Bakk 2 Trajectory Design in Terms of Stress Conditions in the Formation

8/10/2019 Bakk 2 Trajectory Design in Terms of Stress Conditions in the Formation

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Date: 19/02/2009

Alexander Hege

Bakkalaurea Thesis

Trajectory design in terms of stress

conditions in the formation

Supervised by: Prof. Herbert HofsttterApproval date: 16

thFebruary 2009


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Table of Contents

Abstract .......................................................................................................................................... 6

Introduction.................................................................................................................................... 7

Theory ............................................................................................................................................. 8

General terms, definitions, and models .......................................................................................................... 8Stress ................................................................................................................................................................................... 8

Normal stress and shear stress .......................................................................................................................................... 8

Hydrostatic, deviatoric, and lithostatic stresses ...............................................................................................................12

Different types of faults and the according stress regimes ............................................................................................. 12

Determination of the four main stresses: .........................................................................................................................14

Strain ..................................................................................................................................................................................15

Modulus of elasticity ..........................................................................................................................................................16

Linear elasticity ..................................................................................................................................................................16

Viscous strain .....................................................................................................................................................................17

Elastoviscous, plastic, and viscoelastic rock behavior .................................................................................................... 17

Homogeneous and inhomogeneous strain .....................................................................................................................19

Pure shear and simple shear ............................................................................................................................................19

Rock failure ........................................................................................................................................................................20

The Mohr-Coulomb stress diagram .................................................................................................................................20

Rock mechanical properties .............................................................................................................................................22

Stress distribution around the borehole ...........................................................................................................................24

Rock failure due to excessive stresses ............................................................................................................................27

Applications of rock mechanics in drilling .............................................................................. 29

Wellbore-stability ........................................................................................................................................... 29Improving Formation-Strength Tests ................................................................................................................................ 29

Wellpath optimization .................................................................................................................................... 37Use of data from offset wells .............................................................................................................................................37

Formation property analysis .............................................................................................................................................37

Wellbore stability analysis .................................................................................................................................................39

Applications of rock mechanics in production ...................................................................... 42

Fracture mechanics ...................................................................................................................................... 42Strain energy ......................................................................................................................................................................43

Hydraulic fracturing ............................................................................................................................................................43

Sand control .................................................................................................................................................. 45Causes for sand production ..............................................................................................................................................45

Sand control techniques ...................................................................................................................................................45

Sand production prediction ...............................................................................................................................................46

Subsidence .................................................................................................................................................... 47Rock and reservoir compressibility ................................................................................................................................... 47

Subsidence ........................................................................................................................................................................49

Casing collapse and casing shear .................................................................................................................................... 50

Strategies to avoid loss of casing/tubular integrity ...........................................................................................................53

Conclusions ................................................................................................................................. 54

References ................................................................................................................................... 55

Interpretation and analysis..................................................................................................................................... 29Test selection .........................................................................................................................................................31

Complications and considerations ........................................................................................................................32

Pore pressure ......................................................................................................................................................... 37In-situ stress magnitude and direction ..................................................................................................................37

Formation strength .................................................................................................................................................38

Wellbore stability model .........................................................................................................................................39Wellpath optimization .............................................................................................................................................39


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List of Figures

Fig 1: Stress ellipse ............................................................................................................................. 8

Fig 2: Normal stress and shear stress in 2D Fig 3: Normal stress and shear stress in 3D ........ 8

Fig 4: Stress at a fault plane ............................................................................................................... 9

Fig 5: Stress at a bedding plane which is flexural slip folded.............................................................................. 9

Fig 6: Normal and shear stresses acting on a square....................................................................................... 9

Fig 7: System of forces acting on an infinitesimal cube .................................................................. 10

Fig 8: Stress tensor ........................................................................................................................... 10

Fig 10: Planes of maximum shear stress ........................................................................................ 11

Fig 9: Stress axial cross .................................................................................................................... 11

Fig 11: Hydrostatic and deviatoric stresses ..................................................................................... 12

Fig 12: Normal fault ........................................................................................................................... 12

Fig 13: Reverse fault ......................................................................................................................... 13

Fig 14: Strike-slip fault ...................................................................................................................... 13

Fig 15: Pressure gradient diagram2................................................................................................. 13

Fig 17: Dilation and distortion ........................................................................................................... 15

Fig 16: Strain ..................................................................................................................................... 15

Fig 18: Stress-strain curve ................................................................................................................ 16

Fig 19: Elastoviscous rock behavior ................................................................................................ 17

Fig 20: Plastic rock behavior ............................................................................................................ 18

Fig 21: Viscoelastic rock behavior .................................................................................................... 18

Fig 22: Homogeneous and inhomogeneous strain ......................................................................... 19

Fig 23: Pure shear ............................................................................................................................ 19

Fig 24: Simple shear ......................................................................................................................... 19

Fig 25: Planes of maximum shear stress ........................................................................................ 20

Fig 26: Mohr-Coulomb stress circle ................................................................................................. 21

Fig 27: Mohr failure envelope ........................................................................................................... 22


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Fig 28:Uniaxial and triaxial test......................................................................................................... 22

Fig 29: Brazilian test.......................................................................................................................... 23

Fig 30: Stress-strain diagram ........................................................................................................... 23

Fig 31: Poissons ratio ...................................................................................................................... 23

Fig 32: Bulk modulus ........................................................................................................................ 24

Fig 33: Shear modulus ..................................................................................................................... 24

Fig 34: Primary and secondary stress flow3.................................................................................... 24

Fig 35: Stream flow4.......................................................................................................................... 25

Fig 36: Stress distribution around a wellbore5................................................................................. 25

Fig 37: Circular hole in infinite plate ................................................................................................. 26

Fig 38: Hoop stresses ....................................................................................................................... 26

Fig 39: Mohr-Coulomb stress diagram ............................................................................................ 27

Fig 40: Fracture and breakout direction6......................................................................................... 27

Fig 41: Mohr-Coulomb stress diagram for failure5.......................................................................... 28

Fig 42: Mohr-Coulomb stress diagram for surge and axial breakout ............................................. 28

Fig 43: Borehole with stresses and pressures ................................................................................ 28

Fig 44: Pressure points of an FST ................................................................................................... 30

Fig 45: LOT tests............................................................................................................................... 31

Fig 46: LOT tests............................................................................................................................... 32

Fig 47: EMW vs. time diagram ......................................................................................................... 34

Fig 48: Internal external filter cake5.................................................................................................. 35

Fig 49: Log data correlation of Poissons ratio and cohesion ......................................................... 38

Fig 50: Fault map of a Golf of Mexico prospect .............................................................................. 39

Fig 51: Drilling in direction of Hmax1................................................................................................ 40

Fig 52: Stress around the wellbore when drilling in direction of Hmax6......................................... 40

Fig 53: Stress around the wellbore when drilling in direction of hmin1........................................... 40

Fig 54: Drilling in direction of hmin6.................................................................................................. 40

Fig 55: Contour plots of drilling margin ............................................................................................ 41

Fig 56: Trajectories of well A-1 and A-6 ........................................................................................... 41


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Fig 57: Tensile and shear failure ...................................................................................................... 42

Fig 58: Fracture orientation .............................................................................................................. 42

