field performance analysis and optimization of gas
TRANSCRIPT
The Pennsylvania State University
The Graduate School
Department of Energy and Mineral Engineering
FIELD PERFORMANCE ANALYSIS AND OPTIMIZATION OF
GAS CONDENSATE SYSTEMS USING ZERO-DIMENSIONAL RESERVOIR MODELS
A Thesis in
Energy and Mineral Engineering
by
Pichit Vardcharragosad
2011 Pichit Vardcharragosad
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science
August 2011
The thesis of Pichit Vardcharragosad was reviewed and approved* by the following:
Luis F. Ayala
Associate Professor of Petroleum and Natural Gas Engineering
Thesis Advisor
R. Larry Grayson
Professor of Energy and Mineral Engineering
Graduate Program Officer of Energy and Mineral Engineering
Li Li
Assistant Professor of Energy and Mineral Engineering
Yaw D. Yeboah
Professor of Energy and Mineral Engineering
Head of the Department of Energy and Mineral Engineering
*Signatures are on file in the Graduate School
iii
ABSTRACT
Field performance prediction is a crucial piece of information that all relevant parties
have to use in their design and decision processes during the development and exploitation of a
hydrocarbon reservoir. Field performance analysis is an engineering task which requires
knowledge, time, and the right tools and models. Available tools such as commercial reservoir
simulators might not always be the most efficient or the most optimum solution even if they make
use of highly sophisticated or detailed models. This is because these sophisticated models often
require more input data and longer running time than the less detailed ones. These problems
become worse when availability of input data and working time are constrained.
This thesis aims to develop a field performance model which will allow engineer to
perform analysis and optimization tasks more effectively for the case of gas condensate
reservoirs. A gas condensate is one of the many fluid types that can be found in conventional
hydrocarbon reservoirs. The development of a two-phase condition below the dew point pressure
can significantly increases the complexity in engineering performance calculation. The proposed
tool utilizes both zero-dimensional reservoir model customized for gas condensate and pseudo
component model. Results indicate that both models can provide fairly good prediction results
while requiring much less input and running time. Microsoft Excel with built-in Visual Basic for
Applications (VBA) is selected as the platform to develop this simulator due to the user-friendly
interface, useful built-in features, and high flexibility to use and hard-code modification. The
proposed model is able to successfully predict field performance while capturing all major fluid
behavior characteristics of gas condensates as well as being capable of performing various
optimization tasks effectively. Limitations of the implemented pseudo component model, such as
negative solution gas-oil ratios at low reservoir pressure, are elaborated and discussed. The
possible sources of error and associated preventive measures derived from the use of a gas
iv
condensate tank model for the case volatile oil reservoirs are addressed. Further recommended
studies on negative value of decline exponent variable and expanding current capability of the
proposed model are also presented.
v
TABLE OF CONTENTS
List of Figures .......................................................................................................................... vii List of Tables ........................................................................................................................... ix Nomenclature ........................................................................................................................... x Acknowledgements .................................................................................................................. xv
Chapter 1 Introduction ............................................................................................................. 1
Chapter 2 Background ............................................................................................................. 3
2.1 Gas Condensate Hydrocarbon Fluid .......................................................................... 3 2.2 Modified Black-Oil Model ......................................................................................... 5 2.3 Zero-Dimensional Reservoir Model .......................................................................... 7 2.4 Field Performance Prediction ..................................................................................... 8 2.5 Visual Basic for Applications (VBA) ........................................................................ 12
Chapter 3 Problem Statement .................................................................................................. 13
Chapter 4 Model Description ................................................................................................... 15
4.1 Phase Behavior Model (PBM) ................................................................................... 16 4.1.1 Compressibility Factor .................................................................................... 17 4.1.2 Vapor-Liquid Equilibrium ............................................................................... 21 4.1.3 Fluid Property Prediction ................................................................................ 27 4.1.4 Phase Stability Analysis .................................................................................. 37
4.2 Standard PVT Properties ............................................................................................ 42 4.2.1 Definitions, Mathematic Relationships, and Characteristics ........................... 43 4.2.2 Obtaining Standard PVT Properties from Laboratory PVT Reports ............... 51 4.2.3 Obtaining Standard PVT Properties from a Phase Behavior Model ............... 60
4.3 Zero-Dimensional Reservoir Model .......................................................................... 70 4.3.1 Generalized Material Balance Equation .......................................................... 71 4.3.2 Material Balance Equation for a Gas Condensate Fluid ................................. 75 4.3.3 Phase Saturation Calculations ......................................................................... 80 4.3.4 Volumetric OGIP/OOIP Calculations ............................................................. 82
4.4 Flow Rates and Flowing Pressures Calculation ......................................................... 84 4.4.1 Inflow Performance Relationship (IPR) .......................................................... 85 4.4.2 Tubing Performance Relationships ................................................................. 91 4.4.3 Nodal Analysis ................................................................................................ 96
4.5 Field Performance Prediction ..................................................................................... 99 4.5.1 Performance during Plateau Period ................................................................. 100 4.5.2 Performance during Decline Period ................................................................ 103 4.5.3 Annual Production Calculation ....................................................................... 106
4.6 Economic Analysis and Field Optimization............................................................... 109 4.6.1 Simplified Economic Model ........................................................................... 110 4.6.2 Field Optimization ........................................................................................... 116
vi
Chapter 5 Model Performance ................................................................................................. 117
5.1 Simulation of Standard PVT ―Black Oil‖ Properties ................................................. 117 5.1.1 Simulated Standard PVT Properties ................................................................ 117 5.1.2 Limitations of Pseudo Component Model ....................................................... 121 5.1.3 Impact on Standard PVT Properties ................................................................ 127
5.2 Zero-Dimensional Material Balance Calculations for Gas Condensates ................... 129 5.2.1 Simulation Results from Gas Condensate Tank Model .................................. 129 5.2.2 Misuse of Gas Condensate Tank Model in Volatile Oil Reservoir ................. 132
5.3 Field Performance Prediction ..................................................................................... 137 5.3.1 Field Performance Prediction Results ............................................................. 137 5.3.2 Decline Trend Analysis ................................................................................... 143
5.4 Economic Analysis and Optimization ........................................................................ 146 5.4.1 Field Economic Analysis ................................................................................ 146 5.4.2 Field Optimization ........................................................................................... 149
5.5 Application for Other Production Situations .............................................................. 152 5.5.1 Application for Dry Gas / Wet Gas ................................................................. 153 5.5.2 Application for Gas Condensate with Producible (Mobile) Reservoir Oil ..... 155
Chapter 6 Summary and Conclusions ...................................................................................... 158
Appendix A Input Data Summary .......................................................................................... 163 Appendix B User Guide .......................................................................................................... 170
vii
LIST OF FIGURES
Figure 2-1: Phase Diagram of Typical Gas Condensate Reservoir .......................................... 3
Figure 2-2: Distributions of Pseudo Components among Phases in Modified Black-Oil
Model ............................................................................................................................... 5
Figure 2-3: Graphical Representation of Zero-Dimensional Reservoir Model ........................ 7
Figure 2-4: Typical Field Performance of Gas Condensate – Gas and Oil Flow Rates vs.
Time ................................................................................................................................. 9
Figure 2-5: Typical Field Performance of Gas Condensate – Reservoir Pressure,
Bottomhole Flowing Pressure and Wellhead Pressure vs. Time ..................................... 10
Figure 2-6: Typical Field Performance of Gas Condensate – Cumulative Gas and Oil
Production vs. Time ......................................................................................................... 11
Figure 4-1: Graphical Representation of Standard PVT Properties ......................................... 44
Figure 4-2: Typical Characteristic of Gas Formation Volume Factor ( ) and Volatilized
Oil-Gas Ratio ( ) for Gas Condensate .......................................................................... 48
Figure 4-3: Typical Characteristic of Oil Formation Volume Factor ( ) and Solution
Gas-Oil Ratio ( ) for Gas Condensate ........................................................................... 48
Figure 4-4: Graphical Representation of CVD Data used in Walsh-Towler Algorithm .......... 53
Figure 4-5: Graphical Representation of Nodal Analysis ........................................................ 96
Figure 4-6: Graphical Representation of Field Optimization .................................................. 116
Figure 5-1: Simulated Gas Formation Volume Factor and Volatilized Oil-Gas Ratio of
Gas Condensate ................................................................................................................ 118
Figure 5-2: Simulated Oil Formation Volume Factor and Solution Gas-Oil Ratio of Gas
Condensate ....................................................................................................................... 119
Figure 5-3: Simulated Specific Gravity of Reservoir Gas ....................................................... 120
Figure 5-4: Volumes of Surface Gas Pseudo Component in Reservoir Gas Reservoir Oil,
and Cumulative Gas Production ....................................................................................... 121
Figure 5-5: Volumes of Stock-Tank Oil Pseudo Component in Reservoir Gas, Reservoir
Oil, and Cumulative Oil Production................................................................................. 122
Figure 5-6: Densities of Surface Gas and Stock-Tank Oil Pseudo Components at First
Stage Separator, Second Stage Separator and Stock Tank Condition .............................. 124
viii
Figure 5-7: Volumes of Stock-Tank Oil Pseudo Component in Reservoir Gas, Reservoir
Oil, and Cumulative Oil Production in term of Gas-Equivalent ...................................... 125
Figure 5-8: Total Volumes of Stock-Tank Oil Pseudo Component and Surface Gas
Pseudo Component in term of Gas-Equivalent ................................................................ 126
Figure 5-9: Simulated Production Results of Gas Condensate using Simplified Gas
Condensate Tank Model .................................................................................................. 130
Figure 5-10: Phase Envelope and Reservoir Depletion Paths at Two Different Reservoir
Temperatures .................................................................................................................... 133
Figure 5-11: Simulated Gas Formation Volume Factor and Volatilized Oil-Gas Ratio of
Volatile Oil using Gas Condensate PVT Model .............................................................. 134
Figure 5-12: Simulated Oil Formation Volume Factor and Solution Gas-Oil Ratio of
Volatile Oil using Gas Condensate PVT Model .............................................................. 134
Figure 5-13: Simulated Production Results of Volatile Oil using Simplified Gas
Condensate Tank Model .................................................................................................. 135
Figure 5-14: Mole Fraction Behavior of Vapor Phase Molar Fraction ( ) for Gas
Condensates and Volatile Oils ......................................................................................... 136
Figure 5-15: Cumulative Gas and Oil Production vs. Time..................................................... 138
Figure 5-16: Total Gas and Oil Flow Rates vs. Time .............................................................. 139
Figure 5-17: Reservoir Pressure, Bottomhole Flowing Pressure, and Wellhead Pressure
vs. Time ............................................................................................................................ 140
Figure 5-18: Gas Saturation and Specific Gravity of Reservoir Gas vs. Time ........................ 142
Figure 5-19: Total Gas Flow Rate ( ) vs. Cumulative Gas Production during Decline
Period .................................................................................................. 143
Figure 5-20: Decline Rate ( ) vs. Cumulative Gas Production during Decline Period
( ) ........................................................................................................... 145
Figure 5-21: Annual Expenditure, Annual Total Revenue, and Cumulative Discounted
Net Cash Flow vs. Production Time ................................................................................ 147
Figure 5-22: Net Present Value vs. Interest Rate ..................................................................... 148
Figure 5-23: Field Optimization Results .................................................................................. 149
ix
LIST OF TABLES
Table 4-1: Volume-Translation Coefficients for Pure Components (Whitson and Brule,
2000) ................................................................................................................................ 31
Table A-1: Pressures and Temperatures for Standard PVT Properties Calculation
Subroutine ........................................................................................................................ 163
Table A-2: Physical Properties of Pure Components ............................................................... 163
Table A-3: Binary Interaction Coefficients of Pure Components ............................................ 164
Table A-4: Volume Translation Coefficient of Pure Components .......................................... 164
Table A-5: Reservoir Input Data .............................................................................................. 165
Table A-6: Relative Permeability Input Data .......................................................................... 165
Table A-7: Standard PVT Properties ....................................................................................... 166
Table A-7: Standard PVT Properties (Cont.) ........................................................................... 167
Table A-8: Tubing Input Data .................................................................................................. 168
Table A-9: Economic Input Data ............................................................................................. 168
Table A-9: Economic Input Data (Cont.)................................................................................. 169
Table A-10: Field Performance Prediction Input ..................................................................... 169
Table A-11: Field Performance Optimization Input ................................................................ 169
x
NOMENCLATURE
Normal Symbol Definition
Reservoir drainage area
Hyperbolic decline exponent
Co-volume parameter of i-th component
Formation volume factor
Gas formation volume factor
Oil formation volume factor
Two-phase gas formation volume factor
Two-phase oil formation volume factor
Overall molar faction of i-th component
Formation (rock) compressibility
Deitz shape factor
Non-Darcy coefficient / Tubing Diameter
Decline rate
Expansivity of formation (rock)
Expansivity of reservoir gas
Expansivity of reservoir oil
Expansivity of reservoir water
Efficiency factor of tubing
Fanning’s friction factor
Fugacity of i-th component in vapor phase
Fugacity of i-th component in liquid phase
Moody’s friction factor
Molar fraction of vapor phase
Molar fraction of liquid phase at reservoir condition
Molar fraction of liquid phase
Molar fraction of liquid phase at first-stage separator
Molar fraction of liquid phase at first-stage separator produced from
reservoir gas
Molar fraction of liquid phase at first-stage separator produced from
reservoir oil
Molar fraction of liquid phase at second-stage separator
Molar fraction of liquid phase at second-stage separator produced from
reservoir gas
Molar fraction of liquid phase at second-stage separator produced from
reservoir oil
Molar fraction of liquid phase at stock-tank condition
Molar fraction of liquid phase at stock-tank condition produced from
reservoir gas
Molar fraction of liquid phase at stock-tank condition produced from
reservoir oil
Fugacity of i-th component in original fluid
xi
Fugacity of i-th component in liquid-like phase
Fugacity of i-th component in vapor-like phase
Amount of surface gas pseudo component / Gas in place
Amount of gas-equivalent pseudo component
Amount of surface gas pseudo component in reservoir gas phase
Amount of surface gas pseudo component in reservoir oil phase
Amount of cumulative gas injection
Amount of cumulative gas production
Cumulative gas production at year Cumulative gas production at abandonment condition
Cumulative gas production at end of plateau
Cumulative gas recovery
Incremental of cumulative gas production
Annual gas production at year Incremental of gas recovery
Reservoir thickness
Elevation of upstream node
Elevation of downstream node
Difference in elevation of downstream and upstream node
Absolute permeability of reservoir
Effective permeability of reservoir gas
Relative permeability of reservoir gas
Relative permeability of reservoir oil
Volatility ratio of i-th component
Tubing length
Temperature dependency coefficient of i-th component
Molecular weight of vapor phase
Molecular weight of gas at reservoir condition
Molecular weight of i-th component
Molecular weight of oil at reservoir condition
Molecular weight of oil at stock-tank condition
Molecular weight of oil at stock-tank condition produced from reservoir
gas
Molecular weight of oil at stock-tank condition produced from reservoir
oil
Molecular weight of liquid phase
Molecular weight of remaining fluid inside PVT cell
Number of component in multi-component hydrocarbon
Mole fraction of excess gas removed from PVT cell
Mole fraction of remaining gas inside PVT cell
Mole fraction of remaining gas inside PVT cell plus excess gas
Mole fraction of remaining oil inside PVT cell
Mole fraction of remaining fluid inside PVT cell
Amount of stock-tank oil pseudo component / Oil in place
Amount of stock-tank oil pseudo component in reservoir gas phase
Amount of stock-tank oil pseudo component in reservoir oil phase
xii
Amount of cumulative oil production
Cumulative oil production at year Cumulative oil production at abandonment condition
Cumulative oil recovery
Reynolds number
Incremental of cumulative oil production
Annual oil production at year Incremental of oil recovery
Original gas in place
Original oil in place
Pressure
Upstream pressure
Downstream pressure
Average pressure between upstream and downstream
Critical pressure of i-th component
Drawdown pressure inside the reservoir
Pseudocritical pressure
Reservoir pressure
Reservoir pressure at abandonment condition
Reservoir pressure at end of plateau
Reduced pressure of i-th component
Pressure at standard condition
Bottomhole flowing pressure
Bottomhole flowing pressure at end of plateau
Wellhead pressure
Minimum allowable wellhead pressure
Pressure drop from initial reservoir pressure
Total gas flow rate of the field
Total gas flow rate of the field at abandonment condition
Total gas flow rate of the field during plateau period
Total oil flow rate of the field
Total oil flow rate of the field at abandonment condition
Gas flow rate per well
Gas flow rate per well during plateau period
Annual average gas flow rate of the field
Annual average oil flow rate of the field
Reservoir radius
Wellbore radius
Universal gas constant
Gas-oil equivalent factor
Fugacity ratio of i-th component
Solution gas-oil ratio
Solution gas-oil ratio at bubble point pressure
Volatilized oil-gas ratio
Volatilized oil-gas ratio at dew point pressure
Target recovery factor at end of plateau
xiii
Fugacity ratio of i-th component in liquid-like phase Fugacity ratio of i-th component in vapor-like phase
Total skin factor
Volume-translate coefficient of i-th component
Mechanical skin factor
Average reservoir gas saturation
Minimum gas saturation
Sum of the mole number of liquid-like phase
Average reservoir oil saturation
Sum of the mole number of vapor-like phase
Average reservoir water saturation
Connate water saturation
Specific gravity of gas
Production time
Production time at abandonment condition
Production time at end of plateau
Temperature
Temperature of upstream node
Temperature of downstream node
Pipe section average temperature
Critical temperature of fluid
Critical temperature of i-th component
Pseudocritical temperature of
Reduced temperature of i-th component
Temperature at standard condition
Fluid velocity
Retrograde liquid volume fraction
Amount of excess gas at reservoir condition
Amount of remaining gas phase at reservoir condition
Amount of remaining gas phase plus excess gas at reservoir condition
Amount of remaining oil phase at reservoir condition
Pore volume of reservoir
Original volume of PVT cell
Molar volume of phase ―a‖ calculated from EOS
Critical molar volume of i-th component
Molar volume of vapor phase
Molar volume of vapor phase calculated from EOS
Molar volume of liquid phase
Molar volume of liquid phase calculated from EOS
Pseudocritical molar volume
Amount of water pseudo component in reservoir water
Amount of water influx
Amount of cumulative water injection
Amount of cumulative water production
Molar fraction of surface gas pseudo component in reservoir oil
Molar fraction of i-th component in liquid phase
Molar fraction of stock-tank oil pseudo component in reservoir oil
xiv
Molar fraction of surface gas pseudo component in reservoir gas
Molar fraction of i-th component in vapor phase
Molar fraction of stock-tank oil pseudo component in reservoir gas
Molar fraction of i-th component in liquid-like phase Molar fraction of i-th component in vapor-like phase
Molar number of i-th component in liquid-like phase Molar number of i-th component in vapor-like phase
Compressibility factor of fluid
Two-phase compressibility factor
Compressibility factor of phase ―a‖
Average compressibility factor
Greek Symbol Definition
Coefficient to adjust relative permeability of reservoir gas
Turbulence parameter
Specific gravity of gas
Binary interaction coefficient between i-th and j-th component
Tubing roughness
Fluid viscosity
Viscosity of vapor phase / Viscosity of reservoir gas
Viscosity of i-th component at low pressure
Viscosity of liquid phase
Viscosity of liquid phase at low pressure
Viscosity of reservoir oil
Fluid density
Density of vapor phase
Density of gas phase at reservoir condition
Density of liquid phase
Density of oil phase at reservoir condition
Density of oil phase at stock-tank condition
Density of oil phase at stock-tank condition produced from reservoir gas
Density of oil phase at stock-tank condition produced from reservoir oil
Pseudo reduced density of liquid phase
Density of remaining fluid inside PVT cell
Molar density of reservoir gas
Molar density of surface gas pseudo component
Molar density of reservoir oil
Molar density of stock-tank oil pseudo component
Annual production time
Average reservoir porosity
Fugacity coefficient of i-th component in vapor phase
Fugacity coefficient of i-th component
Fugacity coefficient of i-th component in liquid phase
Pitzer’s acentric factor of i-th component
xv
ACKNOWLEDGEMENTS
First and foremost I would like to thanks my advisor, Dr. Luis Ayala, for his continuous
guidance, support and friendship throughout my graduate study. Without his encouragement and
invaluable advice, this research would not have been completed. Additional thanks are extended
to Dr. Larry Grayson, and Dr. Li Li for their interest and time in serving as my thesis committee.
I would like to express my sincere appreciation to Dr. Turgay Ertekin and Dr. Russel
Johns, and Dr. Zuleima Karpyn for the fundamental knowledge they have taught. I am also very
grateful for educational environment that the faculty and staff of the Department of Energy and
Mineral Engineering have created. I highly thank my sponsor, PTT Exploration and Production
Company, for every support they have given.
Many friends and colleagues have been very supportive. I would like to express my
gratitude to Pipat Likanapaisal, Nithiwat Siripatrachai and Kanin Bodipat who always are good
friends throughout my student life at Pennsylvania State University. I also thank all of my
colleagues for making me have meaningful time and experience.
Finally, but most deeply, I am forever in dept to my family, my father Phiraphong
Vardcharragosad, my mother Pikun Tanarungreung, my sister Pungjai Keandoungchun, and
sister’s family, for their support, encouragement, and most importantly their tolerance.
Chapter 1
Introduction
Natural gas is a natural occurring gas which consisting of methane primarily. It plays a
significant role in global economic as one of the main sources of energy. In 2009, world natural
gas reserves equaled 6.29 Trillion Standard Cubic Feet (TCF) while world production reached
106 BCF for the year (EIA, 2011). Conventional reservoirs consist of five different fluid types:
dry gas, wet gas, retrograde gas, volatile oil, and black oils (McCain, 1990). They are
distinguished from each other based on the present of fluid phases inside the reservoir and at
surface production facilities.
Field development and investment decisions in petroleum and natural gas require an
integration of expertise from various areas including geology, reservoir, drilling, completion,
process, and economic. Location and size of reservoirs, production rates and time, total
recoverable volumes, number of wells and platforms, drilling and completion techniques,
processing facilities scheme, cost and revenue, etc. are examples of information required for
adequate field development decisions. Field performance indicators consist of information
regarding flow rates, pressures, and production time is very important for field development. If
field performance indicators are satisfactorily predicted, the hydrocarbon field could be
developed using the best possible exploitation strategy while optimizing its economic
performance. If not, the field might end up with too many wells, processing facilities that are too
large, or wrong equipment sizing which can jeopardize profits or even lead to significant losses of
investor’s capital.
In modern age, computer simulation is used to simulate various types of mathematical
models which can couple geological, fluid property, reservoir, production network, processing
2
facilities, and economic information. Field performance could be predicted by integrating these
models together. However, the required type of mathematical model needs to be carefully
selected to be able to perform the calculation most effectively. For reservoir characterization, for
example, the modeler might utilize either a fully dimensional numerical model - which can aptly
capture all reservoir heterogeneities and geometry by discretizing it into many small grids -, or a
zero-dimensional model - which assumes average reservoir and fluid properties across the
domain. For fluid behavior characterization, the modeler might select either a fully compositional
model based on the use of an equation of state and detailed fluid composition data, or a black-oil
model - which uses the pseudo-component concept and relies on PVT laboratory results.
Selection of those models generally depends on availability of input data, time constraint, and
required accuracy of simulation results. In this study, a zero dimensional model coupled with a
black-oil PVT fluid description is implemented for the study of field development optimization
strategies in retrograde natural gas reservoirs.
Chapter 2
Background
2.1 Gas Condensate Hydrocarbon Fluid
A gas condensate, retrograde gas condensate, or retrograde gas, is one of the five
reservoir fluid types (McCain, 1990). The typical phase envelope of gas condensate reservoirs is
shown in Figure 2-1. Gas condensates contain more intermediate and heavy hydrocarbon
components more than dry gases or wet gases. As shown in Figure 2-1, their reservoir
temperature is located in between the fluid’s critical temperature and their cricondentherm. The
reservoir depletion path of a gas condensate fluid typically crosses the dew point line and a liquid
phase appears at reservoir pressures lower than that of the dew point. The presence of liquid
phase in the reservoir significantly increases the system complexity, even if this liquid phase does
not flow and is very unlikely to be produced under normal production conditions.
