PHASE AND ELECTROLYTE EQUILIBRIUM
MODELING IN DOWNHOLE
ENVIRONMENTS
By
MAHESH SUNDARAM
Bachelor of Technology
Banaras Hindu University
Varanasi, INDIA
1994
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
December, 1996
PHASE AND ELECTROLYTE EQUILIBRIUM
MODELING IN DOWNHOLE
ENVIRONMENTS
Thesis Approved:
Dean of the Graduate College
it
ACKNOWLEDGEMENTS
I wish to express my sincere appreciation and thanks to my advisors Dr. Jan
Wagner and Dr. Martin S High for their guidance, motivation, inspiration, and
encouragement throughout the duration of this project. I also appreciate their patience in
going through this thesis and the corrections. I am also thankful to my other committee
member, Dr. D. Alan Tree, for his support and his suggestions.
I would like to thank all of the industrial sponsors of the Downhole Corrosion
Consortium and the School of Chemical Engineering for their financial support during the
course of this study.
I wish to thank Mr. Venkataraghavan Raman for his sincere and helpful comments
and assistance during the course of this work. Special credit goes to Anand and so many
other friends in Stillwater for having helped me maintain my sanity, especially during the
last six months.
My mother, father, sister, and grandmother deserve praIse for their
encouragement, understanding and the confidence that they have reposed in me. To these
four peoplewho have suffered, in silence, the pain of being away from me and yet have
given me their very bestI dedicate this work.
11l
T ABLE OF CONTENTS
Chapter Page
1 INTRODUCTION .... ...... .. ............ ... ....... ..... .... .. ............. ... ..... ......... ... .. .. .. ... ........ .
1.1 Objectives of this Work.. .......... .... . ........ .. ... .......... .... ... ... ... .... ....... ... .. .. .. ... ... 4
2 LITERATURE REVIEW .......... .. .... ...... .... , ... , ... , .. , ..... .. " .. ............. ..... ... ,', .. ,.. .... ... 6
2.1 Corrosion Fundamentals ........ ..... .. . , .... ......... . , .. .... ....... , ... , ......... .. , .. .. ..... ,. ..... 6
2.2 Factors Influencing Downhole Corrosion.. .. .. .. .. .. .................. .. ......... .. ... .. 7
2.3 Previous Models for Corrosion Prediction .. .......... .... ........... .......... ... .. ..... .. . 12
2.3 .1 TheModelofRobertson(1988) ......... ... ... ....... ........ ....... .. ,...... .... 12
2.3.2 The Model of Liu and Erbar (1990) .......... ... .. ... ........ ...... ...... 15
2.3.3 The Model ofLiu (1991) .................. ... ..... .. .... ...... .. ........... .. .. 16
2.3.4 The Model ofLiu and High (1993) .... ........... .. .. .. ....... ........ ..... .. 17
2.4 Electrolyte Equilibrium Modeling ..... .... ..... ......... . , ...... .... ... .. , ... ..... .. ,...... .... . 18
2.5 The Phase Equilibrium Model used in DREAM ... .. .... ... .. .... .. ......... ............. 24
3 MODEL DEVELOPMENT...... ... ..... .......... .. ..... .. .. .... ... .... .. .... . ... ....... ... ... ..... ...... 27
3.1 Physical Model, ... ..... . , .. " ...... , .. ..... ..... , ... , ... ..... ,., ... , .. .. , .. .. ... ... , .... ,. ...... ...... .. 27
3.2 Model Formulation ....... ....... " ........ ..... ... .. .. .............. .. ....... ', ... .. .. ,. .. ... ..... .... 31
3.2. 1 Concentration at the GasLiquid Interface .. .... ...... .. .. .... ... .. ,... .. .... 33
3.2.2 Coupled Phase and Electrolyte Equilibrium Calculations .. ... . " ..... 43
3 . 3 Numerical Implementation , ... ............. .. , ..... .......... .. .... . , ... .... . , .... .. , .. , ......... ,. 44
3.3.1 Phase Equilibrium Computations... ........ .... .... .... ... .. .... .. .... .... .. .... 45
3.3.2 Electrolyte Equilibrium Computations, ... .... ... . , ... , ... " . ,. ,. . 45
3.3.2.1 Solution of the Fourth Order Equation .... . , .. , .. ... , ... ,. 48
4 RESULTS AND DISCUSSION ..... .... ... .. ...... ...... ,..... .... .. .... ....... ... .. .. ... .. ..... .... 51
4.1 Analysis of the COrHzO System .. ...... .. . ... ....... ... .. ..... ... ....... .. ....... .. , .... , 52
4.2 Analysis of the HzSH20 System .... .. ... .... ..... .. ...... .... ....... ... , ... ...... ' ..... 56
4.3 Discussion .. ... , ... , ............. .. ... ...... .. ....... ... ..... .. ,.. ... .. ...... .... ... ... .. ... .. ... ........ .. 64
4.4 Effect of the Phase and Electrolyte Equilibrium Module
on Corrosion Rate Prediction ...... .... . , ..... ...... ..... ... ....... ... ..... ..... .... ....... .. ,. .. 67
iv
rt1
5 CONCLUSIONS AND RECOMMENDATIONS, .. , .. "" .. " " , ... . "" .. , .... ", .. , .. " ... .. , 93
5.1 Conclusions ....... """ .. " .... , ...... '.,., .... .. .. " ... ... , .. ,." .," .. , .... , .. ,' ... ...... " '" ...... . " 93
5.2 Recommendations ... , .... .. . , .. .. ,", .... .. ,., ... , .. ..... , .. " ... , .... " .. ... ..... .... , ... .... ,.... ..... 93
REFERENCES .. ...... ...... ... ..... , .. , ... .... ,. , ... ,., ... .... ,., ... ..... .. , ..... ..... ..... .... , ... ,., .. ...... ...... 95
APPENDICES .. .... .... ...... ... .. ... ..... ...... .. ... .... , ... ... ... ..... .. .... .... ....... ..... , ... .. , ..... ... .... . 102
A. ERRORS RECTIFIED IN THE PHASE AND ELECTROL YTE
EQUILIDRIUM CALCULATION IN DREAM 3.0..... .. ... .... .. .. ........ .. .... .... ..... 103
B. EXAMPLE CALCULATION FOR PHASE AND ELECTROLYTE
EQUILffiRIUM COMPUTATIONS , .... ....... .. .... .... ..... ... ...... . ,....... .............. ... 105
v
LIST OF TABLES
Table Page
1. Comparison of Flash Calculations With and Without Providing
for Aqueous Phase Dissociations .... ... , .. ... .......... .. .. ....... ........ .. . ......... .. ... . 21
II. Temperature Coefficients for Equilibrium Constants .......... ........ ....... .. . . 38
III. Summary of the Calculated VS. Measured Bubble Point Pressures
for the CO2H20 System .. ............. .. .. ....... .. ... ...... ...... ... ... .. .. .. .... .... .. .. .. ... .. 54
IV. Calculated VS. Measured Bubble Point Pressures for the
COzH20 System Classified by Isotherms .... .. .. .. .. .. .. .. .... .. .. ... .................... . 57
V. Summary of the Calculated VS. Measured Bubble Point Pressures
for the H2SH20 System .. ... ... .. .. .. .... ..... .. ... .... ...... .......... ..... ... .. .. ....... ...... . . 59
VI. Calculated vs. Measured Bubble Point Pressures
for the H2SH20 System Classified by Isotherms ..... ... , .. ...... .... .. .............. . 60
VII. Well Geometry and Production Data ...... .. ... ... .... .. .. ..... .. ... ... .. ..... ........ .. .. 69
VIII. Gas Analysis (mole %) ......... ... ....... .... ... .. .... .. ....... .. .. .. ... .. ... ...... .. ...... .... .... 70
IX. Water Analysis (ppm) ... ... ...... ........ ...... .... .. .... ...... ... .. ... ....... .. .. .. ..... ....... .. . . 71
X. Well Geometry and Production Data for the Hypothetical Well .. ......... ... . 106
Xl. Gas Analysis for the Hypothetical Well .... ... .. . 107
XII. Water Analysis for the Hypothetical Well " . ... .. ...... .. .. ... .. .. .. . .. .. 108
XIII. Comparison of the Values of Equilibrium Constants and
Solubility Products Calculated Manually and from the Code.. .. ...... ... ... .. . 111
XIV. Comparison of the Values of Activity Coefficients
Calculated Manually and from the Code .... ... . 113
o
tI:
l~ 10
XV Comparison of the Values of the Coefficients of Equation (3.30)
Calculated Manually and from the Code .. .. ... , .... .. .... ... ...... ... .. .... ..... ". 114
XVI. Comparison of the Values of Concentrations Calculated Manually
and from the Code ., ... ..... , ... .. " .. , ... .. " ... , ..... , .. .. , .... . ,., .... " ... . , .. .... .... .. .... , Il7
XVII. Final values Calculated by the Program for the Liquid and the Vapor
Phase Mole Fractions ... ..... , .. ..... .... .. ....... .. .... ' .... ,., .. , ..... .. ... ...... .... , ... .. . , 120
o
~ 10
vii
LIST OF FIGURES
Figure Page
1. Physical Model of Downhole System ..... ..... ..... ... ..... ...... ...... ...... ........ ...... .... 28
2. VaporLiquid Equilibrium in a Downhole System ...... .... .. .... ......... ......... . .. .... 30
3. Flow Diagram for Phase Equilibrium Calculation..... .... .. .. .. ........ ... ..... .... .... .. . 46
4. Flow Diagram for Electrolyte Equilibrium Calculation.... . ... ... ... ... .... ... .... ...... 47
5. Average Absolute Percentage Deviation in the Calculated Bubble
Point Pressure as a Function of the System Pressure
for the COzH20 Binary.. ...... ....... .. ... .. .. .. .. .. ... ... .. .. ... .. .. .. .. .. .. .. .... .... ... .. .. .. 55
6 Average Absolute Percentage Deviation in the Calculated Bubble
Point Pressure as a Function of the System Temperature
for the COzH20 Binary ..... ... ........... ..... .... ..... ... .. ... ........ .. ... ...... ... ... ..... ...... 58
7. Average Absolute Percentage Deviation in the Calculated Bubble
Point Pressure as a Function of the System Pressure
for the H2SH20 Binary .... .... .. ... .. ....... .. ...... .... ..... ... .... .. ..... .... ... ... .. .. ... 62
8 . Average Absolute Percentage Deviation in the Calculated Bubble
Point Pressure as a Function of the System Temperature
for the H2SH20 Binary .. .... ... .. ...... ... .. ... .. ... ..... .. . .. ...... .. .... ... ...... .. ... .. 63
9. Corrosion Profile along Well Depth: CASE I .. ... ...... ... .. .. ... ........ ... .. .... .. .. .. 72
10. Corrosion Profile along Well Depth: CASE II .... .. ... ... .. ........ .... .. ... .. .. ...... .... 73
11. Corrosion Profile along Well Depth: CASE IlL..... ..... .. ... .. .... .. ... ....... ....... .. 74
12. Corrosion Profile along Well Depth: CASE IV.... ... .. ..... ..... ... ....... ..... .. .. .. ... . 75
13 . Corrosion Profile along Well Depth: CASE V... .... ... ... .. .... .. ... .. .. .... .. ....... 76
viii
14. Corrosion Profile along Well Depth: CASE VI... ...... ...... .... ... ... .. ... ..... .. ....... 77
IS. Corrosion Profile along Well Depth: CASE VII .. ... .... ...... ......... .... ...... .. ..... . 78
16. Corrosion Profile along Well Depth: CASE VIII .. .. ....... ... ..... .. .. .. ..... .. ... ...... 79
17. Corrosion Profile along Well Depth: CASE IX...... ........ ... ...... ................. ... . 80
18. Corrosion Profile along Well Depth: CASE X. ...... ... ....... ... ...... .. ... .... .. .. .. . 81
19. Corrosion Profile along Wen Depth: CASE XI.. .... .. .... .. .. .. .. .. ... . ........ .. ..... .. . 82
20. Corrosion Profile along Wen Depth: CASE XII.. ....... .. ... ..... .. ...... ... .... .... ... 83
21 . Corrosion Profile along Well Depth: CASE XIII . .. .. .... .. .... .. .... .... .. ... ... . . .... .. 84
22. Corrosion Profile along Well Depth: CASE XIV.. .. .. ... ......... ... ....... ....... ... ... 8S
23. Corrosion Profile along Well Depth: CASE XV..... .. ..... . .... ...... .. ..... ... .. .. 86
24. Corrosion Profile along Well Depth: CASE XVI..... ....... .. ..... .. ...... ... .... ... .. 87
25. pH Profile along Well Depth: Hydrogen Sulfide
Induced Corrosion .. ........ . . . . . .. .. . . . . . . ... . . . . . .. . . . . . . . . . . . . . . . . .. . ... .... .. ........ ....... .. .. . . 92
26. Graphical Solution for the Concentration of Hydrogen Ion ...... ......... .... ... .. lIS
27. Graphical Solution for the Phase Compressibility.. ..... .. .......... ......... ... ... ... 119
ix
NOMENCLA TURE
a Activity, mol/kg solvent.
aO Hard sphere radius, Angstorm units.
a, b Constants used in Equation (2.4), dimensionless
Aj Constants used in Equation (3 .30), dimensionless.
AAPD Average Absolute Percentage Deviation, percentage
A, B Molal DebyeHuckel parameters, dimensionless.
A· Constant defined by Equation (2 .15), kmol2/kpa m6.
B· Constant defined by Equation (2.16), kmol/m3.
Bj j Temperature Coefficients for Equilibrium Constants (Used in Equation 3.34),
mol/kg Kn (n = 1,0, or 1).
b Bias in a property, percentage
bO Deviation function describing the departure of the mean ionic activity coefficient of
an electrolyte from that predicted by the DebyeHuckel expression, molii.
C AO Equilibrium concentration of the hydrogen ion at the gaslliquid interface, molll
Ci Binary interaction parameter, dimensionless.
d Amount dissociated in liquid phase, dimensionless.
D Percentage Deviation in a Property, percentage
f Fugacity, kpa.
x
F total Amount of feed, moles.
G Gibbs free energy, Joules.
H Henry's Law constant, kpakg solvent/mol solute.
