lot-thesis - in situ stress estimation

UNIVERSITY OF OKLAHOMA

GRADUATE COLLEGE

THE VALIDITY OF LEAK-OFF TEST FOR IN SITU STRESS ESTIMATION;

THE EFFECT OF THE BOTTOM OF THE BOREHOLE

A THESIS

SUBMITTED TO THE GRADUATE FACULTY

in partial fulfillment of the requirements for the

Degree of

MASTER OF SCIENCE

By

APIWAT LORWONGNGAM

Norman, Oklahoma

2008

THE VALIDITY OF LEAK-OFF TESTS FOR IN SITU STRESS ESTIMATION;

THE EFFECT OF THE BOTTOM OF THE BOREHOLE

A THESIS APPROVED FOR THE

MEWBOURNE SCHOOL OF PETROLEUM AND GEOLOGICAL ENGINEERING

BY

__________________________________

Dr. Jean-Claude Roegiers, Chair

__________________________________

Dr. Samuel Osisanya

__________________________________

Dr. Jeffrey Callard

iv

ACK�OWLEDGEME�TS

First of all, I would like to express my appreciation to my wonderful advisor, Dr. Jean-

Claude Roegiers, for his inspiration, advice, corrections, support, and guidance

throughout my wonderful time here at the University of Oklahoma.

I would also like to thank all my committee members, Dr. Samuel Osisanya and Dr.

Jeffrey Callard for their assistance on the committee and for their illuminating classes.

I would like to express my respect and appreciation for being my great inspiration,

encouragement, and support for my life and degree here in the University of Oklahoma

to my beloved parents, Kamthorn Lorwongngam and Urai Lorwongngam, and my

wonderful family; Kitima Lorwongngam, Nares Lorwongngam, Drs. John and

Kulwadee Pigott, Anuparb Lorwongngam, Atipat Lorwongngam, Emma Jane

Lawrence, Chungao Sae Lor, Malee Lorwongngam, Tirada Wongdao, Manit and

Nuannoi wongdao, and the rest of my wonderful family.

I would also express my gratefulness to Itasca Houston Inc., as part of this

achievement, for providing FLAC3D for numerical simulation in this thesis.

Special thank to Dr. Gang Li, David Martinez, and Dung Tran for all the help with this

thesis.

v

Special appreciation also to all the staff at the Mewbourne School of Petroleum and

Geological Engineering, especially Shalli Young and Sonya Grant, for their kindness

and assistance throughout my degree.

I am also grateful to all faculty members of the Mewbourne School of Petroleum and

Geological Engineering for all the wonderful coursework and support during my time

in the University of Oklahoma especially; Dr. Roy Knapp, Dr. Yucel Akkutlu, Dr.

Robert Hubbard, Dr. Chandra Rai, Dr. Subhash Shah, and Dr. Djebbar Tiab,

vi

TABLE OF CO�TE�TS

Acknowledgments ……………………………………………………………………… iv

Table of Content …………….………………………………………………………….. v

List of Tables ………………………………………………………………… ……........x

List of Figures ………………………..……………………….……………… …………xi

Abstract ……………………………….……………………………………… ………..xxi

CHAPTER 1: INTRODUCTION ................................................................................. 1

1.1 Introduction............................................................................................................. 1

1.2 Critical literature review ......................................................................................... 3

1.3 Leak-off test for stress estimation issues description ............................................. 8

1.4Definition of Pressure integrity tests (LOT’s, FITs, and ELOT’s or XLOT’s) ..... 10

CHAPTER 2: CRITICAL REVIEW OF LEAK-OFF TESTS (LOT’s)..................... 13

2.1 Generalities ........................................................................................................... 13

2.2 Leak-off test procedure review ............................................................................. 15

2.3 Leak-off tests nomenclature.................................................................................. 16

2.4 Factors that affect leak-off tests ............................................................................ 17

2.4.1 Fluid Properties.................................................................................................. 17

2.4.2 Rock and elasticity............................................................................................. 18

2.4.3 Effect of wellbore .............................................................................................. 18

2.4.4 Fluid penetration ................................................................................................ 19

2.4.5 Permeability ....................................................................................................... 20

2.4.6 Pre-existing cracks ............................................................................................. 20

vii

2.5 Interpretation of leak-off test for stress determination ......................................... 23

2.5.1 Estimating minimum stress from individual leak-off test.................................. 24

2.5.2 Empirical stress estimates from LOT data......................................................... 25

2.5.3 Inversion of LOT data........................................................................................ 26

2.6 Leak-off tests field procedure guidelines.............................................................. 27

2.6.1 Pumping guidelines............................................................................................ 29

2.6.2 Shut-in guidelines .............................................................................................. 30

2.6.3 Interpretation guidelines .................................................................................... 31

CHAPTER 3: REVIEW OF EXTENDED LEAK-OFF TESTS (XLOT’s or ELOT’s)32

3.1 Extended leak-off tests review.............................................................................. 32

3.2 Theory of stress determination by extended leak-off tests and hydraulic fracturing

tests ............................................................................................................................. 33

3.3 The differences between extended leak-off tests and hydraulic fracturing stress tests

..................................................................................................................................... 35

3.4 Extended leak-off test procedures......................................................................... 37

3.5 Extended leak-off test nomenclature .................................................................... 38

3.6 The differences between extended leak-off tests and leak-off tests ..................... 39

CHAPTER 4: PLANE STRAIN STRESS DISTRIBUTION ALONG THE

BOREHOLE WALL................................................................................................... 41

4.1 Overview............................................................................................................... 41

4.2 Borehole wall stresses........................................................................................... 41

4.3 Tangential stress and tensile fracturing................................................................. 45

4.4 Assumptions of the borehole stress calculation .................................................... 46

viii

CHAPTER 5: BOTTOM OF A BOREHOLE STRESS SIMULATION ................... 49

5.1 Simulation software .............................................................................................. 49

5.2 Bottom of a borehole model ................................................................................. 49

5.3 In situ stress condition .......................................................................................... 52

5.4 Bottomhole internal pressure ................................................................................ 54

5.5 Simulation results analysis.................................................................................... 55

CHAPTER 6: RESULTS AND DISSCUSIONS ....................................................... 58

6.1 Stress contours ...................................................................................................... 59

Case 1: ratio of hσ and Hσ equals 1.......................................................................... 59

Case 2: ratio of hσ and Hσ equals 1/2....................................................................... 60

Case 3: ratio of hσ and Hσ equals ¼......................................................................... 61

Case 4: ratio of hσ and Hσ equals 1/8....................................................................... 62

Case 5: ratio of vσ and Hσ equals 1 .......................................................................... 63




Case 9: ratio of vσ and hσ equals 1........................................................................... 67

Case 10: ratio of vσ and hσ equals 2......................................................................... 68



ix

6.2 Discussion ............................................................................................................. 71

6.3 The rotation of stress tensor at the bottom of the borehole................................... 73

6.4 Bottom hole stress rotation angles ........................................................................ 75

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS .............................. 79

7.1 Conclusions........................................................................................................... 79

7.2 Recommendations............................................................................................. 82

REFERENCES……………………………………………………………………...100

APPENDIX A: SIMULATION RESULTS FOR 30, 40, AND 60 MPA INTERNAL

BOTTOM HOLE PRESSURE. …………………………………………..………....83

Simulation results for bottomhole internal pressure equals to 30MPa……………...86

Simulation results for bottomhole internal pressure equals to 40 MPa……………..92

Simulation results for Internal bottomhole internal pressure equals to 80 MPa …....98

APPENDIX B: three-dimensional stress analysis …………………………………..105

Appendix C: NOMANCLATURE………………………………………………..... 109

x

LIST OF TABLES

Table 1.1 : Classification of pressure tests performed at the casing shoe: PITs……..25

Table 5.1: properties of rock (Shale) used in the simulation……………………...…66

Table 5.2 : Initial in situ stresses used in the simulation (in this table, positive value

represents compression)…………………………………………………………...…69

xi

LIST OF FIGURES

Figure 1. 1 plane strain assumptions in an infinite borehole (after Eberhardt [21])..... 9

Figure 1. 2 Idealized extended leak-off test, showing the differences between each

pressure integrity tests (after White et al. [18]). ......................................................... 11

Figure 2. 1: A typical results from standard leak-off tests; leak-off pressure versus

volume (from Addis et al. [8]) .................................................................................... 14

Figure 2. 2: Illustrate a typical open-hole leak-off test plot (from D.P. Postler [9]) .. 15

Figure 2. 3: Effect of pre-existing crack adapt from Postler [9] (top figure shows

illustration of the plot when there is no crack in the wellbore, minimum stress at

wall=x. Bottom figure shows the effect of pre-existing crack for the LOT plot (blue

line-slower pumping rate and black line-faster pumping rate). .................................. 21

Figure 2. 4: Effect of Pump Rate ................................................................................ 23

Figure 2. 5: guide lines on PIT plot (Postler [9])........................................................ 29

Figure 2. 6: Check pump rate with guide lines (Postler [9])....................................... 29

Figure 3. 1: Example of ELOT Ideal responses (Addis [8])....................................... 36

Figure 3. 2: Critical points on extended leak-off tests plot (Økland et al. [15])......... 39

Figure 4. 1: Coordinate system and principal stresses................................................ 43

xii

Figure 4. 2: Illustration of a borehole subjected to both internal fluid pressure and

external compression, and associated coordinates (reproduced from Whittaker et al.

1992, [21])................................................................................................................... 44

Figure 4. 3: Tangential stress distribution at borehole wall as a function of the angle

with respect to the maximum principal stress (reproduced from Whittaker [21])...... 44

Figure 5. 1: schematic of the borehole model............................................................. 50

Figure 5. 2: FLAC3D borehole model........................................................................ 51

Figure 5. 3: cross-section of the borehole model........................................................ 52

Figure 5. 4: Schematic top view of applied stresses vector at the borehole model. ... 54

Figure 5. 5: Example of the executed result from FLAC 3D...................................... 56

Figure 5. 6: Illustration of the selected element for stress analysis ............................ 57

Figure 6. 1: Case 1 Maximum principal stress contour plot ....................................... 59









Figure 6. 10: Case 10 Maximum principal stress contour plot ................................... 68

xiii



Figure 6. 13 Displacement vector at the bottom of the borehole when vσ is eight times

greater than hσ . ........................................................................................................... 72

Figure 6. 14 Cross-section of stress tensor plot from case 13 .................................... 74

Figure 6. 15 Cross-section of stress tensor plot from case 13 .................................... 74

Figure 6. 16 Cross-section stress tensor from Case 2 with the indication of the stress

rotation area ................................................................................................................ 75

Figure 6. 17 Illustration of initiated fracture at the specified element........................ 77

Figure 6. 18 Plot of minimum compressive stress ( 3σ ) versus stress ratio................ 77

Figure 6. 19 Plot of minimum compressive stress ( 3σ ) versus stress ratio................ 78

Figure 6. 20 Illustration of a drastic change in orientation of the minimum compressive

stress from left to right. ............................................................................................... 78

1

CHAPTER 1: I�TRODUCTIO�

1.1 Introduction

Most operations in the petroleum industry require an accurate knowledge of the in situ

stress tensor: drilling, completion, wellbore stability, sanding, waterflooding,

stimulation etc. In drilling operations, such stress estimations help engineers to

determine the required mud weight for the next section of the rock formation before

casing is placed. Moreover, it also helps engineers to determine the optimum trajectory

for horizontal and/or directional wells. There are many different field techniques for

determining in situ stress in rock formations. Such methods include the leak-off test

(LOT) or pressure integrity test (PIT), formation integrity test (FIT), extended leak-off

test (ELOT or XLOT), and the micro-hydraulic fracturing ( µ HF) method. The

recommended method by the ISRM (International Society of Rock Mechanics) and

most widely used in the petroleum industry is the micro- or mini- hydraulic fracturing

method (µ HF). This method was developed from the stimulation operation by creating

a fracture in the formation in order to create more conductivity from the reservoir to the

wellbore. In addition, it is considered to be the most accurate method for determining

the minimum horizontal stress (Gjonnes et al. [7]). Due to the duration and the cost of

the hydraulic fracturing method; simpler tests, leak-off tests, are more widely

performed.