Figure 2-1: Phase Diagram of Typical Gas Condensate Reservoir
Re
serv
oir
Pre
ssu
re
Reservoir Temperature
ReservoirDepletion
Path
SurfaceDepletion
Path
Critical Point
4
The general characteristics of gas condensate reservoir fluid can be summarized as
follows (Walsh and Lake, 2003):
Initial Fluid Molecular Weight: 23 – 40 lb/lbmol
Stock-Tank Oil Color: Clear to Orange
Stock Tank Oil Gravity: 45 – 60 API
C7-plus Mole Fraction: 0.01 – 0.12
Typical Reservoir Temperature: 150 – 300 F
Typical Reservoir Pressure: 1500 – 9000 psia
Volatilized Oil-Gas Ratio: 50 – 300 STB/MMSCF
Primary Recovery of Original Gas In Place: 70% – 85%
Primary Recovery of Original Oil In Place: 30% - 60%
5
2.2 Modified Black-Oil Model
A black-oil fluid model is a fluid characterization formulation which represents multi-
component hydrocarbon mixture in terms of two hydrocarbon pseudo components, namely the
―surface gas‖ and ―stock-tank oil‖ pseudo components. In a traditional black-oil model, the
solubility of the ―surface gas‖ pseudo component in the reservoir oil fluid phase is taken into
account while the solubility of ―stock-tank oil‖ pseudo component in reservoir gas phase is
neglected. The modified black-oil model which also called two-phase two-pseudo component
model does not neglect the ―stock tank oil‖ solubility in the gaseous reservoir phase, thus
including both solubility variables into the formulation. Figure 2-2 shows the distribution of
surface gas and stock-tank oil pseudo components among reservoir gas and reservoir oil phases.
Figure 2-2: Distributions of Pseudo Components among Phases
in Modified Black-Oil Model
The assumptions behind the modified black-oil PVT model can be summarized as
follows (Walsh and Lake, 2003 and Whitson and Brule, 2000):
There are two pseudo components which are surface gas and stock-tank oil.
There are two fluid phases which are reservoir gas (vapor) and reservoir oil
(liquid) phases.
Surface GasStock-Tank
Oil
Surface Gas Stock-Tank Oil
Reservoir GasPhase
Reservoir OilPhase
6
Surface gas pseudo component is reservoir fluid which remains in gas phase at
standard condition.
Stock-tank oil pseudo component is reservoir fluid which remains in oil phase at
standard condition.
The reservoir gas phase, which is reservoir fluid remains in vapor phase at
reservoir condition, consists of surface gas and stock-tank oil pseudo
components.
The reservoir oil phase, which is reservoir fluid remains in liquid phase at
reservoir condition, consists of surface gas and stock-tank oil pseudo
components.
Properties of surface gas and stock-tank oil pseudo components remain the same
throughout the reservoir depletion.
7
2.3 Zero-Dimensional Reservoir Model
The Material Balance Equation (MBE) is a specialized type of mass balance equation that
combines mass balance equations of all pseudo components present in the reservoir into single
equation. The MBE is also called zero-dimensional reservoir model or tank model because it
assumes that a reservoir behaves like a homogeneous tank with average rock and fluid properties
across the domain. Pressure, temperature, and compositional gradients are thus neglected. MBEs
can be derived from integrating diffusivity equations over space and time.
Figure 2-3: Graphical Representation of Zero-Dimensional Reservoir Model
(Source: http://www.joe.co.jp/english/menu2-5.html)
The following assumptions are implemented in traditional in zero-dimensional reservoir
models:
Reservoir is isothermal
Reservoir is under thermodynamic equilibrium condition
There are no chemical and biological reaction in reservoir
Capillary pressures of reservoir fluids are negligible
Gravitational gradients in reservoir are negligible
Pressure gradients in reservoir are negligible
8
2.4 Field Performance Prediction
A field performance prediction consists in the calculations of pressures, flow rates,
cumulative productions, and expected production times based on available reservoir, production
network, and production constraint data. Field life is divided into three periods which are build-
up, plateau, and decline periods (Ayala, 2009a), as depicted in Figure 2-4. During build-up
period, gas flow rate per well ( ) is kept constant while number of wells continuously
increases until total maximum number of wells needed for field development is reached. During
the plateau period, both gas flow rate per well ( ) and number of wells are fixed; therefore,
total gas flow rate ( ) (equal to gas flow rate per well ( ) times number of wells) remains
constant. During decline period, wellhead pressure ( ) is kept constant at the minimum
allowable wellhead pressure ( ). Under such conditions, reservoir pressure ( ) becomes too
low to maintain the target plateau rate, thus gas flow rate ( ) continuously declines until
abandonment condition is reached.
9
Figure 2-4: Typical Field Performance of Gas Condensate
– Gas and Oil Flow Rates vs. Time
Figure 2-4 through Figure 2-6 show the typical field performance predictions for the
development of a gas condensate reservoir. As indicated earlier, gas flow rate ( ) increases
with increasing production time during the build-up period because more wells are put on
production. Then, it is kept constant until the end of the plateau period. During final decline
period, gas flow rate ( ) continuously decreases with production time because reservoir
pressure ( ) becomes not enough to sustain the plateau rate. Above dew point conditions, oil
flow rate ( ) produced at the surface becomes directly proportional to gas flow rate ( ).
However, once reservoir conditions reach the dew point, condensate production at the surface
becomes a function of both gas flow rate ( ) and the volatilized oil-gas ratio ( ) at reservoir
conditions. Figure 2-4 shows that even if gas flow rate ( ) is maintained at a constant target
value during the plateau period, oil flow rate ( ) can actually decreases because of decreasing
volatilized oil-gas ratio ( ) below the dew point.
qo
sc-
Tota
l Oil
Flo
w R
ate
qg
sc-
Tota
l Gas
Flo
w R
ate
Production Time
qgsc
qosc
Dew Point
Build-up Plateau Decline
10
Figure 2-5: Typical Field Performance of Gas Condensate
– Reservoir Pressure, Bottomhole Flowing Pressure
and Wellhead Pressure vs. Time
Figure 2-5 demonstrates that, during field development calculations, reservoir pressure
( ) decreases as production time increases because more oil and gas are being removed from the
reservoir. Wellhead pressure ( ) is also continuously decreased in time in order to maintain the
gas flow rate ( ) per well during the build-up and plateau periods. After that, once wellhead
pressure ( ) reaches the minimum allowable wellhead pressure at surface conditions, the
plateau gas flow rate ( ) cannot be maintained any longer and the decline period starts.
Bottomhole flowing pressure ( ) changes along with changes in reservoir pressure ( ) and
wellhead pressure ( ) in order to provide the required pressure drop within the reservoir and
production tubing.
Pre
ssu
re
Production Time
pr
pwf
pwh
Build-up Plateau Decline
Minimum Allowable Wellhead Pressure
11
Figure 2-6: Typical Field Performance of Gas Condensate
– Cumulative Gas and Oil Production vs. Time
Figure 2-6 shows cumulative gas ( ) and cumulative oil ( ) production are directly
related to their corresponding flow rates. Above dew point conditions, both of them increase at
the same pace. Below the dew point, however, cumulative oil production ( ) builds up at a
much slower rate compared to that of cumulative gas production ( ) because of the increased
reservoir condensation driven by a decreasing volatilized oil-gas ratio ( ). Recovery factor of
gas at abandonment condition would therefore become much higher than the recovery factor of
oil or condensate because large amounts of condensate are left behind as immobile phase inside
the reservoir.
Np
-C
um
ula
tive
Oil
Pro
du
ctio
n
Gp
-C
um
ula
tive
Ga
s P
rod
uct
ion
Production Time
Gp
Np
Build-up Plateau Decline
12
2.5 Visual Basic for Applications (VBA)
Visual Basic for Applications (VBA) is a programming language from Microsoft. The
program is built into most MS-Office applications i.e. MS-Word, MS-Excel, MS-Access. Users
can use VBA to create calculation subroutine and control user interface features such as menus,
toolbars, worksheets, charts, etc (Walkenbach, 2007). VBA can only run within the host
application, and not as a standalone application. VBA is functionally rich, and flexible. Because it
is built into MS-Office applications, VBA subroutines will be able to execute so long as those
applications are available on computer machines. MS-Excel with built in VBA is a very favorable
platform for developing simulations. The main reasons are that most of engineers are familiar
with MS-Excel application and MS-Excel itself is user-friendly software with many useful built-
in features. Excel’s worksheets could be used as table to store input data. Simulation results could
be easily stored in the tabular form and displayed on various types of built-in chart.
Chapter 3
Problem Statement
In the development of a petroleum and natural gas reservoir, projected field performance
is the most important information required by all relevant people involved in the process of
design, risk assessment, and decision-making process. Field performance analysis can require a
significant amount of expertise and time, especially for more complex reservoir fluid system such
as gas condensates. The use of the appropriate modeling approach is the key to analyze the field
performance most efficiently. Full scale, fully dimensional, commercial simulators might not be
able to yield the best or optimized solutions even if they are based on of highly sophisticated
mathematical models. This is because more sophisticated and detailed models are subject to the
availability of very detailed set of reservoir and fluid data, which is typically scarce, and time
constraints and demands. In the analysis of gas condensates, for example, commercial simulators
often rely on compositional modeling for fluid property calculations. Compositional models can
accurately simulate reservoir fluid properties; however, it is sophisticated model and can take a
relatively long time to run. For reservoir fluid flow characterization, commercial simulators
generally rely on fully dimensional numerical models which could perfectly capture reservoir
heterogeneities; yet, they can take a significant amount of time to construct, conceptualize, and
execute. Again, the limited availability and uncertainty of required input data such as fluid
composition, reservoir heterogeneities, capillary pressures, and relative permeabilities could
significantly impact the reliability of the results obtained from these sophisticated models.
This study aims at developing a model which can efficiently and inexpensively perform
field performance analysis and optimization tasks for gas condensate reservoirs. The proposed
model utilizes a zero-dimensional reservoir formulation coupled with a pseudo component or
14
black oil PVT formulation for fluid properties calculation. These models are relatively simple, but
fast, reliable, and robust. Results show that the proposed model is able to predict field
performance while faithfully capturing the most salient characteristics of gas condensate
reservoirs. In addition, optimization on targeted variables can be accomplished without difficulty.
Chapter 4
Model Description
The proposed field performance predictor has been developed using Microsoft Excel with built-in
Visual Basic for Applications (VBA) subroutines. Workflow begins with the simulation of
standard black-oil PVT properties, which could be done either based on standard PVT laboratory
results (such as the Constant Volume Expansion or CVD) or via a phase behavior model based on
cubic equations of state. Next, field performance data is calculated by integrating a zero-
dimensional reservoir model, standard PVT fluid properties, well performance models for flow
rates and pressure calculation, and production constraints. Based on this, an economic analysis
can be performed based on simplified economic model. Finally, optimization on target variables
can be carried out by evaluating field performance and net present value repeatedly for different
and plausible production scenarios. The proposed simulation tool has been designed to simulate a
single gas condensate reservoir based on the continuous drilling of identical wells placed at
different locations of the reservoir area. Wellhead pressure is used to control gas flow rate.
Reservoir pressure is used as the abandonment criteria. Optimization variables are target recovery
factor at end of plateau and total number of wells. Those variables could be re-selected by simple
modification in the VBA code. However, optimization variables can be made independent for a
real field operation.
16
4.1 Phase Behavior Model (PBM)
A phase behavior calculation (or a flash calculation) is used to predict the phase behavior
of a reservoir fluid at an equilibrium condition. A standard phase behavior model consists of four
main calculation modules; namely, compressibility factor calculations, vapor-liquid equilibrium
calculations, fluid properties predictions, and phase stability analysis, which must be fully
integrated to perform the flash calculation. The calculation starts with the determination of
number of co-existent phases or phase stability analysis. If fluid is found in a single phase (stable)
condition, fluid properties are calculated based on the available information on overall fluid
composition. If fluid is found in a two-phase (unstable) condition, composition and molar fraction
of each phase are determined using vapor-liquid equilibrium calculations. Then properties of each
co-existent phase are calculated based on fluid composition of that phase (Ayala, 2009b).
Input data consists of pressure, temperature, overall composition, physical properties,
binary interaction coefficients, and volume translation coefficient of each pure component. Peng-
Robinson Equation-of-State (PR EOS) is used to calculate Pressure-Volume-Temperature (PVT)
relationship of the reservoir fluid (Peng and Robinson, 1976). Vapor-liquid equilibrium is
assumed and an overall species material balance for a two-phase system is enforced. The output
from a PBM subroutine consists of number of phases, molar fraction, composition, molecular
weight, compressibility factor, density, adjusted density and viscosity of each fluid phase.
17
4.1.1 Compressibility Factor
Compressibility factor or Z-factor is volumetric multiplier utilized to convert ideal gas
volumes, as predicted by the ideal gas equation of state, to real gas volumes, as realized
experimentally. Compressibility factor is a fundamental and very important variable because
other fluid properties can be calculated based on compressibility factor data. Z-factor calculation
subroutine is developed based on generalized formulation (Coats, 1985). Although Peng-
Robinson EOS is utilized throughout this study, other EOSs could also be applied by
implementing simple modifications outlined below
When the fluid is in a single phase condition, overall composition will be inputted into
generalized formula for the calculation of the single-phase compressibility factor. However, when
the fluid is in two-phase condition, composition of each phase must be first calculated based on
vapor-liquid equilibrium calculations in order to estimate the corresponding compressibility
factors of each phase.
Generalized Formulation
Compressibility factor depends on the chosen PVT relationship or equation of state
(EOS). The generalized formula for cubic EOS proposed by Coats is utilized (Coats, 1985). This
form can be applied for Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), and Peng-Robinson
(PR) EOSs (Redlich, O. and Kwong, J.N.S. 1949, Soave, G. 1972, and Peng and Robinson,
1976).
18
Equation 4-1
where:
= number of components in the multi-component hydrocarbon
= molar fraction of the i-th component
= binary interaction coefficient between the i-th and j-th components
= reduced pressure of the i-th component =
= reduced temperature of the i-th component =
= critical pressure of the i-th component {psia}
= critical temperature of the i-th component {R}
= pressure {psia}
= temperature {R}
19
, which accounts for the temperature dependency built into the molecular attraction
parameter, is calculated from Equation 4-2 for PR EOS and from Equation 4-3 for SRK EOS.
Equation 4-2
Equation 4-3
where:
= Pitzer’s acentric factor of the i-th component
Pressure, temperature, molar fraction, and properties of pure components are input into
the generalized EOS formula shown above which yields a cubic polynomial in Z. Analytical,
semi-analytical, or numerical approach can be used to solve this cubic equation. In this work, the
analytical approach is applied.
20
Z-Factor Selection
Because of the nature of cubic equation, more than one root could be found for any given
pressure, temperature, and fluid composition. As described by Danesh (p. 176), the following
criteria are used for Z-factor selection (Danesh, 1998). If there is only one real root, Z-factor is
equal to that root. If there is more than one real root, the following criteria must be applied.
The intermediate root will always be rejected.
If the minimum Z-factor is less than B, maximum Z-factor will be selected.
If the minimum Z-factor is higher than B, The root that provides the lower Gibbs
energy will be selected.
Z-factor which is less than B must be rejected because when Z-factor is less than B,
molar volume becomes smaller than the co-volume. For this reason, such Z-factor would have no
physical meaning. For the last condition in the list above, Equation 4-4 is used to find the root
with lower Gibbs energy. Following Danesh (1998), if the right hand side of this equation is
positive, minimum Z-factor will be selected. Otherwise, the maximum Z-factor will be selected.
Equation 4-4
21
4.1.2 Vapor-Liquid Equilibrium
Two main components are considered in order to predict properties of multi-component
hydrocarbon in Vapor-Liquid Equilibrium (VLE) condition: material balance considerations and
thermodynamic considerations. Iterative procedure is applied until the solution that satisfies both
criteria can be determined.
Material Balance Considerations
Rachford and Rice objective function, which is derived from enforcing an overall species
mass balance in a two-phase multi-component system, is utilized to calculate molar fraction of
each phase (Rachford and Rice, 1952):
Equation 4-5
where:
= molar faction of i-th component
= volatility ratio of i-th component =
= molar fraction of i-th component in vapor phase
= molar fraction of i-th component in liquid phase
= molar fraction of vapor phase
22
After solving for from the objective function, molar fraction of liquid phase is
calculated from Equation 4-6, composition of vapor phase is calculated from Equation 4-7, and
composition of liquid phase is calculated from Equation 4-8.
Equation 4-6
Equation 4-7
Equation 4-8
Thermodynamic Considerations
According to the second law of thermodynamics, any system in equilibrium, such as a
VLE condition, must have the maximum possible entropic state under the prevailing conditions.
For such condition to be established, thermodynamics shows that net transfer of heat, momentum,
and mass between both phases must be zero. Thus, temperature, pressure, and every species
chemical potential in both phases must be equal to each other.
23
Chemical potential cannot be measured directly. However, equality of chemical potential
can be represented by equality of fugacity between both phases. Fugacity is the pressure
multiplier to correct non-ideality and to make ideal gas equation work for real gas during Gibbs
energy calculations. In a VLE condition, fugacity of liquid phase must be equal to fugacity of
vapor phase. Equation 4-9 is used to calculate fugacity for vapor phase while Equation 4-10 is
used for liquid phase.
Equation 4-9
Equation 4-10
where:
= fugacity of i-th component in vapor phase
= fugacity of i-th component in liquid phase
= fugacity coefficient of i-th component in vapor phase
= fugacity coefficient of i-th component in liquid phase
= molar fraction of i-th component in vapor phase
= molar fraction of i-th component in liquid phase
= pressure {psia}
24
For the generalized formula of cubic EOSs discussed above, fugacity coefficients can be
calculated using Equation 4-11 (Coats, 1985) below. Definitions of parameters are the same as
definitions used in Equation 4-1. It should be noted that is equal to for calculating fugacity
coefficient of a liquid phase and is equal to for calculating fugacity coefficient of a vapor
phase.
Equation 4-11
Volatility ratio ( ) is equal to ratio between the gas composition and the liquid
composition during an equilibrium condition. For a system with a VLE condition, is equal
to . By substituting Equation 4-9 and Equation 4-10 into definition of volatility ratio, volatility
ratio can be expressed in terms of fugacity coefficients as follows.
Equation 4-12
25
The Successive Substitution Method
From material balance consideration, molar fraction of vapor phase and composition of
each phase are functions of volatility ratios and overall composition. Volatility ratios themselves
are also function of composition of each phase. Thus, an iterative procedure is needed in order to
perform VLE prediction and honor the fugacity equality constraint. The following procedure is
used to perform two-phase flash calculation (Whitson and Brule, 2000, p.52-55).
First, initial guesses of volatility ratios are calculated using Equation 4-13 as proposed by
Wilson (Wilson, 1968). Rachford and Rice objective function (Equation 4-5) is then solved using
a standard Newton-Raphson iterative method. Then, the compositions of each phase are
calculated using Equation 4-7 and Equation 4-8.
Equation 4-13
Next, the fugacity values of each component in both liquid and vapor phases are
calculated using Equation 4-9 through Equation 4-11. Successive Substitution Method (SSM) is
utilized to update volatility ratios (Equation 4-14) for a next iteration as shown below
Equation 4-14
26
where:
= volatility ratio of i-th component at iteration level n
= fugacity of i-th component in liquid phase at iteration level n
= fugacity of i-th component in vapor phase at iteration level n
Once volatility ratios are updated, convergence criteria presented in Equation 4-15 must
be checked. If the criteria are not satisfied, the procedure is repeated by solving Rachford and
Rice objective function and recalculating phase compositions and resulting fugacities until
convergence is attained.
Equation 4-15
The SSM algorithm is expected to have slow convergence rate near the critical point. To
avoid this problem, accelerated SSM algorithm has been proposed. The algorithm proposed by
Michelsen (Michelsen, 1982b) or the algorithm proposed by Merah et al (Merah et al, 1983) are
examples of well-known ASSM algorithms.
27
4.1.3 Fluid Property Prediction
Molecular Weight
Molecular weight of vapor and liquid phases are weighted average of molecular weight
of all pure components, as shown below
Equation 4-16
Equation 4-17
where:
= molecular weight of vapor phase {lb/lbmol}
= molecular weight of liquid phase {lb/lbmol}
= molecular weight of i-th component {lb/lbmol}
= mole fraction of i-th component in vapor phase
= mole fraction of i-th component in liquid phase
= number of components in the multi-component hydrocarbon
28
Density
Density of each phase is calculated from Equation 4-18 and Equation 4-19.
Equation 4-18
Equation 4-19
where:
= density of vapor phase {lbm/ft3}
= density of liquid phase {lbm/ft3}
= molecular weight of vapor phase {lbm/lbmol}
= molecular weight of liquid phase {lbm/lbmol}
= molar volume of vapor phase {ft3/lbmol}
= molar volume of liquid phase {ft3/lbmol }
29
Molar volume of each phase is calculated from real gas law (Equation 4-20), then,
adjusted by using volume-translation technique.
Equation 4-20
where
= calculated molar volume of phase ―a‖ from EOS {ft
3/lbmol}
= compressibility factor of phase ―a‖
= universal gas constant {10.732 psi-ft3/R-lbmol}
= temperature {R}
= pressure {psia}
As discussed by Whitson and Brule (p.51) and Danesh (p.141-143), calculated molar
volume from real gas law can be adjusted by implementing volume-translation or volume-shift
technique (Whitson and Brule, 2000 and Danesh, 1998). This technique improves volumetric
calculation of liquid phase, which is the main problem of two-constant EOS’s, without altering
VLE prediction results. The volume translation technique, originally introduced by Martin and
further developed by Penelous et al and Jhaveri and Youngren, can be summarized as follows
(Martin, 1979, Penelus et al, 1982, and Jhaveri and Youngren, 1988):
30
Calculated molar volumes from the selected EOS are corrected by using Equation 4-21
and Equation 4-22. Component-dependent volume-shift parameters ( ) are calculated from
Equation 4-23 and volume-translate coefficients are in Table 4-1.
Equation 4-21
Equation 4-22
where:
= corrected molar volume of liquid phase
= corrected molar volume of vapor phase
= calculated molar volume of liquid phase from EOS
= calculated molar volume of vapor phase from EOS
= component-dependent volume-shift parameter
= molar fraction of i-th component in liquid phase
= molar fraction of i-th component in vapor phase
= number of components in the multi-component hydrocarbon
31
Equation 4-23
where:
= component-dependent volume-shift parameter
= co-volume parameter of i-th component
= volume-translate coefficient of i-th component
Table 4-1: Volume-Translation Coefficients for Pure Components (Whitson and Brule, 2000)
Component PR EOS SRK EOS
N2 -0.1927 -0.0079
CO2 -0.0817 0.0833
H2S -0.1288 0.0466
C1 -0.1595 0.0234
C2 -0.1134 0.0605
C3 -0.0863 0.0825
i-C4 -0.0844 0.0830
n-C4 -0.0675 0.0975
i-C5 -0.0608 0.1022
n-C5 -0.0390 0.1209
n-C6 -0.0080 0.1467
n-C7 0.0033 0.1554
n-C8 0.0314 0.1794
n-C9 0.0408 0.1868
n-C10 0.0655 0.2080
32
Viscosity
Viscosity of vapor phase is calculated from the correlation proposed by Lee et al in 1966
(Equation 4-24 through Equation 4-27).
Equation 4-24
Equation 4-25
Equation 4-26
Equation 4-27
where:
= viscosity of vapor phase {cp}
= density of vapor phase {lbm/ft3}
= molecular weight of vapor phase {lbm/lbmol}
= temperature {R}
33
The viscosity of a liquid phase is calculated from the correlation proposed by Lohrenz et
al in 1964. The correlation is originally proposed by Jossi et al in 1962 for calculating viscosity
of pure component. Lohrenz et al extend the use of original correlation to hydrocarbon mixtures.
It should be noted that the formula in Lohrenz et al’s paper contains a typing error on coefficient
0.040758 for the cubic density term.
Equation 4-28
where:
= viscosity of liquid phase {cp}
= viscosity of liquid phase at low pressure {cp}
= viscosity parameter of liquid phase (mixture) {cp-1
}
= pseudo reduced density of liquid phase
Viscosity of liquid phase at low pressure is calculated from Equation 4-29, Equation
4-30, and Equation 4-31. A conversion factor of 5.4402 is used to convert original units (K and
atm) to oil field units (R and psia).