I Ionic strength, Coulomb mo12/kg2
kM Mass transfer coefficient in the liquid film, mlsec.
ks Surface reaction rate constant, mlsec.
Ki, VLE Vapor/liquid equilibrium constant, dimensionless.
K
Ksp
m
M
n
NAZ
p
R
T
v
x
y
Equilibrium constant, mol/kg water.
Solubility product, mol/kg water.
Molality, mol/kg solvent.
Apparent molality or stoichiometric concentration of the weak electrolyte in the
aqueous phase, mol/kg solvent.
Molar Strength, Coulomb mol/kg.
Number of Components in a System.
Molar flux of the hydrogen ion at the gas/liquid interface, kg mollm2 sec.
Pressure, kpa.
Ideal Gas Law Constant, kpa m3/kmol K.
Source term defined by Equation (85), dimensionless.
Temperature, K.
Volume, m3.
Liquid phase mole fraction, dimensionless.
Gasphase mole fraction, dimensionless.
xi
z Ionic charge, Coulomb.
Z Compressibility factor, dimensionless
Greek Variables
a. Constant used in Equation (2.4).
y Activity coefficient.
p Density, glcc.
(j) Fugacity coefficient.
(0 Acentric factor
I; Die1ctric constant.
!! Chemical potential.
Subscripts
C Critical .
g Gas.
·th . I speCIes
· th . J specIes.
Liquid.
m Electrolyte of concentration 'm'
s Solid.
Xli
W Water.
Superscript
L Liquid.
S Solid
t Total.
V Vapor.
xiii
CHAPTER 1
INTRODUCTION
Oil and gas wells produce varying amounts of gases such as carbon dioxide (C02),
hydrogen sulfide (H2S), water (H20), and organic acids. These gases dissolve in water
and form a weak acidic solution that is corrosive.
The economic impact of corrosion is tremendous. The cost of corrosion in the
United States alone has been estimated to be between $8 billion and $126 billion per year
(Jones, 1991). The above figure takes into account only the direct economic costs of
corrosion. The indirect costs (such as the shut down of an industrial unit, expenditure on
corrosion control) resulting from actual or possible corrosion are very difficult to evaluate
and are probably greater.
Corrosion is a serious problem in the oil and gas industry. The loss of metal in a
pipeline may lead to failure that could potentially cause an explosive situation. A severely
corroded well may have to be shut down, at least temporarily, leading to loss of
production. Corrosion increases the cost of production due to increased spending on
corrosion control. The severity of the damage and the enormity of the expense associated
with corrosion has promoted a wide range of research activity.
Corrosion in oil and gas wells is controlled by the use of corrosion resistant
materials for construction, protective coatings on the tubing and casing, and the use of
inhibitors. The type of corrosion control varies from well to well and is dependent on
1
specific well conditions. Generally, more than one corrosion control method may be
necessary.
The use of corrosion resistant materials (e.g., chrome steel, nickel steel) for
controlling corrosion is a very reliable, but costly method. These materials must be
resistant to both sulfides and carbonates in order to provide a long term solution to the
corrosion problem. Further, the process of determining whether a particular material is
acceptable for use in a specific case involves the experimental modeling of the actual well
conditions before finalizing the use of that material in a well (Tuttle, 1990) At high
concentrations, oxygen and strong mineral acids attack even corrosion resistant alloys
(Tuttle, 1987).
A more economical, but less reliable, method is the use of protective coatings.
The coatings can be plastic, inorganic, metallic, or nonmetallic. Coatings isolate the
material from the corrosive environment and prevent the material from being attacked
(Newton and Hausler, 1984). Coatings are often inapplicable in situations where severe
erosion and high temperature could occur.
Corrosion inhibitors (e.g., sodium nitrite, ethylene glycol etc.) are used extensively
in oil and gas wells. Most of the commonly used inhibitors are organic chemicals with
polar and nonpolar parts (Newton and Hausler, 1984). The polar group attaches to the
metal while the nonpolar group promotes the formation of a protective oil film over the
inhibitor layer. The effectiveness of the inhibitor depends on the ability of the inhibitor to
cover the metal surface completely. Effective coverage of the metal surface may be
hampered due to chemical or mechanical reasons. Sometimes the inhibitor may not be
2
compatible with the surface of the metal and may not adhere to the surface of the metal. If
the velocity of flow is higher than the erosional velocity then the inhibitor may be washed
away. In certain high pressure wells, organic inhibitors do not penetrate the entire depth
of the well (Bilhartz, 1952) and result in severe corrosion ofthe lower zones of the tubing.
The remote location of many wells may also make inhibition difficult and expensive.
The phenomenon of corrosion in oil and gas wells is highly complicated and is not
understood completely. A survey of the literature shows that the corrosion in an oil or gas
well depends on many factors such as CO2 and H2S concentrations, the system
temperature and pressure, fluid velocity, the corrosion product formed, relative amounts
of liquid water and hydrocarbon vapor, liquid phase pH, the flow regime encountered
downhole, phase behavior, concentrations of ions in the water phase, oxygen
contamination downhole, and the presence of microorganisms. These phenomena are
interrelated, and understanding the corrosion process or predicting the corrosion rate
accurately is difficult.
Authors have used different classification for corrosIOn . Fontana (1986) has
classified corrosion as: galvanic or twometal corrosion, crevice corrosion, pitting,
intergranular corrosion, selective leaching, erosion corrosion, stress corrosion, and
hydrogen damage. However, corrosion occurring downhole can be classified broadly as
uniform corrosion and localized corrosion (Liu, 1991 ). Overal1 weight loss and thinning
of the corroded material is referred to as uniform corrosion, while the appearance of
grooves and pits is called localized corrosion.
3
The need for a mechanistic tool for corrosion prediction is great. The mathematical
modeling of downhole corrosion is complicated because a multiphase, multicomponent,
heterogeneous system in turbulent flow with mass transfer, and chemical reactions has to
be modeled. Crolet and Bonis (1984) emphasized corrosion prediction involves not only
forecasting the risk of corrosion, but also the possibility of a lack of corrosi.on. Thus,
corrosion prediction helps in material selection, and the use of coatings and inhibitors. A
reliable method for corrosion prediction would be a valuable tool which would help reduce
production and operating costs.
A comprehensive mathematical model for predicting corrOSlOn rates was
developed by Liu (1991). The model included modules for thermodynamic phase
equilibria calculations, electrolyte equilibrium computations, mass transfer calculations,
and corrosion rate calculations. All of these modules were incorporated into a user
friendly software, named DREAM (Downhole Corrosion Pr~diction Program), to predict
the corrosion rate.
1.1 OBJECTIVES OF THIS WORK
The principal objective of the present work was to refine DREAM to establish a
consistent and generalized framework for phase and electrolyte equilibrium computations
in gas wells. In DREAM simulations, phase and electrolyte equilibrium computations are
performed initially to estimate the quantity of the liquid and the vapor phases and the
composition of the species present at the gasliquid interface. The compositions at the
4
vaporliquid interface are used to obtain the composition at the surface of the piping
where corrosion occurs. Accurate estimation of the composition at the gasliquid
interface is important for correct corrosion rate calculations
Another objective of this work was to include hydrogen sulfide in the electrolyte
equilibrium module to enable the prediction of hydrogen sulfide induced corrosion. The
previous version of DREAM (Version 3.0) could predict corrosion induced by CO2 alone.
The final objective of this work was to evaluate the performance of the phase and
electrolyte equilibrium model with experimental data for the following binary systems:
CO2H20, and H2SH20. The performance of the old model, DREAM (Version 3.0) was
also evaluated and compared with the performance of the new model (DREAM 3.3).
CHAPTER 2
LITERATURE REVlliW
This chapter discusses corrosion, the factors influencing corrosion in gas wells,
models used for corrosion prediction, electrolyte equilibrium modeling, and the phase
equilibrium model used in DREAM 3.0. The corrosion process is defined and described
briefly. Several factors that influence corrosion in gas and oil wells are analyzed. Some of
the corrosion prediction models developed at Oklahoma State University are discussed.
The need for electrolyte equilibrium modeling and the importance of the approach used in
this work, as applied to downhole environments, is explained. The phase equilibrium
model used in DREAM 3.0 is also documented.
2. 1 Corrosion Fundamentals
Corrosion may be defined as the deterioration or destruction of a material or its
properties due to a reaction with the environment. In the oil and gas industry, corrosion
refers primarily to the destruction of metal, either through a chemical or an
electrochemical reaction with a given environment.
The mechanism by which corrosion proceeds is quite complicated. The presence
of liquid water is a necessary factor for corrosion in oil and gas wells (Tuttle and Hamby,
1977). Corrosion proceeds through an electrochemical mechanism in which water plays
6
the role of the electrolyte. A driving force and a complete electrical circuit are necessary
for current flow. The potential difference existing on the surface of the metals or alloys
used in the construction of the tubing provides the necessary driving force. The electrical
circuit is completed by the presence of the electrolyte which conducts electrical current
from the anode to the cathode. The greater the conductivity of the electrolyte, the greater
the rate of corrosion.
2.2 Factors Influencing Downhole Corrosion
A survey of the literature shows that the phenomenon of downhole corrosion is
dependent on many factors. The presence of CO2 and H2S, the partial pressures of CO2
and H2S, the presence of water, the pH of the produced water, the temperature along the
well string, the presence of corrosion product layers, the water chemistry, the flow regime,
and the nature of steel influence the corrosion rate (Videm and Dugstad, 1989; Bradley,
1986; Crolet and Bonis, 1983; Kuznetsov, 1981; Bradburn, 1977; de Waard and Milliams,
1976; Shock and Sudbury, 1951).
The corrosion of steel equipment in oil and gas wells has been observed for the
past several decades. Bacon and Brown (1943) observed serious corrosion in fittings and
orifice plates in some gas wells. The gas contained nearly 1 % CO2 and traces of H2S.
The pH of the produced water varied between 5.0 and 6.0 at the wellhead. Bacon and
Brown (I943) concluded that the damage to the pipe was probably due to erosioncorrosion
in turbulent twophase flow. Erosioncorrosion in turbulent twophase flow is
7
possible, provided there is a sufficient amount of solids making contact with the wall
(Shock and Sudbury, 1951).
Several authors (Videm and Dugstad, 1989 ~ Bradley, 1986; Crolet and Bonis,
1983 ~ de Waard and Milliams, 1976; Shock and Sudbury, 1951; Zitter, 1973) proposed
that the partial pressures of CO2 and H2S affected the corrosion rate by controlling the
acidity of the medium. Bradley (1986) proposed a ruleofthumb to predict the
corrosiveness of a well using the partial pressure of CO2 as an index. A partial pressure
above 15 psia indicates a corrosive well. If the partial pressure of the corrosive gases is
between 715 psia, the well will probably be corrosive. According to Bradley, partial
pressure of less than 7 psia indicates a noncorrosive well. Videm and Dugstad (1989)
observed that the corrosion rate varied exponentially with the partial pressure of CO2 with
the exponent ranging between 0.5 and 0.8.
Bradburn (1977) stated that the corrosion rate in a well increases with increasing
amount of water produced in the well. The amount of carbonic acid produced in a well
would depend on the carbon dioxide concentration and the water production. Bradburn
(1977) concluded that if two wells produced the same amount of water with a magnitude
of difference in the carbon dioxide concentration, then the well with the higher carbon
dioxide concentration would be more corrosive.
Using the principles offluid mechanics, Videm and Dugstad (1989) concluded that
when the corrosion process is controlled by mass transfer, the corrosion rate varies with
the water flow rate raised to a power of 0.8 for a fully developed turbulent flow. Gatzke
8
and Hausler (1984) extended this to the gas production rate and proposed an empirical
correlation to demonstrate the effect of gas and water flow rates on downhole corrosion.
The effect of pH on the corrosion rate has also been studi.ed extensively. Shock
and Sudbury (1951), found that corrosion took place at pH values less than 5.5. The
authors also concluded that the corrosion phenomenon could be explained satisfactorily by
correlating corrosion with acidity rather than with galvanic action or current flow. A
relationship between corrosion and acidity was also confirmed by Ewing (1955) who
observed a distinct change in the appearance of the solution and the corrosion rates at pH
values close to 6. Experiments conducted by Videm and Dugstad (1987) indicated that
increasing the acidity of the solution increased the ferrous ion (Fe2+) concentration in
solution, and concluded that the corrosion rate increases with decreasing pH and is most
pronounced below a pH of 3 .8.
Temperature has an indirect effect on the corrosion rate. Changes in temperature
cause changes in pH, flow rate, solubility of the various species found in water, the
reaction rate, potential difference, and the properties of the corrosion product layer.
Kuznetsov (1981) performed gravimetric tests in autoclaves and observed that corrosion
rate increases exponentially with temperature up to a temperature of 60°C. The rate of
increase of corrosion was retarded above 60 °C, and the corrosion rate reached a
maximum value at 80°C. He also observed a steady fall in the corrosion rate above 80 0c.
The temperature at which the corrosion rate reaches a maximum is called the
scaling temperature. At this temperature, the local pH, and the Fe ++ concentration formed
at the steel surface are such that a protective film is formed (deWaard et ai. , 1991). The
9
scaling temperature is likely to be dependent on flow rate and increases with increasing
flow rate. Kuznetsov suggested that under dynamic conditions the process is subject to a
mixed anodiccathodic control at low temperatures and an anodic control at high
temperatures. Polarization curves for steel showed that at higher temperatures the anodic
process was retarded owing to corrosion product deposition, leading to a drop in the
corrosion rate.
The effect of temperature on corrosion could also be explained in terms of the
corrosion product layers formed. The precipitation of a corrosion product in itself does
not necessarily result in the formation of a protective film (de Waard et aI., 1991)
Kuznetsov (1981) found that at temperatures below 60°C the corrosion process formed a
soft, noncohesive permeable film which has a smudgelike appearance and is easily
removed by flowing fluids . Above 60 °c the crystals of the corrosion product were
stronger, more compact, and less permeable. This could account for the deviation from
the exponential increase in corrosion rate. At temperatures close to 120 °C, the amount of
film deposited increased and the permeability of the oxide layer decreased, possibly
preventing the metal from corroding further. Similar observations have been reported by
de Waard et al. (1991) and Ikeda et at. (1984) and confirmed in the experiments
conducted by Shoesmith et al. (I 980).
