improved method for selecting kick tolerance during

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LSU Historical Dissertations and Theses Graduate School

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Improved Method for Selecting Kick ToleranceDuring Deepwater Drilling Operations.Shiniti OharaLouisiana State University and Agricultural & Mechanical College

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IMPROVED METHOD FOR SELECTING KICK TOLERANCE DURING DEEPWATER DRILLING OPERATIONS

A Dissertation

Submitted to the Graduate Faculty of the Louisiana State University and

Agricultural and Mechanical College in partial fulfillment of the

requirements for the degree of Doctor of Philosophy

in

The Department of Petroleum Engineering

byShiniti Ohara

B.S., Univcrsidadc Estadual de Campinas, Brazil, 1979 M.S., Univcrsidadc Estadual de Campinas, Brazil, 1989

May 1996


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ACKNOWLEDGMENTS

The author is deeply indebted to Dr. Adam “Ted” Bourgoyne, Campanile

Charities Professor o f Offshore Mining and Petroleum Engineering, under whose

valuable guidance, supervision, and encouragement this work was accomplished. Sincere

appreciation is extended to Dr. Andrzej Wojtanowicz, Dr. Julius P. Langlinais. Dr.

Ronald F. Malone, Dr. William J. Bernard, and Dr. Zaki Bassiouni for serving on the

dissertation committee.

The author extends his deepest thanks to Petroleo Brasileiro S.A. (Petrobras) for

providing him the financial support to attend the doctoral program at LSU. Furthermore,

this research was financed by Petrobras through funds from its Technological

Development Program on Deepwater Production System — PROCAP 2000. Sincere

appreciation is due to Dr. Edson Y. Nakagawa, Mr. Saulo Linhares, Mr. Andre Barcelos.

and Mr. Djalma R. de Souza of Petrobras for their firm support throughout this project.

Special thanks are also due to Mr. O. Allen Kelly and Mr. Richard Duncan of

PERTTL--LSU for their attention, ideas, and support during the experimental phase of

this project Acknowledgments are extended also to Mr. Jason Duhe, Mr. Bryant

LaPoint, Mr. Eddy Walls, Jr., and Mr. Ben Bienvenu for their invaluable help during the

experimental work. Mrs. Jeanette Wooden is thanked for her kind words of

encouragement. The assistance of Mrs. Brenda Macon for proofreading the manuscript is

gratefully acknowledged.

The author thanks the following persons for donating or lending equipment and

material that were crucial to accomplish the experimental work: Mr. Mike Strout. Mr.

ii


Richard Kriege, and Mr. Nicholas Lavolpicella. Geophisical Research Corp.; Mr. Rickie

Menard, Francis Drilling Fluids, Ltd.; Mr. Donald LeJeune, Drillogic, Inc.; Mr. Gene Lee

and Mr. Ed Taupier, Daniel Flow Products, Inc.; Mr. Eurphy Lantier, Production

Wireline Services, Inc.; Mr. George Murphy, SWACO; Mr. James Pontiff, Halliburton

Energy Services; and Mr. Huey Bertrand, Cameron.

Finally, the author dedicates this work to his mother Julia for her constant moral

support, to his wife, Neuza. and to his children. Sara and Fabio for their support and love.

hi


TABLE OF CONTENTS

ACKNOWLEDGMENTS................................................................................................... ii

LIST OF TABLES............................................................................................................ vi

LIST OF FIGURES.......................................................................................................... vi

NOMENCLATURE....................................................................................................... xi

ABSTRACT...................................................................................................................... xvi

CHAPTER

1. INTRODUCTION............................................................................................. 1

2. LITERATURE REVIEW................................................................................. 102.1 Kick Tolerance.......................................................................................... 102.2 Kick Simulators......................................................................................... 172.3 Two-Phase Flow Through Annular Section............................................ 20

3. CIRCULATING KICK TOLERANCE MODEL............................................ 283.1 Wellborc Model......................................................................................... 28

3.1.1 Continuity Equations...................................................................... 293.1.2 Momentum Balance Equation....................................................... 293.1.3 liquations of State........................................................................... 31

3.2 Gas Reservoir Model................................................................................ 323.3 Choke Line Model..................................................................................... 353.4 Upward Gas Rise Velocity M odel............................................................ 353.5 Solution of the Differential Equations.................................................... 363.6 Simplification of the Differential Equations System.............................. 39

4. COMPUTER PROGRAM AND RESULTS OF NUMERICALSIMULATIONS................................................................................................ 424.1 Computer Program..................................................................................... 424.2 Results from a Typical Deep Water Drilling Experience........................ 444.3 Comparison with Commercial Kick Simulator....................................... 474.4 Selecting Kick Tolerance........................................................................... 53

4.4.1 Selecting Kick Tolerance for Well Design.................................... 544.4.2 Selecting Kick Tolerance while Drilling....................................... 55

5. EXPERIMENTAL WORK.............................................................................. 575.1 Description of a Full-Scale Well: LSU No. 2 ......................................... 575.2 Methodology of Experimentation............................................................. 595.3 Instrumentation of the Well...................................................................... 62

iv


5.4 Methodology Used to Measure Gas Rise Velocities................................ 65

6. EXPERIMENTAL RESULTS.......................................................................... 686.1 A Typical Experiment................................................................................. 686.2 Zuber - Findlay P lo t.................................................................................... 74

7. CONCLUSIONS AND RECOMMENDATIONS........................................... 777.1 Conclusions.................................................................................................. 777.2 Recommendations for Future Work............................................................ 78

7.2.1 Gas Distribution Profile.................................................................... 787.2.1.1 The Triangular Gas Distribution Profile............................. 797.2.1.2 Triangular Gas Distribution Velocities............................... 83

7.2.2 Improvement in the Gas Flow Out Measurements.......................... 857.2.3 Modification for Inclined W ell......................................................... 857.2.4 Instrumentation of a Real W ell......................................................... 85

REFERENCES.................................................................................................................. 86

APPENDIX A. SHUT-IN KICK TOLERANCE............................................................ 92A.l Maximum Shut in Casing Pressure (SICP)............................................... 92A.2 Kick Tolerance............................................................................................ 93A.3 Safety Factor and Surge Gradient............................................................. 95

APPENDIX B. INPUT DATA FOR KICK TOLERANCE PROGRAM..................... 97B.l Input Data for a Typical Deepwater W ell................................................. 97B.2 Input Data for the Well RJS - 4 57 ............................................................ 100B.3 Input Data for the Well CES - 112.......................................................... 103

APPENDIX C. GAS DISTRIBUTION PROFILE......................................................... 106

VITA.................................................................................................................................. 152

v


LIST OF TABLES

2.1 Effect of trip and safety margin on the kick tolerance.................................... 11

2.2 Safety factors used in the Beaufort Sea ........................................................... 12

2.3 Kick tolerance, alternate levels and procedures for drilling in theBeaufort S ea ..................................................................................................... 13

4.1 Typical casing setting used for a deep-water well in Campos Basin 45

5.1 Test matrix for water and natural gas experiments........................................ 60

5.2 Test matrix for mud and natural gas experiments with gas injectedthrough tubing.................................................................................................. 60

5.3 Test matrix for mud and natural gas with sensors 1,200 ft apart................. 61

5.4 Test matrix for mud and natural gas with sensors 100 ft apart.................... 61

5.5 Drilling fluid properties utilized in the experiments...................................... 62

5.6 Gas flow out calculations for gas measurements system.............................. 65

7.1 Front and center velocities for different circulation...................................... 83

A. 1 Safety factors used in the Beaufort Sea.......................................................... 96

C. 1 Test matrix for mud and natural gas experiments with gas injectedthrough tubing.................................................................................................. 106

C.2 Test matrix for mud and natural gas with sensors 1,200 ft apart................. 106

C.3 Test matrix for mud and natural gas with sensors 100 ft apart.................... 107

C.4 Drilling fluid properties used in the experiments........................................... 107

vi


LIST OF FIGURES

1.1 Deep-water drilling world records.................................................................... 2

1.2 Deep-water drilling activities for water depth greater than 400 m .................. 3

1.3 World record for subsea completions............................................................... 4

1.4 Kick Tolerance for deep-water.......................................................................... 7

2.1 Effect o f depth and kick volume on kick tolerance.......................................... 11

2.2 Pump-rate requirements and equipment lim its................................................. 16

2.3 Zuber-Findlay plot for flow-loop experiments................................................. 24

3.1 Finite difference scheme for a cell.................................................................... 37

3.2 Flowchart of the complete program.................................................................. 40

3.3 Flowchart of the simplified program................................................................ 41

4.1 A typical well design for deep water drilling in Campos Basin...................... 46

4.2 Kick tolerance, casing pressure, and fracture pressure at casing depthfor a typical deep-water w ell............................................................................ 48

4.3 Pit volume, bottom hole pressure, and drill pipe pressure for a typicaldeep-water w ell................................................................................................. 49

4.4 Gas flow rate and gas leading edge depth for a typical deep-water w ell 50

4.5 Kick tolerance for the well RJS - 457 ............................................................... 51

4.6 Kick tolerance for the well CES - 112.............................................................. 53

5.1 LSU No. 2 well completion schematic............................................................. 58

5.2 Gas flow out measurements system.................................................................. 64

5.3 Downhole pressure sensors disposition............................................................ 66

6.1 Example of downhole pressure data................................................................. 69

6.2 Example of gas flow rates and drill pipe pressure............................................ 70

vii


6.3 Example o f casing pressure, pit volume, and pump speed................................ 71

6.4 Differential pressure between on-line and casing and between downholeand pressure recorders......................................................................................... 72

6.5 Differential pressure between top and on-line sensors and between bottomhole pressure and bottom sensor....................................................................... 73

6.6 Zuber - Findlay plot of experimental data ......................................................... 75

6.7 Zuber - Findlay plot of the present and previous flow loops experiments .... 76

7.1 Gas fraction between sensors for different depths and times forexperiment M 1..................................................................................................... 80

7.2 Gas fraction profile as a function of depth for various tim es............................ 81

7.3 Proposed triangular gas distribution profile....................................................... 82

7.4 Gas velocity profile for various liquids velocities............................................. 84

C.l Gas fraction for different depths and times for experiment Ml ........................ 108

C.2 Gas fraction as a function of depth for experiment Ml ..................................... 109

C.3 Gas fraction for different depths and times for experiment M6...................... 110

C.4 Gas fraction as a function of depth for experiment M 6.................................... 111

C.5 Gas fraction for different depths and times for experiment M 7...................... 112

C.6 Gas fraction as a function of depth for experiment M 7....................................113

C.7 Gas fraction for different depths and times for experiment M8........................ 114

C.8 Gas fraction as a function of depth for experiment M 8.................................. 115

C.9 Gas fraction for different depths and times for experiment M 9..................... 116

C.10 Gas fraction as a function of depth for experiment M 9................................... 117

C.l 1 Gas fraction for different depths and times for experiment M il ..................... 118

C.l 2 Gas fraction as a function of depth for experiment M il .................................. 119

viii


C. 13 Gas fraction for different depths and times for experiment M 1 2 ................... 120

C.14 Gas fraction as a function of depth for experiment M12.................................. 121

C. 15 Gas fraction for different depths and times for experiment M 1 3 ................... 122

C. 16 Gas fraction as a function of depth for experiment Ml 3................................. 123

C.17 Gas fraction for different depths and times for experiment M14.................... 124

C. 18 Gas fraction as a function o f depth for experiment M 14................................ 125

C. 19 Gas fraction for different depths and times for experiment M 1 5 .................. 126

C.20 Gas fraction as a function o f depth for experiment M15................................. 127

C.21 Gas fraction for different depths and times for experiment M l6 .................. 128

C.22 Gas fraction as a function of depth for experiment M l 6 ............................... 129

C.23 Gas fraction for different depths and times for experiment M 17 ................. 130

C.24 Gas fraction as a function of depth for experiment Ml 7 ............................... 131

C.25 Gas fraction for different depths and times for experiment M 1 8 .................. 132

C.26 Gas fraction as a function of depth for experiment M 18............................... 133

C.27 Gas fraction for different depths and times for experiment M l9 .................. 134

C.28 Gas fraction as a function of depth for experiment M l9................................ 135

C.29 Gas fraction for different depths and times for experiment M 20.................. 136

C.30 Gas fraction as a function of depth for experiment M 20............................. 137


C.32 Gas fraction as a function of depth for experiment M 21................................ 139

C.33 Gas fraction for different depths and times for experiment M 22 .................. 140


ix

Reproduced w ith permission o f the copyright owner. Further reproduction prohibited w ithout permission.

C.3 5 Gas fraction for different depths and times for experiment M 23................ 142

C.36 Gas fraction as a function of depth for experiment M 23............................. 143

C.3 7 Gas fraction for different depths and times for experiment M 24................ 144

C.38 Gas fraction as a function of depth for experiment M 24.............................. 145





C.43 Gas fraction for different depths and limes lor experiment M 29................... 150


x


NOMENCLATURE

Roman Letters

an cross sectional area o f annulus

cr formation compressibility

CK ~ gas compressibility

c„ = gas distribution factor

total compressibility

d = distance

D = turbulence or non-Darcy factor

true vertical depth of hole

Dr true vertical depth of weakest formation

3“ II fracture depth or casing depth

4 ,= diameter of hole

d = diameter of drill pipe

dpjdt = shut-in pressure rise rate (choke pressure)

e = ratio of the two-phase slip to no-slip friction factor

f f = no-slip Fanning friction factor

two-phase flow friction factor

g = gravitational acceleration

Xc = conversion factor

h = permeable zone thickness

H = liquid holdup

Reproduced w ith permission of the copyright owner. Further reproduction prohibited w ithout permission.

h,e = gas leading edge height

h,pf = height o f two phase flow

J = productivity index

k = permeability

K = kick tolerance

K = circulating kick tolerance

Lk = true vertical length of influx

M = gas molecular weight

m(p) = real gas pseudopressure

p = pressure

ph = bottom pressure

phh = bottom-hole pressure

P, = choke pressure

/ ’/, = dimensionless pressure

Pf = formation pore pressure

Psc = pressure at surface condition (standard condition)

P s = safety factor pressure

p, = top pressure

O ~ gas flow rate

qt. = average filtrate loss rate to formation

= gas flow rate

q = gas flow rate at standard conditions

X ll


qi = liquid flow rate

R = gas constant

ROP = rate of penetration

rw = wellbore radius

S = skin effect

iSICPmaj. = maximum shut-in casing pressure

Swi = initial water saturation

t = time

T= temperature

tD = dimensionless time

Tsc = temperature at surface condition (standard condition)

vcenter = volume centered gas velocity

Vj= fluid loss volume

vfront= gas front velocity

vg = mean gas velocity

vgs = superficial gas velocity

Vk~ influx volume

V/ = liquid velocity

vh= superficial liquid velocity

vm = mixture or homogeneous velocity

Vm = mud volume

vm£ry= front mixture velocity

xiii


vmixt = tail mixture velocity

Vol = volume

vs= slip velocity

vtaii= g3̂ tail velocity

Vw = wellbore volume

Xk = influx compressibility

Xm = mud compressibility

Xw = wellbore elasticity

YP = yield point

z = gas compressibility factor

Greek letters

a = gas fraction

Pg = velocity coefficient

X = no-slip liquid holdup or input liquid content

<}> = formation porosity

p. = viscosity

p.y= formation fluid viscosity

pg= gas viscosity

p = equivalent mud density

py = fracture gradient expressed in equivalent mud density

pg = density of gas

p̂ . = density of fluid influx

xiv


Pz = density o f Liquid

pm = density o f drilling fluid or mud

pnj = two-phase no-slip density

pp = pore pressure expressed in equivalent mud density

psf= safety factor expressed in equivalent mud density

pjg = surge pressure expressed in equivalent mud density

pt = trip margin expressed in equivalent mud density

dp/ dz = gradient pressure

(dp/ dz)elev = gradient pressure due to elevation

(dp/ dz)fric = gradient pressure due to friction

Subscripts

an = annulus

bh = bottom hole

Dp = differential pressure

frac - fracture

max= maximum

min = minimum

res = reservoir

sc = standard conditions

stab= stabilized


ABSTRACT

One of the most critical aspects in the design of oil and gas wells is the selection

o f the depths at which steel casing is set. As the length of open borehole increases, the

risk o f formation fracturing during drilling operations increases. Formation fracture often

leads to an underground blowout that can be very expensive to control. Because of the

special problems involved in drilling deepwater well, accurately measuring the risk of

formation fracture is essential. A calculated parameter called “kick tolerance” is often

used to measure this risk.

In this study, improved computer software specifically designed for computing

kick tolerance for wells drilled in deep waters was developed. During well design, the

software can be used to confirm previously calculated casing setting depths. The software

can also be used during drilling to estimate the fracture risk of the weakest exposed

formation if a kick was taken and circulated. If an unacceptable fracture risk is indicated,

drilling can be interrupted and the casing string can be set earlier. The developed

computer program has been proven to be fast, reliable, and suitable for available rig site

computers. The accuracy achieved was similar to that obtained using commercially

available well control simulators that are much more time consuming to run. The

availability of this simulator may result in safer drilling operations and improved

capability for drilling in deeper water depths.

Experiments were performed using a drilling fluid and natural gas in a 6,000 ft

research well to verify and improve previously published empirical correlations for gas

rise velocities. An empirical correlation relating the gas velocity to the sum of the average

xvi


mixture velocity and the relative slip velocity was determined using both the available

data from previous flow-loop experiments and data from the present experiments. This

correlation was used in the new computer software. The experimental data may also

allow additional improvement to be made in the accuracy of the kick tolerance

calculation in the future. Investigation of a triangular gas distribution profile along the

path of upward gas migration is proposed as a future area o f study.

XVll


CHAPTER 1

INTRODUCTION

Geologists have long believed that significant hydrocarbon accumulations exist at

deep-water locations. However, these locations have been left unexplored until recently

because they were not considered to be economically and technically viable. Deep-water

exploration and development concepts have changed over the years. For example, in the

early sixties the exploration and development of offshore hydrocarbons were restricted to

46 m (150 ft) by the physical and economic limitations of bottom-supported drilling and

producing rigs. The major concern was to overcome this 46 m limit, which was

considered a deep-water location at the time.

During the oil crisis o f 1973, the oil price jumped from $2.00 to $11.00 per barrel.

A second oil price shock occurred in 1979 when the oil price reached $30.00 per barrel.

Motivated by the improved economics of oil exploration that was brought about by these

oil crises, the oil industry began searching for hydrocarbons in deeper water, as can be

seen in Figure 1.1. Deepwater technology has advanced from moored semi-submersibles

to today’s advanced dynamic positioned (DP) vessels. Today, wells drilled in water

depths over 400 m (1,312 ft) are considered to be deep-water wells. This depth

corresponds to the maximum depth that a human being can dive using saturation

techniques. Beyond this depth ROVs (remotely operated vehicles) are used to service the

well heads on the sea floor, including those of ultra-deep-water wells, which are

considered to be wells in water depths of 1,000 m (3,281 ft) or more. The current world

record for deep-water drilling is held by Shell for a well at the Mississippi Canyon 657 #2

drilled in 1988 in a water depth of 2328.1 m (7,638 ft).

1


1

Year68 70 72 74 76 78 80 82 84 86 88 90

iI

S 500 -I

1000 - -

3 1500

2000 -

2500

Figure 1.1 Deep-water drilling world records

Brazil is now one of the most active countries in deep-water drilling and

producing. The deep-water drilling program using dynamically-positioned (DP) units

began in 1985, when nine wells were drilled in water depths of more than 400 m (1,312

ft). In 1992, 51 deep-water wells were drilled, as shown in Figure 1.2.

The deep-water drilling activities in Brazil were intensified by the discovery of a

giant field, Albacora, in September of 1984 with the wildcat well l-RJS-297. Albacora

field, located in Campos Basin (Southeast Brazil) in water depths ranging from 293 m

(755 ft) to 1,900 m (6,234 ft), has an estimated oil-in-place volume of 4.4 billion barrels

2over an area of 235 km' (90 mi').

Marlim, another giant field, was discovered in 1985 when the well 1-RJS-219A

was drilled at a water depth of 853 m (2,797 ft). Marlim field is also located in Campos

Basin in water depths ranging from 600 m (1,967 ft) to 1,050 m (3,445 ft). The total


reserves (recoverable oil volume) for this field are estimated to be 1.5 billion barrels of

2 2oil (6.6 million of oil-in-place) over an area of 132 km (51 mi ).

90 ---------------------------------------------

80-!-! □ World (excluding Brazil) B Brazil

| 70 -h

i 60 t03 j

1 50 to 40 -U0

| 30 T1 iz 2 0 |

10 -

\ /

\ A

70 72 74 76 78 80 82 84 86 88 90 92 94YearSource: Petrobras E&P

Figure 1.2 Deep-water drilling activities for water depth greater than 400 m

Brazilian offshore exploration was not limited to the Albacora and Marlim fields.

Prospecting in the Campos Basin soon pinpointed the Barracuda, Bijupira and Salema

fields with reserves of 106,43, and 13 million barrels of oil, respectively, in water depths

ranging from 400 m (1,312 ft) to 1,000 m (3,281 ft). In addition, other deep-water

prospects are currently being drilled outside the Campos Basin and may also reveal new

deep-water fields.

The new challenge after these discoveries was overcoming the technological

barriers involved in producing these deep-water fields. Offshore production using fixed

platforms in Brazil started in the shallow water of the Sergipe/Alagoas Basin (Northeast


4

Brazil) in 1968. Nine years later, floating production system (FPS) technology was used

for the first time in Brazil to bring Enchova field on stream. The simplicity o f the FPS

reduced the lead-time needed to bring this field into production. The next step was the

application of FPS for field development using subsea completion techniques. The first

subsea completion in Brazil was performed in 1979 in a water depth of 189 m (629 ft).

Since then the world water depth record for subsea completion has been repeatedly

broken over a short period of time, culminating in the current subsea world record of

1,027 m (3,370 ft) established in May 1994 with the completion of well 3-MRL-4 in

Marlim field, as shown in Figure 1.3. This world record may be broken again in 1997 in

the Mensa field, where the water depth is 1,646 m ( World Oil, July 1995). Currently, of

all subsea trees installed worldwide, one third have been installed in Brazil.

Year

78 80 82 84 86 88 90 92 94 96 98

j f 1000: ♦ Petrobras

o Placid

gS hell (expected in 1997)

' 1500 -

2000

Figure 1.3 World record for subsea completions

Deepwater drilling and production are now a reality. However, deep water

drilling poses special problems, such as low fracture gradients, high pressure loss in


5

choke lines, overbalanced drilling due to a riser safety margin, and emergency riser

disconnection problems. As operators search for hydrocarbons in deeper waters, key

factors for successfully drilling deep-water wells are to have (a) a detailed well design

and drilling plan and (b) a close control while drilling to avoid kicks, loss of circulation,

and a possible underground blowout, which can be especially costly. Therefore, special

care must be used when planning and drilling these wells. The kick tolerance concept is a

powerful tool that can be used during well design, along with the pore pressure and

fracture gradients, to determine depths at which casing should be set. In addition, kick

tolerance can be used during drilling to estimate the fracture risk of the weakest exposed

formation. If a kick is taken and circulated, break down of this formation could lead to an

underground blowout. This parameter can be used to stop the drilling and run the casing

string and to regulate drilling activities by governmental regulatory agencies, such as the

US Mineral Management Service.

Even though kick tolerance has been used in the drilling industry, the concept has

been controversial (Redman, 1991). Much confusion can be credited to the original

definition: “a difference between formation pressure and mud weight in use (expressed

as mud weight equivalents) against which the well could be safely shut in without

breaking down the weakest formation.” According to Redman, much confusion is also

credited to the term “zero gain,” which is either misunderstood or omitted entirely.

