PHASE BEHAVIOR OF CARBON DIOXIDE SEQUESTRATION

IN DEPLETED GAS RESERVOIRS

by

LORRAINE E. SOBERS, B.S.Ch.E.

A THESIS

IN

PETROLEUM ENGINEERING

Submitted to the Graduate Faculty

of Texas Tech University in Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

PETROLEUM ENGINEERING

Approved

Co-Chairperson of the Commit)*!

Co-Chairperson of the Committee

Accepted

»'•*,' ^ • — " - ^ — • ~ "

Dean of the Graduate School

August, 2003

ACKNOWLEDGEMENTS

This thesis would have not have been written, bound and acceptable in content

without the support of several people. First, I would like to thank those whose technical

help were invaluable. My advisor. Dr. Frailey has been as patient, meticulous, and

challenging as the best advisor should be. I hope that in years to come he will be proud

be of this, the last thesis he supervised at Texas Tech Uruversity. I would also like to

thank my co-chair and program advisor. Dr. Lawal, for disagreeing with Dr. Frailey just

when I needed him to and for introducing me to the Petroleum Engineering Department

at Texas Tech.

The technical support would not have been enough to bring this thesis to

fruition. In the CAPRS, I must also thank Rajesh Ramachandran, Vance Vanderburg and

Jeff Gasch for working along with me on nights and weekends and, being available to

help with almost anything without hesitation. And there are those outside of the

CAPRS, who have been my strongest supporters Jenelle Baptiste, my roommate and

friend of three years. Elder and Sis. Loggins, the members M.L.K. Jr. Blvd. SDA church,

and the many friends I have made during my time in Lubbock.

I must tharik my cheer leaders at home: my family and friends, especially

Mandisa Regrello, Jimroy Wyse and Enterprise S.D.A. church who have been supportive

in my journey from Enterprise all the way to Lubbock and back. I am thankful to God

for bringing me through the best three years of my life so far. It has been a wonderful

journey and an answer to my prayers. I am immensely grateful for the financial stability

I enjoyed which was made possible by the Ministry of Energy and Energy Industries,

Trinidad and Tobago, Exxon Mobil Exploration and Production, Trinidad Ltd., the

William Fulbright Foimdation, LASPAU, and CAPRS. This thesis was partially funded

by the U.S. Department of Energy (DE-FC26-01NT41145) and the Carbon Caphire

Project, an international joint industry project. I dedicate this thesis to my parents

Emerson and Doreen Sobers for being who they are, giving everything and then some.

ui

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii

ABSTRACT vii

LIST OF TABLES viii

LIST OF FIGURES ix

NOMENCLATURE xiii

CHAPTER

L INTRODUCTION 1

LI. Background to Sequestration of CO2 1

L2. General Geologic Storage Options 4

1.2.1. Storage of CO2 in Saline Formations 4

1.2.2. Oil and Gas Reservoir Storage of CO2 5

1.2.3. CO2 Storage in Coal Seams 5

1.3. Depleted Gas Reservoir with CO2 Injection Scenario 6

1.4. Thesis Objectives 7

2. LITERATURE REVIEW 11

2.1. Overview 11

2.2. Hydrocarbon Gas Types 11

2.3. General Phase Behavior 12

2.4. Fluid Properties 13

2.4.1. Lab Procedures 14

2.4.2. Correlations 14

2.4.3. Equations of State 15

2.5. General Gas Reservoir 17

2.5.1. Production 17

2.5.2. Analysis Tools 19

2.6. Phase Behavior Software: WinProp 19

IV

3. METHODOLOGY 25

3.1. Problem Description 25

3.2. Equation of State 25

3.3. Flash Liberation: Concept/Calculation 28

3.4. Constant Volume Depletion: Concept 30

3.5. EOS Software Application: WinProp 31

3.5.1. Pressure-Temperature Diagram 31

3.5.2. Two-phase Flash Calculations 33

3.5.3. Constant Volume Depletion 35

4. PHASE BEHAVOIR RESULTS 41

4.1. Phase Behavior 42

4.1.1. Pressure-Temperature Diagrams 43

4.1.2. Vapor and Liquid Fractions 46

4.1.2.1 Dry Gas 46

4.1.2.2. Wet Gas 46

4.1.2.3 . Retrograde Gas 41

4.1.3. Compressibility Factor 48

4.1.3.1. Dry Gas 48

4.1.3.2 .Wet Gas 48

4.1.3.3 . Retrograde Gas 49

4.2. Trend of PVT Relationships 49

4.2.1. Cricondenbar 49

4.2.2. Cricondentherm 50

4.2.3. Critical Points 51

4.3. Summary of Phase Behavior Results 52

5. DISCUSSION 96

5.1. Trends of Phase Behavior Results 96

5.1.1. Relative Drying and Wetting of Natural Gas due to Carbon Dioxide Sequestration 97

5.1.2. Trends of Cricondenbar, Cricondentherm and due to Carbon Dioxide Sequestration 99

5.1.3. Approximating the Dynamic Mixing of Carbon Dioxide

and Natural Gas with Equilibrium Mixture Flash Calculations 100

5.2. Reservoir Considerations 102

5.2.1. Depleted Reservoirs 103

5.2.2. Carbon Dioxide Pressurized Reservoirs 104

5.3. Sequestration Implications by Gas Type 104

5.3.1. Compressibility and Formation Volume Factor 104

5.3.2. Vaporization of Condensate 106

5.4. Enhanced Gas and Condensate Production 107

5.5. Economic Considerations 109

6. CONCLUSIONS AND RECOMMENDATIONS 114

6.1. Conclusions 114

6.2. Recommendations 115

REFERENCES 118

APPENDIX A 124

APPENDIX B 128

APPENDIX C 132

VI

ABSTRACT

Carbon dioxide sequestration in depleted and abandoned gas reservoirs can

accomplish two important objectives. Firstly, it could be important part of present

climate control initiatives to reduce the concentration of carbon dioxide in the

atmosphere. Secondly, it could be instrumental to enhanced gas and condensate

recovery. Using the pressure-temperature diagrams and two phase flash calculations,

the phase behavior of natural gas-carbon dioxide mixtures were analyzed to provide

enlightenment on the carbon sequestration process. From the analysis of simulated

results, it was found that carbon dioxide exhibited a drying effect on wet and retrograde

gas mixtures and a wetting effect on dry gas.The results for retrograde gas condensate

depended on the composition of reservoir fluids at abandonment conditions. The main

difference being the liquid volume percent with increasing pressure and carbon dioxide

concentration. This irifluenced the volume of condensate vaporized with the addition of

carbon dioxide. It was also determined that carbon dioxide lowers the compressibUity

factor of all gas types. These results are favorable for carbon dioxide sequestration

because decreasing compressibility factors represents increasing storage capacity.

vu

LIST OF TABLES

4.1 Median Composition of Dry, Wet and Retrograde gas-condensate in Depleted Gas Reservoirs expressed as Mole Percent of Hydrocarbon Components 54

4.2 Components of the gas sample used by Simon et al 55

Vll l

LIST OF FIGURES

1.1 Schematic showing injection options for ocean sequestiation 9

1.2 Pressure-temperature diagram of pure carbon dioxide showing conditions at which the solid(s), liquid (1) and gas(g) exist 10

2.1 U.S. Greenhouse Gas Emissions in 2001 as reported by the Energy Information Administiation^ 21

2.2 Pressure-temperature diagram of a reservoir fluid showing conditions for different gas types with respect to the critical point and cricondentherm 22

2.3 Example of a p/z plot for a reservoir under water drive and a volumetric reservoir 23

2.4 Example of a pressure-temperature diagram 24

3.1 Main window with panels used to manipulate fluid properties and perform calculations 36

3.2 Two-phase envelope constiuction window displaying the Envelope Specification tab 37

3.3 Two-phase flash calculations window displaying the Calculations tab 38

3.4 Two-phase flash calculations window displaying the Plot Control tab 39

3.5 Constant volume depletion experiment simulation window displaying the Pressure Levels tab 40

4.1 Comparison of simulated PR EOS results and experimental data from Olds et aL for pure metiiane at 70,100,160 and 220 °F 56

4.2 Compressibility factor obtained from experimental results and simulation results (PR EOS) at 100,160 and 220 °F for methane with 39.5% carbon dioxide 57

IX

4.3 Compressibility factor obtained from experimental results and simulation results (PR EOS) at 100,160 and 220 °F of methane with 59.4% carbon dioxide 58

4.4 Compressibility factor obtained from experimental results and simulation results (PR EOS) at 100,160 and 220 °F for methane with 79.6% carbon dioxide 59

4.5 Comparison of compressibility factor of natural gas mixtures obtained by PR EOS simulation and experiment at 70 °F 60

4.6 Comparison of compressibility factor of natural gas mixtures obtained by PR EOS simulation and experiment at 90 °F 61

4.7 Comparison of compressibility factor of natural gas mixtures obtained by simulation PR EOS and experiment at 120 °F 62

4.8 Pressure-temperature diagram of dry gas-carbon dioxide mixtures ranging from 0-99% carbon dioxide with critical points for each mixture labeled 63

4.9 Pressure-temperature diagram of wet gas with 5-65% carbon dioxide 64

4.10 Pressure-temperature diagram of wet gas with 65-99% carbon dioxide with critical point for each mixture labeled 65

4.11 Pressure-temperature diagram of retiograde gas A-carbon dioxide mixtures ranging from 0-95% carbon dioxide with critical points for each mixture labeled 66

4.12 Pressure-temperature diagram of retiograde gas B-carbon dioxide mixtures ranging from 0-95% carbon dioxide with critical points for each mixture labeled 67

4.13 Pressure-temperature diagram of retiograde gas C-carbon dioxide mixture ranging from 0-95% with critical points for each mixture labeled 68

4.14 Critical pressure and temperature of dry gas-carbon dioxide mixtures ranging from 0-99% carbon dioxide 69

4.15 Liquid phase volume percent of wet gas with 0-99% carbon dioxide at 150 °F 70

4.16 Liquid phase volume percent of wet gas with 0-99% carbon dioxide at 60 °F 71

4.17 Liquid phase volume percent of retiograde gas A with 0-70% carbon dioxide at 150 °F 72

4.18 Liquid phase volume percent of retiograde gas A with 70-95% carbon dioxide at 150 °F 73

4.19 Liquid phase volume percent of retiograde gas B with 0-99% carbon dioxide at 150 °F 74

4.20 Liquid phase volume percent of retiograde gas C witii 0-99% carbon dioxide at 150 °F 75

4.21 Relationship between compressibility factor and increasing carbon dioxide concentiation with dry gas mixture at 100 °F 76

4.22 Relationship between compressiblity factor and increasing carbon dioxide concentiation with dry gas mixture at 150 °F 11

4.23 Relationship between compressibility factor and increasing carbon dioxide concentiation with dry gas mixture at 400 °F 78

4.24 Relationship between the compressibility factor and increasing carbon dioxide concentiation with dry gas at 150 °F and 1600 psia 79

4.25 Relationship between the compressibility factor and increasing carbon dioxide concentiation with wet gas mixture at 150°F 80

4.26 Relationship between the compressibility factor and increasing carbon dioxide concentiation with retiograde gas A mixture at 150 °F 81

4.27 Relationship between the compressibility factor and increasing carbon dioxide concentiation with retiograde gas B mixture at 150 °F 82

4.28 Relationship between compressibility factor and increasing carbon dioxide concentiation with retiograde gas C mixhire at 150 °F 83

4.29 Trend of Cricondenbar of dry gas carbon dioxide with increasing carbon dioxide concentiation 84

XI

4.30 Trend of the Cricondenbar of wet gas with increasing carbon dioxide concentiation 85

4.31 Trend of Cricondenbar pressure with respect to carbon dioxide concentiation for three retiograde gas compositions 86

4.32 Cricondentherm and critical pressure and temperature of carbon dioxide-dry gas mixtures as a function of carbon dioxide concentiation 87

4.33 Cricondentherm carbon dioxide-dry gas mixtures as a function of carbon dioxide concentiation 88

4.34 Cricondentherm carbon dioxide-wet gas mixtures superimposed on P-T diagrams for the mixtures 89

4.35 Trend for cricondentherm temperature with respect to carbon dioxide concentiation for three retiograde gas compositions 90

4.36 Cubic relation of the critical points of dry gas-carbon dioxide mixtures 91

4.37 Cubic relation of the critical points of wet gas-carbon dioxide mixtures 92

4.38 Trend for critical temperature with respect to carbon dioxide concentiation for three retiograde gas compositions 93

