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S E T T H E O R Y

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248 pages
S E T T H E O R Y S T H E O RY (c) 2011, Martin Hansen, Shrewsbury School, Shrewsbury. SY3 7BA
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T H E U N I V E R S I T Y O F T U L S A
THE GRADUATE SCHOOL



OPTIMIZATION OF HORIZONTAL WELL COMPLETION




BY
YULA TANG



A dissertation submitted in partial fulfillment of
the requirements for the degree of Doctor of Philosophy
in the Discipline of Petroleum Engineering


The Graduate School
The University of Tulsa
2001 May


T H E U N I V E R S I T Y O F T U L S A
THE GRADUATE SCHOOL


OPTIMIZATION OF HORIZONTAL WELL COMPLETION


BY
YULA TANG


A DISSERTATION APPROVED FOR THE DISCIPLINE OF
PETROLEUM ENGINEERING


By Dissertation Committee

, Co-Chairperson








iiABSTRACT

Yula Tang (Doctor of Philosophy in Petroleum Engineering)
Optimization of Horizontal Well Completion (233 pp. – Chapter VI)
Co-Directed by Dr. Mohan Kelkar, and Dr. Erdal Ozkan

(319 words)

A comprehensive model has been successfully built for slotted-liner and
perforated completions. The Green’s functions or source function method was used for
the development of the reservoir pressure response due to the 3D convergence of flow
toward perforations/slots. The long-time asymptotic solutions were first derived under
pseudo-radial flow. Then, the approach of additional drawdown due to completion
pseudo-skin was developed to express the pressure response under boundary-dominated
flow.
The model strictly considers the influence of well completions on both reservoir
pressure response and wellbore hydraulics. The non-liner coupling matrix equations are
discretized and solved numerically. The semi-analytical model is capable of
incorporating the effects of selective completion, non-uniform mechanical skin, and high-
velocity flow effect. Formulae were derived to predict additional pressure drops due to
mechanical skin and non-Darcy effect in the perforation radial flow, slot semi-radial
flow, and wellbore radial flow.
Based on large quantity of numerical experiments, regression correlations for
productivity ratio (PR) have been obtained and can be used for fast and accurate
prediction and optimization.
Pseudo-pressure function was used to extend the solutions of oil wells to gas
wells. The gas wells have more concentrated flux and pressure drop on the heed end side
due to gas expansion and acceleration. Non-Darcy flow has severe effect on the gas
productivity of slotted-liner completion.
iiiA user-friendly software for horizontal well completion optimization (HORCOM)
was developed to provide a fast design and analysis tool. The software has a graphical
user interface for pre- and post-processing and with windows programming features.
The model was verified by comparing the limiting cases. Sensitivity analysis was
performed for perforation/slot parameters. Unique completion guidelines have been
developed. For example, horizontal wells may need far lower perforation density than the
vertical wells. For anisotropic formations, 180º-phasing along vertical plane is better than
90º-phasing. Using higher perforation/slot density and deeper penetration near the heel
end of the well helps to obtain the highest gain in productivity.





















ACKNOWLEDGEMENTS
iv

I would like to express my deepest appreciation and gratitude to Dr. Mohan
Kelkar for his guidance and support throughout this study. His continuous
encouragement and enthusiasm will never be forgotten. My sincere thanks are also
expressed to Dr. Erdal Ozkan, my co-advisor, for his great guidance. His keen knowledge
and extraordinary understanding made it possible for me to accomplish this study.
Special gratitude is given to Dr. Turhan Yildiz for his enthusiastic help beyond
the normal call of duty. He offered me many valuable criticisms, challenges and
constructive suggestions. I am also grateful to Dr. Dale R. Doty for his serving as a
member of the Dissertation Committee.
I wish to thank Mr. Tom Reid for financial support by awarding me the DOE
fellowship through the Western Universities Inc. The participating member companies of
the JIP, Optimization of Horizontal Well Completion, are gratefully acknowledged.
Appreciation is extended to Ms. Virginia Bentley (Ginny) for her highly efficient
administration and impressive organization work.
I wish to thank all the professors in the department. In particular, I acknowledge
Dr. Albert C. Reynolds, Dr. Cem Sarica, Dr. Ovadia Shoham, and Dr. Leslie G.
Thompson, for their course instruction and encouragement during my Ph. D study.
I would like to thank Dr. Shoubo Wang, Dr. Hongquan Zhang, and Dr. Jianfeng
Chen for many of their helps. Grateful appreciation is expressed to Mr. Jerry Lout, Ms.
Cathy Ambrose, Mr. John Tai, and their families, for their love, and encouragement.
This work is dedicated to my wife, Qing Zhang, my daughter, Anya, and my
parents Yida and Lisheng. Without their unconditional love and support, my Ph. D study
would never have been completed.