2

The leak-off tests are normally performed in a new well (wildcat well) where the

formation characteristics have not yet been established; they are usually performed after

each casing string is cemented in place. The principal purposes of this test are to

evaluate the maximum pressure that the casing shoe can withstand, determine the

integrity of previous cement job, and determine the maximum mud weight which can

be used for the next casing setting depth. However, the data is commonly used beyond

its original purpose, for in situ stress estimations.

The interpretation of leak-off tests for stress estimation has been used in exploration

and drilling planning, including sealing capacity of faults, mud weight design, fracture

gradient estimation, wellbore stability, well array planning and the development of

fractured reservoirs (Addis [8]). It also has been used in some completion and

production problems such as sand production, reduction of production rate, and

reservoir compaction and subsidence (Addis [8]). Even though leak-off tests have been

used for in situ stress estimation, many aspects can be questioned; e.g. testing

procedures, equipment, interpretation and calculation, and measurement uncertainties.

This thesis only addresses the issue of using leak-off test for stress estimation by

focusing on the bottom hole stress concentrations and testified to be not suitable for

stress estimation. The proper methods for stress estimation will also be stated in this

thesis.

3

1.2 Critical literature review

Many authors, Raaen et al (1998), Gjønnes et al (1998), Enever et al (1996), and Kunze

and Steiger (1992), questioned leak-off tests in many aspects and stated limitations for

the tests. Some authors (white et al. [18]) supported the idea that leak-off tests can be

used for stress estimation; others (Raaen et al. [14]) tried to modify the leak-off tests to

reduce uncertainties, errors, in an attempt to get more reliable results from it.

In 2006, Raaen et al. presented a paper called “Improved Routine Estimation of the

Minimum Horizontal Stress Component from Extended Leak-Off Tests.” They

reviewed the high quality extended leak-off tests with flowback data (high density of

measuring points) compare with the low quality data. They found that a properly

performed extended leak-off test (ELOT or XLOT) will give better results for in situ

stress estimations. They underlined another limitation of leak-off tests that, if for some

reason, the open hole is more than a few meters in length; the leak-off test data should

not be used for stress estimation. Moreover, the leak-off test is normally performed

without a downhole packer, and pumping is from the surface. As a result, the leak-off

tests do not qualify for stress estimation by international society of rock mechanics

(ISRM) recommendation. They also used an approach called the “system stiffness”

approach to implement the interpretation of extended leak-off tests. The so called

system stiffness is the concept for pump-in and flowback tests where the stiffness of the

system was measured by plotting flowback volume versus pressure. In the conclusion

of their paper, they proposed that the extended leak-off tests do not give precise

4

estimation of the in situ stress, unless the formation is highly permeable. Further, they

claim that the in situ stress was 6-8% lowers than the final shut in pressure and the leak-

off point (LOP) is not generally equal to the minimum horizontal stress. However, they

recommended the extended leak-off tests with flowback as the recommended practice

for routine measurement of the minimum in-situ stress in deep petroleum wells.

In 2003, the ISRM published a series of papers called “ISRM Suggested Methods for

rock stress estimation,” This document contains four parts. The methods that were

suggested are overcoring, hydraulic fracturing, and hydraulic testing of pre-existing

fractures (HTPF)

In 2002, White et al. presented a paper entitled “The Use of Leak-Off Tests as Means

of Predicting Minimum In situ Stress”. They found that the difference of calculated

minimum horizontal stress (σh) when comparing leak-off pressure (LOP) with

instantaneous shut-in pressure (ISIP) is small, less than 5%. So they stated that if the

testing procedure is well conducted and recorded, selecting the leak-off pressure (LOP)

or instantaneous pressure gives equally valid estimates of minimum horizontal stress.

In 2001, Eberhardt presented a paper entitled “Numerical Modeling of Three-

Dimension Stress Rotation Ahead of an Advancing Tunnel Face”. This paper studies

the changes in orientation and magnitude during an excavation. It shows that the stress

field tensors changes magnitude and rotates ahead of an advancing tunnel face by using

three dimensional finite-element models. It also proved that while drilling the tunnel,

5

the primary in situ stress field is disturbed and redistributed. Therefore, if this

orientation changes in time, such as during the advancement of the tunnel face, the type

of damage and fracture induced in rock mass may vary depending on the type and

degree of stress rotation. In the conclusion, he stated that the results of stress orientation

and magnitude changes ahead of an advancing tunnel controls the preferred direction

for fracture propagation, and it could also be applied to deep borehole drilling.

Essentially, this paper leads to question the validity of the leak-off tests; especially the

influence of the bottomhole.

In 1998, Gjønnes et al. stated in a paper entitled “Leak-off test for horizontal stress

determination?” that leak-off tests were interpreted based on the assumption that all

shear stress components were neglected. They proved that by taking into account the

entire stress tensor at the borehole wall combining with data analysis and field data that

shear stress should not be neglected in the inversion process and that significant errors

(30 to 40%) were introduced. They stated that there are no standards for leak-off tests

for stress estimation in the petroleum industry. They concluded that the use of leak-off

data may be questioned regarding its measurement uncertainty and to what extent the

leak-off point represents fracture initiation, In addition, they stated that inversion

technique based on leak-off data is not sufficient analyzing the horizontal stress field.

In 1998, Addis et al. presented a paper entitled “A Comparison of Leak-Off Test and

Extended Leak-Off Test Data for Stress Estimation.” They stated the procedure for

conducting leak-off tests and extended leak-off tests (XLOT) for stress estimation but

6

they also pointed out that there is no standard methodology in the industry for the tests.

Furthermore, they stated that such tests are invariably performed in shales; and, as such,

any stress estimate is only valid for the shales, which are the most competent

formations, having the highest fracture gradient (Addis [8]). Therefore, the test data

should not be extrapolated directly to other lithologies e.g. sandstones and limestones.

Moreover, they also stated that the use of standard leak-off tests as a stress

measurement technique suffers from a number of uncertainties. The most serious being

that the pressure record may not reflect the initiation of a fracture necessary to predict

the stress field, but may be an artifact of mud compressibility, casing expansion,

cement leakage, etc. Furthermore, they also questioned the instantaneous shut-in

pressure from only one cycle being a representative of the minimum horizontal stress?

In addition, they stated that the assumption of the leak-off pressure to be equal to the

fracture initiation pressure requires an in-gauge impermeable borehole which acts

elastically during pressurization. The last drawback of leak-off test stated in this paper

is that the mechanics and interpretation of the test are poorly understood, as the test is

not designed to be a stress test.

In 1997, Postler presented many factors that affect leak-off tests e.g. elastic rock, effect

of the wellbore, fluid viscosity, fluid penetration and permeability, pre-existing cracks,

pump rate, shut-in pressure, and cement channels. He also developed a guideline to

perform and interpret leak-off tests for better understanding of the plot shapes

associated with those effect factors. See the Section 2.4 “factors that affect leak-off

tests” in this thesis for more detail.

7

In 1996, Enever et al. clearly stated in “Recent Experience with extended leak-off tests

for in-situ stress measurement in Australia” that the standard leak-off test is not a stress

measurement technique but a drilling procedure. Moreover, they also stated that the use

of leak-off tests as a stress measurement technique suffers from many serious

deficiencies. The main point being that the curve may not be an effect from fracture

initiation, but it may be an artifact of mud compressibility, casing expansion, and

leakage of the casing cement, etc. which is similar to what Addis stated latter in 1998.

There is a fundamental question of the validity of data obtained from the single

pressurization cycle of typical leak-off tests and the possibility that such data may be

unduly influenced by formation tensile strength and proximity of a crack to the

wellbore.

In 1992, Kunze and Steiger stated in theie paper called “Accurate In-Situ Stress

Measurements during Drilling Operations” that conventional leak-off tests are

performed routinely to test the integrity of casing cement jobs and are not an accurate

measurement of the earth stresses. Moreover, they also questioned some aspects of

leak-off tests. First, leak off test lacks the tensile strength measurement by assuming it

to be negligible which is true only in the pre-fractured wells. Besides, conventional

leak-off tests usually count only one cycle, while pre-fractured conditions require at

least two cycles of pumping to be created, which means that the first cycle of the test is

to create the pre-fractured condition in a borehole. Second, pressure data are only

recorded once every half barrel or every minute, which is insufficient for identifying

8

pressure changes caused by intiation of a fracture. Third, shut-in time is usually 10

minutes which may not be long enough for the fracture to close; minimum stress is

identified at fracture closure. Because of these uncertainties, they also presented the

modification of the leak-off tests method which is called extended leak-off test.

In 1986, Daneshy et al. presented a paper entitled “In-Situ Stress Measurements during

Drilling” in which they proposed a microfracturing experiments using drilling mud.

The main difference here is that they used one packer to seal off a top section of a

borehole. Six tests were conducted in open hole during drilling operations. Three out of

six test showed fracture extension below the bottom of the open hole and were cored

out to inspect the orientation of the fracture. In conclusion, this paper stated that

engineering value of the least principal stress can be determined from microfracturing

of open hole during drilling, and the core can be used to help determine fracture

orientation.

1.3 Leak-off test for stress estimation issues description

As discussed above, many aspects of this particular test have already been questioned,

but this thesis focuses on the influence of the geometry of the bottom of the borehole on

fracture initiation. Leak-off tests data interpretation is based on the hydraulic fracturing

(HF) method; i.e. assuming an infinite long borehole; hence, plane strain condition. The

plane strain is a two dimensional solution of the stress around the borehole. Such

constraints require that the problem geometry is represented as a cross-section

perpendicular to the infinite borehole axis, as shown in Figure 1.1. Therefore excluding

9

the three-dimension stress concentration due to the bottom of the borehole during the

stress analysis could introduce tremendous errors in the in situ stress measurement.