Another accepted definition is “kick tolerance is the maximum increase in mud weight

allowed by the pressure integrity test of the casing shoe with no influx (zero gain) in the

wellbore.” Often the zero pit gain condition is omitted. For example, with a pressure


integrity test result of 1.68 gr/cm3 (14 lb/gal) at the casing shoe and a mud density of 1.20

gr/cm3 (10 lb/gal), many may consider that they are secure because they have a kick

tolerance o f 0.48 gr/cm3 (4 lb/gal). This is only true if no influx (zero pit gain) occurs, but

generally a kick is detected by the pit gain (increase of volume in the mud pits). As a

result, kick tolerance decreases as kick volume and depth increase.

Kick tolerance is calculated assuming that natural gas (worst case) is the kick

fluid. Another extremely important assumption is the maximum pit gain that would be

expected before the blowout preventers are closed. The maximum pit gain used in the

calculation is critical and must be appropriate for field operating practices,

instrumentation, and rig crew training. Shut-in kick tolerance applies to well conditions

when the well is shut in. Circulating kick tolerance applies to the most severe conditions

expected during the well control operations to remove the kick fluids from the well. The

circulating kick tolerance can easily be calculated as a simple model which assumes that

the influx of gas enters as a slug and remains a slug during the circulation. This simple

model, although easy to calculate, is very conservative if compared with a modem kick

simulator, as shown in Figure 1.4.

However, calculation of kick tolerance using an existing commercial kick

simulator can be very time consuming. For example, it took almost one full day to

calculate the five points used to draw the upper curve in Figure 1.4. Furthermore, existing

kick simulators are known to fail in many deep-water drilling situations (Negrao, 1995).

Although time consuming, using a kick simulator rather than a simplified “slug” model

to calculate kick tolerance in this well saved around SI00,000 in drilling costs. Thus, the


development of a more realistic, reliable, and much faster kick simulator dedicated to

calculate kick tolerance for use in well planning and while drilling at a deep-water

location has motivated the present research.

11.3 ,

11.2Kick S im ula to r

11.0Sim plified Model10.9V5 CJ

=* 10.8c>I 10.7

10.6 -

After Nakagawa and Lage, 1994

30 400 10 20 50 60Pit gain (bbl)

Figure 1.4 Kick Tolerance for deep-water

The concept of kick tolerance is more complex in deep water drilling because

dynamic positioned drilling ships (DPDS) are used, and normally a riser safety margin is

applied to avoid a potential loss of hydrostatic pressure due to an emergency

disconnection and BOP failure. Depending on water depth, leak-off test results, and pore

pressure, the riser margin cannot always be applied because of the risk of formation

fracture. The kick tolerance value can be near zero or even negative in this case without

implying a dangerous situation. Another important factor in deep-water is the high

pressure loss, which was considered in the proposed kick simulator, in the long subsea

flow lines.

A computer model is proposed in this research to calculate circulating kick

tolerance. The model is based on: a) mass-balance equations (continuity equations) for


8

the mud and gas; b) a momentum-balance equation for the gas-mud mixture; c) equations

of state for mud and gas; and d) a correlation relating the gas rise velocity in the annulus

to the average mixture velocity plus the relative slip velocity between mud and gas.

Developing a more accurate circulating kick tolerance calculation procedure

requires the determination of a correlation for the gas rise velocity in the annulus. Many

studies have been performed in this area using flow loops or a real well and using mud,

Xantham gum, or water as a liquid phase and air, nitrogen, or argon gas as a gas phase.

These studies were used to develop empirical methods for computing gas slip velocity

and gas concentrations in well control operations. The empirical gas slip correlation used

in the new circulating kick tolerance simulator is based on this previous work.

Despite these previous studies, no single experiment was made with the

combination o f real well conditions, drilling fluids, and natural gas. The previous studies

concentrated on the bubble front velocity, but how the shape of the gas fraction

distribution profile will change with time during the gas migration is still unknown. Also,

since the velocity of the gas behind the two-phase interface, or tail velocity, is low, its

volume along the well can be considerable. Consequently, these unknowns have

motivated the present experimental works to determine these velocities and distribution

profiles.

In summary, a kick simulator that is dedicated to calculate kick tolerance for deep

water drilling has been developed. The developed software has been proven to be fast,

reliable, and suitable for available rig site computers. Experiments were performed in a

6,000 ft research well, using a drilling fluid and natural gas, to verify and improve


9

previous published empirical correlation for gas rise velocities. An empirical correlation

relating the gas velocity to the average mixture velocity plus the relative slip velocity was

determined using the available data from previous flow-loop experiments combined with

data from the present experimental work. The experimental data may also allow

additional improvement to be made in accuracy of the kick tolerance calculation in the

future. Investigation of a triangular gas distribution profile along the path of upward gas

migration is proposed as a future area o f study.


CHAPTER 2

LITERATURE REVIEW

2.1 Kick Tolerance

Shut-in kick tolerance is defined as the difference between mud weight in use

and formation pressure (expressed as mud weight equivalents) against which the well

could be safely shut-in without breaking down the weakest formation. Circulating shut-in

kick tolerance applies to the most severe conditions expected during the well control

operations that will allow the removal of the kick fluids from the well. The shut-in kick

tolerance can be defined as:

k , = p , - p . = | K p ( - p . ) - ^ - A ( p . - p ( ) - p , (21)

Appendix A presents a derivation of Equation 2.1.

Pilkington and Niehaus (1975) compared the effects of safety margin, trip margin,

and fluid influx on the kick tolerance using the formula:

V (p / _ Ptf — Pm)P/ Pm(^* — Lk )+ p* LkK- -------- D— — + — — 5 ---------------- P - - P .

" u >> (2.2)

The data used for comparison is:

Casing set at: 4,000 ft

Drilling at: 12,000 ft

Fracture gradient: 13.5 lb/gal (at 4,000 ft)

Mud weight: 10.0 lb/gal

Pilkington and Niehaus comparison is summarized in Tabic 2.1.

10


11

Table 2.1 Effect of trip and safety margin on the kick tolerance

Ignoring trip margin and fluid influx

Accounting for trip margin with no influx

Accounting for trip margin and influx

(42 bbl)safety margin safetv maruin safety margin

with (0.5 lb/gal)

without with(0.5 lb/gal)

without with (0.5 lb/gal)

without

1.2 1.3 1.1 1.1 0.7 0.8

Pilkington and Niehaus showed that the kick tolerance decreases with depth and

with increased kick volume, as shown in Figure 2.1.

4000

5000

6000

~ 7000 a£ 8000 ST“ 9000

10000

11000

120000 1 2 3 4

Kick tolerance (lbm/gal)

Figure 2.1 Effect of depth and kick volume on kick tolerance

Pilkington and Niehaus concluded that the fracture gradient gives operators a

false sense of security. In addition, the fracture pressure, and not a mud weight

equivalent, at the shoe is the critical factor in well planning because the fracture pressure

------------------ 1■

■1

1---------------0•

A A

----------------A 1

■VI A

V M

• ▲ «

■ •H A

4 *

wm■ • i

A 1A

0 (A fierP i Ik ington and

■

w m

• MNiehauj . 1975)

AH I03bblinflux

0 42bblinflux

▲ 8.5bblinflux

♦ Obblinflux

■as m

B J+■B V

■ •M A

JKr

*

■ ■ •

B r

W ' ' L


12

(at the casing shoe) minus the hydrostatic pressure o f the mud column (at the casing

shoe) is the maximum surface pressure that can be tolerated.

A practical form of kick tolerance was used to drill in the Canadian Beaufort Sea,

which has high abnormal pressure and an unconsolidated formation, as well as

permafrost, gas hydrates, and plastic shale (Wilkie and Bernard, 1981). The problems

associated with this location made the optimum setting of the casing string critical. As a

result, the safety factor was redefined as a function of depth and expressed in pressure.

Moreover, a surge gradient factor was introduced into the calculation of kick tolerance. A

surge gradient was created on restarting the mud pumps, after the well was shut in, to

read the drill pipe and casing pressures. The formula used to drill in the Beaufort Sea is:

( ^ 0 , - 1 0 1 . 9 4 ^ ) p . ( L , + Df )

A A (2.3)

where the surge gradient is defined as:

5.33x103Y P D f 101.94

Pn ( < w , ) " ' V

Their proposed safety factors (Psf ) are shown in Table 2.2.

Table 2.2 Safety factors used in the Beaufort Sea

(2.4)

Below Casing Safety Factor(mm) (inches) kPa psi406 16 225 33340 13 3/8 345 50244 9 5/8 690 100

In addition, Wilkie and Bernard proposed procedures to be used while drilling, as shown

in Table 2.3.


13

Table 2 3 Kick tolerance, alternate levels and procedures for drilling in the BeaufortSea

Level 1 Level 2 Level 3Kick Volume Vk = 4 nr* (25 bbl) Vk = 2.8 m3 (17.5 bbl) Vk=1.6m 3(10bbl)Kt Greater than zero Greater than zero Greater than zero1. General safety

(a) BOP drills Weekly (each crew) Weekly (each crew) Each tour

(b) Dog house safety meeting

As required Each tour Each tour; written instruction

(c) Drilling rate By cuttings in hole (3.c) By cuttings in hole (See 3.c) < 9 meter per hour(d) Tripping speeds (casing and open hole)

Calculate for each trip based on swab/surge



(e) Barite plug preparation

Pilot test; review procedures; measure chemicals

Pilot test; review procedures; measure chemicals

Prepare mix water; line out cement unit

(f) Weather/ice conditions

Normal forecasts Favorable forecast 24 hr Favorable forecast 48 hr

2. Kick detection(a) Active pit volume

Normal Reduced Minimum

(b) PVT (while circulating)

Sensitivity +/- 1.6 m3 Sensitivity +/-1.1 m3 Sensitivity +/- 0.6 m* Man on pits continuously

(c) On drilling breaks

Flow check Flow check Shut in well

(d) Hole fill procedures

Follow normal hole fill/trip record procedures

Follow normal hole fill/trip record procedures

Supervisors check procedures and records during trips

(e) Mud weight Check every 1 hour* Check every 30 min* Check every 15 min*

(f)Communications

Normal Open from mudlogger to floor

Open from mudlogger to floor

* If mud weight out drops more than 36 kg/m water cutting

, flow check and check mud properties for possible

3. Pressuredetection

(a) General procedures

Observe normal** indicators; report significant trends

Observe all indicators; report significant trends

Observe all indicators; report all trends

(b) Gas units i) Calibrate daily i) Calibrate on each tour i) Calibrate every 4 hours

ii) Run degasser if necessary

ii) Run degasser to check response

ii) Run degasser

iii) Observe and report trends

iii) Limit max gas units iii) Limit max gas units

(c) Cuttings in hole Less than 30 m Less than 18 m Less than 9 m(d) Wireline logs At casing point Approx. every 762 m or as

required for overpressure confirmation (wellsite team recommendation)

Approximately every 305 m

table cont.


14

Level 1 Level 2 Level 3Kick Volume Vk = 4 m ' (25 bbl) Vk = 2.8 m'’ (17.5 bbl) Vk =1.6 n f (10 bbl)(e)Dummyconnections

As required As required As required; every 5 m if increasing pore pressures are indicated

Kick tolerance Greater than zero Greater than zero Greater than zero4. O ther measures

(a) On tripping Flow check after first 5 stands, at sl.oe and before pulling collars into BOP stack.

Flow check every 5 stands, at shoe and before pulling collars into BOP stack.

Consider increasing mud weight for tripping.Flow check every 5 stands, at shoe and before pulling collars into BOP stack.

(b) Short trip (dummy trip)

As dictated by hole conditions

As dictated by hole conditions

Make 5 stands short trip and circulate bottoms up before tripping out of hole.

** Mud gas units, penetration rate, ‘d ’ - exponent or equivalent

Chenevert (1983) presented a microcomputer program to calculate the kick

tolerance. The formula used in this program is similar to Equation 2.1 but without the

safety factor and trip margin gradients.

During the well control process, calculating the pressure of the influx fluid when

it reaches the casing shoe is desirable. Using the "driller's method," which employs the

existing mud weight to remove the influx from the well, Redmann (1991) proposed an

iterative process to calculate the top of the influx pressure and the volume of influx.

Therefore, he defined the circulating kick tolerance as:

K ic ~ P /~ P « i (2.5)

where equivalent-mud density (p ) is calculated by the iterative process.


15

Although an underground blowout is highly undesirable, for a hole section with a

known but manageable underground flow potential, necessary unconventional well

control contingency plans can be developed. Wessel and Tarr (1991) reported a new

strategy to optimize well costs by managing the well-control risks better than an arbitrary

minimum kick tolerance value. A direct tradeoff exists between kick tolerance and well

cost: Specifying a higher kick tolerance than necessary' can increase the well cost because

additional casing strings will be required. Specifying lower kick tolerance can lead to

costly well-control incidents.

Wessel and Tarr first simplified the productivity index (./) as a function of only

the product o f the permeability (k ) and the permeable zone thickness (/i) multiplied by a

constant (y).

J = Y kh (2.6)

By estimating the kh value for a potential gas zone to be drilled, one can determine

whether an underground gas flow can be controlled with the available rig equipment or

whether an additional pumping unit or a relief well will be required. Furthermore,

neglecting the two-phase-flow liquid hold up and any friction pressure loss in the annu

lus, the kill-mud density and pump rate combination required to kill the underground

flow is dependent on the volume of kill-mud available, as shown in Figure 2.2.

Leach and Wand (1992) reported the use of a kick simulator to generate well

control procedures and kick tolerance calculations during the planning stage for a deep

high pressure well in the Norwegian North Sea. Recently Nakagawa and Lage (1994)

reported cases o f exploratory deep water drilling on the Brazilian coast.


16

One open hole annular volume of mud required for kill

Pumping capacity with additional high pressure pum ps

Additional kill options with high pressure f umps

Effective kill options with rig pur ip;

Infinite volume of mud required

Pumping capacity with rig pumps

(After Wessel and Tarr. 1991) KILL MUD WEIGHT

Figure 2.2 Pump-rate requirements and equipment limits

Nakagawa and Lage reported that the kick tolerance was considered to be a

crucial aspect and was calculated both before (during the well design) and during

drilling. One of the cases, a well located in 1,214 m (3,983 ft) of water with 508 mm (20

in) casing set at 1,590 m (5,217 ft) had a low fracture gradient of 1.38 gr/cm’ (11.5

Ibm/gal) and indicated some problems. Wellbore stability problems led to an increase in

mud density to 1.31 gr/cm’ (10.9 lbm/gal) while drilling at 2,000 m (6,562 ft). At this

point the possibility of safely reaching the final depth of 2,340 m (7,678 ft) before

running the 340 mm (13 3/8 in) casing was in doubt. Controlling a 4.8 m’ (30 bbl) gas

kick from a formation with 1.32 gr/cm’ (11.0 lbm/gal) pore pressure was considered to be

possible, and the simulation showed that drilling ahead as planned was also possible.

However, the maximum allowed surface pressure was 1,586 kPa (230 psi), and the

pressure loss through the choke line was 1,241 kPa (180 psi) for 34 m’/hour (150 gpm) of

mud flow rate. Those close pressures could result in some problems during the well


17

control procedure. It was decided that, if a kick occurred, the pump flow rate to circulate

the kick would be reduced to 22.7 m3/h (100 gpm), and the kick would be circulated by

choke and kill line in a parallel arrangement. Fortunately a kick did not occur, and the

casing was set as programmed.

2.2 Kick Simulators

Many old computer models for gas kick simulations were limited by the

assumption of an arbitrary distribution of the gas in the wellbore. The most common

assumption is that the gas enters as a slug and remains as a continuous gas slug through

the annulus to the surface.

One of the first mathematical models using this assumption was presented by

LeBlanc and Lewis (1968). Also assumed were that the annular frictional pressure loss is

negligible, the gas is insoluble in the mud, the annular capacity well is uniform, and the

gas travels at the same velocity as the mud.

Mackenzie (1974) also developed a mathematical model to predict the annular

pressure profile. He broke the circulation o f a kick into six zones. Three of those zones

are due to influx of: a) water and mud; b) oil and mud; and c) gas and mud. The other

three zones are occupied only by the mud. The computer program that was developed

changes the volume of each of the zones as the kick circulated due to gas slip and to fluid

expansion. His model corresponds well with data from a kick generated in the Louisiana

State University (LSU) training well.

A transient model was proposed by Hoberock and Stanbery (1981). They used

equations of motion that describe the pressure and flow in a rigid, vertical fluid


18

transmission line of a constant cross-sectional area. They adjusted the two-phase flow

properties that reflected average fluid properties to allow it to treat two-phase flow as a

single fluid flow. Also, the two-phase region was assumed to be distributed uniformly by

volume with the mud but to change with time due to gas expansion and elongation of the

region.

Later, Nickens (1985) proposed a dynamic computer model complete with

equations, assumptions, computational strategy, boundary conditions, and suggestions on

timesteps. His model is based upon mass-balance equations for the mud and gas, a

momentum-balance equation for the gas-mud mixture, an empirical correlation relating

the gas velocity to the average mixture velocity plus the relative slip velocity between

mud and gas, and equations of state for mud and gas. Chapter III presents a more detailed

description of this model.

Using the Nickens’ model, Podio and Yang (1986) proposed a well control

simulator for personal computers. The main difference between the two models is related

to the solution method of differential equations. While Nickens’ model uses a fixed space

grid, Podio and Yang’s model uses a moving boundary solution. Other differences are the

calculation of influx rate, slip velocity, and friction factor. The benefit o f using Podio and

Yang’s model is that it facilitates simulation of multiple kicks taken in the same well.

Negrao and Maidla (1989) developed a mathematical model to predict the

pressure variation in the choke line and the annular section of the well during a well

control in deep-water. They used the model to select the flow rate for kick control.


19

Element, et al. (1989) presented a complete overview of well kick computer

simulator codes. They compared and contrasted the existing computer models with

respect to the differing modeling capabilities, solution methods, numerical

approximations, and the description o f physical effects using either physical models or

correlations.

Kato (1989) developed a two-phase model with the assumption that no

coalescence nor breakage of bubbles occurs with initial input o f bubble sizes.

Santos (1991) proposed a mathematical model for well control operations in

horizontal wells. He modified his previous work for a vertical well (Santos, 1989), based

on the Nickens’ model, to use in horizontal wells.

Vefring, et al (1991) presented a kick simulator for use on a workstation with a

Unix operating system and X-Window system installed. They reported that many selected

downhole parameters could be plotted graphically on the screen as a function of time and

space. The mathematical model is composed of the conservation of mass (mud, free gas,

dissolved gas, and formation oil), conservation of total momentum, and functional

relationships o f mud density, gas density, free gas velocity, gas influx, rate o f gas

dissolution, and frictional pressure loss. They used a finite difference method to solve the

system of equation with a simple front tracking technique.

Miska, et al. (1991) presented a computer simulation of the reverse circulation

well control procedure for gas kick. Their model assumes a steady-state flow of all fluid

in the well, slip velocity of zero, and gas flowing as a continuous slug.


20

Santos, et al. (1991) analyzed the dynamic pressures developed on the marine

riser and diverter line during gas removal from a riser-diverter system. They studied the

“riser blowout” that can cause collapse o f the riser and the risk o f fire. They developed a

riser model that was coupled with an existing diverter model (Santos, 1989) to simulate

numerically the gas removal from the riser-diverter system.

The dynamic two-phase model OLGA (Bendlksen et al, 1991), originally

developed for two-phase oil and gas flow in pipelines, has been modified to use in well

control. For example, Rygg and Gilhuus (1990) and Rygg, et al. (1992) describe the use

of the two-phase model OLGA during the kill planning phase of a 1989 underground

blowout in the North Sea.

Schofmann and Economides (1991) compared kick control in ultra deep wells

with shallow wells. The basic pressure equations used are similar to the equations used

by LeBlanc and Lewis (1968).

Two commercial kick simulators are available now: the RF kick simulator from

Rogaland (Rommetveit and Vefring, 1991) and the R-model from an association of

Schulumberger Cambridge Research, BP International, and Sunbury, and supported by

the United Kingdom Department of Energy (Tarvin and Walton, 1991; White and

Walton, 1990).

2.3 Two-Phase Flow Through Annular Section

The development of a reliable kick simulator also requires an accurate model of

gas-mud mixture flow as it moves upward in the wellbore. The Department of Petroleum

Engineering at Louisiana State University has been conducting projects in well control


21

(Bourgoyne, 1982) at the Petroleum Engineering Research and Technology Transfer

Laboratory (PERTTL) for more than a decade. Most o f the experiments cited in this

section were performed at this well facility.

Rader, et al. (1975) verified that the assumption of gas flowing as a continuous

slug and with the same velocity as the liquid did not work well when applied in a 1,828

m (6,000 fit) LSU research well. They observed lower gas velocity and lower casing

pressure than expected during a well control operation.

After evaluating kick control methods, Mathews (1980) and Mathews and

Bourgoyne (1983) reported the occurrence of bubble fragmentation. Mathews observed

that the bubble fragmentation is smaller in viscous fluids and less intense using the

dynamic volumetric method.

Caetano (1986) studied two-phase flow in a flow loop using both air-water and

air-kerosene flows. He defined flow pattern maps for concentric and fully eccentric

geometry. He concluded that eccentricity affects both the friction factor and the transition

from bubble to slug flow. Furthermore, he proposed models for liquid hold up and

pressure gradients for each flow pattern based on Taitel’s (1980) equations.

Motivated by the need for a better knowledge of the bubble fragmentation

process, Casariego (1987) and Bourgoyne and Casariego (1988) made theoretical and

experimental studies of gas kicks in vertical wells. Their model closely predicted the

measured casing pressure with data from a 1,828 m (6,000 ft) LSU research well.

Rommetveit and Olsen (1989) used an inclined (maximum of 63°) research well

to perform gas kick experiments using nitrogen and argon gas with oil-base mud. They


used nine surface sensors to monitor the pump strokes, mud return flow rate, pit level,

choke position, choke pressure, gas injection rate, choke line fluid density, standpipe

pressure, and gas injection pressure. In addition, they used one hardwire sensor and four

downhole memory tools to log the pressure and temperature. Based on the differential

pressure among the sensors in the well, and between the choke pressure and the sensors

in the well they concluded that: the gas starts to dissolve immediately as it enters the

wellbore; the bubble flow regime prevails in the two-phase section; the gas bubbles rise

and dissolve; the initial gas-oil ratio (GOR) in the experiment was higher than the

saturated GOR: gas bubbles rise and distribute over a longer section of the well; the gas

dissolution is governed by convective diffusion; and the mud does not become saturated

with gas immediately. They also observed some pulsations on the return flow, and their

explanation was that gas bubbles first coalesce and form a slug of gas, which rises

quickly and expands. After this a new dissolution process takes place in the upper part of

the annulus.

Continuing the well control research at LSU, Nakagawa (1990) and Nakagawa

and Bourgoyne (1992) performed an experimental study in a fully eccentric flow loop at

different inclinations to determine the gas fraction and gas velocity during the gas kick.

They presented a simplified model for the gas-rise velocity eliminating the bubble size

and shape for the calculation. Following this study, Mendes (1992) and Wang (1993)

continued Nakagawa’s experiments with low-er superficial gas and liquid velocities that

were not covered in previous experiments.


23

Using a flow loop, Johnson and White (1990) performed some experiments to

examine gas rise velocities during kicks. They used water and Xanthan gum as the liquid

phase and air as the gas phase. They concluded that, in drilling fluids, the bubbles rise

faster than in water despite the increased viscosity. They explained that these surprising

results are due to the change in the flow regime, with large slug-type bubbles forming at

lower void fractions. Furthermore, their results show that a gas bubble will rise faster

than any previously published correlation would predict. One of their results, for vertical

flow, is shown in a Zuber-Findlay (1965) plot along with Nakagawa’s. Mendes’, and

Wang's data in Figure 2.3. We can observe from this figure that Johnson's and

Nakagawa's data are similar and can be fitted in a Zuber-Findlay correlation for the mean

velocity of gas (vc).