Equation 4-29
34
Equation 4-30
Equation 4-31
where:
= viscosity of liquid phase at low pressure {cp}
= molar fraction of i-th component in liquid phase
= viscosity of i-th component at low pressure {cp}
= viscosity parameter of i-th component {cp-1
}
= reduce temperature of i-th component ( )
= temperature {R}
= critical temperature of i-th component {R}
= critical pressure of i-th component {psia}
= molecular weight of i-th component {lbm/lbmol}
= number of components
Viscosity parameter of liquid phase is calculated from Equation 4-32 to Equation 4-35.
Equation 4-32
35
Equation 4-33
Equation 4-34
Equation 4-35
where:
= viscosity parameter of liquid phase (mixture) {cp-1
}
= pseudocritical temperature of liquid phase {R}
= critical temperature of i-th component {R}
= pseudocritical pressure of liquid phase {psia}
= critical pressure of i-th component {psia}
= molecular weight of liquid phase {lbm/lbmol}
= molecular weight of i-th component {lbm/lbmol}
= molar fraction of i-th component in liquid phase
= number of components
36
Pseudo reduced density of the liquid phase is calculated from Equation 4-36 and
Equation 4-37 shown below.
Equation 4-36
Equation 4-37
where:
= pseudo reduced density of liquid phase
= density of liquid phase {lbm/ft3}
= molecular weight of liquid phase {lbm/lbmol}
= pseudocritical molar volume of liquid phase {ft3/lbmol}
= critical molar volume of i-th component {ft3/lbmol}
= molar fraction of i-th component in liquid phase
= number of components
37
4.1.4 Phase Stability Analysis
The ability to predict whether the system is in single phase (stable) or multiple phases
(unstable) is crucial in a VLE or flash calculation. Whitson and Brule (p.55-61) discuss the
graphical representation as well as numerical algorithm of phase stability analysis based on the
studies by Baker et al and Michelsen (Whitson and Brule, 2000; Baker et al, 1982; Michelsen,
1982a). These studies explain how the Gibbs tangent-plane criteria can effectively be used to
analyze the phase stability problem. The phase stability analysis subroutine utilized by this study
has been developed based on these calculation procedures, which can be summarized in the 11
steps outlined below.
Step 1: Calculate the mixture fugacity from overall composition using Equation 4-9 /
Equation 4-10 and Equation 4-11. The Z-factor yielding the lowest Gibbs energy should be
utilized for the calculation of mixture fugacity.
Step 2: Use Wilson’s equation to estimate initial values (Equation 4-13).
Step 3: Calculate second-phase mole number, , using the mixture composition and the
estimated K values.
Equation 4-38
Equation 4-39
38
where:
= mole number of i-th component in vapor-like phase
= mole number of i-th component in liquid-like phase
= mole fraction of i-th component
= volatility ratio of i-th component
Step 4: Sum the mole numbers of vapor-like phase ( ) and liquid-like phase ( ).
Equation 4-40
Equation 4-41
Step 5: Normalize the mole numbers to get the mole fraction of i-th component in vapor-
like phase, and liquid-like phases,
Equation 4-42
Equation 4-43
39
Step 6: Calculate the fugacity of vapor-like and liquid-like phases based on the calculated
mole fraction from Step 5. Equation 4-9 , Equation 4-10 and Equation 4-11 are utilized.
Step 7: Calculate the fugacity ratio corrections for successive substitution update of the
values.
Equation 4-44
Equation 4-45
where:
= fugacity ratio calculation of i-th component in vapor-like phase
= fugacity ratio calculation of i-th component in liquid-like phase
= fugacity of i-th component in original fluid
= fugacity of i-th component in vapor-like phase
= fugacity of i-th component in liquid-like phase
= Sum the mole numbers of vapor-like phase
= Sum the mole numbers of liquid-like phase
40
Step 8: Check whether convergence criteria is achieved
Equation 4-46
Step 9: If convergence is not obtained, update values
Equation 4-47
Step10: Apply criterion to check whether a trivial solution has been obtained
Equation 4-48
Step 11: If a trivial solution is not indicated, go to Step 3 for the next iteration.
41
The following criteria are used to interpret the results from this numerical algorithm:
If the tests on both vapor-like and liquid-like phases satisfy trivial solution
criterion, the system of interest is stable (single phase)
If sum of the mole numbers on both vapor-like and liquid-like phases is less than
or equal to 1.0, the system of interest is stable (single phase).
If one of the pseudo phases satisfies trivial solution criterion and sum of the mole
numbers of the other pseudo phase is less than or equal to 1.0, the system is
stable (single phase).
Otherwise, the system is unstable; both vapor and liquid phases coexist.
42
4.2 Standard PVT Properties
The standard PVT properties used to describe a two-phase, two-pseudo component fluid
model (―black oil model‖) relies on the definition and calculation of four basic properties,
namely: gas formation volume factor ( ), oil formation volume factor ( ), volatilized oil-gas
ratio ( ), and solution gas-oil ratio ( ). These PVT properties are required inputs for a zero-
dimensional reservoir model. In this study, these required PVT properties can be obtained from
either a laboratory fluid analysis, typically a Constant Volume Depletion (CVD) test, or from a
phase behavior model (PBM) calculation. If the PVT/CVD laboratory report is available, the
resulting PVT properties are calculated using Walsh-Towler algorithm (Walsh and Lake, 2003).
A template has been prepared using MS-Excel worksheet for this purpose. In the absence of a
PVT lab report, a PBM calculation is implemented which combines Walsh-Tolwer method with
the work of Thararoop in 2007 (Thararoop, 2007). This PBM subroutine does not only extend the
flexibility of the main simulator significantly, but also provide very useful information about fluid
properties which could help in thoroughly analyzing the depletion characteristics of the given gas
condensate fluid.
The specific gravity of reservoir gas is required for flow rate and flowing pressure
calculations, as it will be discussed below. The specific gravity of a reservoir gas can be obtained
from either the laboratory fluid analysis or from molecular weight calculations derived from
PBM. If the lab analysis is available, compositions of the produced wellstreams reported in the
experimental depletion study based on the Constant Volume Depletion (CVD) test are used to
calculate molecular weight of reservoir gas. If the lab report is unavailable, the molecular weight
of the reservoir gas is obtained directly from flash/PBM calculation results. Specific gravity of
reservoir gas is equal to molecular weight of reservoir gas divided by molecular weight of air.
43
4.2.1 Definitions, Mathematic Relationships, and Characteristics
A clear understanding of the definitions of standard PVT ―black oil‖ properties that are
used to characterize two-phase, two-pseudo component fluid models is crucial for their
meaningful calculation and prediction. These definitions, mathematic relationships, and their
most significant features have been summarized below (Walsh and Lake, 2003; Whitson and
Brule, 2000).
Definitions
Figure 4-1shows the graphical representation of the definitions of the standard PVT
properties used in the formulation of two-phase, two-pseudo component fluid model (or modified
―black-oil‖ model). In this figure, the gas phase at reservoir condition ( ) results from the mixing
of certain amounts of surface gas ( ) and stock-tank oil ( ) pseudo components. The oil
phase at reservoir condition ( ) results from the mixing of certain amounts of surface gas ( )
and stock-tank oil ( ) pseudo components. The produced gas phase at surface condition ( )
(not shown in the figure) would consists of the combination of surface gas pseudo component
produced from gas phase at reservoir condition ( ) and surface gas pseudo component liberated
from oil phase at reservoir condition ( ). By the same token, the produced oil phase at surface
condition ( ) (not shown in the figure) consists of stock-tank oil pseudo component produced
from oil phase at reservoir condition ( ) and stock-tank oil pseudo component condensed from
gas phase at reservoir condition ( ).
44
Figure 4-1: Graphical Representation of Standard PVT Properties
Based on the pseudo component definitions described above, the definitions of the
associated ―black oil‖ properties can be straightforwardly presented. For example, the formation
volume factor for the gas ( ) would be basically defined as ratio between volume of gas phase at
reservoir condition ( ) and volume of surface gas pseudo component produced from that
reservoir gas, evaluated at surface conditions ( ). Formation volume factor of oil ( ) is
defined as ratio between volume of oil phase at reservoir condition ( ) and volume of stock-tank
oil pseudo component produced from that reservoir oil, evaluated at surface condition ( ).
Volatilized oil-gas ratio ( ) is defined as ratio between volume of stock-tank oil ( ) and
volume of surface gas ( ) pseudo components produced from the same reservoir gas ( ),
evaluated at surface condition. Solution gas-oil ratio ( ) is defined as ratio between volume of
surface gas ( ) and volume of stock-tank oil ( ) pseudo components produced from the same
reservoir oil ( ), evaluated at surface condition. Mathematically, Equation 4-49 through
Vg
Vo
PR, TR
Reservoir Condition Surface Condition
Gfg
Nfg
Gfo
Nfo
Reservoir Gas
Reservoir Oil
Surface Gas
Stock-Tank Oil
Vg
Gfg
Bg = ----------- Rv = -----------
Nfg
Gfg
Bo = ----------- Rs = -----------
Vo
Nfo
Gfo
Nfo
Psc, Tsc
45
Equation 4-52 summarize, in oil field units, the standard PVT properties based on these
definitions and the nomenclature presented in Figure 4-1.
Equation 4-49
Equation 4-50
Equation 4-51
Equation 4-52
It follows from the preceding discussion that reservoir fluid compositions can be
calculated for the envisioned pseudo binary mixture. For example, the molar fraction of surface
gas pseudo component in the gas phase at reservoir conditions, defined as , should be directly
related to the value of Rv. Molar fraction of stock-tank oil pseudo component in gas phase at
reservoir condition would be defined as . Clearly, + = 1. For the oil reservoir phase, the
molar fraction of surface gas pseudo component in the oil phase at reservoir conditions would be
, and should be directly related to the value of Rs The molar fraction of stock-tank oil pseudo
46
component in oil phase at reservoir condition is thus defined as . Clearly, + = 1. Their
formulas are summarized in Equation 4-53 through Equation 4-56.
Equation 4-53
Equation 4-54
Equation 4-55
Equation 4-56
Mathematic Relationships
If only one mole of reservoir fluid is considered, volumes at reservoir condition, and
, can be represented by molar density at reservoir condition, and , respectively.
Similarly, volumes at surface condition, , , , and , can be represented by molar
fraction of pseudo component in reservoir fluid and molar density at surface condition, ,
, , and , respectively. If we substitute these definitions into equations for
47
standard PVT properties and substitute densities of gases with real gas equation, the following
expressions can be derived.
Equation 4-57
Equation 4-58
Equation 4-59
Equation 4-60
Depletion Characteristics
Figure 4-2 and Figure 4-3 show the typical depletion behavior of the standard PVT
properties for the case of a gas condensate reservoir fluid. Similar behavior can be found in the
work by Walsh and Lake (Walsh and Lake, 2003, p.493) for the case of field-data derived
properties.
48
Figure 4-2: Typical Characteristic of Gas Formation Volume Factor ( )
and Volatilized Oil-Gas Ratio ( ) for Gas Condensate
Figure 4-3: Typical Characteristic of Oil Formation Volume Factor ( )
and Solution Gas-Oil Ratio ( ) for Gas Condensate
Rv
-V
ola
tiliz
ed
Oil
-Gas
Rat
io
Bg
-G
as F
orm
atio
n V
olu
me
Fac
tor
Reservoir Pressure
Dew Point Pressure
Rv
Bg
Rs
-So
luti
on
Gas
-Oil
Rat
io
Bo
-O
il Fo
rmat
ion
Vo
lum
e F
acto
r
Reservoir Pressure
Dew Point Pressure
Bo
Rs
49
As shown in Figure 4-2, gas formation volume factors ( ) are expected to increase with
decreasing reservoir pressure ( ) because the denominator, , in Equation 4-57 approaches zero.
Volatilized oil-gas ratio ( ) will remain constant because all parameters in Equation 4-59 remain
the same. Constant values of , , and result from the constant composition of gas phase in
the reservoir. Once dew point conditions are reached, Figure 4-2 also shows that the volatilized
oil-gas ratio ( ) is expected to decrease with decreasing reservoir pressure, mainly because of
decreasing and increasing values in Equation 4-59. Driven by the condensate drop out that
develops in the reservoir below dew point conditions, the reservoir gas will start to contain less
heavy hydrocarbon molecules that can be produced as condensate at surface condition. As a
result, the fraction of stock-tank oil ( ) in the reservoir gas decreases while fraction of surface
gas ( ) increases ( + = 1). As pressure depletion progresses, and if it gets low enough, the
volatilized oil-gas ratio ( ) trend would be reversed.
Figure 4-3 illustrates that at reservoir pressure above the dew point there is no liquid
phase at reservoir condition and therefore no calculations of and can be directly performed
from their definitions. Once dew point conditions are crossed, oil formation volume factor ( ) is
expected to decrease with decreasing reservoir pressure mainly because of increasing and
values in Equation 4-58. As pressure decreases, more surface gas pseudo component will be
liberated from the oil phase. As a result, the molar fraction of stock-tank oil pseudo component in
oil phase ( ) becomes higher and the density of oil phase at reservoir condition ( ) also
increases. Similarly, the solution gas-oil ration ( ) will be expected to decrease with decreasing
reservoir pressure because of the increased molar fraction of stock-tank oil pseudo component in
oil phase ( ) and decreasing molar fraction of surface gas pseudo component in oil phase ( ) in
Equation 4-60. Even though oil formation volume factors ( ) and solution gas-oil ratios ( )
cannot be calculated directly because of the lack of an actual liquid phase at reservoir from their
50
definitions, Walsh and Lake suggest employing the following relationships for oil formation
volume factor ( ) and solution gas-oil ratio ( ) as ―place-holder‖ values above the dew point:
Equation 4-61
Equation 4-62
51
4.2.2 Obtaining Standard PVT Properties from Laboratory PVT Reports
In a laboratory PVT test, a representative sample of the reservoir fluid is subjected to a
series of depletion steps that try to closely mimic or reproduce the expected pressure depletion
path followed by the fluid during reservoir production. Temperature of the test is maintained
constant and equal to prevailing reservoir temperature. Resulting volumes of each phase (liquid
and vapor) are recorded along with the pressure at which the record is made. Fluid composition
and physical properties of the produced fluids are also analyzed. The typical standardized PVT
tests conducted for gas condensate fluids are the Constant Composition Expansion (CCE) and
Constant Volume Depletion (CVD) tests. Details of these PVT tests can be found in many
petroleum engineering textbooks (McCain, 1990; Denesh, 1998; Whitson and Brule, 2000, Walsh
and Lake, 2003); thus, they will be discussed very briefly in this manuscript.
In a CCE test, the reservoir fluid sample is placed inside a PVT cell and is pressurized to
a pressure equal to initial reservoir pressure, while maintaining a constant temperature inside the
PVT cell equal to reservoir temperature. Pressure inside the cell is then decreased to a next lower
pressure level by isothermal expansion. The new volume of each phase is recorded. This process
continues until abandonment pressure conditions are reached. In the CCE testing process, no fluid
is taken out the cell and therefore the overall composition of reservoir fluid inside the PVT cell
remains constant while the volumes and densities of each the co-existing phases below dew point
conditions do change with cell pressure.
In a CVD test, a reservoir fluid sample will be placed inside the PVT cell and pressurized
to the dew point pressure, while the temperature of the PVT cell is kept constant at reservoir
temperature. Then, pressure of the cell will be lowered to the next pressure level by isothermal
expansion. After that, a portion of gas phase inside the cell is produced (i.e., removed out of the
cell) so that the cell’s volume is restored back to the original cell volume at dew point conditions.
52
The volume that the liquid phase occupies inside the PVT cell is recorded and the excess
(produced) gas analyzed. Depletion study which provides the resulting cumulative production
data at every pressure level is recorded and is used during the calculation of the standard PVT
properties from laboratory PVT fluid test report.
In this study, a calculation template is prepared in MS-Excel worksheet. The Walsh-
Towler algorithm is implemented to convert the results from the CVD experiments into the
standard table of PVT properties for a gas condensate fluid. Walsh-Towler algorithm is
summarized below.
Walsh-Towler Algorithm
Walsh-Towler algorithm is one of the methods used to calculate standard PVT properties
for gas condensate based on CVD testing results (Walsh and Towler, 1995; Walsh and Lake,
2003). This algorithm is relatively simple because it based on enforcing material balance
constraints around the PVT cell at every pressure level during the PVT lab test. The algorithm
was originally proposed by Walsh and Towler in 1995 and was later modified by Walsh and Lake
in 2003. By directly using data from a CVD report, this algorithm is implicitly assuming that
actual field separator conditions of the surface production system is the same as those surface
condition used during the CVD PVT test. It also assumes that only the gas phase at reservoir
condition can be recovered and that any condensate drops out inside the reservoir will remain
immobile during reservoir life.
One of the constraints of using this method is the availability of cumulative production
data at surface conditions because such data is not always performed or reported for every CVD
experiment. If such cumulative production data at surface conditions is not available in the CVD
report, it is customarily recommended to implement surface flash calculations using Standing’s
53
K-values to reproduce them (Walsh and Lake, 2003). The algorithm also requires a high accuracy
and reliability of the CVD report in order to obtain a healthy and physically meaningful set of
derived standard PVT properties. It can be demonstrated that small error in the data reported by a
CVD test can result in PVT property values which are physically impossible (e.g., negative
values). And even when the data reported by the CVD report is highly reliable, the Walsh and
Towler algorithm can still lead to unphysical values for standard PVT properties. This limitation
results from combining the two-phase two-pseudo component (―black oil‖) model with material
balance calculation around the PVT cell. This limitation will be discussed in detail in Chapter 5.
Walsh-Towler algorithm consists of six sequential steps which must be fully completed at
every given pressure level before moving to the next pressure. One pre-calculation is also needed
before starting the algorithm. The variables and their nomenclature employed in the sequence of
calculations are graphically illustrated in Figure 4-4.
Figure 4-4: Graphical Representation of CVD Data used in Walsh-Towler Algorithm
Vg,j
Vo,j
Reservoir Condition Surface Condition
Gfg,j
Nfg,j
Gfo,j
Nfo,j
Reservoir Gas
Reservoir Oil
Surface Gas
Stock-Tank Oil
Vg,j
Gfg,j
Bg = ----------- Rv = -----------
Nfg,j
Gfg,j
Bo = ----------- Rs = -----------
Vo,j
Nfo,j
Gfo,j
Nfo,j
VT
VEG,j
PR ≥ PDew PR < PDew ∆Gpj
∆Npj
54
Pre-calculation: In this step, the total cumulative volumes of surface gas ( ) and stock-
tank oil ( ) pseudo components produced from the reservoir fluid, and the resulting volume of
PVT cell ( ) are calculated for the dew point condition. The volume of surface gas pseudo
component ( ) is calculated from the summation of cumulative gas recovery from 1st stage
separator, 2nd
stage separator, and stock tank for all available pressures - from dew point
conditions to the last reported (abandonment) pressure. The volume of stock-tank oil pseudo
components ( ) is equal to cumulative oil recovery from stock tank for all available and reported
pressures (dew point to abandonment). These data are obtained from the calculated cumulative
recovery reported in the depletion table.
PVT cell’s volume is calculated from the definition of gas formation volume factor
(Equation 4-63). The gas formation volume factor ( ) is calculated from Equation 4-57.
Compressibility factor of gas phase ( ) can be obtained from the CVD report. Mole fraction of
surface gas pseudo component in the reservoir gas ( ) is equal to divided by the volume of gas
equivalent at the dew point ( ) which is usually taken as 1000 MSCF.
Equation 4-63
Volatilized oil-gas ratio at dew point ( ) is calculated from Equation 4-64, while oil
formation volume factor ( ) and solution gas-oil ratio ( ) are calculated from Equation 4-61
and Equation 4-62, respectively.
55
Equation 4-64
Step 1: Find and : Starting at the dew point, the volume of surface gas pseudo
component released from the excess gas ( ) at each pressure is calculated from the summation
of cumulative gas recovery from 1st stage separator, 2
nd stage separator, and stock tank. Volume
of and stock-tank oil pseudo component released from the same excess gas ( ) at each pressure
is equal to cumulative oil recovery from stock tank. These data are obtained from the calculated
cumulative recovery reported in the depletion table. Incremental of and from pressure level
j-1 to pressure level j are calculated from Equation 4-65 and Equation 4-66. Please note that
pressure level j begins from zero at the dew point (j=0). , , , and are also
equal to zero.
Equation 4-65
Equation 4-66
Step 2: Find and : Total volume of surface gas ( ) and stock-tank oil ( ) pseudo
components released from both reservoir gas and reservoir oil at pressure level j are calculated
from Equation 4-67 and Equation 4-68. It should be noted that pressure level j begins from zero at
the dew point (j=0), and and are equal to and , respectively.
56
Equation 4-67
Equation 4-68
Step 3: Find and : Volume of oil phase at reservoir condition at pressure level j
( ) is calculated from Equation 4-69. Retrograde liquid volume fraction at pressure level j
( ), can be obtained from CVD report. Volume of gas phase after excess gas removal at
reservoir condition at pressure level j ( ) is calculated from Equation 4-70. Note that pressure
level j begins at zero at dew point conditions (j=0)
Equation 4-69
Equation 4-70
Step 4: Find , , and : Molar fraction of reservoir fluid which remains in the
PVT cell at pressure level j ( ) is calculated from Equation 4-71. For this calculation, two-
phase compressibility factor ( ) data can be obtained from the CVD report. Molar fraction of
excess gas which is removed from PVT cell at pressure level j ( ) is calculated from Equation
4-72. Molar fraction of gas phase which remain in PVT cell at pressure level j ( ) is calculated
from Equation 4-73. Compressibility factor of gas ( ) is also obtained from the CVD report.
57
Please note that pressure level j begins from zero (j=0) at the dew point. and at dew
point are equal to 1.0 while at dew point is equal to zero.
Equation 4-71
Equation 4-72
Equation 4-73
Step 5: Find and : Volume of surface gas pseudo component produced from
reservoir gas at pressure level j ( ) is calculated from Equation 4-74. Volume of stock-tank
pseudo component produced from reservoir gas at pressure level j ( ) is calculated from
Equation 4-75. It is important to note that pressure level j begins from zero at the dew point (j=0).
and at dew point pressure are equal to and , respectively.
Equation 4-74
58
Equation 4-75
Step 6: Find and : Volume of surface gas pseudo component produced from
reservoir oil at pressure level j ( ) is calculated from Equation 4-76. Volume of stock-tank oil
pseudo component produced from reservoir oil at pressure level j ( ) is calculated from
Equation 4-77.
Equation 4-76
Equation 4-77
After completing all six steps outline above for the given pressure level, Equation 4-49
through Equation 4-52 are now directly used to calculate the standard PVT properties. All
applicable unit conversion factors must be checked and adjusted properly. The calculation
process is systematically repeated for all pressure levels until all reported data in the CVD report
have been considered and abandonment conditions have been reached.
Standard PVT properties at pressures higher than the dew point are calculated based on
the properties at dew point pressure. Gas formation volume factor ( ) is the product of gas
formation volume factor at dew point pressure and relative volume obtained directly from CCE
testing results. The relative volume is the ratio between total volume of hydrocarbon at reservoir
conditions and the volume at saturated conditions. For under-saturated gas condensate system,
59
relative volume is equal to the ratio between at specified pressure and at dew point pressure.
Volatized oil-gas ratio ( ) is equal to volatilized oil gas ratio at dew point pressure. Oil
formation volume factor ( ) and solution gas-oil ratio ( ) are calculated from Equation 4-61
and Equation 4-62, respectively.
Finally, it is very important to mention that, in Walsh-Towler algorithm, volumes of
pseudo components produced from the reservoir oil (step 6) do not actually come from direct
surface measurement. In a CVD test, the oil inside the cell is never produced (is assumed
immobile) so surface data for produced oil is not available.. Instead, these values are indirectly
calculated based on the enforcement of mass balance constraints around the PVT cell. Therefore,
actual oil formation volume factor ( ) and solution gas-oil ratio ( ) calculated from actual
surface flashes of the reservoir fluid might be significantly different from the ones estimated
using these indirectly calculated surface volumes. If the calculated and resulting from the
application of this algorithm do not agree with the physically acceptable trends or values, the
results should be disregarded and the laboratory results have to be adjusted.