4.39 Trend for critical pressure with respect to carbon dioxide concentiation for three retiograde gas compositions 94

4.40 Trend for critical points of retiograde gas-carbon dioxide mixtures for three retiograde gas compositions 95

5.1 Sequestiation pressure as a function of carbon dioxide mole

fraction in a dry gas reservoir depleted to 250 psia and 150 °F I l l

5.2 p / z plot of dry gas with 0-99% carbon dioxide mixtures at 150 °F 112

5.3 Pressure-Temperature diagram of natural gas-carbon dioxide mixtures with respect to reservoir conditions 113

xu

NOMENCLATURE

a dimensional equation of state constant accounting for molecular attractive forces,

psia/ (ft3-lbm-mol)2

A numerical constant used in equations; dimensionless equation of state constant

accounting for attiactive forces

Aij intermediate terms used in Newton-Raphson solution of the Michelsen two-

phase isothermal flash

b dimensional equation of state constant accotinting for molecular repulsive forces,

ftyibm

B dimensionless equation of state constant accounting for repulsive forces

Bg formation volume factor,scf/ft3

Bscf billion standard cubic feet

Ci equation of state volume tianslation ("shift") constant, ft^/lbm mol

EOS Equation of state

fi fugacity of Component i in a mixture, psia

iu fugacity of Component i in the liquid phase, psia

fvi fugacity of Component i in the vapor phase, psia

Fv vapor mole fraction

Fvmax upper limit of vapor mole fraction in the Rachford-Rice equation

Fvmin lower limit of vapor mole fraction in the Rachf ord-Rice equation

g* normahzed Gibbs energy

gl liquid phase normalized Gibbs energy

g'y vapor or incipient phase normalized Gibbs energy

Gmj,75 volume of 75 mole % of injected carbon dioxide, scf

Gmj,95 volume of 95 mole % of injected carbon dioxide, scf

Gp cumulative volume of gas produced, scf

kij equation of state binary interaction parameter between Component Pair i-j

Ki yi/xi = equilibrium ratio (K value) of Component i

Xlll

n number of moles, Ibm-mole

nco2 number of moles of carbon dioxide, Ibm-mole

no number of moles at depleted conditions, Ibm-mole

nov number of moles in the vapor phase at depleted conditions, Ibm-mole

nfinai number of moles at the end of sequestiation, Ibm-mole

np number of moles produced, Ibm-mole

np,45 number of moles produced with 45 mole % carbon dioxide, Ibm-mole

npL number of moles produced in the liquid phase, Ibm-mole

npv number of moles produced in the vapor phase, Ibm-mole

nx total number of moles of fluid, Ibm-mole

nif final number of moles of fluid, Ibm-mole

nii initial number of moles of fluid, Ibm-mole

nip total ntmiber of moles of fluid produced, Ibm-mole

nv<ond number of moles of Uquid vaporized, Ibm-mole

Np cumulative number of moles of liquid condensate produced, Ibm-mole

p pressure, psia

pc critical pressure, psia

pr reservoir pressure

pri reduced pressure of component i

PR Peng-Robinson

N total number of components, n; last component in a mixture

R universal gas constant = 10.73146 psia-ft3/°R-lbm mol

scf standard cubic feet

SRK Soave-Redlich-Kwong

T temperature, °F or °R

Tc critical temperature, °R

Tr reservoir temperature

Tr reduced temperature of component i

Tsc standard condition temperature, °F or °R

V molar volume, ft / Ibm mol

xiv

V volume, ft

Vms molar volume, bbls/Ibm-mole

Vp volume of gas produced, scf

Vr volume at reservoir conditions, ft

Vsc volume at standard conditions, scf

Vv<ond volume of condensate vaporized, scf

Xi component i mole fraction in reservoir oil

yi component i mole fraction in gas phase

z compressibility factor/z-factor

Zc critical z-factor

Zi component i mole fraction in overall mixture

Zg compressibil i ty factor of hydrocarbon gas

Zinj compressibility factor of injected carbon dioxide

Zp compressibi l i ty factor of p r o d u c e d gas

Zsc standard conditions z-factor

Zr reduced z-factor

a correction term to Constant A in equations of state

s convergence tolerance

X i chertucal potential at a standard state

|ii chemical potential

(t)i fugacity coefficient for Component i

CO acentiic factor

0.° Cll numerical constants in cubic equations of state

XV

CHAPTER 1

INTRODUCTION

In the year 2000, the fossil fuel combustion in the U.S. accounted for the release

of approximately 114.1 tiillion cubic feet of carbon dioxide (CO2) to the atmosphere.

This number has increased steadily since the industiial era^ leading to concerns of global

warming and the ensuing climatic changes. Sequestiation of carbon dioxide in depleted

gas reservoirs, with storage capacity estimated to be 140 GtC (Gigatonnes Carbon)

worldwide,^ is considered as a possible solution.

1.1. Background to Sequestiation of CO2

Greenhouse gases such as carbon dioxide tiap solar heat energy when released to

the atmosphere that causes an increase in the earth's surface temperature. This

phenomenon is known as global warming, and it is believed to be a negative irifluence

on weather patterns, coastlines and ecosystem changes. This is a grave concern for the

entire world. For this reason the United Nations Framework Convention on Climatic

Change (UNFCCC) sought to address the problem in December 1997 in Kyoto, Japan. *

Given the increasingly large volume of carbon dioxide emitted annually, a plan was

developed for mitigation of anthropogenic carbon dioxide emission to the atmosphere.

The agreement to decrease emission to 5.2% less than 1990 emission levels by 2008 to

2012 was ratified by 193 countiies.

The world population relies very heavily on the combustion of fossil fuels such

as natural gas, fuel oil, and coal to produce energy. The main by-products of fossil fuel

combustion are carbon dioxide and water, hi most power plants and other industiial

processes that use fossil fuels to generate energy, the by-products are vented to the

atmosphere. It has been recommended that carbon dioxide be captured from the flue gas

of these plants and disposed in a more environmentally friendly manner. However, if

industiies are forced to change operations in order to curtail carbon dioxide disposal by

venting, a significant cost increase in most every manufacturing industiy would arise.

Carbon dioxide capture would require extia energy expenditure that could increase

energy cost to 40% above current levels.^ However, coupled with enhanced oil and gas

recovery in depleted reservoirs, carbon sequestiation is economically attiactive with the

sale of produced hydrocarbon fluid. Carbon dioxide sequestiation is also expected to be

instiumental in reservoir pressure support to enhance gas and condensate production.^

With this knowledge, the Third Conference of Parties of the UNFCC earmarked carbon

dioxide sequestiation as an area for research and development.^

The logical justification for carbon dioxide sequestiation in gas reservoirs is that

it mimics nature. Two large carbon dioxide reservoirs exist in Colorado, U.S.A., McElmo

Dome and Sheep Mountain fields, and there is also one in Bravo Dome in New Mexico,

U.S.A. Furthermore, there are some natural gas reservoirs in Terrell and Pecos Counties,

Texas, U.S.A., that produce up to 70% carbon dioxide with natural gas. Additionally,

there are also carbon dioxide reservoirs in Hungary, Greece, and Germany.^ These

natural occurrences demonstiate that underground storage of carbon dioxide is

supported by the geologic stiucture of these reservoirs.

As a hydrocarbon gas reserve, depleted gas reservoirs would likely be well

characterized by seismic, well log, and core data in terms of rock properties, faults,

capstone integrity, and extension. Thousands of gas reservoirs worldwide have stored

natural gas for miUions of years, and it would be reasonable to expect that the same

reUable, imobtiusive and safe storage be expected with carbon dioxide.^

From an engineering standpoint, carbon dioxide sequestiation can be easily

accommodated by using the existing infrastiucture of gas wells. Converting some gas

production wells to carbon dioxide injection wells would involve a low cost work-over,

modest surface facility changes and some non-producing and non-injecting wells used

for monitoring purposes.^

In addition to gas reservoirs, carbon dioxide storage locations such as saline

aquifers, the ocean floor, salt caverns, and coal beds have been considered and are being

investigated by several researchers.^" In particular, significant advances, including field

tests, have been made in considering the possibUity of carbon dioxide storage in the

ocean, coal seams, and oil reservoirs.

There are three natural 'reservoirs' for carbon dioxide: the atmosphere, the

oceans, and the earth, ii The ocean has been identified as being the largest of the

potential sinks. Storage of carbon dioxide on the ocean floor can take place either by

injection or by increasing the drawdown volume of carbon dioxide from the atmosphere

to the ocean through the addition of nutiients. At present, the injection proposal is better

tinderstood and it is proposed that this can be done by pipelines from land, moving

ships and vertical pipes suspended in the ocean. Figure 1.1 shows a schematic of

proposed injection methods.

1.2. General Geologic Storage Options

Geologic formations can be ideal locations for carbon dioxide storage depending

on capacity, structure, porosity and other properties. Initiations of long term geologic

storage of carbon dioxide have the potential to be feasible in the near future. Some of the

proposed storage sites have stored oil, gas and brine for thousands of years, which

prove their abihty to securely tiap and store fluids. These sites include saline formations,

hydrocarbon reservoirs, and coal seams. The mechanism of storage and tiapping in

these three sites are not the same. Coal seams differ from other geologic storage sites in

that chemical as opposed to physical tiapping is exploited. Saline formations are not

proven to 'tiap' fluid with the same mechanism as hydrocarbon reservoirs.

1.2.1. Storage of CO2 in Saline Formations

Saline formations have been identified as the largest of geologic storage options.

Unlike depleted oil and gas reservoirs, saline f ormatioris do not have the advantage of

producing a salable product such as natural gas or oil. However, because of the

abundance of saline formations worldwide, they are very likely to be in close proximity

to carbon dioxide emissions sources. AccessibiUty to storage sites affects the overall cost

of sequestiation because of the cost attiibuted to tiansporting carbon dioxide from

emission sources to storage sites. Currentiy, the first large scale carbon dioxide

sequestiation is being carried out in Sleipner Field, Norway, with injection into a saline

formation.i2

1.2.2. Oil and Gas Reservoir Storage of CO2

Oil and gas reservoirs are targeted as very promising sites for carbon dioxide

sequestiation because the physical and stiuctural properties of these reservoirs are well

characterized. Furthermore, the existing from hydrocarbon production can undergo

minimal modification and used in sequestiation projects. Sequestiation of carbon

dioxide in oil fields has been achieved unintentionally in carbon dioxide flooding of oil

reservoirs as a means of enhanced oil recovery. Intentional sequestiation tests are

currently being done in the first major U.S. field experiment in a depleted oil reservoir in

Hobbs, New Mexico. ^ Gas reservoirs are considered as exceptionally good candidates

because of the proven abihty to store gas for millions of years without leakage to the

atmosphere.

1.2.3. CO2 Storage in Coal Seams

Injection of carbon dioxide in coal seams has proven to be feasible with the

added advantage of methane production. A coal seam candidate for carbon dioxide

sequestiation is one that is homogeneous, of simple geologic stiucture with a

permeabiUty of at least 1 to 5 milHdarcies and saturated with gas. The mechanism is very

similar to that of sequestiation in oil and gas reservoirs with injection and producing

wells for carbon dioxide and methane, respectively. The main difference is that coal

seams tiaps carbon dioxide by chemical adsorption whereas hydrocarbon reservoirs

tiap fluids geologically. This has been carried out successfully in the San Juan Basin.^is

1.3. Depleted Gas Reservoir with CO2 Injection Scenario

Carbon dioxide sequestiation with enhanced gas and condensate recovery is a

process which encompasses gas captured from industiial flue stacks or refineries,

compression for pipeline tiansport to a depleted gas reservoir, injection into the

reservoir and enhanced gas and condensate recovery from producing weUs. After

sustained enhanced natural gas production with sequestiation, the natural gas reserves

become depleted while increased concentiation of carbon dioxide decreases the quaUty

of the produced natural gas. At this time, producing weUs are shut in, and carbon

dioxide injection continues until the initial reservoir pressure is attained.^^ Shut-in

producing weUs may be abandoned or converted to monitoring wells. Other aspects of

carbon dioxide sequestiation imder investigation include monitoring geologic

processes,i''carbon dioxide capture,!^ mixing with natural gas, enhanced gas recovery,1'

reservoir selection, storage^ and cost.

This thesis focuses on predicting the phase behavior of carbon dioxide-natural

gas mixtures in depleted gas reservoirs. The analysis of phase behavior takes into

accoxint the physical characteristics of the natural gas encovmtered in situ and the

physical properties of the injected gas at reservoir conditions.

The injected gas, carbon dioxide, is an acidic, dense, water soluble compound

that exists as a gas at ambient conditions and can be a supercritical fluid at temperatures

greater than 87.9 °F as shown in Figure I.2.20 Carbon dioxide targeted for sequestiation

is not 100% pure however, for simpUcity it is assumed that pure carbon dioxide is used

in for sequestiation. The in situ natural gas prior to sequestiation consists of a mixture of

organic compounds such as methane, ethane, propane, butane, pentane, hexane and

heptane. The composition of natural gas varies considerably and influences the phase

behavior of the natural gas-carbon dioxide mixtures, which is affected by the properties

of both gases.

1.4. Thesis Objectives

The research reported herein is geared towards phase behavior analysis of

hydrocarbon gas and carbon dioxide mixtures. The aim of this thesis is to investigate the

phase behavior of the fluids involved in sequestiation as a function of pressure,

temperature and gas composition. By this means is possible to give a more accurate

estimate of the volume of sequestered carbon dioxide, enhanced gas production and

enhanced condensate production that can be sequestered in a particular reservoir. This

could be a crucial guideline in future sequestiation development schemes.

A key aspect of carbon dioxide sequestiation plarming is predicting the phase

behavior of natural gas when combined with carbon dioxide. The tmderlying

vmcertainty is the effect the addition of carbon dioxide has on the phase behavior of

natural gas at reservoir conditions. For example, does the addition of carbon dioxide to a

depleted retiograde gas reservoir reverse and vaporize the hydrocarbon Uquid

condensed at reservoir temperature and pressure. This question and similar questions

have been answered by employing phase behavior analysis using a commercially

available phase behavior computer program. By using this approach, assessing a

depleted gas reservoir as a candidate for carbon dioxide sequestiation is based primarily

on information that is concise and readily available, that is temperature, pressure and

gas type.

i.and ba^ed pipe Moving ship Vertical pipe

ILL

ISOOm

Pool of liquid CO2 3000m

Figure 1.1 Schematic showing injection options for ocean sequestiation."

-109.3 -69.5 87.9

Temperature ^F

Figure 1.2 Pressure-temperature diagram for pure carbon dioxide showing conditions at which the sohd(s), Uquid(l) and gas (g) exist. o

10

CHAPTER 2

LITERATURE REVIEW

2.1. Overview

Sequestiation of carbon dioxide in depleted gas reservoirs is a relatively new

proposal to curb rising carbon dioxide emission levels and as such it is difficult to find

many publications on the topic prior to 1995. However, in recent years there has been

intense interest in reduction of greenhouse gas using new technology and industiial

processes. These gases include methane, nitious oxide, hydrofluorocarbons,

perfluorocarbons, stdfur hexafluoride and carbon dioxide. Each gas has the potential to

absorb different quantities of heat, measured as its Global Warming Potential (GWP).

Although carbon dioxide has the lowest GWP, its anthropogeruc production far

surpasses that of the other gases. Figure 2.1 shows that in 2001, carbon dioxide

accounted for 83.1 % of greenhouse gases emissions.^ Consequently, there has been a

greater emphasis on carbon dioxide than the other greenhouse gases. As such, capture

and storage of carbon dioxide has been cited by the Kyoto Protocol as a means of

reducing greenhouse gas emissions.*

2.2. Hydrocarbon Gas Types

A crucial part of plaruiing carbon dioxide sequestiation in gas reservoirs is

considering the classification of gas that remains in the reservoir. Traditionally, there

have been various means of classifying gas reservoirs including molecular weight of the

11

heptane plus fraction, gas-oU ratio, tank gravity and liquid color. Generally classification

by gas-oil ratio has been more widely accepted because the other indicators show weak

correlation with the API gravity of the stock tank Hquid. 21

Natural gas is classified as dry, wet or retiograde, depending on the reservoir

temperature, separator conditions critical temperature and cricondentherm of the fluid.

The cricondentherm is the highest temperature of the two-phase envelope at which

Uquid exists (Figure 2.2). The critical point is the temperature and pressure at which the

properties of the Uquid and the gaseous phase are identical. 22

A dry gas is a reservoir fluid that is a vapor at both reservoir and surface

conditions. On a pressure-temperature diagram, these conditions faU outside of the two-

phase region of that particular gas composition. On a dry gas pressure-temperature

diagram, the reservoir temperature is greater than the cricondentherm. A wet gas differs

in that the surface or separator conditions are within the two-phase envelope (Figure 2.2,

point A2). Retiograde gas condensate exists at reservoir temperatures less than the

cricondentherm but greater than the critical temperature (Figure 2.2, point B).2i At

certain reservoir conditions, it is possible for gas to condense and form a Uquid phase

that is difficult to recover from the reservoir by the primary recovery mechanisms.