Hovland and Rommetveit (1992) experimented with gas kicks in the same well

used by Rommetveit and Olsen. In these experiments, the authors used oil and water-

based mud. Nitrogen and argon were injected to simulate the gas kick. They varied mud

type, mud density, gas concentration, mud flow rates, and gas injection depth in their

experiments. They concluded that, in a high concentration gas kick, the gas rises faster

than in low and medium concentration. The gas rise velocity correlations obtained from

v (2.7)

where the superficial mixture velocity (vm) is defined as:

V* +<//( 2 .8 )V


24

these experiments are not significantly dependent on gas void fraction, mud density,

inclination, mud rheology, and surface tension.

4.0

ZUBER-FINDLA Y PLOT Inclination = 0 degree

3.5

3.0

2.5

« 2.0*❖

1.5

Johnson and White (1990)

1.0 Nakagawa (1990)

Mendes (1992)

0.5Wang (1993)

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0

Mixture velocity (m/s)

Figure 23 Zuber-Findlav plot for flow-loop experiments


25

Hovland and Rommetveit presented one Zuber-Findlay plot, but the graphic was

normalized (divided by the maximum value). As a result, the experimental data cannot be

compared with previous work.

Using the same flow loop used by Johnson and White, Johnson and Cooper

(1993) investigated the effects o f deviation and geometry on the gas migration velocity.

For vertical orientation they conclude that the flow in the pipe and annulus are almost the

same. They conclude that the gas distribution coefficient iC0) is the same while the gas

slip velocity (v,) is slightly larger in the annular geometry. In deviated flows, C'0 is larger

for the annulus and v. is larger for the pipe. Up to a deviation of 45°, v, remains almost

constant. They also conclude that, even in a stagnant mud, the gas normally migrates at a

velocity over 0.5 m/s (5,900 ft/hr), almost six times the conventional field model of 0.085

m/s (1,000 ft/hr). The conventional field model considers only the hydrostatic effect of

gas migration as;

where dpc dt is shut-in pressure rise rate. They used an equation developed by Johnson

and Taruin, 1993 ( in Johnson and Cooper, 1993) to calculate the shut-in pressure rise

rate (dpc dt):

Equation 2.9 considers the mud and wellbore compressibility and fluid loss into

formation.

(2.9)

dPc X y iiP mg Vs - < I edt x kvt + x ^ + x mvm

(2.10)


26

Lage, et al.(1994) reported gas kick experiments performed in a 1,310 m (4,298

ft) vertical training well. The well has a 400 mm (13 3/8 in) casing set at 1,310 m and

cemented up to surface. Inside this casing, a second 178 mm (7 in) casing was placed to

simulate the wellbore. A 48 mm (1.9 in) tubing string was used to inject air at the bottom

of the 178 mm casing, and it was placed in the annulus o f400 mm and 178 mm casings.

In this same annulus, an additional 48 mm tubing string was placed at 800 m (2,625 ft)

to simulate the casing shoe and circulation losses. Inside the 178 mm casing, a drillstring

composed of 121 mm (4 3/4 in) drill collars and 89 mm (3 1/2 in) drill pipe was run. A

special sensor sub was made to accommodate the pressure sensor. Four sensors were

placed at 302 m (991 ft), 600 m (1,968 ft), 877 m (2,877 ft), and 1,267 m (4,157 ft). Air

and water were used in four tests. They measured three velocities: bubble front, volume

centered, and bubble tail using data from the pressure sensors. They state that, if no gas is

present, the differential pressure is equal to hydrostatic pressure between two sensors. In

addition, they measured the bubble front velocity dividing the distance between two

upper sensors by the time elapsed between the beginning of differential pressure decrease

in the two upper sensors and two lower sensors. Next, they also measured the volume

centered velocity, but they assumed that the center of the largest gas volume (when the

differential pressure is minimum) is at the middle point o f two sensors. They assumed

that the air expansion and concentration changes are negligible as the air rises from the

center of two the lower sensors to the center o f the pair above. Therefore, the volume

centered velocity could be measured by dividing the distance between the lower and

upper pairs of sensors by the time elapsed between the minimum differential pressure


27

between these two sets o f sensors. Lage, et al. measured the tail velocity considering the

distance and differential pressure stabilization between two sensors. They observed no

significant difference among the velocities for open or shut-in well conditions. They

obtained an average bubble front velocity of 0.26 m/s (3,070 ft/hr), an average tail

velocity o f 0.09 m/s (1,063 fit/hr), and an average volume centered velocity of 0.08 m/s

(944 ft/hr) to 0.15 m/s (1,772 ft/hr). In addition, they derived an interactive equation for

the pressure build-up (choke pressure) prediction that fitted very well with experimental

data:

1 ln- K - K

X" K + vr -Pc

(2 . 11)


CHAPTERS

CIRCULATING KICK TOLERANCE MODEL

Deep-water drilling has intrinsic problems, such as low fracture gradients, high

pressure loss in subsea lines, overbalanced drilling due to a riser safety margin, generally

high permeability formations, and emergency riser disconnection problems. As a result,

key factors to successfully drilling deep-water wells are, first, a detailed well design and

drilling plan; and, second a close control while drilling to avoid kicks, loss o f circulation

and underground blowouts.

Therefore, circulating kick tolerance can be used during the well design, along

with the pore pressure and fracture gradients, to determine depths at which to set casing

strings. It can also be used while drilling to estimate the fracture risk of the weakest

exposed formation if a kick is taken and circulated. Based on this analysis, a decision to

stop the drilling and run the casing string may be made if the results show a dangerous

fracture risk.

A mathematical model of a kick simulator dedicated to calculating the circulating

kick tolerance is presented here. The proposed model is divided into submodels: a

wellbore model, gas reservoir model, choke line model, and upward gas rise velocity

model.

3.1 Wellbore Model

The wellbore unloading model includes the upward two-phase flow inside the

annulus (well/drillstring, casing/drillstring, and riser/drillstring). This model is based on

the model proposed by Nickens (1985). A similar approach was used by Santos (1989)

28


29

and Negrao (1994), but Santos’ program is restricted to only two annular sections. The

proposed model can theoretically handle any number of different annular sections, for

practical purposes the number was limited to 15 different annular sections in this study.

The model is based on: a) mass-balance equations (continuity equations) for the

mud and gas; b) a momentum-balance equation for the gas-mud mixture; c) equations of

state for mud and gas; and d) a correlation relating the gas velocity to the average

mixture velocity plus the relative slip velocity between mud and gas.

3.1.1 Continuity Equations

The continuity equations are founded on the principle of mass conservation.

Under unsteady two-phase flow conditions, the liquid phase continuity equation is given

by.

3.1.2 Momentum Balance Equation

The momentum balance equation is based on Newton's second law of motion,

which states that the summation of all forces acting on a system is equal to the rate of

i ^ V>H) Q (3.1)

where liquid holdup H is defined as:

volume of liquid in an annular segment volume of annular segment

(3.2)

and for the gas phase is given by:

(3.3)


30

change of momentum of that system. For two-phase flow the momentum balance

equation is given by:

The friction term, or frictional pressure gradient, is calculated using Beggs and

Brill’s (1973) correlation modified to account for the non-Newtonian characteristic of

drilling fluids. The Beggs and Brill correlation was adopted for this study because this

correlation can be used in inclined flow (directional drilling) or even in horizontal

drilling. Although the present study does not account for inclined wells, it can be

extended in the future.

The two-phase flow friction factor/ , is given by:

where the no-slip friction factor/*- is obtained from a Fanning diagram (Craft et al, 1962).

The no-slip friction factor used by Beggs and Brill is for a smooth pipe curve on a Moody

diagram. The ratio of the two-phase slip to no-slip friction e' is calculated as:

where (cp / ct) is the gradient pressure.

The elevation term or hydrostatic pressure gradient is given by:

I p = / f - (3.6)

s = (3.7)\ +0.01853 In X,

H' H ‘

A

-0.0523+ 3.182 In -0.8725 In


31

where the no-slip liquid holdup or input liquid content X is defined as:

(3 .8 )

If X I H 2 is greater than 1.2 or less than 1.0 then the exponent s is calculated from:

3.1.3 Equations of State

In deep-water drilling, only water-based mud is used because of environmental

pollution problems that could result from an emergency disconnection of the riser. As a

result, the drilling fluid can be considered incompressible for the well depth range of

interest. Hoberock, et al. (1982) studied the effect of this assumption and showed that an

error of order of hundreds of psi are possible in deep abnormally pressured wells. In the

case of deep-well drilling, or if oil-based mud is used, the effects of temperature and

pressure should be considered (Ekwere, et al. 1990). The reduction in bottom hole

pressure for well depths up to 4,572 m (15,000 ft) is not significant, and the mud density

(3.9)

The frictional term is calculated from:

(3.10)

where the mixture velocity vm is defined as:

v„ = v ,// + vjr(l - H ) (3.11)

and the two-phase no-slip density is defined as:

A,< = p,X + p g( l - X) (3.12)


32

can be considered as incompressible for conditions encountered today in deepwater

drilling operations. Therefore, the density o f mud is given by:

p, = constant (3.13)

As for the gas density, a real gas equation of state is given by:

= pM_ (3.14)* :RT

3.2 Gas Reservoir Model

Since little is initially known during well design or while drilling, about the

properties of the gas reservoir, a detailed reservoir model is not usually justified.

However, in the proposed simulator, two reservoir models can be chosen by the user: the

Thomas, et al. (1982) or the Al-Hussainy, et al. (1966) models.

In 1982 Thomas, et al. (in Element, et al., 1989) introduced the use of the

following equation:

nkhTi t . =

where: PD = ~ ln ( 'D +0.809) (3.16)

and <„ = ■■■ kt— (3.17)4>Pf cf r J

The approximate solution of the diffusivity equation (Equation 3.15) requires the

assumption of a constant gas flow rate. Since, during a gas kick, the bottom hole pressure

and fluid flow rate vary, this assumption is not true. Nickens made a slight modification

to Equation 3.15. He divided the gas formation into axial segments of thickness h, equal


33

to the rate of penetration (ROP) multiplied by the time step in use. Then he considered

that each segment flows independently o f the other. As a result, the total gas-influx rate is

then:

where N(t) is the number of segments at time t. This modification to the flow equation

removes the approximation that gas flow is axially symmetric within the exposed gas.

Implicit also is that the reservoir extends to infinity. In most kick control

situations, this assumption is acceptable because the gas flow time is short, and the

reservoir boundary is not reached. In contrast, simulation of small pockets of gas is not

allowed but should not occur in a serious underground blowout.

Santos used the Al-Hussainy, et al. (1966) equations, modified to account for

changes in flow rate and pressure, in his studies of diverter operations. The wellbore

pressure in an infinite gas reservoir produced at a constant flow rate, including skin and

the turbulence or non-Darcy effects, has the following expression:

(3.18)

0.367p j ~ L 5V

where the real gas pseudo pressure is defined as:

= 0[log(2.245/i)) + 0.87(5 + DO)] (3.19)

(3.20)

and the dimensionless time by:

kt (3.21)D


34

where the total compressibility may be approximated as:

(3-22)

The turbulence or non-Darcy factor is calculated with:

P-Mp-k£> = 0.159 z (3.23)

RpghrKTx

and the velocity coefficient for consolidated sandstone as:

P g = ~ ^ J k (3'24)

Since the bottom hole pressure and gas flow rate vaiy with time, the solution for

the wellbore pressure can be found by applying the principle of superposition for

different flow rates in the right hand side o f Equation 3.19, which becomes:

1 ^ ) - ^ ) ] ^ _ g ( g . , ) log[2245(,„- , o .,)]+0.87a(-S-+/X?„)

(3.25)

After algebraic manipulation of Equation 3.25, the flow rate can be obtained from the

solution of the following quadratic equation:

^ 0.87S + log(2245(,0 - O L . B - A - Q ^ Iog(2.245(,c - O )& ---------------o 5 td -------------- a + ----------------- MTO------------------= 0 (" '26)

where:

0367p J T

and??-i


35

The flow rate for each time step in the computer model is calculated through

Equation 3.26 using the bottom hole pressure in that time step.

The reservoir height or thickness (A) in Equation 3.27, necessary to calculate gas

flow rate, is considered variable with time as a function of the rate o f penetration while

drilling:

ht = R O P it ' - t , ^ ) (3.29)

A'</)

h = Y JK (3-30)i=0

3.3 Choke Line Model

A choke line is employed to carry fluids to the surface after the subsea blowout

preventers (BOP) are closed. The long and narrow (usually 3 inches) choke line in deep-

water leads to high velocity and consequently high pressure loss.

Elfaghi (1982) performed experiments using a full-scale model at LSU, consisting

of 914 m (3,000 ft) of 60 mm (2 3/8 in.) subsurface choke line. For single-phase mud

flow, both the Bingham plastic and the power law non-Newtonian models provided

acceptable comparisons with the observed data. For two-phase flow through the choke

line, the Hagedom and Brown (1965) and Beggs and Brill (1973) correlations provided

acceptable comparisons with the observed data. As a result, the Beggs and Brill

correlation was selected for this work for two-phase flow conditions. In addition, the

power law model is used for the single phase mud flow.

3.4 Upward Gas Rise Velocity Model

An empirical correlation relating the gas velocity to the average mixture velocity-

plus the relative slip velocity was determined using both the available data from flow


36

loop experiments and data from an experimental work with a 6,000 ft well using drilling

fluid and natural gas. Chapter V presents a more detailed description of the experimental

work and the proposed correlation, which is as follows:

vg = 1.425vm + 0.2125 (3.31)

3.5 Solution of the Differential Equations

The solution of the differential equations in Section 3.1 is achieved using the

numerical method of finite difference. This method was also used by Nickens and

Santos. Many techniques can be used to solve the differential equations by the finite

difference method. In the proposed model, a centered in distance and backward in time

with a fixed space grid technique is used because it is a stable method that does not

present a convergence problem. The flow path is divided into a finite number of cells.

Figure 3.1 shows a cell for two different time steps.

The finite difference formulation for the continuity equation in the space

derivative is approximated by:

(3.32)dU = Ue - U s ct Ar

and the time derivative by:

cU UA- U 3 .. Ub +Ui - U 2 - U \ a i 2 a t

where U is a function of r and t. Substituting these approximations into Equations 3.1

and 3.3, the finite difference formulation for the continuity equation becomes for liquid:

( v ; A # ) 6 - ( v ; P | f l ) s [ { P i H \ + { p , H \ - ( p , H ) 2

Ar 2 A/


37

z + Az

Az

FINITE CELL

AT TIME

t - At

FLOW

( 2 ) KNOWN

©Q KNOWN

4depth

:+ Az

FINITE CELL

AT TIME

t

© UNKNOWN

©( ? ) KNOWN

time FLOW

and for gas:

Figure 3.1 Finite difference scheme for a cell

hp,(i-g>L-[v>»a-/oLAr

■ +

[/> ,(!- tt)]t + [p /1 - tf)]s - [ / , .( ! - H ) \ - [p, (1-/J)],2 A/

(3.35)

= 0

The finite difference formulation for the momentum balance equation in the time

derivative is the same as Equation 3.33, but the spatial derivative becomes:

oU U6 +U2 - U 5- U l& 2Ar

(3.36)

and substituting Equation 3.36 into Equation 3.4 gives:

+[v.v,(i- #)], -[v.v.o- *oH”.v,(i- *)],+ +{v,V,* )6 *Wp,h\ -(v ,V ,» )5 *)]4 +

+[v> ,r(I - H ) \ - [vf p s(l - ff)]2 - [vsp ,(1 - //)], + ( v ,p ,H \ +(y,P,H)s - (3.37)

♦ ( £ ) , + ( £ )

(A £l + ( > 1 + fA p)'.A rJ, VA: ) , \A:J< \ A z) .

fiic


38

The calculation of the flow properties at point 6 in Figure 3.1 from the known

properties at points 1, 2, and 5 requires an iterative procedure. Points 1 and 2 represent

the flow properties in the previous time step (t - At) at the lower and upper boundaries,

respectively. Points 5 and 6 represent the same points as 1 and 2, but at the time step t.

Points 3 and 4 represent arithmetic averaging at the center of the cell at the t - A t and t

time steps, respectively. The procedure to calculate the two-phase flow properties at

point 6 in a cell is:

1) Assume an initial liquid hold-up at point 6.

2) Calculate the liquid velocity using Equation 3.34 at point 6.

3) Calculate the gas velocity’ using the empirical correlation (Equation 3.31) at point 6.

4) Calculate the gas density’ using Equation 3.35 at point 6.

5) Calculate the pressure using Equation 3.14 at point 6.

6) Use the flow properties, determined in steps 1 through 4, in the finite difference

approximation for the mixture momentum balance equation (Equation 3.37) and

solve for the pressure at point 6.

7) Compare the pressures calculated in steps 5 and 6. If the difference between them is

less than an arbitrary value, stop the procedure. Otherwise assume another liquid

velocity and repeat the process until it converges.

The discretization procedure is only applied to the two-phase region. A single cell

exists the first time, two cells for the second time, and so on. The process for each time

step starts in the bottom cell and ends in the uppermost cell that coincides with the two-

phase flow leading edge. With this procedure, the pressure at any given time step and


39

position can be determined. The flowchart for calculating the bottom hole pressure is

presented in Figure 3.2.

3.6 Simplification of the Differential Equations System

The procedure explained in Section 3.5 can be simplified with great benefit in the

computation time; it can be 10 to 20 times faster depending on the number of cells. The

simplification was made in the calculation of the liquid hold-up, which is calculated

directly from Equation 3.31. The simplified procedure is:

1) Calculate the superficial liquid and gas velocities.

2) Calculate the liquid hold-up and gas velocity directly from Equation 3.31.

3) Calculate the gas density using Equation 3.35 at point 6.

4) Calculate the pressure using Equation 3.37 at

5) point 6.


40

starti=l

i>N

time step= i *

Calculate pressure @ two-phase leading edge

STOP

Assume: Bottom Hole Pressure Pbh i=i+l

Calculate: vsl and vsg

I Pa - Pc I<sl

i=i

Assume: HI

Calculate: vl and vg

Calculate pg

Calculate: Pressure eq. 3.14

Pa


Pb

I Pa - Pb< e

j= j+ l

Figure 3.2 Flowchart of the complete program


41

starti=l

i >N

time step= i

Calculate pressure ffi. two-phase leading edge

STOP

Assume: Bottom Hole Pressure Pbh i=i+l

Calculate: vsl and vsg

1 Pb - Pc I< e !

Calculate: vl, vg, and HI


Pb

Calculate pg < ►

Figure 3.3 Flowchart of the simplified program


CHAPTER4

C O M PU T E R PR O G R A M AND R ESULTS OF N U M E R IC A L SIM U L A T IO N S

The procedures to calculate the kick tolerance, as explained in Chapter III, have

been implemented as a computer program, and are described in this chapter. In addition,

the developed software was first applied in a typical deep water well design and was then

compared with results from a commercial kick simulator for real drilling problem cases.

Furthermore, selection of the kick tolerance during well design and while drilling is

proposed here.

4.1 C om puter Program

A computer program was written in FORTRAN applying the theory previously

described. During the development phase of the program, the goal was to produce a

program that is fast, reliable, and suitable for available rig site computers.

The program includes four major scenarios:

1. Taking the kick while drilling (the gas enters into the well, mixing with pumped

drilling fluid).

2. Detecting the kick, stopping the mud pump, and making a flow check (the reservoir

produces gas).

3. Closing the well and observing the shut-in-drill-pipe-pressure (SIDPP) and the shut-

in-casing-pressure (SICP) (the reservoir still produces gas until the bottom hole

pressure equalizes with the formation pressure).

4. Circulating the kick out and keeping the bottom hole pressure constant (Driller’s

method).

42


43

The program can theoretically handle any number of different annular sections,

but for practical purposes it was limited to 15 different annular sections. Unlike most

programs that require the annular sections to be input, the new program calculates the

annular sections using the wellbore, casing, and drillstring configurations data.

The two-phase flow region is divided in cells, a necessary step to solve the system

of equations by the finite difference technique. The user can control the size or volume of

the cell. Normally a cell volume of one or two barrels was found to be adequate, but with

a cell volume of ten barrels the program will run faster. A direct tradeoff exists among

the cell size, computing time, and accuracy. A greater cell size allows the program to run

faster with some loss in the accuracy and sometimes with instability of the system.

Internally, the program uses one half of the cell volume input by the user in the

drill collar-wellbore annulus because the cell height can be high. On the other hand, the

cell volume in the large riser and drill-pipe annulus is fourfold because the height can be

small. Initially, a full model was developed, as shown in the flowchart of Figure 3.2.

Because this approach deals with two iterations (one for liquid hold-up and another for

bottom hole pressure), it is more suitable for use on a main frame computer. Using a

typical deep-water well with a cell of one barrel in volume, pit gain o f 30 barrels, and a

Pentium 90 MHz computer, the running time was about 50 minutes. Therefore, this

model has been found to be slow and not adequate for use at a rig site.

In order to achieve a faster run time, the model was simplified by calculating the

liquid hold-up directly from Equation 3.31, as shown in the simplified program flowchart

of Figure 3.3. Consequently, under the same conditions as the previous model, this


44

simplified model calculated the circulating kick tolerance in 5 minutes instead of the

previous 50 minutes. The accuracy o f the simplified model was found to be acceptable

and will be discussed later.

In all simulations, starting the pump was the most critical part of the overall well

control procedure. During the pump start-up, the smallest kick tolerance value was

achieved. This fact also was reported by Bourgovne, et al. (1978) in their studies of well

control procedures for deepwater drilling. The high pressure that developed at the

weakest exposed depth is due to a high choke line friction, which increases with water

depth. To minimize the frictional pressure loss, a slower pump kill speed or the use of the

kill and choke line in a parallel arrangement should be adopted. Unfortunately, a third

option, of using a larger diameter choke line, cannot be applied easily because choke line

diameter is a characteristic of the rig. Thus, the user can specify the start-up pump rate

and determine whether or not a parallel flow arrangement, using the choke and kill line,

will be used.

4.2 Results from a Typical Deep W ater Drilling Experience

A typical well design applied to drill deep water wells in Campos Basin, in

Southeast Brazil, is used here to simulate a kick and to calculate circulating kick

tolerance. The typical casing design up to the surface casing is shown in Table 4.1. The

structural casing is used because of the weakness of the soil at the sea floor that cause the

temporary guide base to sink. The structural casing was placed only by jetting in the past,

but today the structural casing is lowered with a single guide drilling base system (BUP

system) developed by Petrobras, w'hich is an improvement in the guidelines drilling


system. Temporary and permanent guide bases were replaced by the BUP system which

has these advantages:

a. A single guide base;

b. Reusable and mechanically retrievable guide funnel;

c. Allows guideline or guidelineless operations;

d. Cutting returns at mudline elevation, which prevents BUP burial by cuttings;

e. Minimum rig up time; and

f. Low *r costs.

Table 4.1 Typical casing setting used for a deep-water well in Campos Basin

CASING DIAMETER

(in)

THICKNESS

(in)

LENGTH BELLOW

SEA LEVEL (m)

GRADE

STRUCTURAL 42 12 BCONDUCTOR 30 1 1.2*- 1 60 X - 52

SURFACE 20

00*rti*

400 K - 55* f ir s t / w y ; jo in ts only

The selection of weight, grade, and coupling of casings were based on the high

loading conditions in the well head The forces involved in the casing head are

consequences of:

a) Currents at the sea bottom of about 2 knots acting on the riser and blow out preventer

(BOP) stack;

b) Watch circle of the dynamic positioned drill ship;

c) Weight of the BOP stack;

d) Inclination of the well head, which creates a momentum (mostly due to a inclination

of the sea floor); and


46

e) Mud inside the riser.

Calculations presented by Falcao et al (1985) show that, at the well head level,

the acting forces are about 240 tonf (529 Klbf) horizontal, 10 tonf (22 Klbf) vertical, and

130 tonf.m (940 Klbf.ft) momentum. About 10 m (33 ft) below the sea floor, the

maximum shear force of about 30 tonf (66 Klbf) occurs. Also the maximum momentum

of 608 ton.m (1,338 Klbf.ft) occurs at 4.5m (15 fit) below the sea floor with a shear force

of 10.5 tonf (23 Klbf). A typical casing setting profile used in Campos Basin is shown in

Figure 4.1.