60
4.2.3 Obtaining Standard PVT Properties from a Phase Behavior Model
Another method for simulating standard PVT properties for gas condensate is to utilize
Phase Behavior Model (PBM). This method is based on combination of the algorithm used in
Walsh-Towler method and the work of Thararoop in 2007. The general idea of this method is to
substitute CVD testing results with the outputs from flash calculation. Mass balance around PVT
cell, which is used to obtain the properties of reservoir oil in Walsh-Towler algorithm, is replaced
with an actual flash calculation performed for both the reservoir gas and oil phases. Chapter 5
will discuss about the impact from these changes in more detail.
Input data required for this method include initial reservoir condition, surface separator
conditions, initial reservoir fluid composition, physical properties, binary interaction coefficients,
and volume translation coefficients of pure components. The simulation algorithm consists of
nine calculation steps and a pre-calculation. Parameters used in those equations were represented
graphically in Figure 4-4.
Pre-calculation: First, dew point pressure is determined using a phase stability
calculation. Then, mole of initial reservoir fluid inside PVT cell ( ), volume of PVT cell ( ),
volume of surface gas ( ) and stock-tank oil ( ) pseudo components are evaluated at dew point
condition.
The dew point pressure is determined by performing Phase Stability Analysis. Stability of
initial reservoir fluid is continuously evaluated at different pressure levels, while temperature is
controlled at reservoir temperature. Pressure level starts at initial reservoir pressure; then, it is
continuously decreased by 1.0 psi interval until the initial reservoir fluid becomes unstable. The
last pressure level that initial reservoir fluid is in stable condition is the dew point pressure. A
61
direct calculation of saturation pressure at the prevailing reservoir temperature could be also
alternatively employed (Whitson and Brule, 2000).
The initial amount of mole of the reservoir fluid sample inside PVT cell ( ) is
calculated from Equation 4-78. Standard condition is set to be 14.7 psia and 520 R. Volume of
initial reservoir fluid in term of gas equivalent ( ) is assumed to be 1.0 MMSCF which is used
as the basis for the calculation.
Equation 4-78
The associated volume of PVT cell ( ) is calculated from Equation 4-79. Molecular
weight ( ) and density ( ) are obtained by performing flash calculation on initial reservoir
fluid composition at the dew point condition.
Equation 4-79
The molar fractions of surface gas ( ) and stock-tank oil ( ) pseudo components in
reservoir fluid are calculated from Equation 4-80 and Equation 4-81. Molar fraction of liquid
phase at first-stage separator (
) is obtained by performing flash calculation on initial
reservoir fluid composition at first-stage separator condition. Molar fraction of liquid phase at
second-stage separator (
) is obtained by performing flash calculation on liquid composition
62
from first-stage separator at second-stage separator condition. Molar fraction of liquid phase at
stock-tank condition ( ) is obtained by performing flash calculation on liquid composition
from second-stage separator at stock-tank condition.
Equation 4-80
Equation 4-81
Total volume of surface gas ( ) and stock-tank oil ( ) pseudo components initially
present in the reservoir fluid are calculated from Equation 4-82 and Equation 4-83. Value of
379.56 is molar volume of gases at standard condition which is constant. Molecular weight
( ) and density (
) of oil at stock-tank condition are obtained from flash calculation
results at stock-tank condition. Please note that these values (G and N) are not being obtained by
cumulative adding cumulative production values at every pressure level, as done in the original
Walsh and Tower algorithm. Chapter 5 will present a discussion on this regard and justification.
Equation 4-82
Equation 4-83
63
The gas formation volume factor ( ) is calculated from Equation 4-84. Volatilized oil-
gas ratio at dew point ( ) is calculated from Equation 4-64 by implementing the proper unit
conversion factor. Oil formation volume factor ( ) and solution gas-oil ratio ( ) are calculated
from Equation 4-61 and Equation 4-62, respectively.
Equation 4-84
Step 1: Find and : Moles of gas phase present at reservoir conditions before
the removal of excess gas at every pressure level j ( ) is calculated from Equation 4-85.
Moles of oil phase remaining at reservoir conditions at pressure level j ( ) is calculated from
Equation 4-86. Molar fraction of gas phase at reservoir condition at pressure level j ( ) is
obtained from performing flash calculation on overall composition from pressure level j-1, at
pressure level j. Note that pressure level j begins from zero (j=0) at the dew point. is
equal to , is equal to zero, and is equal to .
Equation 4-85
Equation 4-86
64
Step 2: Find and : The volume that the gas phase occupies at reservoir
condition before the removal of the excess gas at every pressure level j ( ) is calculated
from Equation 4-87. The volume of reservoir oil phase present at pressure level j ( ) is
calculated from Equation 4-88. Molecular weight and density of gas and oil phases at reservoir
condition at pressure level j ( ,
, ,
) are obtained by performing flash
calculation on overall composition from pressure level j-1, at pressure level j. Note that pressure
level j begins from zero at the dew point (j=0). is equal to and is equal to zero.
Equation 4-87
Equation 4-88
Step 3: Find and : The volume of reservoir gas phase after excess gas removal at
pressure level j ( ) is calculated from Equation 4-89. Volume of excess gas at reservoir
condition at pressure level j ( ) is then calculated from Equation 4-90.
Equation 4-89
65
Equation 4-90
Step 4: Find and : Remaining moles of gas phase at reservoir condition after
excess gas removal at every pressure level j ( ) is calculated from Equation 4-91. Moles of
excess gas which are removed at pressure level j ( ) is then calculated from Equation 4-92.
Density and molecular weight are the same as those in Equation 4-87.
Equation 4-91
Equation 4-92
Step 5: Find and : The molar fractions or compositions of surface gas ( ) and
stock-tank oil ( ) pseudo components in the reservoir gas at every pressure level j are
calculated from Equation 4-93 and Equation 4-94. The fraction of liquid phase at first-stage
separator recovered from reservoir gas at pressure level j (
) is obtained by performing flash
calculation on composition of reservoir gas at pressure level j, at first-stage separator condition.
The fraction of liquid phase at second-stage separator recovered from reservoir gas at pressure
level j (
) is obtained by performing flash calculation on liquid composition from first-stage
66
separator at second-stage separator condition. The fraction of liquid phase at stock-tank condition
recovered from reservoir gas at pressure level j ( ) is obtained by performing flash
calculation on liquid composition from second-stage separator at stock-tank condition.
Equation 4-93
Equation 4-94
Step 6: Find and : Volume of surface gas ( ) and stock-tank oil ( )
pseudo components in reservoir gas at pressure level j are calculated from Equation 4-95 and
Equation 4-96. The value of 379.56 is molar volume of gases at standard condition which is a
constant for ideal gases. Molecular weight ( ) and density (
) of oil at stock-tank
condition recovered from reservoir gas at pressure level j are obtained from flash calculation
results at stock-tank condition in Step 5.
Equation 4-95
Equation 4-96
67
Step 7: Find and : The molar fractions of surface gas ( ) and stock-tank oil
( ) pseudo components in the reservoir oil at every pressure level j are calculated from
Equation 4-97 and Equation 4-98. The fraction of liquid phase at first-stage separator recovered
from reservoir oil at pressure level j (
) is obtained by performing flash calculation on
composition of reservoir oil at pressure level j, at first-stage separator condition. The fraction of
liquid phase at second-stage separator recovered from reservoir oil at pressure level j (
) is
obtained by performing flash calculation on liquid composition from first-stage separator at
second-stage separator condition. The fraction of liquid phase at stock-tank condition recovered
from reservoir oil at pressure level j ( ) is obtained by performing flash calculation on liquid
composition from second-stage separator at stock-tank condition.
Equation 4-97
Equation 4-98
Step 8: Find and : The volume of surface gas ( ) and stock-tank oil ( )
pseudo components in reservoir oil at pressure level j are calculated from Equation 4-99 and
Equation 4-100. The value of 379.56 is molar volume of gas at standard condition which is
constant. Molecular weight ( ) and density (
) of oil at stock-tank condition recovered
from reservoir oil at pressure level j are obtained from flash calculation results at stock-tank
condition in Step 7.
68
Equation 4-99
Equation 4-100
Step 9: Find and : Remaining moles of reservoir fluid inside PVT cell at pressure
level j ( ) is calculated from Equation 4-101. Overall composition of i-th component insider
PVT cell at pressure level j ( ) after gas removal is updated by implementing Equation 4-102.
Note that pressure level j begins from zero (j=0) at the dew point. is equal to . Liquid
composition ( ) and vapor composition ( ) of i-th component at pressure level j are obtained
by performing flash calculation on overall composition from pressure level j-1, at pressure level j.
Equation 4-101
Equation 4-102
After completing all nine steps outlined above at every given pressure level, Equation
4-49 through Equation 4-52 will be used to directly calculate standard PVT properties. All unit
69
conversion factors must be checked and properly adjusted. This calculation process must be
continuously repeated for the every pressure level until abandonment pressure is reached.
Standard PVT properties at pressures higher than the dew point are calculated based on
available properties at dew point pressure. Gas formation volume factor ( ) is calculated from
gas formation volume factor at dew point pressure using Equation 4-103. The ratio between
( ) at dew point pressure and ( ) at specified pressures above the dew point is equivalent to
ratio between volume of reservoir gas ( ) at specified pressures above the dew point and volume
of reservoir gas ( ) at dew point pressure. Volatized oil-gas ratio ( ) is equal to volatilized oil-
gas ratio at dew point pressure ( ). Oil formation volume factor ( ) and solution gas-oil ratio
( ) are calculated from Equation 4-61 and Equation 4-62, respectively.
Equation 4-103
70
4.3 Zero-Dimensional Reservoir Model
The Material Balance Equation (MBE) (also known as zero-dimensional reservoir model
or tank model) is a mass balance statement that combines mass balance equations of all pseudo
components present in the reservoir fluid. The assumptions behind a tank model have been
already addressed in Section 2.3. Walsh and Lake (2003) have presented a generalized form of
material balance equation that could be used for the analysis of depletion performance for all five
types from reservoir fluids, based on the work originally published by Walsh (1995). They also
developed the MBE specialized for gas condensate fluids by simplifying the generalized MBE for
the conditions particular to these kind of fluids. Section 4.3.1 discusses and presents the GMBE
proposed by Walsh as implemented in this study.
In zero-dimensional reservoir model, cumulative productions of pseudo components and
saturations of reservoir fluids are calculated as functions of reservoir pressure, standard PVT
properties, and initial reservoir condition. This model treats a reservoir as a homogeneous tank;
thus only average reservoir pressure and average PVT properties are required as the model inputs.
In this study, a VBA subroutine has been developed to simulate cumulative oil and gas
productions as well as their saturations as a function of reservoir pressure, by implementing the
MBE specialized for gas condensate fluids. Most of the time, the MBE is used to simulate the
results explicitly as a function of time and depletion. However, if some target outputs are
specified, such as cumulative recovery at end of plateau, an iterative procedure would need to be
implemented in order to honor the additional constraint.
71
4.3.1 Generalized Material Balance Equation
Generalized Material Balance Equation (GMBE) is the most generalized form of Material
Balance Equation which can be applied to all types of reservoir fluids. Walsh and Lake derived
the GMBE by combining mass balance equation of pseudo components, surface gas, stock-tank
oil and stock-tank water, with the saturation constraint and standard PVT properties described in
section 4.2 (Walsh and Lake, 2003). The following assumptions are assumed in addition to the
general assumptions for zero-dimensional reservoir model.
Reservoir consists of surface gas, stock-tank oil, and stock-tank water pseudo
components
Reservoir consists of gas, oil, and water phases.
Surface gas pseudo component is in reservoir gas and oil phases.
Stock-tank oil pseudo component is in reservoir gas and oil phases.
Stock-tank water pseudo component is in reservoir water phase.
Surfaces gas, stock-tank oil, and stock-tank water can be produced
Surface gas and stock-tank water can be injected into the reservoir
Water phase can enter into reservoir by water influx from aquifer
GMBE can be manipulated into many different forms. One of the most useful forms of
the GMBE is shown in Equation 4-104. The terms on the left-hand side represents net reservoir
expansion terms while terms on the right-had side represents net reservoir withdrawal. Net
reservoir expansion consists of net reservoir gas expansion, net reservoir oil expansion, net
reservoir water expansion, net formation expansion, and water influx. Net reservoir withdrawal
consists of net gas and oil withdrawal, and net water withdrawal.
72
Equation 4-104
where:
= volume of surface gas pseudo component in reservoir gas at initial
condition {SCF}
= volume of stock-tank oil pseudo component in reservoir oil at
initial condition {STB}
= volume of water component in reservoir water at initial condition
{STB}
= pore volume at initial condition {RB}
= volume of water influx {RB}
= cumulative gas production {SCF}
= cumulative gas injection {SCF}
= cumulative oil production {STB}
= cumulative water production {STB}
= cumulative water injection {SCF}
= expansivity of reservoir gas {RB/SCF}
= expansivity of reservoir oil {RB/STB}
= expansivity of reservoir water {RB/STB}
= expansivity of formation (rock) {Dimensionless}
= gas formation volume factor {RB/SCF}
= oil formation volume factor {RB/STB}
73
= water formation volume factor {RB/STB}
= volatilized oil-gas ratio {STB/SCF}
= solution gas-oil ratio {SCF/STB}
Expansivity of reservoir fluid is defined as the total expansion of a unit mass of reservoir
fluid between two reservoir pressures at the same reservoir temperature. Expansivities of
reservoir gas, reservoir oil, and reservoir water are calculated from Equation 4-105, Equation
4-106, and Equation 4-107, respectively. Expansivity of formation (rock) is defined in a different
form from fluid expansivity and is calculated in terms of formation (rock) compressibility as
indicated by Equation 4-108.
Equation 4-105
Equation 4-106
Equation 4-107
Equation 4-108
74
where:
= two-phase gas formation volume factor {RB/SCF}
= two-phase oil formation volume factor {RB/SCF}
= formation (rock) compressibility {psi-1
}
= pressure drop from initial reservoir pressure {psi}
The two-phase formation volume factor implemented above is defined as the ratio
between total volume of reservoir fluid (gas and oil phases) and total volume of the pseudo
component. Two-phase formation volume factor of gas ( ) and oil ( ) are calculated from
Equation 4-109 and Equation 4-110, respectively. If reservoir is a single phase gas reservoir, two-
phase gas formation volume factor ( ) will be equal to gas formation volume factor ( ) while
two-phase oil formation will remain undefined. Similarly, if reservoir is single phase oil reservoir,
two-phase oil formation volume factor ( ) will be equal to oil formation volume factor ( )
while the two-phase gas formation volume factor will remain undefined.
Equation 4-109
Equation 4-110
75
4.3.2 Material Balance Equation for a Gas Condensate Fluid
GMBE can be simplified significantly when condensate drop out, developed below dew
point saturation conditions in the reservoir, is considered immobile. The immobile condensate
assumption is a fairly reasonable one for gas condensates; however, it cannot be applied for other
types of reservoir fluid (Walsh and Lake, 2003). The Simplified Gas Condensate Tank model,
SGCT, is derived from Generalized Material Balance Equation with the following additional
assumptions:
Reservoir is under-saturated at initial reservoir pressure
Expansivities of water and formation are negligible
There is no water influx, water production, and water injection
There is no gas injection
Condensate drop out in the reservoir is immobile
Gas Condensate Performance Below Dew Point
At initial undersaturated conditions, the volume of surface gas pseudo component in
reservoir gas at initial condition is equal to the Original Gas In Place (OGIP or G) while and the
volume of stock-tank oil pseudo component in reservoir oil at initial condition is equal to zero.
Equation 4-111 is the SGCT model after applying all these additional assumptions:
Equation 4-111
76
This SGCT model can be further manipulated in order to obtain a more useful form by
dividing it through by and substituting by . After that, finite difference
approximation is applied, resulting in expressions for the calculation of incremental oil and gas
production. As a result, Equation 4-112 through Equation 4-118 are a set of equations that can be
used to calculate reservoir performance from SGCT model.
Equation 4-112
Equation 4-113
Equation 4-114
Equation 4-115
Equation 4-116
77
Equation 4-117
Equation 4-118
where
= incremental gas recovery from pressure level to
= incremental oil recovery from pressure level to
= cumulative gas recovery at pressure level
= cumulative oil recovery at pressure level
= gas formation volume factor at pressure level {RB/SCF}
= oil formation volume factor at pressure level {RB/STB}
= volatilized oil-gas ratio at pressure level {STB/SCF}
= solution gas-oil ratio at pressure level {SCF/STB}
= two-phase gas formation volume factor at pressure level
{RB/SCF}
= two-phase oil formation volume factor at pressure level
{RB/SCF}
78
It is important to note that this set of equations (Equation 4-112 through Equation 4-118)
only applies for pressure below the dew point. Pressure level j begins at the first pressure below
the dew point. and at pressure level j-1 are cumulative results from the calculation
above the dew point. The standard PVT properties are either obtained from any of the procedures
described in section 4.2 or are given as input data. Two-phase formation volume factors are
calculated from Equation 4-109 and Equation 4-110. Calculation of SGCT model must be fully
completed at one pressure level before moving onto the next pressure level.
Gas Condensate Performance Above Dew Point
At pressure higher than dew point pressure, SGCT model should be further modified by
substituting and into Equation 4-111. As a result, the MBE for an
under-saturated gas condensate collapses to the typical MBE for a wet gas, shown in Equation
4-119. A set of equations which mimic the calculation procedure of SGCT model below dew
point can be developed by using a finite difference approach. Resulting performance prediction
equations are shown in Equation 4-120 to Equation 4-123.
Equation 4-119
Equation 4-120
79
Equation 4-121
Equation 4-122
Equation 4-123
It should be noted that this set of equation (Equation 4-120 to Equation 4-123) only
applies for pressures above dew point. The pressure level j begins from zero at initial reservoir
and end at the last pressure above the dew point. , , , and are equal to
zero at the initial reservoir pressure. The calculation has to be completed at one pressure level
before moving to the next pressure level.
80
4.3.3 Phase Saturation Calculations
One of the methods to derive a phase saturation equation is to combine the mass balance
equation for the stock-tank oil pseudo-component with the saturation equation constraint in order
to eliminate gas saturation parameter ( ) and then combine the resulting
equation and volumetric OGIP calculation equation so that the pore volume variable is
eliminated. The resulting saturation equation for the oil phase is shown in Equation 4-124.
Equation 4-124
where:
= average reservoir oil saturation
= average reservoir gas saturation
= average reservoir water saturation
= cumulative oil production {STB}
= original oil in place {STB}
= average reservoir porosity
= gas formation volume factor {RB/SCF}
= oil formation volume factor {RB/STB}
= volatilized oil-gas ratio {STB/SCF}
= subscript for initial condition
81
For the typical gas condensate reservoir, initial oil saturation ( ) is equal to zero
because its initial pressure is typically found above dew point conditions. If formation/rock
expansion is neglected, porosity of the porous medium would remain constant at the value of
initial porosity ( ). If net water withdrawal, influx, and expansion are neglected, water
saturation would remain constant at the value of connate water saturation ( ).
Thus, for such conditions, Equation 4-124 can be significantly simplified to Equation 4-125.
Equation 4-125
For saturation calculation of gas condensate reservoir, if reservoir pressure is equal to or
higher than dew point pressure, average reservoir oil saturation is equal to . Otherwise,
average reservoir oil saturation is calculated from Equation 4-125.
82
4.3.4 Volumetric OGIP/OOIP Calculations
Original Gas In Place ( ) and Original Oil In Place ( ) can be calculated using
volumetric method. Equation 4-128 and Equation 4-129 are used to calculate OGIP and OOIP,
respectively, based on the premise that both surface gas and stock-tank oil pseudo components
can be found in the reservoir gas and reservoir oil phases. In these equations, multiplication of
drainage area, reservoir thickness, and porosity represent the pore volume of the reservoir. The
conversion factor of 7758 is used to convert ―acre-ft‖ unit to ―RB‖ unit. The first and the second
terms inside the bracket of Equation 4-126 represent volumes of surface gas pseudo component in
reservoir oil and reservoir gas phases, per reservoir pore volume, respectively. The first and the
second terms inside the bracket of Equation 4-127 represents volume of stock-tank oil pseudo
component in reservoir oil and reservoir gas phases, per reservoir pore volume, respectively.
Equation 4-126
Equation 4-127
where:
= reservoir drainage area {acre}
= reservoir thickness {ft}
= reservoir porosity
83
= initial oil saturation
= initial gas saturation
= oil formation volume factor at initial condition {RB/STB}
= gas formation volume factor at initial condition {RB/SCF}
= solution gas-oil ratio at initial condition {SCF/STB}
= volatilized oil-gas ratio at initial condition {STB/SCF}
For gas condensate reservoir which do not initially have an oil phase ( ), Equation
4-126 and Equation 4-127 can be simplified into Equation 4-128 and Equation 4-129,
respectively. Reservoir properties which are drainage area ( ), thickness ( ), porosity ( ), and
initial water saturation ( ) must be known. Fluid properties which are initial gas formation
volume factor ( ) and initial volatilized oil-gas ratio ( ) are obtained from standard PVT
property estimations.
Equation 4-128
Equation 4-129
84
4.4 Flow Rates and Flowing Pressures Calculation
In this study, flow rates and flowing pressures calculations are based on the
implementation of Inflow Performance Relationships (IPR) and Tubing Performance
Relationships (TPR). The IPR equation relates flow rates from reservoir into the wellbore with
the difference between reservoir pressure and bottomhole flowing pressure. The TPR equation
relates wellbore flow rates between a bottomhole to a surface location in terms of the difference
between bottomhole flowing pressure and wellhead pressure.
Because of the immobile condensate assumption, oil flow rates can be calculated as a
function of gas flow rates and volatilized oil-gas ratio. Moreover, because a pipeline equation
based on the homogeneous flow assumption (single pseudo phase) can be used as the TPR
equation, by implementing an appropriate tubing efficiency factor, gas flow rate is the only
parameter that needs to be determined. In field performance prediction, either the desired gas
flow rate or the target wellhead pressure will be specified. If gas flow rate is specified, the IPR
equation will be used to explicitly calculate bottomhole flowing pressure, and the TPR equation
will be used to explicitly calculate wellhead pressure. If wellhead pressure is specified,
bottomhole flowing pressure and gas flow rate are simultaneously solved by using nodal analysis
method to determine the solution of the IPR and TPR system of equations. In this study, two
subroutines have been developed for gas flow rate and bottomhole flowing pressure calculations
based on IPR equations. Similarly, two subroutines have been developed for gas flow rate and
wellhead pressure calculations based on TRP equations. For the numerical solution, nodal
analysis method is also implemented by using bisection iterative procedure.
85
4.4.1 Inflow Performance Relationship (IPR)
The pseudo steady state (PSS) flow rate from the reservoir into the wellbore of radius
flow in cylindrical-shape reservoir, closed boundary can be calculated using Equation 4-130 (Lee
et al, 2003).
Equation 4-130
For other reservoir shapes, PSS flow rates can be calculated by applying shape factor
concept (Deitz, 1965). Flow rate calculation with Deitz shape factor ( ) is shown in Equation
4-131. The Deitz shape factor ( ) is equal to 31.62 for a circular drainage area with a well
located at the center of the reservoir, and equal to 30.88 for a square drainage area with a well
located at the center of the reservoir.
Equation 4-131
For the two-phase two-pseudo component model, the surface gas pseudo-component is
recovered from both reservoir gas and reservoir oil (as dissolved gas); while stock-tank oil pseudo
component is recovered from reservoir oil and reservoir gas (as volatilized oil). By introducing
the concept of phase mobilities and phase relative permeabilities, Equation 4-131 can then be
modified to calculate flow rates for this two-phase two-pseudo component model. Gas flow rate
86
( ) and oil flow rate ( ) can be calculated from Equation 4-132 and Equation 4-133,
respectively.