Based on Eberhardt [24], one can question that whether vertical fractures are always

created by the pressurization of the bottom of a borehole while the stress concentration

changes its magnitude and orientation during the drilling operation.

The approach to this issue, in this thesis, is by incorporating the bottom of the borehole

in the overall stress analysis. One can observe its effect during the pressurization. This

was achieved by using the finite difference commercial software called FLAC3D (Fast

Lagrangian Analysis of continua in 3-Dimensions). As will be seen, vertical fractures

are not always created, leading to question the validity of the leak-off test for in situ

stress estimations.

Figure 1. 1 plane strain assumptions in an infinite borehole (after Eberhardt [24])

10

1.4 Definition of Pressure integrity tests (LOT’s, FITs, and ELOT’s

or XLOT’s)

To prevent confusion from the different names used in the test methods, the terms of

each test need to be defined. Pressure integrity test (PIT) is a general term for any test

that implies borehole pressurization. It is used to help design casing programs for kick

tolerance and blowout prevention. What defines each different type of pressure

integrity tests and the usefulness of data for stress estimation is the point where the

pressurization stops (Addis et al. [8]). Leak-off tests (LOT’s) are pressure integrity tests

in which the pressurization continues until the rate of pressure increase declines which

is an indication of fluid leak-off in the formation. Raaen et al. (2006) gave a definition

of leak-off tests as tests where the pressurization phase is stopped between the leak-off

point (LOP) and the formation breakdown point (FBP). Formation integrity tests

(FIT’s) are tests for which the pressurization phase continues to reach the pre-defined

maximum value but no leak-off is established, as shown in figure 1.2. Extended leak-

off tests (ELOT’s or XLOT’s) are tests for which the pressurization phase continues

beyond the formation breakdown pressure and they are usually preformed with two or

more pressurization cycles. In order to explicitly show the differences and the

usefulness of each test, it is useful to clarify different type of pressure integrity tests in a

following table.

11

Figure 1. 2 Idealized extended leak-off test, showing the differences between each

pressure integrity tests (after White et al. [18]).

12

Pressure Integrity test name Test Description

Usefulness in

stress

estimation

Formation Integrity Test (FIT):

The test is run until planned maximum mud

weight is reached but does not reach leak-off

pressure

little

Leak-off test (LOT)

The test is run beyond leak-off pressure (LOP),

and proper leak-off pressure is determined.

poor

Leak-off test (LOT)

The test is run beyond leak-off point but shut-in

before any apparent breakdown and the pressure

decline is monitored.

poor

Leak-off test (LOT)

The test is run beyond formation break down

pressure, determine formation break down

pressure, and pressure decline is monitored.

Moderate

Extended Leak-off Test (ELOT) or

(XLOT)

The well is shut-in beyond formation break-

down pressure, and the pressure decline is

monitor. A two or more cycles of pressurization

and shut-in are performed.

GOOD

Table 1.1 : Classification of pressure tests performed at the casing shoe: PITs.

(Modified and reproduced from Addis et al. [8])

13

CHAPTER 2: CRITICAL REVIEW OF LEAK-OFF TESTS (LOT’s)

2.1 Generalities

Over the past 40 years leak-off tests have been used for stress estimation due to the

apparent similarity to the micro hydraulic fracturing tests. However, the leak-off tests

do not use the same equipment yielding a number of uncertainties.

The basic procedure to run a leak-off test is to pressurize the bottom of the borehole

until the fracture is initiated, monitor the pressure, and interpret the data. Figure 2.1 and

2.2 illustrate typical leak-off test plots. However, in figure 2.2, the test carries further

into the shut-in period. Leak-off pressure, point A in figure 2.2, is the point where the

data starts to deviate from the linear trend due to the fracture being initiated in the

formation or effect of increasing stress to the permeability; i.e. the formation starts to

take fluid. After the fracture has been initiated, fluid is lost by two ways which are:

filtrate lost across the permeable faces of the fracture; and, the mud lost through

fractures. These fluid losses tend to increase the pressure as more fluid is being pumped

and eventually causes the slope of the plot to change after the leak-off pressure.

From the leak-off pressure to the maximum pressure point, regarding figure 2.1, the

line shows that pump pressure increasing steadily. This increasing in pressure identify

that there is a stable fracture growth or the extension of existing fractures, which

14

commonly occurs in leak-off tests (Postler 1997 [9]). On the other hand, unstable

crack, breakdown, can occur when sufficient fluid is pumped to overcome losses and

transmit more pressure to the tip of the crack or when pressure and fluid losses in the

crack are small. If this case happens, it will show the decline or level out the plot.

Shortly after the plot reaches point B in figure 2.2, the pump is stopped. Then, shut-in

pressure will be monitored to check for leaks in casing or cement job. Normally, shut-in

pressure will drop drastically at the beginning due to the loss of fluid into the opened

fractures and the loss of pump friction pressure. The significantly decreasing in shut-in

pressure causes the fracture to close. After the fracture closes, pressure will slowly

reduce due to less fluid losses in to formation. The leak-off test will be concluded when

the shut-in pressure declines to approximate constant value.

Figure 2. 1: A typical results from standard leak-off tests; leak-off pressure versus

volume (from Addis et al. [8])

15

Figure 2. 2: Illustrate a typical open-hole leak-off test plot (from D.P. Postler [9])

2.2 Leak-off test procedure review

As proposed by many authors, there is no standard field procedure for leak-off tests.

Therefore, the test procedure and interpretation have been questioned by many authors.

To obtain reliable mud weight and fracture pressure; proper procedure of leak-off test is

required. The following procedure is based on the recommended methods from Kunze

and Steger paper [6].

Before beginning a leak-off test, the well should be circulated until the drilling fluid

density is uniform throughout the well and verify that there are no cuttings or slugs of

16

heavy mud in the drillpipe. The proposed procedure to conduct a leak-off test is the

following after the casing is cemented and the cement is consolidated:

1. Drill 10-20 feet (3-6 meters) down in to new fresh formation. The depth of fresh

formation drilled varies for each service company.

2. Pull up the drill string 3-4 feet from the bottom of the wellbore.

3. Close blowout preventer (BOP).

4. Pump down drilling fluid into bottom of the hole at a slow constant rate; normally

0.25-1.5 barrel/min(0.04-0.16 m3/min)

5. Continue pumping until the rate of pressure slowly increases or the curve starts

deviating from a straight line which is an indication of formation breakdown

6. After the formation is broken down, stop the pump.

7. Shut in the formation

8. Monitor the decrease of pressure for 10 minutes.

2.3 Leak-off tests nomenclature

The following are definitions of the nomenclature for the leak-off tests. However, this

nomenclature can be different depending on the service company performing the job.

Leak-off pressure (LOP) is the pressure where the pressure/time or pressure/volume

curve starts to deviate from the straight line. In other words, it is the pressure where

fluid starts to leak into the formation. It generally depends on the type of formation,

permeability, and the presence of pre-existing fractures.

17

Formation breakdown pressure (FBP) or breakdown pressure (BDP) is the maximum

pressure during leak-off test where rock tensile strength and the stress concentration at

the borehole wall and the bottom of the borehole is overcome.

Instantaneous shut-in Pressure (ISIP) is the pressure immediately after pumping has

stopped. This pressure will fall off to a level where it balances the formation stresses

trying to close the fracture (Rocha et al. [11]).

2.4 Factors that affect leak-off tests

Not all leak-off tests plots yield similar results. It is sometimes difficult to interpret the

leak-off plot because the plot does not show the standard expectation. Moreover,

sometimes the plot shows nonlinear behavior, several slopes, or it may seem that the

fracture has not closed. These issues can make the result difficult to interpret. In fact, it

is difficult to identify the leak-off point in these non-typical behaviors of leak-off tests

plots.

2.4.1 Fluid Properties

Fluid properties, especially viscosity, have an enormous effect on the leak-off tests

plots since fluid is used to transmit the pressure to the bottom of the hole. Therefore,

18

fluid viscosity will play an important role on “crack stability” of the formation. The

higher the viscosity, the greater the pressure drop in the fracture. As the result, the

higher viscosity fluid (such as drilling mud) tends to show the delay between fracture

opening and formation breakdown. However, for less viscous fluid (such as water) the

delay is less.

2.4.2 Rock and elasticity

For rock elasticity, stress vs. strain plots in rocks will show a straight line relationship

due to the elasticity of the rock until it reaches the point of failure. This straight line

trend will start to deviate at the point of fracture. Not all rocks behave this way; other

types of formation such as salt and unconsolidated clays behave plastically. In other

words, it can deform to a certain point without losing strength. In such formations, leak-

off tests tend to show non-linear plot which can cause difficulties during interpretation

(Postler [9]).

2.4.3 Effect of wellbore

When a wellbore is pressurized, fluid pressure tends to deform both the bottom of the

borehole as well as the borehole wall. To create a fracture, fluid exerts a force to

overcome the tensile strength at the wellbore. When the wellbore is drilled, stress

orientation in the formation is distorted and amplified by the drilling operation. The

19

pressure requires to create a fracture in the formation is usually greater than the natural

minimum stress (Postler [9]). This could explain the phenomena why leak-off pressure

monitored by leak-off tests usually yields higher value than the natural minimum stress.

Using empirical stress estimates from basinal LOT data, leak-off pressure is 11%

higher than minimum horizontal stress conducted by minifrac method (Addis et al. [8]).

In unconsolidated formations, due to low horizontal stress ratios, the distortion effect

can cause the fracture opening pressures to be lower than the propagation pressure

(Postler [9]). In other words, there is a weaker region near the wellbore, and a stronger

elastic region further away. This phenomena can be explained by the “plastically–

strained” zone may be created in the near-wellbore region. This zone only occurs

around the wellbore region. Therefore, in such formations two different stress zones

can be created. This causes the fracture initiating pressure to be lower than the far-field

stress and the leak-off tests result yielding two fracture initiating pressures, one for

plastic zone and another higher one for elastic zone.

2.4.4 Fluid penetration

If a penetrating fluid (such as water or oil-base mud) is used, the leak-off pressure will

be lower than that of the non-penetrating fluid. This results in a temporary increase in

pore pressure in the penetrated area. The pressure opposes the compressive stress; there

will be a temporary reduction in the breakdown pressure (Postler [9]).

20

2.4.5 Permeability

By the same token, permeable rock formations tend to show a lower breakdown

pressure when compared to impermeable rock with the same condition. However, the

result from highly permeable rock formations will be more difficult to interpret because

of the nonlinear result caused by the fluid losses.