2.3. General Phase Behavior

Condensation and vaporization of components constitutes the phase behavior of

a system. Phase behavior is defined as the behavior of vapor, Uquid and soUd phases as

a fvmction of pressure, temperature and composition.23 jn this thesis, the primary

12

concern is the volumetiic behavior and compressibiUty of the vapor phase. Emphasis is

placed on the presence of single or two-phase mixtures at reservoir and surface

conditions.

2.4. Fluid Properties

It is not sufficient to simply know the number of phases of the fluid mixture that

are present at reservoir conditions. The volumetiic behavior of the phases, particularly

the gas phase, is at the crux of estimating the storage capacity of a depleted reservoir.

The compressibiUty factor, z, of a phase is used to relate the volume of the phase at ideal

conditions to the volume at actual conditions. The gas formation volume factor, Bg,

relates the volume of gas in a reservoir to the volume of the same gas at surface

conditions.22 These parameters are used to estimate the volume of gas that can be

contained in a reservoir.

When carbon dioxide is injected into a reservoir, the volume of the compressed

gas at reservoir conditions is different from surface conditions. The formation volume

factor, accounts for this change in volume,

^ . ~ - (2-1) sc

The volume of the gas mixture at the surface, Vsc, could be easUy measured. At

reservoir conditions of increased temperature and pressure, the reservoir volume, Vr,

occupied is estimated by equations of state or experimental values. With the volume

expressed in terms of pressure, temperature and compressibiUty factor, the formation

volume factor can be calculated as:

13

1 D Z scl^ r sc

2.4.1. Lab Procedures

The compressibiUty factor of a gas mixture is calculated from lab measurements

with the use of a pressure, volume, and temperature (PVT) ceU. The basic operation

consists of pressurizing a known volume of the gas in a sealed oven. A portion of the gas

vented periodicaUy and its standard volume and the volume occupied in the oven are

recorded. Measurements are taken for a range of temperatures and pressures and the

compressibiUty factor is calculated by dividing the actual volume of the gas to the

volume it would occupy if it were an ideal gas. ^

V actual

z= 2 3 ' ideal

lA.l. Correlations

For natural gas mixtures, several methods for predicting phase behavior

especiaUy, PVT behavior, have been proposed. The most common approach is using the

principle of corresponding states to make an approximation to PVT data when

experimental data is not avaUable. Correlations using this principle together with

composition data or gas gravity estimates yield compressibiUty factor estimates.

Standing and Katz24 developed a chart for determining the compressibiUty factor of

sweet gases natural gas with Uttle or no acidic inorgaruc compovmds. Comparable work

has been done for by Sutton, 25 Stewart et al., ^and Wichert and Aziz, ^ for both sweet

14

and sour gases. Work done by Wichert and Aziz was particularly geared toward

hydrocarbon mixtures with carbon dioxide and hydrogen sulfide. Stewart et al. and

Sutton's work used correction factors that accounted for hydrogen sulfide, carbon

dioxide, and water. Sutton's correlation was appUcable for hydrocarbon gas gravity

between 0.57 and 1.65.

One of the more promising modifications was that of Wichert and Aziz.27

Intended for natural gas with high carbon dioxide concentiations, their modification is

vaUd up to 55 mole percent of carbon dioxide.

2.4.3. Equations of State

The accuracy of the modeling of phase behavior of reservoir fluids depends on

the accuracy of the EOS used and reUabUity of pertinent raw data. Equations of state

relate pressure, temperature and volume; they are used to describe the phase behavior

of pure substances and mixtures alike.22 In 1873, Van der Waals28 was the first to publish

an equation of state. Since then, many authors have modified Van der Waals

relationship with deviation functions to fit PVT data, vapor-Uquid equUibrium

predictions and Uquid density values.29 The most popular EOS are the Peng-

Robinson^'and the Soave-RedUch-Kwong^o which relate pressure, volume, and

temperature using constants to correct for the assumptions of the size, interactions and

pressure exertion of molecules. Equations of state are usuaUy cubic equations with either

one or two real roots. The Soave-RedUch-Kwong (SRK) and the Peng-Robinson (PR)

equations of state are widely accepted and provide a standard for comparison of results.

15

Thus, the SRK and PR were the only EOS considered in this thesis. Furthermore,

WirJ^rop, the software available for use at Texas Tech University Petioleum Engineering

Department, used for predicting phase behavior offered only these two equations.^i

Olds et al. studied the volumetiic behavior of binary mixture of n-butane and

carbon dioxide and showed that the compressibility factor derived from the PR equation

was in better agreement with experimental results than the SRK. However, it must be

recognized that this equation does not exactiy represent the phase behavior of real gases.

Gomez-Nieto and Robinson^s questioned some appUcations of the PR EOS in the

pubUcation of "A New Two-Constant Equation of State," addressing a shortcoming of

both the SRK and the PR. Both equations can be expressed as third-order polynomials

which yield one real root in the single phase region and two real roots in the two-phase

region. Gomez-Nieto pointed out that in some instances the solution of the polynomial

yields three real unequal roots and care should be taken when using these equations for

large temperature values. Robinson repUed, "Only the largest root has physical meaning.

We have always assumed users of these equations took this for granted. We do not

beUeve the point deserves further comment. "33

Six years after this correspondence, Lawal * showed that this assumption does

not hold for aU EOS in the form of Van der Waals equation as Gomez-Nieto suggested.

This explains discrepancies that may arise with the use of equations available in

WinProp. The PR and SRK EOS are widely accepted and simulation results are

supplemented with experimental data from Uterature, particularly work done by Olds et

16

al.32 Based on literature, the PR was the EOS of choice but is should be benchmarked

with existing data, which was done in this thesis.

2.5. General Gas Reservoir

2.5.1. Production

Equations of state help to predict gas behavior on the gigascopic-scale of gas

reservoirs, which is on a scale that considers the entire reservoir.^^ Primary production

from gas reservoirs is supported by natural reservoir energy. Gas is displaced from the

reservoir by fluid expansion, fluid displacement and/or capUlary expulsion.21 Water

influx from a connected aquifer can also aid in displacing gas from the reservoir to the

weU bore. If there is no water encroachment into a reservoir, it is referred to as a

volumetiic reservoir. A plot of pressure divided by the compressibiUty factor on the y-

axis (p/z) and cumulative production on the x-axis show the clear difference between

the volumetiic and water drive reservoirs shown in Figure 2.3. For a reservoir xinder

water drive, the pressure decline with production is slower than a volumetiic reservoir.

As gas from a reservoir is produced, the reservoir pressure may decline such that

pressure maintenance may be necessary to prolong production at an economical rate.

Pressure maintenance may take the form of gas injection in retiograde gas condensate

reservoirs, however rarely are gas reservoirs waterflooded. Gas injection is often a

development option Ui retiograde gas condensate reservoirs using produced gas. With

continued production from the reservoir, the natural energy of the reservoir decUnes.

17

With retiograde gas condensate reservoirs this decline in pressure causes gas to

condense and remain in the pore spaces.^*

Condensation of retiograde gas reduces the overaU hydrocarbon recovery. In

order to counteract this occurrence, gas injection is usually implemented to maintain the

reservoir pressure above the dew point of the fluid.s'' TraditionaUy, reinjection of lean

gas* or gas cycling has been practiced for pressure maintenance, gas storage meet

envirorvmental regulation mandates.^s However, the high value of lean gas has propelled

research into injecting alternative gases such as carbon dioxide and nitiogen into

retiograde condensate gas reservoirs.39'4o

Lean gas is a valuable resource and ideaUy a less expensive gas capable of

serving the same purpose should be used. Nitiogen has also been used for pressure

maintenance, however, the mixture of natural gas and nitiogen can cause undesirable

Uquid dropout in the reservoir.^i Carbon dioxide sequestiation with enhanced gas

recovery borrows technology and leans on the principles of secondary and tertiary

recovery in pressure maintenance and Uquid condensate vaporization.

To tinderstand and predict properties such as vaporization of condensates,

analysis is done on fluid phase behavior. Equations that relate pressure, temperature

and volume are instiumental in precUcting condensation, vaporization and other

processes that occur in the reservoir.

* produced gas that has been processed to remove relatively higher molecular weight hydrocarbons

18

2.5.2. Analysis Tools

The main analytical tools used in this research are the pressure-temperature and

phase volume diagrams. Pressure-temperature diagrams are plots with pressure on the

y-axis and temperature on the x-axis. The two-phase boundary envelope demarcates

regions of single and two-phases shown in Figure 2.4. Within the envelope, the Uquid

and vapor phases are in equiUbrium, while outside of the envelope would be single gas

or Uquid phase. Figure 2.4 shows an example of this type of diagram that is very useful

in analyzing phase behavior.

The other analytical tool, phase volume diagrams, is obtained by performing

flash calculations. '*2,43 These diagrams quaUtatively show the presence and the absence

of the respective phases. The y-axis is the mole or volume percent of one of the phases

and pressure is plotted on the x-axis.

Plots are made for isothermal flash calculations for a range of temperatures and

carbon dioxide mole fractions.

2.6. Phase Behavior Software: WinProp

Whereas analysis can be done by hand calculations, this would be time

consuming and error prone. In recent years, use of computer technology has increased

the speed at which calculations can be performed. It has also accommodated for greater

complexities in equations that may have numerous variables. In the line of this research,

WinProp,3i the equation of state multiphase eqxiiUbrium and properties determination

software program of the Computer Modeling Group Ltd. (CMG) simulation package.

19

was used. WinProp uses a number of equations and programs to generate phase

diagrams, estimate fluid properties and calculate critical points, dew points, bubble

points, cricondentherms and cricondenbars. These calculations are made using well

estabUshed equations from several discipUnes.44'45,46,47 Some of the features afford the

user a choice of certain equations, while other features have equations that are

imbedded in the code written by the programmers. To substantiate results from this

program, a comparison is made to actual laboratory results.32' 48Peatures within WinProp

are used as tools for analysis of the phase behavior of each natural gas and carbon

dioxide mixture over a range of temperature and pressure.

20

U.S. Greenhouse Gas Emissions by Gas, 2001

Energy related Carbon Dioxide

82% HFCs, PFCs and SF6 2%

Nitrous Oxide 5%

Ottier Carbon Dioxide 2%

Figure 2.1 U.S. Greenhouse Gas Emissions in 2001 as reported by the Energy Information Administration.^

21

•000

}»0«

,300O

12000

1500

900 too ISO t o o ( 9 0 RESERVOIR TEMt>ERATURe, *F

990

Figure 2.2 Pressure-temperature diagram of a reservoir fluid showing conditions for different gas types with respect to the critical point and cricondentherm.21

22

p/z

6000

5 0 0 0 -

4000

3000

2000

1000

2 3 4

Cumulative Production/BSCF

Figure 2.3 Example of a p/z plot for a reservoir xmder water drive and a volumetiic reservoir

23

3000

2500

2000

Pressure (psia) 1500

1000

500

0 -250 -150 -50 50 150

Temperature (deg F)

250 350

Figure 2.4 Example of a pressure-temperature diagram

24

CHAPTER 3

METHODOLOGY

3.1. Problem Description

The sequestiation of carbon dioxide in depleted gas reservoirs results in contact

and eventual mixing between carbon dioxide and natural gas. Early in the sequestiation

process, portions of the reservoir contain pure natural gas, mixtures of natural gas and

carbon dioxide, and pure carbon dioxide. Eventually the entire reservoir becomes a

homogeneous mixture of the two fluids. Before there is complete mixing of natural gas

and injected carbon dioxide within the reservoir, there is variation of carbon dioxide

concentiation in the reservoir. Analyzing the phase behavior of sequestiation aids in

tmderstanding how the properties of natural gas vary with carbon dioxide concentiation

of a homogeneous mixture and can be extended for known compositional gradients.

In planning sequestiation projects, it would be important to know how natural

gas would behave under reservoir conditions as carbon dioxide is injected. In particiilar,

the compressibiUty factor of the gas phase and the amount of Uquid present at reservoir

and surface conditions are particularly useful in predicting phase behavior, enhanced

gas and condensate recovery.

3.2. Equation of State

The volume and compressibiUty factor of the gas phase are related to

composition pressure and temperature by equations of state. In order to achieve a clear

25

understandmg of this dependence, the vapor volume and compressibiUty factor need to

be calculated for a range of temperatures and pressures.

The Peng-Robinson (PR) equation of state, used throughout this thesis, is

_ RT a ^~v-b viv + b)+b{v-b) ^^-^^

where p =pressure, R = universal gas constant, T = temperature, v = molar volume, a =

"attiaction" parameter and b = "repulsion" parameter. In this equation, 'a' is calculated

as

a = n° '-a (3.2)

where Q° =0.45724 , a =

Similarly,

l + w ( l - ^ ) J ^ and m = 0.37464 +1.54226(0 -0.26992co2.

b=Ql-

where Q^ =0.07780 and co = acentiic factor.2'

(3.3)

In terms of the z-factor the PR EOS may be expressed as

z -{\-B)Z^ +{A-3B^ -2B)Z-{AB-B^ -B')=0, (3.4)

where A=a-^-^ ,B^b— andZc = 0.3074. (RTY RT

The PR EOS was chosen over the SRK EOS because it gives a better representation of the

volumetiic behavior of gas mixtures.29 The volumetiic behavior is calculated by solving

the EOS in terms of the z-factor since z = py/RT and the molar volume, v, can be

determined. The cubic z-factor equation is solved by tiial and error. If there is more

26

than one real root ui the EOS solution for mixtures, the correct root selected is the root

with the lowest normalized Gibbs energy, g*,43

1=1

sl=Yj^Mfi(^)

(3.5)

(3.6) 1=1

where yi = mole fraction of vapor, xi = mole fraction of liquid, fi = multi-component

fugacity and N is the ntunber of components is expressed as

Ui^= ln^ = z - l - l n ( z - 5 ) ^ I n fz + il + yfl]

2V25"1 z - I-V2I (3.7)

and

I n A . In ,. =^ (z - l ) - l n (z - f i )+ -A^ ln yiP B 2V25

5, 2 ^ In

z-l- (1 + V2)

(l-V2)sJ (3.8)

A and B use the tiaditional and linear mixing rule, respectively. For example,

with a vapor phase of composition >>,

N N

^'TLy-.y,^ i=\ 7=1

5 = E yi^i

(3.9)

(3.10) 1=1

where A^^ =(l - k^. JJA^AJ and kij =binary interaction parameter.23

EOS are also used for calculating phase equilibria by satisfying the condition of

chemical equiUbrium. For a system consisting of two phases, chemical equiUbrium is

identified as the conditions at which the chemical potential of each component in the

27

vapor phase, )Xi(x), is equal to that component in the liquid phase, |a.i (y). Chemical

potential as expressed in terms of fugacity is determined as,

^ ,= /?nny ;+A, ( r ) . (3.11)

3.3. Flash Liberation: Concept/Calculation

Flash Uberation determines the mole percent or volume percent of equUibrium

phases, Uquid and vapor, for given pressure, temperature, and composition. To achieve

equiUbrium, the chemical potential in both phases must be equal. Equal chemical

potential is satisfied by the equal fugacity constiaint,/Li = fvi. solved numerically as

N { f V

1=1

J Li 1

V fvi J

<e (3.12)

where E is a predetermined convergence tolerance. Flash calculations are initialized by

determining a set of K values from Wilson's equation: ^

[5.37(l+<«,)[l-7-;:']]

Ki = . (3.13) Pri

Estimated K values are used with the Rachford-Rice^o or the Muskat-McDoweU^i

equations to solve for Fv, the vapor mole fraction. The Muskat-McDoweU equation gives

an estimate of Fv outside the range Fvmin< Fv < Fvmax:

28

" z. ''(''v)=S^r^=0. (3.14)

Fv is bounded by Fv min and F v max as determined from Kmin and K„

p ^ Cmin

F ' Cmax

=

=

1-

1-

1 - K

m a x

1

"-^min

<

>

0

1 .