Equation 4-132
Equation 4-133
where:
= flow rate of surface gas {SCF/D}
= flow rate of stock-tank oil {STB/D}
= absolute permeability of reservoir {md}
= relative permeability of reservoir gas
= relative permeability of reservoir oil
= average reservoir pressure {psia}
= bottomhole flowing pressure {psia}
= reservoir thickness {ft}
= reservoir drainage area per well {acre}
= wellbore radius {ft}
= Detiz Shape Factor
= total skin factor
87
= viscosity of reservoir gas {cp}
= viscosity of reservoir oil {cp}
= oil formation volume factor {RB/STB}
= gas formation volume factor {RB/SCF}
= solution gas-oil ratio {SCF/STB}
= volatilized oil-gas ratio {STB/SCF}
The first terms in the last bracket of Equation 4-132 and Equation 4-133 represent fluid
production that comes from the reservoir oil, while the second terms represent fluid production
that comes from the reservoir gas. However, for a gas condensate reservoir, reservoir oil is
typically assumed to be immobile ( ). Thus, gas flow rate ( ) and oil flow rate ( )
equations are simplified into Equation 4-134 and Equation 4-135, respectively
Equation 4-134
Equation 4-135
88
In Equation 4-134 and Equation 4-135, only gas and oil flow rates ( and ) or
bottomhole flowing pressure ( ) could be specified. Absolute reservoir permeability ( ),
reservoir thickness ( ), drainage area per well ( ), wellbore radius ( ), and Deitz shape factor
( ) are required reservoir data. Gas formation volume factor ( ), volatilized oil-gas ratio ( ),
and specific gravity of gas ( ) are functions of average reservoir pressure ( ). Average
reservoir pressure ( ) is obtained from the SGCT (zero-dimensional material balance)
subroutine. Gas viscosity ( ) is calculated from correlation proposed by Lee et al in 1966
presented as Equation 4-24 through Equation 4-27.
Even though the relative permeability to oil ( ) can be safely assumed to remain zero
or close to zero during depletion of a gas condensate reservoir, the relative permeability to gas is
not expected to remain equal to one in the presence of condensate. Typically, the mobility of the
gas phase and thus its relative permeability are expected to decrease with increased condensate
drop out. The relative permeability of the gas phase will be further hindered if average water
saturation in the reservoir increases because of the presence of an active water drive. Relative
permeability of reservoir gas ( ) is a function of the average reservoir gas saturation (
). In this study, there are two input options for relative permeability data. The first option
is to input gas saturations and their corresponding values manually in a tabular form. Such
data could be obtained from core study results performed in a laboratory. The second option is to
use a correlation for three-phase relative permeability. Any relative permeability model can be
utilized; however, Naar, Henderson, and Wygal’s model (Ertekin et al, 2001) has been used as a
default model in this work. The correlation is shown in Equation 4-136.
Equation 4-136
89
where:
= average reservoir gas saturation
= connate water saturation
= average reservoir gas saturation
= coefficient to adjust relative permeability of reservoir gas, typically
one when is expected to take value of one at the end point ( = 1-
)
Gas saturation ( ) can change from a minimum gas saturation ( ) to a maximum gas
saturation ( ). Relative permeability of reservoir gas ( ) is equal to zero at the minimum
gas saturation ( ) or lower. Connate water saturation ( ) is a required reservoir data. The
coefficient, , is used to adjust relative permeability anchor point at the initial gas saturation
( ). If at the initial gas saturation, or if there is no further core or lab data
available indicating otherwise, adjustment coefficient value is set to 1.0.
Skin factor is dimensionless pressure drop around the wellbore, which accounts for the
differences between reservoir model’s analytical assumptions and actual conditions in reservoir
flow. Total skin factor ( ) consists of mechanical skin ( ) and non-Darcy skin ( ).
Mechanical skin can be estimated from pressure transient analysis or from other analogous
approaches such as type curve matching. Non-Darcy coefficient ( ) can be obtained from the
analysis of multi-rate well test, or analogous approaches, or from Equation 4-138 (Lee et al,
2003. Eq. 3.19) if its required input data is known
90
Equation 4-137
Equation 4-138
where:
= mechanical skin factor
= non-Darcy coefficient {Day/SCF}
= flow rate of surface gas {SCF/D}
= turbulence parameter
= effective permeability of reservoir gas ( ) {md}
= molecular weight of reservoir gas {lbm/lbmol}
= pressure at standard condition {14.7 psia}
= reservoir thickness {ft}
= wellbore radius {ft}
= temperature at standard condition {520 R}
= viscosity of reservoir gas at bottomhole flowing pressure {cp}
Total skin factor ( ) is a function of gas flow rate, because of the presence of the non-
Darcy skin component, while gas flow rate also is function of skin factor. Thus, Equation 4-134
cannot be solved explicitly for gas flow rate. When the non-Darcy component is expected to be
significant, Equation 4-134 can be recast in terms of a quadratic expression in gas flow rate ( )
91
which can be solved analytically. Alternatively, Equation 4-134 can be solved directly by
implementing an iterative numerical approach. The latter is the approach employed in this study.
4.4.2 Tubing Performance Relationships
For a gas condensate reservoir, condensate drop out is not only expected to occur at
reservoir conditions but also along the surface depletion path as produced fluids make their way
to the surface. For the case of the two-phase two-pseudo component model, the amount of
reservoir condensation can be estimated for the isothermal reservoir conditions using the concept
of volatilized oil-gas ratio. The amount of condensate at the surface is estimated using the surface
pseudo-component concept. However, the table of ―black oil‖ standard PVT properties provides
no information about how much condensate can be expected as a function of both pressure and
temperature changes inside the well tubing during the wellstream fluid travel from reservoir to
surface conditions. The difference in the values of volatilized oil-gas ratio between for any two
points of pressure inside the tubing would provide a measure of gas condensation—but assuming
that those two points are found at separator temperature conditions. To overcome this problem,
this study invokes the homogeneous flow assumption at tubing conditions and applies the well-
known expressions for the flow of gases in a pipeline, adjusted according to an appropriate value
of tubing efficiency. The homogeneous single phase flow equation used to calculate gas flow rate
( ) for a given downstream pressure ( ), and vice versa is shown in Equation 4-139. Pipeline
efficiency factor ( ) is defined to account for the extra pressure drop that should be
expected due to presence of liquid phase.
92
Equation 4-139
Equation 4-140
where:
= gas flow rate {SCF/D}
= upstream pressure {psia}
= downstream pressure {psia}
= pressure at standard condition {14.7 psia}
= pipe section average temperature {R}
= temperature at standard condition {520 R}
= average compressibility factor
= Fanning’s fraction factor
= specific gravity of gas
= tubing diameter {inch}
= tubing length {mile}
= difference in elevation of downstream and upstream {ft}
= efficiency factor of tubing
93
Upstream pressure ( ), tubing diameter ( ), tubing length ( ), elevation at upstream
( ) and downstream ( ) of the tubing are required input data. Difference in elevation is
calculated as . Tubing temperature changes are assumed to follow the geothermal
gradient. An average temperature ( ) is assumed to be equal to an average between
temperatures at upstream ( ) and downstream ( ) nodes for any given tubing section. Average
pressure ( ) is calculated from Equation 4-141. Average compressibility factor ( ) is
calculated at average pressure ( ) and average temperature ( ).
Equation 4-141
In Equation 4-140 above, the Fanning’s friction factor ( ) is equal to a quarter of
Moody’s friction factor ( ). The Moody’s fraction factor ( ) can be calculated from Equation
4-142 (Colebrook, 1939). This equation is solved using iterative procedure because Moody’s
friction factor appears implicitly on both sides of the equation. The Reynolds number is
calculated from Equation 4-143. In situ fluid density ( ) and velocity ( ) of gas are evaluated at
average pressure and temperature using real gas equation of state. Gas viscosity is calculated
from the correlation proposed by Lee et al in 1966.
Equation 4-142
94
Equation 4-143
where:
= Moody’s friction factor
= tubing diameter {inch}
= tubing roughness {ft}
= Reynolds number
= fluid density {lbm/ft3}
= fluid velocity {ft/sec}
= fluid viscosity {cp}
The concept of tubing efficiency factor ( ) is applied to for the detrimental
presence of a liquid phase on pipe performance. For gas condensate fluid, amount of liquid phase
in pipeline is partially related the change in volatilized oil-gas ratio ( ) and tubing flowing
pressure, which both of them are also functions of reservoir pressure. Therefore, the efficiency
factor would also implicitly depend on reservoir pressure. In this study, a single value of tubing
efficiency factor, assumed to be representative of the entire tubing flow, is employed. The
efficiency factor should be calculated in such a way that the calculated flow rate and pressure
would match actual production data for the period of interest.
During calculations, the tubing is divided into several pipe sections. The calculation is
performed section by section, starting at the bottommost section and marching towards the
topmost section of the tubing. The upstream pressure of the bottommost section is the bottomhole
flowing pressure, while the upstream pressure of the upper section is the calculated downstream
95
pressure from the lower section. Wellhead pressure represents the downstream pressure of the
topmost section of the tubing.
TPR calculations can be performed in two ways. One possibility is calculating wellhead
pressure ( ) as a function of gas flow rate ( ). For such scenario, downstream pressure ( )
in gas flow equation is sequentially solved starting at the bottommost section until reaching the
topmost section of the tubing. For each section, an iterative process is needed to determine
downstream pressure ( ) because downstream pressure ( ) affects the value of average
compressibility factor ( ) and Reynolds number ( ). The downstream pressure ( ) of the
topmost section of the tubing is the desired target.
The second possibility for TPR calculations is finding the corresponding gas flow rate
( ) for a given wellhead pressure ( ). In this case, initial guess of gas flow rate ( ) is
calculated using well-known Weymouth correlation. Then, wellhead pressures ( ) are
calculated for the initial guess of gas flow rate ( ). Based on the ensuing sensitivity analysis,
incremental wellhead pressure ( ) and incremental gas flow rate ( ) can be estimated.
The gas flow rate ( ) is now updated based on the derivative of gas flow rate ( )
and the difference between calculated and specified wellhead pressures ( ). This procedure is
repeated until the difference between calculated and specified wellhead pressure is less than a
prescribed tolerance value.
96
4.4.3 Nodal Analysis
In petroleum engineering, nodal analysis is used to determine pressure and flow rate at
some node or location of interest in the production system. In this study, sand-face location is the
selected node or location of interest. Incoming gas flow rate to the node (―inflow‖) can be
calculated from inflow performance relationships (IPR), while outgoing gas rate from the node
(―outflow‖) can be calculated using tubing performance relationships (TPR). Nodal analysis is
then performed to determine pressure ( ) and flow rate ( ) that satisfies both IPR and TPR
relations at the same time – which correspond to the point where ―inflow‖ and ―outflow‖ curve
cross each other, as depicted in Figure 4-5.
Figure 4-5: Graphical Representation of Nodal Analysis
Figure 4-5 shows the graphical representation of nodal analysis method. IPR curve is
constructed using Equation 4-134, and TPR curve is constructed using Equation 4-139. The
Pw
f-
Bo
tto
mh
ole
Flo
win
g P
ress
ure
qgsc - Gas Flow Rate
IPR TPR
Tubing Performance Relationship
Inflow Performance Relationship
Pwf and qgsc
that satisfy both IPR & TPR
97
intersection between IPR and TPR curves represents the solution of the nodal analysis problem.
As it can be seen from the figure, as the bottomhole flowing pressure ( ) is lower than the
intersection pressure, more gas would be able to flow from reservoir into the wellbore; however,
the tubing would not be able to deliver all of gas to the surface for the given pressure drop. In
contrast, if the bottomhole flowing pressure ( ) is higher than the intersection pressure, less
gas is able to flow from reservoir into the wellbore even though the tubing would be able to
deliver more than that. Both scenarios are not physically possible for a steady state condition
where the flow from the reservoir and in the tubing must be equal to each other. There is only one
possible flow condition which is found at the intersection point. At the intersection pressure, all
of gas which flows from the reservoir into the wellbore can be delivered to the surface production
system.
The solution of the IPR and TRP point of intersection requires an iterative procedure. In
this study, the bi-section method is applied. Reservoir pressure ( ) and wellhead pressure ( )
are the independent variables while bottomhole flowing pressure ( ) and gas flow rate ( )
are the dependent variables. Initial guess of bottomhole flowing pressure ( ) is taken as an
average between the higher pressure boundary which is equal to reservoir pressure ( ) and lower
pressure boundary which is equal to wellhead pressure ( ) for the first iteration. Then, gas flow
rates ( ) from IPR and TPR correlations are calculated for the current guess of bottomhole
flowing pressure ( ). If gas flow rate calculated from the IPR curve is less than gas flow rate
from TPR, then the higher pressure boundary is replaced by current bottomhole flowing pressure
( ). If not, the lower pressure boundary is replaced by current bottomhole flowing pressure
( ) instead. New iteration starts by averaging the bottomhole flowing pressure ( ) from the
updated higher and lower pressure boundaries. The iterative process is repeated until the
98
difference between calculated gas flow rate ( ) from IPR and TPR is less than a prescribed
tolerance.
99
4.5 Field Performance Prediction
Field performance predictions are based on the integration of reservoir tank models with
flow rates and flowing pressure (IPR/TRP) models, subjected to a given set of production
constraints, with the goal of predicting pressures (reservoir, wellhead, bottomhole), flow rate, and
cumulative production evolution with respect to reservoir production time. The production time
variable, which is eliminated during the development of reservoir tank or zero-dimensional
models, is now calculated by combining tank models and flow rate models (IPR/TRP) in the same
calculation.
In this work, substantial drilling capacity is assumed; thus build-up period is neglected.
Field life is divided into two periods: the plateau period and decline period. All wells are put on
production at the beginning of plateau period. During the plateau period, gas flow rate ( ) is
kept constant by adjusting wellhead pressure ( ). During the decline period, wellhead pressure
( ) is kept constant at the minimum allowable wellhead pressure. The field is abandoned when
the reservoir pressure reaches the specified abandonment pressure. The following sections
described the algorithm for predicting field performance in a step-by-step procedure.
100
4.5.1 Performance during Plateau Period
During plateau period, the delivered gas flow rate ( ) from the field is kept constant.
In order to achieve this, in spite of decreasing pressure and gas flow capacity in the reservoir,
wellhead pressures ( ) are adjusted throughout the plateau period in order to honor the
constant production specification. Naturally, the reservoir must have the capacity (in terms of
reserves or OGIP) of delivering such target plateau rate throughout the plateau period. Therefore,
the gas flow rate during plateau period (
) is constrained by the feasibility of productive
reservoir performance at the end of plateau period. The following procedure is used to predict the
field performance during plateau period.
Estimation of Cumulative Production at End of Plateau ( )
Cumulative production at end of plateau is calculated from target recovery factor at end
of plateau ( ) (which is considered a given or specified variable provided to the model)
times original gas in place ( ) (which must be known before field performance predictions can be
undertaken).
Estimation of Reservoir Pressure at End of Plateau (
)
Reservoir pressure at end of plateau (
) is calculated from cumulative gas
production at end of plateau ( ) and the SGCT model. In the SGCT model, reservoir
pressure ( ) is an independent variable, and cumulative gas recovery ( ) is the dependent
variable. Cumulative gas production ( ) is calculated from cumulative gas recovery ( )
times original gas in place ( ). Therefore, finding reservoir pressure ( ) at a given cumulative
101
gas production ( ) requires an iterative process or pressure that is build around matching the
prescribed gas production at the end of plateau ( ). Bi-section iterative method is utilized
in this study.
Estimation of Plateau Gas Flow Rate (
)
Plateau gas flow rate (
) is calculated using the nodal analysis method. Because in
this calculation the minimum allowable wellhead pressure ( ) fixes the gas rate at the end of
plateau, nodal analysis is applied at the prevailing conditions at the end of the plateau period. For
the IPR calculation, for example, the reservoir pressure ( ) is equal to reservoir pressure at end
of plateau (
). For the TPR calculation, wellhead pressure ( ) is fixed to be equal to
minimum allowable wellhead pressure ( ). Intersection of IPR and TPR curves are the plateau
gas flow rate per well (
) and bottomhole flowing pressure at end of plateau (
).
Total plateau gas flow rate (
) is equal to the plateau rate per well (
) times total
number of wells.
Estimation of Reservoir Pressure ( ), Bottomhole Flowing Pressure ( ), and Wellhead
Pressure ( ) during plateau period
During the plateau period, reservoir pressure ( ) decreases continuously from initial
reservoir pressure ( ) to reservoir pressure at end of plateau (
) based on the
predictions from the SGCT model. Bottomhole flowing pressures ( ) are calculated as a
function of plateau gas flow rate per well (
) at different reservoir pressures ( ) by
implementing the IPR equation (Equation 4-134). Wellhead pressures ( ) are calculated as a
102
function of plateau gas flow rate per well (
) at different bottomhole flowing pressures
( ) by implementing the TPR calculation.
Estimation of Gas Flow Rate ( ) and Oil Flow Rate ( )
Total gas flow rate production ( ) during plateau period is constant and equal to the
prescribed plateau gas flow rate (
) for the entire field. Total oil flow rates ( ) are
calculated from total gas flow rate ( ) times volatilized oil-gas ratios ( ). Volatilized oil-gas
ratios ( ) at different reservoir pressures ( ) are linearly interpolated from the table of standard
PVT properties.
Estimation of Cumulative Gas Production ( ) and Cumulative Oil Production ( )
Cumulative gas production ( ) is calculated as cumulative gas recovery ( ) times
original gas in place ( ). Cumulative oil production ( ) is calculated as cumulative oil
recoveries ( ) times original oil in place ( ). Cumulative gas ( ) and cumulative oil
( ) recoveries at different reservoir pressures ( ) are calculated from the SGCT model.
Estimation of Production Time ( )
Production times ( ) at different reservoir pressures during the plateau period are
calculated from cumulative gas productions ( ) divided by total plateau gas flow rate
(
). Plateau time ( ) is equal to cumulative gas production at end of plateau
( ) over total plateau gas flow rate (
).
103
4.5.2 Performance during Decline Period
During decline period, wellhead pressure ( ) is kept at a constant value equal to the
minimum allowable wellhead pressure ( ). As a consequence of this, total gas flow rate ( )
would continuously decrease as a function of reservoir pressure ( ). The following procedure is
used to predict field performance during decline period.
Estimation of Reservoir Pressure ( ), Bottomhole Flowing Pressure ( ), and Wellhead
Pressure ( ) during decline
During the decline period, reservoir pressure ( ) continues to decreases from reservoir
pressure at the end of plateau (
) to abandonment reservoir pressure ( ) based on
predictions from the SGCT model. Bottomhole flowing pressures ( ) are calculated using
nodal analysis. In the IPR calculation, reservoir pressures ( ) change with production. Wellhead
pressure is fixed ( ) in the TPR calculation. Intersections of IPR and TPR curves at different
reservoir pressures ( ) yield the resulting bottomhole flowing pressures ( ) and gas flow rates
per well ( ) for the decline period.
Estimation of Gas Flow Rate ( ) and Oil Flow Rate ( )
Gas flow rates per well ( ) at different reservoir pressures ( ) are calculated along
with bottomhole flowing pressures ( ) using the nodal analysis discussed earlier. Total gas
flow rate ( ) is equal to gas flow rate per well ( ) times total number of wells. Oil flow
rate ( ) is calculated from total gas flow rate ( ) times the volatilized oil-gas ratio
104
( ).Volatilized oil-gas ratios ( ) at different reservoir pressures ( ) are linearly interpolated
from the table of standard PVT properties.
Estimation of Cumulative Gas Production ( ) and Cumulative Oil Production ( )
Cumulative gas productions ( ) and cumulative oil production ( ) calculation for
decline period follows the same protocol discussed for the plateau period.
Estimation of Decline Rate ( i)
If the reservoir decline behavior is assumed to be an exponential decline, the decline rate
( ) is expected to remain constant throughout decline period. Overall decline rate ( ) is
calculated from difference between total gas flow rates at end of plateau (
) and
abandonment ( ) over difference between cumulative gas production at end of plateau
( ) and abandonment ( ).
Equation 4-144
Estimation of Production Time ( )
Production times ( ) at different reservoir pressures ( ) are calculated from Equation
4-145. The calculation is based on the exponential decline assumption and constant decline rate
105
( ) discussed earlier. Abandonment time ( ) is calculated from Equation 4-145 at for the
condition at which flow rate equals abandonment total gas flow rate ( ).
Equation 4-145
106
4.5.3 Annual Production Calculation
Annual hydrocarbon production is the principal input for economic evaluation. Annual
production volumes during plateau period can be straightforwardly calculated because rates are
constant for the case of gas production. For the decline period, however, calculating annual
production is more involved because flow rates are time dependent. Iterative procedures can be
used to find exact values of annual production during decline period; however, because of the
exponential decline assumption, produced volumes can be determined directly, as outlined below
for annual gas and oil production calculations. Annual production time ( ) is defined as Equation
4-146. It converts production time ( ) from ―day‖ unit to ―year‖ unit. Annual production time ( )
begin from zero at initial condition.
Equation 4-146
Annual Gas Production
Annual gas production at year ( ) is calculated from difference between cumulative
gas production at year ( ) and cumulative gas production at year ( ).
Equation 4-147
107
For plateau period ( ), cumulative gas production at year ( ) is calculated
from Equation 4-148. For decline period ( ), cumulative gas production at
year ( ) is calculated from Equation 4-149.
Equation 4-148
Equation 4-149
Annual Oil Production
Annual oil production at year ( ) is calculated from the difference between
cumulative oil production at year ( ) and cumulative oil production at year ( ).
Cumulative oil production ( ) is calculated using linear interpolation with respect to cumulative
gas production ( ).
Equation 4-150
Instantaneous and Annual Average Flow Rates
Instantaneous flow rates of gas ( ) and oil ( ) are calculated using linear
interpolation with respect to cumulative gas production ( ). Annual average flow rates of gas
( ) and oil ( ) are calculated from the annual gas production ( ) and the annual oil
108
production ( ) divided by 365.25, respectively. In general, annual average rates can be used as
close approximation of instantaneous rates. They can also be converted to annual production
volumes easily. Because of this, annual average rates are more meaningful to report than
instantaneous flow rates for the purpose of economic analysis.
109
4.6 Economic Analysis and Field Optimization
Economic analysis is the analytical method that quantifies economic performance or
monetary value of a field investment project and provides a meaningful metric for the
optimization of field operations. Economic model which used in this study is based on typical
cash flow before tax regime (Mian, 2002).
An economic evaluation subroutine has been developed to perform the economic analysis
in this study. It consists of three main parts: compilation of production data, calculation of net
present value (NPV), and calculation of rate of return (ROR). The economic subroutine has been
constructed independently of the subroutine for field performance prediction. In this way,
economic analysis can be performed either with or without calculating new field performance
data. This is especially useful when performing parametric studies on economic parameters rather
than field operational constraints.
An optimization subroutine was also developed to find the recommended target recovery
factor at end of plateau to be contracted and total recommended number of wells to be drilled for
optimal field development. The optimization module requires the use of a variety of values of
target recovery factor and total number of wells that need to be economically screened. The
subroutine would repeatedly call the field performance prediction subroutine for a number of
different values of target plateau recovery factor and total number of wells. Economic analysis is
then performed for each development scenario and calculated NPVs are stored into an
optimization table or matrix. Production profiles corresponding to each of the investigated target
recovery factor and total numbers of well combinations are stored in the same worksheet.
A separate subroutine is available for the formulation of economic analysis decoupled
from field performance calculations. This subroutine would recall the stored production profiles
which were generated earlier during the economic evaluation discussed above. This subroutine is
110
useful because the generation of production profiles is the step in the analysis that requiring the
most significant computational time, and its availability allows to re-evaluate the sensitivity of
field optimization to different values of economic parameter(s). The subroutine is especially
useful when there are no changes in field operational constraints.
4.6.1 Simplified Economic Model
Net annual productions are calculated from annual production volumes times the net
hydrocarbon interest (Equation 4-151). Annual production volumes can be obtained from the
annual production calculation outlined in Section 4.5.3. The net hydrocarbon fraction or interest
is the fraction of the hydrocarbon production which is earned by the operator or investor. The
remaining portion of hydrocarbon belongs to the owner of land or the mineral rights.
Equation 4-151
Annual revenues are calculated by multiplying the annual production volume with the
estimated price of the product (Equation 4-152). The estimated price of gas has to be provided in
the units of $ per MSCF while the price of oil or condensate has to be provided in the unit of $
per STB. Generally, gas price is quoted in the unit of $ per MMBTU, which can be converted to $
per MSCF by multiplying $/MMBTU times the gas heating value {BTU/SCF} and dividing
through by 1000. Total annual revenue becomes the sum of annual revenue from gas and oil
(Equation 4-153).