2.4.6 Pre-existing cracks

The breakdown pressure may not exist or can be reduced by the presence of pre-

existing cracks (figure 2.3). Since the tensile strength of cracked rock is zero, the

pressure required to open an existing fracture in most rocks downhole will be less than

the pressure required to initiate a fracture. Work done by Ishijima and Roegiers [25]

confirms that the length of pre-existed cracks does affect the pressure versus time plot.

21

Figure 2. 3: Effect of pre-existing crack adapt from Postler [9] (top figure shows

illustration of the plot when there is no crack in the wellbore, minimum stress at

wall=x. Bottom figure shows the effect of pre-existing crack for the LOT plot (blue

line-slower pumping rate and black line-faster pumping rate).

Pump rate, it has been stated clearly by Postler [9] that the faster the pump rate, the

higher the fracture initiation pressure and breakdown pressure (figure 2.4). The cause of

this effect is associated with permeability, fluid penetration, and time. Performing leak-

off tests with high pump rate may not give accurate wellbore strength. Due to this

22

effect, leak-off tests are recommended to use the slowest practical pump rate to

estimate a reliable formation leak-off pressure.

Shut-in Pressure, This part of leak-off tests is in between C and D in figure 2.2. It

shows that when the pump stops, pressure will significantly drop due to fluid loss in the

formation and the loss of pump friction pressure. When the pressure reaches the same

values as the minimum horizontal stress, the fracture stop growing and starts to close.

Shut-in pressure can be used as an index for determining the leak inside the cement and

casing. If the pressure at point C falls below half the pressure at point A, it indicates

that there is a leak in surface equipment or casing or a cement channel. From figure 2.2,

point C illustrates what is believed to be the minimum horizontal stress (MHS) at the

end of the crack. If the crack, created by leak-off tests, is extended farther than the

distorted region of the stress, the minimum horizontal stress obtained in the pressure

integrity tests is a reasonable approximation of the minimum undistorted stress of the

formation (Postler [9]).

23

Figure 2. 4: Effect of Pump Rate

2.5 Interpretation of leak-off test for stress determination

Even though leak-off tests are simple and inexpensive tests run during drilling

operations. Interpretation aspect of leak-off test is essentially one of the main factors

leading to obtain accurate and reliable results. However, when the plots show non-

linear behavior, misinterpretation can lead to a variety of problems. For example, if low

leak-off pressure is interpreted as a cement channel, the operator may conduct a

squeeze job in an attempt to increase leak-off pressure. In fact, low leak-off pressure

can result from other factors such as at that point the fracture gradient is somehow

lower-than-expected. This can cause the drillers and mud engineers to determine an

unrealistically low value for an upper limit to the mud weight. In the worst case, this

will lead to well control problems. Moreover, the misinterpretation of leak-off tests can

24

also lead the drillers to determine higher mud weight than it should be. This can cause

lost circulation problems. Therefore, interpretation of leak-off tests is essentially

important.

The minimum stress is obtained from leak-off tests data while the maximum horizontal

stress is rarely stated. The followings are the two methods for LOT interpretation for

stresses (Addis et al. [8]).

• Analysis of individual leak-off tests: from direct analysis of data and through use

of a “stress bound” type analysis.

• Empirical correlations of a large numbers of LOP data for a basin or field.

2.5.1 Estimating minimum stress from individual leak-off test

Both approaches for stress estimation methods postulate that the leak-off pressure

corresponds to the initiation of a fracture at the wellbore wall, and equals to “fracture

initiation pressure” from the elasticity theory for stress distributions around an infinite

cylindrical borehole as shown in equation 2.1 (Addis [8]). The leak-off tests results

generally based on vertical boreholes. Moreover, the fracture initiation is only created

due to the horizontal stresses. The derivation for equation 2.1 is presented in chapter 4.

25

pHhlo PTP −+−= σσ3 Equation 2.1

The approaches for estimation of the in situ stress by leak-off test normally;

• Assume the leak-off pressure to be equal to the minimum horizontal stress

• Use the “instantaneous shut-in pressure” as an indication of the minimum horizontal

stress.

2.5.2 Empirical stress estimates from LOT data

There are empirical correlations for U.S. Gulf Coast, Brunei, Venezuela and the North

Sea showing clear trends for leak-off pressure versus depth. Essentially in Brunei, leak-

off tests and minifrac data are available; they show that leak-off pressure were observed

to be 11% higher than the minimum horizontal stress estimates via instantaneous shut-

in pressure (ISIP). Likewise, leak-off pressure data from other basins are assumed to

overestimate the minimum stress magnitude by similar percentage. In normal

consolidated tectonically relaxed basins the minimum horizontal stress were postulated

to be computed by the following equations (Addis [8]):

26

)(46.0053.0 145.1

poph PPD ++=σ for D≤ 3,500m Equation 2.2

)(46.0317264,9 poph PPD −+−=σ for D> 3,500m Equation 2.3

The works of Caillet et al. (1994) show that the minimum principal stresses determined

from LOTs are in the order of 90% of the overburden stress Lille Frigg area. They use

of an upper envelope to the leak-off pressure values as an interpretation for minimum

principal stress as following equation (Addis [8]):

75.30172.03 −= Dσ for D≤ 4,500m Equation 2.4

2.5.3 Inversion of LOT data

Derivation of leak-off tests data was generally from vertical wells. If one needs to apply

leak-off tests correlations to an inclined well, inversion of leak-off tests data needs to be

performed. Results from the Snorre oil field, operated by Saga petroleum (Addis [8]);

show consistent magnitudes of both the major and minor horizontal stress based on the

inversion of the leak-off data as shown in the following equations:

27

8.1023.0 += DHσ for D≤ 3,600m Equation 2.5

5.002.0 += Dhσ for D≤ 3,600m Equation 2.6

The extended leak-off test was developed in order to improve the reliability of stress

evaluations. This will be discussed later in this thesis.

2.6 Leak-off tests field procedure guidelines

Leak-off tests are plotted with the horizontal axis label representing the increments of

pumping volume in ¼ bbl. The vertical axis labels pressure in 100-psi increments.

The interpretation guidelines are discussed below and shown in figure 2.6.

• After labeling the graph, the operator has to predict the leak-off pressure (LOP)

which is added as a horizontal line. It is important to underline that this predicted leak-

off pressure is based on analysis of offset well data, local overburden, and pore pressure

gradient. This line is used as a guideline during the test when the operator observes a

deviation from the trend. However, if the rightward bend is detected below this

predicted LOP line, it is probably not leak-off and pumping should continue.

28

• The minimum leak-off pressure which is another horizontal line equals to the

pressure equivalent of the predicted leak-off Equivalent Mud Weight (EMW) minus ½

ppg. The minus ½ ppg is from observation in leak-off measurements, from inaccuracies

caused by mud gellation effects, predicted leak-off, measurement of pressure, volume,

and mud weight.

• The maximum allowable pressure is a third horizontal line that represents

equipment limitations or lost circulation experience.

• The minimum Volume Line is a diagonal line drawn from the origin to the highest

pressure/volume data point of the casing test. This line represents the minimum volume

of drilling fluid compression required to reach any pressure with the mud system.

• The comparable maximum Volume Line is used for a lower limit reference during

the test, diagonal line. If the LOT data showed a deviated line below this line, it can be

interpreted as high formation permeability and too low pumping rate. This line starts

from the origin to a pressure maximum volume should be twice the minimum volume

line.

• Data from leak-off tests should be plotted in real time while the test is running to be

able to determine if losses occur and to precisely determine the leak-off point, by

plotting data every ¼-bbl.

29

Figure 2. 5: guide lines on PIT plot (Postler [9])

Figure 2. 6: Check pump rate with guide lines (Postler [9])

2.6.1 Pumping guidelines

• Use a low-volume high-pressure pump, such as a cementing pump, better to control

pump rate than using rig pumps. For volume indication, use pump strokes, as they are

30

more reliable than using mechanical barrel counter on the pump or mark the tanks in ¼

-bbl increment and monitor the volume from there.

• Use uniform clean mud. Mud should be circulated until the shaker is free of cuttings

and the mud weight out equals to mud weight in. The purpose of this is to make sure

that one has uniform known density drilling mud.

• Use slow and steady pump rate. Fast pump rate can lead to unclear leak-off point. If

the pump rate is not steady, it can make the slope of the plot change before leak-off and

leads to difficulty in the interpretation of the results. The rule of thumb is to use ¼ bpm

for impermeable formations and ½ bpm for permeable formations in order to reduce

filtration losses. If the leak-off tests require pump rate, exceeding 1 bpm that can

indicate a leak in the equipment, bad cement job, or cement channeling.

• The true leak-off pressure can best be obtained by using the lowest rate required

to overcome filtration losses.

• Using guidelines to determine if higher pump rate is needed as illustrated in figure

6. If the data fall below maximum volume line, shut down the pump, and retest at ¼

bpm higher than the previous test.

• When a leak-off point has been established, pump small additional amount to

confirm leak-off, and then stop pumping.

2.6.2 Shut-in guidelines

• Use shut-in valve instead of pump to perform this operation. This will reduce to

possibility of fluid leaking pass the pump during the shut-in period.

31

• Monitor shut-in pressure in one-minute intervals until the pressure levels off.

Normally 10-15 minutes of shut-in period is used.

2.6.3 Interpretation guidelines

• Estimate the leak-off by drawing the best fit straight line through the data without

including the first point which is often affected by air in the mud or irregular pump

speed.

• Accept the result of leak-off pressure if the result is in the range of predicted value

and predicted value minus ½ ppg. If the result is below the minimum leak-off value, a

cement channel may exist; redo the test to confirm. Predicted leak-off values are not

always correct.

• The first slope decrease in shut-in pressure indicates the minimum horizontal stress.

Compare this pressure with the leak-off pressure. Normally leak-off pressure should be

greater than the minimum horizontal stress. Accept the result if the gauge pressure is at

the minimum horizontal stress is greater or equal to ½ gauge pressure at leak-off.

32

CHAPTER 3: REVIEW OF EXTE�DED LEAK-OFF TESTS

(XLOT’s or ELOT’s)

3.1 Extended leak-off tests review

Extended leak-off tests have been used in the industry for over 20 years due to the facts

that they can overcome many limitations of leak-off tests without taking significantly

more time. The extended leak-off tests have the most similar methods to hydraulic

fracturing methods without requiring a complete set of equipment as in hydraulic

fracturing.

Procedures to conduct leak-off tests (LOT) and extended leak-off tests (ELOT or

XLOT) are similar. In order to reduce main shortcomings of leak-off tests, extended

leak-off tests add repeated pressurization cycles

The test starts by pumping in the formation, the same as in leak-off tests, until a leak-

off point is established, and then the pump is shut-in to monitor the pressure decay until

the curve indicates the fracture closure, usually about 30 minutes. Then two or more

cycles are performed. First cycle shut-in pressure gives an estimation of the minimum

stress magnitude, and the fracture propagation pressure is recorded in the 2nd

and 3rd

cycles. The best estimation of stress magnitude can be obtained from second and third

shut-in pressure cycles (Addis [8]).