Fig 59: Fracture toughness .............................................................................................................. 43

Fig 60: Gravel pack ........................................................................................................................... 45

Fig 61: Slotted liner ........................................................................................................................... 46

Fig 62: Formation compressibility diagram ...................................................................................... 47

Fig 63: Hysteresis effect ................................................................................................................... 48

Fig 64: Pore volume compressibility diagram ................................................................................. 49

Fig 65: Influence of subsidence on pressure gradients .................................................................. 50

Fig 66: Deviated casing subjected to stress regime ....................................................................... 51

Fig 67: Casing bent due to compaction ........................................................................................... 51

Fig 68: Reactivation of faults ............................................................................................................ 52

Fig 69: Casing shear ......................................................................................................................... 52

Fig 70: Radial deformation and axial load change .......................................................................... 53


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Trajectory design in terms of stress conditions in the formation

Author: Alexander Heger Page: 6

Abstract

This bakkalaurea thesis is meant to give an overview about general terms, definitions, andmodels in rock mechanics and the different applications in terms of optimum trajectory design

and problems encountered during a drilling operation with respect to the stress conditions in theformation as well as the use of rock mechanics for production purposes. It should be mentionedat this point that basic knowledge of mechanics and strength of materials is a prerequisite forthis thesis and assumed to be known from a person with technical background.

This thesis deals with stress in general, the different types of stress, the common way todescribe the stress state for a cube as a representative of soil, the stress distribution for themost typical faults and the determination of the four main stresses in the formation.

Also contained are models for description of rock behavior and the different types of strain andshear.

The Mohr-Coulomb modulus is introduced to describe rock failure and will be used in thecontinuing chapters.

Rock properties and typical values are presented as well as the stress distribution around awellbore and typical types of failure.

With respect to drilling operations the different pressures of formation strength tests areexplained and a list of critical issues and recommendations that should be reminded to carry outFSTs in an appropriate way is given.

The workflow and according advices to gather and generate the required data for an optimumwell path design are presented. There are also two examples contained which demonstrate theneed and success of appropriate well path design.

There is given a short overview about the stimulation process of fracturing, the principaldirection of fractures governed by the stress condition in the formation and evaluation of the

required pressures to carry out a fracturing job.The problem of sand production is introduced and the main solutions for sand control arepresented. Three tensile failure models are mentioned but not discussed in any detail becauseof the limited extent of this thesis.

The last chapter discusses the reasons for subsidence, casing collapse and casing shear, andstrategies to avoid loss of casing/tubular integrity.


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Introduction

Formation is the medium every petroleum engineer has to deal with and rock mechanics is thediscipline to describe its behavior. From my point of view at least a basic understanding of the

processes in terms of stress in the formation is an undeniable prerequisite for every petroleumengineer if she/he takes her/his job serious. The whole exploration and production process isgoverned by the stress conditions in the surrounding formation and tremendous amounts ofmoney have been spent due to disregard of rock-mechanical issues. As requirements for drillingand production become higher and higher it is essential to have a good understanding of rockbehavior to push the limit and explore new frontiers.

This thesis should give an overview about general terms, definitions and models which areessential for the use of rock mechanics for drilling and production purposes. It is structured in atheory, drilling, and production part whereas it is recommended to read through the first part intotal to get the necessary background for the following chapters. Many pictures and diagramsare used to visualize conditions and the main formulas are added. It was also an objective tosensibilize the reader for the numerous variety of encountered problems according to stress in

the formation and applications of rock mechanics which provide solutions and predictions.

Unfortunately the extent of this thesis is limited thus a more detailed discussion of the singleparts is not possible. It should transport some basic understanding of the subject and thementioned terms and models should help for further research if more information is required.


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Theory

General terms, definitions, and models

Stress

Stress () = Force/Area [pounds/square inch = psi, N/m = Pa]

The amount of stress is related to the quantity of applied force and the area it is subjected to.

F=m*a=m*dv/dt

Force (F) is the result of mass and its acceleration. Force has two main characteristics, itsmagnitude and direction thus it can be represented by a vector

1. In general a force subjected to

a body produces a change in its motion. If the body is hindered in its motion it becomesstressed which means that force causes particle displacement and hence deformation. Applied

forces act on a body externally whereas body forces act on every point within the body.The motion of a body subjected to a force can just be avoided by an opposite compensatingforce. Thus in the case of non-isotropy the representative geometrical figure is elliptic shaped.

1= maximum compression

2= compression, zero or tension

3= minimum compression or tension

Fig 1: Stress ellipse

Normal stress and shear stress

Fig 2: Normal stress and shear stress in 2D Fig 3: Normal stress and shear stress in 3D

A force acting perpendicular on a plain is called a normal force whereas a force acting parallel toa surface is called a shear stress. In general the symbol for normal stress is (sigma) and forshear stress it is (tau). Shear stress is also named tangential stress. In three dimensions canbe separated into two components which are perpendicular to each other. A force F is

subdivided into two mutually perpendicular stresses in the case of two dimensions and threemutually perpendicular stresses when three dimensions are used.


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To compare stresses it is useful to convert them into forces by multiplying them by the area theyare subjected to. Normal and shear stresses can also be illustrated easily in simple geologicalstructures.

Fig 4: Stress at a fault plane

Fig 5: Stress at a bedding plane which is flexural slip folded

The force F can be divided into normal and shear stresses by simple use of sinus and cosinus.

Normal and shear stress in two dimensions

The stresses acting on a two dimensional x-y square plain with no translational or rotationalforce acting on it are:

Fig 6: Normal and shear stresses acting on a square


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When no translational or rotational force is acting on the square, all shear stresses are equal.

xy= yx

The applied terminology uses for ijthe first subscript (i) as the axis normal to the actual surfaceand the second subscript (j) as the direction of the force. The subscripts can also be 1, 2 and 3which stand for the x, y and z axis.

May the best way to represent stress about a point is the use of a tensor. In three dimensionswe must imagine a system of forces acting on an infinitesimal cube. All forces can be reducedto one force acting at the center of the cube. Six planes of a cube with three forces each planeends up with 18 stresses for such a volume element.

Fig 7: System of forces acting on an infinitesimal cube

The illustration shows a cube with parallel edges to the orthogonal axes x, y, and c, and theaccording stresses acting on the cube. In sum there are nine stress components (the oppositeforces has to be equal, accounting also for them there would give 18 as mentioned before),three on each face.

Fig 8: Stress tensor

Because per definition stress does not include any rotation of the cube, the opposing shearstresses about the three axes must balance. Thus:

xy= yx, xz= zxand yz= zy

This prerequisite causes that six independent stresses (x, y, z, xy, yz, zx) are needed toquantify completely the stress system at a point.


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Principal stresses

Normal stresses on planes where shear stresses are zero are called principal stresses. Theprincipal stress planes are the three planes which are perpendicular to each other and on whichshear stresses are zero. The normal axes according to them are the principal stress aces andgiven by convention the notation 1, 2, and 3with sigma one larger than sigma two and sigma

two larger than sigma three, also named greatest, intermediate, and least principal stress. Tospecify a stress condition in total it is sufficient to quantify the direction and magnitude of thethree principal stresses.