111
Equation 4-152
Equation 4-153
Capital expenditure (CAPEX) is a group of one-time costs which occur in order to make
production possible. Total CAPEX consists of fixed CAPEX such as platform costs, flowline
costs, and production facilities costs, and variable CAPEX includes the variable costs of
operations such as drilling and completion (D&C). D&C cost is equal to D&C cost per well times
total number of wells (Equation 4-155). For this simplified economic model, CAPEX is assumed
to occur at the beginning of the project.
Equation 4-154
Equation 4-155
Operating expenditure (OPEX) is a group of costs which occur periodically in order to
maintain the day-to-day operation. OPEX may include maintenance cost, utilities cost, overhead
cost, production cost, etc. In this work, OPEX has to be given in the unit of $ per month. Annual
OPEX is calculated from monthly OPEX times 12 months (Equation 4-156).
112
Equation 4-156
Severance tax is a government or state tax which is imposed on the production of non-
renewable resources such as oil and natural gas. Ad Valorem tax is a tax which imposed at the
time of transaction. In this economic model, severance taxes for oil and gas have to be given in
terms of a percentage of the total oil and gas revenue, respectively. Annual severance taxes are
calculated from annual revenues times the severance tax rate (Equation 4-157). Ad Valorem tax
has to be given in percentage of total revenue. Annual Ad Valorem tax is calculated from annual
total revenue times the Ad Valorem tax rate (Equation 4-158). Annual total tax is summation of
severance taxes and Ad Valorem tax (Equation 4-159).
Equation 4-157
Equation 4-158
Equation 4-159
113
Annual expenditure is the sum of total CAPEX, annual OPEX, and annual total tax
(Equation 4-160). Annual net cash flow is the difference between annual total revenue and annual
expenditure (Equation 4-161). Cumulative net cash flow at year is the summation of annual net
cash flow from the beginning ( ) to year .
Equation 4-160
Equation 4-161
Equation 4-162
Commodity prices and operating cost can be escalated according to the economic
inflation. In this simplified economic model, gas price, oil price, and monthly OPEX are escalated
independently. The escalation is applied from the start to the end of the project. Today’s product
prices, monthly OPEX, and their escalation rates have to be provided to the model. Future prices
and monthly OPEX are calculated from Equation 4-163 and Equation 4-164. Un-escalated
economic analysis, which is required for some official reports, can be evaluated by specifying all
escalation rates to be equal to zero.
114
Equation 4-163
Equation 4-164
Annual net cash flow in the future is discounted to today’s equivalent value using concept
of ―time value of money‖. Annual discounted net cash flow at year is calculated using Equation
4-165. Annual net cash flow at year can be obtained from Equation 4-161. The effective interest
rate, which is interest rate applied on an annual basis, has to be provided. Cumulative discounted
net cash flow at year is the summation of annual discounted net cash flow from the beginning
( ) to year .
Equation 4-165
Equation 4-166
115
Net present value ( ) is equal to cumulative discounted net cash flow at abandonment.
The rate of return ( ) is the interest rate which results in zero NPV. The NPV profile is
calculated from evaluating NPV for a variety of interest rates. In this model, the interest rates are
varied from 5% to 40%. However, the range can be adjusted depending on the analyst and desired
economic results.
116
4.6.2 Field Optimization
In this study, target recovery factor at end of plateau and total number of wells are targets
for optimization because they can be controlled by the operator of the field. Net present values
( ) at differences target recovery factor and total number of wells are evaluated and
compared. The combination of target recovery factor and total number of wells which providing
the global maximum NPV is the desired result.
Figure 4-6: Graphical Representation of Field Optimization
Production profiles of oil and gas at differences target recovery factor and total number of
wells are calculated based on field performance prediction concept (Section 4.5). The predicted
results are then imported into the simplified economic model (Section 4.6.1). The production
scenario which provides the highest NPV is selected.
TotalNumberof Wells
Net
Pre
sen
t V
alu
e
Target Recovery Factor at End of Plateau
Optimum NPV
Chapter 5
Model Performance
5.1 Simulation of Standard PVT “Black Oil” Properties
A model has been developed to simulate standard PVT properties from a phase behavior
protocol. Input data presented in Appendix A is set to the subroutine and standard ―black oil‖
PVT properties - gas formation volume factor ( ), oil formation volume factor ( ), volatilized
oil-gas ratio ( ), and solution gas-oil ratio ( ) - are calculated based on fluid compositional
data. Section 5.1.1 shows calculation results from the procedure described in Section 4.2.3.
Section 5.1.2 discusses the limitations inherent to representing a multi-component hydrocarbon
mixture as a binary pseudo-component fluid model. Section 5.1.3 elaborates about the impact of
such limitations on the values and behavior of standard PVT properties.
5.1.1 Simulated Standard PVT Properties
The standard PVT properties calculated from data set in Appendix A are shown in Figure
5-1 and Figure 5-2. The values of these properties depend on pressure (reservoir and surface),
temperature (reservoir and surface), and original composition of in-situ reservoir fluid. The trends
depicted in Figure 5-1 and Figure 5-2 are consistent with the typical phase behavior of gas
condensate reservoir fluids discussed in section 4.2.1 and the standard PVT properties for the
Anschutz Ranch East rich-gas condensate presented by Walsh and Lake (2003).
118
Figure 5-1: Simulated Gas Formation Volume Factor
and Volatilized Oil-Gas Ratio of Gas Condensate
For this reservoir fluid, gas formation volume factor ( ) equals 1.040 RB/MSCF at the
initial reservoir pressure of 4000 psia. As shown in Figure 5-1, its value increases with decreasing
reservoir pressure with an increased slope at lower reservoir pressures. At final abandonment
pressure of 500 psia, gas formation volume factor ( ) reached the value of 7.816 RB/MSCF.
Volatilized oil-gas ratio ( ) remains initially constant at the value of 205.9 STB/MMSCF for
reservoir pressures higher than the fluid’s dew point. Its value starts decreasing as soon as the
pressure decreases below dew point conditions. The decreasing slope of volatilized oil-gas ratio
( ) is largest at conditions around dew point conditions and lower as reservoir pressure
decreases. As the pressure continues to decrease, volatilized oil-gas ratio ( ) starts increasing
again because of re-vaporization of oil. Volatilized oil-gas ratio ( ) reaches a minimum value of
63.5 STB/MMSCF around 1100 psia before increasing up to 80.8 STB/MMSCF at the final
pressure of 500 psia.
0
50
100
150
200
250
0
2
4
6
8
10
0 1000 2000 3000 4000 5000
Rv
-V
ola
tiliz
ed
Oil
-Gas
Rat
io (
STB
/MM
SCF)
Bg
-G
as F
orm
atio
n V
olu
me
Fac
tor
(RB
/MSC
F)
Reservoir Pressure (psia)
Bg (RB/MSCF) Rv (STB/MMSCF)
Dew Point Pressure
Rv
Bg
119
Figure 5-2: Simulated Oil Formation Volume Factor
and Solution Gas-Oil Ratio of Gas Condensate
At reservoir pressure higher than dew point pressure, oil formation volume factor ( )
and solution gas-oil ratio ( ) are not actually defined because there is no free liquid phase in the
reservoir. However, oil formation volume factor ( ) and solution gas-oil ratio ( ) values above
the dew point can be calculated from Equation 4-61 and Equation 4-62. Those relationships are
defined force the Material Balance Equation (MBE) for gas condensate to collapse to the MBE
for wet gas at pressures above the dew point. As shown in Figure 5-2, oil formation volume factor
( ) starts at 2.858 RB/STB around dew point conditions and monotonically decreases to a value
of 1.206 RB/STB at the final pressure of 500 psia. Similarly, solution gas-oil ratio ( ) begins at
2067 SCF/STB around dew point conditions and then monotonically decreases to a value of 61.5
SCF/STB at the final pressure.
0
1000
2000
3000
4000
5000
6000
7000
0
1
2
3
4
5
6
7
0 1000 2000 3000 4000 5000
Rs-
Solu
tio
n G
as-O
il R
atio
(SC
F/ST
B)
Bo
-O
il Fo
rmat
ion
Vo
lum
e F
acto
r (R
B/S
TB)
Reservoir Pressure (psia)
Bo (RB/STB) Rs (SCF/STB)
Dew Point Pressure
Bo
Rs
120
Figure 5-3: Simulated Specific Gravity of Reservoir Gas
In addition, specific gravity ( ) of reservoir gas is also estimated. The results of this
estimation are shown in Figure 5-3. Above the dew point, specify gravity ( ) of reservoir gas is
constant and equal to 1.147. After that, its value decreases with decreasing reservoir pressure to
the minimum value of 0.876 at 1150 psia and then slightly increases back to 0.919 at the final
pressure of 500 psia due to condensate re-vaporization.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 500 1000 1500 2000 2500 3000 3500 4000 4500
SG -
Spe
cifi
c G
ravi
ty o
f R
ese
rvo
ir G
as
Reservoir Pressure (psia)
Specific Gravity of Reservoir Gas
Dew Point Pressure
SG
121
5.1.2 Limitations of Pseudo Component Model
The calculated volumes of surface gas and stock-tank oil pseudo components in reservoir
gas, reservoir oil, and cumulative gas production below dew point pressure are displayed in
Figure 5-4 and Figure 5-5, as they were estimated during the simulation of a CVD experiment
using a phase behavior model. They are calculated from 1000 MSCF of equivalent gas at dew
point pressure.
Figure 5-4: Volumes of Surface Gas Pseudo Component in
Reservoir Gas Reservoir Oil, and Cumulative Gas Production
As shown in Figure 5-4, the amount of surface gas pseudo component remaining in the
reservoir gas phase ( ) decreases from a value of 847 MSCF at the dew point to a value of 121
MSCF at the final pressure because of continuous gas production and retrograde condensation of
reservoir gas. Amounts of surface gas pseudo component in the reservoir oil phase ( ) starts at
0
100
200
300
400
500
600
700
800
900
1000
0 500 1000 1500 2000 2500 3000 3500
G -
Surf
ace
Gas
Pse
ud
o C
om
po
ne
nt
(MSC
F)
Reservoir Pressure (psia)
Gfg (MSCF) Gfo (MSCF) Gp (MSCF) Gfg +Gfo + Gp (MSCF)
Gfg
Gp
Gfg+Gfo+Gp
GfoDew Point
Pressure
847
121
735
5
861
122
zero at dew point pressure because there is no reservoir oil. Then, it increases to the maximum
volume of 92 MSCF at 2700 psia before decreasing to 5 MSCF at 500 psia. This reversing trend
is dominated by the changing amounts of reservoir oil volume or oil saturation during depletion.
Cumulative gas production ( ), which is the volume of surface gas pseudo component
recovered from the production of excess gas out of the PVT cell, increases from zero at dew point
pressure to 735 MSCF at the final pressure.
Figure 5-5: Volumes of Stock-Tank Oil Pseudo Component in
Reservoir Gas, Reservoir Oil, and Cumulative Oil Production
Figure 5-5 shows that the amount of stock-tank oil pseudo-component in the reservoir gas
phase ( ) decreases from a value of 174 STB at dew point pressure to a value of 10 STB at the
final pressure point due to gas production and retrograde condensation of reservoir gas. The
amount of stock-tank oil pseudo-component in reservoir oil ( ) increases from zero at dew
point pressure because of the lack of a reservoir oil phase and reaches a maximum volume of 96
0
20
40
60
80
100
120
140
160
180
200
0 500 1000 1500 2000 2500 3000 3500
N -
Sto
ck-T
ank
Oil
Pse
ud
o C
om
po
ne
nt
(STB
)
Reservoir Pressure (psia)
Nfg (STB) Nfo (STB) Np (STB) Nfg +Nfo + Np (STB)
Nfo
Nfg
Nfg+Nfo+Np
Np
DewPoint
Pressure
174
10
88
67
165
123
STB at 1450 psia before decreasing to 88 STB at the final pressure. This reversing trend mainly
stems from changes in reservoir oil saturation in the reservoir during depletion. Cumulative oil
production ( ), which is the volume of stock-tank oil pseudo-component recovered from the
excess gas produced from the PVT cell, increases from zero at dew point pressure to 67 STB at
the final pressure.
Let us now consider how the basic statements of species conservation are being honored
during the simulated depletion. The sum of the amounts of surface gas pseudo-component in
reservoir gas, in reservoir oil, and cumulative gas production ( ) in Figure 5-4
should be always equal to the total amount of surface gas pseudo component originally present in
reservoir gas at dew point conditions if the surface gas pseudo-component was to be fully
conserved throughout the simulated experiment. However, Figure 5-4 clearly shows that the total
amount of surface gas pseudo component ( ) is not constant throughout the
simulated process; instead, it increases from 847 MSCF at the dew point to 861 MSCF at the final
pressure. This suggests that total mass of surface gas pseudo component actually increases with
decreasing reservoir pressure which is physically impossible as is in violation of mass
conservation. Similarly, the fact that the total amount of stock-tank oil pseudo component
( ) decreases from 174 STB at dew point conditions to 165 STB at the final
pressure, suggests that total mass of stock-tank oil pseudo-component actually decreases with
decreasing reservoir pressure. These unphysical trends are caused by one of the key assumptions
used in pseudo component model, which establishes that the properties of the surface gas and
stock-tank oil pseudo-components are supposed equal and unchanging during depletion.
In reality, the properties of pseudo components, which are actually two multi-component
mixtures in their own right, do change throughout reservoir depletion. Compositions of reservoir
gas and reservoir oil change continuously because of retrograde condensation. In addition, there
are three points of surface separation; first stage separator, second stage separator, and stock tank.
124
Figure 5-6 displays the estimated densities of surface gas and stock-tank oil pseudo components,
as calculated by the Phase Behavior Model. They clearly suggest that fluid properties of these
pseudo-components are not necessarily constant, although they do not change dramatically during
depletion.
Figure 5-6: Densities of Surface Gas and Stock-Tank Oil Pseudo Components
at First Stage Separator, Second Stage Separator and Stock Tank Condition
Figure 5-7 shows the amount of stock-tank oil pseudo-component in the reservoir gas
phase ( ), reservoir oil phase ( ) and cumulative production ( ) in term of gas-equivalent
volume. The conversion from oil volume to equivalent-gas volume is based on molar
equivalency. Gas-oil equivalency factor ( ) is calculated from Equation 5-1. Densities and
molecular weights of stock-tank oil from reservoir gas, reservoir oil, and cumulative oil
production are directly obtained from Phase Behavior Model.
0
10
20
30
40
50
0.0
0.6
1.2
1.8
2.4
3.0
0 500 1000 1500 2000 2500 3000 3500
De
nsi
ty o
f St
ock
-Tan
k O
il (l
bm
/ft3
)
De
nsi
ty o
f Su
rfac
e G
as (
lbm
/ft3 )
Reservoir Pressure (psia)
Gfg at Sep 1 (lbm/ft3) Gfg at Sep 2 (lbm/ft3) Gfg at STO (lbm/ft3) Gfo at Sep 1 (lbm/ft3)
Gfo at Sep 2 (lbm/ft3) Gfo at STO (lbm/ft3) Nfg at STO (lbm/ft3) Nfo at STO (lbm/ft3)
Nfg at STO
Nfo at STO
Gfg at Sep1
Gfo at Sep1
Gfg at Sep2
Gfg at STO
Gfo at Sep2
Gfo at STO
125
Equation 5-1
Figure 5-7: Volumes of Stock-Tank Oil Pseudo Component in
Reservoir Gas, Reservoir Oil, and Cumulative Oil Production
in term of Gas-Equivalent
Figure 5-8 shows the volume of surface gas ( ), volume of stock-tank oil
( ) expressed in term of gas-equivalent volume, and total volume from both
surface gas and stock-tank oil volumes. The total volumes are constant and equal to 1000 MSCF
which is the original volume at dew point conditions. These results clearly prove that pseudo
component model is able to honor overall material balance, but not species material balance.
0
20
40
60
80
100
120
140
160
180
0 500 1000 1500 2000 2500 3000 3500
GE
-Su
rfac
e G
as E
qu
ival
en
t (M
SCF)
Reservoir Pressure (psia)
Nfg Nfo Np Nfg+Nfo+Np
Nfg
Ngo
Nfg+Nfo+Np
Np
Dew Point
Pressure
153
62
67
10
139
126
Figure 5-8: Total Volumes of Stock-Tank Oil Pseudo Component and
Surface Gas Pseudo Component in term of Gas-Equivalent
0
100
200
300
400
500
600
700
800
900
1000
0 500 1000 1500 2000 2500 3000 3500
GE
-Su
rfac
e G
as E
qu
ival
en
t (M
SCF)
Reservoir Pressure (psia)
Nfg+Nfo+Np Gfg+Gfo+Gp TOTAL
Gfg+Gfo+Gp
Dew Point
Pressure153
847
139
861
Nfg+Nfo+Gp
TOTAL
127
5.1.3 Impact on Standard PVT Properties
The limitations of representing a multi-component hydrocarbon mixture using a binary
pseudo-component model, as discussed in the preceding section, would definitely have an effect
on the calculation of the standard PVT ―black-oil‖ properties. As discussed below, solution gas-
oil ratios ( ) could become negative at low reservoir pressures; or oil formation volume factors
( ) could become over-estimated.
The Walsh-Towler algorithm applies concept of mass balance around the PVT cell by
calculating amounts of pseudo components in the reservoir oil at any pressure level j ( and
) from the differences between total pseudo-component amounts from the previous pressure
level ( and
) and the summation of pseudo-
component amounts in the reservoir gas phase and cumulative production ( and
).
The combination of this mass balance concept and simulated results from a phase
behavior model can lead to negative values of surface gas pseudo component in oil phase ( )
and over-estimated values of stock-tank pseudo component in the oil phase ( ) when reservoir
depletion is extensive (i.e., at low pressures). For example, at final abandonment pressure of 500
psia and using the data of Figure 5-4, the value of surface gas pseudo component in oil phase
( ), which is equal to 5 MSCF based on a rigorous flash calculation, would be equal to -9
MSCF (847 – 735 – 121 = -9) when this mass balance concept is applied. In Figure 5-5, the value
of stock-tank oil pseudo component ( ), which is equal to 88 STB from a flash calculation,
would be equal to 97 STB (174 – 67 – 10 = 97) using the same mass balance concept. Thus, the
resulting solution gas-oil ratio ( ) calculated from Walsh-Towler algorithm at this condition
would become equal to -96 SCF/STB, while 61.5 SCF/STB is the simulated value from flash
128
calculations as shown in Figure 5-2. Similarly, oil formation volume factor ( ) calculated from
Walsh-Towler algorithm would be equal to 1.082 RB/STB, while 1.206 RB/STB is the simulated
value from flash calculations as shown in Figure 5-2.
129
5.2 Zero-Dimensional Material Balance Calculations for Gas Condensates
A reservoir model has been developed in order to predict cumulative gas production,
cumulative oil production, production gas-oil ratio, and average reservoir gas saturation based on
the procedure described in Material Balance Equation for Gas Condensates and Saturation
Calculation sections discussed above. Input data in Appendix A is used by the model, which
generates its outputs as function of reservoir pressure. Section 5.2.1 discusses the simulation
results and section 5.2.2 discusses the significant pitfalls of misusing the proposed gas condensate
fluid tank model for performance prediction for other near-critical fluid: the volatile oil reservoir.
5.2.1 Simulation Results from Gas Condensate Tank Model
Figure 5-9 plots the results of gas condensate tank model for the reservoir scenario
described in Appendix A. Initial reservoir pressure is 4000 psia, dew point pressure is 3031 psia,
and abandonment pressure is 750 psia. In Figure 5-9, cumulative gas recovery ( ) and
cumulative oil recovery ( ) increase with decreasing reservoir pressure. The recovery slopes
are identical for conditions above dew point pressure; however, the increasing trend or slope of
cumulative oil recovery becomes significantly flatter than that of gas for pressures below the dew
point. At abandonment pressure conditions, in this example, cumulative gas and oil recoveries are
equal to 80.6% and 45.7%, respectively. Gas saturation ( ) remains constant at 79% (
) above the dew point. As reservoir pressure decreases below the dew point, gas saturation
( ) decreases to the minimum value of 66.6% at 2350 psia, and then slightly increases back to
69.5% at the abandonment pressure. Production gas-oil ratio ( ), which is the inverse of
volatilized oil-gas ratio ( ) for a gas condensate system whose reservoir condensate remains
immobile, is constant at 4.857 MSCF/STB above the dew point. As reservoir pressure decreases
130
below dew point conditions, production gas-oil ratio ( ) increases to the maximum value of
15.756 MSCF/STB at 1050 psia, and then slightly decreases back to 14.863 MSCF/STB at the
abandonment pressure.
Figure 5-9: Simulated Production Results of Gas Condensate
using Simplified Gas Condensate Tank Model
Qualitatively, the production trends calculated from the gas condensate zero-dimensional
model fully agree with the typical and expected trends observed in the field and through fully-
dimensional numerical reservoir simulation (Walsh and Lake, 2003). A standard numerical
simulator also suggests, and field experience corroborates, that ultimate gas recovery - i.e.,
cumulative gas recovery at abandonment conditions - is much higher than ultimate oil recovery.
The reason is that, after dew point conditions are reached, stock-tank oil is continuously being left
behind as immobile condensate trapped in the reservoir. Gas saturation ( ) remains constant
0
10
20
30
40
50
60
70
80
90
100
0 1000 2000 3000 4000 5000
OO
IP R
eco
very
(%
) /
OG
IP R
eco
very
(%
)P
rod
uct
ion
GO
R (
MSC
F/ST
B)
/ G
as S
atu
rati
on
(%
)
Reservoir Pressure (psia)
Gp/G (%) Np/N (%) GOR (MSCF/STB) Sg (%)
Dew Point Pressure
Sg
GOR
Np/N
Gp/G
131
above the dew point because there is no oil phase in the reservoir and water saturation ( ) is
assumed to be constant when no water encroachment is acting on the reservoir system. Gas
saturation ( ) decreases as reservoir pressure decreases around dew point conditions because of
the new presence of reservoir oil phase in the reservoir. Condensate dropout rate is maximum at
conditions near the dew point. When gas condensate is rich enough and pressure is low enough,
gas saturation can slightly increase with reservoir pressure. Gas phase production, oil phase
expansion, and retrograde condensation near to dew point conditions tend to decrease gas
saturation ( ). Expansion of the reservoir gas and re-vaporization of condensate at low pressures
tend to increase gas saturation ( ). Production gas-oil ratio ( ) is constant above the dew
point because composition of produced reservoir gas remains unchanged for such conditions.
Below the dew point, production gas-oil ratio ( ) increases with decreasing reservoir pressure
because of retrograde condensation and the changing nature of the produced reservoir gas.
Production gas-oil ratio ( ) can slightly decreases at low reservoir pressure due to liquid re-
vaporization.
132
5.2.2 Misuse of Gas Condensate Tank Model in Volatile Oil Reservoir
Simulation results from the Simplified Gas Condensate Tank (SGCT) model must be
crosschecked against the typical phase and depletion behavior of gas condensate reservoirs
outlined in the preceding section. If the reservoir fluid is not a gas condensate, prediction results
will be inconsistent with those typical PVT property and depletion behavior. For example, if the
SGCT model is inadvertently used for the analysis of a different type of near-critical fluid, such
as a volatile oil reservoir, calculated gas saturation ( ) profiles will start from zero at saturation
conditions (which would actually represent a bubble point) and monotonically increase with
decreasing reservoir pressure below saturation conditions. Such gas saturation profile is
significantly different from the typical -profile for gas condensates which must starts at one if
no water is present (or at initial gas saturation equal to ) and decreases with decreasing
reservoir pressure at conditions below the dew point. In this case, all simulation results must be
disregarded because the assumptions used for the gas condensate tank model (SGCT) are not
applicable for volatile oil reservoir.