Crolet (1983) and Crolet and Bonis (1983) concluded that water chemistry is more
important in forecasting downhole corrosion rate than temperature or partial pressure of
CO2. The presence of certain species in the produced water greatly affects the rate of
corrosion. Chloride ion is corrosive, but only in the presence of oxygen. The bicarbonate
10

ion alters the pH of the produced water and affects the corrosion rate. The presence of
compounds such as calcium carbonate and calcium chloride also have a significant effect
on the acidity of the produced water. In general, chemical species that increase the acidity
of the produced water increase the corrosion rate.
Another important factor that affects the corrOSlOn rate is the nature of the
dispersed and the continuous phases along the production string. Water may form an
emulsion with the hydrocarbon liquid that is present in the downhole environment. Choi
et al. (1989) found a marked increase in the corrosion rate at a water cut of 40% or more.
The increase in the corrosion rate was attributed to the phase inversion from oilcontinuous
phase to watercontinuous phase at water cut values close to 50%. However,
in certain wells pitting corrosion occurred at water cuts less than 30%. The pitting
corrosion was attributed to the flow velocity. The corrosion rate also increased with the
flow velocity, irrespective of the type of emulsion. Choi et al. (1989) reasoned that in the
oilinwater emulsion (o/w) the flow velocity increased both the local turbulence and the
contact time of the water phase with the tubing material. In the waterinoil emulsion
(w/o), an increase in flow velocity increased the corrosion rate by washing off the iron
carbonate protective film and by increasing the mass transfer through the pores of the iron
carbonate layer. luswandi (1995) developed a mathematical model to predict the location
of phase inversion in a gas/oil well and concluded that the oil viscosity and the turbulence
in the liquid phase have a significant effect on the phase inversion.
The flow regime has a profound effect on the corrosion rate. The type of flow
regime present is dependent on the fluid properties and pipe size. Johnson et al. (1991)
11
found that corrosion rates in slug flow could be seven times higher than the corrosion
rates in annular flow. Johnson et aL. (1991) also concluded that the corrosion rates
increased with increasing flow rates because the protective corrosion product film was
washed away by the flowing fluids.
Apart from all the factors discussed above, the nature of the steel used in the
construction of the tubing and casing also deterrnines the corrosion rate. Different types
of steel corrode differently, since their response to flow rates vary (Videm and Dugstad,
1989; Videm and Dugstad, 1987). However, the presence of sman amounts of chromium
was shown to improve resistance to corrosion appreciably (Videm and Dugstad, 1989;
Ikeda et aI. 1984).
2.3 Previous Models for Corrosion Prediction
Various models have been proposed from time to time to predict the nature and
rate of corrosion in a gas well. A brief discussion of the corrosion prediction models
developed at Oklahoma State University is given below.
2.3.1 . The Model of Robertson (1988)
One of the earliest attempts at predicting the nature of downhole corrosion was
made by Robertson (1988). The onset of water condensation was assumed to be the point
in the tubing above which corrosion occurred. Robertson developed an easytouse
12
J
computer program which predicted the location of the water condensation zone in gas
wells. The program, called DOWN*HOLE (Robertson, 1988), combined an existing
thermodynamic phase equilibrium calculation package (Erbar, 1980) with subroutines for
the calculation of the fluid flow phenomena. The subroutines for fluid flow were
developed by Robertson (1988).
The thermodynamic phase equilibrium calculation package calculated the phase
behavior of the produced fluids at high temperature and pressure. The thermodynamic
package of DOWN*HOLE used the industrially tested GPA· SIM (Erbar, 1980), which
used the SoaveRedlichKwong (SRK) equation of state (Soave, 1972) to calculate the
thermodynamic properties. Liquid densities were calculated by the COST ALD method
(Hankinson et al., 1979). The pipeline was divided into 500 feet sections and the
thermodynamic properties were calculated for each section. The SRK equation predicted
vapor densities to within 45% while the liquid phase densities were predicted by the
COSTALD method to within 24% (Robertson et al., 1988).
The fluid flow calculation subroutines, added by Robertson, calculated the
pressure profile along the welJ string. These subroutines used four methods to calculate
the pressure profile along the production string. The pressure profile calculation included
the simple linear pressure profile method, a twophase homogeneous flow method, the
Orkiszewski flow regime dependent correlation method, and the YaoSy]vester mistannular
flow regime method (Robertson, 1988). The linear model assumed a linear
pressure and temperature profile along the well depth. The other three models assumed
either a linear enthalpy profile or a linear temperature profile along the length of the well.
13
After the pressure drop was estimated, the flash calculations were carried out using
GPA*SIM (Erbar, 1980).
The calculation of the surface tension and the fluid viscosity is essential for the
estimation of the two phase flow pressure drop. The surface tension of the fluid produced
downhole was taken to be the surface tension of water at that temperature. Fluid
viscosities were calculated by one of the following three methods:
1. the hydrocarbon liquid phase viscosity is determined by the method of Beggs and
Robinson (1975),
2. liquid water phase viscosity was detennined by a simple curve fit (Robertson, 1988),
and
3. the method of Lee et al. (1966) was used to estimate the gas phase viscosity.
The model of Robertson (1988) generated a pressuretemperature diagram of the
gas well system. The pressuretemperature diagram included the water and hydrocarbon
rich dewpoint curves and a pressure traverse of the production string at a given flow rate
(Robertson et aI., 1988). The program was also equipped with an option to determine the
fluid velocity at various points along the tubing. The differenc·e in the fluid velocity and
the erosional velocity is called the excess velocity. The excess velocity was used as an
indicator of the well corrosivity.
14
2.3 .2 The Model. ofLiu and Erbar (J990)
The first model which predicted the corrosion rate along the depth of the pipeline
incorporating the principles offluid mechanics, mass transfer, and surface reaction rates
was developed by Liu and Erbar (1990). In this model, the key corrosive specie was the
hydrogen ion in aqueous solution. This model predicted unifonn corrosion rates in the
absence of protective films, using the following fonnula:
1
(2.1)
CAO
NAZ = 1 X / 2  AO
where
CAO = equilibrium concentration of the hydrogen ion at the gasliquid interface,
XAO = mole fraction of the hydrogen ion in the liquid film at the gasliquid
interface,
kM = mass transfer coefficient in the liquid film, and
ks = surface reaction rate constant.
The first step in the use of this model involved the use of the DOWN*HOLE
program (Robertson, 1988). The program calculated the downhole temperature and
pressure profile, liquid and gas density, the liquid and the gas flow rate at each section,
and the flow regime of the downhole twophase flow. All these values were used as input
for the corrosion rate calculations.
15
The second stage of the model computed the downhole pH at different depths.
This step gave the equilibrium concentration of the hydrogen ion in the liquid film at the
gasliquid interface.
The third step was the calculation of the twophase flow parameters, the mass
transfer coefficient, and reaction rate constants from data reported in literature (Liu and
Erbar, 1990). The final step involved the corrosion rate calculation from Equation (2.1).
The model neglected the presence of protective films, and predicted the worst case
corrosion rate.
2.3.3 The Model ofLiu (1991)
Liu (1991) modified his earlier model. (Liu and Erbar, 1990) for corroSIon
prediction by including the effect of protective films on the corrosion rate. In this model
Liu also eliminated the need for gross assumptions such as diffusion control or reaction
rate control made in the previous model.
Electrolyte equilibrium computations used in the previous model (Liu and Erbar,
1990) were adapted to the principles of Edwards et al. (1978). The electrolyte equilibrium
module estimated the temperature dependent equilibrium and Henry's constants. The
activities of the molecular species (i.e., CO2 and H2S) were estimated from the Henry's
constants. These relationships were then used to estimate the pH of the system. All
activity coefficients were determined from the work of Kerr (1980). The concentrations
of all other species at the gasliquid interface were estimated from the cal.culated pH.
16
The corrosion rate was calculated by using the mass transfer equations in each of
the following layers: turbulent layer, diffusion layer, and the corrosion product layer. In
this model, the corrosion product layer was considered as another diffusion layer, and the
mass balance equation for the diffusion layer was solved for the corrosion product layer to
yield the concentrations at the pipeline surface.
2.3.4 The Model ofLiu and High (1993)
Further modifications of the corrosion rate calculations were made by Liu and
High (1993) and incorporated into software named DREAM. The phase equilibrium
module used GP A * SIM, but the program structure of GP A * SIM was altered so that the
resulting code was smaller. The threephase flash calculation procedure was changed.
The new flash calculation method used the objective function ofBunz et al. (1991)
The pressure drop calculation module used the flow regime dependent
correlations. The first part of the pressure drop calculation involved the flow regime
estimation; the second part calculated the pressure drop with modified literature models.
Three flow regimes that werte modeled in this program are: bubble flow, slug flow, and
annular flow. Chum flow was included in the slug flow regime. The pressure drop
calculations for bubble flow were taken from the correlation by Orkiszewski (1966). The
slug flow pressure drop was calculated from the model by Sylvester (1987). The pressure
drop in the annular flow regime used the Yao and Sylvester (1987) model and was the
same correlation used by Robertson (1988).
17
Two modifications were made to the uniform corrosion rate calculation module
from the previous model (Liu, 1991). The numerical scheme used in the computation of
the differential equation for the mass balance in the diffusion layer was changed. The
model of Liu (1991) used a process of quasilinearization (Na, 1979) before writing the
equation in the finite difference form. The model of Liu and High (1993) iterarted on the
nonlinear source term to solve the differential equation (Patankar, 1980). The other
change was the modification of the correlation for the diffusivity of the species in the iron
carbonate film. The effective diffusivity was correlated (Liu and High, 1993) based on the
experimental data reported in literature (Ikeda et al ., 1984).
2.4 Electrolyte Equilibrium Modeling
A description of electrolytic systems and the impact of electrolyte equilibrium
modeling on corrosion rate predictions are described in this secti.on.
Various fields ranging from astronomy to zymology are critically dependent on the
nature and the behavior of aqueous electrolytes. Many geological processes are modeled
in terms of the equilibrium existing between the electrolyte (aqueous phase) and the ions
(various mineral phases). Electrolytic behavior significantly affects the metallurgical
operations in the extraction of metals, such as iron and aluminum, and the design of
furnaces. The distribution and the activity of the species in aqueous solutions, affected by
electrolyte behavior, are pertinent to corrosion engineers concerned with pipeline
corrosion and solid deposition in gas and oil wells. Electrolytes control the chemical
18
reaction equilibria Ln aqueous solutions, thereby influencing industrially important
processes such as sour water stripping for pollution control, regenerative flue gas
scrubbing for S02 removal, plating processes, chemical and biochemical unit operations
(e.g., oxidation, fennentation etc. ), and ion exchange operations.
Generally, multiple phases are involved in electrolytic systems. Common industrial
processes involve aqueous electrolytic solutions in equilibrium with another phase. The
other phase could be
1. a vapor (e.g., acid gas scrubbing, distillation ofHN03 or HCI)
2. a liquid (e.g., metal extraction in hydrometallurgy), or
3. a solid (e.g., adsorption, ionexchange).
In downhole gas wells, electrolytes in the liquid phase are in constant contact with vapors
consisting primarily of low molecular weight hydrocarbons (Cl and C2), CO2, and H2S.
The estimation of the vaporliquid and electrolytic behavior is important in the
design of oil and gas wells. Estimation of properties such as phase density, surface
tension, and viscosity affect the pressure drop in gas and oil wells. Pressure drop
calculations and the flash calculations are coupled. Vaporliquid and electrolyte
equilibrium calculations also provide estimates of the quantity and composition of the
various phases present in the downhole environment. The electrolyte equilibrium module
calculates the concentration of all the species at the gasLiquid interface. The liquid phase
concentration of components such as !t, HS, S2, HC03, and CO? detennine the
acidity/alkalinity of the solution. The species at the gasliquid interface are transported to
19
1&
the metal surface where corrosion reactions occur. Thus, accurate estimation of phase
and aqueous electrolyte behavior is essential to predict corrosion rates correctly.
Despite the fact that electrolytic systems are encountered in many disciplines of
science and engineering, the ability to predict their vapor liquid behavior is extremely
limited. When the solvent is sufficiently polar, electrolytes dissociate into ions. The
ionization effects introduce a high amount of nonideality to the system. The presence of
multiple phases further complicates the matter. Although the thermodynamic basis for
such systems has been documented, there is no satisfactory understanding of the physical
chemistry of aqueous systems containing volatile weak electrolytes (Mather, 1986).
Systems containing volatile weak electrolytes are modeled in two steps. Vaporliquid
equilibrium is primarily modeled using classical equations of state. Aqueous
electrolyte equilibrium is described in terms of temperature dependent dissociation
constants. Such modeling introduces error when certain factors such as liquid phase
dissociation and/or liquid phase reactions are neglected while building the model.
Traditional modeling of systems containing volatile weak electrolytes, using cubic
equations of state, has proven to be inaccurate and unreliable (Friedemann, ] 987).
Friedemann (1987) showed that a typical equation of state based flash calculation does not
predict the phase compositions accurately (Table I). While the compositions of the inerts
are predicted quite closely, the acidgas component distribution is inaccurate. This
inaccuracy is glaring in the liquid phase prediction visavis the experimental data of
Wilson (1978).
20
~
.t....I
TABLE I
Comparison of Flash Calculations With and Without Providing for Aqueous Phase Dissociations
Temperature = 300 ~ Pressure = 500 psia
Component Vapor (mol %) Vapor (mol %) Vapor (mol%) Liquid (mol %) Liquid (mol %) Liquid (mol %)
Experimental without with Experimental without with
I
dissociation dissociation dissociation dissociation
NH3 157 2.07 1.75 2.02 1.56 1.84
I
i
CO2 29.20 28.98 2910 060 0.15 0.36
H2S 468 5.00 4.79 0.52 0.08 0.36
i
H2O 13 .93 14.52 14.40 96.83 98.18 I 97. 14
N2 6.40 6.26 6.32 0.0024 0.00 0.00
C~ 10.09 986 997 0.0065 0.01 0.01
H2 34. 13 33 .35 33 .70 0.0227 0.03 0.03
Reference: Friedemann (1987)
""'
The capability of an equation of state to predict the vaporliquid behavior can be
improved by providing for aqueous phase dissociation. Friedemann (1987) used this
approach to improve upon the results obtained in Table I for the system studied by Wilson
(1978). The improved results have also been tabulated in Table 1. A comparison of the
flash calculation results indicate that the inclusion of the aqueous phase dissociations
reduced the error in the composition prediction of acidgas components by nearly twothirds.