(3.15)

(3.16)

Material balance equations, functions of Fv, are then used to calculate phase

compositions as foUows:

Xi =—-,—^^r— (3.17)

zK. and yi= ' \—= x,X. . (3.18)

Using the z-factors for the Uquid and vapor phase with the EOS, the fugacity of

components are calculated. The Gibbs free energy is then calculated to determine the

correct z-factor root if there are multiple roots. Using the equal fugacity constiaint,

convergence to the correct z-factor is checked with condition

N

I 1=1 X(ln^ , ) '<10- '* (3.19)

which verifies that the solution is tiivial.

29

3.4. Constant Volume Depletion: Concept

Constant volume depletion is used to repUcate the depletion of retiograde gas-

condensate reservoirs. A sample of gas is placed in a cell at reservoir temperature and

dew point or saturation pressure of the fluid. Starting at the dew point pressure, the

volume of the ceU is expanded to a predetermined lower pressure and then it is returned

to the original volume by releasing gas. After equiUbrium conditions have been restored

in the ceU, the retiograde liquid volume is measured, and the process is repeated

starting at the dew point pressure until the final pressure is achieved. At each pressure

decrement, the volume of gas released and the composition of gas are determined. By

simulating reservoir depletion of retiograde condensate reservoirs to a minimum or

depleted pressure, it is possible to determine the composition of the remaining reservoir

fluid in the gas and vapor phases. This composition needs to be used in calculations

because this is the initial condition of carbon dioxide sequestiation.

The composition of retiograde reservoir fluids is dependent on temperature and

pressure: as pressure decreases, the heavier ends of the gas condense and the Ughter

components are produced. As such, the composition of the natural gas mixed with

carbon cUoxide in a depleted gas reservoir depends on the abandoriment pressure of that

reservoir. In this thesis, three abandonment pressures are considered 50, 250 and 500

psia.

30

3.5. EOS Software Application: WinProp

3.5.1. Pressure-Temperature Diagram

A two-phase envelope is generated for each natural gas and carbon dioxide

combination. This gives a visual description of the phases that exist at reservoir

conditions. Fluids outside the two-phase envelope are either single-phase Uquid, single-

phase gas, or critical fluid, within the envelope, there is a mixture of the two phases.

Flash calcvilations definitively show which of the two phases are present outside of the

two-phase region.

The changing shape and coverage range of pressure and temperature of the two-

phase envelopes indicate how the adcUtion of carbon dioxide modifies the phase

behavior of natural gas. With the pressure-temperature diagram for each composition

compUed on a single plot, it is possible to see tiends easily. Other important information

that are gleaned from a compilation of aU the pressure-temperature diagrams for a

particular gas-carbon dioxide mixture includes the tiends of the critical point,

cricondentherm and cricondenbar loci and their relative positions to each other.

On the main WinProp window, three input panels specifying imits, equation of

state and composition, precede envelope and flash calculations (Figure 3.1). The first

panel Titles/EOS/Units allows the choice from four equations of state, which are

basicaUy the original PR and SRK with subsequent modifications to the SRK by

Grabowski and Daubert.52 Also within that panel there is a choice of xmits for

temperature and pressure. Titles for graphs and other output can be specified m this

panel. In the second panel Component Selection/Properties, the components of the feed

31

are specified. The third panel. Composition, is used to specify the mole fraction of each

component.

The Two-phase Envelope panel leads to the Two-phase envelope construction

window, as shown in Figure 3.2 separated into three tabs: Envelope Specification,

Envelope Construction Controls, and FeeiVK-Values/Outpu^Stability. The two main

tabs used in this thesis were Envelope Specification and Fee<VK-

values/OutpuVStability. On the left of the Envelope Specification tab, the Envelope Type

is specified. X-Y Phase Envelopes display plots on Cartesian coordinates, whereas Pseudo-

Ternary Envelopes show the boundaries between phases as a fxinction of composition at

fixed temperature and pressure. For the purpose of this investigation, X-Y Phase Envelope

was used. There are three options for X-Y Phase Envelopes:

i. Pressure-temperature,

U. Pressure-composition,

Ui. Temperature-composition.

From the window in Figure 3.2, it can be seen that a pressure-temperature

diagram is selected. Given that pressure and temperature are specified for reservoir

conditions, this was the most appropriate choice. The diagram is constiucted by taking

increments in terms of temperature and determining the corresponding value of

pressure for each mcrement. Phase boimdary calculations estimate the critical point by

interpolation.^!

32

3.5.2. Two-Phase Flash Calculations

Isothermal flash calculations determine the quantity of the Uquid and gas phases

at constant temperature for a determined pressure range. These calculations are

performed on each hydrocarbon gas-carbon dioxide mixture in order to quantify results

from the pressure-temperature diagrams. Plots from flash calculations give insight into

the equiUbrium phases present, gas and/or liquid, and the proportions of each. From

these plots, it is possible to define the dew point curve and bubble poUit curve of a gas

mixture.

The two-phase flash calculation window is divided into four tabs Calculations,

Experimental, Experimental K-values and Plot Control (Figure 3.3). The furst tab on this

window. Calculations, is divided into six main sections:

i. Pressure Data,

u. Temperature Data,

ui. Feed Composition,

iv. K-Values,

V. Output Level /Stability Level,

vi. Flash Type,

The Pressure Data and Temperature Data sections require similar information

related to the range and scale of the respective parameters. The Feed Composition

section specifies which composition should be used in the calculations. This is useful if a

calculation is carried out on one particular phase as determined by a previous

33

calculation. For example, if flash calculations determine that there are two phases

present and only the vapor phase is needed for further consideration, that vapor feed is

specified and only that phase is used in further computations. Mixed feed refers to a

mixture of the primary and secondary composition. If there is no secondary

composition, only the primary composition is used. The Primary Mole Fraction can be

specified if there are two fluid compositions considered, primary and secondary.

Flash calculations are initiaUzed with an estimation of K-values. For aU

calculations in this study, K-values are estimated internally from the Wilson equation.^s

The Output level, ranging from 1 to 4, can be increased if the results of each iteration are

required. The stabiUty test uses a multidimensional Gibbs free energy surface search for

stationary points which enhances the accuracy of the K-values estimated by the Wilson

equation (equation 3.13). The Stability test level, ranging from 1 to 4, gauges the

completeness of the search for stationary points. Level 1 is sufficient for most two-phase

oU/gas systems.3i

The Flash Type combo box aUows flash calculations to be set to either

QNSS\ Newton or Negative. This specifies that the first convergence of the two-phase

flash equations is through a Quasi-Newton Successive Substitution algorithm foUowed

by Newton's method to refine the roots. The Negative flash does not refine the roots of

the algorithm; this aUows generation of K-value estimates outside of the two-phase

envelope.3i QNSS\ Newton was chosen for the calculations in this study.

The next two tabs Experimental and Experimental K-values were not

manipulated. These are used if there is experimental data available. Figure 3.4 shows the

34

last tab. Plot Control, which is used to choose the properties to be plotted for each phase

of the mixture.

3.5.3. Constant Volume Depletion

The Constant volume depletion experiment simulation consists of four tabs,

Pressvure Levels, Consistency Checks, Separator and Feed/Kvalues/Output

Level/Stability Test Level. Figure 3.5 shows the Pressure Levels tab. The first column

on this window is used to specify the pressure levels to which the gas sample would be

lowered to fiom its saturation pressure. If available, subsequent columns are for

experimental results of gas released from the PVT cell, liquid saturation and z-factor of

the gas. The next tab. Consistency Checks, is used to input gas composition if available.

The Separator tab is used to specify the conditioris of pressure and temperature for each

separator. The Fee<VK-Values/Output Level/Stability Test Level tab is identical to that

in the Two-Phase Envelope window and serves the same purpose.

35

iop 2002.10

File Edit Preferences Regression Characterization Calculations Lab Simulator PVT Window Help

Dlai^lyl •iQtlssI j^Nfeh-^l f I 41 $ • ! I 2f i f Mf

fKESJENVr FLSH FLSH UAH mt HOC Idj J U L CMr

lEST CdLC STRT KE6

Jnj2<J

line Slal Form* CommenU

• j - / i-/ iv" l y iv^ 1 1

Titles/E OS/Units Component Selection/Properties Composition Two-phase Envelope Two-phase Flash

3 i'

*•

A i i iP*""" iWII I I IM^^^^HII IM ~~

Figure 3.1 Main window with panels used to manipulate fluid properties and perform calculations

36

'"'^Two-phase envelope construction Ed» lable Help

Envelope Specification | Envelope Construction Controls | Feed/K-valuesy'Dutput/Stability |

Comments

• Envelope Type

fJ" X-Y Pliase Envelope C Pseudo-Ternary Phase Envelope

adjii

X-Y Phase Envelope-

1 -KXIi —

(* Pressure C Temperature

Minimum Presswe (psia): o 000

l»taximum Pressure (psia): 14695 95

' ' -XiAxrs

<^ Temperature C Composition

Minimum Tanper^re (deg IT: -148,00

Maximum Temperature (deg F); 1292,00

Minimuni mole iix-. step ci;e, ij fi3

Maximum mote fiac. step size: [i i ^

-Pressure/Temperature SpecrRcalion

Pressure (psiaj: J14,69G .:

1 empKalure (deg F): 132.00 ' WKK^

Minimum vapor mole frac: l i o o 1

Maximum vapor mote frac: i o 0

OK Cancel

Figure 3.2 Two-phase envelope constiuction window displaying the Envelope Specification tab

37

Two-phase flash calculations

Edit Help

Calculations | Experimental | Experimental K-values | Plot Control |

Comments

Jnjjij

-Pressue Data

Pressure (psia):

Pressure step (pwia):

No. of pressure steps:

2000

•20

100

Feed CtMrposition Feed

[Mixed j j

Mote fraction step:

No. of mole fraction steps:

Primary mole fraction

1,0

0,2

Flash type: |QNSS\Newton 3

-Temperature Data

Temperature (deg F):

Temperature step (deg F):

No. of temperature steps:

400

-50

8

r K values— K-values Phase Number

Internal T [ |Nui.jpp|i,:.3ble

Output level/Stability level Output level Stability test level

1 H r H

OK Cancel

Figure 3.3 Two-phase flash calculations window displaying the Calculations tab

38

Two-phase flash calculations Edit Help

Select a niiaximum of three properties to be plotted for each phase.

[ 7 Phase Volume Fraction

[ 7 Phase Mole Fraction

p" Z Compressibility Factor

f Mass Density

r* Molar Volume

r* Viscosity

r " Molecular Weight

r" K-values (y/x)

Calculations I Experimental! Experimental K-values |...P.!ot..Q°n!l°!

Property Selection

OK Cancel

Figure 3.4 Two-phase flash calculations window displaying the Plot Contiol tab

39

[....P!.5??y.?.?..C?.y.?.li?.l| Consisieticv Checks | Separator |Feed/Kvalues/'Output level/Stability Test level j

Comments

Temperature (deg F): 150

P I Improve saturation pressure estimate

No. of pressure levels (first value reserved for sat. pres.): 1 Copy Consistency Checks Table

No.

1

Pres. (psia)

2915

250

Cum. Gas Prod. [Z]

0.0 Liq.Sat.(%ofQ/S]

Cum. Gas Prod. [X) \ Liq. Sat. [Z of CVS) | Gas Z factor

Gas Z factor B

Ld

Table Import Wizard OK Cancel

Figure 3.5 Constant volimie depletion experiment simulation window displaying the Pressure Levels tab

40

CHAPTER 4

PHASE BEHAVIOR RESULTS

The flash and phase envelope calculations described in Chapter 3 were appUed

to dry, wet and retiograde condensate median gas compositions determined by Gasch

(2003). The retiograde compositions were considered for abandonment pressures of 50,

250 and 500 psia, referred to as A, B and C, respectively, at a temperature of 150 °F.

Table 4.1 gives the composition of each gas type used in phase behavior simulation

calculations. The table shows that dry gas has the highest mole fraction of methane

followed by wet gas and retiograde gas-condensate at initial reservoir pressure. The

compositions of the depleted median retiograde gas varied mostiy with respect to the

mole fraction of methane and decane. Retiograde gas C has the highest mole fraction of

methane and the lowest mole fraction of decane compared to gases A and B. The reverse

is true for retiograde gas A. Although the actual media composition specifies the

heaviest fraction as C7+, decane is used to represent the C7+ fraction of the gas in order

to facihtate the measurement of the liquid volume in laboratory procedures.

Carbon dioxide was added to the normalized composition of each gas type in

5% increments up to 95% and including 99%. Plots of the results of flash calculations and

the two-phase envelope of the mixtures provided the foci for analysis of phase behavior

of the gas mixtures.

The compressibility factors calculated by using the Peng-Robirison EOS were

benchmarked against pubUshed experimental results. The phase behavior results for

carbon dioxide-natural gas mixtures are presented in terms of Hquid voltmae percent.