DYNAM IC POSITIONED D R ILL SH IP

v — -i- 1—• J

W a te r dep th = 1OOO m

Asea f lo o r i—

^ BOP

ST R U C T U R A L C A SIN G £ « " (12 m)

CONDUCTOR 3 0 " (60 m )

SURFACE “ *-20" (400 m )

-I I- 13 3 /8"(1 5 0 0 m )

F ra c tu re G ra d ie n t =12 ppg"* ^ 9 5 /8 " (2800 m )

M ud W eigh t =9.8 ppg

G A S IN FLU X 1' [ N 9 i P o re P ressu re= 1 0 .5 ppg

T V D =3500 m

Figure 4.1 A typical well design for deep water drilling in Campos Basin


47

Low fracture gradients (Holden and Bourgoyne. 1982) are known to occur in deep

water wells. Campos Basin deep water wells are no exception. The results of leak-off

tests at the 20-in casing depth have shown lower values of about 10 to 11 lbm'gal

equivalent mud weight. In the beginning, to overcome this low fracture gradient, many

attempts were made to set the 20-in casing at a depth of 550 m (1805 ft) below the sea

floor, but the casing got stuck many times with little significant gain in the fracture

gradient. Because of this experience, setting the 20-in casing at a depth of 400 m below

the seafloor has become a standard.

The results using the simulator for a typical deep water well design is presented in

Figures 4.2. 4.3, and 4.4. The simulation represents a case using 15 bbl of pit gain, an

equivalent fracture gradient of 12 lbm/gal. mud weight of 9.8 lbm/gal. and a pore

pressure o f 10.5 Ibm gal Complete input data for this simulation is given in Appendix B

4.3 Comparison with Commercial Kick Simulator

Two real drilling cases were analyzed. The first case, a well drilled in Campos

Basin, was simulated by Lage, et al. (1994) using the RF kick simulator developed b\

Rogland to analyze two options of casing design:

a. Option 1

• 30-in casing from 345 m to 420 m


• 16-in casing from 345 m to 2.490 m

• 11 3/4-in casing from 345 m to 4,290 m

• 9 5/8-in liner from 4,190 m to 4,740 m

• 7-in liner from 4,640 m to 5.600 m


Pres

sure

®

Frac

ture

D

epth

(p

si)

Cas

ing

Pres

sure

(p

si)

48

KICK TOLERANCE

<sotI

Kiel fluids enter the wellOC*

Gas let ding edge atthe casnig shoe depth

0 20 40 60 80 100 120Time (min)

CASING PRESSURE6000

5000

4000

3000B low out p re v e n te r2000

closed1000

0 20 40 60 80 100 120Time (min)

PRES S URE ® FRACTURE DEPTH6000

5000

4000P u m p s ia r te d3000

2000

1000

0 20 40 60 80 100 120Time (min)

Figure 4.2 Kick tolerance, casing pressure, and fracture pressure at casing depth for a typical deep-water well


49

PIT VOLUME

.*=- 7000

3000-

5 2000 -

41ua.01s . 1000

100

XS

Kick wafe detected

G as a t su rface

4020 60 SO0 100 120Time (min)

BOTTOM HOLE PRESS I'RE

20 40 60 80

DRILL PIPE PRESSURE

100 120 Time (min)

I20 40 60 80 100 120

Time (min)

Figure 4.3 Pit volume, bottom hole pressure, and drill pipe pressure for a typical deep-water well


50

GAS FLOW RATE

80 10040 60 1200 20Time (min)

GAS LEADING EDGE DEPTH

2000

Z 4000- ■ ex5 6000-et

8000-

J lOOOOr

5 12000-

Gps a t surface

100 12040 60 80200Time (min)

Figure 4.4 Gas flow rate and gas leading edge depth for a typical deep-water well

b. Option 2





• 7 5/8-in liner from 4,190 m to 4,740 m

• 5 1/2-in liner from 4,640 m to 5600 m


51

A fracture gradient of 2.10 gr/cm3 (17.5 lbm/gal) was expected at the 9 5/8”

casing shoe depth (4,740 m) for option 1 with a mud weight of 1,92 gr/cmJ (16 lbm/gal).

Additional input data from well RJS - 457 that was used for this comparison is given in

Appendix B. Figure 4.5 shows a comparison of results among the proposed model, the

RF kick simulator, and the simplified model for the drilling phase between 4,740 m to

5,600 m.

Well: RJS - 45717.4

Simplified mode!17.2

RF kick simulatorS. 17.0

Proposed simulator16.8

16.6

U 16.4

16.2

16.00 10 20 30 40 50 60 80 90 10070

Pit gain (bbl)

Water depth: 1,132 ft Fracture pressure: 17.5 ppg@ 15,552 ftWell depth : 18,374 ft Casing 9 5/8" @ 15,552 ftM ud weight: 16 ppg Open hole: 8 1/2 "

Figure 4.5 Kick tolerance for the well RJS - 457

The simplified model considers that the kick enters into the well as a slug and

remains as a slug throughout the upward path of the kick circulation. Although this


52

simplified approach is simple to calculate, it is very conservative and can result in an

expensive well design. On the other hand, using a commercial kick simulator to calculate

kick tolerance is time consuming, because the simulator is not specifically designed to

calculate the kick tolerance parameter. Figure 4.5 shows the kick tolerance as a function

of the pit gain volume and the pore pressure that might be encountered during the

drilling. When drilling a wildcat well the formation pressure or pore pressure is

frequently an unknown parameter. For this reason, the analysis was made as a function of

pore pressure because this parameter can greatly influence the final decision regarding

which option should be selected.

A second case, a well drilled offshore of Ceara State, Northeast Brazil, was also

simulated by Lage. et al. (1993) using the RK kick simulator. The well CES - 112 had

been drilled in water depth of 1.314 m (4,311 ft) with an 8.5-in bit when the possibility

that a high pressure formation could be encountered was raised, jeopardizing the drilling

operation. The main concern was whether to continue drilling to the depth of the original

well design or to set the casing early. The initial plan was to place the 7-in casing at the

depth o f4,500 m (14,765 ft). After analysis, the decision was made to continue according

to the previous plan. The complete input data from well CES-112 that was used for this

comparison is given in Appendix B. Figure 4.6 shows a comparison of results among the

proposed model, the RF kick simulator, and a simplified model for this well.

The results of kick tolerance calculations using the proposed circulating kick

tolerance model have shown a good agreement when compared with results of a

commercial kick simulator. The advantages of using the proposed model are that the


53

program can run in the available rig site computers, is reliable, and is much faster than

the currently available commercial simulators.

Well: CES 11210.4

£ 10.0

Simplified model

RF kick simulator9.8

Proposed simulator

9.6100 1200 40 8020 60

Pit gain (bbl)

Water depth 4,311 ft Fracture pressure: 10.5 ppg @ 12,993 ftWell depth : 14.764 ft Casing 9 5/8" @ 12,993 ftM ud weight: 9.5 ppg Open hole: 8 1/2 "

Figure 4.6 Kick tolerance for the well CES-112

4.4 Selecting Kick Tolerance

Since the shut-in kick tolerance can be calculated using an ordinary calculator,

many drilling plans have a value for the kick tolerance (for a given pit gain) with which

compliance is expected at the well site. An example of the kick tolerance notation is 0.5

lbm/gal' 30 bbl, which should be understood as a kick tolerance o f 0.5 lbm/gal with a pit


54

gain of 30 barrels. As drilling proceeds, the kick tolerance is calculated, and if it falls

below 0.5 lbm/gal, the drilling is interrupted.

In contrast, the calculation for the circulating kick tolerance is more complex and

involves a kick simulator. Furthermore, the simulations with a dynamic model have

shown that for deep water wells the worst case occurs when the pump starts to circulate

the kick out of the well, not when the well is shut-in. Therefore, a circulating kick

tolerance should be used, which can be defined as a difference between the maximum

circulating pressure and the fracture pressure, at the w-eakest exposed formation depth,

expressed in equivalent mud weight:

K!c = P-f- ~ Pf™ (4.1)D,*

Since the circulating kick tolerance cannot be calculated as a single equation, a

kick simulator should be used to calculate this value.

4.4.1 Selecting Kick Tolerance for Well Design

After the casing setting depths are determined, the circulating kick tolerance

should be calculated to confirm those depths. Selecting the pit gain is the most important

step in kick tolerance calculations, eclipsing all other unknowns such as reservoir and

mud properties, pore pressure, and temperature. A particular pit gain should be adopted

based on the ability o f the rig crew to detect a kick. Confirming the casing setting depths

using a high selected pit gain can be expensive because additional casing strings may be

necessary. On the other hand, using a small pit gain that the drilling rig crew cannot

detect can be very' costly if a kick or blowout occurs. As a result, three levels of pit gain

are proposed here to be used in well design:


55

a. Level 1:30 barrels of pit gain

b. Level 2: 20 barrels of pit gain

c. Level 3:10 barrels of pit gain

If level 3 is adopted, additional procedures should be taken, such as:

a. Use a mud logging unit to monitor the pit gain and to calculate the pore pressure

while drilling.

b. If a drilling break occurs, close the BOP without any flow-check.

c. The hard shut-in should be adopted to avoid further influx.

d. If the pore pressure increases, intermediate well logging is recommended to estimate

the pore pressure from a sonic log.

e. Someone must monitor the pit level constantly.

f. Each person on the rig should be advised about the meaning of level 3. The dog

house safety meeting should cover this before each tour.

The minimum value of the circulating kick tolerance that is obtained when

adopting one of the pit gain levels should be reported in the drilling plan Moreo\er, the

complete input data used to calculate this value should also be reported for comparison

purposes if a circulating kick tolerance must be calculated while drilling.

4.4.2 Selecting Kick Tolerance while Drilling

If a Level 3 pit gain is adopted in the drilling plan, or if the pore pressure

increases, the circulating kick tolerance should be calculated each 30 m (100 ft) drilled or

each time that the mud weight changes. The pit gain to be simulated should be equal to

the adopted pit gain in the drilling plan, or should be one that the crew can detect. Based


56

on this calculation, a decision to stop and run the casing or continue the drilling as

planned can be made.


CHAPTER 5

EXPERIMENTAL WORK

The experimental procedure for determining the upward gas rise velocity during

well control operations is presented here. This procedure was performed using a full scale

well and natural gas. Despite many studies in this area using flow loops and well, as

described in Chapter II, no experiment that had used a full scale well with natural gas as a

gas phase was found in the literature reviewed. During this project, thirty seven

experiments were performed — 8 with water and 29 with drilling fluid.

5.1 Description of a Full-Scale Well: LSU No. 2

The experiments were carried out in the existing LSU No. 2 w'ell (also known as

the DEA well), as shown in Figure 5.1, located at the Petroleum Engineering Research

and Technology Transfer Laboratory (PERTTL) at Louisiana State University in Baton

Rouge, Louisiana. The drilling and completion o f this well was funded through the

Drilling Engineering Association (DEA Project 7). The LSU well No. 2 is a vertical well

that is 1,793 m (5,884 ft) deep and cased with 244 mm (9 5/8 in) casing. The w’ell is

completed with a 32 mm (1 1/4 in) gas injection line that runs concentrically inside a 89

mm (3 1/2 in) drilling fluid injection line. The well also contains 60 mm (2 3/8 in)

perforated tubing (94 half-inch holes per joint) that serves as a guide for w'ell logging

tools to be run in the annulus without risk of the logging cable wrapping around the drill

string and becoming stuck. The research facility also has these features: a choke manifold

containing four 15,000 psi adjustable drilling chokes; a 250 hp triplex pump; two mud

tanks with a combined capacity of 550 bbl; and a high capacity mud-gas separator.

57


58

Loggkig Cable

H *

y \2 3/8” J55 Perforated

Tubing (4.7 Ibf/ft)94 x 1/2" hoies/jont

Pressure On-Line Sensor

Pressure Recorder Sensors ------

SSlffTVD

S822'T\D

Wei Logging Tiixiar

L

II

T

958" Casing

0-3170 f t-53.5 lb/ft 3170-3908 ft -47.0 lb/ft 3908-5553 ft - 43.5 lb/ft 5553-5876 ft - 53.5 lb/ft 5876-5884 ft - 47.0 lb/ft

31/2'J55 EUE Tubing — (93 lb/fit)

1j66"N 80 Tubing (3j02t>/ft)Last joint perforated

40x1/4" holes

Gasnjection Line

Mri njection Line

4" Gas/Fluid Return line

Figure 5.1 LSI' No. 2 well completion schematic


59

5.2 Methodology of Experimentation

A drilling fluid with properties matching those used to drill deep-water wells in

the Campos Basin, offshore of Brazil, was used, and it was circulated down the annulus

between the 89 mm (3 1/2 in) and 42 mm (1.66 in) tubing at the desired mud flow rate

with returns taken from the 244 mm (9 5/8 in) casing.

The gas was injected through the 32 mm (1 1/4 in) tubing, or was pumped down

at the desired injection rate through the annulus between the 89 mm (3 1/2 in) and 32 mm

(1 1/4 in) tubing. Before injecting the gas into the well to simulate a kick, the gas was

compressed up to 4,200 psi. This pressurization was accomplished using three 610m

(1,200 ft) storage wells cased with 7-in. 38 lb/ft N-80 and P-l 10 casings connected to a

152.4 mm (6-in) natural gas pipe line that operates at 700 psi pressure. First, one w'ell

annulus was filled with gas from the pipeline, and then the gas was compressed by

pumping mud down the tubing forcing the gas into the annulus of the other well. The

final desired pressure was obtained by alternating the fill-and-compress cycle.

After compressing the gas, it was injected or pumped down until the desired pit

gain was obtained. Following this, the circulation of the gas kick began until all the gas

was out of the well. In most o f the experiments, a back pressure of 150 to 200 psi at the

choke was kept by using an automatic choke (Warren choke). This procedure was used to

avoid a dangerous situation in case a large volume of gas reached the surface. After the

mixture of gas and drilling fluid left the well, it passed through a separator, where the

drilling fluid and gas were separated. The liquid phase returned to the mud pit, and the

gas phase was directed to the flare line, where it was burned. Some parameters were


60

varied in the experiments, such as the water or drilling fluid circulation rate, gas pump-

down circulation rate, kick size measured by the pit gain, and position of the downhole

pressure sensors. Table 5.1 shows the test matrix for the water and natural gas

experiments. Tables 5.2 and 5.3 show the test matrix used for drilling fluid and natural

gas experiments. Table 5.4 shows the drilling fluid properties used in the experiments.

Table 5.1 Test matrix for water and natural gas experiments

Experiment Pit gain Pump speed(b bl) (spm)

# 10 20 0 32* 62* 90*W1 10 0W2 10 32W3 10 62W4 10 90W5 20 0W6 20 32W7 20 62W8 20 90

32* spm — vl= 0.64 ft/sec 62* spm — vl= 1.24 ft/sec 90* spm — vl= 1 80 ft/sec

Table 5.2 Test matrix for mud and natural gas experiments with gas injected through tubing

Downhole Pressure Sensors 1200ft Apart

Testpit gain Pump

speedChoke

back pressure Note# <bbl) (spm (psi)

10 20 0 32 62Ml 10 62 170M2 0 choke closed Failure due to valve leakM3 10 32 100 Downhole pressure lostM4 20 62 170 Downhole pressure lostM5 20 0 choke open Downhole pressure lostM6 10 32 170M7 20 0 choke closed


61

Table 5.3 Test matrix for mud and natural gas with sensors 1,200 ft apart

Gas Was Pump Down Through 3.5 J55 Eue (93 #/ft) X 1.66” N-80 (3.02 #/ft) Innulus

TestU

Gas pump down speed

(spm)

Pump speed (spm)

Choke back pressure

(psi)Note

62 82* 0 32 62M8 82 0 choke openM9 82 32M10 62 62 170 on line data was lostMil 62 32 170 middle downhole sensor failedM12 62 62 180 middle downhole sensor failedMl? 82 62 170 middle downhole sensor failedM14 82 0 choke closed middle downhole sensor failed

82* spm — v=I 64 ft/sec

Table 5.4 Test matrix for mud and natural gas with sensors 100 ft apart

Test#

Gaspumpdownspeed(spm)

Position of downhole

tools

Pumpspeed(spm)

Viscousfluid

Chokeback

pressure Note

62 82 b* m* 1 t* 0 32 62 yes noM15 82 j B 62 N 0 one sensor failedM16 62 B 62 N 0 one sensor failedM17 82 B 62 N 170 one sensor failedM18 82 M 32 N 170 one sensor failedM19 82 M 62 N 180 one sensor failedM20 82 M 0 N 170 one sensor failedM21 82 M 62 N 170 one sensor failedM22 62 M 32 N 170 one sensor failedM23 62 M 62 N 0 one sensor failedM24 82 T 32 N 200 one sensor failedM25 82 T 0 N choke open one sensor failedM26 82 T 62 N 200 one sensor failedM27 82 M 62 Y choke openM28 82 M 0 Y choke

closedM29 82 M 0 Y choke open

b* = bottom (on line tool @ 5.422 ft) m* = middle (on line tool @ 2.761ft) t* = top (on line tool @ 100 ft)


62

Table 5.5 Drilling fluid properties utilized in the experiments

Experiment#

Mudweight(lb/gal)

Marshviscosity

(sec)

Plasticviscositv

(cp)

Yieldpoint

Gel strengthlOsec IOmin

lbf/lOOsq ftMl 9.9 54 15 5M2 9.9 54 15 5

M3-M4 9.9 53 15 5M5 9.9 54 15 5

M6 - M7 9.9 53 15 5M8 9.9 54 14 5

M9-M10 10.0 53 12 5M il -M12 9.8 49 10 2

M13 9.6 62 15 8M14 9.6 58 15 7

M15-M16 9.7 40 12 9 o 10M17-M18-M19 9.6 38 11 6 2 5M20-M21 -M22 9.6 40 12 3 2 9

M23 - M24 9.6 42 12 6 2 15M25 - M26 9.6 43 12 6 2 13M27 - M28 9.7 78 30 15 4 25

M29 9.7 78 30 15 4 25

5.3 Instrumentation of the Well

A data acquisition system from National Instruments was used to acquire and

record data and included:

a) The SCXI-1200: A data acquisition and control module that acquires the signal in the

SCXI-1200, digitizes the conditioned analog signals, and transmits the digital data to

the parallel port o f the PC.

b) The SCXI-1100: A 32-differential channel multiplexer that allows the module to

sample the volt source.

c) The SCSI -1001: A chassis that can house 12 modules.

d) The SCXI-1124: A 6-channel isolated digital to analog converter (DAC) module.

e) The SCXI-1163: A-32 channel isolated digital output module.


In addition, a data acquisition and recording program was developed using

LabView for Windows (a graphical programming software) and was used with the data

acquisition system. The following parameters were continuously monitored using the

data acquisition system and program:

a. Drill pipe pressure (psi);

b. Casing pressure (psi);

c. Gas-injection line pressure (psi);

d. Down-hole on-line pressure (psi);

e. Pump speed (spm);

f. Percent of gas-in-mud at the shale shaker (%);

g. Gas flow in (MSCF/hour);

h. Gas flow out through 12-in. line (MSCF/hour);

i. Gas flow out through 4-in. line (MSCF/hour);

j. Gas flow out through 1-in. line (MSCF/hour);

k. Gas flow out through 0.5-in. line (MSCF/hour); and

1. Pit volume (bbl).

In addition to one wired-to-surface downhole pressure sensor, three downhole

pressure recording sensors monitored the pressures developed at desired depth during the

well control experiments. The pressure recorders (model EMR710) used were from

Geophysics Research Corporation (GRC). These recorders acquire and record about

21,000 pressure points. The recording interval could be programmed with a minimum

time of 3.8 seconds. The on-line pressure sensor was connected to the surface through a


64

logging cable to the Schulumberger logging unit. The three downhole pressure recorders

were connected to each other and to the on-line sensor with a single strand wireline

(slickline).

A modification was made in the gas-out or vent line gas measuring system. The

previous system had only a 12-in Daniel’s Senior orifice meter installed. A 4-in Junior

orifice meter, a 1-inch honed flow section, and a 0.5-inch honed flow section were added

as shown in Figure 5.2. The measuring system of 12,4, 1, and 0.5-inch configuration was

chosen based on orifice calculations that overlap the expected gas flow rate. The results

of the calculations are presented in Table 5.6.

Orifice(4.625 ’) Valve

1.625

Valve Valvi

OrificeValve 0.5" 0 . 2 "

Figure 5.2 Gas flow out measurements system

The gas could be diverted into different line sizes by opening and closing

pneumatic valves using a switch board. The gas flow out was measured initially with a

12-in line, and as the gas flow rate decreased, the flow was diverted to the 4-in line, and

so on. An accurate gas flow out measurement was important because it could be used to

calculate the gas distribution profile along the well, which was one of the objectives of

this research. Unfortunately, the gas flow out measurements for the different orifices did

not overlap as expected and could not be measured continually. When the gas flow- rate


measurement for a given orifice size was minimum or zero, the gas was diverted to the

next smaller line, but sometimes the maximum flow rate for this new orifice size was

exceeded. As a result, the gas had to be diverted back to the original line, and the system

did not measure any gas flow.

The gas flow rate was calculated using the Daniel model 2500 flow computer that

acquires signals for differential pressure, absolute pressure, and temperature.

Table 5.6 Gas flow out calculations for gas measurements system

Linediam eter(inches)

Orificediam eter

Differential pressure

(inches o f water)

Flow ra te (M SCF/hour)

12 4.62567.0 250,0007.28 83,3330 65 25.000

4 1.62563 3 30,00044.0 25.0006.81 10,0000.60 3,000

1 0.500100.0 3,655

65 2,94110.55 1.2180.92 365

0.5 0.200

47.5 40026 30011 200

2.8 1001.8 80

0.69 50

5.4 Methodology Used to M easure Gas Rise Velocities

The velocities of the kick front (leading edge), the peak gas concentration, and

the tail of the two-phase region were calculated through an analysis of the measured

differential pressures. The rationale of this analysis was that if no gas is present between


66

two consecutive pressure sensors and mud is not being circulated, the differential

pressure should reflect the hydrostatic pressure between them. Also, when mud is being

circulated, the differential pressure between two sensors should be equal to the sum of

the hydrostatic pressure and the pressure losses between them.

When the gas front reached each sensor, the differential pressure began to

decrease, denoting the arrival o f the bubble front. Thus, the velocity o f the front could be

estimated by dividing the distance between the sensors by the elapsed time between the

first arrival o f the front. Figure 5.3 ilustrates the sensor positioned and the parameters

used for this estimate. The bubble front velocity between sensors 3 and 4 could be

estimated if the distance d3A and the time elapsed between the observed initial decrease

in differential pressure between sensors 2,3 and sensors 3,4 is known by using the

following equation:

frontSAini^p (5.1)

S 1

- i — S 2

t2,3S 3

d3,4S 4 — L .

Figure 5.3 Downhole pressure sensors disposition


Similarly, the tail velocity could be calculated as the distance between two

sensors (for example, sensors 2 and 3) divided by the elapsed time to stabilize two

adjacent differential pressures:

In general, when the differential pressure between two sensors is a minimum, the

largest amount of gas is present between the sensors, but the exact position of the peak

concentration is not known. If it is assumed that the peak concentration occurs at the

mid-point between two sensors, then the velocity of peak concentration can be computed

as the distance between two mid points (e.g. at the mid-point between sensors 3 and 4,

and at the mid-point between sensors 2 and 3) divided by the elapsed time between them

when the minimum values of differential pressure were recorded in the two adjacent

well segments.