To illustrate the differences between the phase and flow behavior between gas
condensates and volatile oils, reservoir temperature can be manipulated. A volatile oil reservoir
behavior can be obtained using the same fluid characterization and composition presented in
Appendix A, but with a reservoir temperature reduced from 300 F to 190 F. Figure 5-10 plots the
phase envelope of reservoir fluid and the two different reservoir depletion paths for the two
reservoir temperatures under consideration. The depletion path at the reservoir temperature of 300
F represents the path of the gas condensate ( ), while the depletion path at the reservoir
temperature of 190 F represents the path of the volatile oil ( ). Both fluids are near critical
fluids but they are found at the opposite sides of the critical point. Simulation results for the gas
condensate were discussed in Figure 5-1 through Figure 5-9 in the preceding section.
133
Figure 5-10: Phase Envelope and Reservoir Depletion Paths
at Two Different Reservoir Temperatures
The resulting standard PVT properties of the volatile oil, which are calculated using the
PVT model for a gas condensate, are shown in Figure 5-11 and Figure 5-12. The characteristics
of gas formation volume factor ( ), oil formation volume factor ( ), volatilized oil-gas ratio
( ), and solution gas-oil ratio ( ) are similar to the typical characteristics of gas condensates.
However, these results cannot be used and are physically meaningless for an actual volatile oil
because their calculation has been based on assuming that the reservoir oil, which is the main
hydrocarbon phase produced in a volatile oil reservoir, remains immobile in the gas condensate
PVT cell.
0
500
1000
1500
2000
2500
3000
3500
4000
-300 -200 -100 0 100 200 300 400 500
Res
ervo
ir P
ress
ure
(psi
a)
Reservoir Temperature (F)
ReservoirDepletion
Path at 300 F"Gas Condensate"
Critical Point
ReservoirDepletion
Path at 190 F
"Volatile Oil"
134
Figure 5-11: Simulated Gas Formation Volume Factor and Volatilized Oil-Gas Ratio
of Volatile Oil using Gas Condensate PVT Model
Figure 5-12: Simulated Oil Formation Volume Factor and Solution Gas-Oil Ratio
of Volatile Oil using Gas Condensate PVT Model
0
50
100
150
200
250
0.0
2.0
4.0
6.0
8.0
10.0
0 1000 2000 3000 4000 5000
Rv
-V
ola
tiliz
ed
Oil
-Gas
Rat
io (
STB
/MM
SCF)
Bg
-G
as F
orm
atio
n V
olu
me
Fac
tor
(RB
/MSC
F)
Reservoir Pressure (psia)
Bg (RB/MSCF) Rv (STB/MMSCF)
Saturated Pressure
Rv
Bg
0
1000
2000
3000
4000
5000
6000
7000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0 1000 2000 3000 4000 5000
Rs
-So
luti
on
Gas
-Oil
Rat
io (
SCF/
STB
)
Bo
-O
il Fo
rmat
ion
Vo
lum
e F
acto
r (R
B/S
TB)
Reservoir Pressure (psia)
Bo (RB/STB) Rs (SCF/STB)
Saturated Pressure
Bo
Rs
135
Production data predictions for the volatile oil, as simulated by the SGCT model using
the PVT properties in Figure 5-11 and Figure 5-12, are shown in Figure 5-13. Characteristics of
cumulative gas recovery ( ), cumulative oil recovery ( ), and production gas-oil ratio
( ) are similar to those simulated for gas condensate but the gas saturation ( ) trend is
significantly different, as discussed above. The typical gas saturation ( ) of condensate should
start at initial gas saturation ( ) at conditions above saturation (dew point) conditions
because there should be no liquid hydrocarbon in that state. However, gas saturation ( ) plotted
in Figure 5-13 approaches zero around the saturation pressure, which indicates that oil saturation
( ) does not approach zero but rather approaches a maximum value ( ). Therefore,
all simulation results must be disregarded.
Figure 5-13: Simulated Production Results of Volatile Oil
using Simplified Gas Condensate Tank Model
0
10
20
30
40
50
60
70
80
90
100
0 1000 2000 3000 4000 5000
OO
IP R
eco
very
(%
) /
OG
IP R
eco
very
(%
)P
rod
uct
ion
GO
R (
MSC
F/ST
B)
/ G
as
Satu
rati
on
(%
)
Reservoir Pressure (psia)
Gp/G (%) Np/N (%) GOR (MSCF/STB) Sg (%)
Saturation Pressure
Sg
GOR
Np/N
Gp/G
136
In short, models developed for gas condensate fluids should not be recklessly used
without proper precautions and crosschecks. A crosschecking process has to be carried out either
before or after having generated the simulation results. Before running the simulation, for
example, the calculated fractions of vapor and liquid phases inside the PVT cell and along the
reservoir depletion path should be analyzed. Molar fraction of vapor phase ( ) for a gas
condensate must approach 1.0 as the saturation pressure is approached because there should be no
liquid at a dew point line, and molar fraction of vapor phase ( ) for a volatile oil must approach
zero as the saturation pressure is approached because there should be no vapor at a bubble point
line. This situation is illustrated in Figure 5-14. After running the simulation, the resulting gas
saturation ( ), for example, should be crosschecked as well.
.
Figure 5-14: Mole Fraction Behavior of Vapor Phase Molar Fraction ( )
for Gas Condensates and Volatile Oils
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 500 1000 1500 2000 2500 3000 3500 4000
F ng
-Ma
lar
Frac
tio
n o
f V
apo
r P
has
e
Reservoir Pressure (psia)
Fng of Gas Condensate Fng of Volatile Oil
Volatile Oil
Gas Condensate
137
5.3 Field Performance Prediction
Field performance prediction calculations were described in Section 4.5 and have been
developed in a stand-alone VBA application. The model is able to predict pressures, flow rates,
cumulative productions, and expected production time by integrating a zero-dimensional
reservoir model, a flow rate and pressure (IPR/TBR) model, and production constraints together.
The input data set used by the model is presented in Appendix A and the generated results are
discussed in Section 5.3.1. In addition, the appearance of a slightly negative hyperbolic decline
coefficient during the decline period, which is very rare to encounter in conventional decline
curve analysis, is observed from this simulation results. This is discussed in Section 5.3.2. Note
that, in this study, field performance predictions begin at a plateau period because built-up has
been neglected by assuming that the operator has a substantial drilling capacity available to
develop the field.
5.3.1 Field Performance Prediction Results
Predictions for cumulative gas production ( ) and cumulative oil ( ) production vs.
production time ( ) are displayed in Figure 5-15. Cumulative gas production ( ) linearly
increases during plateau period because plateau gas flow rate (
) is being maintained.
Plateau period ends when the 55% target recovery factor is reached. Cumulative gas production at
end of plateau ( ) is equal to 216 BSCF. Cumulative gas production at abandonment
condition ( ) is equal to 317 BSCF, which is equivalent 81% gas recovery factor.
Cumulative oil production ( ) also linearly increases at the beginning because of constant
plateau gas flow rate (
) during plateau period and constant volatilized oil-gas ration ( )
above the dew point. When reservoir pressure goes below the dew point, cumulative oil
138
production ( ) increases at lower rate than cumulative gas ( ) production due to a decreasing
volatilized oil-gas ratio ( ). Cumulative oil production at abandonment condition ( ) is
equal to 37 MMSTB, which is equivalent to a 46% condensate recovery factor. These results
indicate, as expected, that total recovery factor of oil/condensate is significantly less than total
recovery factor of gas in typical depletion operations for gas condensate fluids. This is expected
because a large portion of original oil in place is being left as an immobile condensate phase
inside the reservoir.
Figure 5-15: Cumulative Gas and Oil Production vs. Time
Figure 5-16 plots total gas flow rate ( ) and total oil flow rate ( ) vs. production
time ( ). Total gas flow rate ( ) is maintained at the plateau gas flow rate (
) of 213
MMSCF/D during the plateau period. During the decline period, reservoir pressure is not enough
to maintain the plateau gas flow rate (
), thus total gas flow rate ( ) declines with
0
10
20
30
40
50
60
70
80
0
50
100
150
200
250
300
350
400
0 1 2 3 4 5 6 7
Np
-C
um
ula
tive
Oil
Pro
du
ctio
n (
MM
STB
)
Gp
-C
um
ula
tive
Gas
Pro
du
ctio
n (
BSC
F)
Production Time (Year)
Gp (BSCF) Np (MMSTB)
End of Plateau
Gp
Np
Dew Point
G = 393 BSCFN = 81 MMSTBRvi = 206 STB/MMSCF
139
decreasing reservoir pressure. At abandonment condition, total gas flow rate ( ) is equal to 19
MMSCF/D. Total oil flow rate ( ) is constant at 44 MSTB/D above the dew point. Total oil
flow rate ( ) declines because of decreasing volatilize oil-gas ratio ( ) below the dew point
and because of declining total gas flow rate ( ) during decline period. At low pressures, even
when the volatized oil-gas ratio ( ) slightly increases, total oil flow rate ( ) continues to
decline. This is because increasing volatilized oil-gas ratio ( ) is not enough to compensate for
decreasing total gas flow rate ( ) at that condition. At abandonment conditions, total oil flow
rate ( ) equals 1.3 MSTB/D.
Figure 5-16: Total Gas and Oil Flow Rates vs. Time
Figure 5-17 plots reservoir pressure ( ), bottomhole flowing pressure ( ), and
wellhead pressure ( ) vs. production time ( ). During plateau period, production time ( ) is
directly proportion of cumulative gas recovery ( ) variable because total gas flow rate ( )
0
10
20
30
40
50
0
50
100
150
200
250
0 1 2 3 4 5 6 7
qo
sc-
Tota
l Oil
Flo
w R
ate
(M
STB
/D)
qg
sc-
Tota
l Ga
s Fl
ow
Ra
te (
MM
SCF/
D)
Production Time (Year)
q_gsc (MMSCF/D) q_osc (MSTB/D)
End of Plateau
qgsc
qosc
Dew Point
140
and original gas in place ( ) are constant. Thus, the relationship between reservoir pressure ( )
and production time ( ) during plateau period is similar to the relationship between reservoir
pressure ( ) and cumulative gas recovery ( ) calculated from the gas condensate tank
model. Reservoir pressure ( ) decreases from 4000 psia at initial condition to 3031 psia at the
dew point. After that, reservoir pressure ( ) decreases at a slower rate as a result of the
implementation of a two-phase mode of operation in the gas condensate tank model. This
behavior could be observed in Figure 5-9 as well. In addition, reservoir pressure ( ) during the
decline period decreases at an even slower pace thanks to a declining gas flow rate ( ).
Reservoir pressure ( ) reaches abandonment pressure of 750 psia after 6.23 year of production.
Figure 5-17: Reservoir Pressure, Bottomhole Flowing Pressure,
and Wellhead Pressure vs. Time
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 1 2 3 4 5 6 7
Pre
ssu
re (p
sia)
Production Time (Year)
Pr (psia) Pwf (psia) Pwh (psia)
End of Plateau
pr
pwf
pwh
Dew Point
141
Figure 5-17 reveals that bottomhole flowing pressure ( ) decreases from 3440 psia at
initial conditions to 668 psia at abandonment conditions. Bottomhole flowing pressure ( )
depends on reservoir pressure ( ) and drawdown pressure ( ), which is the pressure drop
required to produce hydrocarbons out of the reservoir. Wellhead pressure ( ) decreases from
2438 psia at initial condition to minimum allowable wellhead pressure ( ) of 550 psia at end
of plateau. After that, wellhead pressure ( ) is maintained at constant level of 550 psia.
Wellhead pressure ( ) varies with bottomhole flowing pressure ( ) and pressure drop inside
the tubing, which is a pressure drop that must be maintained in the tubing in order to produce
hydrocarbon out of the wellbore.
Drawdown pressure ( ), which is the difference between reservoir pressure ( ) and
bottomhole flowing pressure ( ), is relatively constant above the dew point because most of
the variables in IPR equation (Equation 4-134) are relatively constant. Drawdown pressure ( )
found within the range 545 to 560 psia during this period. Below the dew point, drawdown
pressure ( ) increases with decreasing reservoir pressure ( ) mainly because of decreasing
relative permeability of gas ( ). At reservoir pressures close to the dew point, relative
permeability of gas ( ) decreases significantly due to decreasing gas saturation ( ), while the
product of gas viscosity ( ) times gas formation volume factor ( ) decreases slightly. As a
result, drawdown pressure ( ) has to increase in order to maintain plateau gas flow rate
(
) so that it can compensate for the decreased mobility of the gas phase. As reservoir
pressure continues to decrease, relative permeability of gas ( ) is relatively constant because
gas saturation ( ) is relatively stable (see Figure 5-18), while the product of gas viscosity ( )
times gas formation volume factor ( ) slightly increases. As a result, drawdown pressure ( )
has to continue to increase in order to maintain the plateau gas flow rate (
). During
142
decline period, drawdown pressure ( ) is lower mainly because of declining total gas flow rate
( ).
Figure 5-18: Gas Saturation and Specific Gravity of Reservoir Gas vs. Time
Pressure drop inside the tubing is the difference between bottomhole flowing pressure
( ) and wellhead pressure ( ). Pressure drop inside the tubing is relatively constant above
the dew point because most of the variables in TPR equation (Equation 4-139) are relatively
constant. This pressure drop ranges between the values of 870 to 1000 psi during this above-dew-
point period. During decline period, pressure drop inside the tubing continues to decrease owing
to decreasing total gas flow rate ( ). At abandonment condition, pressure drop inside the
tubing reaches the minimum value of 118 psi.
0.5
0.7
0.9
1.1
1.3
1.5
0.00
0.20
0.40
0.60
0.80
1.00
0 1 2 3 4 5 6 7
Spe
cifi
c G
ravi
ty o
f R
ese
rvo
ir G
as
Gas
Sat
ura
tio
n (
Frac
tio
n)
Production Time (Year)
Gas Saturation SG of Reservoir Gas
End of Plateau
Gas Saturation
Specific Gravity of Reservoir Gas
Dew Point
143
5.3.2 Decline Trend Analysis
Total gas flow rate ( ) and cumulative gas production during decline period (
) is calculated by combining gas condensate tank model and nodal analysis as described
in Section 4.5. These results, for the scenario of interest, are plotted in Figure 5-19. The
exponential decline trend which calculated from exponential decline equation is also plotted into
the same figure. Total gas flow rate ( ) from exponential decline trend is calculated from
Equation 5-2 and the decline rate ( ) of exponential decline trend is calculate from Equation
4-144.
Equation 5-2
Figure 5-19: Total Gas Flow Rate ( ) vs.
Cumulative Gas Production during Decline Period
0
50
100
150
200
250
0 20 40 60 80 100 120
qgs
c-
Tota
l Gas
Flo
w R
ate
(M
MSC
F/D
)
(Gp - Gpplateau) - Cumulative Gas Production during Decline Period (BSCF)
Field Performance Preidction Data Exponentail Decline Trend (b = 0.0)
Exponential Decline TrendDi = 1.92 * 10-3 {Day-1}
Field Performance Prediction Data
144
From Figure 5-19, calculated results from field performance prediction and exponential
decline equation agree with each other, which is not surprising. The assumptions used in this
simulator, including pseudo steady state flow condition, no water production, no water injection,
no water influx, and constant wellhead pressure during decline period, are favorable assumptions
for an exponential decline. Therefore, the exponential decline is a fairly good assumption for
calculating production time ( ) based on total gas flow rate ( ) and cumulative gas production
( ).
However, detailed analysis of the decline trend shows decline rate ( ) actually varies -
although very slightly. If exponential decline is assumed between each decline interval, decline
rate ( ) of each interval can be calculated from Equation 5-3. The calculation results which are
plotted in Figure 5-20 show that decline rate ( ) increases with increasing cumulative gas
production ( ) for most of the time. In other words, they suggest that decline rates are slightly
increasing in time, which in turn implies having a hyperbolic decline exponent ( ) of negative
value. In conventional decline curve analysis, decline rates ( ) are always expected to dampen in
time and thus hyperbolic decline coefficients ( ) are always expected to be positive (
). A negative value for the decline exponent ( ) is extremely rare scenario. It became
apparent during this study that this decline behavior was coupled with the appearance/
disappearance of the condensate phase and related property changes during decline, as suggested
by Figure 5-20. In this figure, decline rates slightly increase with reservoir production but they
reach a maximum after which they start to decrease. This event seems to closely follow the
behavior of GOR presented in Figure 5-9. It is suggested that condensate effects and the inherent
evolution of fluid properties in time impose the increase in the decline rate at earlier times during
the decline period but this trend is reversed around the moment GOR reaches its maximum. It is
important to note that these decline rate changes are not very large or significant; therefore the
exponential decline assumption still remains largely valid for engineering evaluation purposes. It
145
should also stressed that conventional decline curve analysis is based on the assumption of
production at a constant bottomhole pressure ( ) which is not strictly valid for the scenario
under consideration as displayed in Figure 5-17 during decline.
Equation 5-3
Figure 5-20: Decline Rate ( ) vs. Cumulative Gas Production
during Decline Period ( )
1.6E-03
1.7E-03
1.8E-03
1.9E-03
2.0E-03
2.1E-03
2.2E-03
0 20 40 60 80 100 120
D -
De
clin
e R
ate
(1/D
ay)
(Gp - Gpplateau) - Cumulative Gas Production during Decline Period (BSCF)
Decline Rate (1/Day)
Decline Rate of 1.92 * 10-3 {Day-1}
146
5.4 Economic Analysis and Optimization
An economic evaluation model has been developed to calculate net present value (NPV)
and rate of return (ROR) based on the simplified economic model described in Section 4.6.1.
Results from field performance prediction from the previous section and economic parameters
from Appendix A are inputted into this economic model, and the generated results are shown and
discussed in Section 5.4.1. For field optimization studies, results of the sensitivity analysis of
NPVs for different target recovery at end of plateau and total number of wells are displayed and
elaborated upon in Section 5.4.2.
5.4.1 Field Economic Analysis
Figure 5-21 presents the predictions for annual expenditure, annual revenue, and
cumulative discounted net cash flow vs. production time for the reservoir exploitation scenario
under consideration. Annual expenditure is equal to 1480 Million $ at the beginning. It is very
large because all CAPEX, including drilling and completion cost, platform cost, pipeline cost,
and production facilities cost, is spent at that time. Annual expenditure drops drastically to 116
Million $ in the 1st year of production because it consists of OPEX and taxes only and they are
relatively small when compared to initial CAPEX. Annual expenditure continuously decreases
because ad valorem and severance taxes decrease resulting from decreasing in annual revenue.
Annual expenditure at the last year of production is equal to 8.21 Million $. Annual revenue is
equal to 1373 Million $ in the 1st year of production. Then, it continuously declines due to
decreasing gas and oil flow rates. Annual revenue at the last year of production is equal to15.70
Million $.
147
Figure 5-21: Annual Expenditure, Annual Total Revenue,
and Cumulative Discounted Net Cash Flow vs. Production Time
Figure 5-21 shows that the cumulative discounted net cash flow is equal to (-1480)
Million $ at the beginning of the project. Cumulative discounted net cash flow increases every
year because annual revenue is higher than annual expenditures throughout the production period.
However, the rate of net cash increase decreases at late time because net cash flow is lower and
time discount factor is higher. The cumulative discounted net cash flow at the last year of
production, which is equivalent to the project’s NPV, is equal to 1189 Million $. Figure 5-21 also
shows that cumulative discounted net cash flow turns from negative value to positive value
between the first year and the second year of production. Thus, the payback period, which is the
time period required for cumulative discounted net cash flow to be equal to zero, is between one
to two years.
(2000)
(1500)
(1000)
(500)
0
500
1000
1500
2000
0 1 2 3 4 5 6 7
Mo
ne
tary
Val
ue
(M
illio
n $
)
Production Period (Year)
Annual Expenditure Annual Revenue Cumulative Discounted Net Cash Flow
Annual Expenditure
Annual Revenue
Cumulative Discounted Net Cash Flow
148
Figure 5-22: Net Present Value vs. Interest Rate
Figure 5-22 shows project’s NPVs at different interest or discount rates ranging from 5%
to 60%. The NPV decreases with increasing interest or discount rate because future net cash flow
is more heavily discounted and penalized. The discount interest rate has less impact on project’s
expenditures than on its revenue because most of the investment is spent at the beginning of the
project while most of the revenue is actually generated later in time. The NPV is equal to 1590
Million $ at interest rate of 5% and monotonically decreases to 245 Million $ at interest rate of
40%. Rate of return (ROR), which is the interest rate that results in zero NPV, is equal to 53%.
(500)
0
500
1000
1500
2000
0.00 0.10 0.20 0.30 0.40 0.50 0.60
NP
V -
Net
Pre
sen
t Val
ue
(Mill
ion
$)
Interest Rate (Fraction)
ROR = 53%NPV @ 12% Interest Rate = 1189 Million $
149
5.4.2 Field Optimization
Figure 5-23 is a composite figure that shows field optimization results in both tabular and
graphical forms. Target recovery factors at end of plateau are varied between 30% and 75% while
total number of wells required for development is varied between 3 and 30 wells. It is readily
realized from this figure that the optimized NPV can be placed at 1326 Million $ for the
combination of 30% target recovery factor and the use of 15 wells for field development.
Figure 5-23: Field Optimization Results
3
12
21
30
0
200
400
600
800
1,000
1,200
1,400
0.300.40
0.500.60
0.70
TotalNumberof Wells
Net
Pre
sen
t V
alu
e (M
illio
n $
)
Target Recovery Factor at End of Plateau
NPV Target Recovery Factor at End of Plateau
(Million $) 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75
3 639 601 550 482 394 281 136 -50 -283 -579
6 1,077 1,052 1,016 966 895 801 667 480 210 -194
9 1,244 1,226 1,199 1,161 1,106 1,028 917 753 499 76
12 1,310 1,296 1,275 1,244 1,199 1,134 1,040 899 670 262
15 1,326 1,315 1,298 1,273 1,233 1,179 1,098 975 771 388
18 1,313 1,304 1,290 1,269 1,238 1,189 1,120 1,010 827 469
21 1,284 1,277 1,264 1,247 1,217 1,177 1,117 1,018 852 521
24 1,241 1,236 1,225 1,209 1,186 1,151 1,096 1,010 856 550
27 1,195 1,190 1,182 1,167 1,147 1,113 1,065 985 847 561
30 1,139 1,136 1,129 1,115 1,097 1,070 1,024 954 827 559
Tota
l Nu
mb
er o
f W
ell
150
If a target plateau recovery factor is fixed due to contractual obligations or market
saturation demands, optimum number of wells could be determined. When too few wells are
drilled to develop a hydrocarbon deposit, resulting field flow rates will be smaller and the
required production period needed to reach abandonment will be prolonged. Thus, annual revenue
from a distant future will be dramatically discounted, which will result in lower NPVs. In
contrast, if total number of wells used to develop the reservoir is too high, the additional revenue
that would be obtained from production acceleration will not be able to compensate or offset the
significantly increased drilling and completion costs. As a result, NPV will not be maximized
under either scenario.
When the total number of wells is fixed, an optimum target recovery factor could not be
found. Under the current model, NPV will always increases with decreasing target recovery
factor. This is because CAPEX does not change with total flow rates in this economic model. If
target recovery factor is lowered, initial flow rates will be higher and annual revenue will be
accelerated. However, production facilities costs, required to handle such an increased volume of
fluids, remain constant in this study. As a result, NPV will always be better for lower target
plateau recovery factor because the production is accelerated and the revenue can be received
earlier in the life of the field. In actual field applications, there is always a maximum fluid volume
that can be reasonably handled at the surface and accepted by the market. This justifies the need
for a plateau period. In the limiting case when target plateau recovery becomes zero, which
effectively eliminates the plateau period, initial flow rates for the decline period will be extremely
large. This is good news for the simplified economic model but bad news in real applications
because those fluid volumes might not be able to be marketed effectively and the required surface
facilities would become extremely expensive. In addition, facilities designed to handle such large
volumes just during the first year alone would become awfully overdesigned for the rest of the
reservoir life - a situation that is far from optimal. In order to be able to actually determine a more
151
realistic and optimum target recovery factor, the CAPEX model has to be adjusted. Surface
production facilities cost and/or flowline costs have to be made functions of maximum expected
flow rates by introducing either a continuous- or step- cost function in the CAPEX model.
152
5.5 Application for Other Production Situations
This section discusses recommendations on how to extend the capabilities of field
performance simulator for gas condensate fluids in order to tackle other possible production
scenarios. Two other scenarios, such as dry gas / wet gas production and gas condensates with
producible reservoir oil, are elaborated upon. The fundamental differences and the required
modifications to current gas condensate scenario build in the present model, as well as the
expected results from such modified models, are the main areas of discussion in this section.