TABLE OF CONTENTS
v
TITLE PAGE …………………………………………………………………………… i
APPROVAL PAGE …………………………………………………………………… ii
ABSTRACT iii
ACKNOWLEDGEMENTS …………………………………………………………… v
TABLE OF CONTENTS ……………………………………………………………… vi
LIST OF TABLES ……………………………………………………………………… xi
LIST OF FIGURES ……………………………………………………………………
xiii

CHAPTER I INTRODUCTION AND LITERATURE REVIEW ………………………
1
1.1 Introduction to Horizontal Well Completions …………………………………… 1
1.1.1 Openhole Completion ……………………………………………………… 2
1.1.2 Slotted-Liner Completion ………………………………………………… 3
1.1.3 Perforated Completion 5
1.2 Literature Review …………………………………………………………………
7
1.2.1 Horizontal Well Completion Hydraulics…………………………………… 7
1.2.2 Wellbore and Reservoir Coupling ………………………………………… 8
1.2.3 Analytical Studies on Perforated and Slotted-Liner Completions ………… 9
1.2.4 Formation Damage and High-Velocity Flow Effect ……………………… 11
1.3 Summary of the Study …………………………………………………………
12
1.3.1 Semi-Analytical Approach……………………………………………… …13
1.3.2 Coupling Reservoir Flow with Wellbore Hydraulics ………………………14
1.3.3 Significance of the Study ………………………………………………… 15
1.3.4 Objectives of the Study …………………………………………………… 15

viCHAPTER II Theory of Source Function and Fundamental Solution …………………
17
2.1 Diffusivity Equation and Source Density Function …………………………… 17
2.2 Green’s Function and Fundamental Solution …………………………………
21
2.3 Superposition Principle and Newman’s Product Method ……………………… 24
2.4 Point-Source Solution in Real Time Domain and in Laplace Domain ………… 26
2.4.1 Instantaneous Plane Source (1D) …… …………………………………… 27
2.4.2 Instantaneous Point-Source (3D) ……………………………………… … 27
2.4.3 Continuous Point-Source (3D) … … 28
2.5 Point Source Solutions for Bounded Reservoir 30
2.5.1 Slab Reservoir (Prescribed Flux, impermeable at z=0 and z=h) ………… 30
2.5.2 Cylindrical Reservoir (impermeable at z=0 , and z=h) ……………………32
2.6 Coordinate Transform for Anisotropic Reservoir and Alternative System of
Dimensionless Variables… ………………………………………………………33
2.6.1 Transformation of Governing Equations ………………………………… 33
2.6.2 Conventional System of Dimensionless Variables ……………………… 35
2.6.3 Alternative System of Dime…………………………
37
2.6.4 Fundamental Solutions in Alternative System of Dimensionless Variable 39

CHAPTER III RESERVOIR PRESSURE RESPONSE WITH COMPLETIONS …… 41
3.1 Flow Regimes, Dimensionless Variables and Wellbore Discretization ……… 41
3.1.1 Reservoir Flow Regimes for Horizontal Wells…………………………… 41
3.1.2 Dimensionless Variables ………………………………………………… 42
3.1.3 Discretization of Rate Equation ………………………………………… 43
3.2 Pressure Response for an Openhole Completed Horizontal Well ……………… 44
3.2.1 Long-Time Asymptotic Solution in a Slab Reservoir (Pseudo-Radial Flow)
…………………………………………………………………………… 44
vii3.2.2 Asymptotic Solution in Boundary-Dominated Flow (Pseudo-Steady-
State or Steady State) …………………………………………………… 47
3.2.3 Discrete Form for the Long-Time Asymptotic Solutions …………… … 48
3.3 Pressure Response with a Perforating Completed Horizontal Well …………… 50
3.4 Pressure Response with a Slotted-Liner Compell …..………54
3.5 Pressure Response for Horizontal Gas Wells ………………………………… 57
3.6 Method of Additional Drawdown due to Completion Pseudo-Skin for Boundary
Dominated Flow ……………………………………………………………… 59
3.7 Additional Pressure Drops due to Mechanical Skin and High-Velocity Flow 62
3.7.1 High-Velocity Flow Effect for Oil and Gas Reservoirs …………………
62
3.7.2 Additional Pressure Drop for Openhole Completed Horizontal Wells……65
3.7.3 Additional Pressure Drop for Perforating Compells … 65
3.7.4 Additional Pressure Drop for Slotted-Liner Completed Horizontal Wells 69