Aqueous phase dissociation can be described in terms of the following generalized
ionic equilibria.
AB H A + + B (2.2)
The ionic equilibrium can be described in tenns of the equilibrium constant and the ionic
activities as given below.
K (2.3)
TypicaJly, concentrations are expressed in terms of molality and ionic activity coefficients.
Ionic activity coefficients are calculated from empirical models.
The ionization effects can be studied by means of molecular and empirical models.
Molecular models are based on the effects of the various types of forces on the structural
and thermodynamic properties and are defined by particle interactions. Empirical models
are usually derived from excess Gibbs energy or the Helmholtz energy (Renon, 1986).
Various properties such as mean activity coefficients of molecular solutes, excess partial
22
molar volumes, enthalpies, entropies, and heat capacities can be derived from the excess
Gibbs energy or the Helmholtz energy.
This work utilizes a combination of molecular and empirical models to describe the
phase and electrolyte equilibrium in gas wells. The generalized thermodynamic framework
is based on a molecular approach by Edwards et a1. (1978). The constituent properties
required to complete the framework are based on empirical approaches and are described
in detail in Chapter III of this work.
An important feature of any empirical approach is the number of adjustable
parameters. In the electrolytic systems encountered in most industries, there are numerous
species resulting in a large number of binary or even ternary interactions. The inability to
measure binary interaction parameters, directly and independently (Renon, 1986),
necessitates multiproperty, multiparameter regression. Approximate methods are
available for parameter regression, the specific problem is to take into account many
properties at the same time, to check the validity of the parameters and the model, and
achieve the phase equilibrium computations. Using a model with a very sman number of
adjustable parameters would therefore be advantageous.
A new approach to predicting phase equilibria by Chen et a1. (1994) has been used
in this work. This model uses a single molecular interaction parameter for aqueous binary
mixtures. The model has the capability to predict phase equilibria for light hydrocarbons
and inert gases encountered in gas wells using the SoaveRedlichKwong equation of
state. Further, this model has been extensively tested over an extensive range of published
23
experimental data. Chen et al. (1994) indicated that the model predicted partial pressures
with errors on the order of the uncertainty in the experimental measurements.
2.5 The Phase Equilibrium Model used in DREAM
Phase equilibrium calculations give the quantity and composition of the liquid and
vapor phases at every point along the gas well. The rate of corrosion depends on the
amount of condensed water in the tubing and the concentration of the acidic components.
The change in the temperature and pressure from the wellhead to the bottomhole changes
the amount of water condensed at various locations in the well.
The SoaveRedlichKwong (Soave, 1972) equation of state used to model the
behavior of the molecular components in both the vapor and the liquid phases is described
below:
P
RT aa
(Vb) V(V+b)
where a, b, and a are constants and are given by:
a =
b
0.08664 R Tc
P c
a = [ 1 + (0.48508 + 155171 ro 0.15163 ro2)(1  Tro5) f
(2.4)
(25)
(2.6)
(2.7)
In Equation (2.7), ro is the pure component acentric factor and can be taken from
GPA*SIM (Erbar, 1980). Tr is the reduced temperature and is given by:
24
(2.8)
F or mixtures the following rules apply:
(2.9)
(2.10)
(b) rru.x =L".... x·I b·, (2.11)
where Cj is the binary interaction parameter. The values for Cjj are taken from GPA ·SIM
(Erbar, 1980) for all binaries. The interaction between different species in the fluid can be
categorized as
1. moleculemolecule interaction
2. ionion interaction
3. moleculeion interaction.
These interactions can be binary, ternary, or even higher (i.e., multiple particle interaction)
in nature. Studying or accounting for all of these interactions in the model is virtually
impossible. To simplify the computation process only binary moleculemolecule
interaction is accounted for and is defined in Equation (2.10).
Flash calculations estimate the quantity of the liquid and vapor at any point in the
system. The vaporliquid equilibrium constant, Kj,VLE, is calculated as a ratio of the
fugacity coefficients.
,J,L
K '1',
i ,VLE = Qljv (2.12)
The vaporliquid equilibrium constant values are used in the flash calculations. The two
25
phase flash calculation can be determined from the RachfordRice criterion (Smith and
Van Ness, 1987):
f(L/F) = = 0 (2 .13)
Equation (2.13) was solved by means of a NewtonRaphson iteration technique by
providing an initial guess for the value ofLIF.
The fugacity coefficients can be calculated from the SRK equation of state using
the following formulae:
bi • A ' 2 (aa:)i b· B·
In cj) = b  (Z  1)  In (Z  B )   . [(  _I ] In ( 1 + )
mix B aa:)ij bmix Z
where,
bmix P
RT
The compressibility factor, Z, can be calculated from Equation (2.4) rewritten as:
26
(2.14)
(2.1 5)
(2.16)
(2 .17)
.. ....
i:1
• , I
• I c"')
III ~ .l
IS!
II , C>
'I
CHAPTER 3
MODEL DEVELOPMENT
The principal objective of this work, is to establish a consistent, generalized
framework for the phase and electrolyte equilibrium computations required for corrosion
prediction in downhole gas wells. This chapter discusses the physical model of the
downhole system, the generalized electrolyte equilibrium model developed as part of this
work, and the numerical technique for coupled phase and electrolyte equilibrium
calculations.
3. 1 Physical Model
The system downhole can be described as one in which natural gas, with or
without formation water, leaves the reservoir and enters the tubing at high temperature
and pressure (Liu, 1991). The decrease in pressure and temperature experienced by the
upward flowing gas, may cause water condensation to occur in some part of the well. The
gas flow rates in most of the wells encountered are very high, so the flow is in the annular
or the slug flow regime.
The downhole corrosion phenomenon has been viewed as a three layer model as
shown in Figure 1 (Liu, 1991). The three layers are the turbulent film layer, the diffusion
layer, and the corrosion product layer. The corrosive species at the gasliquid interface
27
~
0 a::
~
"iii
Q) .. > ....
02 ~ II
 > (J~
~ Cb .£ E ~ > ~ ~a c I  0 £:=
c: om
Q) ::I ~~
S  ... :;, If L.a. j5 • ::I 0 f ~
~ .. < I ....
1:1
, II .• )
~ ~=X:l
!S!
.1 C)
Figure 1 Physical Model of Downhole System
28

are first transported through the turbulent liquid film. interfacial shear and wall roughness
strongly influence the transport of the various species through the turbulent layer. In the
diffusion layer, molecular diffusion and ion migration are the dominant mechanisms. in a
multicomponent corrosion process encountered downhole, surface electrochemical
reactions set up an electric field. Hence, the mass transport expression in the diffusion
region includes the effect of the concentration gradients and the electric potential. Finally,
the corrosive species diffuse through the corrosion product layer to reach the metal
surface. Corrosion reactions occur at the tubular surface, and a corrosion product may be
formed . The corrosion product layer protects the piping material. The diffusion of CO2
and H2S through the corrosion product layer is highly dependent on the temperature ( de
Waard et aI. , 1991 ; Ikeda et aI., 1984; Kuznetsov, 1981; Shoesrnith et al., 1980).
The system encountered downhole can be represented by Figure 2. At a given
temperature and pressure, the weak electrolyte and water will equilibrate between the
liquid and the vapor phase. In the liquid phase, weak electrolytes exist in two forms:
molecular and ionic. The chemical equilibrium between the molecular and ionic forms of
the electrolytes is described by the dissociation constant. Electrolytic dissociation occurs
only at very high temperatures in the vapor phase. Such high temperatures are not
prevalent in gas wells. Therefore, vapor phase dissociation was neglected.
In Figure 2, the phase equilibrium is determined by the molality of the molecular
(not ionic) solute; that molality is in tum affected by the chemical dissociation equilibrium.
Since ions are not volatile, the phase equilibrium of the system is not governed by the total
electrolyte concentration in the liquid phase; only by the concentration of the liquid phase
29
Gas Phase (T, P)
Molecular Electrolyte (H20, CO2, H2S)
Molecular Electrolyte ~ .. Ions
(H20 , CO2, H2S)
Ions: W, Off, HC03, C03  , HS, SN
a+, K+, Sr ++ , B a++, C a++ , M g++ , F e++ , C], SO4 
Liquid Phase (T, P)
Figure 2 VaporLiquid Equilibrium in a Downhole System
30
I
II
electrolyte that exists in the molecular (undissociated) form.
3.2 Model Fonnulation
The equilibrium conditions for phase equilibria can be derived using the concept of
Gibbs free energy, G. For an open system with n components, like the one considered
downhole, the condition of equilibrium can be written as:
dGl = S dT + V dP + I Ili dni (3 .1)
where !li is the chemical potential of component i and is defined as the change in the Gibbs
free energy of a system as a result of the addition of dni moles of component i at constant
temperature and pressure, holding the moles of the other components constant.
According to the second law of thennodynamics, the total Gibbs free energy of a
closed system at a constant temperature and pressure is minimum at equilibrium, i.e. ,
dGt=O (3 .2)
• I
Figure 2 depicts the downhole system at equilibrium. At the gasliquid interface at ., ,c.
II ~~;
I~~
I C)
Equation (3.2) reduces to
i.e ., the chemical potential of component i in the liquid phase and the vapor phase are the
same. The chemical potentials can be related to the mole fraction (or concentration) by
means of the fugacity as follows:
dlli = RT d In fi (3.4)
The fugacity of the ith component in a mixture is defined as
31
(3 .5)
From Equation (3 .3) and Equation (3 .4) the following condition exists at equilibrium:
(3 .6)
Substituting Equation (3 .5) into Equation (3 .6):
(3 .7)
The gasphase mole fraction, Yi, is known. The fugacity coefficient, cP, is calculated for
both the vapor and the liquid phase using the SoaveRedlichKwong equation of state as
described in Chapter II (Equations 2.4 to 2.17). The calculation of the liquid phase mole
fraction, Xi, is described in this chapter.
The following assumptions were made in the model development:
1. The concentrations of the species across the gasliquid interface are In
thermodynamic equilibrium.
2. The system is at steady state.
3. Electroneutrality holds in the bulk liquid and also at the liquidsolid interface.
4. All the inorganic ions present in the formation water do not necessarily take
part in the corrosion reactions but do contribute to the electroneutrality of the
solution.
5. Precipitation is a sufficient condition for film formation.
6. Iron dissolution kinetics are neglected
This model uses assumptions (1) and (2) to determine the concentrations of the
species in the liquid and vapor phases. These concentrations are used to estimate the pH
32
of the system and the boundary conditions in the mass transport expressions for the
subsequent three layers.
3.2.1 Concentration at the GasLiquid Interface
The thermodynamic analysis of aqueous weak electrolytes in this model is based on
the following four principles outlined by Edwards et al. (1978)
1. Overall mass balance in the liquid phase,
2. Electroneutrality in the bulk liquid,
3. Chemical equilibrium between the undissociated (molecular) and the
dissociated (ionic) forms of the weak electrolyte in the liquid phase, and
4. Vaporliquid equilibrium for the molecular solute.
The equilibrium relationship at the gasliquid interface can be summarized as
follows (Sundaram et al., 1996):
(3 .8)
(3 .9)
The ionic dissociation reactions at the gasliquid interface are given below:
(3 .] 0)
(3 .11 )
(3 .12)
IfH2S is present, the following relations are included:
33
(3 .13)
(3.14)
(3 .15)
The tubulars and casings could react with the carbonk acid or the sulphurous acid
present and fonn iron carbonate, calcium carbonate, and/or iron sulfide. The corrosion
product layers so fanned could retard the rate of corrosion in the gas well. This model is
based on the assumption that precipitation is a sufficient condition for film formation . In
the presence of these protective corrosion product films, the following relations should be
taken into consideration.
(3.16)
(3.17)
(3 .18)
The assumption of electroneutrality for the mixture of charged species can be written as:
(3 .19)
where Zj is the charge associated with the ilb ionic species and mj is the corresponding
concentration.
A mass balance between the undissociated and the dissociated forms of the
molecular species yields the following two equations:
(3.20)
(3.21)
34
The variables appeanng 10 Equation (3 .20) and Equation (3.21) have units of
concentration (mole/kg solvent).
For dissociation of the molecular and the ionic species the following relations hold:
K J co , 2
ID H+ mOHo Y H+ Y ow
IDH20Y H20
mHCO)Y HCO) mH+ Y H+
m H10 Y H20 mCOl Y cO2
mcol Y CO/ ffiH+ Y H+
mHC03 Y HCO)
ffi HS' Y us' ffiH+ Y H+
ffi H2SY H2S
m g2' Y g2. ffiH+ Y H+
ffiHg Y Hg
(3.22)
(3 .23)
(3 .24)
(3 .25)
(3.26)
The solubility products of the corrosion product layers are estimated from the
[oHowing relations
KSP CaCOJ =
Kgp FeS
m Fe2+ Y Fe2+ ffi C032 Y cola
FeC03
mCa1+ Y Ca2+ mcol Y CO)2
aCaCo3
mFe2+ Y Fe2+ mg2. Y S2
a FeS
(3.27)
(3 .28)
(3 .29)
Equations (3.19 and 3.22 to 3.29) contain 9 equations and 9 unknowns (viz. ,
All the
35
unknowns can be expressed in terms of mH+ and substituted into Equation (3.19) and
solved to obtain the following expression involving the molality of the hydrogen ion:
where,
KSp FeS
Kw Y H20 mH20
Yow Y H+
K1, CO2 mC02 Y CO2 mH20 Y H20
Y H+ Y HCO)
36
(3 .30)
(3.31)
(3 .32)
(3 .33)
(3 .34)
(3.35)
(3 .36)
(3 .37)
(3.38)
(3 .39)
(3.40)
K1, c 0 2 K2,c02 m H20 'YH20 m C02 'YC02
Y col
K 1, H2S K 2, H2S m H1S YH 2S
'Y 52
(3.41)
(3.42)
The corrosion rate along the well depth also depends on the ionic species present
in the produced water. The quantity of the ionic species present in the production water is
estimated from the water analysis. Generally, the water analysis supplied for the
prediction of corrosion rates is not electroneutral. In this work the sodium Ion
concentration is adjusted to satisfy the charge balance.