41

compressibility factor and tiends observed with the critical point, cricondentherm and

cricondenbar.

4.1. Phase Behavior

The first data series investigated is that of Olds, Reamer, Sage, and Lacey.54 They

obtained relatively pure methane from purified natural gas from the San Joaquin Valley,

CaUfomia to conduct their experiments. The volumetiic behavior of this methane

sample was investigated at temperatures of 70,100,160 and 220 °F. Their experimental

results are compared to PR EOS results in Figure 4.1. The results from the two sources

are not in agreement. The compressibility factor calculated from the experimental results

of Olds et al. are consistently lower than that predicted by the PR EOS. However, the

tiend is the same for both experimental and PR EOS WinProp simulated results. The

discrepancy between simulated results and experimental data could be attiibuted in part

to shortcomings inherent in EOS when considering single component substances.^s

Additionally, there are tuning adjustments that can be made to an EOS so that there is a

better match between experimental and simulated data. At pressures less than 500

psia, however, there is reasonable agreement between the two data sets. Fortunately,

compressibiUty factor comparison with multi-component mixtures give much better

results and these form the major focus of this thesis.

One year later the same authors. Olds et al., 7 investigated the volumetiic

behavior of methane-carbon dioxide mixtures at pressures up to 10,000 psia with

temperatures ranging from 100 to 460 °F. The source of the methane was the same, San

Joaquin Valley, with a methane purity of 99.9995 mole percent. The carbon dioxide used

42

was obtained by the thermal decomposition of sodium bicarbonate resulting in a carbon

dioxide purity of 99.999 mole percent. The methane-carbon dioxide mixtures

investigated were weight fractions ranging from 0 to 0.6685 methane. As can be seen

from Figures 4.2,4.3 and 4.4, tiiere is agreement between PR EOS simulated results and

the Olds et al.57 experimental data, even at high concentiations of carbon dioxide.

The third series of experimental data compared to the PR EOS is the work

presented by Simon et al.ss based on a mixture of natural gas with a small concentiation

of nitiogen and carbon dioxide in a visual PVT cell. Table 4.2 shows the composition

analysis of the sample used in their investigation. The z-factor measurements are

compared to results with the same fluid using the PR EOS. Figures 4.5,4.6 and 4.7

demonstrate that there is reasonable agreement between the PR EOS and experimental

data at the temperatures shown.

The foregoing discussion shows that the PR EOS produces results that are

consistent in tiend for the single component gas mixtures and a reasonable match for

mixtures pubHshed in the Hterature.54,57,58 The same consistency between the tiends of

experimental and PR EOS simulated compressibility factors is expected in the

appHcation of natural gas-carbon dioxide mixtures in this thesis.

4.1.1. Pressure-Temperature Diagrams

Pressure-temperature diagrams were generated for carbon dioxide-natural gas

mixtures of all proportions for each gas type, Ulustiating the variation of phase behavior

over a range of temperature and pressure. Conditions of pressure and temperature that

43

fall within the envelope exhibit a fluid mixture of liquid and vapor. Outside of the two-

phase region fluids are either single-phase Uquid, single-phase gas or a critical fluid

depending on the relative position of the critical point.22

There are several aspects of phase behavior such as decreasing compressibility

factor and changing size of the two-phase envelope with respect to carbon dioxide

concentiation that are cormnon to aU gas types. The most stiiking feature is the general

decrease of the phase envelope size as the concentiation of carbon dioxide is increased

for mixtures with dry and wet gases. Figure 4.8 shows that as the concentiation of

carbon dioxide in the dry gas mixture increases, the coverage of the two-phase envelope

decreases and shifts toward higher temperatures and pressures. The shifting pressure-

temperature diagram indicates that the mixture is becoming wetter.

Figure 4.9 shows that for carbon dioxide concentiations of 65 mole % and less in

the median wet gas mixture phase botmdary equiUbrium Unes are almost concentiic

above 200 psia and 0 °F. At higher concentiatioris of carbon dioxide, between 65 and 90

mole %, the phase envelope takes on an M-like shape laying on its side as shown in

Figure 4.10. This shape is beUeved to be related to the location of the dew point of pure

carbon dioxide. The lower portion of the 'lazy-M' is a region with low Uquid saturation

and rich in the heptane plus fraction. Above the dew point pressure of carbon dioxide,

the Uquid phase is richer in carbon dioxide than the vapor phase.s' Much like Figure 4.8

for dry gas, the two-phase envelope gets progressively smaller and eventually

approximates the phase diagram of pure carbon dioxide as carbon dioxide concentiation

increases. This effect is easier to see in Figure 4.9 than in Figure 4.10; however, the

44

coverage of the two-phase envelope decreases as carbon dioxide concentiation increases

which is a marufestation of the drying effect of carbon dioxide.

The change of the pressure-temperature diagram of retiograde gas-carbon

dioxide mixtures differ from the dry and wet gas mixtures. Retiograde gas A is the gas

composition of median retiograde gas composition depleted to 50 psia at 150 °F. The

pressure-temperature diagram of retiograde gas A-carbon dioxide mixture in Figure

4.11 shows that the size of the two-phase envelope first increases with carbon dioxide

concentiation and then decreases between 80 and 99% carbon dioxide. Retiograde gas B,

median retiograde gas composition depleted to 250 psia, has a more complex

compilation of overlapping saturation Unes in the area of the circondenbar of each

carbon dioxide-retiograde B same mixture of pressure-temperature diagrams for

mixtures with carbon dioxide in Figure 4.12 than its counterpart in Figure 4.11.

However, in both cases, the cricondentherm decreases with carbon dioxide

concentiation while the cricondenbar increases up to a maximum and then decreases.

The cricondenbar of retiograde gas B-carbon dioxide mixtures decreases between 65 and

95 %. The same effect is seen with retiograde gas C-carbon dioxide mixtures (median

gas composition depleted to 500 psia). However, Figure 4.13 shows that in this case the

cricondenbar decreases between concentiations of 45% and 99% carbon dioxide. The

overaU effect in each case (A, B, and C) is that the phase envelope increases sUghtly and

then decreases as more carbon dioxide is added to the mixture.

45

4.1.2. Vapor and Liquid Fractions

4.1.2.1 Drv Gas

Essentially for aU dry gas-carbon dioxide mixtures, there is no liquid present

above 90 °F. This is evident in the results presented with the loci of the critical point of

the mixtures superimposed on the pressure-temperature diagram in Figure 4.8. (The

critical points are shown separately in Figure 4.14.) At temperatures higher than the

critical temperature Uquid does form even if the gas mixture is compressed.22

Conversely, at temperatures less than the critical temperature, at 60 °F there may be

Uquid between 800 and 1100 psia for concentiations of carbon dioxide exceeding 90%.

This Uquid would essentiaUy be carbon dioxide with very Uttle hydrocarbon present.

4.1.2.2. Wet Gas

At 150 °F, the wet gas is in the gaseous state as shown in Figure 4.15. Therefore, if

average reservoir temperature is above this temperature, there is no Uquid in a wet gas

reservoir regardless of carbon dioxide concentiation. This is in agreement with the

pressure-temperature diagram for this gas (Figure 4.9 and 4.10), which shows no Uquid

for as low as 140 °F. At surface temperatures, for example 60 °F, there is some Uquid

depending on pressure as shown in Figure 4.16. Typical ambient temperatures may be

in the vicinity of 60 °F at which it is possible to have more than 50% Uquid volume when

the concentiation of carbon dioxide concentiation exceeds 80% (not shown). The Uquid

present consists of primarily of hexane which represents the C7+ fraction of the wet gas.

46

Figure 4.16 clearly shows the drying effect of carbon dioxide on the gas mixtures as the

volume percent of Uquid decreases up to 75% carbon dioxide.

4.1.2.3. Retiograde Gas

The general tiend with retiograde gas samples varies with carbon dioxide

concentiation. The two tiends are exhibited, one at low and another at high

concentiations of carbon dioxide. For the retiograde gas compositions A, B, and C, the

tiend for low concentiations extends from 0 to 70,0-55 and 0-40 % carbon dioxide,

respectively. The tiend for low concentiation carbon dioxide demonstiated in Figure

4.17 is increasing Uquid volume with increasing pressure, until only Uquid phase is

present. This would orUy occur under laboratory conditions where pressure is increased

with as the volume of the ceU is decreased. Under reservoir conditions, pressure cannot

be increased by decreasing volume; a pressure increase can orUy be the result of

additional fluid being added to the reservoir. The path of sequestiation is likely to

tiaverse Figure 4.17 from one iso-composition Une to another, as the presstue increases

with addition of carbon dioxide.

The other tiend is increasing Uquid volume percent as pressure increases up to a

100 % Uquid. This retiograde gas-condensate behavior is seen in Figure 4.18 for 75 to

95% carbon dioxide with retiograde gas A. The tiends for low and high concentiations

are observed for retiograde compositions B and C in Figures 4.19 and 4.20 and are

consistent with the pressure-temperature diagrams. Figures 4.11 through 4.13. Also with

both trends the volume of Uquid present at a particular temperature decreases with the

addition of carbon dioxide, this is basically the drying effect of carbon dioxide.

47

4.1.3. CompressibiUty Factor

The compressibiUty factor for mixtures of dry gas and carbon dioxide were

estimated using the Peng-Robmson EOS for two-phase flash calculations for 100,150

and 400 °F for a range of 0 to 5000 psia. Because the tiends for each temperature were

similar, the compressibility tiend at 150 °F was studied in detail for all mixtures.

4.1.3.LDrvGas

Figures 4.21, 4.22 and 4.23 show the compressibiUty of dry gas-carbon dioxide

mixtures at 100,150 and 400 °F. At pressures less than 200 psia the compressibihty

factors for the varying concentiations have very similar values ranging from 0.91 to 0.96.

AU three plots show the same tiend, decreasing compressibiUty factor with increasing

concentiations of carbon dioxide. The compressibiUty factor of 0-99% carbon dioxide at

150 °F and 1600 psia is shown as a bold vertical line on Figure 4.22. The paraboUc tiend

at that condition of temperature and pressure is shown in Figure 4.24. As the pressure

increases there is increasing difference in the compressibiUty factor of the various

mixtures.

4.1.3.2.WetGas

A cursory glance at the compressibiUty factor of wet gas as a function of pressure

in Figure 4.25 shows a stiiking similarity to Figures 4.21,4.22 and 4.23 for dry gas. The

relationship of compressibiUty factor of wet gas-carbon dioxide mixtures as a function of

pressure and carbon dioxide is very similar to that of dry gas-carbon dioxide mixtures.

The most noticeable difference is the steeper slopes (positive and negative) of the wet

48

gas-carbon dioxide mixture because the pure wet gas has a steeper slope. As expected

the compressibility factor of 99% carbon dioxide-natural gas mixture is essentially the

same for both wet and dry gas.

4.1.3.3. Retiograde Gas

The tiend observed with dry and wet gas is present with retiograde gas mixtures

in the vapor phase as seen in Figures 4.26,4.27 and 4.28 for retiograde gas compositions

A, B and C, respectively. The discontinuity in the compressibility factor tiend for 35 to

100 percent carbon dioxide corresponds to conditions at which there is only Uquid

present. OveraU, the compressibiUty factor tiend is the same for dry and wet gas in that

the compressibiUty factor decreases as the concentiation of carbon dioxide increases.

And there is no major crossing of the tiend Unes to indicate formation of a new phase.

4.2. Trend of PVT Relationships

4.2.1. Cricondenbar

For dry gas mixtures, the cricondenbar tiend is shown in Figure 4.29. The

cricondenbar for any mixture does not exceed 1300 psia. As the concentiation of carbon

dioxide increases, the cricondenbar increases to the maximum pressure of 1300 psia for

about 60% carbon dioxide foUowed by a smaU decrease in pressure at higher carbon

dioxide concentiations.

With wet gas mixtures, there are two cricondenbar tiends: one for mixtures with

45% and less carbon dioxide and another tiend for mixtures with greater than 45%

carbon dioxide. The tiend of mixtures with 45% and less carbon dioxide is decreasing

49

cricondenbar pressure as carbon dioxide concentiation increases. The tiend for higher

concentiations is the same; however, the temperature range is wider (Figure 4.30). Pure

wet gas exhibits the highest cricondenbar when compared to the other wet gas-carbon

dioxide mixtures and the lowest cricondenbar occurs with the 99% carbon dioxide

nuxture. The discontinuity in the cricondenbar coincides with the changing shape of the

two-phase envelope of the wet-gas mixture (Figures 4.9 and 4.10).

For retiograde gas-carbon dioxide mixtures, the tiend for the cricondenbar is

paraboUc in nature. The maximum cricondenbar pressure occurs at lower concentiations

of carbon dioxide as the abandonment pressure of the retiograde gas sample increases.

Abandorunent pressures of 50, 250 and 500 psia have maximum cricondenbar pressures

at approximately 70, 60 and 40% carbon dioxide, respectively, at 150 °F (Figure 4.31).The

maximum cricondenbar occurs at lower concentiations as the abandonment pressure

increases.

4.2.2. Cricondentherm

For dry gas-carbon dioxide mixtures, the cricondentherms and critical

temperatures are separated by only a few degrees Fahrenheit. However, the pressure at

the cricondentherm is lower than the critical pressure. Both the cricondentherm and

critical points are shown in Figures 4.32 and 4.33. This impUes that the phase behavior

with respect to temperature can be predicted by considering the loci of the critical

temperature only.

Wet gas mixed with carbon dioxide exhibits decreasing cricondentherm

temperatures with increasing CO2 concentiation (Figure 4.34). However, at

50

concentiations greater than 80%, the cricondentherm occurs at higher pressures. The

tiend for retiograde-carbon dioxide mixtures is decreasing cricondentherm temperature

with increasing carbon dioxide concentiations (Figure 4.35).

4.2.3. Critical Points

The critical points of the dry gas-carbon dioxide mixtures follow the tiend of a

cubic equation (Figure 4.36). For the temperatures between 30 and 100 °F, as the carbon

dioxide concentiation increases, the critical temperature also increases while the critical

pressure decreases. A mixture with 99% carbon dioxide has a critical point at 1077.8 psia

and 86.6 °F.t The overaU effect of adding carbon dioxide to dry gas is to increase the

critical temperature with a modest increase in critical pressure.

For wet gas-carbon dioxide mixtures, there is a decrease of the critical pressure

and an increase of the critical temperature as the carbon dioxide concentiation increases.

Like the dry gas, the critical points of the wet gas with carbon dioxide can be related by

a cubic equation (Figure 4.37). With retiograde gas-carbon dioxide mixtures the critical

temperature decreases as the critical pressure increases with increasing carbon dioxide

mixtures (Figures 4.38 and 4.39). The tiend for each reservoir fluid's critical points can

be described by a quadratic equation (Figure 4.40).