CHAPTER IV COUPLING RESERVOIR FLOW WITH WELLBORE HYDRAULICS
73
4.1 Wellbore Hydraulics for Single-Phase Liquid Flow …………………………… 73
4.1.1 Wellbore Pressure Gradient ……………………………………………… 74
4.1.2 Apparent Friction Factor for Completions ……………………………… 75
4.1.3 Horizontal Well Conductivity …………………………………………… 76
4.1.4 Horizontal Well Flow Model 78
4.1.5 Coupling and Solution Approach …………………………………………
81
4.2 Wellbore Hydraulics for Single-Phase Gas Flow ………………………………
86

CHAPTER V RESULTS AND DISCUSSION …………………………………………
93
5.1 Model Verification and Flow Characteristics……………………………………93
viii 5.2 Effects of Perforation Parameters ……………………………………………… 96
5.2.1 Effects of Perforation Parameters on Productivity Index (PI) …………… 96
5.2.2 Effects of Perforation Parameters on Productivity Ratio (PR) …………… 99
5.3 Effects of Slotted-Liner Parameters…………………………………………… 103
5.3.1 Effect of Slot Phasing Angle 104
5.3.2 Effect of Slot Size at Fixed SPR………………………………………… 105
5.3.3 Effect of Slot Penetration Ratio ………………………………………… 106
5.4 Effect of Partial Completion and Perforation Strategy ……………………… 109
5.5 Inflow Performance with Completion Pseudo Skin ………………………… 111
5.6 Additional Drawdown due to Pseudo-Skin ( ∆p ) and Regression Correlations D, PS
for Productivity Ratio (PR) ………………………………………………… 112
5.6.1 Productivity Ratio (PR) and Additional Drawdown
due to Pseudo-Skin ( ∆p ) …………………………………………… 113 D, PS
5.6.2 Computation of Additional Drawdown for Perforation by using PR ……115
5.6.3 Development of PR Regression Correlations for Perforated Completion 118
5.6.4 Application of PRpletion 122
5.6.5 General Remarks on ∆p and PR for Slotted-Liner Completion …… 125 D, PS
5.7 Effects of Mechanical-Skin and Non-Darcy Flow (Oil Wells) ………………
127
5.7.1 Effect of Drilling Damage ……………………………………………… 127
5.7.2 Effect of Perforating Damage and Perforation Penetration …………… 129
5.7.3 Effect of Drilling Damage for Slotted-Liner Completion ……………… 132
5.7.4 Effect of High-Velocity Flow (non-Darcy Effect) ……………………… 133
5.8 Performance of Completed Horizontal Gas Wells …………………………… 135
5.8.1 Flow Characteristics for Openhole Completion………………………… 135
5.8.2 Performances of Perforating / Slotted-Liner Completed Gas Wells …… 138

CHAPTER VI CONCLUSIONS ………………………………………………………
141
ix 6.1 Effects of Perforation Geometry Parameters ………………………………… 142
6.2 Effects of Slotted-Liner Geometers ……………………………… 143
6.3 Effects of Mechanical Skin and High-Velocity Flow ………………………… 143
6.4 Characteristics for Horizontal Gas Well Completions…………………………144
6.5 Guidelines for Horizontal Well Completion Optimization ……………………144

NOMENCLATURE …………………………………………………………………
146
REFERANCES ………………………………………………………………………155
APPENDIX A − DERIVATION OF PRESSURE RESPONSE FOR PERFORATED
HORIZONTAL WELLS ……………………………… ……………162

APPENDIX B − DERIVATION OF PRESSURE RESPONSE FOR SLOTTED-LINER
COMPLETED HORIZONTAL WELLS ………………………… 173
APPENDIX C − DERIVATION OF ADDITIONAL PRESSURE DROPS DUE TO
MECHANICAL SKIN AND HIGH-VELOCITY FLOW …………
181
APPENDIX D − DERIVATION OF THE JACOBIAN MATRIX FOR THE COUPLING
EQUATION ……………………………………………………… 188
APPENDIX E − DATA FROM 3D MODEL (PERFORATING COMPLETION)……
198
APPENDIX F − DATA FROM 3D MODEL (SLOTTED-LINER COMPLETION)
…214
APPENDIX G − DESCRIPTION FOR HORCOM SOFTWARE ……………………219


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