1= max, often = v(vertical stress)

2= int, often = H(maximum horizontal stress)

3= minoften = h(minimum horizontal stress)

Maximum shear stress

For logical reasons the maximum shear stresses will appear at an angle of 45 to a pair ofprincipal stresses and intersect the third principal stress. Thus there are three possibilities toarrange this circumstance for three principal stresses.

Fig 10: Planes of maximum shear stress

Effective stresses

Reservoir rock has pores which are filled with one or more fluids. The force acting on a volumeof rock is opposed by the pore fluid as well as by the rock matrix. The pore pressure ishydrostatic and acts in all directions whereas the sum of the pore pressure and the matrix stressmust be equal to the total stress acting on the rock. The stress carried by the rock matrix iscalled effective stress (introduces by Terzaghi 1923), which is the total stress minus the porepressure. To distinguish between total and effective stress, latter is noted with a prime ()symbol.

'OB= OB pore

Fig 9: Stress axial cross


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Hydrostatic, deviatoric, and lithostatic stresses

The definition of hydrostatic stress state is used for a stress condition where the principalstresses are equal as for a fluid. Shear stresses are zero and there will be no change of shapebut of volume. If the stress state is not hydrostatic, a mean stress P (P = (1+ 2+ 3) / 3 )can

be calculated as a representative for the hydrostatic stress. The remaining part of the stresssystem is called the deviatoric stress component and can be evaluated as 1 P, 2 P, and 3 P. Deviatoric stresses count for the variation from symmetry and are responsible for theamount of shape change in a body. In comparison the hydrostatic stress component is thefactor for change in volume. If the stresses for a rock in depth are hydrostatic they are calledlithostatic. The effects of hydrostatic and deviatoric stresses are explained in the two followingexamples. In case A. hydrostatic forces reason a change in volume and in case B. deviatoricstresses cause a change in shape.

Fig 11: Hydrostatic and deviatoric stresses

Different types of faults and the according stress regimes

Normal fault

Fig 12: Normal fault

Gravity is the main driving force for normal faulting. The hanging wall moves downward relativeto the footwall.


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Reverse fault

Fig 13: Reverse fault

Due to reverse faults the maximum principal stress (1) is a horizontal one and the minimumprincipal stress (3) is vertical. The main mechanism behind reverse faulting is compression.

Strike-slip fault

Fig 14: Strike-slip fault

In strike-slip faults 1and 3are horizontal and 2is orientated vertically. Blocks tend to slidelaterally in strike-slip faulting.

Pore pressure and tectonics

Pore pressure in porous rocks can normally be calculated with p=r*g*h, so hydrostatic pressurewith a value around 0.433 to 0.465 psi/ft. Subnormal pore pressures can be the result of a trapwhich is gas or/and oil-filled due to a density difference of oil and gas compared to water.

Fig 15: Pressure gradient diagram2


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Pore pressure as well as formation pressure can also be increased due to directed dynamictectonic pressure as long as the system stays closed and does not rupture. Tectonic pressurecan be increased by gravity sliding, thrusting, and salt, mud, and shale tectonics, causing 2unequal 3and so deviatoric stress. This is especially the case in compressional environments.

Over-pressured reservoirs can be the result of artesian or structural effects, differential

compaction, rapid deposition and burial of sediments, and diagenesis which could be claydehydration.

Determination of the four main stresses:

1. vertical (overburden) maximum stress (1)

2. reservoir (pore) pressure (Pi)

3. intermediate horizontal stress (2=H)

4. fracture pressure minimum stress (3=h)

Vertical stress

The vertical (overburden) stress (1) can be determined by bulk density wire line log, gravitymeters, seismic velocity analysis or rules of thumb.

Vertical stress calculation

vertical= (z)*g*dz acerage*g*z

Water depth consideration

vertical= w*g*zw+ (z)*g*dz acerage, w*g*zw+ *g*z

Reservoir (pore) pressure

The reservoir pressure can be obtained by pressure transient techniques like wire line formationtesters or measurement/logging while drilling (MWD/LWD).

Intermediate horizontal stress

The evaluation of the maximum horizontal stress is difficult and can just be done with somedegree of accuracy if the other stresses are known and if information of the direction and extendof break-outs and/or fractures on offset wells is available. This information is further on used forstress-inversion techniques.

Rough approximation for effective horizontal compressive stress

h =[ / (1 ) ]*(v p)

= Poissons Ratio

The minimum horizontal stress is of great importance because it is the FIP (fracture initiationpressure) as well as the stress that propping agents have to withstand to keep the fractureopen. It can also be evaluated by a formation strength test like a leakoff test.


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Modulus of elasticity

If a material behaves elastic it returns to its initial shape if stress is removed. When stressexceeds the so called yield point, the material is required too much and departs from linearity. Inthis non-linear zone of the stress-strain curve deformation is plastic and the material will not

return to its original shape when stress is released. An important property of material is itsmodulus (stretch ability) which is defined as stress divided by strain.

Fig 18: Stress-strain curve

These assumptions are just valid for isotropic materials whereas for non-isotropic materialsmodulus tensor analysis is required.

Linear elasticity

If the elasticity of a material behaves in a linear way, Hookes law can be applied which meansthat the magnitude of distortion is directly linear proportional to the magnitude of the distorting

force, and their directions are the same.

= E*

= axial stress

= axial strain

E = Youngs Modulus (modulus of elasticity)


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Viscous strain

Ideal viscous strain means no recovery after removal of the deforming stress so all themovement is remaining. Ideal viscous or also called Newtonian behavior is explained by theflow of fluids. The according formula is

= *

(eta) = a viscous constant

= strain rate (rate of change in shape with time)

In the case of linear viscous strain the relationship between stress and strain rate is linear. Thehigher the stress the faster the deformation will appear. The total strain depends on themagnitude of the stress and the duration of time it is acting. Stress=viscosity * strain rate. For aconstant stress situation, the strain is increasing in a linear manner with time (t).

e=*t/

Elastoviscous, plastic, and viscoelastic rock behavior

In rocks ideal and viscous behavior are combined. A simple approximation to the total strain atconstant stress is:

e = /E (elastic component) + *t/(viscous component)

Elastoviscous material behaves mainly like viscous but elastically if stress is applied for a shortduration (e.g. tar).

Fig 19: Elastoviscous rock behavior


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Plastic materials show at low stress values an elastic behavior but act perfectly viscous beyonda certain critical stress level called yield point. The inelastic strain above the yield point is calledplasticity. Plastic deformation is permanent but excludes failure or rapture of the material.

Fig 20: Plastic rock behavior

A material is defined as viscoelastic if its strain behaves elastic for a given stress but whichtakes a certain time to reach its limiting value. If stress is removed the material does not returnto its unstrained state but has a delay in its recovery of elastic strain. Most of the rocks exhibitviscoelastic behavior at low stress values.

Fig 21: Viscoelastic rock behavior


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Homogeneous and inhomogeneous strain

If strain is equal in all directions it is called homogeneous and straight lines must remain straightand parallel ones parallel. In the case of inhomogeneous (heterogeneous) strain, the strain isunequal in different parts of the body and so parallel lines become non-parallel and straight lines

become curved.