33

3.2 Theory of stress determination by extended leak-off tests and

hydraulic fracturing tests

Extended leak-off tests can be used for estimating in-situ stress. It gives more reliable

results than that of leak-off tests due to the tensile strength (T) is overcome by the first

cycle of the test. Then it can be removed from the equation to ease the interpretation, as

shown in equation 3.2 and 3.4. Maximum stress can be clearly estimated in case which

the plot shows clear breakdown and re-opening cycles. The theoretical framework for

stress determination from hydraulic fracturing and extended leak-off tests are similar.

In an ideal poroelastic rock type, when a fracture is created in an orientation that is co-

axial with the borehole axis, the magnitude and orientation of the stress field in the

plane normal to the hole axis can be determined (Addis [8]). This requires the

following:

• The magnitude of σh is estimated from the shut-in/closure pressure;

• The magnitude of σH is determined from either of these following equations:

For fracture initiation;

pohH PkTkPi )2(3 −−+−= σσ Equation 3.1

For fracture re-opening;

34

pohH Pkk )2(Pr3 −−−= σσ Equation 3.2

If one neglects the effect of poroelastic term, one obtains;

pohH PTPi −+−= σσ 3 Equation 3.3

For fracture re-opening;

phH P−−= Pr3σσ Equation 3.4

Where

Hσ = maximum horizontal stress, MPa

hσ = minimum horizontal stress, MPa

Pi = fracture initiation pressure, MPa

pP = pore pressure, MPa

rP = fracture re-opening pressure, MPa

k = the poroelastic constant )1(≈

oT = tensile strength, MPa

θ = angle along the hole periphery, degree

35

Equations 3.1 and 3.2 are used when the poroelastic effect of rocks is taken into

consideration. These two equations are the long-time solution for poroelasticity. If

poroelastic effect of rocks is neglected, k=1, then Equations 3.3 and 3.4 can be applied.

More detail of the borehole stress correlations are discussed in Chapter 4. Estimation of

fracture orientation and fracture tensile strengths are commonly two essential analysis

procedures in hydraulic fracturing test but these two procedures are not performed in

the case of extended leak-off tests. Moreover, it should be noted that the calculated

stresses from the above equations are total stresses as determined by this procedure. To

find the effective stress magnitudes, they can be determined by subtracting the

formation pore pressure from the total stress estimate.

3.3 The differences between extended leak-off tests and hydraulic

fracturing stress tests

• Extended leak-off tests still mainly use procedures from leak-off tests, therefore

open bottomhole or “barefoot” well configuration is pressurized without using packers.

This results in the accuracy of determining the orientation of maximum and minimum

horizontal stress due to the fracture initiation orientation. Similarly, to obtain the best

result of stress test downhole pressure gauges should be used.

• In hydraulic fracturing, the pressurizing fluid is water or brine which makes the

interpretation of the test itself easier compare to non-Newtonian drilling fluid used in

extended leak-off tests.

36

• In extended leak-off tests, the open-bottomhole length is around ten feet or three

meters, in comparison to hydraulic fracturing test the pressurized bottomhole length is

around one meter. The longer hole length increases the probability of reopening pre-

existing crack or fracture instead of creating a new fracture.

Even though there are many differences between the two tests, extended leak-off tests

appear to provide consistent stress data and pressure records compared to that obtained

from hydraulic fracturing test. Addis [8] and Enever et al. [15] claim that extended

leak-off tests are the reliable tests compared to leak-off tests but it is not as precise as

hydraulic fracturing test. Extended leak-off tests plots are shown in figure 3.1 and 3.2.

Figure 3. 1: Example of ELOT Ideal responses (Addis [8])

37

3.4 Extended leak-off test procedures

There is no standard procedure either for leak-off tests or extended leak-off tests.

Therefore, the following procedure is the usual procedure for extended leak-off tests

recommended by Kunze [6].

1. Drill 10 feet into new fresh formation.

2. Rig up surface transducer to choke manifold for annular measurements.

3. Pump down drilling fluid long enough to receive “bottom up” (circulated mud

from the bottom reaches the surface since the start of the circulation) and check

properties in and out of the fluid.

4. Pull out drill bit 10 feet into casing, hang off drill string

5. If a wireline downhole gauge is used, rig up a pump-in sub, wireline blowout

preventer, and pressure lubricator with downhole gauge assembly.

6. Connect surface transducer to pump-in sub for drill pipe pressure measurement.

7. Rig up cement pumper

8. Run downhole gauge to top of bit or baffle plate on a wireline, pull up 25 feet and

hang off.

9. Shut-in annular blowout preventer.

10. Pump at ¼ bbl per minute (0.04 m3/min) or lower constant rate until pressure rise

shows definite change in rate of increase. Pump an additional ¼ barrel into formation.

38

11. Shut-in pumps and monitor pressure decrease for 30 mins.

12. Bleed off pressure, record returned drill fluid volume

13. Repeat steps 10-12 for cycles 2 and 3.

3.5 Extended leak-off test nomenclature

Other than conventional leak-off test nomenclature above, other points on extended

leak-off tests plots are the following (Økland et al. [10]):

Fracture initiation pressure (FIP) is a point where the first fracture is believed to be

created. It shows in different forms such as usual slope change or a more formation

breakdown event. In the formation breakdown event; pressure falls rapidly during

pumping, indicating that the volume of the induced fracture increases faster than the

pump rate. This point can also indicate that the well is cracked and created a lost

circulation.

Fracture closure pressure (FCP) is the pressure when fractures are believed to be

closed, after pump has stopped. It can be identified in the shut-in or flow-back phase.

Fracture propagation pressure (FPP) is the stable pumping pressure after the

formation is broken down. It also indicates that pump rate and fracture volume grows

are at the same rate.

39

Fracture reopening pressure (FRP), this pressure will yield after the first cycle of the

tests. It is lower than formation breakdown pressure or fracture initiating pressure in the

first cycle. The fracture reopening pressure increases with time due to the change of

conditions at the borehole wall, especially when leak-off tests were performed by

water-base mud (WBM).

Figure 3. 2: Critical points on extended leak-off tests plot (Økland et al. [15])

3.6 The differences between extended leak-off tests and leak-off tests

As stated above in the review of both methods, leak-off tests and extended leak-off

tests, the extended leak-off tests were modified from standard leak-off test. This part of

the thesis will point out the differences between the two tests which are the following:

40

• Leak-off tests usually pressurized the well until leak-off pressure is established but

extended leak-off tests pressurized the borehole pass leak-off pressure and reach the

formation breakdown pressure.

• Extended leak-off tests perform more than 1 cycle to overcome the effect of tensile

strength while standard leak-off tests usually perform only 1 cycle. Therefore, more

parameters can be obtained and extended leak-off tests give closer estimation of in situ

stress when compare to hydraulic fracturing stress tests.

• Downhole gauge is recommended to use for both methods.

• Shut-in time for standard leak-off tests is 10-15 minutes while extended leak-off

tests procedure recommended 30 minutes for shut-in time, in order to make sure that

the fracture closes.

41

CHAPTER 4: PLA�E STRAI� STRESS DISTRIBUTIO� ALO�G

THE BOREHOLE WALL

4.1 Overview

This chapter discusses the derivation of borehole stress correlations which were

presented in the tests review section. Moreover, this chapter also delineates the

assumptions of the pressure integrity tests and explains into more details how pressure

integrity test equations were obtained. In addition, limitations of the equations are

stated at the end of this chapter.

4.2 Borehole wall stresses

During drilling operations, rock cuttings are transported upward to the surface.

However, there are the inherent in situ stresses concentrations around the borehole wall,

since no force can be transmitted through the interior void. These stresses

concentrations at the borehole wall will play a critical role in its stability. Moreover, the

theoretical background of the pressure integrity test stated that the borehole wall

fractures initiate when the tangential stresses or vertical stress, in case of shallow well,

become tensile. (Whittaker et. al, 1992, [21]):

The solution for stress on a borehole wall was given by Fairhurst (1968) by combining

it with the linear elasticity theory by Kirsch (1898) as follows (Whittaker et al. 1992,

[21]):

42

wr P=σ

wxyyxyx P−−−−+= ∞∞∞∞∞ θσθσσσσσ θ 2sin42cos)(2

θνσθσσνσσ 2sin42cos)(2 ∞∞∞∞ −−−= xyyxxz Equation 4.1

0=θσ r

θσθσσ θ sincos(2 ∞∞ −= xzyzz

0=rzσ

where

),,,( zyxjiij =∞σ = in situ stress compontents at infinity referred to the borehole

coordinate system.

),,,( zrjiij θσ = = stress components on the borehole wall

wP = hydraulic fracturing fluid pressure acting inside the borehole wall

ν = Poisson’s ratio

The above equations were derived assuming compressive stress as positive. Often time,

the far-field in situ stresses are given in terms of principal stresses. Especially, when the

hole is drilled vertically and the vertical stress or overburden stress ( vσ ) is in the same

direction as the borehole axis. In addition, minimum horizontal stress ( hσ ) and

maximum horizontal stress ( Hσ ) are in the same direction as y- and x-axis of the

43

Cartesian coordinate, respectively. As a result of this stress condition, Jaeger and Cook,

1979 simplified the above equations as follows:

wr P=σ

whHhH P−−−+= θσσσσσ θ 2cos)(2

θσσνσσ 2cos)(2 hHvz −−= Equation 4.2

0=θσ r

0=zθσ

0=rzσ

Figure 4. 1: Coordinate system and principal stresses

hσ hσ

vσ

vσ

Hσ

Hσ

x

z

y

θ

r

44

Figure 4. 2: Illustration of a borehole subjected to both internal fluid pressure and

external compression, and associated coordinates (reproduced from Whittaker et

al. 1992, [21])

-4

-2

0

2

4

6

8

10

0 30 60 90 120 150 180

ө (degree)

Tan

gen

tial

str

ess (

σө

)

Figure 4. 3: Tangential stress distribution at borehole wall as a function of the

angle with respect to the maximum principal stress (reproduced from Whittaker

[21]).

y

x

r

3σ

3σ

1σ 1σ

p

ө

45

4.3 Tangential stress and tensile fracturing

The tangential stress varies ( θσ ) with the radial angle θ with respect to the maximum

horizontal stress ( Hσ ). By plotting tangential stress versus angle, there is a transition

point when the transient crossing line of 0 stresses which indicates the transition from

tensile to compressive regimes. The angle where stress equals to zero can be defined by

the following equation:

)(4

3

0 arcsinhH

hH p

σσσσθ −

+−= Equation 4.3

where 0θ is tensile for 0≤ θ ≤ 0θ and compressive for 0θ ≤ θ ≤ 90 o . The tangential

stress versus angle plot shows that the maximum tensile stress max,θσ occurs at o0=θ ,

which can be defined by the following equation:

wHh P−−= σσσ θ 3max, Equation 4.4

On the other hand, the maximum compressive stress would occur at o90=θ and is

defined as follows:

whH

com P−−= σσσ θ 3max, Equation 4.5

46

If p > hH σσ −3 , θσ is always tensile on the borehole surface without compressive

tangential stress. In this case, max,θσ still occur at θ = 0 o . Hence, if the tensile

tangential strength is overcome, the radial tensile fracture is possible. In addition the

tensile fracturing is most likely to occur at θ = 0 o , perpendicular to minimum

principal stress direction or parallel to the maximum principal stress. This case is

considered to be the simplest case of hydraulic fracturing by internal pressure which

was presented by Hubbert and Willis, 1957.