The solution of Equation (3 .30) yields the pH from which the concentrations of all
the other species are calculated. The estimation of the parameters and the constants
required for solving Equation (3.30) are detailed in the remaining part of this section.
Chemical dissociation constants are strong functions of temperature and very weak
functions of pressure (Helgeson, 1969). AU dissociation constants used in this work are
functions of temperature alone. The chemical dissociation constants used in this work are
calculated using the correlations by Edwards et a!. (1978) and Kawazuishi and Prausnitz
(1987). The generic equation for the dissociation constant can be expressed as:
In Ki = Bi, 1 / T + Bi, 2 In T + Bi, 3 T + Bi,4 (3 .43)
The constants Bi,j are given in Table II.
The solubility products of the corrOSIon product layers are also functions of
temperature. Liu (1993) fit the following equation for the solubility product of iron
carbonate to the data reported by Garrels and Christ (1965).
37
TABLE II
Temperature Coefficients for Equilibrium Constants
Species Bj, l Bj, 2 Bj , 3 Bi,4 Valid Reference
Range [>C)
CO2 12092.1 36.781t 0.0 235.482 0225 I
H2S 18034.7 78.071 <; 0.092 461.716 0275 2
HC03' 12431.7 35.481 <; 0.0 220.067 0225 1
HS' 406.004 33 .889 0.054 214.559 0225 2
H2O 13445 .9 22.4773 0.0 140.932 0225 1
Reference 1: Edwards et al. (1978)
Reference 2: Kawazuishi and Prausnitz (1987)
38
2784.51
In Ksp CaCOJ = 65.92499  0.09288796 T + 14.6247 ]n T 
T
(3.44)
The data reported by Helgeson (1969) for the solubility products of iron carbonate
and iron sulfide have been correlated (Liu, 1993) as:
In K spFeC03 = 20.0717 + 0.003165 T  6.318 X 105 T2
4
In K spFeS = 3l.0813 _ 2.02024 x ]0 _ 2.0026 x log (T)
T
(3.45)
(3.46)
The activity coefficients of the ionic species are calculated by the Bdot method
(Lewis and Randall, 1961) using the following expression by Helgeson (1969)
(3.47)
where I is the ionic strength defined by
(3.48)
The activity coefficient is the ratio of the activity of a substance and the
concentration of the substance. The activity coefficient can be defined to take a value of
unity under ideal conditions. Two types of ideality are generally used: one leading to
Raoult's law and the other leading to Henry's law (Prausnitz, 1969)
If the activity coefficients (y) are defined with reference to a solution that is ideal
over the entire range of composition (Raoult's law) then for both the solute and the
solvent
y ~ l.0 as x ~ 1.0 (3.49)
If the activity coefficients are defined with reference to an ideal dilute solution, then the
following two equations hold:
39
11 ~ l.0 as XI ~ l.0 (Solvent) (3 .50)
12 ~ 1.0 as X2 ~ 10 (Solute) (3.51)
The Henry's constants are defined as the ratio of the fugacity to the concentration in a
dilute solution.
H= (3.52)
The activity coefficient represents the deviation from ideality. The deviation for
the completely dissociated solute is given by the first term in Equation (3.47). Charged
ions exert longrange electrostatic forces upon one another even in dilute electrolytic
solutions, lowering the activity coefficients significantly (Garrels and Christ, 1965). The
effects of the longrange electrostatic forces have been evaluated using the DebyeHuckel
theory and several usefuJ equations similar to Equation (3.47) have been proposed to
evaluate activity coefficients (Lewis and Randall, 1961; Klotz, 1950). The activity
coefficients are expressed in terms of the molal DebyeHuckel parameters (A and B) and
are functions of temperature (Helgeson, 1969):
__ l.8246 x 10\[;;;;
A
(8w T)3 1 2
(3 .53)
(3.54)
where pw represents the density of water and Ew represents the dielectric constant of water.
An equation was fit (Liu, 1993) to the density and dielectric constant of water data
reported by Helgeson (1967).
40

The term aO in Equation (3.47) represents the distance of closest approach of ions
in an electrolyte solution. Thus aO may be thought of as the effective diameter of the
particular species in solution. This quantity is an empirical parameter, but has a magnitude
slightly larger than values of ionic diameters. The deviation in the value of the ionic
diameter is possibly due to the envelope of the water molecules that surround the ions in
aqueous solution (Garrels and Christ, 1965). The values for aO used in the model are
those reported by Klotz (1950). The value of aO varies significantly with temperature.
Due to the lack of data for most ions at higher temperatures and the absence of any
computational procedure available in the literature (Helgeson, 1969), the values for the
hard sphere radius available at 25°C are used in the model.
The second term in Equation (3.47) represents the deviation of the ionic activity
coefficient from that prescribed by the DebyeHuckel expression at 25°C. This deviation
function is represented by the term bO and accounts for the short range (Van der waals)
interactions between solute species. These interactions are of three types (Edwards et aI. ,
1978):
(1) moleculemolecule,
(2) ionion, and
(3) moleculeion.
The quantity bO has been found to be dependent on temperature, but independent of
concentration at ionic strengths of 0.5 or more in most electrolyte solutions at 25°C
(Helgeson, 1969). Helgeson (1969) concluded that bO approaches zero at temperatures
41
close to 300 °c. A correlation has been fit (Liu, 1993) to calculate the variation ofbo with
temperature using the data reported by Kharaka et at. (1988) and Helgeson (1969).
The activity coefficients of the molecular species are calculated by a different
procedure. The activity coefficients of CO2 and H2S are calculated as the ratio of the
Henry's law coefficients in an electrolyte of given concentration (m) to that in pure water
(Kharaka and Mariner, 1985; Helgeson, 1969).
¥ C02 = Hm, CO2 / Hw, CO2 (3.55)
¥H2S = Hm, H2S / Hw, H2S (3.56)
The generic equations for the Henry's constants for H2S and CO2 are functions of
both temperature and molar strength (Kharaka et aI., 1988) and are given below:
In (Hco2 ) = 21.2572  O.017603T  1.0312Ms 
0.0012806 T
+
3885.6
T
2021 .5
In (HH2s) = 11.1255  0.0071704 T  0.2905 Ms  T
46.2 Ms
 0.0001574 T Ms  T
0.001777 T
where Ms is the molar strength defined by
Ms = 0.5 L Zj m i + 1. 0
+
+
0.4445
Ms
0.5705
Ms
(3.57)
(3.58)
(3.59)
The Henry's law coefficients for CO2 and H2S in an electrolyte are calculated by using the
molar strength of the electrolyte from Equation (3 .59). The Henry's law coefficients for
CO2 and H2S in water are calculated by using a value of 1.0 for Ms in Equation (3.57) and
Equation (3.58).
42
The activity of water in dilute solutions is calculated using the following formula
(Kharaka and Mariner, 1985; Garrels and Christ, 1965)
Ymo = 1  0.017 L ffij (3.60)
32.2 Coupled Phase and Electrolyte Equilibrium Calculations
A new method for the computation of phase and electrolyte equilibrium, based on
the work of Friedemann (1987) with interaction parameters for phase equilibrium
calculation from Chen et al. (1994) has been incorporated in this work. The model
calculates the dissociation of the weak electrolytes in the liquid phase and uses the
corrected value of the concentrations to update the vaporliquid equilibrium constants.
As discussed in Chapter II of this work, accurate modeling of the phase behavior
of the weak electrolytes should include liquid phase dissociations of the molecular species.
CO2 dissociates into HC03, and CO/, while H2S dissociates into HS, and S2. The
extent of dissociation (di) of the molecular species is calculated by the following
equations:
d 1
m I (3.61)
M · I
where mj is the actual (undissociated) concentration of the molecular species in the liquid
phase and Mj is the apparent concentration (sum of the undissociated and the dissociated)
of the molecular species in the aqueous phase.
43
• I '\ I
II i
,,~~ l::t'
.ct~
'S~ C)
The effect of the dissociation of the molecular species on the phase equilibrium is
incorporated with the vaporliquid equilibrium calculations. For the liquid phase the
component K, VLE values are corrected to include the extent of dissociation of the weak
electrolytes as follows:
K Yi
i,YLE = ~
I 1
(3 .62)
Phase equilibrium calculations are continued with the corrected K;,VLE values.
Chen et al. (1994) performed bubble point calculations for various aqueous binary
systems. The results were used to fit binary interaction parameters for these systems. For
systems of interest to us (C02H20 and H2SH20) a single molecular interaction
parameter has been fit and is given below
131
C· co = 0.457  1J . 2 T
104
C·· H S = 0.432  1J, 2 T
where T is the temperature in Kelvin.
3.3 Numerical Implementation
(3.63)
(3.64)
The numerical implementation of the model can be described in terms of two major
loops. The outer loop accomplishes the phase equilibrium calculations. The inner loop
computes the composition of the molecular and the ionic species in the aqueous liquid
phase (electrolyte equilibrium computations).
44

3.3 .1 Phase Equilibrium Computations
The overall computation procedure for the phase and electrolyte equilibrium computations
is depicted in Figure 3 and is described below
1. The vaporliquid equilibrium constants (Ki,VLE) are calculated from Equation (2 .16).
2. The dissociation constants are computed (Equations 3.22 to 3.29).
3. An iterative calculation is performed to estimate the pH.
4. The concentrations of all the molecular and ionic species are calculated from the pH
and the dissociation constants.
5. The aqueous phase dissociations of the molecular specIes are then computed
(Equation 3.61)
6. The vaporliquid equilibrium constants are modified by including the aqueous phase
dissociations (Equation 3.62).
7. The phase equilibrium is checked by checking for convergence in the values of K;,VLE.
If the phase equilibrium condition is satisfied then corrosion rate computations are
initiated.
3.3 .2 Electrolyte Equilibrium Computations
The electrolyte equilibrium computation procedure is represented pictorially in Figure 4
and is summarized below:
I. An initial value for pH is calculated by neglecting all second dissociations.
45
• I ::?:!
.1 • :::t~
'~~
C)
No
Start
Get VLE K Values
Calculate Dissociation
Constants
Estimate pH
Compute Dissociation
of Molecular Species
Compute Effective K
Values
Figure 3 Flow Diagram for Phase Equilibrium Calculation
46
.........
') ' ... IQ
.>
'ooC I::
,:;)
;~
:~ •
:~I : :r.: I
No
Start
Guess pH
Calculate Composition
of all Species
Compute Coefficients
of Equation (3.30)
Solve Equation (3 .30)
Compute pH and
Concentrations
Yes
End
Figure 4 Flow Diagram for Electrolyte Equilibrium Calculation
~7
2. The pH value calculated in step 1 is used to estimate the compositions of all other
molecular and ionic species.
3. The coefficients of the fourth order equation (Equation 3.30) are computed from the
known value of concentrations calculated in step (2) and step (3).
4. The fourth order equation (Equation 3.30) is solved by the bisection method. This
gives a new value for the pH.
5. The concentration of all other species is calculated from the new value of pH obtained
in step 5.
6. A check is made to ensure that the charge balance converges within a prespecified
tolerance limit.
3.3.2.1 Solution ofthe Fourth Order Equation
The most important step in computing the concentration of the species at the gasljquid
interface lies in obtaining the correct solution for the fourth order equation
(Equation 3.30). A detailed descripti.on of the nature of the roots of the above equation
and the solution procedure is given below.
A fourth order equation has four roots. These roots may be real (positive or
negative) or complex. Equation (3.30) is expressed in terms of the concentration of the
hydrogen ion. The point of interest as far as this work is concerned is in finding the
correct positive root of the equation.
48
The nature of the roots of Equation (3 .30) were examined. If F(x) denotes a
polynomial function in 'x', then according to the Descartes rule of signs (Niles, 1978):
1 . There can be no more positive roots than the number of changes of sign in
F(x). The number of positive roots may however be smaller by an even integer
because complex roots always occur in pairs.
2. There can be no more negative roots than the number of changes of sign in
F(x). The number of negative roots may however be smaller by an even
integer because complex roots always occur in pairs.
The constants Aj that appear in Equation (3.30) are functions of equilibrium constants,
activity coefficients, and concentrations and are always positive. From Equations (3 .31)
to Equation (3.42), we know that
• AI and A2 take a positive sign
• A3 and ~ take a negative sign
.....
Based on the Descartes rule of signs (Niles, 1978), Equation (3.30) has only one ~ '':':
positive root. There are two possibilities for the coefficients in the fourth order equation
(Equation 3.30):
• Al term takes a zero value, or
• Al term takes a nonzero value.
The specific case of the Al term being non zero is taken up for analysis here. To aid the
above analysis let Equation (3 .30) be represented as FCmH+).
1. The number of changes of sign in F(mH) is ] .
2. Hence the maximum number of positive roots for this equation is 1.
49
CHAPTER 4
RESULTS AND DISCUSSION
This chapter describes the results obtained as part of this work and discusses the
interpretation of these results. The effect of the new method of phase and electrolyte
equilibrium computations (Chen et aI., 1994) has been evaluated, and the results have been
compared with experimental data. A similar evaluation of the old phase equilibrium
module (Liu and High, 1993) has also been performed to measure the improvement in the
prediction of the system pressure for the two binaries (COr H20 and H2SH20). The
effect of the new phase equilibrium module on the corrosion rate prediction has been
studied. Manual calculations were perform.ed and the results were compared with those
from the program to validate the computer code developed as part of this work.
The performance of the model of Chen et al. (1994) and the model of Liu and
High (1993) have been evaluated by performing classical bubble point checks at specified
temperatures. The modeling results obtained for the bubble pressure predictions were
compared with experimental data.
The phase and electrolyte equilibrium model has been incorporated into DREAM.
DREAM has been evaluated, and the effect of the electrolyte equilibrium on the corrosion
rate has been studied using sixteen test cases. The corrosion rates predicted by the old
and the new model were compared with field data.
51
......
~ a >
04 " ~
~
~
.~...
7:1
I
I
_i
) ::t4
ct~
I s~
c)
3. Number of changes of sign in F( mH +) is 3.
4. The maximum number of negative roots for Equation (3 .30) is 3.
5. If there are less than three negative roots for Equation (3 .30) then the equation can
have only one negative root.
6. If there is only one negative root then there are two complex roots.
7. So in this case, Equation (3.30) has
• I positive root and 3 negative roots, or
• 1 positive root, 1 negative root, and 2 complex roots.
