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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




4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5 CH4+CO2+H2O Solubilities 46

5.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47




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


6.6.1 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


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


Figure 2.1: Water cavities present in Structure I, Structure II and Structure Hhydrate (adapted from Hester and Brewer (2009)).


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.


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-


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).


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


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


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).


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.


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


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).


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


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


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).


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


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


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.,


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.


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).


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


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.


Figure 3.1: Jefri - DBR Phase Behaviour System


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-


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


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


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


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).


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


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).



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.


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


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.


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


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)


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


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)


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


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).


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-


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;


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.


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


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


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


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


(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.


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


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


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




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).


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-


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.


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-


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


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)


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


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.


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).


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


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


0.000

0.005

0.010

0.015

0.020

1000 2000 3000 4000 5000

XC

O2

Pressure [KPa]


Figure 6.2: Predicted vs experimental liquid phase mole fraction of CO2 in theCH4+CO2+H2O system under H-Lw-V equilibrium


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]


Figure 6.3: Predicted vs experimental vapor phase mole fraction of CO2 in theCH4+CO2+H2O system under H-Lw-V equilibrium


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.


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


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


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


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).


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).


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


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.


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.


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


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.


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.


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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