(^3.4skj6.V ^2.3 s a b ip (5.2)

v. 2 2(5.3)


CHAPTER 6

EXPERIMENTAL RESULTS

The results of the experimental work are presented in two forms: first, data

acquired during a typical experiment are shown in graphs as functions of time; second,

the results of the experimental work described in Chapter V are presented here in Zuber-

Findlay plots. In addition, a simplified gas distribution profile is proposed based on

observation of the data.

6.1 A Typical Experiment

The data from each downhole pressure recorder (GRC EMR710) was downloaded

to a file in a PC computer using the parallel port. In addition, all the data from surface

sensors and the on-line downhole pressure sensor were recorded in a file using the data

acquisition system (DAQ) and a special computer program developed for this project

using LabView. Then, the four files (three from EMR710 sensors and one from DAQ)

were combined and adjusted to the same time scale. Since a time delay between the clock

from the EMR710 sensors and the DAQ system was observed, the time was corrected.

This was accomplished by observing a major pressure change at the beginning and end of

each experiment, for example, pump start-up and pump shut-down. Typical data collected

during the experiment are shown in Figures 6.1 through 6.3. These data and graphs are

from experiment M9 in which the gas was pumped down at 82 spm (v=1.64ft/sec), and

the kick was circulated out at 32 spm (v=0.64 ft/sec). Differential pressures used to

calculate gas rise velocities are shown in Figures 6.4 and 6.5.

68


Down

hole

On-

line

Pres

sure

(p

si)

Down

hole

Pres

sure

(p

si)

69

3000

Bottom sensor

Middle se nsor2000

1500 •Top sensor

10000 20 40 60 80 100 120 140 160 180 200

Time (minutes)

1000

900

800

700

600

500

4000 20 40 60 80 100 120 140 160 180 200

Time (minutes)

Figure 6.1 Example of dow nhole pressure data


70

600Gas Flow In

G is FlovO ut 1:5 In.500

200 in.c

100

20 80 100 120 140 160 180 2000 40 60

3500

3000

C- 2500uK 2000oclo 1500C.

£1000

500

0

Time (minutes)

Ik 1

mm

- ---

0 20 40 60 80 100 120 140 160 180 200Time (minutes)

Figure 6.2 Example of gas flow rates and drill pipe pressure


71

500

400

C.IT 300

m 200’{ftU

100

00 20 40 60 80 100 120 140 160 180 200

Time(minutes)

300 300

250 250iii: volurr

200 200

§ 150“ 150gas jlumped down pump speed increased

£ 100 100

pumf pressure

0 20 40 60 80 100 120 140 160 180 200Time(minutes)

Figure 6.3 Example of casing pressure, pit volume, and pump speed


choke cl oss

ed

cho te opei ined

j t------ r

ch ake wi ie opei ined

! ■ > «

nr

. y i. , i

Pump

sp

eed

(spm

)

72

700ONLINE itND CASING

s 600

500

!= 400

3000 20 40 60 80 100 120 140 160 180 200

Time (minutes)

650

\ 6000 k.

1 550!sco

§ 500 d

4500 20 40 60 80 100 120 140 160 180 200

Time (minutes)

Figure 6.4 Differential pressure between on-line and casing and between downhole and pressure recorders

f|o LE PRES S j RE R k o RpDO\\7V

Bottom - Middle s >nsors


73

700C P DO1 VNHOLE R IC O R I ER

650

8 600

fc 550

500

-= 450

!= 400

350

3000 20 40 60 80 100 120 140 160 180 200

Time (minutes)

900BOTTOM HOLE PRES AND BOTTOM RECO

SURERDER

800

* 700

t 600

400

3000 20 40 60 80 100 120 140 160 180 200

Time (minutes)

Figure 6.5 Differential pressure between top and on-line sensors and between bottom hole pressure and bottom sensor


74

6.2 Zuber - Findlay Plot

The leading edge gas velocities obtained from experimental data are shown in the

Zuber - Findlay plot of Figure 6.6 for different superficial liquid velocities. This data is

plotted with published flow' loop data, as shown in Figures 6.7 and 6.8, in w'hich a fair

agreement can be seen between the present and previous experimental work. The

regression analysis of Figure 6.8 provided the empirical correlation for gas rise velocity

that was used in the kick tolerance computer program:

vg = 1.426vm+0.2125 (6.1)


Gas

velo

city

(ni/s

ec)

75

Mixture velocity (ft/sec)0.0 1.0 2.0 3.0

2.0

- 6.01.8

1-1= 0.64 ft, sec1.6-i= 1.24 ft sec

-5.0

1.4

-4.01.2slope = 1.4

1.0

-3.0

0.8

- 2.00.6

0.4

- 1.0

0.2

0.0 hO.O0.0 0.2 0.4 0.6 0.8 1.0 1.2

MixtureveIocity(m/sec)

Figure 6.6 Zuber - Findlay plot of experimental data


Gas

velo

city

(ft/s

ec)

76

Mixture Velocity (ft/sec)0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Johnson and White (1990)V Nakagawa (1990)G Mendes (1992)□ Wang (1993)♦ Ohara (1995) j

f - 1 2 .0

- 10.0

Vg = 1.42575 Vmix + 0.2125 R*2 =0. 96

0.0 0.5 1.0 1.5 2.0 2.5 3.0Mixture Velocity (m/sec)

Figure 6.7 Zuber - Findlay plot of the present and previous flow loop experiments


Gas

V

eloc

ity

(ft/

sec)

CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

7.1 Conclusions

Deep-water exploration and development are now a reality, and hydrocarbons

have been produced from water depths as much as 1,027 m (3,370 ft). However, deep

water drilling poses special problems, such as low fracture gradients, high pressure loss in

choke lines, overbalanced drilling due to a riser safety margin, and emergency riser

disconnection problems. Therefore, special care must be used when planning and drilling

these wells. The kick tolerance concept is a powerful tool that can be used during well

design, along with the pore pressure and fracture gradients, to determine depths at which

casing should be set. In addition, kick tolerance can be used during drilling to estimate

the fracture risk of the weakest exposed formation. This parameter can be used to stop the

drilling and run the casing string and to regulate drilling activities by governmental

regulatory agencies.

1. The proposed simplified computer model, which calculates the liquid hold up

directly from the empirical equation of Zuber and Findlay, not only saves computing

time, but has been shown to be accurate when compared with a commercial kick

simulator. Furthermore, the developed computer program is suitable for use with the

available rig site computers.

2. The minimum kick tolerance values for deep water wells in all computer simulations

performed were found to occur at the beginning of the circulation to remove the kick

out of the well. This fact is due to the high pressure loss inside the long choke line.

77


78

3. Results of gas rise velocity obtained using flow loop data and the present full scale

well experiments are in a close agreement.

4. Based on the experiments results, a simplified triangular gas distribution profile along

the upward migration of the gas is proposed. The accuracy of circulating kick

tolerance calculations may be further improved with the use of this distribution

profile.

7.2 Recommendations for Future W ork

7.2.1 Gas Distribution Profile

Even though extensive data were collected during experimental work, a fully

study of the gas distribution profile was not possible because of time restraint.

Improvement in the kick simulator may be made through prediction of the gas

distribution profile along the flow path in the annulus. The use of a proposed triangular

gas distribution profile (discussed later) in the circulating kick tolerance simulator is

strongly recommended.

The kick tolerance can be calculated easily if the gas distribution profile along the

upward path of gas migration is known. The differential pressure between two pressure

sensors shows the hydrostatic pressure between them if no gas nor liquid is flowing. If

only liquid phase is flowing then the differential pressure shows the hydrostatic pressure

plus the pressure drop due to friction losses between the sensors. As the gas flows

between two sensors, the differential pressure drops until the gas starts to leave the

interv al between sensors. This fact can be transformed in calculation of gas fraction as a

function of time for a given interval between two sensors by:


79

Api (7.1)

where the numerator represents the difference between two pressure sensors and the

denominator represents the initial differential pressure (no gas is present between two

sensors). Figure 7.1 shows calculations for the gas fraction as a function of time from the

experiment for migration with the choke closed.

However, the main interest here is not the gas fraction as a function of time for a

given interval as shown in Figure 7.1, but how the gas fraction profile will van,' along the

well. For a fixed time an average gas fraction can be picked up from the graphs on Figure

7.1 and plotted as a function of depth as shown in Figure 7.2. Appendix C shows more

examples of gas distribution profiles as a function of time and depth.

7.2.1.1 The Triangular Gas Distribution Profile

Observing the Figure 7.2, the gas fraction profile as a function of depth may be

approximated by a triangle. Figure 7.3 shows a scheme of section of the well and the

proposed triangular gas distribution profile. The triangular gas distribution profile is a

function o f the two-phase leading depth:

where hle(Q) = Initial two-phase-flow depth

The length of the base o f the triangle or the two-phase flow interval is given by:

(7.2)

(7.3)

where hlpf{ 0) = Initial two-phase-flow height


80

T ype o f ex p e rim en t: M igration w ith choke closed E xperim ent: M7

s 0.1501 °-10 t 0.05

~ 0.00

: Interval == 0 - 1,000« 1 J U U

i1 J T T1 U l _________

0 50 100 150 200 250 300Tim e(m inutes)

5 0-15 ̂ Interval f 1.000 - 2,

Z 0.10

200 250 300T im e (m inutes)

0. 10 -

0.05-1/3 V.V+.

o.oo-

i Interval = 2,235 - 13.470 ft I! !

] k i i/ V i !

1 ' 1 i i t

50 100 150 200 250 300Tim e( m inutes)- 0.15

cZ 0.10e;

5 0.05

0.000 50 100 150 200 250 300

es

0.15-

0.10-

0.05-

0.00-

Tim e(m inutes)

4 Interval = 4 ,705- ?,822 ft

3

l

Oft

On-line 1,000 ft

Top

2,235 fi

Middle

3,470 ft

Bottom

U 4,705 fi

5,822 ft

0 50 100 150 200 250 300Tim e(m inutes) j TD = 5,884 ft

F igure 7.1 G as frac tio n between sensors fo r d ifferen t dep ths an d tim es fo r experim en t M l


Depth

(ft

) De

pth

(ft)

Depth

(ft

)

SI

Experim ent:M 7

01000

2000

3000

I

4 0 0 0 i

5000o cs -a- >o 00 oo o o o o —o' © o d d ©

Gasfraction

0-1000

- 2000 -

oD

4000

5 0 0 0 -™o cs rr o oo o© © © © o —d o ' d d d d

Gasfr;

0-1000-

2000-

oO

4000-

5000-

IIF ■— ,—.

9——,—

O TT \C 00O O C O Od o d d o

Gasfraction

2000 -

3000- oQ

1000- • 2000 -

■3000-

4000-

5000-

■—

>*

o o o o o o Gas fraction

O CN TT so 00 oo o o o o —o o o o o o

Gasfraction

110.03 min

g-3000Q

4000-J

C tN -o- O 00© o © c ©© © © © c

Gasfraction

■ ■ 130.02min

|

yyiio o oo oO O O O O «—O 0 * 0 0 * 0 o’

Gasfraction

40 0 0 -

PTTT TTT1 PT TTT1

lOOOi

■ 2000 -

4 0 0 0 i

5000o CN TT so oo oo o o o o —o o o © o o

O rsj tt O oco o o o oo o © o' o

Gasfraction

Figure 7.2 Gas fraction profile as a function of depth for various times


82

In Equation 7.2, one can observe that when hle(t)=0, the two-phase flow has

reached the top of well and starts to leave the well.

The average gas fraction can be defined as:

VoIgJ 0a( t ) =4 » V ( 0

(7.4)

max

wjixfmud Depth

Figure 7.3 Proposed triangular gas distribution profile

If h/r(t) > 0 implies that the two-phase flow has not reached the surface, and the

volume of gas can be defined as:

o)m p (o) T( t ) (7.5)r(0) p{t) T(0)

w'here VoI%a!L{0) is the initial gas volume.

The gas will expand as it migrates upward, but its volume at standard conditions

must be the same. This condition will change when the gas reaches the surface After

this, a mass balance must be applied to calculate the volume of the gas inside the well


83

The height of the triangle is determined by equating the area o f a rectangle and

the triangle:

ff(O A ^(0 = ^ ( 0 - M ' ) (7.6)

therefore:

« « ( ' ) = 2a(t ) (7.7)

7.2.1.2 Triangular Gas Distribution Velocities

Each vertex of the triangle will move with a different velocity. The front velocity

( v/i.« ) travel faster than the center velocity ( vcmler ). Also was observed that the

center velocity will travel faster than the tail velocity. Those velocities equations as a

function of depth were determined using the experimental data and are shown Table 7.1

and Figure 7.4.

Table 7.1 Front and center velocities for different circulation

CASE FRONT VELOCITY CENTER VELOCITYMigration with

choke openV_. exp( 1.2~3-3.014E-4*d) vcenter = exp(l.255-4.161E-4*d)

Migration with choke closed

v,_, - exp(l.332-4.83lE-4*d) vce„,cr = exp(1.407-6.382E-4*d)

Circulation with V|S = 0.64 ft'sec

xv.,» = exp(1.613-2.780E-4 *d) vcenter = exp(l.686-2.883E-4*d)

Circulation with vk = 1/24 ft/sec

Vim = exp(l ,767-2.953E-4*d) vcenter = exp(1.772-2.274E-4*d)

The equations of front and center velocities could be determined from

experimental data , as can be seen in Table 7.1, but unfortunately few tail velocities

could be calculated In the proposed model, the tail velocity will be assumed to be equal

to the liquid velocity or equal to vmm in Figure 7.3.


84

1. Migration with choke dosed (vsl=0) 0

_ 10 0 0 r 2000

£■3000 a 4000

5000

1w

/f

Fr ant

t rveh icil;

_ 1000r 2000

C inter

0 1 2 3 4 5Gasfrontvelocity(ft/sec)

2. Migration with choke open (vsl=0)0-

0 1 2 3 4 5Gas center velocity (ft/sec)

_ 1000 2000

£•3000 ° 4000

5000

/ ■

i i i•ron

I Vt:IuCi >

0 1 2 3 4Gas front velocity (ft/sec)

3. Circulation with vsl=1.24ft/sec0-

^ 1 0 0 0 -r 2000-

40005000

; HV

i- i

l r

I 1

i'H 111

; 1J

0 1 2 3 4 5 6 7 8 Gas front velocity (ft/sec)

4. Circulation with vsl=0.64 ft/sec

^ 1000

rontv ilm ity

0 1 2 3 4 5 6 Gas front velocity (ft/sec)

0_ 1000 ~ 2000 £-3000 C 4000

5000

i /<,ent

i /tIocity 1

0 1 2 3 4Gas center velocity (ft/sec)

0_ 1000 ~ 2000 £■3000 ° 4000

5000

H/ y p B-|

y

A1L« ni er

- tJ/ ve u<:i I r

....

0 1 2 3 4 5 6 7 8 Gas center velocity (ft/sec)

_ 1000

£-3000 Lenter vcljci

0 1 2 3 4 5 6 Gas center velocity (ft/sec)

Figure 7.4 Gas velocity- profile for various liquids velocities


85

The proposed triangular gas distribution profile needs to be implemented

in a kick tolerance model, and the results should be compared with the commercial kick

simulators results. If the results show a good agreement between them, the calculation of

circulating kick tolerance may be performed using a simple hand calculator.

7.2.2 Improvement in the Gas Flow Out Measurements

Since the knowledge of the gas distribution profile along the well can simplify the

circulating kick tolerance calculations, additional experimental work should be done for

different well geometry. Better gas flow out measurements should be sought, or a

gamma-ray density meter at the flowline may be used. Moreover, the downhole pressure

sensors should be installed at least 300 ft apart, or a differential pressure sensor like

gradiomanometer should be utilized to obtain the differential pressures

7.2.3 Modification for Inclined Well

The computer program should be modified to simulate inclined or even horizontal

wells. Data from flow loops experiments performed by Nakagawa. Mendes. and Wang

can be used to obtain the empirical correlation of gas rise velocity for various angles.

7.2.4 Instrumentation of a Real Well

A rig should be fully instrumented with mud logging unit and gas out

measurements to collect data from a kick in deep water drilling. The analysis of the

collected data will improve the present circulating kick tolerance model. Furthermore,

the collected data can be used to verify the accuracy of the proposed kick tolerance

model.


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5. Bourgoyne Jr., A. T., and Casariego, V. “Generation, Migration, and Transportation of Gas-Contaminated Regions o f Drilling Fluid.” SPE 18020. 63r<* Annual Technical Conference and Exhibition of the Society o f Petroleum Engineers, Houston, TX, October 2 -5 , 1988, 19-28.

6. Caetano Filho, E. Upward Vertical Two-Phase Flow through an Annulus. Ph.D. dissertation, The University o f Tulsa, 1986.

7. Casariego, V. Generation, Migration, and Transportation o f Gas Contamined Regions o f Drilling Fluid. Ph.D. dissertation, Louisiana State University, July 1987.

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9. Craft, B. C., Holden, W. R., and Graves, E. D. Well Design: Drilling andProduction. Prentice-Hall, Inc., 1962.

10. Ekwere, J. P., Chenevert, M. E., and Zhang, C. “A Model for Predicting the Density of Oil-Based Mud at High Pressures and Temperatures.” SPE Drilling Engineer, June 1990,141 - 148.

11. Element, D. J., Wickens, L. M., and Butland A. T. D. “An Overview of Kicking Computer Models.” International Well Control Symposium/Workshop, Baton Rouge, LA, November 27 - 29, 1989.

12. Elfaghi, F. A Pressure Losses in Subsea Choke Lines During Well ControlOperations. M.S. thesis, Louisiana State University, May 1982.

86


87

13. Falcao, H.L.M., Chita, L.C., and Rodrigues, R.S. “Perfura^ao em Aguas Profundas no Brasil.” (in Portuguese) 3° Congresso Brasileiro de Petroleo, Rio de Janeiro, RJ, Brazil, October 5 - 10, 1986.

14. Hagedom, A. R., and Brown, K. E. “Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in Small Diameter Vertical Conduits.” Journal o f Petroleum Technology’, April 1965.

15. Hoberock, L. L., and Stanbery, S. R. “Pressure Dynamics in Wells During Gas Kicks: Part 1 - Fluid Line Dynamics.” Journal o f Petroleum Technology\ August1981, 1357- 1366.

16. Hoberock, L. L., and Stanbery, S. R. “Pressure Dynamics in Wells During Gas Kick: Part 2 - Component Models and Results " Journal o f Petroleum Technology, August 1981,1367- 1378.

17. Hoberock, L. L., Thomas, D. C., and Nickens. H. V. “Here's how compressibility and temperature affect bottom-hole mud pressure.” Oil and Gas Journal, March 22,1982, 159- 164.

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19. Hovland, F., and Rommetveit, R. “Analysis of Gas-Rise Velocities From Full-Scale Kick Experiments." SPE 24580. 67th Annual Technical Conference and Exhibition of Society of Petroleum Engineers, Washington DC, October 4 - 7,1992,331 - 340.

20. Johnson, A. B., and White. D. B. "Gas Rise Velocities During Kicks.” SPE 20431 65th Annual Technical Conference and Exhibition of Society of Petroleum Engineers, New Orleans, LA, September 23 - 26, 1990, 295 - 304.

21. Johnson, A. B., and Cooper, S. “Gas Migration Velocities During Gas Kicks in Deviated Wells.” SPE 26331. 68th Annual Technical Conference and Exhibition of the Society o f Petroleum Engineers, Houston, TX, October 3 -6 ,1993,177 - 185.

22. Johnson, A. B., and Tarvin, J. A. “Field calculations underestimate gas migration velocities.” IADC European Well Control Conference, 1993.

23. Kato, S. “A New Two Phase Flow Model of Kick Control.” International Well Control Symposium,'Workshop. Baton Rouge, LA, November 27 - 29,1989.

24. Lage, A.C.V.M., Nakagawa, E. Y., and Cordovil, A.G.D.P. “Experimental Tests for Gas Kick Migration Analysis." SPE 26953, III SPE-LACPEC, Buenos Aires. Argentina, 1994.


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25. Lage. A.C.V.M., Gonsalves, C.J.C., Nakagawa, E.Y., and Cordovil, A.G.D.P., “Analise do Pogo CES-112, Fase V Atraves do Simulador de Kicks.” (in Portuguese) Comunicagao Tecnica - 034/93, Petrobras/Cenpes, September, 1993.

26. Lage, A.C.V.M., Gonsalves, C.J.C., Nakagawa, E.Y., and Cordovil, A.G.D.P., “Analise do Pogo RJS-457, Fase VI Atraves do Simulador de Kicks.” (in Portuguese) Comunicagao Tecnica - 044/94, Petrobras/Cenpes, January, 1994.

27. Leach, C. P., and Wand, P. A. “Use of a Kick Simulator as a Well Planning Tool.” SPE 24577. 67th Annual Technical Conference and Exhibition, Washington DC, October 4 - 7, 1992.

28. LeBlanc, J. L., and Lewis. R. L. “A Mathematical Model of a Gas Kick.” Journal o f Petroleum Technology. August 1968. 888 - 898.

29. Mackenzie, M. F. Factor Affecting Surface Casing Pressure During Well Control Operations. M.S. thesis. Louisiana State University, August 1974.

30. Mathews, J. L. Upward Migration o f Gas Kicks in a Shut-in Well. M.S. thesis, Louisiana State University’. 1980.

Sl.Matheus, J. L., and Bourgoyne Jr., A. T. “Techniques for Handling Upward Migration of Gas Kicks in a Shut-In Well." IADC/SPE 11376. IADC/SPE Drilling Conference, New Orleans. LA. February 20 - 23, 1983, 159 - 170.

32. Mendes, P. P. M. Two-Phase Flow in Vertical and Inclined Eccentric Annuli. M.S. thesis, Louisiana State University. August 1992.

33. Miska. S.. Beck. F. E.. and Murugappan. B S. “Computer Simulation of the Reverse Circulation Well Control Procedure for Gas Kicks.” SPE/LADC 21966. SPE/IADC Drilling conference, Amsterdam, March 11 - 14, 1991.

34. Nakagawa, E. Y. Gas Kick Behavior During Well Control Operations in Vertical and Slanted Wells. Ph.D. Dissertation, Louisiana State University, December 1990.

35. Nakagawa, E. Y., and Bourgoyne Jr., A. T. “Experimental Study of Gas Slip Velocity' and Liquid Holdup in an Eccentric Annulus.” Multiphase Flow in Wells and Pipelines, ASME - FED vol. 144, 1992, 71- 79.

36. Nakagawa, E. Y., and Lage. A. C. V. M. “Kick and Blowout Control Developments for Deepwater Operations.” IADC/SPE 27497. IADC/SPE Drilling Conference, Dallas. TX. February 15 - 18, 1994.

37. Negrito, A. F., and Maidla E. E. "Optimization of Flow Rate Selection for Kick Control.” SPE 19656. 64th Annual Conference and Exhibition o f the Society' of Petroleum Engineers. San Antonio. TX, October 8 - 11, 1989.


89

38. Negrao, A. F. Personal Communication. October, 1995.

39. Nickens, H. V. “A Dynamic Computer Model of a Kicking Well: Part II Predictions and Conclusions.” SPE 14184. 60th Annual Technical Conference and Exhibition o f the Society o f Petroleum Engineers, Las Vegas, NV, September 22 - 25, 1985.

40. Nickens, H. V. “A Dynamic Computer Model of a Kicking Well.” SPE Drilling Engineering, June 1987, 159 - 173.

41. Petrobras/E&P - Personal Communication.

42. Pilkington, P. E., and Niehaus, H. A. “Exploding the myths about kick tolerance." World Oil, June 1975, 59-62.

43. Podio, A. L., and Yang, A. P. “Well Control Simulator for IBM Personal Computer.” IADC/SPE 14737. IADC/SPE Drilling Conference, Dallas. TX, February 10- 12, 1986.

44. Quitzav, R., and Muchtar, J.B. “Drilling Safely at Well Design Limits: A Critical Well Design Case History." IADC/SPE 23930. IADC/SPE Drilling Conference New Orleans, LA, February 18 - 21,1992, 749 - 754.