A similar analysis proves that Equation (3 .30) has only 1 positive root even if Al is zero.
Since the system has only 1 positive root the equation is solved by bisection which
guarantees the calculation of the one real, positive root.
50
r.1
I 2!
~)
::1::
4Ctf
I .~
04 C,
.....
The accuracy of the computer code developed as part of this study for the phase
and aqueous electrolyte equilibrium calculation has been verified. In order to verify the
accuracy of the FORTRAN subroutines developed, manual calculations were performed
for one test case; and the results were compared with the values calculated by the code.
The details of the manual calculations and the comparison with the values calculated by
the code are given in Appendix B. The liquid phase concentrations calculated manually
were found to deviate only in the 6th significant figure from the concentrations computed
by the FORTRAN code. The difference can be attributed to roundoff errors.
The following formulae have been used in Section (4.1) and Section (4.2) for the
purpose of statistical analysis:
Percentage deviation in property 'Y', D
Bias in property 'Y', b =
L (D)
N
Average absolute % deviation, AAPD
Yal  Y
( . c c e,,:p ) X I 00
Yexp
L Absolute (D)
'' x 1 00
N
4.1 Analysis of the CO2H20 System
(4 .1 )
(4 .2)
(4.3)
A total of 266 data points from Stewart and Munjal (1970), Takenouchi and
Kennedy (1964), Wiebe and Gaddy (I939), Zawisza and Malesinska (1981), Gillespie et
aL (1986), and Muller et al. (I988) were used to evaluate the model performance for the
CO2H20 system. A wide range of temperature (32 OF  662 Op) and a wide range of
52
pressure (86 .9 psia  22,038.2 psia) were covered in the analysis. Experimental values of
temperature and the liquid phase composition of CO2 were used to calculate the bubble
point pressure of the COr H20 binary. The calculated bubble point pressures and the
experimental bubble point pressures were compared, and the results are summarized in
Tables III and IV.
Table III gives the summary of the results for the CO2H20 system. The average
absolute percentage deviation (AAPD) for the model ofLiu and High (1993) is 48.9 %.
The AAPD is 14.5 % for the model of Chen et al. (1994). The bias ( average) is 24.1 %
for the model ofLiu and High (1993) and 2.0 % for the model of Chen et al. (1994). For
the individual authors studied as part of this work, the AAPD varies from 119.1 % to
20.4 % for the model ofLiu and High (1993). For the model of Chen et al. (1994), the
corresponding AAPD is 31.3 % to 5.5 %. The model of Chen et al. (1994) performs
better for each of the individual authors studied.
Table III also presents the results of the CO2H20 system classified by reference
for the models of Liu and High (1993) and Chen et al. (1994). This analysis has been
done, because considerable differences exist in the experimental studies conducted by
different authors (Chen et aI., 1994).
Figure 5 shows a plot of the AAPD as a function of the total system pressure (on a
semilogarithmic scale) for both the models studied. The model of Liu and High (1993)
shows a wider scatter than the model of Chen et al. (1994) over the entire range of
pressure studied. The scatter is particularly significant at pressures below 5,000 psia.
53
VI
~
1
TABLE III
Summary of the Calculated vs. Measured Bubble Point Pressures for the COr H20 System
Reference Number Temperat Pressure Range Average Bias Average Bias
of ure (psia) Absolute % (Liu and Absolute % (Chen et
Points Range Deviation High) Deviation al.)
(oF) (Liu and High) (Chen et al.)
1 12 32  77 147  661 37.0 32.4 28.7 7.2
2 115 230  662 1469.2  22038.2 20.4 175 5.5 0.9
3 62 53  167 367.5  10290 50.3 46.5 16.5 3 .5
4 15 302  392 111.5  669.3 119.1 117.6 7.6 6.3
5 20 60  250 100  2940 87.1 54.0 31.3 16.6
6 42 248  392 86.91175.9 79.9 13.1 26.7 5.7
Summary 266 32  662 86.9  22038.2 48.9 24.1 14.5 2.0
1. Stewart and Munjal (1970)
2. Takenouchi and Kennedy (1964)
3. Wiebe and Gaddy (1939)
4. Zawisza and Malensinska (1981 )
5 Gillespie et aL (1986)
6. Muller et al. (1988)
}J<J.4Hf '1\1114 "Jiil£l ULUfLJ.lWJ ........
"' ... a...L,.IiA. ........ __ ._
o AAPD (Chen et al ,)
+ AAPD (Liu and High)
600,00
+
,..
?f? ~
0
'+=1 +
CI:I ' ~ 400.00
II)
Cl
(!)
.~.... ~ +
II)
.(...).
II)
t:l..
II) * .
~
"0 +
<Il
.0 < 200,00 + + II) + 0.0
.C.I.:.I II) > <
+ 8
* +t + + t :t+' + +
+
0.00
10,00 100,00 1000.00 10000.00 100000.00
System Pressure (psia)
Figure 5. Average Absolute Percentage Deviation in the Calculated Bubble Point
Pressure as a Function of the System Pressure for the CO2H20 Binary
55
....
r..
Table IV classifies the results obtained for the CO2H20 binary by isotherms. A
classification of the data points by isotherm has been done because most authors have
measured the liquid phase composition of CO2 along isotherms, moving from higher to
lower pressures. Figure 6 plots the AAPD as a function of temperature. From Figure 6
and Table IV it can be concluded that the model of Chen et al. (1994) performs better
than the model of Liu and High (1993) at every i.sotherm studied. For the individual
isotherms analyzed the AAPD of the model of Chen et at. (1994) varies between 1.04 %
and 32.70 %, while for the model of Liu and High (1993) the variation in the AAPD is
between 3.13 % and 97.11 %.
4.2 Analysis of the H2SH20 System
A total of 472 data points from Selleck et al. (1952), Gillespie and Wilson (1980),
Clarke and Glew (1971), Wright and Maass (1932), and Lee and Mather (1977) were
used to evaluate the model performance for the H2SH20 system. Temperatures range
from 32 OF to 600 OF; the pressure range was 5.3 psia to 3,000.0 psia. Experimental
values of temperature and the composition of H2S in the liquid phase were used to
calculate the bubble point pressure of the H2SH20 binary. The calculated and
experimental bubble point pressures were compared. The deviations are summarized in
Tables V and VI.
For this set of data, average absolute percentage deviation (AAPD) is 53 .0 % for
the model ofLiu and High (1993) and 8.6 % for the model of Chen et al. (1994). There is
56
I
r>o!
' ) • <t' ..:~
'">
,
TABLE IV
Calculated vs. Measured Bubble Point Pressures for the CO2H20 System Classified by
Isotherms
Temperature Number Pressure Range Average Average
(oF) of (psia) Absolute % Absolute %
Points Deviation (Liu Deviation (Chen
and High, 1993) et aI., 1994)
32.0 3 147.0  441.0 96.90 18.53
41.0 3 147.0  558.6 96.89 28.93
50.0 3 147.0  558.6 96.94 32.70
53.6 6 735.0  4410.0 7.44 6.78
54.3 1 661 .5 6.33 2.37
60.0 1 735.0 30.85 1.04
64.4 7 367.5  4410.0 17.24 21 .89
77.0 6 294.0  5880.0 61.35 21.67
85 .0 1 800.0 83 .74 6.91
87.9 II 100.0  7300.0 65 .11 30.10
95 .0 8 367.5  7350.0 54.53 16.37
104.0 9 367.5  7350.0 5721 15 .89
122.0 11 367.5  10290.0 67.78 22.06
167.0 14 100.0  10290.0 97.11 26.23
200.0 4 367.5  2940.0 68 .39 28.95
230.0 15 1469.2  22038.2 13 .44 4.77
248.0 7 86.9  413.0 79.44 28.75
"
250.0 5 100.0  2940 .0 50.64 14.36
284.0 7 94.3  470.8 67.01 9.27
302.0 20 111.5  22038 .2 95.46 6.05
320.0 7 127.3  504.6 54.63 9.76
347.0 5 173.6  591.6 35.33 10.66
356.0 7 208.7  909.1 56.85 15 .05
392.0 34 267.4  22038.2 50.08 22.55
482.0 15 1469.2  11753.7 18.89 8.10
500.0 15 2938.4  22038.2 15.36 4.86
518.0 12 2938.4  17630.6 19.48 4] 0
527.0 10 1469.2  11753.7 27.53 74.~
572.0 ]0 1469.2  8080.7 25.85 606
617.0 6 . 2203.8  5876.8 18.29 492
662.0 3 2938.4  4407.6 3.13 2.35
57
It
....

o AAPD (Chen et al.)
+ AAPD (Liu and High)
600.00
+
,..,
0
0
'' c
0
',p + ~:> 400.00 II)
0
II)
..~.... c +
II)
u.... Q)
Il..
II) ..:.:.s.. + ::j:
0 +
V1
.0 < 200.00 + +
II) tlJ) +
.~... + II) +++ > + + + + < :tt+ + ::j: + !
+++ +c&±, Cl 8 0 + t + !tt ::j:
+ 4 !
+ +++ +
0.00
+ ,
0.00 200.00 400.00 600.00 800.00
System Temperature (F)
Figure 6. Average Absolute Percentage Deviation in the Calculated Bubble Point Pressure
as a Function of the System Temperature for the COr H20 Binary
58
• ~
.~.
'l
.~....
)
~
~
'""'1 ",
I ;:..,! ::)
1:4
~ ~}
~ :.,
Ul
1.0
TABLE V
Summary of the Calculated vs. Measured Bubble Point Pressures for the H2SH20 System
Reference Number Temperature Pressure Average Bias Average
of Points Range (oF) Range (psia) Absolute % (Liu and Absolute %
Deviation High) Deviation
(Liu and High) (Chen et al .)
1 35 100  340 100  3000 41.3 22.4 8.5
2 27 100 ~ 600 450  3000 36.1 11.7 7.1
3 36 32  122 6.8  13.8 98.1 87.4 13.2
4 52 41  140 5.3  71.7 77.2 53.1 11.6
5 323 50  356 22.4  967.2 46.8 16.6 7.8
Summary 472 32  600 5.3  3000 53 .0 3.4 8.6
1. Sellecketal(1952)
2. Gillespie and Wilson (1980)
3. Clark and Glew (1971)
4. Wright and Maass (1932)
5. Lee and Mather ( 1977)
r'"'.LlMII'V''1 .11iJ,J.U V.6u ........ 
v~~ ....... · 
':.,
Bias
(Chen et
aI.)
1.2
0.8
3.5
7.6
0.1
0.9
TABLE VI
Calculated VS . Measured Bubble Point Pressures for the H2SH20
System Classified by Isotherms
Temperature Number Pressure Average Absolute A verage Absolute
(,F) of Range (psia) % Deviation (Liu % Deviation (Chen
Points and High, 1993) et al. 1994)
32 .0 3 7.9  120 215.22 15.57
41.0 8 5.3  22.7 169.95 8.59
50.0 19 5.9  524 131.50 1l.91
59.0 9 134189.1 106.72 3.08
68.0 26 7.0  196.6 7454 10.84
770 15 7.6  50.7 64.62 15.07
86.0 37 8.2  328.5 57.64 13.37
100.0 10 50.0  360.0 12.78 4.72
104.0 40 7.2  3714 42.37 14.11
122.0 38 8.0  419.6 48.59 6.92
140.0 60 12.6  612.5 44.06 8.14
159.9 29 54.3  743.3 3747 6.73
194.1 43 34.5  953.2 35.83 2.97
200.0 5 120  1080 30.71 2.99
220.0 8 1250  3000 33.72 5.00
248.1 34 71.9  967.2 43.29 7.31
280.0 8 200  3000 93.62 11.16
300.0 4 450  3000 67.18 955
302.1 34 1004  957.2 31.88 6.87
340.0 13 200  3000 25.73 11.54
356.1 16 155.3  858.] 31.88 6.87
400.0 6 450  3000 30.89 9.39
500.0 3 800  3000 42.36 788
600.0 4 2000  3000 40.89 6.08
60
I
• I
I
! • ~

a bias of 3.4 % in the results for the model of Liu and High (1993), while the bias reduces
to 0.9 % for the model of Chen et al. (1994).
Figure 7 shows a plot of the AAPD as a function of the total system pressure for
both the models studied. The model of Liu and High (1993) shows a wider scatter than
the model of Chen et al. (1994) over the entire range of pressure studied for the H2SH20
system.
Table V also presents the results of the H2SH20 system by reference, for the
models ofLiu and High (1993) and Chen et al. (1994), respectively. As in the case of the
COr H20 binary, an analysis of the data points of individual studies has been conducted
because considerable differences exist in the experimental studies conducted by different
authors (Chen et al ., 1994).
Table VI classifies the results obtained for the H2SH20 system by isotherms
because most authors measured the liquid phase composition along isotherms, moving
from higher to lower pressures. Figure 8 is a plot of the AAPD as a function of
temperature. From Figure 8 and Table IX it can be concluded that the model of Chen et
al. (1994) performs better than the model of Liu and High (l993) at every isotherm
studied. For the individual isotherms, the AAPD of the model of Chen et al. (1994) varies
between 2.97 % and 15.57 %, while for the model. ofLiu and High (1993) the variation in
the AAPD is between 12.78 % and 215 .22 %.
61
I
I
I
t • ~

 'Cf(
'" =0
',c
~ > <1.l
0
<1.l
0.0
..~... = <1.l
C,) .....
<1.l
0..
.<..1...l
:l
0 en
.D
<C
<1.l
~ .....
<1.l > <
o AAPD (Chen et al.)
250.00 + AAPD (Liu an.d High)
++ +
200.00
+ ++ it +
+
+
150.00 +
++
+++ + * + +
++ + .t;..
+ ....
+
+ +
+ + + * + ++ +
100.00 + + +
t
ij..+ + ~ +
+ + * + +
+ + +
.Jt ~4+ ++ + + It 't + ++
+ t,tf,p +
+ + +
+ + +'1 + +t
50.00
#
+
+
+
0
0
0.00
1.00 10.00 100.00 1000.00 10000.00
System Pressure (psia)
Figure 7. Average Absolute Percentage Deviation in the Calculated Bubble Point
Pressure as a Function of the System Pressure for the H2SH20 Binary
62
I
I
I ,
1
oC
• )
".".'.'I. .,
~I ...... .!