Fig 22: Homogeneous and inhomogeneous strain

Pure shear and simple shear

Pure share is defined as deformation with no change in orientation of the principal strains, x, y,and z (non-rotational).

Fig 23: Pure shear

When change in orientation appears the deformation is known as simple shear (rotational).

Fig 24: Simple shear

It is favorable to describe strain with a distortional component measuring the elliptic shape and arotational component determining the rotation of the principle strain axes from their initialunstrained position.


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Rock failure

Brittle failure stress conditions

The case when rock fails under brittle deformation is called brittle failure. The stress conditionsat the point of failure involve hydrostatic pressure and shear stress. If failure appears under

triaxial compression two sets of planar shear fractures are formed that intersect in a line parallelto the intermediate principle stress axis (2). The acute angle between the shear fractures isbisected by the maximum principle stress (1). The fracture planes are not related to themaximum shear planes which have an angle of 45 with 1. The angle between the two fractureplanes is assumed to be 2 (=) so the difference between this acute angle and the anglebetween the maximum shear stresses (2*45) can be calculated with

(Beta) or (phi) = 90 - 2

The angle phi is the angle of internal friction which is an inherent material property.

Fig 25: Planes of maximum shear stress

Categories of peak strength criterion are Drucker Prager (van Mises) which is a function of 1,2, and 3and a linear criterion, Mohr-Coulomb which is a function of 1 and 3 and also a linearcriterion, Pariseau which is a function of 1, 2, and 3 and a non-linear criterion, and Hoek-Brown which is a function of 1 and 3 and also a non-linear criterion. Other categories would beGriffith, Lade, and Tresca to name some.

The Mohr-Coulomb stress diagram

Yielding or fracturing is assumed to appear when the cohesive strength of the material and thefrictional resistance is outreached by the acting shear stresses. The Mohr stress diagram offers

a simply way to represent the relationship of shear stress, hydrostatic pressure (normal stress),and the angle of failure at the point of failure in a two dimensional manner. States of stressesare illustrated by circles which centers and radii can be easily determined by simple geometricalcalculations. The center can be evaluated with

(1 + 3)/2

which is also the mean stress or hydrostatic component and the radius can be determined with

(1 - 3)/2

1 > 2= 3

The normal and shear stress on a plain with failure angle () to the plain of the major principal

stress and perpendicular to the plain of the intermediate principal stress can be calculated bythe following equations.


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n= * (1+ 3) * (1- 3) * cos (2) or sin ()

R= * (1- 3) * sin (2) or cos ()

additional equations for the Mohr stress diagram

Cohesion: 0= n* tan ()

Navier-Coulomb equation: = 0+ n * tan ()

max shear stress at failure condition: max = (1 - 3)/2

~ 45 - /2, = 90 - 2

shear stress at failure: R= * (1- 3) * sin (2) or cos ()

coefficient of internal friction: tan () = /

for rocks: 10


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When the shear stress is increased to reach failure, the hydrostatic pressure has to beincreased as well. In general it can be stated that the shear stress acting along the fracture plainto induce failure is counteracted by the compressive stress acting across the fracture with thetendency to close the crack and to avoid failure of the rock. On the left side of the shear stressaxis tensile stress is represented. It can be seen that a rock without any cohesion cant take anytensile stress without failure and that for rocks with cohesion the amount of tensile stress which

can be withstood is much smaller compared to the strength against compression. The overallshearing resistance of an isotropic material is governed by the cohesive strength and theproduct of the effective normal stress across the failure plain and a coefficient of internal friction.

total shearing resistance = 0+ n* tan ()

The use of the Navier-Coulomb equation is a simplification for easier handling of the Mohr stressdiagram. In reality the straight line is an envelope which is named Mohr failure envelope. Itconnects the points of failure for different stress conditions and divides the stable stress statefrom the area of failure.

Fig 27: Mohr failure envelope

Another more realistic approach is the Griffith Failure Criterion, which is based on the concept offailure due to propagation and linking of very small defects in a material known as GriffithCracks, but this concept is not widely used in the petroleum industry.

Rock mechanical properties

Compressive Strength (C)

Compressive strength is the ability to withstand stresses.

Uniaxial (unconfined) compressive strength (C0)

C0= amax (psi)

Triaxial (biaxial) compressive strength (C)

C(3) =amax (3) (psi)

Typical values (psi)

Igneous/metamorphic rocks >80,000

Sedimentary rocks 10,000 - 80,000Soft sediments


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Tensile Strength (T0)

Maximum tensile stress a material can handle before failure. There are direct tension tests (DogBone Test, Burst (expandable packer) Test) and indirect tension tests (Brazilian Test) applied.

Brazilian (indirect) tension

T0= 2P/td (psi)

t = thickness

d = diameter

Typical values (psi)

Igneous/metamorphic rocks >30,000

Sedimentary rocks 500 - 3,500

Soft sediments


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Bulk Modulus (K)

The inverse of the bulk modulus is called the compressibility (k) of the material.

K = / (3*(1 - 2) (F/A)/ (/0)

Fig 32: Bulk modulus

Shear Modulus (S) or (G)

The shear modulus is related to the rigidity.

S = / (2*(1+) (F/A)/(L/L0)

Fig 33: Shear modulus

Stress distribution around the borehole

If a well is drilled the stress conditions in the formation near the wellbore are changed drastically.The initial stress flow has to bend around the borehole which induces high hoop/tangential

stresses.

Fig 34: Primary and secondary stress flow3


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Fig 35: Stream flow4

For a vertical well the stress distribution will look like this:

Fig 36: Stress distribution around a wellbore5


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The radial and hoop stresses as well as the shear stress at failure at any point of investigationcan be calculated with the following formulas

4(assumed no wellbore-fluid present):

r= * (x+ y)*(1 ) + * (x y)*(1 + 34- 42) * cos (2)

= * (x+ y)*(1 + ) - * (x y)*(1 + 34) * cos (2)

R= - * (x y)*( 1 - 34+ 22) * sin (2)where = a/r

If there is no wellbore-fluid present as assumed the radial stress at the borehole-wall is zero (=1r= 0)

.

Fig 37: Circular hole in infinite plate

The maximum and minimum hoop/tangential stresses at the borehole-wall5can be calculatedwith:

tmax= * [z+ + ((z- ) + 4R)0.5]

tmin= * [z+ - ((z- ) + 4R)0.5]

Fig 38: Hoop stresses


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The Mohr-Coulomb stress diagram can be utilized to represent the stress conditions of awellbore.

Fig 39: Mohr-Coulomb stress diagram

Rock failure due to excessive stresses

Insufficient mud weight can cause a failure of the rock with the result of breakouts4. Classical

breakouts are in direction of the minimum horizontal stress.

Classical breakout:

1= - Pp

3= Pb Pp

Fig 40: Fracture and breakout direction6


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Fig 41: Mohr-Coulomb stress diagram for failure5

Two other types of breakout are possible which are surge and axial breakouts4. These areoriented in the direction of the maximum horizontal stress.

Surge breakout:

1= Pb Pp

3= Pp

Axial breakout:

1= v- Pp

3= Pp

Another type of failure is due to excessive borehole-pressure which reasons fracturing of theformation. This effect is used in fracturing operations for the purpose of stimulation.