^ The critical point of carbon dioxide is at 1069.9 psia and 87.9 °F as determined by WinProp library of component properties.

51

4.3. Summary of Phase Behavior Results

The phase behavior results of carbon dioxide-hydrocarbon gas mixtures were

presented in terms of the critical points, cricondentherms, cricondenbars,

compressibiUty factors and two-phase envelope of each mixture. Results show

similarities and differences between the gas types. In terms of critical points the tiend of

dry and wet gas mixtures with carbon dioxide are similar in that the critical temperature

increases with carbon dioxide concentiation (Figures 4.36 and 4.37). On the other hand,

the retiograde gas-carbon dioxide mixtures exhibit decreasing critical temperatures with

increasing carbon dioxide concentiation (Figure 4.38).

The cricondentherm of dry gas-carbon dioxide mixtures increases with carbon

dioxide concentiation (Figure 4.32), but wet and retiograde gas-carbon dioxide mixtures

it is the opposite ( Figures 4.34 and 4.35). The cricondenbar tiend of dry and retiograde

gas-carbon dioxide mixtures is parabolic in nature with respect to carbon dioxide

concentiation (Figures 4.29 and 4.31). The cricondenbar tiend for wet gas-carbon dioxide

mixtures depend on whether the mixture is greater of less than 45% carbon dioxide.

GeneraUy, the cricondenbar decreases with carbon dioxide concentiation in both tiends.

The two-phase envelope tiends for dry and wet gas-carbon dioxide are similar in

that both show shrinkage of the envelope as carbon dioxide concentiation increases

(Figures 4.8,4.9, and 4.10). The change in pressure-temperature coverage of the two-

phase envelope of retiograde gas-carbon dioxide mixtures is not as stiaightforward

(Figures 4.11,4.12, and 4.13). The only tiend that appears to be common to aU three

gases is the compressibility factor versus pressure (Figures 4.23,4.25 - 4.28). For each gas

52

type, the compressibUity factor decreases as carbon dioxide concentiation increases.

While each of these tiends represents an equilibrium mixture of natural gas and carbon

dioxide, the tiends can be used to approximate dynamic mixing by relating pressure to

concentiation.

53

Table 4.1 Median Composition of Dry, Wet and Retiograde gas-condensate in Depleted Gas Reservoirs expressed as Mole Percent of Hydrocarbon Components

Components

Methane

Ethane

Propane

n-Butane

n-Pentane

Hexane

Heptane

Decane*

Dry Gas o

96.54

2.73

0.51

0.21

0.00

0.00

0.00

0.00

Wet Gas o

90.03

4.74

2.03

1.03

0.42

0.35

1.4

0.00

Retiograde gas-

condensate at initial reservoir pressure^"

73.04

8.57

4.53

3.40

1.89

1.64

0.00

6.88

Retiograde gas-

condensate A

(50 psia)**

24.77

5.27

5.41

7.71

6.67

7.34

0.00

42.82

Retiograde gas-

condensate B

(250 psia)**

39.05

6.99

5.82

6.83

5.25

5.49

0.00

30.57

Retiograde gas-

condensate C

(500 psia)**

50.78

7.92

5.64

5.75

4.05

4.07

0.00

21.76

* Decane is used to represent the C7+ fraction of the gas in order to faciUtate measurement of the liquid volume in laboratory procedures.

** Obtained from simulation of Constant Volume Depletion at 150 °F described in Chapter 2.

54

Table 4.2 Components of the gas sample used by Simon et al. s

Component Nitiogen

Carbon Dioxide Methane Ethane

Propane n-Butane n-Pentane

Hexane

Mole percent 0.04 89.94 9.44 0.21 0.10 0.06 0.05 0.16

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95

CHAPTER 5

DISCUSSION

The objective of this thesis is to investigate the phase behavior of carbon dioxide-

natural gas mixtures with the aim of efficiently sequestering carbon dioxide, enhancing

gas and condensate recovery in depleted gas reservoirs. Understanding the phase

beha"vior of the carbon dioxide-natural gas mixtures in the reservoir requires knowledge

of the phases that are present as a result of varying pressure, temperature and carbon

dioxide concentration (mole fraction). Pressure-temperature diagrams, liquid phase

(volume) flash calculations and compressibiUty factors of the vapor phase are

instrumental in determining the carbon dioxide storage capacity, enhanced gas and

condensate recovery of depleted gas reservoirs.

5.1. Use of Phase Behavior Trends

Several observations were made with regards to the trends of Uquid volume

percent, critical point, cricondentherm, cricondenbar and compressibiUty factor as a

fimction of carbon dioxide concentration for aU three gas types. However, these trends

and observations are limited to equiUbrium carbon dioxide-natural gas mixtures. Due to

the principles of diffusion and dispersion, a composition gradient in the reservoir is

expected between the carbon dioxide injector(s) and the gas producer(s) of sequestration

projects. This thesis does not address the determination of the phase behavior of

compositional gradients, but vmder certain circumstances the methods may be

appUcable.

96

5.1.1. Relative Drying and Wetting of Natural Gas Due to Carbon Dioxide Sequestration

The dry gas pressure-temperature diagram of Figure 4.8 shows that as the

concentration of carbon dioxide increases, the two-phase envelope moves towards

higher temperatures and pressures, implying that the dry gas mixture becomes wetter.

Furthermore, for aU carbon dioxide-dry gas mixtures, the cricondentherm is less than

90°F. As such a dry gas would remain as a dry gas at reservoir temperatures exceeding

this temperature. As the carbon dioxide mole fraction increases, a dry gas could possibly

have some separator Uquid present. However, this would occur only at separator

pressures between 800 and 1100 psia and separator temperatures between 60 and 70 °F

for very high (greater than 0.95) carbon dioxide mole fraction. (This Uquid is Ukely to be

predominantly carbon cUoxide.) As such when deaUng with dry gas-carbon dioxide

mixtures, it is not expected that a Uquid phase will form at reservoir or surface

conditions.

Figures 4.15 and 4.16 show that a wet gas contains no Uquid at reservoir or

surface conditions; however Uquid, is present between 100 and 2000 psia at 60 °F which

is likely to encompass separator conditions. In effect this proves that wet gas-carbon

dioxide mixtures retain the characteristics of a wet gas when mixed with carbon dioxide

although the Uquid volume decreases with the addition of carbon dioxide. At conditions

that faU within the two phase envelope, flash calculations show that the Uquid present

consists mainly of heavier hydrocarbon fraction.

A retrograde gas reservoir depleted to pressures lower than 500 psia may have a

composition that no longer exhibits retrograde behavior. Figures 4.17 through 4.20 show

97

that, depending on the concentration of carbon dioxide, as pressure increases the fluid

may either become 100% Uquid or exhibit retrograde gas behavior. In the cases where

there is retrograde behavior (for example. Figure 4.18), the Uquid formed is essentiaUy

carbon dioxide. On the other hand, when the liquid volume percent increases to 100%,

the Uquid present consists mainly of the heavier hydrocarbon fractions. Pressure-

temperature diagrams are Umited in that they are not representative of a dynamic

reservoir process of carbon dioxide mixing with natural gas for a single equiUbrium

mixture. A Uquid volume of 100% can only occur with laboratory procedures, which

aUow for increasing pressure by decreasing volume. With carbon dioxide sequestration

in depleted gas reservoir, pressure increase is faciUtated by an increase of sequestrated

carbon dioxide volume in the reservoir such that a single composition tiend is not

possible in the reservoir.

For the purpose of sequestering carbon dioxide, the retrograde gas behavior is

more desirable, because storage of Uquid carbon dioxide compared to gaseous carbon

dioxide is greater per unit pressure due to the density difference between Uquid and

gaseous carbon dioxide. Furthermore, liquid carbon dioxide is at low saturation and is

thus immobUe in the reservoir. Enhanced condensate recovery occurs with retrograde

behavior because injected carbon dioxide vaporizes hydrocarbon Uquid and increases

condensate production.

98

5.1.2. Trends of the Cricondenbar, Cricondentherm and Critical Point

The trends for the cricondenbar and cricondentherm are opposite for dry gas

compared to wet and retrograde gases as shown in Figures 4.29 through 4.35. In both

instances the respective parameters of pressure and temperature increase with carbon

dioxide concentration for dry gas and decreases with carbon dioxide concentration with

wet and retrograde gas. (Correlations could be developed for these trends based on

future appUcations.) By comparing the reservoir temperature and pressure to the

cricondentherm and cricondenbar, it can be determined whether or not the reservoir

conditions considered faU within the two phase region.

The trend of the critical points is also useful for determiriing the gas type and

whether there are two phases or one phase present. The trend of the critical points is fit

with equations in Figures 4.36 through 4.40 for each gas type. These equations, shown

on the respective figures, are a convenient way to predict the phase behavior of the

respective carbon dioxide-hydrocarbon gas mixtures by determining the critical point of

the mixture of interest when compared to the cricondentherm and, reservoir

temperature and pressure.

The trend of the compressibiUty factor shows that, for all gas types, the

vapor phase compressibiUty factor decreases with increasing carbon dioxide

concentration (Figures 4.21 through 4.28). For maximum carbon dioxide storage capacity

a low compressibiUty factor is optimal because the addition of carbon dioxide lowers the

compressibility factor and thus increases the surface volume of carbon dioxide that can

99

be stored in the natural gas reservoir. These trend lines also tend to separate from each

other and the lack of crossing trend lines indicates that there are no new phases.

5.1.3. Approximating the Dynamic Mixing of Carbon Dioxide and Natural Gas with EquiUbrium

Mixture Flash Calculations

To determine the relationship between reservoir pressure and carbon dioxide

concentration, it is necessary to construct a chart of p /z versus pressure for the

corresponding gas at reservoir temperature. For example, if the reservoir contains dry

gas and carbon dioxide at 150 °F, using the compressibiUty factors in Figure 4.23, a p/z

versus pressure plot is constructed. This plot, shown in Figure 5.1, can be used together

with the real gas law,

(5.1) _znT _ final

\pv] znT - depleted

to determine the pressure-carbon dioxide concentiation relationship. The 'final'

condition is defined as the reservoir condition at which carbon dioxide injection has

ceased and fluids are aUowed to mix completely in the reservoir. The 'depleted'

condition is defined as the current reservoir condition, encovmtered at the start of

sequestration with no hydrocarbon production. Rearranging equation 5.1, gives:

z

n final

final ^depleted L

P_

Z depleted (5.2)

Although constant volume is not mandatory, the pore volume, V, of the reservoir is

considered to be invariable, n depleted is defined as the number of moles of natural gas in

100

the reservoir at the depleted pressure or start of the sequestration process. This is

determined as

^ Initial Gas in place

"depie,ed = (1" recovevy factor) — - — . 5.3 Molar volume

nfinai is defined as the total number of the moles (natural gas and carbon dioxide)

at the end of the sequestration process. If there is no hydrocarbon production, nfmai is

equal to the sum of ndepieted and the number of moles of carbon dioxide injected into the

reservoir. If there is production of natural gas and no production of carbon dioxide, nfmai

is equal to the sum of ndepieted and the number of moles of carbon dioxide injected into

the reservoir minus the number of moles of natural gas produced. The final mole

fraction of the respective gases can be determined by calculating the number of moles of

carbon dioxide added to the reservoir and the number of moles natural gas present in

the reservoir at the start of carbon dioxide injection. The volume of gas injected or

produced is converted to moles by dividing the volume in standard cubic feet (scf) by

the molar volume of 380.7 scf/lbm-mol (standard conditions: 60 °F and 14.65 psia).

For example, if a 1 Bscf dry gas reservoir depleted to 250 psia at 90% recovery

and 150 °F with 0.233 Bscf of carbon dioxide injected into a reservoir with the remaining

0.1 Bscf dry gas, the foUowing terms can be calculated:

1. z depleted (hydrocarbon gas) from Figure 4.22 is equal to 0.98.

2. p depleted / z depleted (250/0.98) equals to 255.1.

3. n im^i/n depleted equals to 3.33 (*70% carbon dioxide).

*The ratio nfinai to ndepieted is equal to the reciprocal of 1 minus the mole fraction of carbon dioxide, if there is no carbon dioxide in the reservoir at depleted/abandoned conditions.

101

Substituting these values into Equation 5.2, (p/z) final is calculated to be 850.333.

In Figure 5.1, a (p/z)finaiof 850.333 and 70% carbon dioxide, corresponds to a pressure of

730 psia. This methodology can be used for any carbon dioxide concentration in

conjimction with a plot of p /z versus pressure for a specific gas type and temperature.

Figure 5.2 shows the relationship between final pressure and mole percent carbon

dioxide for depleted conditions of 250 psia and 150 °F assuming no hydrocarbon

production. This chart can be used directly to determine the carbon dioxide mole

percent in the reservoir at a particular pressure and vice versa. With this method, the

reservoir pressure can be used to calculate the carbon dioxide mole fraction that is

sequestered in that reservoir if there is no hydrocarbon production.

5.2. Reservoir Considerations

The pressure-temperature diagrams of natural gas and carbon dioxide were a

major part of this research and provided information such as loci of the two-phase

envelope, critical points, cricondentherms and cricondenbars as a function of carbon

dioxide concentration. Carbon dioxide alters the Uquid volume percent of carbon

dioxide-natural gas mixtures. With dry gas, the addition of carbon dioxide shifts the

two-phase envelope to higher temperatures and pressure which causes the dry gas to

become relatively wetter. However, the temperatures and pressure encompassed by the

two-phase envelope for dry gas-carbon dioxide mixtures are not within the usual

temperature range of reservoir conditions. Carbon dioxide has a 'drying' effect on wet

and depleted retrograde hydrocarbon gases. This drying effect is manifested in the

shrinkage of the two-phase envelope, the reduction in Uquid volume percent (Figures

102

4.16 through 4.20) and the shift of the two-phase region to lower temperatures (Figures

4.9 through 4.13). The drying and wetting effects are quantified for sequestration with

and without natural gas production in the foUowing section.

5.2.1. Carbon Dioxide Sequestration in Producing Reservoirs

There are three possible scenarios for carbon dioxide sequestration in depleted

gas reservoirs: (1) Carbon dioxide injection without natural gas production, (2) Carbon

dioxide injection with natural gas production at constant reservoir pressure, and (3)

Carbon dioxide injection with natural gas production and increasing reservoir pressure.