4.4 Assumptions of the borehole stress calculation

The above borehole stress calculations are based on Kirsch’s (1898) solution for stress

distribution around a circular hole in an infinite medium subjected to compressive

stresses at infinity. The above equations, used in any type of pressure integrity test,

verify the following assumptions (Whittaker et al, [21]).

• The rock mass around the borehole behaves elastically, isotropically,

homogeneously, and impermeable. In addition, no preexisting fracture are present. That

also means there is no fluid leak-off into the formation.

• The intermediate stress is parallel to the borehole axis, as stated before in the

review part of the pressure integrity test.

47

• The hydraulic fracture is initiated at a point on the borehole wall where the

tangential stress ( )θσ reaches a maximum tensile stress ( )max,θσ and attains the in situ

tensile strength of the rock ( )Tσ . The breakdown pressure refers as the pressure where

fracture initiation takes place.

• The fluid pressure does not penetrate the rock (e.g. because of the presence of

mudcake) (Economides et al. [19]). If the fluid penetrates the rock, poroelastic effects

of rock need to be put into consideration. This case will not be stated in this thesis.

According to above assumptions, fracture will occur when the internal pressure reach a

breakdown pressure. Hence the fracture criterion for the classical method can be

expressed as (Hubbert and Willis, 1957):

( )max,θσ = ( )Tσ− Equation 4.6

or

( )Tv σσ −= Equation 4.7

When substituting above equation into equation 4.4, we obtain:

THhbP σσσ +−= 3 Equation 4.8

The subcritical stable fracture propagation is neglected (Whittaker et al. 1992, [21]).

48

The above equation is not applicable in porous rock; therefore by adding the effect of

pore pressure the above equation can be written as (Haimson and Fairhurst, 1970):

pTHhb PP −+−= σσσ3 Equation 4.9

Where, Pp is the pore pressure which is assumed to be defined as the height of water

column in the borehole above the test interval (Rummel and Baumgartner, 1985).

The above equations are the analytical solution of the borehole stress estimation which

are widely applied in petroleum industry such as in leak-off test, extended leak-off test,

and hydraulic fracturing. These tests are based on the stated assumptions and

correlations. Hence, pressure integrity tests calculations are established by the same

derivation and share the same limitations.

49

CHAPTER 5: BOTTOM OF A BOREHOLE STRESS SIMULATIO�

5.1 Simulation software

The solution for verifying leak-off tests was approached by creating a series of three-

dimensional finite-difference model in a commercial software called FLAC3D (Fast

Lagrangian Analysis of Continua in 3-Dimensions) which is available from Itasca

Consulting Group, Inc. The particular version used in this thesis is version 3.10 (32 bit).

FLAC3D is commercial software for advanced geotechnical analysis of rock, soil, and

structural support in three dimensions. FLAC3D has been widely used to analyze,

solve, and test a wide variety of complex problems in geomechanics, civil, and mining

engineers. It is applied in this research since its explicit calculation scheme enables a

large three-dimensional calculation to be made without excessive memory

requirements. In addition, FLAC3D can give very sophisticated graphical contour plots

of stress in the model with different colors for the different stress values which ease the

analysis process.

5.2 Bottom of a borehole model

A model was created as to simulate the bottom of the borehole with different internal

pressure and principal stress in FLAC3D. Properties of shale (table 5.1) were used due

50

to the fact that shale is the common formations that leak-off tests are usually performed

(Addis et al. [8]). The model of the borehole is a void cylindrical borehole with

diameter d. The length of the borehole is 10d located in a parallelepiped with

dimensions 5dx5dx20d, as shown in figure 5.1. The properties of the shale formation

that were used are: the density of 2210 kg/m3, bulk modulus of 8.8x109 Pa, shear

modulus of 4.3x109

Pa. The reference axes that are used in this model is x, y, z co-

ordinate system where the y-axis parallels to the borehole axis, as shown in figure 5.1.

The element sizes and aspect ratios are smaller near the borehole and gradually

increased in size outwards, as shown in figure 5.2 and 5.3. Moreover, the borehole

model is assumed to be impermeable. To emphasize, in this thesis we are only focusing

on the bottom part of a vertical borehole, as shown below.

Figure 5. 1: Schematic of the borehole model

51

Table 5.1: properties of rock (Shale) used in the simulation (after FLAC3D

manual)

Figure 5. 2: FLAC3D borehole model

52

Figure 5. 3: cross-section of the borehole model

5.3 In situ stress condition

After the borehole model is created, the in situ principal stresses are applied and their

ratio of the principal stress was varied to created different conditions. Table 5.2 shows

the stress ratio values that were used.

The three main simulated series of different stress ratios1 were:

1. The ratio of the vertical stress ( )vσ to the minimum horizontal stress ( )hσ ; fixing

the maximum horizontal stress ( )Hσ

1 The selected stress ratio were based on the stress regimes I (i.e. σv<σh<σH) and II (i.e. σh<σv<σH) from

the depth versus stress plot in “PE 5243 Rock Mechanics Class Note [23]”.

53

2. The ratio of the minimum horizontal stress ( )hσ to the maximum horizontal

stress ( )Hσ ; fixing the vertical stress ( )vσ

3. The ratio of the vertical stress ( )vσ and to maximum horizontal stress ( )Hσ ;

fixing the minimum horizontal stress ( )hσ

In situ principal stresses

(MPa)

Model

Case No.

Stress

ratio

Stress ratio

value

σv σh σH

1 1 30 40 40

2 1/2 30 20 40

3 1/4 30 10 40

4

σh/σH

1/8 30 5 40

5 1 40 25 40

6 2 80 25 40

7 4 160 25 40

8

σv/σH

8 320 25 40

9 1 30 30 40

10 2 60 30 40

11 4 120 30 40

12

σv/σh

8 240 30 40

Table 5.2 Initial in situ stresses used in the simulation (in this table, positive value

represents compression)

54

5.4 Bottomhole internal pressure

Different internal bottomhole pressures (30, 40, 60, and 80MPa) were also used in the

numerical simulation to yield different results; since we already have 12 cases for one

internal bottomhole pressure, as shown in table 5.2. Hence, 48 combinations were

created. Figure 5.4 shows the stresses vector which are applied on the borehole and the

boundary of the model. Since leak-off tests are always performed with internal

bottomhole pressure that exceeds the formation fracturing pressure, the simulation is

designed to obtain the numerical result either when the pressure is below or above the

formation fracturing pressure. In addition, the simulation model is incorporated with the

effect of gravity.

Figure 5. 4: Schematic top view of applied stresses vector at the borehole model.

55

5.5 Simulation results analysis

After the FLAC3D and boundary condition is set up, then FLAC3D is executed until

the numerical solution converges. The cross-section in the x-direction of the

bottomhole maximum principal stress contour is plotted to observe the section where

tension overcame the compression and caused the fracture to initiate. Regarding the

borehole failure theory, the fracture will initiate when the tangential stress or vertical

stress exceeds the tensile strength of the borehole. The part of the borehole that the

fracture is created can first be designated by the color of the model after execution.

Yellow to red gradient in the model represents tension, and green to blue gradient

represents compression, as shown in figure 5.5. After the first observation of the stress

is conducted, then the value at particular section of the borehole that seems to have

fractured is observed. The positive number of stress represents the tension in the model,

and negative number of the stress represents the compression in the wellbore. The value

of stress in different color sections are shown on the color bar on the left side of the

result, shown in figure 5.5. Then the tangential stress and the orientation of the

principal stress is calculated and plotted to assure the result.

56

Figure 5. 5: Example of the executed result from FLAC 3D

Moreover, in order to prove that the horizontal fracture is created. The small element at

the bottom of the borehole wall is selected, shown in figure 5.6, and stress data from

that element is obtained from FLAC3D. After that the orientation of principal stress at

that particular element is calculated by using equations in Appendix B. To clarify, the

model was created with right-hand coordinate system with y-axis as a parallel borehole

axis. However; to ease the understanding of the calculations, different coordinate

system with z-axis as a parallel borehole axis was used. The calculation of principal

stresses angles gives the knowledge of the direction of the initiated fracture. Since the

stress around the bottom of the borehole is rotated and the fracture will initiate in the

direction of the minimum principal stress (maximum tension), the orientation of the

principal stress will, essentially, provides the direction of the fracture. This can also

prove that because of the effect of the bottom of the borehole, the inclined or horizontal

57

fracture can be created and make the interpretation of the leak-off test invalid.

Figure 5. 6: Illustration of the selected element for stress analysis

58

CHAPTER 6: RESULTS A�D DISSCUSIO�S

In this chapter, the simulation results are presented and interpreted. There are 64

cases that were run in this thesis, refer to Section 5.4 for more detail. This chapter

discusses only the case of internal bottomhole pressure equals to 60MPa due to the

fact that 30MPa and 40MPa cases do not show clear initiation of fracture, and 80MPa

case show very similar result to the 60MPa case. Therefore it is sufficient to show and

analyze only the 60MPa case. The 30Mpa, 40Mpa, and 80Mpa cases results are

shown in the appendix. The results in this chapter are the maximum principal stresses

contour plot which are obtained from FLAC 3D after the runs were completed. The

interpretation of these contours plot is stated in Section 5.5. There are total of 16

cases which were executed with 60MPa internal bottomhole pressure.

59

6.1 Stress contours

Case 1: ratio of hσ and Hσ equals 1

Figure 6. 1: Case 1 Maximum principal stress contour plot

Case 1, the borehole was conditioned with hσ = 40MPa, Hσ = 40MPa, and

vσ =30MPa. This case clearly shows that the bottom part around the periphery of the

borehole is fractured, and the rest of the model was under compression. The

horizontal fracture can be identified by the tension (shown in yellow) around the

periphery of the bottom of the borehole.

