).
7.6 Conclusion
A novel kinetic model has been proposed for multicomponent hydrate forming
systems. The model is based on the kinetic growth model of Bergeron and Servio’s
model for simple hydrate systems combined with how Englezos et al. expanded
their model to multi-components systems. Additional data and analysis are needed
to test the model.
Chapter 8
Thesis Conclusion and Future
Work Recommendations
8.1 Comprehensive Conclusion
In chapter 3 and 4 hydrate-liquid-vapor equilibrium conditions for two binary
hydrate forming systems were mapped using a novel technique. The two chapters
also emphasized that it is insufficient to only satisfy Gibbs’ phase rule when re-
porting equilibrium data. An additional intrinsic variable is required to report the
uniqueness of the system.
In Chapter 3 the hydrate-liquid-vapor equilibrium plane for the nitrogen+carbon
dioxide+water system was mapped. The equilibrium temperature and pressure was
justified with the measured mole fraction of nitrogen in the vapor phase. The
system was mapped along several isotherms and the equilibrium pressure was found
to increase with an increased mole fraction of nitrogen in the vapor phase.
Chapter 4 considers the methane+ethane+water system which is unique as
it forms either structure I and structure II depending on the ratio of the guest
molecules although both methane and ethane form structure I only as simple hy-
drates. The hydrate-liquid-vapor equilibrium planes for the methane+ethane+water
system were mapped and a 3D representation of the phase diagram was presented.
80
CHAPTER 8. CONCLUSION AND FUTURE RECOMMENDATIONS 81
It was found that the equilibrium pressure of structure I is found to be less sen-
sitive to temperature and composition changes than structure II. Although the
system contained two structures the respective planes are connected and exhibited
the same overall trends. Along the isotherms and isobars the equilibrium pressure
increased and the equilibrium temperature decreased respectively with increasing
mole fraction of methane in the gas phase.
In Chapter 5 the focus was on the establishment of the composition in the liquid
phase for a binary hydrate forming system under hydrate-liquid-vapor equilibrium
conditions. The solubility of methane and carbon dioxide in the methane+carbon
dioxide+water system under hydrate-liquid-vapor equilibrium was determined. In
the experiments, the solubility of methane was found to increase with increasing
pressures and decreasing temperatures and the solubility of carbon dioxide was
found to increase with decreasing pressures and increasing temperatures.
The experimental data from Chapter 5 was modelled in Chapter 6. The calcu-
lations were performed using a flash based technique based on the Trebble-Bishnoi
equation of state and the van der Waals & Platteeuw and Holder models. All the
parameters required were optimized from independent data. The model predictions
were found to fit the experimental data in both the vapor and liquid phase.
Chapter 7 contains a proposed expansion of Bergeron and Servio’s kinetic model
from simple hydrate systems to hydrate mixture. The model is currently only in
the theoretical phase, but an important piece of the driving force in the model has
been established in the work presented in chapter 5 and 6.
In order to verify the kinetic growth model for multiple hydrate formers, ex-
perimental data on the rate of growth, occupancy and bulk liquid mole fraction of
the hydrate formers at defined driving forces must be obtained. While most of the
required fundamental understanding of mixed systems has been presented in this
work, difficulties could still arise when attempting to maintain constant properties
during kinetic experiments. Other challenging scenarios arise when there is a struc-
tural difference between the individual hydrate formers as simple systems and that
of respective mixtures. The determination of the intrinsic reaction rate constant
CHAPTER 8. CONCLUSION AND FUTURE RECOMMENDATIONS 82
for the individual components in the model must be carefully considered in such
scenarios.
A well-established kinetic growth model for mixed hydrate systems could prove
very useful for a variety of kinetic applications as hydrates are believed to be eco-
nomically competitive in industrial fields such as gas transportation. The kinetic
model could prove even more successful with proper handling of multi-structural
systems due to their frequent occurrence and the advantages that the thermody-
namic properties of such systems could offer.
CHAPTER 8. CONCLUSION AND FUTURE RECOMMENDATIONS 83
8.2 Future Work Recommendations
The following is a list of recommended future work directly linked to the knowl-
edge presented in this thesis:
– Test the multicomponent kinetic model proposed in Chapter 7
– Obtain solubility data for the CH4+C2H6+H2O system under H-Lw-V equi-
librium and model the structure I and structure II parts of the system
– Examine the applicability of the multicomponent kinetic model for system
such as CH4+C2H6+H2O which contains a structure I and a structure II re-
gion.
– Perform morphological studies on the CH4+C2H6+H2O system and compare
structure I to structure II morphology.
CHAPTER 8. CONCLUSION AND FUTURE RECOMMENDATIONS 84
8.3 Other Significant Contributions
In addition to the work presented as part of this thesis, the following significant
contributions were made during the research project:
– Bruusgaard, H., Lessard, L. & Servio, P., Morphology Study of Structure I
Methane Hydrate Formation on Water Droplets in the Presence of Biological
and Polymeric Kinetic Inhibitors, Crystal Growth and Design, 9(7), 3014-302,
2009
– Beltran, J., Bruusgaard, H. & Servio, P., Gas hydrate phase equilibria: Loading
vs Equilibrium composition, To be submitted to Journal of Chemical Thermo-
dynamics
– Design of morphology reactor and setup
– Design of kinetic/equilibrium reactor and setup
– Construction and setup of LABVIEW® data-acquisition systems for the lab-
oratory setups
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