Tensile hydraulic fracture:

3= Pp

3


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Applications of rock mechanics in drilling

Wellbore-stability

Improving Formation-Strength Tests

In terms of wellbore-stability the verification of pressure integrity of casing and nearby formation7

is one main objective during a drilling operation, moreover because in general there areregulations of the government to have a minimum integrity proven before a well is drilled. Thisprocess including the decisions on mud weight, kick tolerance, and setting depth of the nextcasing is based on formation-strength tests (FSTs) like leakoff tests (LOTs) or formation-integrity tests (FITs).

The FSTs carried out at the moment are of poor quality and accuracy because of reasons likeuse of high compressible synthetic or oil based mud, poorly understood formation-stress and strength behavior or just because of poor data capturing e.g. due to use of hand-generatedplots. This inadequate working leads to sever wellbore-stability problems especially when tightdrilling margins are present.

FITs are applied after the casing is set and cemented and before a new hole-section is drilled.First of all there is the need to drill through the casing shoe and a sufficient length of formation(10-20 ft) to get access to the environment which is going to be tested. Continuing the BOPcloses the annulus and the well is pressured up slowly by injecting mud. The purposes of thetest are to prove the strength of the cement shoe and so to ensure that neither a flow path toupper formations nor a connection to the previous annulus is present, test the capability of theformation to withstand additional pressure like encountered during a well control operation (e.g.circulating out a kick) which is necessary to drill the next hole section safely, and to collect dataon formation strength and in-situ stresses that can be used for wellbore-stability and lost

circulation predictions for the present as well as for future wells.Interpretation and analysis

There is still much erroneous information on FST around so the following will be a section ontest interpretation and analysis.

Fig.44 can be used as a guideline presenting the different pressure responses during variousFIT types. The pressure-points are:

LP=limit pressure (jug pressure). This is the highest pressure reached during a limit test (jugtest). It will not reach the fracture-initiation pressure (FIP) on the linear part of the pressure-vs.-volume (or vs. Time when the volume is pumped at a constant rate) curve that characterizeselastic compression of mud, drill string, casing, and openhole.

FIP=fracture-initiation pressure, also named leakoff pressure (LOP). It indicates the point atwhich the pressure-build up curve starts to deviate from straight line behavior. The FIPproduces a near-wellbore fracture that causes a change in stiffness of the pressure system.

PSP=pump-stop pressure. LOTs would in general be stopped at this pressure. This pressurepoint is still in the range of stable fracture propagation which means that it would need additionalpressure to continue the growth of the near-wellbore fracture. It has to be stated that the growthof the near wellbore fracture would mainly appear in width. An eye should be kept on thepressure for the purpose of not reaching the uncontrolled fracture pressure (UFP) or fracture-propagation pressure (FPP), which would result in uncontrolled fracture growth. PSP is normallythe highest pressure encountered during an LOT and the according equivalent mud weight isusually reported to the regulatory authorities as the strength of the casing shoe. It is important tonote that the characterization of formation strength at the casing shoe during an LOT is not aproper definition; the test characterizes near-wellbore stress as well as formation tensile


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strength whereas the formation tensile strength normally makes just a small contribution. Amore accurate term would may be formation stress at the casing shoe-test.

Fig 44: Pressure points of an FST


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UFP=uncontrolled fracture pressure. When this pressure is reached enough energy is stored inthe fracture that it grows uncontrollable predominant in length (tens to thousands of feet). At thispoint the casing shoe will have suffered severe damage as well as the damage to the near-wellbore stress state, loss of formation strength, and created fractures may cause the disabilityto continue the well as long as the casing shoe is not repaired by cement squeeze or similartreatments. For logical reasons it is highly recommended not to exceed the UFP.

FPP=fracture-propagation pressure. At this point uncontrolled fracture propagation takes place.It can be equal to UFP, but also significantly lower. Again it is not recommended to reach thispressure during an FIT cause fracture damage to the formation will grow exponentially.

ISIP=instantaneous shut-in pressure. The pressure reached immediately after shut-in.

FCP=fracture-closure pressure. It is of high importance to know this certain pressure, although itis sometimes hard to discover. FCP can be equalized with the minimum horizontal stress(MHS), an important parameter. To determine the FCP the pressure has to be plotted vs. timeduring shut-in or pressure vs. volume during backflow sequence, where the last procedure isthe more accurate but also more demanding one. The objective is to identify the point ofinflection on the pressure vs. time or the pressure vs. volume curve. It indicates a change instiffness of the pressure system. Fig.45 shows examples of MHS evaluation in backflow and

shut-in applications.

Fig 45: LOT tests

FRP=fracture-reopening pressure. When repeating a LOT due to the produced formationdamage of the previous LOT (loss of tensile strength, breakdown of near-wellbore hoop stress)the fracture will reopen usually at a lower pressure than the original FIP and close or equal tothe FCP.

Test selection

With the knowledge and understanding of the different pressure points in an FST it becomespossible to make the right choice of test for different applications.

For most of the cases it is recommended to use a continuous pump- in LOT. If there is the caseof an exploratory or appraisal well in unknown pressure/stress regimes it is a must to define thefracture gradient, available drilling margins, and kick tolerance for the next section to drill. Oneshould try to get as much information as possible also for the use in geomechanical andborehole-stability modeling for following wells.

In the case of a permeable formation at the shoe it makes more sense to apply a pump-and-hold, or stepped LOT. The reason for this is, that the pressure build-up curve would not be

linear from the start due to mud loss through the filter cake into the permeable formation. This


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unfavorable behavior makes it very difficult or even impossible to indicate the FIP. Thus apump-and-hold test could help to be successful with this task.

The main principle is to measure the fluid loss to the formation which is more or less constantunder FIP. For gather the lost volume the pressure drop during the hold phases is used. Assoon as the FIP is reached a larger pressure drop will appear on the basis of larger fluid volume

lost. By comparing the maximum pumping pressure and the minimum holding pressure it couldbe able to detect the FIP. Fig.46 expresses the statement in an example.

Fig 46: LOT tests

For production wells in mature fields with very precise known fracture gradients and for wellswhere a number of cement squeezes have not been successful to rise the FIP (low formationstrength or cement channel which is plugged and easily broken again) a limit test or jug testshould may be preferred, cause a LOT always induces a formation damage (although damagecan heal over time, particularly when in use of a dispersive water-based mud). Compared to aLOT a properly done limit test will not produce any formation damage.

In general it can be stated that the reduction in formation strength does not automatically resultin operational problems. The experience proves that as long as the applied pressure duringdrilling is kept in the range of stable fracture growth (i.e., the range in which the PSP isidentified) the well can be deepened without sever difficulties. Minor mud losses and fracturebreathing can occur due to the opening and closing of small near-wellbore fractures when

equivalent circulating density (ECD) is used in the stable fracture growth range. It is still ofimportance to realize that for low-margin wells it is inevitable to exploit the stable fracture-propagation range if it is the case that FIPs and FRPs are too low to drill a section. Fig.45 showsthe results of a LOT test for a deepwater-well in the Gulf of Mexico which could not have beendrilled without fully exploiting the stable fracture-propagation range.