Any one of these scenarios can have piston-Uke displacement or transitional

displacement depending on dispersion and diffusion. At the end of scenarios 2 and 3,

sequestration continues while gas production ceases due to a prescribed carbon dioxide

mole fraction limitation. To iUustrate the concept of this thesis, quaUtative presentations

of two sequestration scenarios, without production and with production at constant

reservoir pressure, are explained with pressure-temperature diagrams.

Figure 5.3 shows a pressure-temperature diagram of hydrocarbon gas-carbon

dioxide mixtures with two possible reservoir conditions superimposed on it. For this

example, at the start of sequestration, the reservoir can be considered to be at depleted

conditions of 150 °F and 250 psia. These reservoir conditions faU within the two-phase

region of mixtures having less than 75% carbon dioxide in Figure 5.3. If carbon dioxide

is injected to the reservoir and there is no change in temperature and pressure due to the

simultaneous natural gas production, the mixture would eventuaUy become a single

phase gas when the mole fraction of carbon dioxide exceeds 75%. With pressure

103

increasing simultaneously with carbon dioxide injection a single phase gas will form at

a lower carbon dioxide mole fraction.

5.2.2. Carbon Dioxide Sequestration in Non-Producing Reservoirs

For sequestration in reservoirs without gas production, reservoir temperature

remains relatively constant and pressure increases. The pressure limit of the reservoir in

Figure 5.3, likely to be determined by geologic factors, is labeled Final Condition. The

drying effect is driven by two interdependent actions; increasing carbon dioxide

concentration and increasing pressure. In Figure 5.3, at Final Condition, because the

two-phase region is shrinking, the mixture would be a single phase gas if the carbon

dioxide concentration exceeds 25%. Thus when carbon dioxide concentration and

pressure are increasing simultaneously, a two-phase mixture of carbon dioxide and

natural gas eventuaUy becomes a single phase gas if the reservoir conditions are greater

than the critical temperature or the reservoir pressure exceeds the saturation pressure

within the two-phase region.

5.3. Sequestration ImpUcations by Gas Type

5.3.1. CompressibiUty and Formation Volume Factor

The general trend shown in Figures 4.21 through 4.23 and 4.25 through 4.28 is

decreasing compressibiUty factor of the vapor phase with increasing carbon dioxide

concentration. If the compressibiUty factor is less than one, the actual gas volume is less

than the ideal volume of the gas. Conversely, if the compressibiUty factor is greater than

one, the actual volume of the gas is greater than the ideal volume. The importance of this

104

to carbon dioxide sequestration is realized by considering the formation volume factor,

Bg. The compressibiUty factor is directly proportional to Bg as such if the compressibiUty

factor of a gas sample increases for a given pressure and temperature, the formation

volume factor increases (equation 2.2). A dry gas reservoir containing dry gas only at

150 °F and 250 psia has formation volume factor of 0.00596 ftVscf (standard conditions

of 14.65 psia and 60 °F). If the same reservoir contains 99% carbon dioxide, its formation

volume factor is 0.00320 ft^/scf, representing a 45% increase in standard cubic feet of

carbon dioxide volume stored as compared to hydrocarbon gas originally in place.

The objective of sequestration is to inject and store as much carbon dioxide as the

reservoir can support. For carbon dioxide sequestiation operations, it is desirable to

have a low formation volume factor. Therefore it is preferable to have a larger surface

volimie occupying the same reservoir pore volume. Because of decreasing

compressibiUty factor with the addition of carbon dioxide, more carbon dioxide gas

compresses into the pore spaces than with pure natural gas. On the other hand if there

is hydrocarbon Uquid present in the reservoir, there is decreased carbon dioxide storage

capacity due to Uquid hydrocarbon occupying pore space not accessible to the carbon

dioxide; however carbon dioxide would likely be sUghtly soluble in the hydrocarbon

Uquid.

In terms of compressibiUty, retrograde gas C is the most compressible foUowed

by retrograde gas B, rebrograde gas A, wet gas and dry gas, for comparable reservoir

conditions of temperature and pressure. Ui tiie example above, if the reservoir initiaUy

has the composition of retrograde gas C at 150 °F and 250 psia, the formation volume

105

factor is 0.00530 ft^/scf. This shows that the vapor phase of retrograde gas C is 1.1 times

more compressible than dry gas.

5.3.2. Vaporization of Condensate

As long as the temperature of a dry gas reservoir is greater than 90 °F, aU carbon

dioxide-dry gas mixtures are single phase gas or critical fluid. There is no condensate

present at reservoir conditions. This can be seen from the pressure-temperature

diagram, and the trend of the critical points of the mixture in Figure 4.8. Furthermore,

there are no phase changes or new phases that are expected to be formed in dry gas

reservoirs with the addition of carbon dioxide at reservoir conditions. Also from Figure

4.8, it can be seen that at temperatures between 60 and 70 °F, pressure would have to be

between 800 and 1100 psia with a gas mixture consisting of at least 90% carbon dioxide

for the two-phase region to be encountered. This may occur at separator conditions but

at surface conditions there is no Uquid present. Any Uquid present in the separator at

these conditions would be primarily carbon dioxide.

Figure 4.10 shows that with wet gas mixtures consisting of greater than 65%

carbon dioxide, due to the irregular shape of the two-phase envelope it would be

advisable that the cricondentherm and cricondenbar be considered when determining

whether or not two phases are present. To remain outside of the two-phase region, a

general rule would be to consider reservoirs that have temperatures greater than 120°F.

Only with retrograde gas, it is possible for the two-phase envelope to encompass

aU feasible reservoir temperatures. Given that reservoir temperatures are Ukely to be less

than 500 °F, retrograde gas-carbon dioxide mixtures are within the two phase region for

106

a wide range of pressures. The exceptions to this are (1) 99% carbon dioxide at a

minimum 150 °F as in the case of retrograde gas C (Figure 4.13) and (2) reservoir

pressures exceeding the respective saturation pressures. For all other conditioris for

retrograde gas A, B and C, a liquid and gas phases are present. The drying effect of

carbon dioxide is seen clearly from the flash calculations in Figures 4.15 through 4.20.

For any given temperature and pressure, the volume of liquid decreases as carbon

dioxide concentration increases.

The same drying effect is evident in the pressure-temperature diagrams of

Figures 4.11 through 4.13 in the manner iUustrated in Figure 5.3. Even though the initial

composition of the median retrograde gas had the characteristics of a retrograde gas-

condensate (Table 4.1), the composition of the gas at the depleted pressures of 50,250

and 500 psia become 100% Uquid as pressure increases. This is evident in the plots of

Uquid volume versus pressure in Figures 4.18 through 4.20. In carbon dioxide

sequestration of depleted gas reservoirs, a pressure increase is faciUtated by an increase

of sequestrated carbon dioxide volume in the reservoir. However, it has already be

reasoned that a Uquid volume of 100% can only occur with laboratory procedures which

aUow for increasing pressure by decreasing volume.

5.4. Enhanced Gas and Condensate Production

There are several important impUcations that weigh heavily on the validation of

geologic carbon dioxide sequestration in depleted gas reservoirs as a means of climate

control. The process involves the mixing of carbon dioxide and natural gases that may

combine to form a single phase or two phases under reservoir conditions. The

107

distribution of the two phases, as a result of dispersion and diffusion mechanisms can be

highly dependent on the particular geology of the reservoir. This is a crucial factor in

estimating natural gas production. However, an estimate of gas recovery, condensate

production, the volume of carbon dioxide sequestered and the corresponding pressure

can be approximated if it is assumed that there is no mixing between fluids (piston-like

displacement) while the reservoir is under production.

For example, a 1 Bscf dry gas reservoir at 150 °F is depleted to 250 psia,

representing a 90% dry gas recovery. Carbon dioxide is injected into the reservoir and

hydrocarbon gas is displaced and produced. Here it is assumed that this displacement is

piston-Uke, which impUes that there is no mixing between natural gas and carbon

dioxide. Furthermore, the production and injection rates are balanced such that the

pressure of the reservoir remains at 250 psia and reservoir pore volume is held constant.

Assuming production of 75 mole % of this depleted gas reservoir yields 75 MMscf.

If production has ceased at this stage and carbon dioxide injection continues, the

reservoir pressure increases. At the end of sequestiation, the final reservoir pressure can

be determined from the relationship given in equation 5.2. The standard volume of

carbon dioxide injected can be converted to moles and this can be used to determine the

nfinai/ndepieted, (ndepieted is the total number of moles in the reservoir at before pressure

begins to increase.) If natural gas production ceases after 75 mole percent is produced

and carbon dioxide injection continues until the volume of carbon dioxide injected

accounts for 95 mole % of gas in the reservoir, the p /z plot of Figure 5.1 shows that the

reservoir pressure is approximately 950 psia. (See Appendix for aU detailed

108

calculations.) If there is no hydrocarbon production during carbon dioxide injection and

repressurization of the reservoir starts with the injection of carbon dioxide. Figure 5.2

shows that the corresponding pressure for a carbon dioxide mole fraction of 95% is 2500

psia.

Wet gas reservoirs are similar to dry gas reservoir in that there is no Uquid in the

reservoir; however, at separator conditions Uquid is present. Figure 4.16 shows that at

60°F and 700 psia the Uquid volume is 2.75 %. As such if the last example was based on

wet gas instead of dry gas, at the surface there is 75,187 scf/STB (13.3 STB/MMscf)

produced when 75 mole % of wet gas has been replaced by carbon dioxide. Assuming

production of 75 mole % of this depleted gas reservoir yields 72.9 MMscf of gas and

sequesters 75 MMscf of carbon dioxide.

Retrograde condensate reservoirs contain gas condensate in the reservoir as a

result of reservoir pressure decrease with gas production. Consider a retrograde

condensate reservoir depleted to 500 psia at 150 °F, leaving 0.1 Bscf of hydrocarbon gas.

From Figure 4.20, at 500 psia, a reservoir with pure natural gas contains 11.8 percent

Uquid volume Assuming constant pressure of 500 psia, 75 mole % of the hydrocarbon

gas is produced and replaced by 77.8 MMscf carbon dioxide. The total gas and

condensate recovery at this condition are 71.6 MMscf and 369bbls, respectively.

5.5. Economic Considerations

The main focus of this thesis is predicting the phase behavior of carbon dioxide-

hydrocarbon gas mixtures in depleted gas reservoirs. As a waste product that is at

109

higher than desirable levels in the atmosphere, the objective is to dispose as much

carbon dioxide as possible at minimum cost and maximum profit. Gas reservoirs are

capable of storing billions of cubic feet of gaseous fluid. With a dollar value attached to

both the fluid (possible payment for carbon dioxide disposal) that is injected into and

fluid produced from the reservoir (sale of natural gas), this cycle of storage and

production can translate to a substantial amount of cash flow.

The importance of the hydrocarbon Uquid phase volume and compressibiUty

factor of carbon dioxide-hydrocarbon gas mixtures are directly linked to the most

dominant controlling factor of carbon dioxide sequestration- economics. Maximum

profits can be realized by having a maximum volimie of carbon dioxide sequestered and

maximum volume of natural gas produced and sold with minimal carbon dioxide

contamination of the natural gas.

To increase the volume of carbon dioxide stored in the reservoir, the gas must be

compressed as much as possible. Given the relationship between the carbon dioxide

concentration (mole fraction) and the compressibiUty factor shown in equation 5.1, the

compressibiUty factor should be low and as such the carbon dioxide concentration

should be as high as possible. However, the chaUenge in sequestering carbon dioxide in

depleted gas reservoirs is balancing the need to sequester a large volume of carbon

dioxide while maintaining the quaUty of remairung natural gas produced.

110

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113

CHAPTER 6

CONCLUSIONS AND RECOMMENDATIONS

6.1. Conclusions

The objective of this thesis was to enable the prediction and improve the

understanding of carbon dioxide-natural gas mixtures in terms of sequestered carbon

dioxide volume, enhanced gas and condensate production. From the work done, several

important observations were made that formed a crucial part in achieving these

objectives. Firstiy, carbon dioxide has a drying effect on wet and retrograde gas mixtures

and a wetting effect on dry gas. Furthermore, when deaUng with dry gas-carbon dioxide

mixtures, it is not expected that a Uquid phase wUl form at reservoir or surface

conditions. On the other hand, retrograde gas-carbon dioxide mixtures wiU form liquid

at reservoir, separator and surface conditions and wet gas-carbon dioxide mixtures

forms Uquid at separator conditions. This was evident in both the pressure-temperature

diagrams and flash calculations.

The second important observation was the decrease of the compressibiUty factor

of the vapor phase due to addition of carbon dioxide. CompressibiUty factor is directly

proportional to formation volume factor which is inversely proportional to storage

capacity. This means that carbon cUoxide lowers the compressibiUty of natural gas,

thereby faciUtating greater storage capacity of surface volume carbon dioxide. As such

the standard volume of natural gas mixed with carbon dioxide would exceed the

standard volume of gas originally in the reservoir because of the decreased

compressibiUty factor.

114

Using the information gleaned from this research, sequestration projects must be

designed with the aim of having an equilibrium mixture of carbon dioxide with low

concentrations of natural gas as the final reservoir fluid in order to maximize reservoir

storage. It has been shown that carbon dioxide and carbon dioxide-natural gas mixtures

occupy less reservoir volume than pure hydrocarbon gas. If there is no hydrocarbon

production as carbon dioxide is injected into the reservoir, the pressure of the reservoir

increases. With the use of p/z versus pressure plots it is possible to relate this pressure

increase to the mole fraction of carbon dioxide present in the reservoir. There is very

modest pressure increase between 0 and 0.5 carbon dioxide mole fraction.

Hydrocarbon production as a result of carbon dioxide sequestration is

considered as enhanced gas or condensate recovery. Assuming piston-Uke displacement,

natural gas is produced from the depleted reservoir. The Uquid percent volume in

retrograde gas reservoirs decreases as the carbon dioxide concentration increases. The

vaporized Uquid increases the reservoir gas volume and pressure, and it may be

produced with carbon dioxide.

6.2. Recommendations

As purported in Chapters 1 and 2, phase behavior is dependent on gas type

composition. Accuracy in composition leads to accuracy in predicting phase behavior. Ui

this investigation, it was assumed that the carbon dioxide injection stiream was

essentiaUy 100% pure. In practice, however, carbon dioxide captured from flue gas

stacks are Ukely to contain otiier gases. The effect of these impurities should be

115

considered in further work on this subject. Furthermore, natural gas may also contain

inorganic compounds such as hydrogen sulphide and nitrogen and the effect of these

should also be investigated.

Even though the Peng-Robinson equation of state has proven to be satisfactory in

predicting the phase behavior of the mixtures, it would be ideal to have an equation-of -

state timed specificaUy for natural gas and carbon dioxide mixtures in aU proportions.

