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**ABSTRACT**

The consideration of pipe eccentricity and its impact on hole cleaning has not been widely reported

in literature. Pipe eccentricity affects the average velocity of the drilling fluid in the annulus which

is one of the most important factors considered in hole cleaning.

In this study, developed equations of motion for a couette flow of non-Newtonian power-law fluid

through an eccentric annulus are used to determine the effect of pipe eccentricity on hole cleaning.

A graph for the velocity profile in the annulus is developed and the average velocity of the drilling

fluid for each eccentricity factor is used to analyse the parameters that indicate hole cleaning

efficiency. Some of the parameters include transport velocity, carrying capacity index, cuttings

concentration, and equivalent circulating density.

From the analysis, hole cleaning is said to be less effective when deviating from concentric annulus

to highly eccentric annulus. Secondly high eccentricity can cause high losses of the drilling fluid

after fracturing of the formation especially when the difference between the fracture pressure and

the pressure of the formation is very small.

**TABLE OF CONTENTS**

ABSTRACT i

TABLE OF CONTENT ii

LIST OF FIGURES v

LIST OF TABLES vii

ACKNOWLEDGEMENT viii

CHAPTER ONE 1

1.0 INTRODUCTION ……………………………………………………………………………………………….. 1

1.1 PROBLEM STATEMENT …………………………………………………………………………………….. 3

1.2 OBJECTIVES …………………………………………………………………………………………………….. 3

1.3 APPROACH……………………………………………………………………………………………………….. 3

CHAPTER TWO 4

LITERATURE REVIEW 4

2.0 INTRODUCTION ……………………………………………………………………………………………….. 4

2.1 CUTTINGS REMOVAL ……………………………………………………………………………………….. 4

2.1.1 Cuttings Transport in Wells …………………………………………………………………………….. 4

2.2 PARAMETERS AFFECTING HOLE CLEANING ……………………………………………………. 7

2.2.1 Pipe Eccentricity …………………………………………………………………………………………… 8

2.2.2 Other Parameters …………………………………………………………………………………………. 9

2.3 COUTTE FLOW ……………………………………………………………………………………………….. 10

2.4 ECCENTRICITY EFFECTS ON ANNULUS PRESSURE DROP ……………………………… 11

2.5 HOLE CLEANING INDICATORS ……………………………………………………………………….. 14

iii

2.5.1 Transport Ratio …………………………………………………………………………………………… 14

2.5.1 Carrying Capacity Index (CCI) ……………………………………………………………………… 15

CHAPTER THREE 16

DEVELOPMENT OF PERTINENT EQUATIONS 16

3.1 BASIC ASSUMPTIONS …………………………………………………………………………………….. 16

3.2 GOVERNING EQUATIONS ……………………………………………………………………………….. 16

3.3 GEOMETRIC ANALYSIS OF ECCENTRIC ANNULUS ………………………………………… 17

3.4 DIMENSIONLESS EXPRESSIONS …………………………………………………………………….. 19

3.5 LEADING-ORDER EQUATIONS AND SOLUTIONS ……………………………………………. 20

3.6 FIRST-ORDER EQUATIONS AND SOLUTIONS ………………………………………………….. 22

3.7 FLOW RATE …………………………………………………………………………………………………….. 23

3.8 MOORE’S CORRELATION FOR VS DETERMINATION ……………………………………….. 25

CHAPTER FOUR 27

APPLICATION OF EQUATIONS 27

4.1 DIMENSIONLESS VELOCITY DETERMINATION ……………………………………………… 27

4.2 SLIP VELOCITY DETERMINATION USING MOORE’S CORRELATION ……………. 36

4.3 AVAILABLE DATA (LIAO, 1993 AND CHUKWU, 2009)…………………………………………… 37

CHAPTER FIVE 38

RESULTS AND DISCUSSION 38

5.1 VELOCITY PROFILE IN THE ANNULUS …………………………………………………………. 38

5.2 TRANSPORT VELOCITY ……………………………………………………………………………….. 38

5.3 CARRYING CAPACITY INDEX ………………………………………………………………………. 40

5.4 CUTTING CONCENTRATION ………………………………………………………………………… 41

5.5 EQUIVALENT CIRCULATING DENSITY…………………………………………………………. 42

5.5.1 Sample Problem ……………………………………………………………………………………….. 43

iv

CHAPTER SIX 46

CONCLUSIONS AND RECOMMENDATIONS 46

6.1 CONCLUSIONS …………………………………………………………………………………………….. 46

6.2 RECOMMENDATIONS ………………………………………………………………………………….. 46

NOMENCLATURE 48

REFERENCES 51

APPENDIX

**CHAPTER ONE**

1.0 INTRODUCTION

Hole cleaning is the process of removing solid particles from the wellbore to the surface. These

solid particles are acted upon by four factors. They are Gravity, Viscous Drag, Impact and

Buoyancy. The transportation medium used to effect the removal of drilled solids is the drilling

fluid. Ability to lift particles of various sizes out of the hole is one of the most important functions

of drilling fluids. The factors which affect the carrying capacity of the fluid includes: fluid density

and rheology, annular velocity and flow regime, pipe rotation, cuttings density, size and shape of the

cutting, and annulus size and eccentricity. An optimum drilling fluid is expected to lift cuttings from

the wellbore and suspend them when circulation is stopped (Chukwu, 2009). The annulus size and

eccentricity is of great consideration in this study.