153
5.5.1 Application for Dry Gas / Wet Gas
Even though the proposed model has been specifically tailored to the analysis of gas
condensate reservoir fluids, it could be actually be applied to any other natural gas reservoir, such
as dry gases and wet gases, with few modifications. In dry gas and wet gas reservoirs, the
hydrocarbon fluid is always found in a 100% vapor phase state throughout their isothermal
reservoir depletion path. One of the main differences between dry gas and wet gas is that, along
the surface depletion path, dry gas will also stay in a 100% vapor phase condition, while wet gas
will experience two-phase condition or condensate dropout as it flows through the surface
production system.
The procedure used to calculate standard PVT properties of gas condensate at the dew
point could be applied for the dry gas and wet gas. Characteristic of gas formation volume factor
( ) is expected to be the same for dry gases, wet gases, and gas condensates. Volatilized oil-gas
ratio ( ) for a dry gas will be zero, while volatilized oil-gas ratio ( ) of the wet gas will be
constant. Oil formation volume factor ( ) and solution gas-oil ratio ( ) will not be defined or
calculated in dry gas and wet gas because there is no presence of reservoir oil phase along the
reservoir depletion path. In addition, specific gravity of reservoir gas will be constant for both dry
gas and wet gas.
For the reservoir zero-dimensional model, the gas condensate tank model above the dew
point could be applied directly to dry gases and wet gases. However, because there is only
surface-gas in the reservoir gas phase, cumulative oil recovery ( ) and original oil in place
( ) for a dry gas will be zero. Based on the same assumptions as gas condensate tank model, gas
saturation ( ) in dry gas and wet gas will be constant at initial gas saturation ( ).
In IPR calculations, relative permeability of gas ( ) will be constant because gas
saturation is constant. Gas flow rate ( ) will depend on drawdown pressure ( ) and the
154
multiplication of gas viscosity ( ) and gas formation volume factor ( ). Oil flow rate ( ) for
dry gas will be zero because volatilized oil-gas ratio ( ) is zero. Oil flow rate ( ) for wet gas
will be equal to gas flow rate ( ) times volatilized oil-gas ratio ( ) which is constant. In TPR
calculations, pressure drop inside the tubing of dry gas and wet gas will be relatively stable
comparing to gas condensate because specific gravity of reservoir gas are constant. For the case
of the dry-gas, there is no liquid drop out in the tubing.
Field performance prediction, economic analysis, and field optimization for dry gases and
wet gases are carried out using the same procedure as for a gas condensate above the dew point.
Cumulative gas recovery ( ) at abandonment condition of dry gas is expected to be higher
than wet gases and gas condensates because lighter hydrocarbons exhibit larger expansivity
coefficients or isothermal compressibility values and there is no obstruction to fluid flow due to
the presence of a liquid hydrocarbon phase. Cumulative oil recovery ( ) at abandonment
condition for wet gases is expected to be much higher than gas condensate because the reservoir
system does not leave any immobile condensate inside the reservoir. In term of NPV, dry and wet
gases are expected to generate less NPV than gas condensates because they produce much less oil
which can be sold for a much higher commodity price. In terms of optimization of target recovery
factor at end of plateau and total number of wells, dry and wet gases are expected to exhibit
similar characteristics as those of gas condensates.
155
5.5.2 Application for Gas Condensate with Producible (Mobile) Reservoir Oil
One of the significant assumptions of the gas condensate tank model is that reservoir oil
phase is immobile. However, this assumption is not always valid, especially around the wellbore
where oil saturation might build up to a high enough value so that the relative permeability to oil
might not be equal to zero anymore. This situation would increase complexity of gas condensate
system.
Standard PVT properties simulated from procedures described in either section 4.2.2 or
4.2.3 will carry certain degree of error toward the final results because those algorithms assumed
that the reservoir oil remained immobile. However, there is no practical approach for modifying
those procedures in order to fully represent the producible reservoir oil scenario. In order to
simulate the producible reservoir oil situation within a standard PVT properties calculation
algorithm, the ratio between excess gas and excess oil which should be removed from the PVT
cell during the constant volume expansion has to be given. This ratio depends on the expected
relative mobility ratio between gas and oil phases which are the functions of their relative
permeabilities and fluid properties. Relative permeability depends on saturation fraction and
saturation fraction could be obtained from saturation equation; thus, relative permeability is also
the function of fluid properties. Moreover, the shape of the relative permeability curves is also
rock-dependent and not solely fluid property dependent. In short, there is no simple method to
fully and reliably represent producible reservoir oil situation.
In the reservoir zero-dimensional model, the gas condensate tank model has to be
modified by substituting Equation 4-115 with Equation 5-4 (below), substituting Equation 4-118
with Equation 5-5 (below), and calculating instantaneous production GOR at pressure level j ( )
using Equation 5-6 (below). Relative permeability in Equation 5-6 might be evaluated from
156
saturation value calculated at the preceding pressure level j-1. The definition of each parameter in
these equations can be found in the gas condensate tank model section.
Equation 5-4
Equation 5-5
Equation 5-6
For IPR calculations, gas flow rate ( ) and oil flow rate ( ) should be calculated by
implementing Equation 4-132 and Equation 4-133 instead. For TPR calculations, the single phase
gas flow equation is still applied; but pipe efficiency factor ( ) is expected to be lower
because of additional liquid phase flow into wellbore.
Procedures used to perform field performance prediction, economic analysis, and field
optimization remain unchanged. Cumulative gas recovery ( ) at abandonment condition for
producible reservoir oil scenario is expected to be close to the value obtained from immobile
reservoir oil scenario. In contrast, cumulative oil recovery ( ) at abandonment condition for
producible reservoir oil scenario is expected to be higher than the value obtained from immobile
reservoir scenario because less oil is left immobile inside the reservoir. In term of NPV
157
estimations, larger NPVs are expected from producible reservoir oil scenario because reservoir oil
could yield more stock-tank oil, which is more expensive product, than reservoir gas. For field
optimization, the similar characteristic is expected whether reservoir oil is producible or not.
Chapter 6
Summary and Conclusions
A model able to perform field performance analysis and optimization of exploitation
strategies for a gas condensate reservoir has been successfully developed. The model has been
constructed using Microsoft Excel with built-in Visual Basic for Applications (VBA) program.
The model includes a fluid property calculation subroutine which estimates standard PVT
properties based on a binary pseudo-component model using fluid compositional information as
input. The subroutine demonstrates to produce reliable standard PVT properties typical of gas
condensate fluid phase behavior. Limitations of the pseudo-component model, such as the
generation of negative solution gas-oil ratio ( ) at low reservoir pressure, are clearly shown and
explained using the simulated results produced by the fluid property calculation subroutine.
A zero-dimensional reservoir model based on the generalized material balance equation
for gas condensates has also been developed. The results from this gas condensate tank model are
able to mimic the typical reservoir performance data found in gas condensate fields. Possible
sources of error and misinterpretation from using a gas condensate tank model in the analysis of
other near critical fluids, such as volatile oils, are discussed and recommended crosschecking
procedure that should be implemented before and after running the simulation model is
addressed.
A field performance prediction that couples zero-dimensional reservoir models with
nodal analysis concepts has been successfully developed for the screening of field development
strategies. The field performance prediction tool has also been coupled with an economic model
which enables the prediction of optimum field development strategies. The reservoir model
demonstrates to provide results which are consistent with reservoir depletion behavior for gas
159
condensates. A discussion of the observed decline trend analysis has been included to shed some
light on the possibility of obtaining slightly negative hyperbolic decline coefficients in gas
condensate fields. The economic evaluation subroutine was implemented based on simplified
economic model. The subroutine is used to optimize target development variables, such as target
recovery factor at end of plateau and total number of wells required to optimally develop the
field. This proposed model is shown to be able to perform economic analysis and field
optimization effectively. Economic and optimization results are analyzed in detail. Limitations of
the economic model assumptions are addressed and discussed.
The proposed model is suitable for real field applications when either input data or
working time is constrained. For example, this model is appropriate to be used to simulate field
performance data for feasibility study of gas condensate reservoirs because, during that phase of
field development, reservoir data is usually limited and all available data are highly uncertain;
thus constructing highly sophisticated model is impractical. In addition, this model can effectively
simulate field performance data for numerous production scenarios, which is a very important
factor to cope with the high uncertainty found in that period. Another proper application is to use
this proposed model to perform project evaluations for new asset acquisitions because, during the
acquisition process, the evaluation of each project has to be completed within a short period of
time; thus utilizing the less complicated model, which takes less time to construct and execute, is
more feasible, even if there are plenty of reservoir and field development data.
Additional recommendations for avenues for future work are also provided for the
improvement of the reliability and the capabilities of the proposed field performance model. The
first recommendation is to validate the accuracy of the model’s outputs with the outputs
calculating from full scale full dimensional numerical simulator using both hypothetical data and
actual field data. With the hypothetical data validation, the error resulting from a single-
homogeneous tank assumption (neglecting all gradients) can be analyzed. With the actual field
160
data validation, the impact of heterogeneity on naturally occurring reservoirs can be determined.
The second recommendation is to perform sensitivity analysis to investigate how the variation in
economic outputs can be attributed to the variation in reservoir and field development input
variables. With this understanding, the limited resources (time and man-hour) can be properly
spent to evaluate the expected values and uncertainties of the variables with highly economic
impact. In most cases, product prices, development costs, and reserves are expected to be the
variables with the highest impact on the project’s economic. The other recommendations include
the handling of production from dry gas and wet gas reservoirs and the modeling of gas
condensates with producible (mobile) reservoir oil. Further avenues include allowing the model
to handle multiple reservoirs and multiple types of producing wells, which would make the model
applicable to be used in complex reservoir structures and marginal fields development.
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Appendix A
Input Data Summary
Table A-1: Pressures and Temperatures for
Standard PVT Properties Calculation Subroutine
Pressure Temperature
(psia) (F)
Reservoir Condition 4000 300
1st Stage Separator 500 90
2nd Stage Separator 150 65
Stock Tank Condition 100 60
Table A-2: Physical Properties of Pure Components
Component Mole
Fraction
Critical
Pressure
(psia)
Critical
Temperature
(R)
Acentric
Factor
Molecular
Weight
(lbm/lbmol)
Critical
Volume
(ft3/lbm)
N2 0.0223 493.10 227.49 0.037 28.013 0.0510
C1 0.6568 666.40 343.33 0.010 16.043 0.0988
C2 0.1170 706.50 549.92 0.098 30.070 0.0783
C3 0.0587 616.00 666.06 0.152 44.097 0.0727
i-C4 0.0127 527.90 734.46 0.185 58.123 0.0714
n-C4 0.0168 550.60 765.62 0.200 58.123 0.0703
i-C5 0.0071 490.40 829.10 0.228 72.150 0.0679
n-C5 0.0071 488.60 845.80 0.251 72.150 0.0675
n-C6 0.0138 436.90 913.60 0.299 86.177 0.0688
n-C10 0.0832 305.20 1112.00 0.490 142.285 0.0679
CO2 0.0045 1071.00 547.91 0.267 44.010 0.0344
164
Table A-3: Binary Interaction Coefficients of Pure Components
δij's N2 C1 C2 C3 i-C4 n-C4 i-C5 n-C5 n-C6 n-C10 CO2
N2 0.0000 0.0180 0.0390 0.0460 0.0470 0.0470 0.0480 0.0480 0.0000 0.0000 0.0000
C1 0.0180 0.0000 0.0050 0.0100 0.0145 0.0145 0.0182 0.0182 0.0000 0.0000 0.0000
C2 0.0390 0.0050 0.0000 0.0017 0.0032 0.0032 0.0048 0.0048 0.0000 0.0000 0.0000
C3 0.0460 0.0100 0.0017 0.0000 0.0012 0.0012 0.0024 0.0024 0.0000 0.0000 0.0000
i-C4 0.0470 0.0145 0.0032 0.0012 0.0000 0.0000 0.0008 0.0008 0.0000 0.0000 0.0000
n-C4 0.0470 0.0145 0.0032 0.0012 0.0000 0.0000 0.0008 0.0008 0.0000 0.0000 0.0000
i-C5 0.0480 0.0182 0.0048 0.0024 0.0008 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000
n-C5 0.0480 0.0182 0.0048 0.0024 0.0008 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000
n-C6 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
n-C10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
CO2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Table A-4: Volume Translation Coefficient of Pure Components
Component Si for PR
EOS
Si for SRK
EOS
N2 -0.19270 -0.00790
C1 -0.15950 0.02340
C2 -0.11340 0.06050
C3 -0.08630 0.08250
i-C4 -0.08440 0.08300
n-C4 -0.06750 0.09750
i-C5 -0.06080 0.10220
n-C5 -0.03900 0.12090
n-C6 -0.00800 0.14670
n-C10 0.06550 0.20800
CO2 -0.08170 0.08330
165
Table A-5: Reservoir Input Data
Reservoir
Number
Initial
Reservoir
Pressure
(psia)
Abandonment
Reservoir
Pressure
(psia)
Dew Point
Reservoir
Pressure
(psia)
Reservoir
Temperature
(Deg F)
Temperature
Gradient
(Deg F / ft)
1 4000 750 3031 300 0.0205
Temperature
Surface
(Deg F)
Reservoir
Depth
(ft)
Reservoir
Drainage
Area
(Acres)
Reservoir
Thickness
(ft)
Reservoir
Pososity
(Frac)
Connate
Water
Saturation
(Frac)
60 6560 5000 55 0.200 0.210
Original Gas
Equivalent
In Place
(BSCF)
Absolute
Permeability
(md)
Wellbore
Radius
(ft)
Shape Factor Mechanical
Skin
Non-Darcy
Flow Coeff
(D/MSCF)
393.15 80 0.375 30.88 10 0.0011
Table A-6: Relative Permeability Input Data
Reservoir
Number
Connate
Water
Saturation
Connate
Gas
Saturation
Maximum
Gas
Saturation
Krg at
Maximum
Gas
Saturation
1 0.20 0.20 0.80 0.80
166
Table A-7: Standard PVT Properties
Pressure Bo Bg Rs Rv SG Gas
(psia) (RB/STB) (RB/MSCF) (SCF/STB) (STB/MMSCF)
4000 5.052 1.040 4856.8 205.9 1.147
3950 5.089 1.048 4856.8 205.9 1.147
3900 5.127 1.056 4856.8 205.9 1.147
3850 5.166 1.064 4856.8 205.9 1.147
3800 5.206 1.072 4856.8 205.9 1.147
3750 5.248 1.081 4856.8 205.9 1.147
3700 5.291 1.089 4856.8 205.9 1.147
3650 5.336 1.099 4856.8 205.9 1.147
3600 5.382 1.108 4856.8 205.9 1.147
3550 5.429 1.118 4856.8 205.9 1.147
3500 5.479 1.128 4856.8 205.9 1.147
3450 5.530 1.139 4856.8 205.9 1.147
3400 5.583 1.149 4856.8 205.9 1.147
3350 5.638 1.161 4856.8 205.9 1.147
3300 5.695 1.173 4856.8 205.9 1.147
3250 5.754 1.185 4856.8 205.9 1.147
3200 5.815 1.197 4856.8 205.9 1.147
3150 5.879 1.211 4856.8 205.9 1.147
3100 5.946 1.224 4856.8 205.9 1.147
3050 6.015 1.239 4856.8 205.9 1.147
3031 6.042 1.244 4856.8 205.9 1.147
3000 2.858 1.251 2067.5 195.4 1.128
2950 2.706 1.265 1903.7 181.4 1.102
2900 2.582 1.280 1768.5 170.0 1.081
2850 2.479 1.297 1652.8 160.3 1.062
2800 2.389 1.315 1551.4 151.9 1.046
2750 2.311 1.335 1461.0 144.5 1.032
2700 2.241 1.356 1379.3 137.9 1.019
2650 2.178 1.378 1304.9 131.9 1.007
2600 2.120 1.401 1236.4 126.4 0.996
2550 2.067 1.426 1173.1 121.4 0.986
2500 2.019 1.452 1114.1 116.8 0.977
2450 1.974 1.480 1059.0 112.6 0.969
2400 1.932 1.509 1007.3 108.6 0.961
2350 1.892 1.539 958.5 105.0 0.954
2300 1.855 1.571 912.5 101.5 0.947
167
Table A-7: Standard PVT Properties (Cont.)
Pressure Bo Bg Rs Rv SG Gas
(psia) (RB/STB) (RB/MSCF) (SCF/STB) (STB/MMSCF)
2250 1.821 1.605 868.9 98.3 0.941
2200 1.788 1.641 827.5 95.3 0.935
2150 1.757 1.678 788.1 92.5 0.929
2100 1.728 1.718 750.5 89.9 0.924
2050 1.700 1.759 714.6 87.4 0.919
2000 1.673 1.803 680.3 85.1 0.914
1950 1.648 1.850 647.4 82.9 0.910
1900 1.623 1.899 615.9 80.8 0.906
1850 1.600 1.952 585.6 78.9 0.902
1800 1.578 2.007 556.5 77.1 0.899
1750 1.556 2.066 528.4 75.4 0.896
1700 1.536 2.128 501.4 73.8 0.893
1650 1.516 2.195 475.4 72.3 0.890
1600 1.497 2.266 450.3 71.0 0.887
1550 1.479 2.342 426.1 69.7 0.885
1500 1.461 2.424 402.7 68.6 0.883
1450 1.445 2.511 380.1 67.6 0.881
1400 1.428 2.606 358.2 66.6 0.880
1350 1.412 2.707 337.1 65.8 0.879
1300 1.397 2.817 316.6 65.1 0.878
1250 1.382 2.936 296.8 64.5 0.877
1200 1.368 3.065 277.6 64.1 0.876
1150 1.354 3.207 259.0 63.7 0.876
1100 1.341 3.361 241.0 63.5 0.876
1050 1.328 3.532 223.6 63.5 0.877
1000 1.315 3.720 206.8 63.6 0.877
950 1.303 3.928 190.4 63.9 0.879
900 1.291 4.161 174.6 64.3 0.880
850 1.280 4.423 159.3 65.0 0.882
800 1.269 4.719 144.3 66.0 0.885
750 1.257 5.056 129.2 67.3 0.888
700 1.246 5.444 114.5 68.9 0.892
650 1.236 5.894 100.5 71.0 0.897
600 1.226 6.423 86.9 73.5 0.903
550 1.216 7.053 73.9 76.8 0.910
500 1.206 7.816 61.5 80.8 0.919
168
Table A-8: Tubing Input Data
Min Allow Wellhead Pressure (psia) 550
Tubing Roughness (inch) 0.0018
Tubing Efficiency (Frac) 0.70
Depth
(MD - ft)
Depth
(TVD - ft)
Tubing ID
(inch)
Temperature
(F)
0 0 60.0
650 650 4.5 83.8
1300 1300 4.5 107.6
1950 1950 4.5 131.3
2600 2600 4.5 155.1
3250 3250 4.5 178.9
3900 3900 4.5 202.7
4550 4550 4.5 226.5
5200 5200 4.5 250.2
5850 5850 4.5 274.0
6500 6500 4.5 297.8
Table A-9: Economic Input Data
General
Net Hydrocarbon Fraction 87.50%
Price
First Year Gas Price 4.000 $/MSCF
Gas Price Escalation 1.00%
First Year Oil Price 80.000 $/STB
Oil Price Escalation 2.00%
Discount Rate
Discount Rate 12.00%
169
Table A-9: Economic Input Data (Cont.)
Capital Expenses
Capex Total 1,480.0 Million $
- Drilling (per well) 25.0 Million $
- Flowlines and Trunklines 100.0 Million $
- Production Facilities 500.0 Million $
- Platform (for Offshore) 400.0 Million $
- Others 30.0 Million $
Operating Expenses
First Year Opex 0.5 Million $/Mth
Opex Escalation 2.50%
Tax
Gas Severance Tax 8.00%
Oil Severance Tax 8.00%
Ad Valorem Tax 0.00%
Table A-10: Field Performance Prediction Input
Target Recovery
at End of Plateau
Total Number
of Wells
0.55 18
Table A-11: Field Performance Optimization Input
Target Recovery
at End of Plateau
Total Number
of Wells
0.30 3
0.35 6
0.40 9
0.45 12
0.50 15
0.55 18
0.60 21
0.65 24
0.70 27
0.75 30
170
Appendix B
User Guide
1. Open ―Field Development Plan.xlsm
2. Simulate standard PVT properties
a. Simulate standard PVT propertied from Walsh-Tolwer algorithm
i. Select worksheet ―PVT from CVD‖
ii. Input data in ―Reservoir Input‖ section
iii. Input data in ―Pressure Volume Relation‖ section
iv. Input data in ―Constant Volume Depletion‖ section
v. Input data in ―Calculated Cumulative Recovery‖ section
vi. Input data in ―Z-Factor of Produced Wellstreams‖ section
vii. Input data in ―Composition of Produced Wellstreams‖ section
viii. Adjust formulas in ―Pre-Calculation‖ section
ix. Adjust formulas in ―Walsh-Towler Algorithm‖ section
x. Adjust formulas in ―Standard PVT Properties at Dew Point and Below‖
section
xi. Adjust formulas in ―Standard PVT Properties Above Dew Point‖ section
xii. Copy all calculated standard PVT properties to ―FDP_Input_PVT‖
worksheet
171
172
b. Simulate standard PVT properties from compositional data
i. In ―PVT_Input_Pres‖ worksheet, input reservoir and surface separators
pressure and temperature conditions
ii. In ―PVT_Input_Comp‖ worksheet, input composition (mole fraction)
and properties of pure components
iii. In ―PVT_Input_BiCo‖ worksheet, input binary interaction coefficient
iv. In ―PVT_Input_Si‖ worksheet, input volume-translate coefficient data
v. In ―PVT_Output_Prop‖ worksheet, click ―Calculate Black Oil PVT
Properties‖ button
vi. In ―PVT_Output_Envelope‖ worksheet, click ―Create Phase Envelope‖
button (optional)
vii. In ―FDP_Input_PVT‖ worksheet, click ―Import from PVT Calculation‖
button
173
174
175
176
3. Perform field performance analysis
a. Run field performance prediction and economic analysis
i. In ―FDP_Input_Tank‖ worksheet, input reservoir data
ii. In ―FDP_Input_RelPerm‖ worksheet, input relative permeability data
iii. In ―FDP_Input_TPR‖ worksheet, input tubing data
iv. In ―FDP_Economic‖ worksheet, input economic data
v. In ―FDP_Input_Main‖ worksheet, input target recovery factor at end of
plateau and total number of wells required for field development
vi. Click ―Run Performance Prediction and Economic Analysis‖ button
vii. Obtain economic results from ―FDP_Economic‖ worksheet
viii. Obtain field performance data from ― FPD_Output_Perf‖ worksheet
ix. Obtain reservoir performance data from ―FDP_Output_SGCT‖
worksheet
x. Obtain decline trend analysis data from ―DCA‖ worksheet
xi. Obtain graphical display of flow rates, pressures and cumulative
production from ―QgGp‖, QoNp‖, and QwPrPwfPwh‖ worksheets
177
178
179
180
181
182
b. Run economic analysis from latest field performance data
i. In ―FDP_Economic‖ worksheet, input economic data
ii. In ―FDP_Input_Main‖ worksheet, click ―Run Economic Analysis from
Latest Performance Data‖ button
iii. Obtain economic results from ―FDP_Economic‖ worksheet
183
184
4. Perform field optimization
a. Run optimization with new performance prediction and economic analysis
i. Repeat 3.-a.-i ) to 3.-a.-iv)
ii. In ―FDP_Input_Main‖ worksheet, input target recovery factor at end of
plateau and total number of wells required for field development
iii. Click ―Optimization 1: Run Performance Prediction and Economic
Analysis‖ button
iv. Obtain field optimization results from ―Optimization‖ worksheet
185
b. Run optimization with new economic analysis only (utilize latest performance
prediction data)
i. In ―FDP_Economic‖ worksheet, input economic data
ii. In ―FDP_Input_Main‖ worksheet, click ―Optimization 2: Run Economic
Analysis only‖ button
iii. Obtain field optimization results from ―Optimization‖ worksheet
186
187