Complications and considerations

The impact of Mud Compressibility, Thermal Expansion, and Sag

The usual way to record data from an FST is to use the mud weight and the pressuresmeasured at the surface. If the used mud density is not corrected due to mud compressibility,thermal expansion, and sagging of weighting material the fracture gradient will be incorrect and

so can cause trouble in low-margin drilling applications. The three mentioned effects are a


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depending on the mud type in use whereas oil-based and synthetic based mud are morecritical than water-based mud.

In deepwater wells with low temperatures downhole the predominant effect is the mudcompressibility which induces normally a higher density on bottom in comparison with surfaceconditions. Unfortunately the increase in density follows a non-linear behavior and is a function

of pressure and temperature.

Still the hydraulic-simulation packages of the major drilling fluid suppliers are accurate alsoincluding the compressibility-effect.

In high-pressure/high-temperature wells the expansion of the drilling mud as a result ofincreasing temperature is the dominating effect, which compensates the compression due topressure downhole and leads to a mud density effectively lower than on surface. As well ascompressibility the thermal expansion is a function of pressure and temperature too.

Sagging appears when the weighting material can no longer be suspended. This can happendue to contamination when mud which is not conditioned for it gets in contact with cement orspacers. Normally the weighting material settles out of the mud column and produces a loss ofbottomhole pressure. If weighting material is originally placed in an upper lager diameter holesection and travels downwards into a smaller deviated hole section it can cause an increase inbottomhole pressure. For logical reasons the mud should be conditioned and circulated beforean FST is executed so that sagging cannot appear.

To summarize the points mentioned above, it is of great importance to include the three effects

on mud density downhole which are compressibility, thermal expansion, and sag if surface mudweight (surface) and surface pressures (PFST) are used.

C,TE,S can either be positive or negative. Another chance to get downhole is to directly measure itfrom a pumps off static-mud pressure reading when using a PWD tool.

The impact of Gel Strength

By the use of downhole data recording during FSTs it was realized , that the assumed pressuredownhole was not present but lower. For example in Fig.47 it can be seen, that for the givencircumstances the downhole-pressure is 241 psi lower than the surface pressure. The pressureapplied at surface does not fully act at the casing shoe. It is obvious that this effect will cause anoverestimation of the drilling margin and leads to sever problems while drilling the next section.


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Fig 47: EMW vs. time diagram

The reason for this pressure difference is the thixotropic behavior of the mud so its gel strength.Fortunately the pressure loss related to this effect can be calculated by

Pgelis the pressure loss (psi), Lmud is the length of the mud column (ft), G10 min is the 10-minutegel strength of the mud (lbf/100 ft), and Doand Diare outer and inner diameter (in.) of the drillpipe or annulus holding the mud column.

To account for this effect the PFSTshould be calculated with

This new corrected value should be used instead of P FST in the calculation of shoe strengthpreviously mentioned.

Another effect which was found out according to the gel strength is a difference or delaybetween the readings of the standpipe gauge and the annular gauge (see Fig. 46). Toovercome this problem pumping should be done through DP and annulus so that readings onthe surface gauges are equal.

The influence of Mud Type

It was established that if FIP is used to detect fracture gradient and casing-shoe strength it is notdependent on mud type, but if one uses PSP (or UFP/FPP), as usual in the field, it can behighly dependent on mud type.

The difference between WBM and OBM or SBM relates to their build up of external and internalfilter cakes (Fig. 48). WBM have a high spurt loss in increasing fractures and build up anexternal filter cake which isolates the tip of the fracture from the full hydraulic force. In

comparison OBM and SBM create an internal filter cake which provides no barrier for the tip ofthe fracture to the acting hydraulic force. Thus smooth fracture propagation appears at lower


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pressures in comparison to WBM. This also results in a larger drilling margin for WBM takingthe mud window from pore pressure to UFP as discussed before and may offers the opportunityto deepen a well where OBM/SBM would not be applicable anymore.

Fig 48: Internal external filter cake5

It should always be kept an eye on the type of mud used for an FST cause the shoe strength7

and fracture gradient for a WBM will be different from an OBM/SBM. If there is a change in mudtype it is recommended to retest the shoe strength and fracture gradient to identify an increaseor decrease for these values due to different mud type in use.

It has already been achieved to increase the drilling margin by adding certain particles atspecific concentrations and sizes in the mud, but it was not possible to raise the FIP. This effectleads to the assumption that the reasoning mechanism is an improvement of fracture tip-screen-out behavior rather than a modification of the near-wellbore stress state.

The influence of Temperature

Temperature has two main effects on FST. If the used mud temperature downhole is higherthan the undisturbed formation temperature it will heat the formation and so increase thermalstress around the wellbore. This will result an increase in FIP and UFP/FPP because theadditional stress will act against the fracturing of the formation. The change in thermal stress iscalculated with

Where E is Youngs modulus, is Poissons ratio, thermalis the formations thermal expansioncoefficient, and Tmud and Tformationare downhole temperature of the mud and the formation.

The effect of temperature on formation stress is often underestimated so it is advisable to recordand document the actual downhole temperature at which the FST was performed and to makethe rig crew more attentive to the fact that shoe strength and fracture gradient will increase ordecrease with change in mud temperature.

The second but minor influence is the heating or cooling effect during the FST which is ofimportance in deepwater wells where the water column has the tendency to cool the riser andworkstring. The change in temperature will also change the compressibility, thermal expansionand gel-strength behavior as mentioned before.


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The influence of Variation in Time

The fracture gradient and the formation strength do not stay constant over time. After an LOTthe formation strength is lower and if testing is repeated there is additional damage producedeach time. But there is still the chance of fracture healing due to clay swelling in WBMs with adispersive tendency. This effect does hardly appear when OBMs or SBMs are in use. Another

healing process can be enforced due to circulation of warmer mud from deeper well sectionswhich causes an increase in near wellbore thermal stresses and thus a rising of shoe strengthand fracture gradient.

The influence of Location of Cementing Unit

What seems to be trivial but is of relevance is the location of the cement unit. In many cases thecement unit is located on a deck below the point of reference of the well. For the purpose ofaccuracy the initial gauge pressure should be subtracted from the final FST pressure. Thisprocedure does not account for downhole measurements.

Recommendations

To execute an accurate FST all these points should be considered. If possible it is alwaysadvised to use downhole recorded PWD data, which will eliminate any test artifacts according to

mud gellation, temperature effects appearing during the FST test, and the location of thecementing-unit pressure gauge.


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Wellpath optimization

In general it can be recommended to involve all relevant disciplines8 like well engineering,

petrophysics, geology, geomechanics and rock mechanics in the well planning process togather more information and knowledge about the formation and its behavior. Although this is aconsiderable investment before a well is drilled, it is worth the time and money spent inpresence of the enormous values of money spent for wellbore stability problems.

Use of data from offset wells

Is seems quite trivial to use data of nearby wells, but workload, time-pressure and lack ofresources often avoid to use this source of information. The gathered data can be very useful topredict the problems which will most likely be encountered during the drilling operation. Forinstance if borehole stability problems seem to be mainly based on mechanical issues then

more attention can be paid to rock mechanical analysis. Offset well reviews also play animportant role for calibration of models used in borehole stability, hole cleaning/ECD and torqueand drag modeling.