45. Rader, D. W., Bourgoyne Jr., A. T., and Ward, R. H. “Factors Affecting Bubble- Rise Velocity of Gas Kicks.” Journal o f Petroleum Technology, May 1975, 571 - 584.

46. Redman Jr., K. P. “Understanding Kick Tolerance and Its Significance in Drilling Planning and Execution.” SPE Drilling Engineering, December 1991, 245 - 249.

47. Rommetveit, R., and Olsen, T. L “Gas Kick-Experiments in Oil-Based Drilling Muds in a Full-Scale Inclined Research Well.” 64th Annual Technical Conference and Exhibition of the Society o f Petroleum Engineers, San Antonio, TX, October 8 - 11, 1989,433-446.

48. Rommetveit, R., and Vefring, E. H. “Comparison of Results From an Advanced Gas Kick Simulator With Surface and Downhole Data From Full Scale Gas Kick Experiments in an Inclined Well.” 66th Annual Technical Conference and Exhibition of the Society o f Petroleum Engineers, Dallas, TX, October 6-9 ,1991 .

49. Rygg, O. B., and Gilhuus, T. “Use of a Dynamic Two-Phase Pipe Flow Simulator in Blowout Kill Planning.” SPE 20433. 65th Annual Technical Conference and Exhibition of the Society o f Petroleum Engineering, New Orleans, LA, September 2 3-26 , 1990.

50. Rygg, O. B., Smestad, P., and Wright, J. W. “Dynamic Two-Phase Flow Simulator: A Powerful Tool for Blowout and Relief Well Kill Analysis.” SPE 24578. 67th


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Annual Technical Conference o f the Society of Petroleum Engineers, Washington, DC, October 4 - 7 , 1992.

51. Santos, O. L. A. A Dynamic Model o f Diverter Operations for Handling Shallow Gas Hazards in Oil and Gas Exploratory Drilling. Ph.D. dissertation, Louisiana State University, May 1989.

52. Santos, O. L. A., Lima, H. R. de P., and Bourgoyne Jr., A. T. “An Analysis of Gas Removal From the Marine Riser.” SPE/LADC 21968. SPE/IADC Drilling Conference Amsterdam, March 11 - 14,1991.

53. Santos, O. L. A. “Well Control Operations in Horizontal Wells." SPE Drilling Engineering. June 1991, 111 - 117.

54. Scf offmann. F., and Economides, M. J. “ Controlling Kicks in Ultradeep Wells and Comparison With Shallow Wells.” SPE 22561. 66th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Dallas. TX, October 6 - 9 , 1991.

55. Taitel, Y., Bamea, D., and Dukler, A. E. “Modeling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes.” AIChEJ. 26(3), 1980, 345 - 354. '

56. Tarvin, J. A., Walton, I., and Wand, P. “Analysis of a Gas Kick Taken in a Deep Well Drilled With Oil-Based Mud.” SPE 22560. 66th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Dallas, TX, October 6 - 9 , 1991.

57. Thomas. D. C., Lea, J. F., and Turek, E. A. “Gas Solubility in Oil-Based Drilling Fluids: Effects on Kick Detection." SPE 11115. 57th Society of Petroleum Engineers Annual Fall Technical Conference and Exhibition, September 26 - 29, 1982.

58. Up-to-date. Published by Petrobras Public Affairs Service, number 3, April 1994.

59. Vefring, E. H., Rommetveit, R., and Borge, E. “An Advanced Kick Simulator Operating in a User-Friendly X-Window System Environment.” SPE 22314. Sixth SPE Petroleum Computer Conference, Dallas, TX, June 17 - 20, 1991.

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91

62. White, D. B., and Walton, I. C. “A Computer Model for Kicks in Water-and Oil- Based Muds.” IADC/SPE 19975. IADC/SPE Drilling Conference, Houston, TX, February 27 - March 2, 1990.

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APPENDIX A

SHUT-IN KICK TOLERANCE

Shut-in kick tolerance can be defined as the difference between the formation pore

pressure (expressed in equivalent mud weight) and mud weight that, if a kick occurs, the

well can be shut in without breaking the weakest open hole formation (normally at the

last casing set depth).

K, = Pp - p m (A.l)

where: Kr = kick tolerance [kg/nr]

p p = formation pore pressure [kg/m3]

p„, = mud weight [kg/m3]

A.1 Maximum Shut in Casing Pressure (SICP)

If a kick occurs, the maximum shut-in casing pressure SICPmax that will not

fracture the weakest formation below the last casing set depth can be found as:

Hydrostatic pressure Fracture pressure = SICP.’ + (A.2)

due to a mud column

P f gDf = SICPm3x + p mgDj (A.3)

p j = equivalent density o f fracture [kg/m3]

g = acceleration of gravity [m/s3]

Dj = depth o f weakest formation [m]

SICPmax = maximum shut in casing pressure [Pa]

p m = mud density [kg/m3]

SICpm3x = ( p / — P

then:

or in field units:

(A.4)

92


93

or in field units:

SICPmlx = 0.052(p f - pS)P j (A.5)

where: SICPm2x = [psi]; p / ,p m[lbm /gal]; D7[ft]

Since after setting the casing, cementing the casing, and drilling a few feet of

formation, a leak off test (LOT) is made, the p^ can be assumed as the value obtained

from LOT, and Df can be adopted as last casing set depth.

It is not always true that the weakest formation is at the casing set depth because

normally the casing is set at the shale formation. If. for example, a sandstone appears

below the casing set depth, this sandstone should be the weakest point. On the other hand,

if the LOT is made, we know the p ; value, and in most of cases we do not know the

sandstone fracture pressure unless we also do a LOT at the sandstone depth. Therefore, in

m o st of the cases, we assume that the weakest formation is at the last casing set depth

( D, = depth of last casing set depth).

A.2 Kick Tolerance

If a kick occurs, and we assume that the gas enters into the well as slug:

Hydrostatic PressureFormation Pore Pressure

max at the bit depthdue to a mud (A.6)

at the bit depth

s ic p m„ = (p r ~ P „ ) A (A.7)

where Dh = bit depth


94

substituting (A.7) in (A.6) becomes:

(p / - P = p pgDb - p mgDb (A.8)

Since the kick tolerance Kt = p p - p m as defined in equation (A.1):

(A.9)

The equation (A.9) is same for field units with K, , p p , p m, p } in [Ibm/gal], and

Dj and D h [ft].

The equation (A.9) is valid only for a “zero pit gain." That is, the kick will be

detected without any increase in the pits, and no fluid will enter the well. However, the

kick is normally detected by the increase in the mud pits due to influx of fluids (water,

oil, or gas) into the well. Therefore, if we consider that the influx fluid will enter as a slug

we will have:

/ Hydrostatic PressureN + due to a influx (A. 10)

fluid column ,

Formation Pore Hydrostatic PressurePressure due to a mud column

V

SICPm3X = p„gDb - [pmg (A - Lk)+ p kgLk (A-l 1)

where: Lk = kick height [m]pk = equivalent kick fluid density [kg/m3]

Applying the concept of equation (A.l), equation (A.l 1) becomes:

(A. 12)


95

Equation (A.12) is the same for field units with p p , pm, pf , p k in [lbm/gal];

and Df . Dh , Lk in [ft]

A.3 Safety Factor and Surge Gradient

A practical form of kick tolerance was used to drill in the Canadian Beaufort Sea

which has a high abnormal pressure, unconsolidated formation, presence of permafrost,

gas hydrates, and plastic shale (Wilkie and Bernard, 1981). All of the problems associated

have made the optimum setting of casing string critical.

As a result, the safety factor was re-defined as a function of depth and expressed

in pressure instead of a fixed value expressed in equivalent mud weight. Moreover, a

surge gradient factor was introduced in the calculation of kick tolerance. A surge gradient

is created on restarting the mud pumps after the well was shut in to read the drill pipe and

casing pressures. The surge gradient was defined as:

The shut-in kick tolerance equation considering safety factor and surge gradient is

given by:


where: p 1R = surge gradient [kg/m3]

P5.33x10 *YPDf 101.94

(4, -< * ,) ' ~ a T

[kg/m3](A.13)

y?= Yield Point [Pa]

dh = diameter of hole [m]

dr = diameter of drill pipe [m]

The proposed safety factors {Psj) are shown in Table A.l

96

i' ( \ Lk ( \k > = « - (P / - P . j - T J - " p*>- P*Sc1'/) u h

where: Ps, = safety factor [Pa]

gk = conversion factor [9.807 kg.m/kgf.sec']

using the conversion factor Equation A. 14 becomes:

f, D, f ^ 101.97x10 Ps{ L k {

' = aT^P/ ~ Pm' ----------Dh—

Table A.l Safety factors used in the Beaufort Sea

BELO W CASING SAFETY FACTOR

(mm) (inches) kPa psi

406 16 225 33

340 13 3/8 345 50

244 9 5/8 690 100

(A. 14)

(A-15)


APPENDIX B

INPUT DATA FOR KICK TOLERANCE PROGRAM

Data used to run the kick tolerance program are presented in this appendix.

B .l INPUT DATA FOR A TYPICAL DEEPWATER WELL

f t * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** INPUT DATA FOR KICTOL PROGRAM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *•WELL ID: TYPICAL*• a. Complete table bellow for each section of the WELL having a different• ID and the respective depth (from top to bottom).

WELL ID DEPTH[inches] [ft]

18.8 3281.8.755 9187.8.5 11483.

b. Complete table below starting at top for drillstring OD.lD.and DEPTH

PIPE OD PIPE ID DEPTH[inches] [inches] [ft]

5.0 4.28 105836.25 2.81 11483

-------- -------- ------

c. Enter option: (1) for bit jet diameter in [ /32] (2) for total flow area in [inchesA2]

d. Enter table below with: bit jet diameter (option 1) or TFA (option 2)

JET 1 JET 2 JET 3 JET 4 Total Flow Area [/32] [/32] [/32] [/32] [inchesA2]

14. 14. 14. 0.

e. Enter the following mud properties

MUD VISCOMETER VISCOMETER DENSITY READING READING

@600 rpm @300 rpm

97


98

9.8 53. 34.

f. Enter the pipe absolute roughness

.00065

g. Enter the following RESERVOIR data

POROSITY PERMEABILITY THICKNESS RADIUS PORE INITIAL GAS SPECIFICPRESSURE WATER VISCOSITY GAS

SATURAT. DENSITY[d'less] [mD] [ft] [ft] [ppg] [d'less] [cp] [d’less]

.20 350. 66. 8000. 10.5 .2 0.015 0.604

h.Enter the following temperature and pressure data

SURFACE OCEAM BOTTOM STANDART STANDARTTEMP. BOTTOM HOLE TEMP. PRESSURE

TEMP TEMP.[F] [F] [F] [F] [psia]

70. 40. 220. 60. 15.0

* i. Enter the mud flow rate

* MUD REDUCED* FLOW MUD

FLOW* Ispm] [gpm]

500. 100.

j. Enter the volume(s) of pit gain(lf more than one enter data in column)

VOLUMEPIT

GAIN[bbl]

15.

k. Enter the factor that control the size of each cell (factor^ 1 - Ibbl)

1.0

1. Enter the fracture data

SKINFACTOR

[d’less]

0.0


FRACTURE DEPTH GRADIENT [ppge] [ft]

12.0 9187.

m. Enter the rate of penetration ROP [ft/hours]

n. Enter the time to close the BOP after the kick was detected [min]

1.0

o. Enter the time between closing the BOP and starting to pump [min]

5.0

p. Enter the inside diameter of:Choke line (in) and Kill line (in)

3.0 3.0

q. Enter option: (1) for circulation through kill line only(2) for circulation through kill line AND choke line (paralell)

1

r. Enter the pressure above the bottom hole pressure to be maintenaine security factor (normally 50-300 psi)

0.


100

B.2 INPUT DATA FOR THE WELL RJS - 457

INPUT DATA FOR KICTOL PROGRAM

WELL ID: RJS-457

a. Complete table bellow for each section of the WELL having a different ID and the respective depth (from top to bottom).WELL ID DEPTH

[inches] [ft]

18.8 1132.8.535 155528.5 18374

b. Complete table below starting at top for drillstring OD.ID.and length

PIPE OD PIPE ID DEPTH [inches] [inches] [ft]

5.0 4.28 17291.6.5 2.81 18374.

c. Enter option: (1) for bit jet diameter in [ '32] (2) for total flow area in [inches'^]


JET 1 JET 2 JET 3 JET 4 Total Flow Area[/32] [/32] [/32] [/32] [inchesA2]

17. 17. 17. 0.----- ----- ----- ----- ----------------



@600 rpm @300 rpm [ppg] [d’less] [d’less]

16. 53. 34.


.00065


101



SATURAT. DENSITY[d’less] [mD] [ft] [ft] [ppg] [d'less] [cp] [d'less]

.08 50. 66. 8000. 17.0 .2 0.015 0.604


SURFACE OCEAM BOTTOM STANDART STANDART TEMP. BOTTOM HOLE TEMP.

TEMP TEMP.[F] [F] [F] [F]

70. 50 . 2 9 0 . 60.

i. Enter the mud flow rate

MUD REDUCED FLOW MUD

FLOW [gpm] [gpm]

4 0 0 . 100.

j. Enter the volume(s) of pit gaindf more than one enter data in column)

VOLUMEPIT

GAIN[bbl]

10.

k. Enter the factor that control the size of each cell (factor=i - lbbl)

2.0



17.5 15552.

PRESSURE

[psia]

15.0

SKINFACTOR

[d’less]

0.0


m. Enter the rate o f penetration ROP [ft/hours]

19.7


0.5


0.5

p. Enter the inside diameter of: Choke line (in) and Kill line (in)

2.5 2.5


1

r. Enter the pressure above the bottom hole pressure to be maintenaine security factor (normally 50~200 psi)

0.


103

B.3 INPUT DATA FOR THE WELL CES - 112

• • • * • * • * * * * * * • * * • • • * « • * * * * * * « * * • * • * * * * * * * « *

* rNPUT DATA FOR KICTOL PROGRAM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *’ WELL ID: CES-112* a. Complete table bellow for each section of the WELL having a different* ID and the respective depth (from top to bottom).* WELL ID DEPTH* [inches] ♦ _____

[ft]

17.6 4311.8.7 12993.8.5 14764.

b. Complete table below starting at top for drillstring OD,ID,and length

PIPE OD PIPE ID DEPTH [inches] [inches] [ft]

5.0 4.28 13780.6.5 2.81 14764.

c. Enter option: (1) for bit jet diameter in [ /32](2) for total flow area in [inchesA2]


* JET 1 JET 2 JET 3 JET 4 Total Flow Area* [/32] [/32] [/32] [/32] [inchesA2]

12. 12. 12. 0.



@600 rpm @300 rpm [ppg] [d'less] [d’less]

9.5 46. 29.


.00065


104



SATURAT. DENSITY[d’less] [mD] [ft] [ft] [ppg] [d'less] [cp] [d'less]

-10 500. 34.5 8000. 10.2 .2 0.015 0.604


SURFACE OCEAM BOTTOM STANDART STANDARTTEMP. BOTTOM HOLE TEMP. PRESSURE

TEMP TEMP.[F] [F] [F] [F] [psia]

70. 40. 200. 60. 15.0______ _____ ----—

i. Enter the mud flow rate

MUD REDUCED FLOW MUD

FLOW [gpm] [gpm]

430. 100.

j. Enter the volume(s) o f pit gain(If more than one enter data in column)

VOLUMEPIT

GAIN[bbl]

16.

k. Enter the factor that control the size o f each cell (factor=l ~ lbbl)

1.0



10.5 12993.

SKINFACTOR

[d'less]

0.0


m. Enter the rate o f penetration ROP [ft/hours]

10.


0.5


0.5

p. Ent :r the inside diameter of:Choke line (in) and Kill line (in)

3.0 3.0


1

r. Enter the pressure above the bottom hole pressure to be maintenaine security factor (normally 50-100 psi)

50.


APPENDIX C

GAS DISTRIBUTION PROFILE

The gas fraction as a function o f time was calculated from the experimental data

and is shown here in odd numbered figures for a given depth. The gas distribution profile

as a function of depth was derived from the gas fraction and is shown in even numbered

figures. Experimental details are shown in Tables C.l through C.3, and the drilling fluid

properties used are shown in Table C.4.

Table C .l Test matrix for mud and natural gas experiments with gas injected through tubing

Downhole Pressure Sensors 1200 ft Apart

Test#

pit gain

(bbl)

Pumpspeed(spm)

Choke back pressure

(psi)Note

10 20 0 32 6262M l 10 170

M2 0 choke closed Failure due to valve leakM3 10 32 100 Downhole pressure lostM4 20 62 170 Downhole pressure lostM5 20 0 choke open Downhole pressure lostM6 10 32 170M7 20 0 choke closed |

Table C.2 Test matrix for mud and natural gas with sensors 1,200 ft apart

Gas Was Pump Down Through 3.5 J55 Eue (9.3 #/ft) X 1.66” N-80 (3.02 #/ft) Annulus

Test#

Gas pump down speed

(spm)

Pump speed (spm)

Choke back pressure

(psi)Note

62 82* 0 32 62M8 82 0 choke openM9 82 32

M10 62 62 170 on line data was lostM il 62 32 170 middle downhole sensor failedM12 62 62 180 middle downhole sensor failedM13 82 62 170 middle downhole sensor failedM14 82 0 choke closed middle downhole sensor failed82* spm — v=1.64 ft/sec

106


107

Table C.3 Test matrix for mud and natural gas with sensors 100 ft apart

Test#

Gaspumpdownspeed(spm)

Position o f downhole

tools

Pumpspeed(spm)

Viscousfluid

Chokeback

pressure Note

62 82 b* m* t* 0 32 62 ves noM15 82 B 62 N 0 one sensor failedM16 62 B 62 N 0 one sensor failedM17 82 B 62 N 170 one sensor failedM18 82 M 32 N 170 one sensor failedM19 82 M 62 N 180 one sensor failedM20 82 M 0 N 170 one sensor failedM21 82 M 62 N 170 one sensor failedM22 62 M 32 N 170 one sensor failedM23 62 M 62 N 0 one sensor failedM24 82 T 32 N 200 one sensor failedM25 82 T 0 N choke open one sensor failedM26 82 T 62 N 200 one sensor failedM27 82 M 62 Y choke openM2 8 82 M 0 Y choke

closedM29 82 M 0 Y choke open

b* = bottom (on line tool @ 5,422 ft); m* = middle (on line tool @ 2,761ft), t* = top (on line tool @ 100 ft)

Table C.4 Drilling fluid properties used in the experiments

Experiment#

Mudweight(lb/gal)

Marshviscosity

(sec)

Plasticviscositv

(cp)

Yieldpoint

Gel strengthlOsec | 10m in

Ibf/lOOsq ftMl 9.9 54 15 5M2 9.9 54 15 5

M3 -M 4 9.9 53 15 5M5 9.9 54 15 5

M6 - M7 9.9 53 15 5M8 9.9 54 14 5

M 9-M 10 10.0 53 12 5M il -M 12 9.8 49 10 2

M13 9.6 62 15 8M14 9.6 58 15 7

M 15 - M 16 9.7 40 12 9 3 10M 1 7 -M 1 8 -M 1 9 9.6 38 11 6 2 5M 20-M 21 -M 22 9.6 40 12 3 2 9

M23 - M24 9.6 42 12 6 2 15M25 - M26 9.6 43 12 6 2 13M27 - M28 9.7 78 30 15 4 25

M29 9.7 78 30 15 4 25


Gas

fr

actio

n G

as

frac

tion

Gas

fr

actio

n G

as

frac

tion

Gas

fr

acti

onType of experiment: Circulation at 62 spm (vsl=1.24 ft/sec)

Experiment: M l

0.80-0.60-0.40-0.20-0.00-

| Interva = 0 - 1,(100 ftg 1jj I i i

i i f f lW ™ L0 20 40 60 80 100 120 140

0.301

0.20-0.1510.10H0.050.00

T im e (m inutes'-1,000 - 2.238 ft 1LI 1

: / \: / HJlwif I= /

- r - r - 4 1 1 W w p L

0.30-0.25-0.20-0.15-0.10-0.05-

0 20 40 60 80 100 120 140Time (minutes)

- 2,23^ 3 476 ft

i /1 / ViI 1 • ! i i i

0.30-0.25-0.200.1510.1010.050.00

20 40 60 80 100 120 140Time(minutes)

i Interval = 3.476 - 4.714 f t:;: A; / V

/■ , s -----i * * 120 40 60 80

0.301 0.251 0.201 0.151 0.101 0.05 0.00

100 120 140Time(minutes)

: Interval = 4,714 -5 .822 t:

=::

4 .

0 20 40 60 80 100 120 140Time(minutes)

O ft

On-line

1,000 ft

Top

2,238 f

M iddle

3,476 ft

Bottom

4,714 f

5,822 ft

TD = 5,884 ft

Figure C.l Gas fraction for different depths and times for experiment Ml


109

Experiment:Ml

51 min

0 1000

« 2000i£ 3000- I " 4000H

50006000-

2000-

0.00 0.05 0.10 0.15 0.20 Gas fraction

q 4000- 5000- 6000-

—H - 55 min

i

?

! “ u

;

i l — — I

I1 -------1------- '

60 min

0 1000

« 2000 5 3000 q 4000

5000 6000

T

0.00 0.05 0.10 0.15 0.20 Gas fraction

0.000.05 0.10 0.15 0.2 Gas fraction

S 2000 £ 3000' q 4000'

5000 6000

— 70 min

■ BlB II

IK----- —■

n

i

i ____

= 3000 o 4000

75 min

0 1000

S2000- 5 3000- Q 4000-

5000 6000

80 min

X 5=

0.00 0.10 0.20 0.30 Gas fraction

0.000.05 0.100.15 0.20 Gas fraction

0.00 0.05 0.100.15 0.2 Gas fraction

—B 85 min —H — 90 min —B 110 min

0 1000

« 2000

1

= 3000 I " 4000-

5000 j 6000

I

T

° 21000-11« 2000-ii= 3000- I" 4000-

5000- 6000-

t0q

1000£;2000H: !