This thesis does not address the determination of the phase behavior of

compositional gradients, but under certain circumstances the methods may be

appUcable. Due to the effects of dispersion and diffusion there is a transitional region

(concentration gradient) between natural gas producer(s) and carbon dioxide injector(s)

in the reservoir. In order to project salable hydrocarbon production, it would be useful

to determine the expanse of this region between the two gases and examine the

distribution of carbon dioxide. In so doing, the formation volume factor for each region-

pure CO2, trarisitional and pure natural gas, would be known, and the storage capacity

of the reservoir could be calculated at each stage of the sequestration process.

Preliminary calculations have shown that assuming piston-Uke displacement it is

possible to enhance gas and gas condensate recovery. The mechanism of the mixing

between natural gas and carbon dioxide is very important in these calculations because

of the relation between carbon dioxide mole fraction, the overaU compressibiUty factor

of the vapor phase within the compositional transition and reservoir pressure.

Additionally, vaporization of condensate in retrograde condensate reservoirs as a

dynamic process can lead to even more involved calculations. As the mole fraction of

116

carbon dioxide increases, pressure increases and the liquid phase volume percent

decreases carbon dioxide concentration and reservoir pressure. It would be useful to

chart these three parameters in order to determine the phase behavior as a function of

pressure of a dynamic mixing process. This would aid in determining the reservoir pore

volume of the gaseous phase and the condensate recovery in retrograde reservoirs.

117

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123

APPENDIX A

Dry Gas Reservoir Enhanced Gas Recovery Calculations with Carbon Dioxide

Sequestration

Plots of compressibiUty as a function of pressure and temperature for a range of

hydrocarbon gas-carbon dioxide mixtures can be useful in performing calculations that

aid in estimating the carbon dioxide storage capacity and enchanced gas recovery of

depeleted dry gas reservoirs. An example of these dry gas calculations for carbon

dioxide sequestration and enchanced gas recovery are shown here.

Initial Conditions:

Original reservoir volume = 1 Bscf

Reservoir temperature = 150 °F

Reservoir depletion pressure = 250 psia

Recovery at depletion pressure = 90%

Remaining hydrocarbon = 0.1 Bscf

Dry gas compressibUty factor (z) = 0.974 (Figure 4.22)

Carbon dioxide compressibiUty factor = 0.936

Standard ConcUtions:

Pressure = 14.65 psia

Temperatiire = 60 °F = 520 °R

Molar volume = 380.7 scf/lbm-mole

R = 10.732 psia it^/ Ibm-mole °R

124

The standard volume of a gas is converted to number of moles by using the

following relation:

Volume (scf) no. 01 moles = . (p^i)

Molar Volume ^ '

At the start of carbon dioxide sequestration in depleted dry gas reservoirs, the number

of moles of hydrocarbon gas in 0.1 Bscf of the depleted gas reservoir, (no) is,

0.1x10' , «£,= =2.62x10^ Ibm-mole.

380.7

Assume 75 mole % of the natural gas is produced by piston-Uke displacement at

constant pressure by injecting carbon dioxide (nmj). The number of moles of dry gas

produced (np) is,

«p =(0.75) (2.62x10') = 1.97X 10'Ibm-mol •

The number of moles of hydrocarbon gas remaining in the reservoir (nnc) is,

nfjc={0.25) (2.62xl0')=6.55xl0'' Ibm-mol-

Because the pressure of the reservoir at this stage is very low, 250 psia, the

compressibUity factor of natural gas and carbon cUoxide are approximately equal (this

introduces a modest 4% error). As such since pressure, temperature, number of moles

produced/injected and compressibiUty factor of both gases are essentiaUy equal. The

volume of carbon dioxide (Gmj,75) displacing the produced natural gas (Gp) is equal to

the volume of the produced natural gas (enhanced gas recovery) is,

G =G =( 1 97 xloO(380.7) = 7.50x10^scf = 75.0 MMscf-

125

If dry gas production ceases and additional carbon dioxide is injected into the

reservoir vmtU the reservoir has 95% carbon dioxide, the remaining hydrocarbon gas

moles, nnc, represents 5% of the total number of hydrocarbon and carbon moles of gas in

the reservoir (nri):

nif = nHc/hydrocarbon mole fraction = 6.55 x lO /O.OS = 1.31 x 10* Ibm-moles.

The total number of moles of carbon dioxide injected (ninj),

ninj= (0.95) (1.31 X10') = 1.24 x 10* Ibm-moles,

represents 95% of nfmai.

This corresponds to a volume (Gmj,95) of,

Ginj,95 = (1.24 X 10*) (380.7) = 4.72 x 10' scf = 472 MMscf.

Assuming the temperature and pore volume at final and depleted conditions are

the same and complete mixing of carbon dioxide and dry gas takes place, the real gas

law can be expressed as.

P_ z

n final

n. final depleted

P_

L • -i depleted (A2)

which can be used to determine the final pressure of the reservoir. In this example,

n fmai= nif = 1.31 x 10* Ibm-mole,

and

Therefore,

n depleted = no = 2.62 X10^ Ibm-mole.

- final

1.31x10* V 250^

2.62x10' 0.972 = 1333psia.

126

Figure 5.1 is a plot of the relationship between p/z and pressure for a range of

carbon dioxide mole fractions with dry gas, derived from a compressibiUty chart of the

gas at 150 °F. A [p/z]finaiof 1275.5 on Figure 5.1 corresponds to a reservoir pressure of

approximately 970 psia when the mole fraction of carbon dioxide is 95%.

If there is no hydrocarbon production during carbon dioxide injection, and the

reservoir pressure increases from 250 psia at the start of carbon dioxide injection. Figure

5.2 can be used to determine the final pressure. (This figure is derived from equation A2,

with the depleted conditions of the dry gas reservoir at 250 psia and 150 °F, varying

•••nfmai/ndepieted for carbon dioxide mole fractions increasing in increments of 0.1.) In this

example for a mole fraction of 95% carbon dioxide in the reservoir corresponds to a

pressure of approximately 2500 psia. In summary, the displacement of 75% of the dry

gas moles with carbon dioxide foUowed by carbon dioxide injection to 95% mole fraction

yields:

Total volume of CO2 sequestered =472 MMscf

Final carbon dioxide mole fraction in the reservoir = 0.95

Volume of enhanced gas recovery = 75 MMscf, and

Final reservoir sequestration pressure = 1275.5 psia.

^ n /n d is equal to the reciprocal of 1 minus the mole fraction of carbon dioxide if there is initially no carbon dioxide prior to reservoir repressurization.

127

APPENDIX B

Wet Gas Reservoir Enhanced Gas Recovery Calculations with Carbon Dioxide

Sequestration

Plots of compressibiUty as a function of pressure and temperature for a range of

hydrocarbon gas-carbon dioxide mixtures can be useful in performing calculations that

aid in estimating the carbon dioxide storage capacity, enchanced gas and condensate

recovery of depeleted wet gas reservoirs. In this example, 75 mole % of wet gas is

produced and replaced by an equal number of moles of carbon dioxide through piston-

Uke displacement at constant pressure. Unlike dry gas, wet gas produces liquid at

separator conditions the results in lower hydrocarbon gas recovery (Bscf). The

calculation of the surface vapor and Uquid phase volumes is emphasized here.

Initial Conditions:

Original reservoir volume = 1 Bscf

Reservoir temperature = 150 °F

Reservoir depletion pressure = 250 psia

Recovery at depletion pressure = 90%

Remaining wet gas = 0.1 Bscf

Wet gas compressibUty factor (z) = 0.965 (Figure 4.25)

Carbon dioxide compressibUity factor = 0.936

Standard Conditions:

Pressure = 14.65 psia

Temperatiire = 60 °F = 520 °R

128

Molar volume = 380.7 scf/lbm-mole

R = 10.732 psia ffs/ Ibm-mole °R

At the start of carbon dioxide sequestiation in a depleted wet gas reservoirs, the number

of moles of hydrocarbon gas in 0.1 Bscf of the depleted gas reservoir, (no) is,

0.1x10' , Ho = =2.62x10' Ibm-mole.

380.7

Assume 75 mole % of the natural gas is produced by piston-Uke displacement at

constant pressure by injecting carbon dioxide (ninj). The number of moles of wet gas

produced (np) is,

„^ = (0.75)(2.62xl0')= 1.97x10'Ibm-mol-

The number of moles of hydrocarbon gas remaining in the reservoir (nnc) is,

«^c=(0-25)(2.62xl0^)=6.55xl0''lbm-mol-

Because the pressure of the reservoir at this stage is very low, 250 psia, the

compressibUity factor of natural gas and carbon dioxide are approximately equal. (This

introduces a modest 3% error.) As such since pressure, temperature, number of moles

produced/injected and compressibiUty factor of both gases are essentially equal. The

volume of carbon dioxide (G75,co2) displacmg tiie produced natiiral gas (Gp) is equal to

the volume of the produced natural gas (enhanced gas recovery) is,

Q ^Q =(i.97xl0')(380.7) = 7.50xl0'scf = 75.0 MMscf-^-' inj,75 p \ / N '

129

Consider the case where produced wet gas is passed through a separator at 60 °F

and 700 psia. PR EOS flash calculations show that 2.75 mole % is Uquid at separator

conditions. To determine the condensate yield, the condensate and gas volume are

calculated from the cumulative number of liquid moles (npu) and gas moles (npv) as,

npL = (0.0275) np = (0.0275) (1.97 x 10') = 5.42 x 10' Ibm-mole,

and

npv = (1-0.0275) np = (0.9725) (1.97 x 10') = 1.92 x 10' Ibm-mole,

respectively.

Flash calculations given for the liquid phase at 700 psia and 60 °F has a molecular weight

of 66.4 Ibm/lbm-mole and density of 65.8 Ibm/ft . The separator molar volume (Vms) is,

^ _ (Molecular weight) 66.4 ^^^^^ bbls/Ibm-mole. (5.615)(density) (5.615)(65.8)

Using the molar volume of the gas, the cumulative condensate volume (Np) and the

cumulative gas produced (Gp) are calculated as,

Np = npL Vn,s= (5.42 x 10') (0.18) = 975.6 bbls,

and

Gp = npv Vms = (1-92 x lO') (380.7) = 7.29 x 10' scf = 72.9 MMscf.

The overaU yield of condensate at separator conditions is the ratio of the cumulative gas

produced and the cumulative condensate volume,

7.29k 10' Condensate Yield = Gp/Np = — ^ ^ =74700 scf/bbl = 13.4 bblMMscf

In summary, the displacement of 75 % of the wet gas moles witii carbon dioxide

yields:

130

Volume of CO2 sequestered = 75 MMscf

Enhanced condensate recovery = 973.7 bbls

Enhanced gas recovery = 72.9 MMscf.

131

APPENDIX C

Retrograde Gas Reservoir Enhanced Gas and Condensate Recovery Calculations with Carbon Dioxide

Sequestiation

Plots of compressibiUty as a function of pressure and temperature for a range of

hydrocarbon gas<arbon dioxide mixtures can be useful in performing calculations that

aid in estimating the carbon dioxide storage capacity, enchanced gas and condensate

recovery of depeleted retrograde gas reservoirs. Retrograde gas condensate differs from

dry and wet gas in that at depleted conditions there is Uquid condensate present in the

reservoir at the start of sequestration. The foUowing calculations focus on the condensate

vaporized in the reservoir and gas production, due to the addition of carbon dioxide at

constant pressure.

Initial Conditions:

Original reservoir volume = 1 Bscf

Reservoir temperature = 150 °F

Reservoir depletion pressure = 500 psia

Recovery at depletion pressure = 90%

Remaining retrograde gas = 0.1 Bscf

Remaining hydrocarbon Uquid condertsate volume = 11.8 %

Hydrocarbon gas compressibUty factor = 0.901 (Figure 4.28)

Carbon dioxide compressibUity factor = 0.868

Standard Conditions:

Pressure = 14.65 psia

132

Temperatiire = 60 °F = 520 °R

Molar volume = 380.7 scf/lbm-mole

R = 10.732 psia ftV Ibm-mole °R

At the start of carbon dioxide sequestration in a depleted retiograde gas

reservoir, the number of moles of hydrocarbon gas (nov) in 0.1 Bscf is,

0.1x10' 5 nnv= =2.62x10 Ibm-mole.

380.7

Assume 75 mole % of the natural gas is produced by piston-Uke displacement at

constant pressure by injecting carbon dioxide. The number of moles of natural gas

produced (np) is,

np = (0.75) (2.62 x lO') = 1.97 x 10' Ibm-moles

From PR EOS calculations, nearly 100% of the produced gas is vapor because the

gas composition is approximately 80% methane, which is due to the condensation of the

Uquid in the reservoir. So the entire 75% of the gas results in the standard volume of gas

recovered (Gp) is,

Gp = npv Vm = (1.97 X lO') (380.7) = 2.00 x 10' scf = 75.0 MMscf.

The assumption of piston-Uke displacement of the vapor phase of the retrograde gas

would vaporize and produced some of the Uquid condensate in the reservoir. PR EOS

estimates that the addition of the carbon dioxide vaporizes the retrograde liquid present

in the reservoir from 11.8 volume % to 5.08 volume % for this example. Estimates based

on PR EOS calculations give an average condensate yield of 5.15x10"' bbl/Mscf. This is

very low due to the high % mole fraction of the carbon dioxide; however, it is relatively

higher that the case without carbon dioxide which was 0.00 bbl/Mscf.

133

PR EOS gave 0.957 mole %vapor and 0.043 mole % Uquid for the gas phase

enriched with the vaporized condensate. The vapor moles produced (npv)are

npv = (0.957)(1.97xl0') = 1.88x10'Ibm-moles,

and the liquid moles produced (npL) are

npL = (0.043)(1.97xl0') = 9.00x10' Ibm-moles.

This yields a gas volume (Gp)of,

Gp = (380.7)(1.88xl05) = 71.6 MMscf,

and a Uquid volume produced (Np) of,

Np = Gp (Yield) = (71.6) (5.15x10') = 369 bbls.

The calculated condensate production is likely a maximum value because it was

assumed that the vaporized retrograde Uquid is instantaneous, instead of a function of

carbon dioxide concentration. WhUe the calucated enhancement to condensate recovery

is Ukely a maximum, compositional simulation wiU give an improved estimate.

In summary, the displacement of 75 % of the retrograde gas (vapor phase) moles

with carbon dioxide yields:

Volume of CO2 sequestered = 77.8 MMscf

Enhanced gas recovery = 71.6 MMscf

ErJianced condensate recovery = 369 bbls

134

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