60

Case 2: ratio of hσ and Hσ equals 1/2


Case 2, the borehole was conditioned with hσ = 20MPa, Hσ = 40MPa, and vσ =

30MPa. The bottom of the borehole shows both fractures (vertical and horizontal) are

created. The red to yellow color shows tension in the borehole. The vertical fracture

was created in the direction parallel to the maximum horizontal stress.

61

Case 3: ratio of hσ and Hσ equals ¼



30MPa. Results from Case 3 are similar to results from Case 2 but the horizontal

tension at the bottom part of the borehole doesn’t show as clear as in case two. By

looking at the positive numbers and color, it indicates that both vertical and horizontal

fractures are created.

62

Case 4: ratio of hσ and Hσ equals 1/8



30MPa. This case shows that the both type of fractures (vertical and horizontal) are

still created.

63

Case 5: ratio of vσ and Hσ equals 1



40MPa. The result shows that both types of fracture are created.

64




80MPa. This case vertical stress is twice as much as the maximum horizontal stress. It

shows differently result from the former case. The horizontal bottomhole failure does

not show up anymore, only the vertical fracture remains.

65




160MPa. When the well was subjected to vertical stress 4 times as much as the

maximum horizontal stress, the bottom of the borehole shows tension which means

that there will be failure at the bottom part of this particular well.

66




320MPa. The vertical fractures remains but there are more tensions at the bottom of

the borehole when the vertical stress increases.

67

Case 9: ratio of vσ and hσ equals 1



30MPa. There is a clear horizontal failure around the bottomhole periphery.

68



Case 10, this case the borehole was conditioned with hσ = 30MPa, Hσ = 40MPa, and

vσ = 60MPa. Only the vertical fracture governs this case and without sign of

horizontal fracture.

69



This case the borehole was conditioned with hσ = 30MPa, Hσ = 40MPa, and vσ =

120MPa. This case shows consistence result comparing to case 7 and 8, due to the

bottom part of the wellbore fails when it is subjected to high vertical stress.

70



This case the borehole was conditioned with hσ = 30MPa, Hσ = 40MPa, and vσ =

240MPa. The result in this case shows consistent results when compares to case 7 and

8.

71

6.2 Discussion

The simulated results from H

h

σσ

series clearly show the peripheral horizontal fracture

around the bottom of the borehole for all four different stress ratios, as shown in

Figures 6.1 to 6.4. This series support the theory that horizontal fractures can be

created. However, the only other cases when peripheral horizontal fractures occur is

when the stress ratio equals one (refer to Figure 6.1, 6.5, and 6.9). For H

v

σσ

andh

v

σσ

series, they show very similar results when vσ is increasing. When H

v

σσ

and h

v

σσ

equals 4 and 8 (refer to Figure 6.7, 6.8, 6.11, and 6.12) the significance of high

vertical stress governs the borehole failure mechanism and result in the failure of the

bottom of the borehole. The failure of the bottom of the borehole can be specified by

the yellow bulb shape of tensile stress at the bottom of the borehole. This effect can

be illustrated more by plotting the displacement vector contour of the bottom of the

borehole, as shown in Figure 6.17. This figure shows the direction of displacement

vectors points to be upward which means that the effect of high vertical stress causes

lifting the bottom of the borehole. As a result, leak-off tests interpretation are not

valid in these cases.

There are some cases in which wellbore vertical failure is fully created in the

direction of maximum horizontal stress (e.g. Figures 6.6, and 6.10). For when the

stress ratio is two. Hence, the vertical fracture can be created when vσ is twice as

much as Hσ or hσ . If this type of failure occurs at the borehole wall, leak-off tests

interpretation would be valid for in situ stress estimation under the plane strain

72

assumption. Essentially, the vertical stress plays a vital role in initiation of fracture.

In this thesis, it appears that when the ratio of vertical stress is approximately equal to

one; the horizontal or inclined fractures, depends on the direction of the minimum

stress, can be created. This causes leak-off test interpretation to be invalid.

Figure 6. 13 Displacement vector at the bottom of the borehole when vσ is eight

times greater than hσ .

73

6.3 The rotation of stress tensor at the bottom of the borehole

The stress tensor plot around the bottom of the borehole is an indication of how

stresses at the bottom of the borehole are disturbed both in magnitude and orientation

by the drilling operation. Figure 16.7 illustrates such changes in the orientation of the

principal stresses. In this figure, the principal stress orientation is altered around 0.5d

away from the bottom of the borehole, the closer the element to the bottom of

borehole, the greater the rotation of the principal stress tensor. Moreover, this stress

tensor plot can also present an important indication of the fracture around the bottom

of the borehole. A red principal stress tensor represents tension while blue ones

represents compression. Figure 6.18 shows the cross section model of stress tensor at

the bottom of the borehole. In this particular figure, the red tensor locates around the

bottom of the borehole and also represents the horizontal fracture around the bottom

of the borehole.

Figure 6.19 shows the area where stress concentrations around the bottom of the

borehole are rotated. It appears that the distance upward from the bottom of the

borehole to the point where there is no rotation in stress concentration is around 0.5d

to 0.7d. This distance could be a potentially useful indication for packer setting

distance from the bottom of the borehole in order to isolate the borehole from where

the stress is rotated. If the stress-rotated section of the borehole is isolated before the

test is performed, the bottomhole will not be affected by the rotation of stress and

74

likely provide more reliable result, since the plane strain assumption is valid in this

case.

Figure 6. 14 Cross-section model of stress tensor plot from case 1

Figure 6. 15 Cross-section model of stress tensor plot from case 1

75

Figure 6. 16 Cross-section stress tensor from Case 2 with the indication of the

stress rotation area

6.4 Bottom hole stress rotation angles

One can specify the orientation of the initiated fracture by indentifying the angle of

the minimum compressive stress (σ3). The fracture is indeed most likely to initiate

perpendicular to the minimum compressive stress (σ3), as shown in Figure 6.17.

Moreover, the plots of angles of minimum compressive stress versus stress ratio were

created to observe the stress rotation trend and potentially specify the ratio at which

horizontal fracture occurs. The plots are shown in Figures 6.18 and 6.19. Figure 6.18

presents the H

h

σσ

series with different vertical stresses ( vσ ), and Figure 6.19 presents

the H

v

σσ

and h

v

σσ

. Figure 6.18 illustrates three magnitudes of vertical stresses (10MPa,

30MPa, and 50MPa). For the 10MPa and 30MPa cases, they reveal that the horizontal

0.7d

76

or inclined fractures can be created at the bottom of the borehole in all cases.

However, when the vertical stress is changed to 50MPa, it shows horizontal fracture

only when the ratio of H

h

σσ

is equal to one. Figure 6.19 shows that in both series

when the stress ratios are equal to one, inclined fractures perpendicular to the

minimum compressive pressure were created. At this ratio, the angle of the minimum

compressive stress respected to z-axis is approximately 20 degrees. Figure 6.17

represents the angle of the initiated fracture at the element at the bottom of the

borehole. When the stress ratios were increased to 1.5, the H

v

σσ

series show a drastic

change (flip) of the minimum horizontal stress from approximately 20 degrees

respected to z-axis to about 2.5 degrees with respected to the x-axis. Then, it remains

at approximately 90 degrees for all stress ratio increments up to eight. A sudden

change in angle occurs at the transition between 1.5 to 2. Figures 6.18 and 6.19

reprecsent stress contour plots related to Figures 6.5 to 6.12. As can be seen at the

stress ratio of one, a horizontal/inclined fracture is created, and when the ratio of

stress increases above one, a vertical fracture is induced.

77

Figure 6. 17 Illustration of initiated fracture at the specified element

0

10

20

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1 1.2

Stress ratio

An

gle

of

σ3 r

esp

ecte

d t

o z

ax

is (

deg

ree)

sh/SH30MPa Sv

sh/SH50MPa Sv

sh/SH10MPa Sv

Figure 6. 18 Plot of minimum compressive stress ( 3σ ) versus stress ratio

78

0

20

40

60

80

100

120

0 2 4 6 8 10

Stress ratio

An

gle

o

f σ

3 r

esp

ecte

d t

o z

ax

is (

deg

ree)

sv/sH

sv/sh

Figure 6. 19 Plot of minimum compressive stress ( 3σ ) versus stress ratio

Figure 6. 20 Illustration of a drastic change in orientation of the minimum

compressive stress from left to right.

79

CHAPTER 7: CO�CLUSIO�S A�D RECOMME�DATIO�S

7.1 Conclusions (Refer to Table 7.1)

• Three-dimensional stress concentrations prevailing at the bottom of a borehole

stress were conducted. Out of the cases considered, six showed the horizontal

induced fractures at the bottom of the borehole, leading to the invalidation in

those cases of the leak-off tests classical interpretation.

• Varying the ratio of the minimum to the maximum horizontal stress revealed

transverse or a combination of transverse and longitudinal fractures.

• Varying the ratio of overburden stress over the maximum or minimum

horizontal stress reveals that when the vertical stress is four to eight times, the

bottom of the wellbore will fail in tension. Therefore, under these conditions the

leak-off tests data interpretation for in situ stress measurements are not valid,

since there is no longitudinal fracture created.

• The stress tensor plots obtained from the simulation are consistent with the

results of Eberhardt who demonstrated that the stress tensor in the neighborhood

the tunnel face is disturbed in magnitude and orientation.

80

• The extent of this above-mentioned disturbance is around 0.5d to 0.7d (beyond

the bottom) and 1.5d (ahead of the bottom), depending upon the field

conditions.

• Out of twelve conducted cases, there are five cases for which LOTs are valid

due to the initiation of a vertical fracture. It also reveals that when the vertical

stress (σv) is a minimum principal stress, a horizontal fracture is created, and

when the longitudinal stress is equal to either one of the transverse stress,

horizontal fractures are also initiated. In these cases, LOT’s are considered to be

invalid. On the other hand, vertical fractures were created in five cases where

the vertical stress was the intermediate principal stress, or when it is the

maximum principal stress. However, in the cases when the vertical stress is the

intermediate principal stress, both types of fractures were created, but the

longitudinal fractures reveals higher tension in the borehole model which means

that the transverse fracture might not initiate due to the early existing of the

longitudinal fracture.

in situ principal stresses (Mpa) Case

�o. stress ratio stress ratio

value σv σh σH SV

Fracture

type

Validity of

LOTs

1 1 30 40 40 min H NO

2 1/2 30 20 40 int H+V YES

3 1/4 30 10 40 int H+V YES

4

σh/σH

1/8 30 5 40 int H+V YES

5 1 40 25 40 max H NO

6 2 80 25 40 max V YES

7 4 160 25 40 max BOTTOM NO

8

σv/σH

8 320 25 40 max BOTTOM NO

9 1 30 30 40 min=int H NO

10 2 60 30 40 Max V YES

11 4 120 30 40 max BOTTOM NO

12

σv/σh

8 240 30 40 max BOTTOM NO

H = Horizontal fracture, V = Vertical fracture, BOTTOM = Bottom of a borehole failure

min = minimum principal stress, max = maximum principal stress, int = intermediate principal stress

Table 7.1 summary of the simulation cases

81

82

7.2 Recommendations

• One of the assumptions in this thesis is that the rock is dry and there is no pore

pressure in the simulation. One of the possible extensions therefore, the next

step would be to incorporate poroelasticity in the analysis.