)
t:~
:~
~
)
250.00 ~ + AAPD (Liu and High) (1)
I<
;:l
(/l
(/l (1) 0 AAPD (Chen et al. )
I<
0... 200.00 0
(\)
~
"'3 u ca * u +
(1)
5 +
.s 150.00 +
c:: i + 0
.~
;; + + + (1) + 0 f +
(1)
~ 100.00 + + c:: + + (1)
u.... + (1) 0... t + :j:
(1)  + ;:l + + + + '0 50.00 0 ! i til + , I + +
..0 +
~ +
I
(1) :t of ~ + +
.... e +
(\)
> ~ 0 ~ 000 8
0.00 200.00 400.00 600.00
System temperature (F)
Figure 8. Average Absolute Percentage Deviation in the Calculated Bubble Point Pressure
as a Function of the System Temperature for the H2SH20 Binary
63
• )
~
'11
~ .. ~
I
~ !
I
)
~ ~
~2
.,~..
4.3 Discussion
The model of Chen et a1. (1994) provides better values for the bubble point
pressures than the model of Liu and High (1993), in the temperature and pressure range
studied, due to the inclusion of the aqueous phase dissociation in the overall phase
equilibrium computation. Instead of using the apparent composition of the weak
electrolytes (C02 or H2S) in the liquid phase (Liu and High, 1993), the true composition
of the weak electrolytes was used in this work. The corrected compositions result in a
better representation of the vaporliquid equilibrium and an improvement in the phase
equilibrium prediction.
The results given in Table III and Table V indicate that the model of Chen et al.
(1994) performs better for the H2SH20 binary system than for the CO2H20 binary
system. This discrepancy can be explained in terms of the polarity and the acentricity of
the molecules.
The polarity of the constituents of a system affect the vaporliquid equilibrium
behavior of the system. Electrostatic forces can arise even in those molecul.es that do not
possess a net electric charge. All molecules that have an uneven spatial distribution of
electronic charges about the positively charged nuclei develop a permanent dipole. The
greater the asymmetry of the molecule, the greater the dipole moment. H20 has a dipole
moment of 1.8 debye; H2S has a dipole moment of 0.9 debye; and CO2 has a dipole
moment of 0.0 debye. The wide difference in the polarity of CO2H20 results in a larger
64
• )
1
"Co
.~.
....
error in the prediction of the vaporliquid equilibrium behavior for the COr H20 binary
(Gerdes et al" 1989),
The acentric factor correlates the extent of deviation of a molecule from simple
molecule behavior. The acentric factor is a measure of the acentricity [i.e., the noncentral
nature of the intermolecular forces (Prausnitz, 1969)]. For simple molecules the acentric
factor is 0, The acentric factor increases as the complexity of the molecules increases. An
increase in the complexity of a molecule increases its deviation from ideality and
introduces a greater error in the modeling of that molecule. The acentric factor for H2S is
0.095 and the acentric factor for CO2 is 0.225 , The increased nonideality of CO2 is a
reason for the poorer vaporliquid equilibrium prediction of the COr H20 system.
The modeling results obtained as part of this work have to be studied in the light of
certain limitations. Errors in calculating phase equilibria are larger than expected for nonreacting
systems for the following reasons (Gerdes et aI. , 1989):
• Numerous and simultaneous chemical reactions,
• Enhanced nonideality of the systems due to the electrostatic effects of ions
• Phase and chemical equilibria in a highly polar liquid phase
• Phase and chemical equilibria involving mixtures of nonpolar compounds
(e,g" CO2) with highly polar compounds (e,g., H20), and
• Difficulty in measuring vaporliquid equilibrium data.
The problems mentioned above combine to produce larger errors in the measured data for
reacting systems visavis nonreacting systems and increase the chance of errors arising
due to the mismatching of the various effects on the modeling process, Unfortunately,
" Of
.....
information is not available to quantify the errors in the experimental database used in this
study.
The agreement between the various experimental studies is generally poor. For the
COr H20 binary the data of Takenouchi and Kennedy (1964) are in good agreement with
the results of Malinin (1959) but depart sharply from the results of Todheide (1963). For
the H2SH20 binary the data of Lee and Mather (1977) are in fairly good agreement with
the data of SeHeck et a1. (1952) at 159.8 ~, but at higher temperatures there is a deviation
of up to 10 %. This necessitated a statistical analysis of all the data points classified by
reference for both the binaries (C02H20 and H2SH20) studied as part of this work.
Another area of disagreement is the time required for the attainment of equibbrium
between the mixture components. Ellis and Golding (1963) concluded that at least 24
hours were required before equilibrium between H20 and CO2 was reached. Malinin
(1959) does not report the time required for the attainment of equilibrium in his
experiments. Todehide (1963) reported that only 1 hour was required for the attainment
of equilibrium. Experimental investigation by Takenouchi and Kennedy (1964) showed
that equilibrium was attained in over 3 days at a temperature of 392 OF, and more than]
week was required at a temperature of 230 OF. All the data for the time required for
attainment of equilibrium detailed above is for the CO2H20 binary. Time required for the
attainment of equilibrium has not been reported for the H2SH20 binary.
The inherent limitations of the SoaveRedlichKwong (SRK) equation of State
(Soave, 1972) used in this work introduces a certain degree of error to the modeling
results. The SRK equation of state has been used in DREAM for corrosion prediction
66
• )
~
11
.,
because of its excellent predictive capabilities for the phase equilibrium of hydrocarbons.
However SRK does not perform well for nonhydrocarbons, especially polar and
associative systems (Sandler et aI., 1994) like the two binaries (COr H20 and H2SH20)
of interest in this work. These factors contribute to the deviations obtained in the bubble
point pressure predictions.
When model predictions are compared to experimental data, the difference
between the prediction and the measurement is examined. The best model would have a
lower average relative error, compared to experimental data, than any other model. The
above criterion clearly indicates that the performance of the model of Chen etal. (1994) is
superior to that of the model ofLiu and High (1993). Based on the results obtained it was
decided to implement the model of Chen et al. (1994) in DREAM for purposes of phase
and electrolyte equilibrium calculations.
4.4 Effect of the Phase and Electrolyte Equilibrium Module on
Corrosion Rate Prediction
The model of Chen et al. (1994) has been incorporated in DREAM for phase and
aqueous electrolyte equilibrium calculations. The ultimate purpose of DREAM is to
predict the corrosion rates in gas wells. The impact of the model of Chen et al. ( 1994) on
the corrosion rate calculations was evaluated. The effect of the old model (Liu and High,
1993) was also evaluated and the results obtained in both these cases were compared with
field data.
67
,
".•,
Sixteen test cases were examined to measure the impact of the changed phase
equilibria calculation scheme on the corrosion rate calculations. The input data for these
sixteen gas wells i.8 given in Tables VII to IX. The conditions prevailing in these wells
cover a wide range of temperature, pressure, and concentration.
The corrosion profile for the sixteen test cases is presented in Figures 9 to 24 and
can be classified into the following three categories:
I. wells with high or moderately high unifonn corrosion,
2. wells with low uniform corrosion, and
3. wells with pitting corrosion.
Cases I, VII, VIII, IX, X, and XII represent wells with high uniform corrosion. In
Case I (Figure 9), the model of Chen et at. (1994) better predicted the corrosion rate than
the model of Liu and High (1993) from the wellhead to a depth of 2000 foot and from
6500 foot to the bottomhole. Both the models predicted the same corrosion rates
indicating that high corrosion was possible. The caliper survey data indicated that high
uniform corrosion occurred in Case 1. The model predicted the absence of a protective
film, indicating that high corrosion was possible.
In Case VII (Figure 15), the model of Chen at al. (1994) and the model of Liu and
High (1993) perform poorly visavis the corrosion rate indicated by the caliper survey
data. The gas well in Case VII contained 2.22 % CO2 indicating that a high corrosion rate
was possible. However the corrosion rate indicated by the caliper survey was much lower
than that predicted by the model. between 2000 foot and 3000 foot.
68
Q\
\0
Case
I
I II
I III
IV
V
VI
VII
VIII
IX
X
XI
XII
. XIII
XIV
XV
XVI .
ID Depth
(in.) (ft.)
2.441 9700
2.441 9450
2.441 9620
2.441 11080
2.441 9130
1.995 9220
2.992 10506
1.995 9540
1.995 10350
2.441 11175
2.441 11246
2.441 10883
1.995 9350
1.995 9337
1.995 9910
1.995 9527
1
TABLE VII
Well Geometry and Production Data
Water Gas Oil Wellhead Bottomhole Wellhead Bottomhole
Production Production Production Temperature Temperature Pressure Pressure
(bbllday) (MSCFD) (bbl/day) (OF) e'F) (psia) (psia)
28 2150 23 130 290 1890 4000
27 1352 8 130 290 1440 4000
. 
124 2800 146 130 290 1270 4000
20 4000 20 100 230 415 1015
5 4200 32 130 290 1440 4000
40 3400 92 130 290 1200 2300
10 3300 62 130 290 1200 2510
5 3320 34 130 290 1200 2225
10 3500 10 130 290 2900 4000
8 440 1 78 190 275 450
3 413 0 81 200 4700 1600
10 905 0 95 355 250 800
1 150 1 130 290 1180 4000
53 528 13 130 290 1560 4000
7 4600 89 130 290 1200 7000
11 3420 58 130 290 2570 4000
.. _ •• r .. _
v~ ................... ·
.I
¢
 .
I
I
I Case I
Case II
Case III
Case IV
Case V
Case VI
Case VII
Case VIII
Case IX
Case X
Case XI
Case XII
Case XIII
Case XIV
Case XV
Case XVI
C14
90.94
91.60
90.10
95 .10
90.17
88.31
88.68
90.44
93 .55
84.60
92.04
92.75
89.03
8879
88.68
89.42
C2~ C3Hs ICJIIO
4.37 1.14 0.27
4.39 1.18 0.33
6.00 1.68 0.45
1.92 0.49 0.12
5A9 1.70 0.54
6.90 2.21 0.66
5.69 1.69 OA4
5.07 1.36 0.32
250 OA7 0.10
7.88 2.64 065
3.72 0.60 0.14
3.24 0.42 0.08
6.74 1.98 0.54
6.73 2.14 0.64
5.5 1.65 0.42
6.00 1.84 050
v ... &.ar...a& ........ "' 
l
TABLE VIII
Gas Analysis (mole %)
NCJIIO ICsH12 NCsH12 C6H14 C7 + N2 CO2 H2S
0.23 0.13 008 0.11 0.27 0.25 2.21 0.00
025 0.14 0.09 0.13 0.33 0.30 1.26 0.00
0.34 0.20 0.12 0.18 0.40 0.22 0.31 0.00
011 0.05 0.03 0.11 0.15 0.08 1.84 0.00
OAl 0.22 0.15 0.24 0.59 0.23 0.26 0.00
0.50 0.26 0.17 023 0.52 0.12 0.12 0.00
0.37 020 0.12 0.16 0.28 0.15 2.22 0.00
0 27 0.15 0.09 0.14 0.32 0.12 1.72 0.00
0.06 006 0.04 0.07 0.58 0.10 2.45 0.00
0.32 0.32 0.18 0.00 0.17 0.60 2.40 0.00.
0.00 0.00 0.00 0.00 0.06 0.09 3.34 0.00,
0.00 0.00 0.00 0.00 0.05 0.07 3.40 0.00
OAO 0.17 0.12 0.12 022 0.28 OAO 0.00
OA8 0.24 0.16 020 0.34 0.24 0.04 0.00
0.36 0.20 0.12 0.16 0.37 0.13 2.14 0.001
0.40 0.22 014 0.20 0.40 0.23 0.65 0.00 I
1
TABLE IX
Water Analysis (ppm)
Na+ Ca2+ Mg2+ Ba2+ Sr2+ K+ Fe2+ cr SO/ C032 HC03
Case I 6490 298 38 4 0 0 36 10100 III 0 879
Case II 6280 454 50 2 0 0 0 10300 196 0 313
Case III 127 21 0 3 0 0 0 195 0 0 60
Case IV 20104 326 166 6 0 0 3 30540 800 0 1648
Case V 35 7 1 1 0 0 12 15 0 0 90
.I Case VI 4580 197 1140 4 0 0 170 10300 32 0 696  Case VII 4740 200 17 1 0 0 74 7490 94 0 257 i
Case VIII 7110 371 21 20 0 0 0 11500 0 0 335
Case IX 4580 197 1140 4 0 0 0 10300 32 0 696
Case X 31000 7000 900 40 200 130 100 62000 280 0 260
Case Xl 31000 7000 900 40 200 130 100 62000 280 0 260
Case XlI 31000 7000 900 40 200 130 100 62000 280 0 260
Case XlII 4580 197 1140 4 0 0 170 10300 32 0 696
Case XlV 4580 197 1140 4 0 0 170 10300 32 0 696
Case XV 7830 319 14 13 0 0 1380 12600 0 0 146
Case XVI 5850 564 33 1 0 0 40 9800 218 0 263
v ... ~ ..... "'·
• Caliper Survey Data
o Corrosion Rate (Chen et al.)
Corrosion rate (Liu and High)
80.00 No film formed
60.00
..
><
~ '"
v ~ 40.00 • c::
0
' (ij
0
t:: • • 0 u
20.00
4
~
~ ~
:>
0.00
0.00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft)
Figure 9. Corrosion Rate Profile along Well Depth: CASE I
• Caliper Survey Data
o Corrosion Rate (Chen et a1 .)
40.00
Corrosion Rate (Liu and High)
No film fonned
30.00
.. >
~
Q)
';j
~ 20.00
c::
0 . iii
.0... . ..... • 0 u
10.00 \ 4 • ~ •• • • • • • ~ ~ ,
0.00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft.)
Figure 10. Corrosion Rate Profile along Well Depth: CASE II
73
....
Caliper survey indicated no corrosion
o Corrosion Rate (Chen et al .)
Corrosion Rate (Liu and High)
Calcium Carbonate film fonned throughout the well
8.00
6.00
.
~ C)
~
~ 4.00
c::
0
. v.;
0 t::
0
U
I
2.00 I
;
)
~
& ,
~..
~
0.00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft.)