Effective hole cleaning is of great importance in oil well drilling operations, because inadequate

hole cleaning can lead to, but not limited to the following severe problems: fill, packing off, stuck

pipe and excessive hydrostatic pressure. Initially, it was considered that the primary purpose of the

mud was to remove the cuttings continuously (Chukwu, 2009).

Pipe eccentricity, usually expressed as a percentage, is a term that describes the deviation-fromcentre

of a pipe within another pipe or open hole. A pipe is considered to be fully (100%) eccentric

if it lies against the inside diameter of the enclosing pipe or hole and concentric (0% eccentric) if it

is perfectly centred in the outer pipe or hole. One of the most important factors that affect the

carrying capacity of mud is the velocity profile in the annulus. The velocity profile, in turn, depends

on the annulus cross-sectional area, and the eccentricity of the inner core and its rotation. This work

involves the use of couette flow analysis to determine eccentricity. (Anon, 2010)

Couette flow is the phenomenon whereby the fluid is confined between two coaxial cylinders one of

which is stationary and the other is moving at a uniform velocity. This flow characteristic is

representative of flow in the wellbore annulus where the wall of the wellbore is represented by the

stationary cylinder and the drill string or casing pipe is represented by the moving cylinder. The

fluid average velocity is dependent on the velocity of the moving cylinder or pipe (Chukwu, 2009).

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A real wellbore annulus is highly unlikely to be concentric and uniform through its entire length

especially in deviated wells in which the drill pipe lies along the “low side” of the wellbore annulus,

thereby creating extreme eccentricities. The eccentricity varies along the portions of the drill string

and it depends on the hole depth and its inclination angle with the vertical (Jawad and Akgun,

2002).

Hole cleaning is a more severe problem in high-angle holes than in vertical holes. It is not only

more difficult to carry the cuttings out of the hole, but they need to settle only to the low side of the

hole and causes problems like stuck pipe. Consequently, more attention should be paid to hole

cleaning requirements in directional holes (Annis and Smith, 1996).

From Zamora and Hanson (1991), four zones (0o-10o, 10o-30o, 30o-60o and 60o-90o) were

distinguished for critical hole cleaning and the zones where cleaning is most difficult are between

30o to 60o. This is due to slip of the cuttings bed and sagging. The experimental results confirmed

that probability of stuck pipe while drilling is higher when the angle is between 30o to 60o

(Saintpere and Marcillat, 2000). Tomren et al. (1983) also stated that increase in hole angle greatly

decreases the cuttings transport efficiency. He reported that 40o degree from vertical was found to

be the most difficult angle for hole cleaning (Zhou, 2006). Published experimental observations

(Jawad and Akgun, 2002) emphasized that during the transportation of cuttings in the annulus,

phase segregation occurs in the annulus. This causes cuttings accumulation on the low side of the

annulus, and leads to the cuttings bed formation in some drilling operations. Also, for the same

drilling conditions, the directional well requires higher flow rate than that of the vertical well to

obtain the same cleaning efficiency in both wells (Jawad and Akgun, 2002).

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1.1 PROBLEM STATEMENT

In an eccentric annulus, fluid flows preferentially through the larger annulus which means that

varying the eccentricity will result in different rates at which the hole is cleaned. Increasing the

velocity of the fluid in the annulus is a way of trying to clean the hole efficiently. However, this

approach results in higher equivalent circulating density (ECD) which can lead to uncontrollable

losses after fracturing. There is therefore the need to investigate the effect of increasing or

decreasing eccentricity, on hole cleaning taking into consideration the actual mechanism of cutting

transport through an eccentric annulus.

1.2 OBJECTIVES

The objectives of this work are to:

1. Determine the velocity profile in the annulus for different eccentricities

2. Determine the effects of eccentricity on some hole cleaning indicators

3. Determine the effect of eccentricity on equivalent circulating density (ECD) and its impact

on hole cleaning.

1.3 APPROACH

The proposed approach consists of;

1. using the Couette flow analysis of Power-law fluids to determine the velocity for different

eccentricities

2. applying Moore’s correlation to determine slip velocity for different eccentricities

3. using graphical relationships to evaluate the impact of eccentricity on some hole cleaning

indicators