• In this thesis, only the case of a vertical borehole was simulated. However, leak-

off tests are also performed in inclined boreholes. Therefore, further analysis

could be useful in which the results of leak-off tests are simulated for inclined

or horizontal boreholes.

83

REFERE�CES

1. J.A. Hudson,*, F.H. Cornet, R. Christiansson 2003 “ISRM SuggestedMethod

s for rock stress estimation—Part 1: Strategy for rock stress estimation”. International

Journal of Rock Mechanics & Mining Sciences 40 (2003) 991–998.

2. A.A. Daneshy, G.L. Slusher, P.T. Chisholm, D.A. Magee “In Situ Stress

Measurements During Drilling” Journal of Petroleum technology, August 1986, SPE

13227

3. B.C. Haimson,*, F.H. Cornet 2003 “ISRM Suggested Methods for rock stress

estimation—Part 3: hydraulic fracturing (HF) and/or hydraulic testing of pre-existing

fractures (HTPF)”. International Journal of Rock Mechanics & Mining Sciences 40

(2003), pp. 1011–1020.

4. R. Christiansson,*, J.A. Hudson 2003 “ISRM Suggested Methods for rock

stress estimation—Part 4: Quality control of rock stress estimation”. International

Journal of Rock Mechanics & Mining Sciences 40 (2003), pp. 1021–1025

5. A.M. Raaen_, P. Horsrud, H. Kjørholt, D. Økland 2003 “Improved routine

estimation of the minimum horizontal stress component from extended leak-off

tests”. International Journal of Rock Mechanics & Mining Sciences 43 (2006), pp.

37–48

6. K.R. Kunze and R.P. Steiger, Exxon Production Research Co. 1992 “Accurate

In situ Stress Measurements During Drilling Operations”. SPE 24593

7. Morten Gjønnes , Antonio M.G.L. Cruz , Per Horsrud , Rune M. Holt 1998

“Leak-off tests for horizontal stress determination?” Journal of Petroleum Science

and Engineering 20_1998., pp. 63–71

8. M. A. Addis’, SPE, T,H, Hanssen’, SPE, N. Yassir’, SPE, D.R. Willoughby’,

SPE, and J. Enever’, SPE, ‘ CSIRO Petroleum, Australia, 2Norsk Hydro, Norway,

now with Statoil, Norway. 1998 ” A Comparison Of Leak-Off Test And Extended

Leak-Off Test Data For Stress Estimation” SPMSRM 47235

9. D.P. Postler, SPE, Exxon Company, International 1997 “Pressure Integrity

Test Interpretation” SPE/IADC 37589

10. Dag Økland, SPE, Glenn K Gabrielsen, SPE, Jørn Gjerde, Koen Sinke, Ernest

L Williams, Statoil 2002 “The Importance of Extended Leak-Off Test Data for

Combatting Lost Circulation” SPE/SIRM 78219

84

11. Luiz A. S. Rocha, José L. Falcão, C. J. C. Gonçalves, Petrobrás, Cecília

Toledo, Karen Lobato, Silvia Leal and Helena Lobato, PUC-RJ 2004 “Fracture

Pressure Gradient in Deepwater” IADC/SPE 88011

12. G. Altun, SPE, J. Langlinais, SPE, and A.T. Bourgoyne, Jr., SPE, Louisiana

State University 1999 “Application of a New Model to Analyze Leak-Off Tests” SPE

56761

13. A M Raaen, SPE and M Brudy1, SPE, Statoil ASA 2001 “Pump-in/Flowback

Tests Reduce the Estimate of Horizontal in-Situ Stress Significantly” SPE 71367

14. A.M. Raaen*, E. Skomedal, H. Kj_rholt, P. Markestad, D. Økland

2001“Stress Determination from Hydraulic Fracturing Tests: The System Stiffness

Approach” International Journal of Rock Mechanics & Mining Sciences 38 (2001),

pp. 529–541

15. J.R. Enever, N. Yassir, D.R. Willougby and M.A. Addis “ Recent Experience

with Extended Leak-Off Tests For In-situ Stress Measurements in Australia” APPEA

Journal 1996, pp. 528-534

16. C. Fairhurst 2003 “Stress estimation in rock: a brief history and review”

International Journal of Rock Mechanics & Mining Sciences 40 (2003), pp. 957–973

17. C. Ljunggrena,*, Yanting Changa, T. Jansonb, R. Christiansson 2003 “An

overview of rock stress measurement methods” International Journal of Rock

Mechanics & Mining Sciences 40 (2003) 957–973

18. Adrian J. White, Martin O. Traugott, and Richard E. Swarbrick “The use of

leak-off tests as means of predicting minimum in-situ stress” Petroleum Geoscience,

Vol. 8 2002, pp. 189–193

19. Michael J. Economides and Kenneth Nolte “Reservoir Stimulation” Third

Edition

20. Adam Bourgoyne Jr, Martin Chenevert, Keith Millheim, and F.S. Young Jr.

“Applied Drilling Engineering” SPE textbook series, VOL.2

21. B.N. Whittaker, R.N. Singh, and G. Sun “ Rock Fracture Mechanics,

Principles, Design and Applications” Development in Geotechnical Engineering, 71

22. FLAC3D (Fast Lagrangian Analysis of Continua in three dimensions) version

3.1 user’s manual

23. Jean-Claude Roegiers, university of Oklahoma “PE 5243 Rock Mechanics

Class Note”

85

24. E. Eberhardt, 2001 “Numerical Modelling of Three-Dimensional Stress

Rotation Ahead of an Advancing Tunnel Face” International Journal of Rock

Mechanics & Mining Sciences 38 (2001), pp. 499-518

25. Ishijima, Y., and Roegiers, J. C. “Fracture Initiation and Break down

Pressure- Are They Similar?” Proc. 24th

U.S. Symp. On Rock Mech., 1983, pp. 761-

772.

86

APPE�DIX A SIMULATIO� RESULTS FOR 30, 40, A�D 60 MPA

I�TER�AL BOTTOM HOLE PRESSURE.

Simulation results for bottomhole internal pressure equals to 30MPa.

Figure B. 1 the maximum stress cross-section contour of bottom of a borehole

model when the internal borehole pressure is 30MPa, hσ = 40MPa, Hσ =

40MPa, and vσ =30MPa.

87


model when internal borehole pressure is 30MPa, hσ = 20MPa, Hσ = 40MPa,

and vσ =30MPa.



and vσ =30MPa.

88



and vσ =30MPa.



and vσ =40MPa.

89



and vσ =80MPa.



and vσ =160MPa.

90



and vσ =320MPa.



and vσ =30MPa.

91



and vσ =60MPa.



and vσ =120MPa.

92



and vσ =240MPa.

Simulation results for bottomhole internal pressure equals to 40MPa



and vσ =30MPa.

93



and vσ =60MPa.



and vσ =120MPa.

94



and vσ =240MPa.



and vσ =40MPa.

95



and vσ =80MPa.



and vσ =160MPa.

96



and vσ =320MPa.



and vσ =320MPa.

97



and vσ =60MPa.



and vσ =120MPa.

98



and vσ =240MPa

Simulation results for internal bottomhole pressure equals to 80MPa



and vσ =30MPa

99



and vσ =30MPa



and vσ =30MPa

100


model when internal borehole pressure is 80MPa, hσ = 5MPa, Hσ = 40MPa, and

vσ =30MPa



and vσ =40MPa

101



and vσ =80MPa



and vσ =160MPa

102



and vσ =320MPa



and vσ =30MPa

103



and vσ =60MPa



and vσ =120MPa

104



and vσ =240MPa

105

APPE�DIX B: three-dimensional stress analysis

The following equations are used in the orientation of the principal stress calculation

at the specific element at the bottom of a borehole.

Figure C. 1 Three-dimensional stress components (After

www.engapplets.vt.edu/Mohr/java/nsfapplets/MohrCircles2-

3D/Theory/theory.htm)

106

Figure C. 2 Three-dimensional stress components on an inclined plane.

From Figure C.2 director cosines (l, m, and n) are obtained for each angle (α, β, and

ɣ):

αcos=l

βcos=m Equation B. 1

γcos=n

Where α, β, and ɣ are the angles between the normal to the inclined plane as shown in

figure C.2and the x, y, and z axes, respectively. The three direction cosines are related

by the following expression:

1222 =++ nml Equation B. 2

z

x

y

α β

ɣ

107

Where xp , yp , and zp be the x, y, and z components of stress pr

on inclined plane in

figure C.2. Writing the equation of equilibrium in the x, y, and z directions,

respectively, leads to the following equation:

( ) ( )

−

−

−

=

zzyzx

yzyyx

xzxyx

zyx nmlppp

στττστττσ

Equation B. 3

It can be shown that the maximization of minimization of σ gives the following

relationship:

Σ===n

p

m

p

l

p zyx Equation B. 4

Substitute equation C.4 into equation C.3, the system of three homogeneous equations

is obtained as following:

108

( ) 0=

Σ−−

−Σ−

−Σ−

zzyzx

yzyyx

xzxyx

nml

στττστττσ

Equation B. 5

The cubic equation in term of Σ can be obtained, if Equation C.5 determinant is

equal to zero.

( ) ( )Σ−−−+++Σ++−Σ 22223

zxyzxyxzzyyxzyx τττσσσσσσσσσ

( ) 02222 =−−−−− zxyzxyzxyyzxxyzzyx ττττστστσσσσ Equation B. 6

The concise form of equation C.6 is the following:

032

2

1

3 =−Σ+Σ−Σ III Equation B. 7

109

Appendix C: �OMA�CLATURE

Hσ = maximum horizontal stress, MPa

hσ = minimum horizontal stress, MPa

vσ = principal stress in vertical direction, MPa

θσ = tangential stress, MPa

max,θσ = maximum tangential stress, MPa

Tσ = tensile strength of the formation, MPa

Pi = fracture initiation pressure, MPa

pP = pore pressure, MPa

rP = fracture re-opening pressure, MPa

k = the poroelastic constant )1(≈

oT = tensile strength, MPa

θ = angle along the hole periphery, degree

D = Depth (meter or ft)

),,,( zyxjiij =∞σ = in situ stress components at infinity referred to the borehole

coordinate system.

),,,( zrjiij θσ = = stress components on the borehole wall

wP = hydraulic fracturing fluid pressure acting on the borehole wall, MPa

ν = Poisson’s ratio

lot-thesis - in situ stress estimation

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