Formation property analysis

The objective of this process is to characterize the underground according to pore pressure, in-situ stress and formation strength to provide input data for borehole stability modeling. Theanalysis should especially concentrate on the hot spots of the formation like zones that have atendency to compact and subside, low-strength formations, formations with high pore pressuresand so on.

Pore pressure

Data from offset wells can be a good indicator of pore pressure when RFT/MDT pressures havebeen taken from permeable zones as well as mud weights used to avoid entrance of formationfluids. There are also numerous correlation methods to get pore pressures from seismic andwell log data. It can be stated that one single method does not work for every drillingenvironment.

In-situ stress magnitude and direction

Stress regime

The first step of stress analysis is to let geologists and geomechanical engineers establish thestress regime. For borehole stability and so for the well path it makes a great difference if thewell will be drilled in a normal fault, thrust fault or reverse fault area.

Vertical stress

The development of the vertical stress with depth can be evaluated from an integration of thedensity logs of similar offset wells. A possible mistake can appear if the logged formation of theoffset well has its density due to interaction with drilling fluid (e.g. shale reacting with WBM).

Minimum horizontal stress/fracture gradient

How this information is obtained was already presented in the previous chapter Applications ofrock mechanics in drilling/Wellbore Stability.


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Maximum horizontal stress

The evaluation of the maximum horizontal stress is difficult and can just be done with somedegree of accuracy if the other stresses are known and if information of the direction and extendof break-outs and/or fractures on offset wells is available. This information is further on used for

stress-inversion techniques. If the horizontal stresses are unequal (normal faulting region) andthe information about the shape of the offset wells is not on-hand it is a good first approach totake the average of the minimum horizontal stress and the vertical stress as the maximumhorizontal stress. Even the direction of the maximum horizontal stress can be set to be parallelto the strike direction of faults in this area.

Formation strength

For borehole stability analysis elastic formation parameters like Youngs modulus andPoissons ratio are required as well as failure parameters like cohesion and the internal frictionangle. These are mainly derived from core tests in the laboratory of representative formation.When cores are not available or of poor quality it is possible to correlate the rock parametersfrom log data.

Fig 49: Log data correlation of Poissons ratio and cohesion

Some formations have anisotropic strength behavior resulting in different effective strengths andfailure parameters depending on the orientation the rock is intersected. It is obvious that such afeature has great influence on the optimum well path, cause there will be an optimum way todrill through such a formation according to borehole stability. Such anisotropies can so far justbe measured in the laboratory.


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Wellbore stability analysis

Wellbore stability model

For a proper wellbore stability analysis an accurate and calibrated simulator is needed. One

problem of the most simulators is their use of an analytical linear elastic model. It enables fastresults but the mud weight they calculate are higher than the wellbore would actually need toremain stable. The reason is that rock mainly behaves elasto-plastic and not linear elastic. Sofor a quick estimation for well path optimization the linear elastic model is useful but a numericalfinite-element elasto-plastic model will generate more realistic mud weight predictions.

Wellpath optimization

Wellbore stability modeling requires formation parameters (in-situ pore pressure and stress,strength and failure parameters) and well trajectory information (depth, well deviation, andazimuth) as input data. the overall objective is to find the trajectory with the optimum mudwindow (difference between fracture gradient and mud weight required to stabilize the

wellbore).

Fig. 50 shows a fault map of a Gulf of Mexico prospect including the trajectories of severaldeviated development wells. The yellow numbers are the trouble costs for these wells whichwere drilled in different azimuths relative to the maximum horizontal stress direction. There wasan obvious increase in trouble cost from the wells drilled perpendicular to the direction of themaximum horizontal stress (e.g. A-2ST, 0% trouble cost) to the wells drilled parallel to thedirection of the maximum horizontal stress (e.g. A-4, 32% trouble cost due to stuck pipe and lostcirculation. In general it can be stated that deviated wells drilled in the direction of the maximumhorizontal stress are the most difficult ones in tectonically relaxed environments.

Fig 50: Fault map of a Golf of Mexico prospect


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An explanation why it is easier to drill a horizontal well perpendicular to the direction of themaximum horizontal stress is the stress regimes around the wellbore.

If the well is drilled in direction of Hmaxthe stress condition around the wellbore will look like this:

It can be seen that hminis the stress that acts againstthe inducing of a fracture. Thus it influences the FIP

(fracture-initiation pressure).

If the well is drilled perpendicular to Hmaxthestress condition around the wellbore will look like this:

Now Hmaxis opposing against the induction of a fractureand influences the FIP.

In each case the mud weight has to be sufficient tostabilize the wellbore and the requirements are equal.But in the case of drilling perpendicular to the directionof the maximum horizontal stress the FIP will be higher because Hmax has a higher valuecompared to hmin. This effect will cause a larger mud window and make the trajectoryperpendicular to Hmaxthe optimum well path in terms of wellbore stability.

Fig 51: Drilling in direction of Hmax1

Fig 52: Stress around the wellbore when drilling in

direction of Hmax6

Fig 54: Drilling in direction of hmin6

Fig 53: Stress around the wellbore when drilling

in direction of hmin1


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Another example for well path optimization8is Fig. 56 which shows a Gulf of Mexico sub-salt

prospect.

The A-1 appraisal well was drilled into weak-salt formations at high angle. Due to boreholestability problems and lost circulation problems it was necessary to drill multiple sidetracks. Afterwell A-1 was drilled a well path optimization study was carried out. The result was to build angle

high up the hole, drop angle in salt, and intersect the sub-salt zones nearly vertically.Above salt the mud weight windows of well A-1 and well A-6 are quite the same (1.5-2.0 ppg).This is sufficient to accommodate the pressure difference between static and dynamic condition(static density, circulating density). Below salt the mud window for A-1 had sunk to less than 0.5ppg whereas the mud window for A-6 was still at 2.0 ppg. In this case below salt 1.0 ppg wereadded to the mud density downhole due to mud circulation Thus well A-1 was either in thesituation to keep the mud weight high enough to prevent stability problems but fracturing theformation and risk lost circulation or to keep the mud weight low enough to prevent fracturingbut deal with wellbore stability problems. Well A-6 had a sufficient mud weight for ECD and wasdrilled to target without sever problems and well-ahead of budget.

Fig 56: Trajectories of well A-1 and A-6

Fig 55: Contour plots of drilling margin


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Applications of rock mechanics in production

Fracture mechanics

A fracture is defined as a crack, joint, fault or other break1in the rock. It is induced due to loss ofcohesion or resistance to differential stress. When a fracture is formed the stored energy isreleased. A joint is a fracture or parting without displacement and a fault is fracture or fracturezone where relative displacement of the sides has appeared.

The fracture evaluation and propagation for artificially induced fractures is mainly governed bymechanical properties and stresses like in-situ stress field, tensile and compressive strength,permeability (leak off), elastic module contrast, fracture toughness, and fluid properties.

Fig. 57 shows the two brittle criteria and Mohr circles for tensile (a) and shear (b) failure.