= 3000 q 4000

5000 i6000 i

0.00 0.05 0.10 0.15 0.20 Gas fraction

0.00 0.05 0.10 0.15 0.20 Gas fraction

0.00 0.05 0.10 0.15 0.2 Gas fraction

Figure C.2 Gas fraction as a function of depth for experiment M l


Gns

frac

tion

Gas

fr

actio

n (j

flS Tr

actio

n G

as

frac

tion

Gas

fr

acti

on

110

Type of experiment: Circulation at 32 spm (vsl=0.64 ft/sec)Experiment: M6

Interval = 0 -1,000 ft

0.00150 200 250

Time(minutes)

0.3010.25 H0.20 H0.15HO.lOi0.050.00

: 1 _4 1 -1 000 **1 mji krU 1 I: 1 j0 50

0.30-0.25-0.20-0.15-0.10-0.05-=o .oo4-

100 150 200 250Timefminutes)

| In te rv a l = 2 .228 - 3 ,456 f t111

1 - A - I1 ■ ■ ■ ■ 1[— 4-------- r - j — ------- - ----------- --- 1 — 1 l

0.30-q 2S 3 Interval -0l20-0.15- 0.10- 0.05- 0.00-

T

0.301 0.25 i

0 50 100 150 200 250Time(minutes)

0.15i0.10H0.050.00

: Interval = 4.684 - 5,82: ft::::

J

0 50

50 100 150 200 250Time(minutes)

100 150 200 250Time(minutes)

Oft

On-line 1,000 ft

Top 2,228 fi

Middle 3,456 ft

Bottom 4,684 fi

5,822 ft

TD = 5,884 ft

Figure C.3 Gas fraction for different depths and times for experiment M6


Dept

h (ft

) De

pth

(ft)

Dept

h (ft

)

111

Experiment: M6

2000-3000-

5000-6000-

— 50 min

1--------■

1

1

1

60 min 70 min

0-p 1000

§2000•5^3000- q 4000-

5000-6000-

0- 1000-*

§2000- £ 3000- q 4000-

5000- 6000-

0.00 0.05 0.10 0.15 Gas fraction

0.00 0.05 0.10 0.15 Gas fraction

0.00 0.05 0.10 0.15 Gas fraction

90 min

1000-:§ 2000-1

f . 3000^1*4000

50006000

100 mm 110 min

S 3000

0.00 0.05 0.10 0.15 0.00 0.05 0.10 0.15 0.00 0.05 0.10 0.15Gas fraction Gas fraction Gas fraction

—B — 120 min —B — 150 min —B — 150 min

o-1000-2000-3000-4000-5000J6000-

t ----- S■j

B-|■

rH B

----------

o-1000-

§2000-

f . 3000'q 4000-

5000- 6000-

0.00 0.05 0.10 0.15 Gas fraction

0.00 0.05 0.10 0.15 Gas fraction

0 1000

§ 2 0 0 0 5 3000 q 4000-

5000-7 6000-

0.00 0.05 0.10 0.15 Gas fraction

Figure C.4 Gas fraction as a function of depth for experiment M6


112

Type of experiment: Migration with choke closedExperiment: M7

c 0 .2 0_o

0 .1 5eer4-

0 .1 0V3«5 0 .0 5

O 0 .0 0

: Interval = 1I - 1.000 f t i: 1:

ft u bj l , 1 m

5 0 100 150 200 2 5 0

eeo

0.20- 0 .1 5 - 0.10- 0 .0 5 -

0 J

3 Interval =1 ,000 - 2,228 t1

t

-̂---------------iJJ ijiii latfi

5 0 100 150 2 0 0 2 5 0Time(minutes)

c 0 .20 -g

0 .15 -:ec> 0 .10 -f(fiec 0 .0 5

0 .0 0 J

Interval = 2,228 - 3,45 . ft

5 0 100 150 200 2 5 0

= 0.20-q

* | 0 .1 5 i | 0.10- S 0 .0 5 H

Interval = 3,456-4,68-1 ft

0 5 0 100 150 200 250Time (minutes)

- 0 .2 0 -30 .15 -:

ec£ 0 .10-:(fiec 0 .0 5 -E

o 0 .0 0 J

Interval = 4,684 - 5,82; : ft

5 0 100 150 2 0 0 25 0Time (minutes)

Oft

On-line

1,000 ft

Top

2,228 f

M iddle

3,456 ft

Bottom

4,684 f

5,822 ft

TD = 5,884 ft



113

Experiment: M7

1000- S2000- :S 3000- q 4000-

5000- 6000-

—B — 50 min

I------------■

1

B

1

60 min

o - p 1000

£ 2 0 0 0 i t5 3000- ( f 4000-

0.00 0.05 0.Gas fraction

5000-f 6000-

10 0.00

£ 2000

70 min

q 4000- 5000- 6000-

0.05 0.10Gas fraction

0.00 0.05 Gas fraction

0.10

1000 S2000-

3000' O 4000'

5000- 6000

— 80 min

1------------■

r ■“ 1■ i ,,

1

01000 +

£ 2 0 0 0-£^3000 q 4000

5000 i 6000

90 min

OH f1000+

£ 2000-j f £ 3000 §4000

5000 6000

100 min

£0.00 0.05 0.10

Gas fraction0.00 0.05 0.10

Gas fraction0.00 0.05 0.10

Gas fraction

110 min 120 min 180 min

1000- £2000- :£ 3000- q 4000-

5000- 6000-

HE-- -- - - - - - - -H I - - - - - - - - - - -

: B ----------

HI -- - - - - - - -

I ——

1

o- 1000-

£2000- £ 3000- 1*4000-

5000- 6000-

I- f —

I _IIF------j |

= £ —

1

0 llo o o i

£ 2 0 0 0 3000o.oq 4000H 5000-! 6000

II

0.00 0.05 Gas fraction

0.10 0.00 0.05 0.10Gas fraction

0.00 0.05 0.10Gas fraction



114

Type of experiment: Migration with choke openExperiment: M8

e 0 .8 0 1.2 a /rc\ J Interv il = 0 1,000 [ft

U.oU ;

U.4U"(mCSS U.2U ;

° 0 .0 0 j r r-r-r

5 0 7 0 9 0 110 130 150 170 190 2 1 0 2 3 0

•2 0.161ues 0 .1 2ch 0 .0 8wes 0 .0 4o 0 .0 0

0 .2 00 .1 6

e; 0 .1 2£ 0 .0 8«5a 0 .0 4O 0 .0 0

0 .2 0 -o 0 .1 6 -

: Interval #1 000 - 2L228 f t: I I\ U . . I llj:

J f"l 'I . . . . 1 u • I 1 •5 0 7 0 9 0 1 1 0 130 150 170 190 2 1 0 2 3 0

Time(minutes)1 In ten al = 2 .2 2 8 -1 4 5 6 t1

1

j---- - 41 1 • 1 -----/ ' ■ ■ 15 0 7 0 9 0 110 130 150 170 190 2 1 0 230

Time(miRutes)

S 0.12 * 0 .0 8 -

o.oo-

: In ten a l= 3!.456 J 1.684 f |:jI ^ ):

• * * . . . [ . , T ] ‘ • ‘

- 0.20- •2 0 .1 6 - 3 0.12-

* 0 .0 8 -

5 0 7 0 9 0 110 130 150 170 190 2 1 0 2 3 0Time(minutes)

3 0.04-° o.oo-

1 In ten al = 4,6 8 4 -: i,822 i t114

5 0 7 0 9 0 110 130 150 170 190 2 1 0 2 3 0Time(minutes)

O ft

O n-line

1,000 ft

T op

2,228 f

M iddle

3,456 ft

lottom

,684 ft

5,822 ft

TD = 5,884 ft



Dept

h (ft

) De

pth

(ft)

Dept

h (ft

)

115

Experiment: M8

0-1000-2000-3000-4000-5000-6000-

— 50 min

■—n

■

■

■

01000

£2000£ 3000 q 4000

5000^ 6000

o o o o o o o o O — N r r l T < n ' O P ' o ' o o o o o ’ o ' o '

Gas fraction

0100020003000400050006000

—® 130 min

i J i—

.11: 1

m

J■ t

j i ii i

200 min

o-1000-2000-3000-4000-5000-6000-

%

70 min

1000 £2000 £ 3000

4000 5000 6000

—H — 100 min

■■1 R

IT: ■-11

in 11 1o o o o o o o oO — N n ^ ’ i n ' O t 'o o o ' o ' © o ' o ’ o '

Gas fraction

150 min

o o o o o o oO —̂ 04 i/%o o* o ' o ' o ' o* o '

Gas fraction

0- 1000-

£2000- £ 3000- q 4000-

5000- 6000-

0 1000

£2000- ■5̂ 3000- | ’ 4000-

5000- 6000-

170 min

-L

i t i

I

o o o o o o o o o o ' o o o o* o ' o

Gas fraction

o o o o o o o o o — ( S n T u - . o r -o o ' o ' o ' o o ' o ' o '

o o o o o o o cO — M r , T f ' A ' S fo o o ' o o ' o ’ o ’ c

—® 220 min —® 228 min

o- 1000-

£ 2000- •£ 3000- q 4000-

5000- 6000-

o-1000-

£2000 '

O O O O O O O O O — c N m T T * / - . o r - *o o* o* o ' o ’ o ' o ' o '

Gas fraction

io o o o o o o o o ' o ' o ' o ’ o o ' o ' o

Gas fraction

£ 3000 q 4000-i)

5000- 6000-

t

I io o o o o o oo - n n m oo> o o ' o ' o ’ o ' o

Gas fraction



0L 0

ni'n

i

1 1

1 1

1 r

-0Z, 0

Gas

fr

actio

n G

as

frac

tion

Gas

fr

actio

n G

as

frac

tion

Gas

fr

acti

on

116


0.60|0.5010.4010.3010.2010.1010.00"

Interv; il = 0 - 1.000

0 20 40 60 800.400.300.200.10

Int< rval =1 000 - 2, 228 ft

i W T|- ." ." P lT V T *

0.40-0.30-0.20-0.10-0.00-

0 20 40 60 80 100 120 140 160Time (minutes)

Interv: il= 2,2 28-3 ,4 56 ft

/ \: V

. . . . . . i t . . . .

0.40- 0.30 H

0 20 40 60 80 100 120 140 160Time (minutes)

0.20 i 0.10 0.00

Interv: il = 3,456 - 4,6 54 ft •

jj / \ l: / K

r • • • ! ' . . 1 1 1 ♦ ‘ . . 4

0.20-0.15-:

20 40 60 80 100 120 140 160Time (minutes)

0.1010.050.00

~ Interval = 4,684 - 5,82: : ft::

!

0 50 100 150 200 250Time (minutes)

O ft

On-line 1,000 ft

Top 2,228 f

Middle 3,456 ft

Bottom [ J 4,684 ffi

5,822 ft

TD = 5,884 ft



Dept

h (ft

) De

pth

(ft)

Dept

h (ft

)

117

Experiment: M9

20 min 30 min

o- 1000-

3 2000 -

•5̂ 3000- q 4000-

5000- 6000-

1000 3 2000 = 3000 q 4000

5000 6000

— 40 min

i ■

\m 1M .

: p - l i

i i - a

i i0.00 0.20 0.40 0.60

Gas fraction


0.6 0.00 0.20 0.40 0.60 Gas fraction

o-1000-2000-3000-4000-5000-6000-

—® 50 min

1--------|■11 "■

1T -1B

1---- 1H;

1

o- 1000-

3 2 0 0 0 - = 3000- i 4000-

5000- 6000-

— 55 min

■■

I f iI1

ri 1K----- — ■

i i

o- 1000-

3 2000- = 3000- q 4000-

5000- 6000-

60 min

0.00 0.20 0.40 0.60 0.00 0.20 0.40 0.60 0.00 0.20 0.40 0.60Gas fraction Gas fraction Gas fraction

—H — 65 min — 70 min —B - 80 min

o- 1000

3 2 0 0 0 - = 3000- q 4000-

5000 6000

I t

* 01000-

3 2 0 0 0 - = 3000- q 4000-

5000- 6000-

I t

0.00 0.20 0.40 Gas fraction

0.600.00 0.20 0.40 0.60

Gas fraction0.00 0.20 0.40 0.60

Gas fraction



118

Type of experiment: Circulation at 32 spm (\sl=0.64 ft/sec)Experiment: M il

_ 0.80TT"— : 5 3 Interval = 0-1,0 )0ft•- 0.60 4" n in l n« 0.40 4 i / \g 0.20 q j | ( \£ o.oo I !

0 20 40 6

00o

o V-4 )o i: Time (r

>0 14 ninutes

- 0.601 o Interval =1,000 - 2,225 ft sZ 0.40Fes / \ l« 0.201 j J k^ O.OOT . . ,

20 40 60 80 100 120 140Time (minutes)

- 0.30-qcZ 0.20czt 0.10-:

Interva = 2,225-4.675

0.000 20 40 60 80 100 120 140

Time(minutes)

= 0.20 | 0.15 .2 0.10

o0.050.00

Interval = 4,675 5,822

1 !20 40 60 80 100 120 140

Time (minutes)

O ft

O n-line

1,000 ft

Top 2,225 f

M iddle

3,450 f t

(failed)

Bottom 4,675 f

5,822 ft

..TJQ .=..5*884. f t .

Figure C.l 1 Gas fraction for different depths and times for experiment M l 1


Depth

(ft)

De

pth

(ft)

Depth

(ft

)

119

Experiment: M il

1000-112000-jr

3000-i4000-i-

6000-

—B - 30 min

■-------■ 1

i

l1

0 *looo-ii

S 2000i f£ 3000- Q 4000-

s50 min

° Tlooo-p 2000 3000 4000 5000 6000

0.00 0.20 0.40 Gas fraction

70 min

o-1000-2000-300040005000-q6000

f-H I

5000i6000

40 min 45 min

I H i

o-1000H

3 2 0 0 0 - £ 3000- q" 4000-

5000- 6000-

0.00 0.20 0.40 0.60 Gas fraction


0.6 0.00 0.20 0.40 0.6 Gas fraction

01000

« 2000 £ 3000 |"4000-i

5000-1 6000

55 min

" I .

o-p 1000

g 2 0 0 0£ 3000 q 4000

5000-6000-

60 min

0.60 0.00 0.20 0.40 Gas fraction

0.60 0.00 0.20 0.40 Gas fraction

0.60

—B - 80 min —B — 90 min

1000-11- S 2 0 0 0 if £ 3000-; 1*4000-

5000- 6000-

0q1000

s 2000 i f£ 3000- 1*4000-

5000 i 6000

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.6 Gas fraction

Figure C.12 Gas fraction as a function of depth for experiment M il


Gas

fr

actio

n G

as

frac

tion

Gas

fr

actio

n G

as

frac

tion

Type of experiment: Circulation at 62 spm (\sl=1.64 ft/sec)Experiment: M12

0.40 ~ 0.301 0.201 0.10 0.00

: Interval = 0 - 1,(r r,Aj Ai\ / Ij i \ _ .

i ■ ■0

0.4(T0.3CF0.20T0.10"o.otr

20 40 60 80 100 120 140Time(minutes)

'̂ >■<4 ii

nterval = *1,000 - ; ,225 ft

20 40 60 80 100 120 140Time (minutes)

0.40-0.30-0.20-0.10-0.00-

3 Interval = 2,225 - 4,675 rt1

j

f

0 20 40 60 80 100 120 140Time (minutes)

0.200.150.100.050.00

Interval = 4,675 -5 ,822 t

20 40 60 80 100 120 140Time (minutes)

O ft

On-line

1,000 ft

Top

2,225 f

Middle

3,450 ft

(failed)

Bottom

4,675 f

5,822 ft

..TJD.= .5JS84.Xt.



121

Experiment: M12

20 min

o-100(H

§2000- £ 3000- |"4000-

5000- 6000

25 min

OH 1000H

§2000- ■£^3000- q 4000-

5000- 6000-

0.00 0.20 0.40 0.60 Gas fraction


35 min

<=: 2000

40 min

•£ 3000 O 4000

5000 6000

o- 1000-

§2000- £ 3000- q 4000-

5000- 6000-

0.00 0.20 0.40 0.60 Gas fraction

01000%

§ 2 0 0 0 £ 3000 q 4000

5000 6000

30 min

0.00 0.20 0.40 0.6 Gas fraction

0-11 1000%

§ 2 0 0 0£ 3000- n 4000-

5000i6000

45 min

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

— 50 min ' H 55 min 70 min

§ 4000

02 1000%

§2000% £ 3000- § 4000-

5000- 6000-

0%lo o o -ii

§2000-ir

o.Q>Q£ 3000i ^4000-

5000 6000t

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.6 Gas fraction



122


mm0.40-© 0.30-es£ 0.20-crCC o .io -o o.oo-

0.400.30

eeeh 0.20«5ec 0.10o0.00

Interval = 0 - 1,000 ft

20 40 80 100 120 Time(min

interval =1,000 - 2,

80 100 120 Time (minutes)

- 0.40- 3 0.30-S 0 .2 0 -

s 0.10- ° o.oo-

a Interval ■= 2,222-. 1,666 ft

i13i • * 1 i • • • ■ • • 1 • ■ • 1

20 40 60 80 100 120Time (minutes)

s 0.200.15

<h 0.10ifiCS 0.05o 0.00

jj Interval = 4,666 - 5 ,822 ft

iii1 ■ ■ ■ ‘

20 40 60 80 100 120Time(minutes)

0 ft

On-line 1,000 ft

n Top J 2,222 ft

r*i Middle 3,444 ft

(failed)

Bottom 4,666 f

5,822 ft



Depth

(ft

) De

pth

(ft)

Depth

(ft

)

123

Experiment: M13

1000-2000-jf3000-i4000 H

6000-

—B - 20 min

I-------■

1

1

30 min

o- 1000 -

S 2 0 0 0 - :5 3000- Jj" 4000-

5000- 6000-

40 min

200030004000

6000-

—H — 45 min

II-------■ ■I

11----- ■

j

60 min

o-1000-2000 -

3000-4000-5000-6000

0-^ 1000

« 2000|[3000 i 4000-

5000-1

0.00 0.20 0.40 0.60 Gas fraction


0.6

0 *1000

S2000- •S 3000- I t 4000-

5000-6000

50 min

o- 1000-

S 2 0 0 0 - ■5 3000- q 4000-

5000- 6000-

u ------0.00 0

G.20 0 as frac

.40 0 tion

j —■— 55 min

1 _ 1L i

1

-!—0.00 0.20 0.40 0.60

Gas fraction0.00 0.20 0.40 0.60

Gas fraction0.00 0.20 0.40 0.60

Gas fraction

— 70 min —® 80 min

£

o-* 1000

S 2 0 0 0 tE 3000^ q 4000

5000 6000

o-1000-lt

S20oo-jr5 3000- Q 4000-

50006000

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction



124

Type of experiment: Migration with choke dosedExperiment: M14

_ 1.00 -a .2 0.80 i

:0.40 30.20 ^ 0.00

Interval = 0 - 1.000 ft

2 0.60 -

50 100 150 200 250 300 350 400

£ 0.2(

0 Interv: II © o ) - 2.222 ft I0 ju

10i r i

i 1t 1

50 100 150 200 250 300 350 400Time(minutes)

g 0.30 iI 0 .2 0 -jg 0.10 u 0.00

Interval = 2,2 22-4.666 ft | |

!| |

1 i -0 50 100 150 200 250 300 350 400

Time (minutes)

“ 4 Interval =n i t - -{ 4,666 - 5 ,822 ftU.lJi 4

O 3 C5 A i n 1U*lUT

Wa j

CS v.U-> J u 0 .00 ■

20 40 60 80 100 120 Time(minutes)

0 ft

On-line 1,000 ft

Top 2,222 f

Middle 3,444 ft (failed)

Bottom 4,666 f

5,822 ft

..TO.=.5*884.0.



Depth

(ft)

De

pth

(ft)

Depth

(ft

)

125

Experiment: M14

1000H*2000i f 3000-i4000-i500016000

—® 30 min

1-------■

1 '

1

40 min

o- 1000-

£ 2000 -

■£ 3000- q 4000-

5000 6000

o- 1000 -

£ 2000 -

£ 3000- q 4000-

5000- 6000-

— 50 min

i i i0.00 0.20 0.40 0.60

Gas fraction0.0 0.2 0.4 0.6

Gas fraction0.00 C.20 0.40 0.60

Gas fraction

o-1000 -

2000 -

3000-4000-5000-6000-

- » ~ 60 min

1 B-----] |

I ■

70 min 80 min

o- 1000-

S 2 0 0 0 - £ 3000- I" 4000-

5000- 6000-

leto-

1000-ft- £ 2000 -

£ 3000- I" 4000-

5000-6000-

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

90 min ~ S — 100 min —B — 200 min

02 1000-j* 20003000-i 4000-i 5000 6000

0-1000*

£ 2000 -

£ 3000- q 4000-

5000-6000

0^1000

£ 2 0 0 0 i f£ 30001 a 40001

50006000

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.25 0.50 0.75 l.00 Gas fraction



Gas

fr

actio

n fr

flct

i011

frac

tion

Gas

fr

acti

on


0.10

0.05

0.00

Interval = 0 -5 ,4 12 ft

0 5 10 15 20 25 30 35Tirae(minutes)

0.20H

0.10

0.00

Interv: j =5,422

t5

- 5, 522 rt

-I10 15 20 25 30 35

Time(minutes)

0.60-

0.40-i

0.20-i 0.00 J

Interva = 5,52^ -5 ,622

0 10 15 20 25 30 35Time(minutes)

0.200.150.100.050.00

Interva = 5,622 - 5,822 ft

10 15 20 25 30 35Time (minutes)

Oft

On-line

5,422 ft

Top

5,522 ft

M iddle

5.622 ft

JL, Bottom

5,722 ft

(failed)

5,822 ft

TD = 5.884 ft

Figure C.19 Gas fraction for different depths and times for experiment MI5


Dept

h (ft

) De

pth

(ft)

Dept

h (ft

)

127

Experiment: Ml 5

5400-

5500-

5600-

5700-

5800 a

—® 15 min

1

1

1

—B - 16 min —B 17 min

.5500-

■B 5600-Q.o° 5700-

5800-

5400-

> 5500 -

•B 5600-Q.oQ 5700-

5800-0.00 0.20 0.40 0.60

Gas fraction

0.0 0.2 0.4 0.6Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

5400-

5500-

5600-

5700 ■

5800 a

18 min

0.00 0.20 0.40 0.60 Gas fraction

19 min 20 min

5400 5400

5500 5500-e:■S 56005600

5700 t5700 7

580058000.00 0.20 0.40 0.60 0.00 0.20 0.40 0.60

Gas fraction Gas fraction

—B - 21 min —B - 22 min —f i - 23 min

58004

5400-

.5500-

■B 5600-C-o° 5700-

5800

5400-

.5500-

•B 5600-O.oQ 5700-

58000.00 0.20 0.40 0.60

Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction



Gas

Trac

tion

Gas

frac

tion

128


0 .0 6

0 .0 4

0.020.00

3 Interval = 0 - 5,422 ft

j N *

/| , . i . . . . . • • • ‘

10 15 20 25 30Time(minutes)

0 .4 0 : Interva] =5,422 - 5. 522 ft0 .3 0 :

0 .2 0 "0 .1 0 :

j

10 15 20 25 30Time (minutes)

c 0.60

“ 0.40Interval := 5,522 1,622 ft

0 5 10 20 2515 30Time (minutes)

s 0 .2 00 .1 5

c;c 0 .1 0(/]C 0 .0 5w 0 .0 0

In terval:= 5,622-i 1,822 ft

10 15 20 25 30Time (minutes)

0 ft

On-line 5,422 ft

Top 5,522 ft

Middle 5.622 ft

Bottom

5,722 ft (failed)

5,822 ft

TD = 5,884 ft



Dept

h (ft

) De

pth

(ft)

Dept

h (ft

)

129

Experiment: M16

20.7 21 min

54005400

55005500

rS 5600a .<aa 5700

5600

5700

580058000.0 0.2 0.4 0.60.00 0.20 0.40 0.60

22 min

5400

.5500

■S 5600a .oD 5700

05800-

Gas fraction Gas fraction0.00 0.20 0.40 0.60

Gas fraction

5400-

5500-

5600-

5700-

5800-

23 min

0.00 0.20 0.40 0.60 Gas fraction

24 min 25 min

5400 5400

5500cS 5600c.o° 5700

tS 5600

5700

5800 58000.00 0.20 0.40 0.60 0.00 0.20 0.40 0.60


26 min 27 min 30 min

5400-

5500-

5600-

5700

5800

B~ T

r■—■

5400-

^5500-cS 5600-

C l.o° 5700-

5800

5400-

.5500-I

5 5600*a .oQ 5700

5800-

II- I

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction

0.00 0.20 0.40 0.60 Gas fraction



130


- 0.061

Z 0.041

Iu 0.00-

In terval= 0 - 5,422 rt

I* ,

. A0 20 40 60 80 100 120

Time(minutes)

- 0.40joos* 0.201C/3cz

LOO

Interv; J =5,422 - 5, 522 ft

20 40 60 80 100 120Time(minutes)

- 0.60-q oZ 0.40

« 0.201 u 0.00

Interval = 5,522 - 5, 522 ft

— J 10 20 40 60 80 100 120

Time (minutes)

c 0 .2 0 1 *“ 0 1 5 "

Interval == 5,622 -4,822 ft— U.1S . « A in - :V*1U W A AC 'cc : ° 0 .00 J

10 15 20 25 30Time(minutes)

Oft

On-line 5,422 ft

Top 5,522 ft

Middle 5,622 ft

Bottom 5,722 ft (failed)