Figure 11 Corrosion Rate Profile along Well Depth: CASE III
7~
• Caliper Survey Data
o Corrosion Rate (Chen et al,)
Corrosion Rate (Liu and High)
Calcium and Iron Carbonate film formed throughout the well
160.00
•
•
120.00
•
• •
•
• • •
•
80.00 • • • •
•
• • •
• • • • •
•
40.00
\ 0.00 +,,&wB~~P__€f____€7_e__tj)___B~
0.00 4000,00 8000.00 12000.00
Well Depth (ft.)
Figure 12. Corrosion Rate Profile along Well Depth: CASE IV
75
)
I
~
1 ~
)
.....
• Caliper survey data
o Corrosion rate (Chen et a1. )
Corrosion rate (Liu and High)
12.00 Calcium Carbonate film formed beyond 3850 ft.
• •
• • • •
• • •
8.00 ,.
><
~ • •
 Q)
~
!:
0 . iii
0
t:
0
U
4.00
..
:>
000 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft.)
Figure 13 . Corrosion Rate Profile along Well Depth: CASE V
76
....
Caliper survey indicated no corrosion
o Corrosion rate (Chen et al.)
t Corrosion rate (Liu and High)
Calcjum and Iron Carbonate film formed throughout the well
5.00
4.00
 ;:..
~ 3.00
Q)
~ r:x:
I=:
.8
r.'l
.0.. . 2.00 ....
0
l.i
•
1.00 + I
1 • )
0.00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft.)
Figure 14. Corrosion Rate Profile along Well Depth: CASE VI
77

100.00
80.00
~ 60.00
Q)
~
~
§
' 1ii
2.... o
U
40.00
20.00
•
• Caliper Survey Data
o Corrosion rate (Chen et al.)
Corrosion rate (Liu and High)
No film is formed
•
• •
• ••
• •
•• •
0.00 +.r.,,:::~"'$~~~
0.00 4000.00 8000.00 12000.00
Well Depth (ft.)
Figure 15. Corrosion Rate Profile along Well Depth: CASE VII
78
c
....
• Caliper survey data
o Corrosion rate (Chen et al. )
60.00
Corrosion rate (Liu and High)
No film is formed
.... 40.00
~
~ ''
Q) ...... •
~
t:
0
' ;;j
.0.... . • 0 u
20.00 •
• ..
•
• •
•
• • • •
000 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft .)
Figure 16. Corrosion Rate Profile along Well Depth: CASE VIII
79

120.00
.... 80.00 >
~ ''
a)
~
~
t::
0
Vi
0
t:
0
U
40.00
... . •• •. .. •..• .•.. • . .. . . .. . ... .... ..... . .. •• •
•
o
Caliper survey data
Corrosion rate (Chen et al.)
Corrosion rate (Liu and High)
No fi lm is fo rmed
.••. ..
•
0.00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft)
Figure 17. Corrosion Rate Profile along Well Depth: CASE IX
80
..
• Caliper Survey Data
o Corrosion rate (Chen et al .)
Corrosi.on rate (Liu and High)
120.00
No film is formed
•
•
. .•. ...
• •
80.00 ,.. >
~
_.. ...
  .. C1>
~
~
•
•••••••
c::
0  .. '{jj
0 .... . ........
0 • U
40.00  ... . • • •
• •• •
•
0.00
0.00 4000.00 8000.00 12000.00
Well Depth (ft.)
Figure 18. Corrosion Rate Profile along Well Depth: CASE X
81
• Caliper survey data
o Corrosion rate (Chen et al.)
Corrosion rate (liu and High)
40.00
No film is formed
•
30.00 ••
>
~
• •
'"
Q)
&j
~ 20.00 •••
c::
0
. (;j
0...... ..
u0 •
10.00 .
0.00 t,r,,,,,
0.00 4000.00 8000.00 12000.00
Well Depth (ft. )
Figure 19. Corrosion Rate Profile along Well Depth: CASE Xl
82
• Caliper survey data
o Corrosion rate (Chen et al.)
+ Corrosion rate (Liu and High)
60.00
No film is formed
•
•
40.00
~
~ .. •
v
~
~ • ••
I::::
0
' (ij
..0..... ..
0 u
20.00
0.00 + ___ . __ . __ ,_.r.
0.00 4000.00 8000.00 12000.00
Well Depth (ft)
Figure 20. Corrosion Rate Profile along Well Depth: CASE XlI
83
Caliper survey indicated no corrosion
o Corrosion rate (Chen et al.)
Corrosion rate (Liu and High)
Calcium and Iron Carbonate film formed throughout the well
2.00
1.60
.
><
~ 1.20
Cl)
tU
~
c::
0 . til
0t:: 0.80
0
U
0.40
0.00 t,,,,,...,y,T,
0.00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft.)
Figure 21 . Corrosion Rate Profile along Well Depth CASE XIII
84
Caliper survey indicated no corrosion
o Corrosion rate (Chen et aJ.)
Corrosion rate (Liu and High)
Calcium and Iron Carbonate film formed
>
~ 0.30
Q)
~
~
~
0 'm
0 ........ 0.20
0
U
0,00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft.)
Figure 22. Corrosion Rate Profile along Well Depth: CASE XIV
85
•
• Caliper survey data
o Corrosion rate (Chen et al.)
Corrosion rate (Liu and High)
160.00
No film is formed
120.00
 ><
~ '"
11>
1a
~ 80.00
c::
0
·tii
0
t:
0 u
40.00 •
• •
• • • • • •
0.00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft. )
Figure 23. Corrosion Rate Profile along Well Depth: CASE XV
86

• Caliper survey data
o Corrosion rate (Chen et al .)
Corrosion rate (Liu and High)
10.00 • • No film is formed
8.00 •
,... >
~ 6.00
~
1;:j
~ = 0
'r;j
..0..... .. 4.00
0
l.i
200
0.00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft.)
Figure 24 Corrosion Profile Along Well Depth: CASE XVI
87
m
In Case vrn (Figure 16), the model of Chen et al. (I 994) was closer to the caliper
survey data from the well head to a depth of3500 foot. Beyond 3500 foot, the model of
Liu and High (1993) performed better. Below a depth of 6500 foot to the bootomhole,
both the models predicted a zero corrosion rate and were in perfect agreement with the
caliper caliper survey data.
In Case IX (Figure 17) there was a gross over prediction of corrosion rates.
However, the model of Chen et al. (1994) was closer to the caliper survey data from the
wellhead to a depth of 5500 foot. From 5500 foot to the bottombole, the model of Liu
and High (1993) was in better agreement with the caliper survey data. The model
predicted the absence of protective films substantiating the high corrosion rates indicated
by the caliper survey data.
In Case X (Figure 18) both the models under predicted the corrosion rates from
the wellhead to a depth of 6000 foot. The gas and water production rates were very low
for case X indicating that DREAM would predict a low corrosion rate. Beyond a depth of
6000 foot, both the models predicted a low corrosion rate and were in agreement with the
caliper survey data.
Case XII (Figure 20) was a well with uniform corrosion from the wellhead to a
depth of 4000 foot and zero corrosion from 4000 foot to the bottomhole. The model of
Chen et al. (1994) performed better than the model of Liu and High (1993) in predicting
uniform corrosion between 500 foot and 1500 foot and once again between 2500 foot and
4000 foot. Both the models under predicted the corrosion rates between 1500 foot and
2500 foot. The model of Chen et al. (1994) predicted very low corrosion beyond 6500
88
foot, while the model ofLiu and High (1993) predicted a very low corrosion beyond 8000
foot.
Cases HI, VI, XIII, and XIV represent wells with very low corrosion rates. The
caliper data shows corrosion rates below the threshold of detection which is 7 Mils Per
Year (MPY). The corrosion rate predicted by both the models were comparable for the
wells with very low corrosion rates and were in excellent agreement with the catiper
survey data. The corrosion rate predicted by the model was below 7 MPY for Cases III,
VI, XIII, and XIV. The model also predicted the fonnation of a protective film
throughout the well, indicating that the wells could be noncorrosive.
The corrosion product film may be removed from the sections of the tubular due to
the action of flowing fluids, exposing the wall to corrosive species. The exposed segment
of the pipe wall is then subjected to intense corrosion resulting in the fonnation of
localized pits or grooves. This phenomenon is called pitting corrosion and is observed in
Cases II, IV, V, XI, XV, and XVI. The caliper survey data represents such pits in Cases
II, IV, V, XI, XV, and XVI. Segments of the pipe wall where there are no pits there is no
corrosion. DREAM has the capability to predict uniform corrosion only.
In Case II (Figure 10) the model of Chen et at. (1994) predicted a very low
corrosion rate below 1000 foot indicating that the uniform corrosion prediction agreed
with the caliper survey data. The model ofLiu and High (1993) predicted a low corrosion
rate below a depth of 3 500 foot.
In Case IV (Figure 12), the model of Chen et al. (1994) predicted corrosion rate
below 7 MPY throughout the entire depth of the wen. The model of Liu and High (1993)
89

predicted a high corrosion rate (greater than 12MPY) from the well head to a depth of
7500 foot and a low corrosion rate (less than 7 MPY) below 7500 foot. The model also
predicted the formation of a protective film throughout the well.
In Case V (Figure 13) the uniform corrosion exhibited by the well was predicted
equally well by both the models. Both the models predicted corrosion rates below 7
MPY. The model also predicted that a film was formed below 3850 foot
The uniform corrosion rate predicted by both the models for Case XI (Figure 19)
is high. Both the models over predicted the uniform corrosion rates from a wellhead to a
depth of 8500 foot. From 8500 foot to the bottomhole, both the models predicted a very
low corrosion rate.
In Case XV (Figure 23) the model of Chen et al. (1994) predicted a high corrosion
rate from the wellhead to a depth of 3500 foot and a low corrosion rate (less than 7 MPY)
below 3500 foot. Thus the model of Chen et al. (1994) was in consonance with the
caliper survey data below a depth of 3500 foot for Case xv. However, the model of Liu
and High (1993) was in agreement with the caliper survey data only after a depth of 6000
foot.
In Case XVI (Figure 24), both the models predicted a zero corrosIOn rate
throughout the well and were accurate with regard to uniform corrosion prediction.
Corrosion rate was thought to be a very strong function of the phase and
electrolyte equilibrium calculations. The results in Figures 9 to 24 indicated that the
corrosion rate was not improved significantly due to an improvement in the phase and the
electrolyte equilibrium calculations. The corrosion rate calculation depends on many
90
modules: phase and electrolyte equilibrium, pressure drop along the production string,
mass transfer of the corrosive species to the pipe wall and the corrosion product film to
the bulk liquid, and corrosion kinetics. The accuracy of the corrosion prediction depends
on the accuracy of each of the modules used.
The phase and electrolyte equilibrium modeling carried out as part of this work
incorporated hydrogen sulfide characterization in DREAM. No case studies of actual gas
wells containing hydrogen sulfide are available. In order to demonstrate the capability of
DREAM to predict phase equilibrium with hydrogen sulfide. Well number 1 was used as
an "experimental well". In this well, the composition of hydrogen sulfide was given four
values: 00 %, 0.1 %, l.0 %, and 10.0 %; and the gas composition was normalized. All
other well operating conditions remained the same as given in Tables VII, VIII, and IX.
The pH profile for all these four cases is shown in Figure 25. With an increase in the
amount of the hydrogen sulfide, the pH increases till the concentration of H2S reaches a
value of 0.1 % and then decreases. This is due to the fact that dissociation of H2S is
suppressed at concentrations above 0.4 %.
The present work fonnulated a generalized framework for the coupled phase and
electrolyte equilibrium calculations in gas wells and has also verified the accuracy of the
generalized model. Even though the improvement .in the phase and electrolyte equilibrium
computations have not dramatically affected the corrosion rates, this work has succeeded
in getting one step closer to the accurate estimation of corrosion rates in gas wells.
91
0 0% H2S • 0.1 % H2s
0 1 %H2S .. 10 %H2S
4.00
3.60
3.20
2.80 +...,,,,,,.,...,,
0.00 2000.00 4000.00 6000.00 8000.00 10000.00
Well Depth (ft.)
Figure 25 . pH Profile along Well Depth: Hydrogen Sul.fide Induced Corrosion
92
CHAPTERS
CONCLUSIONS AND RECOMJ\..1ENDATIONS
5.1 Conclusions
The following conclusions can be made on the basis of this study:
1. The model of Chen et al. (1994) performs better than the model of Liu and
High (1993) for the entire range of temperature and pressure tested. Therefore the
model of Chen et at. (1994) has been incorporated into DREAM for purposes of
corrosion prediction.
2. DREAM now has the phase and electrolyte equilibrium calculation necessary to
predict corrosion induced by hydrogen sulfide.
3. The corrosion rate predictions are not affected significantly due to the new phase and
electrolyte equilibrium model.
5.2 Recommendations
The present work can be carried on in the following directions:
I. The corrosion prediction in DREAM does not take into account the dissolution of the
iron at the pipe wall. Hence the corrosion product film is assumed to be formed only if
93
there is sufficient iron (Fe2+ ions) in the input water analysis. Iron dissolution is an
anodic reaction and can be represented as
(5.1)
The concentration of the iron that dissolves from the tubular can be calculated from
the equilibrium potential for the electrode reaction represented by Equation (5 .1). The
anodic dissolution reaction (Equation 5.1) and the equilibrium potential for the
reaction are discussed by Bard and Faulkner (1980).
2. In this work precipitation of the corrosion product layer is assumed to be a sufficient
condition for film formation. However the precipitation of a corrosion product layer
in itself does not necessarily result in the formation of a protective film (de Waard et
aI. , 1991) Johnson and Tomson (1991) concluded that iron carbonate film formation
was a slow temperature dependent process and occurred when the supersaturation was
1.3 times the thermodynamic solubility. The accuracy of corrosion rate predictions, in
the presence of protective films, needs to be improved by incorporating a suitable
model for the product film supersaturation.
3. Evaluation of DREAM for the prediction of hydrogen sulfide induced corrosion has
not been possible. This work has included hydrogen sulfide characterization in the
phase and electrolyte equilibrium module of DREAM. However no case studies of gas
wells containing hydrogen sulfide are available. Acquiring field data of gas wells
containing hydrogen sulfide would help benchmark DREAM for corrosion rate
prediction due to the presence ofH2S.
94
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