Fig 57: Tensile and shear failure

In general a fracture will be extended in the direction of the maximum horizontal stress, becausethe compressive strength of the minimum horizontal stress is easier to overcome (Fig. 58). Butdue to more tectonic events in reality the direction will look more chaotic (Fig. 58).

Fig 58: Fracture orientation


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Strain energy

The value of the strain energy predicts failure at some point in the material when the strain orpotential energy per unit volume reaches a critical level.

W = (11+ 22+ 33)/2

The strain energy per unit volume is the fracture toughness and is calculated by the area underthe stress-strain curve from origin till fracture.

Fig 59: Fracture toughness

Hydraulic fracturing

Hydraulic fracturing is the most applied stimulation process in oil and gas wells. A specialblended fracturing fluid is pumped with sufficient rates and pressure into the pay zone toproduce fractures and extend them. The purpose of these fractures is to increase production bytheir high conductivity compared to the reservoir permeability at some distance away from theborehole. To keep the fractures open after the pressure is released proppants (sand) arepumped into the openings of the formation. The strength of the propping material has to besufficient to withstand the compressional stress which they are subjected to. Another possibilityis to apply acid fracturing but this will not be discussed here in any more detail.

Rock mechanics

Rock mechanics is a major effect according to fracture propagation. Factors governing thepropagation are the variation of in-situ stresses in different rock layers, the relative bedthickness closer area of the fracture, the connection between formation and permeability whichdefines the fracture efficiency, changes in the mechanical properties like Youngs modulus, andPoissons ratio, fluid pressure gradients and variation in pore pressures between zones.

Candidate selection

It is advised to select reservoirs where problems with undesired communication due to the

produced fractures can be avoided. Long zones need special consideration (geology, stresses,reservoir drive, fluid properties, and rock properties).


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Facture initiation

The fracture is induced by pumping a suitable volume of fluid into the formation at a higher ratethan it can leak off into the rock. The fluid pressure has to be sufficient to overcome thecompressive strength of the rock. As already presented in previous chapters the fracture willpropagate in the direction of the maximum horizontal stress.

Vertical fractures

If vertical fracturing appears depends on the relative strength of the two principal horizontalstresses. To create a vertical fracture the tensile strength of the rock has to be exceeded.

(Pi)v= 3h2 h1+ Sh+ Pr

for the effective stresses pore pressure has to be subtracted

(Pi)v= borehole pressure required to initiate vertical fracture

h1= maximum principal horizontal matrix stress

h2= minimum principal horizontal matrix stress

Sh= horizontal tensile strength of rock

Pr= formation pore pressure

Horizontal fracture

To induce a horizontal fracture the pressure in the wellbore must exceed the vertical stress andin addition the tensile strength of the rock.

(Pi)h= v+ Sv+ Pr

for the effective stresses pore pressure has to be subtracted

(Pi)h= borehole pressure required to initiate horizontal fracture

v= total vertical stress

Sv= vertical tensile strength of rock

Pr= formation pore pressure

Fracture extension

The growth of the fracture will stop as the leak off to the formation is equal to the volume ofinjected fluid. The different pressures (e.g. FIP (fracture initiation pressure), FPP (fracturepropagation pressure), FCP (fracture closure pressure which is nearly equal to the minimum

horizontal stress)) which are encountered during an FST (formation strength test) like an leak offtest and which play also an important role in hydraulic fracturing can be reviewed in the chapterApplications for rock mechanics in drilling/Wellbore Stability. There are still a lot moreimportant things to mention about hydraulic fracturing, but due to the limited extent it is notpossible to discuss the issue in more detail.


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Sand control

Sand production appears related to shallow formations1with little or no cementation. When the

well is produced the wellbore pressure is lower than the reservoir pressure and drag forces areapplied to the sand grains due to fluid production. Sand can plug the pores and/or be produced.

One big problem with sand production is its erosional effect on equipment and settlement insurface vessels. Controlling Sand production is costly and mainly done with slowing theproduction rate or by the use of gravel packing or sand consolidation techniques.

Causes for sand production

The main reason for sand production is the pore pressure depletion and drawdown whichresults in higher hoop/tangential stresses at the borehole wall. When the stress value reachesthe shear strength of the rock failure of the material and fragmentation of sand grains willappear.

There is a proportional relationship between the pressure drop from the wellbore to the reservoirand the amount of sand production. Another logical conclusion is the relation of the drag force

due to fluid flow and the velocity and viscosity of the fluid. Also the wettability of the grainseffects its production as well as the production rate and the degree of natural consolidation.Intergranular bonds, intergranular friction, gravity forces, and capillary forces are the opposingforces against fluid drag. Multi phase flow will have a negative impact and increase sandproduction. For instance water production can lead to solution of natural cementing material.Thermal effects and high temperature can make the sand production more severe (e.g. steaminjection).

Sand control techniques

To avoid the production of the sand screens (2.5 *san grain diameter), slotted liners (2.5*sandgrain diameter) and gravel packs are in use. Spherical particles will not flow continuously

through rectangular slots twice as wide as the diameter of the particle or circular hole threetimes their size.

Fig 60: Gravel pack


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Fig 61: Slotted liner

In terms of gravel packs it is important to stay below a certain critical flow velocity or the packsbridging mechanism will not work properly. It is also of interest to determine the criticalproduction rate at which sand production becomes intolerable. It is recommended to increasethe flow step-wise because surge can break weak bridges and once this has appeared theywont reform again. Thus the sand production will continue at a higher level.

Sand production prediction

Prediction can be done by offset or analog well data, correlations, sand stability modeling within-situ stress, rock, and fluid data, and log analysis.

Tensile failure models

This model is based on a tensile radial stress (r) which exceeds the tensile failure envelopeand is controlled by the drawdown pressure (Veeken SPE 22792, 1991). It was developed forunconsolidated sands and does not include in situ stresses and changes in the in-situ stressesdue to depletion. It is generally overly conservative.

Another model is after Weingarten and Perkins which produces especially in oil reservoirs toohigh values and the Mohr Coulomb model which is intermediate to Veeken and Weingarten

and Perkins.

There is even more to say about sand control but this would go beyond the scope of this thesis.


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Subsidence

Rock and reservoir compressibility

Compressibility is a major effect in terms of production1in many reservoirs. Bulk compressibility

is the fractional change of the bulk volume of the rock with a unit change in pressure. Graincompressibility is the fractional change in volume of the solid rock grain with a unit change inpressure. Pore volume compressibility is the fractional change in pore volume of the rock withunit change in pressure and formation compressibility is the relative change in pore volumedivided by the change in reservoir pressure that caused the change in pore volume, usuallymeasured under hydrostatic conditions.

The measurement of pore volume compressibility is affected by things like coring conditions,core handling and preservation, compressibility of the pore fluid, micro-crack development and

rock fabric, pore space connectivity and cementation, morphology, distribution and aspect ratioof pore system, experimental methods/apparatus, loading path sensitivity, hysteresis andpressure cycling, prior knowledge of in-situ stresses, rock mechanical properties, poroelasticconsiderations, linear elasticity and laboratory stress redistribution.

Compressibility type curves for clastic reservoirs

Fig 62: Formation compressibility diagram

Bakk 2 Trajectory Design in Terms of Stress Conditions in the Formation

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