5,822 ft

TD = 5,884 ft



131

Experiment: M17

38 min

54005400

55005500

- 56005 56006 OQ 5700 5700

580058000.00 0.20 0.40 0.60

39 min 40 min

i t

Gas fraction


5400

5500

■B 5600

5700

58000.00 0.20 0.40 0.60

Gas fraction

■E 5600

41 min

0.00 0.20 0.40 0.60 Gas fraction

42 min 43 min

54005400

5500 5500

£ 5600 ~ 5600a.o° 57005700

580058000.000.200.40 0.600.80 0.00 0.20 0.40 0.60


— 45 min —H 46 min —B - 49 min

5400

.5500

•S 5600CL.oa

i

£5700 t

5800-0.00 0.20 0.40 0.60

Gas fraction

5400

5500

S 5600

5700

58000.00 0.20 0.40 0.60

5400

.5500 L

5 5600-CL.0>° 5700-

Gas fraction

5800-r0.00 0.20 0.40 0.60

Gas fraction

Figure C.24 Gas fraction as a function of depth for experiment M l 7



Oft= 0.16

— 0.12 1 0.08 «« 0.04' «0.00

Interv al = 0 - i ,422 ftj

/ " I * *

J H] !—— -

P

0 20 40 60 80 100 120 140Time(minute:

- 0.60 Interval 5, 522 ft=5,422 -

25 0.40

0 20 40 60 80 100 120 140Time(minutes)

- O M t T Z —3 3 In te rv a = 5,52: - 5,622 f t

w U.4U JjA" j a 1« U-20 J

« d ^ 0.00 i ------------ 11 '

0 20 40 60 80 100 120 140Time(minutes)

= 0.20- •§ 0.15- 1 0.10-

0.05-0.00-

3 Interva = 5,62: - 5.822 ft1111 1

20 40 60 80 100 120 140Tin

On-line 5,422 ft

Top 5,522 ft

Middle 5,622 ft


5,822 ft

TD = 5,884 ft



133

Experiment: M18

18.4 19 min

54005400

5500-

£ 5600

5700mu

580058000.0 0.2 0.4 0.60.00 0.20 0.40 0.60

20 min

5400'

^5500-s£ 5600 £2.° 5700

5800


Gas fraction

22 min

5400

5500

£ 5600 o. cjQ 5700

58000.00 0.20 0.40 0.60

23 min

5400

5500

-£ 5600

5700

58000.00 0.20 0.40 0.60

5400-

5500'c:£ 5600

CLCJ>° 5700-

5800'

24 min


Gas fraction

— 25 min — 30 min —B — 40 min

5400-

—. 5500-

£ 5600-c .oQ 5700-

5800-

1

0.00 0.20 0.40 0.60 Gas fraction

5400

5500

£ 5600a.oQ 5700

58000.00 0.20 0.40 0.60

5400-

.5500-

£ 5600-o.oQ 5700-

Gas fraction

5800 t0.00 0.20 0.40 0.60

Gas fraction



Gas

fr

actio

n ^

as fr

actio

n G

as

frac

tion

Gas

fr

acti

on

134

Type of experiment: Circulation at 62 spm (>sl=1.24 ft/sec)Experiment: M19

0.08-; Interval =

0.04-j

0.00

0-2,761 It

0.30"

0.20'

0.10'

0.00"

0.60-

0.40-i

0.20 i

0.000 20

0.20-0.15-0.10-0.05-0.00-

A Co—0 20 40 60 80 100 120

Time (minutes)

i iInterva = 2,761 - 2,861 ft

j

§1 *

20 40 60 80 100 120Time (minutes)

Interval = 2,861 - 2, 161 ft

—.. . - j 140 60 80 100 120

Time (minutes)

3 Interva = 2,961 - 5,822 ft1

j . . . 1 . ‘ ‘ 1 . •0 20 40 60 80 100 120 140

Time (minutes)

Oft

On-line 2,761 ft

Top 2,861 ft

Middle 2,961 ft

Bottom

3,061 ft (failed)

5,822 ft

TD = 5.884 ft



Depth

(ft)

De

pth

(ft)

Depth

(ft

)

135

Experiment: M19

2500-

2600 i 2700- 2800- 2900- 3000-

—B - 30 min

1

1

1

32 min

25002600

34 min

ciL'2700-

2500-2600-2700-2800-2900-3000-

—® 34.5 min

, m1 1J. |T I' 11

1 I

36 min

2500-2600-2700-

2800-2900-3000-

0.00 0.25 0.50 0.75 1.00 Gas fraction

§•2800-Q

29003000-

2500 ^2600 * 2700C^2800D

2900 i 3000

0.00 0.20 0.40 0.60 Gas fraction


0.00 0.25 0.500.751.00 Gas fraction

35 min

25002600

'2700-^2800^oa

2900j 3000

25002600

'2700-HI

HI

35.5

§-2800i D

2900 i3000-

0.00 0.25 0.50 0.75 1.00 Gas fraction

0.00 0.25 0.500.751.00 Gas fraction

0.00 0.25 0.50 0.75 1.00 Gas fraction

—M— 37 min — 38 min

2500 t2600-

'2700-

^2800-3<ua2900-J 3000

25002600

'2700-

^■2800-OQ

2900-3000-

0.00 0.100.200.30 0.40 Gas fraction

0.00 0.10 0.200.30 0.40 Gas fraction



136

Type of experiment: Circulation at 62 spm (>sl=1.24 ft/sec)Experiment: M20

Interval = 0 - 2 '

e 0.30 ‘ o

V)aO

0.10'

0.00'

D !0 40 60 80 100 120 14Time (mi

0 If nutes

Interv al = 2, 761 - 2. 861 ft

10 15 20 25 30 35 40 45Time (minutes)

e 0.30 qoZ 0.20cs* 0.10

$ 0.00

Interval = 2,361-2.951 ft

£

JL0 20 40 60 80 100 120 140 160

Time (minutes)

c 0.20-3 0.15

.£ 0.10-« 0 .0 5 1

° o.oo-

: Interv; il= 2,9 61-5 ,8 22 ftj:

j* 1 ‘ 1 1 I . i i 1 !

0 20 40 60 80 100 120 140 160Time(minutes)

Oft

On-line 2,761 ft

Top 2,861 ft

Middle 2,961 ft


5,822 ft

TD = 5,884 ft



Dcpt

ii (fi

) De

pth

(ft)

Dept

h (ft

)

137

Experiment: M20

2500-

2600-

2700-

2800-

2900-

3000-

I —® 45 min

j

II1

46 min

c. • u ■Q

2500

2600

2700

2800

2900

3000

—H- 48 min

TI1'

1

51 min

2500-q

2600

2800-

2900-

3000-

1

1 1 1J

1-111

2500

2600

'2700

■2800

2900-

3000-

47 min

1 B 11f v11iii

2500 n

2600 H

’ 2700

g-2800^ O

2900

3000'II

0.00 0.20 0.40 0.60 Gas fraction


0.6 0.000.25 0.500.751.00 Gas fraction

49 min

2500

2600

2700

g-2800-

2900-

3000-

Va

2500-2600-

•2700-

•2800-

2900'

3000

50 min

0.00 0.25 0.50 0.75 1.00 Gas fraction

0.000.25 0.500.75 1.00 Gas fraction

0.000.25 0.50 0.75 1.00 Gas fraction

52 min 55 min

oa

2500-

2600-

■2700-

•2800-

2900

3000ii—m

2500-

2600 •

2700-

oD

2900 i

30000.00 0.25 0.500.75 1.00

Gas fraction

0.000.25 0.50 0.75 1.00 Gas fraction

0.00 0.25 0.50 0.751.00 Gas fraction



138


_ 0.16:Interv il = 0 -2,76 I ft L;5 U.1Z”g

£ O.OSl a / m2 U.U4"Cq

/0.00“^ ♦ • * i * * *0 20 40 60 80 100 120 140 160 180 200

Time(minutes)

0.20'■x 0.15“ej «. i .«O

<so

0.10 ■: 0.051 0.00‘

0.30-

0.20-

0.10-

0.00-

■ Inter fal = j ,761- 2,861 Ift f ]/

i /= -r-rr-

1 i,

0 20 40 60 80 100 120 140 160 180 200Time(minutes)

Intei val = 2,861 -2,96 ft

f ]

i /

0 20 40 60 80 100 120 140 160 180 200Time(minutes)

*“ 0 15 :Inter val = 2,961 - 5,82: I ft

- U.15 ; c: a i n "> U*JLU -IM55 U»Uj -

° o .o o -

0 20 40 60 80 100 120 140 160 180 200Time (minutes)

Oft

On-line 2,761 ft

Top 2,861 ft

Middle 2,961 ft

Bottom 3,061 ft

(failed)

5,822 ft

TD = 5,884 ft



Dept

h (ft

) De

pth

(ft)

Dept

h (ft

)Experiment: M21

2500-2600-2700-2800-2900-3000-

j —® 118 min

jjIj |f

120 min 122 min

aa

2500-2600-

'2700--2800-2900-3000-it

2500-

2600-'2700-

§" 2800 iD

29003000

11-9i i - a

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

2500-2600-2700-2800-2900-3000-

124 min 128 min

F ti i— ■

oQ

2600-2700-

•2800-29003000

L SI

1

<uQ

2500-2600-

'2700-•2800-2900-3000-

130 min

I

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

132135 min 135 min

250026002700280029003000-

iTI■ i

i

aD

2500-2600-

'2700-•280029003000 3

2500-2600t

2700-oD

2900-3000-

3

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction



Gas

fr

actio

n ^

as fr

flCt'o

n G

as

frac

tion

Gas

fr

acti

on

140

Type of experiment: Circulation at 32 spm (■vsl=0.64 ft/sec)Experiment: M22

261-ftinterva0.16i

0 .0 8 i0.0410.00

0 20 40 60 80 100 120 140 160Time (minutes)

0 .3 0 10 .25=0.2010 .15=o.ion0 .0 5 10.001

In tp rv

I0 20 40 60 80 100 120 140 160

Time (minutes)

0 .3 0Interval = 2,861-2,96

0.20

0.0020 40 60 80 100 120 140 1600

Time(minutes)

0.20-0.15-0.10-0.05-0.00-

| Inter val = 2,961 - 5,82: : ft1111 ■ ■ • • ‘ ‘ ‘ i • *

0 20 40 60 80 100 120 140 160 180 200Time (minutes)

Oft

On-line 2,761 ft

Top 2,861 ft

Middle 12,961 ft

JL, Bottom 3,061 ft

(failed)

5,822 ft

TD = 5,884 ft



Depth

(ft)

De

pth

(ft)

Depth

(ft

)

141

Experiment: M22

2500260027002800-2900-q 3000

—B — 38 min

i i

IE

i i

40 min

2500-2600-i

45 min

^Q O S'2800-

25002600270028002900 i

3000

50 min

60 min

25002600270028002900-}3000 *

2900-3000-

25002600

'2700

oQ

2900 i 3000

a

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

52 min

2500-2600-

'2700-^ 2800 -oQ

2900-3000-

ua

2500-2600-

'2700-•2800-2900-

3000-

55 min

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

70 min 70 min

2500-32600-

'2700-<DG

2900 i 3000

2500-q 2600

'2700-

<DQ

2900 3000

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction



142


s 0.03-

Z 0.02- «u o.oru 0.00-

In ter ■al = 0 - 2,761 ft

1

[ ^ k i ,0 20 40 60 80 100 120 140 160 180

Time (minutes)

C 0.3(T . 2

Interv al = 2 , '61 - 2 . 861 f t

« 0.2CF

O.lflFC5

r •*w O.OCr ‘ * 1 1 . . .

0 20 40 60 80 100 120 140 160 180Time(minu

c 0.30

Z 0.20cz0.10 -=

u 0.00

j In ten al = 2i A

,861 -: :,96l i t

jLa

' ‘ 'it/j • A

0 20 40 60 80 100 120 140 160 180Time (minutes)

B 0 .2 0 -q-2 n

In te r a! = 2 ,961 - i1,822 1

?• ft 1 f t- \ f " *--------.U v*lU

n n c — \ l / ]C5 U.VO - ° 0 .0 0 J

0 20 40 60 80 100 120 140 160 180Time (minutes)

0 ft

O n-line

2,761 f t

Top

2,861 ft

M iddle

J 2,961 ft

Bottom

3,061 ft

(failed)

5,822 ft

TD = 5,884 ft



Depth

(ft

) De

pth

(ft)

Depth

(ft

)

143

Experiment: M23

2600-2700-

2900-3000-

— 20 min

1

1

1

22 min

2500 n 2600

25 min

'2700-

28 mm

35 min

2500-2600-2700-2800^29003000

2500-2600-

'2700-oQ

2900-3000-

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

30 min

25002600

'2700-

Q2900 i 3000

250012600 ~

'2700-

32 min

8“ 2800 D

2900 i3000

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

40 min 50 min

25002600

'2700-^ 2800a>D

2900-3000-

iiII !■

i M

25002600

'2700§-2800iQ

29003000 II

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

Figure C36 Gas fraction as a function of depth for experiment M23


Gas

fr

actio

n G

as

frac

tion

Gas

fr

actio

n G

as

frac

tion

144


0.20i

0.05-

1 J n te rv s 1 = 0 - 100 f t5 3) 4

5 J "

) T-t t t - T T —t - j

0 20 40 60 80 100 120 140 160 180Time (minutes)

0.301

0.201

0.101

0.00

o.oi-

o.oi-

o.oo-

Inteival = 100 - 200 ft

0 20 40 60 80 100 120 140 160 180Time (minutes)

Interval = 200 -303 ft

J0 20 40 60 80 100 120 140 160 180

Time(minutes)

0.20- 0.15-j 0.10-! 0.05 0.00 J

In ten al = 3 00 - 5,1■22 ftj[l

* ‘ ‘ * * • ' • ‘ 1 . * .0 20 40 60 80 100 120 140 160 180

Time (minutes)

Oft

On-line 100 ft

Top 200 ft

Middle 300 ft

Bottom 400 ft

(failed)

5,822 ft

TD = 5,884 ft



Depth

(ft

) De

pth

(ft)

Depth

(ft

)

145

Experiment: M24

200-

— 75 min

B-------

if

■

B_____

78 min

100

200

—M— 85 min

K-------

M■

f

i ■_____

100

0

100

200

300

S ioo.c

£200

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

300-

80 min

s ioo. s

£ 200

300-

*

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

s ioo

£ 200

300

90 min

0

gioo

£ 2 0 0

300 -p-

95 min

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

0.00 0.10 0.20 0.30 Gas fraction

—fit- 115 min —® 125 min

0-

« ioo

£ 2 0 0

300

« -

T

0

g 100Q 200-*-

300410.00 0.10 0.20 0.30

Gas fraction0.00 0.10 0.20 0.30

Gas fraction



146

Type of experiment: Circulation at 62 spin (vsl=1.24 ft/sec)Experiment: M27

__ 0.2(h•I o.isig 0.10-

0.051O 0.00^

In ten al = 0 2.761 f

Ifctrl20 40 60 80 100 120 140 160

s 0.40 -3 ••§ 0.30wi 0.20 1S 0.10 -j ° 0.00

In ten a! = 2,/ 61 - 2.8 SI ft ,1 1j j i L i , 11nHi

M i M B

20 40 60 80 100 120 140 160Time(minutes)

s 0.401.2 A *5 A " Interv; J = 2,? 61-2 ,9 SI ft

".jU •

« 5 A ‘‘J A 1> U.ZU -

r \cs U-lU : u 0.00 J J . .

20 40 60 80 100 120 140 160Time (minutes)

c 0.40-g0.30H

c:<2= 0.20-2V5 0.10 H

0.00 J

Interva

Os*fSII ;i - 3,o< l ftw>

\\

- J . \ - 4

20 40 60 80 100 120 140 160

s 0 .2 0 -g• 2 n i c ■

Interval = i i,061 - 5,822 ftz °*15 =J ? a i n *> U . I U -

CZ V « u J ;

° 0 .0 0 J50 100 150 200 250

Time(minutes)

0 ft

On-line 2,761 ft

Top Lj-12,861 ft

Middle J 2,961 ft

Bottom 3,061 ft

5,822 ft

TD = 5,884 ft



147

Experiment: M 27

2850-'2950-

§■305013150-3250-

—® 65 min

B-----

1

1

1

70 min

D

0.0 0.1 0.2 0.3 0.4 Gas fraction

75 min

2750 -BW28501I

'2950"§•3050-* Q

3150

32500.0 0.1 0.2 0.3 0.4

Gas fraction

79 min

27502850

2950§-3050-fe= a

3150-3250

0.0 0.1 0.2 0.3 0.4 Gas fraction

2750-2850-

'2950-•3050-3150-3250-

72 min

3 1

2750 ■»

2850 H■2950-

8" 3050-jfa

31503250-

I

0.0 0.1 0.2 0.3 0.4 Gas fraction

0.0 0.1 0.2 0.3 0.4 Gas fraction

77 min

2750-2850-

'2950-

oO

3150-

3250 4-

275028502950

8-3050^1 D

3150i

3250-

78 min

m = m

0.0 0.1 0.2 0.3 0.4 Gas fraction

0.0 0.1 0.2 0.3 0.4 Gas fraction

H 82 min —H — 85 min

27502850

2950^-3050<x>O

31503250

0.0 0.1 0.2 0.3 0.4Gas fraction

0.0 0.1 0.2 0.3 0.4 Gas fraction



Type o f experiment: Migration with choke closedExperiment: M28

s ° - 1 0 1 S

g 0 . 0 5 H

3 o.oo-

Interval = <) - 2,761 ft

5 0 100 1 5 0 200 2 5 0

0 . 8 0 -

0 . 6 0 -

0 . 4 0 -

3 0. 2 0 -

Time (minutes3 Interval = *.761 - 2.861 ft

i 1............. , A tflpBBLk—

5 0 1 0 0 1 5 0 2 0 0 2 5 0

Time(minutes)s

° * 4 0 1

0 . 3 0 H

c s* 0 . 2 0 - j

C/3C3 0 . 1 0 - ^

u0 . 0 0 -

Interval = 2 ,861-2 ,96 | ft

1

5 0 1 0 0 1 5 0 2 0 0 2 5 0

T:me(minutes)- 0 . 4 0 ^

0 . 3 0 i

c:

,h 0 . 2 0 H

C/3c5 0 . 1 0 H

u o.oo-

Interval = 2,961 - 3,06 ft

r —

j5 0 100 1 5 0 200 2 5 0

s 0 . 2 0 - q

I 0 . 1 5 - i

. £ 0 . 1 0 - 3

3 0 . 0 5 -

u 0.00-

Time [minutes)Interval = .5,061 - 5,822 ft

::

=

5 0 1 0 0 1 5 0 2 0 0 2 5 0

Time(minutes)

Oft

O n - l i n e

2,761 ft

Top 2,861 ft

Middle 2,961 ft

□ Bottom 3,061 ft

5,822 ft

TD = 5,884 ft



Depth

(ft

) De

pth

(ft)

Depth

(ft

)

149

Experiment: M28

2750-

2850-2950-3050-3150-3250-

— I5l min

f

j f

f

f

160 min

2750-

2850-2950-

I

^3050-OQ

275012850129503050-

165 min

180 min

2750-

2850- 2950- 3050- 3150- 3250

at0.0 O.l 0.2 0.3 0.4

Gas fraction

3150- 3250-

2750-■

163 min

0.0 O.l 0.2 0.3 0.4 Gas fraction



170 min

275 0H 2850

CD

D

'2950-•3050-3150-

3250 3

27502850

2950

QJQ

3150

3250

175 min

I


0.0 O.l 0.0 O.lGas fraction Gas fraction

—® 190 min — 200 min

oQ

2750-2850

'2950•305031503250

' L -

- H ----- II

I F = = 1-

2750 2850-fc

'2950-g-3050-a

3150 - 3250-

m=W





Gas

fr

actio

n G

»s fr

actio

n G

as

frac

tion

Gas

fr

actio

n G

as

frac

tion


0.60“

0.40

0. 20"

0.00

Interval = ) - 2,7 51 ft

0.4010.30i

0 20 40 60 80 100 120 140 160 180 200Time (minutes i

Interval = !.761

0.40-0.30-0.20 -

0.10-0.00-

0 20 40 60 80 100 120 140 160 180 200Time(minutes)

3 Intei val = 2,861 -2,96 ft1 \1 r J

N i

0 20 40 60 80 100 120 140 160 180 200Time(minutes)

0.40-0.30-0.200.10

E Intei val = 2,961 -3,06E / Vj r V ij

i ,X

w* ‘ ‘ • * ‘

0.400.300.200.100.00

0 20 40 60 80 100 120 140 160 180 200Time (minutes)

d Inter val = ; 1,061 ■5,822 ft

3 / r1 /3 / r1 ■ ‘ • * 1 . * 1 »0 20 40 60 80 100 120 140 160 180 200

Time(minutes)

Oft

On-line 2,761 ft

Top LJ2,861 ft

Middle 2,961 ft

Bottom 3,061 ft

5,822 ft L

TD = 5,884 ft



Depth

(ft)

De

pth

(ft)

Depth

(ft

)

151

Experiment: M29

2750-II2850-iff2950iff

3250-

—B - 60 min

1-----

B

I

1

65 min

275012850

70 min

<oQ

2750Tjff 2850 2950 3050

3150 3250

80 min

3

110 min

2750t

2850-1---- i « -2950------ * -3 0 5 0 il= = « -3150i3250

'2950•305031503250

E0.0 0.1 0.2 0.3 0.4

Gas fraction0.0 0.1 0.2 0.3 0.4

Gas fraction

90 mm

0.0 0.1 0.2 0.3 0.4 Gas fraction

120 min

27502850

'2950§•3050

31503250

* = *

0.0 0.1 0.2 0.3 0.4 Gas fraction

JCn. -

27502850

'2950

31503250

—S 100 min

1-----

1* !8 —i i

IS—

0.0 0.1 0.2 0.3 0.4 Gas fraction

0.0 0.1 0.2 0.3 0.4 Gas fraction

130

27501B = =*ff28501 H 12950"

*5I1

o ivjU "1Q

n B3150 . 3250 J

0.0 0.1 0.2 0.3 0.4 Gas fraction

0.0 0.1 0.2 0.3 0.4 Gas fraction

0.0 0.1 0.2 0.3 0.4 Gas fraction



VITA

Shiniti Ohara, bom in Sao Paulo, Brazil, received a Bachelor of Science degree in

Civil Engineering from Universidade Estadual de Campinas, Sao Paulo, Brazil, in 1979.

Following graduation, he joined Petroleo Brasileiro S.A. (Petrobras) where he took two

years of graduate courses in petroleum engineering at Petrobras Training Center in

Salvador. Upon finishing the course, he moved to Petrobras headquarters in Rio de

Janeiro. There he worked for five years as a drilling engineer in offshore rigs and well

design activities. In August 1987, he entered Universidade Estadual de Campinas where

he earned his Master of Science degree in petroleum engineering in March 1989. After

his graduation he was relocated to the Special Techniques Sector of the Drilling

Department, where he worked with new drilling bits, air drilling in the Amazon jungle,

and turbo-drilling. In 1990, he was the head of the Directional Drilling Sector, where he

worked on the first Latin American offshore horizontal well. Following this, in 1991, he

was the head of exploration drilling for South and Southeast Regions o f Brazil. He

worked there until Spring 1992 when he entered the doctoral program in the petroleum

engineering at Louisiana State University. He is married to Neuza F. Suguihara Ohara

and they have two children: Sara Hitomy (12 years old) and Fabio Shinji (10 years old).

152


DOCTORAL EXAMINATION AND DISSERTATION REPORT

Candidate: Shiniti Ohara

Major Field: Petroleum Engineering

Title of Dissertation: Improved Method for Selecting Kick ToleranceDuring Deepwater Drilling Operations

Approved:

fk h r tn ~T. /WMajor P rofessor send Ghai

'LDean of the—Graduate School

EXAMINING COMMITTEE:

7/ 0. £&

£

Date of examination:

1 2 /0 8 /9 5 ___________


improved method for selecting kick tolerance during

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