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UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE

EVALUATION OF EQUIVALENT CIRCULATING DENSITY OF DRILLING FLUIDS UNDER HIGH PRESSURE-HIGH TEMPERATURE CONDITIONS

A THESIS SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requirement for the degree of MASTER OF SCIENCE (Petroleum Engineering)

By Oluseyi Harris Norman, Oklahoma 2004

EVALUATION OF EQUIVALENT CIRCULATING DENSITY OF DRILLING FLUIDS UNDER HIGH PRESSURE-HIGH TEMPERATURE CONDITIONS

A THESIS APPROVED FOR THE MEWBOURNE SCHOOL OF PETROLEUM AND GEOLOGICAL ENGINEERING

BY

Chair: Dr. Samuel Osisanya

Member: Dr. Subhash Shah

Member: Dr. Djebbar Tiab

Copyright by Oluseyi Harris 2004 All Rights Reserved.

ACKNOWLEDGEMENTSThe author wishes to express his profound gratitude and appreciation for Dr. Samuel Osisanya. His guidance, moral and financial support, and encouragement were invaluable. The author would like to thank the members of the thesis committee, Dr Samuel Osisanya, Dr Subhash Shah, and Dr. Djebbar Tiab for their helpful comments and suggestions. Heartfelt thanks go to Dr. Subhash Shah for his assistance in allowing use of WCTC facilities in performing research for this thesis. The author wishes to extend special

thanks to colleagues whose assistance and encouragement was invaluable during the course of this research work- Ricardo Michel-Villazon, Aristotelis Pagoulatos, Kayode Aremu, Kola Ayeni. The author wishes to thank his other half, Lola for always being there. The author would also like to express immeasurable gratitude towards his parents for their constant and unwavering support and faith. Last and most importantly, thanks and praise are extended to God almighty who alone makes all things possible.

Oluseyi Harris Norman, Oklahoma July, 2004

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TABLE OF CONTENTSPAGE ACKNOWLEDGEMENTS ..............................................................................iv LIST OF TABLES ........................................................................................viii LIST OF FIGURES.........................................................................................ix ABSTRACT....................................................................................................xi CHAPTER PAGE

1. FORMULATION OF THE PROBLEM .........................................................1 1.1. Introduction ..........................................................................................1 1.2. Literature Review .................................................................................3 1.3. Objectives and Scope of Work...........................................................13 1.4. Study Organization ...........................................................................14 2.FUNDAMENTAL CONCEPTS FOR ESTIMATION OF EQUIVALENT STATIC AND CIRCULATING DENSITY ....................................................15 2.1 Equivalent Static density ......................................................................15 2.2 Estimating Equivalent Static Density....................................................18 2.2.1 Compositional Models ...................................................................18 2.2.1.1 Volumetric Models for Mud Constituents ..................21 2.2.2 Empirical Models ...........................................................................23 2.3 Equivalent Circulating density ..............................................................23 2.4 Frictional Pressure Loss.......................................................................24 2.5 Fluid Rheology .....................................................................................26 2.5.1 Bingham Plastic Model ..................................................................27 2.5.2 Power Law Model ..........................................................................28 2.5.3 Herschel-Bulkley Model.................................................................30 2.5.4 Casson Model ...............................................................................31

v

2.5.5 Ellis Model .....................................................................................31 2.5.6 Carreau Model...............................................................................32 2.6 Temperature and Pressure Dependent Rheological Parameters.......33 2.6.1 Temperature/Pressure Dependent Plastic Viscosity....................33 2.6.2 Temperature Dependent Yield point..............................................35 2.7 Bingham Plastic Pressure Loss Equations......................................36

3.DRILLING FLUID TEMPERATURE PROFILE ESTIMATION ...................40 3.1 Heat Transfer in the Wellbore ..............................................................41 3.2 Analytical Method.................................................................................43 3.2.1 Assumptions of Analytical Model ..................................................43 3.2.2 Heat Balance in the DrillPipe........................................................44 3.2.3 Heat Balance in the Annulus ........................................................45 3.2.4 Heat Flow in the Formation and System Heat Balance ................46 3.3 Numerical Method ................................................................................50 3.3.1 Equations Governing Heat transfer in the Wellbore and Formation ...............................................................................................................50 3.3.2 Discretizing Heat Flow Equations for Finite difference Analysis ....53 3.4 Summary.........................................................................................68

4.DEVELOPMENT AND VALIDATION OF THE DYNAMIC DENSITY SIMULATOR AND MODELLING OF DYNAMIC DENSITY .......................69 4.1 4.2 Program Lay-Out.............................................................................70 DDS Program Execution .................................................................71

4.2.1 General Well Parameters Form ...................................................71 4.2.2 Mud Properties Form ...................................................................77 4.2.3 Formation Properties Form..........................................................77 4.2.4 Heat Transfer Coefficients Form..................................................77 4.2.5 Results and Results Form ...........................................................80 4.3 Equations used in DDSimulator Program........................................82

4.3.1 Fluid Properties ...........................................................................82 4.3.2 Temperature Profile Estimation ...................................................83

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4.3.3 Equivalent Hydrostatic Head and ECD ........................................84 4.4 4.5 Model Validation..............................................................................84 Dynamic Density Estimation............................................................91

Summary..................................................................................................107 5.SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS...................108 5.1 5.2 5.3 Summary.......................................................................................108 Conclusions...................................................................................109 Recommendations ........................................................................110

NOMENCLATURE ......................................................................................112 REFERENCES ............................................................................................115 APPENDIX ..................................................................................................119 Code for DDSimulator Program ...............................................................119

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LIST OF TABLESTABLE 4.1 4.2 4.3 4.4 PAGE

: Well and mud circulating properties for a gulf coast well.85 : Simulated Well Conditions92 : Results of Well Simulation92 : Well simulation results for parameters detailed in Table 4.2 with gG = 0.015 oF/ft......96

4.5

: Well simulation results for parameters detailed in Table 4.2 with gG = 0.025 oF/ft..96

4.6

: Well simulation results for parameters detailed in Table 4.2 with inlet fluid temperature = 80 oF......97

4.7

: Well simulation results for parameters detailed in Table 4.2 with circulation rate = 210 gal/min.....102

4.8

: Well Simulation Results for Parameters Detailed in Table 4.2 with Circulation Rate = 300 bbl/hr.105

viii

LIST OF FIGURESFIGURE 1.1 : Schematic Diagram of Fluid in the Well bore at the Start of Circulation..9 2.1 : Volumetric behavior of various liquids under varying conditions of temperature and pressure......17 2.2 2.3 3.1 3.2a 3.2b 3.3 3.4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 : Shear-thinning in a typical non-Newtonian Fluid........29 : Flow curves for time-independent fluids...29 : Schematic of Heat Balance for Fluid Circulating in a Wellbore....42 : Solution grid for Finite Difference Analysis......51 : Heat Flow at Formation Annulus Boundary.....51 : Finite Difference Grid...54 : Heat Balance at Bottom-Hole....60 : DDSimulator Program Flow Chart.....72 : Title Form..73 :DDSimulator Launch Command Button....74 : Well Parameters Form....75 : Mud Properties Form...76 : Formation Properties Form....78 : Heat Transfer Coefficients Form.......79 : Results Form....80 : A Sample Temperature Profile Using Excel Graph Feature.....81 : Plot of Temperature Profile For Gulf Coast Well.86 PAGE

ix

4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.30

: Well Tem