Borehole Stresses.pdf

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  • Stresses Around a Borehole

    Prof. Dr. Eissa Mohamed Shokir

  • Common Borehole Stability Symbols

    s1,s2,s3: Major, intermediate, minor stress

    Sv, Sh, SH: Total earth stresses, or Sv, Shmin, SHMAX, or sv, shmin, sHMAX

    sr, sq: Radial, tangential, borehole stresses

    sr, sq, sv, shmin, sHMAX, etc: Effective stresses

    r, ri: Radial direction, borehole diameter

    po, p(r): Initial pressure, p in radial direction

    MW, pw: Mudweight, pressure in borehole

    E, n: Youngs modulus, Poissons ratio

    f, r, g: Porosity, density, unit weight

    k: Permeability

    These are the most common symbols we use

  • Terminology and Symbols Problems

    Often, the terminology and symbols used are confusing and irritating

    This complexity arises because: The area of stresses and rock mechanics is

    somewhat complex by nature

    The terminology came from a discipline other than classical petroleum engineering

    There is still some inconsistency in symbology, such as Sh, Sh, Shmin, sh, all for shmin

    We will try to be consistent

    Please spend the time to understand

    Physical principles are the most important

  • Other Conundrums How do we express stresses?

    As absolute stresses? As stress gradients? As equivalent density of the overburden? As equivalent mud weights?

    e.g. PF = 18 ppg means 18 pounds per US Gallon is the fracture pressure at some (unspecified) depth (fracture gradient = (s3/z).

    e.g. shmin gradient is 21 kPa/m (or 21 MPa/km)

    e.g. The minimum stress is 2.16 density units

    e.g. shmin is 66 MPa (at z = 3.14 km depth)

    All of these are the same! (or could be)

    Which method is used usually depends who you are talking to! (Drillers like MW)

  • The Basic Symbols, 2-D Borehole

    Far-field stresses are natural earth stresses and pressures, genera-ted by gravity, tectonics

    Borehole stresses are generated by creation of an opening in a natural stress field

    Far-field stresses: scale: 100s of metres

    Borehole stresses scale: 20-30 ri (i.e. local- to small-scale)

    Far-field stress

    r q

    sr

    sq

    ri

    pw

    shmin

    sHMAX

    po

    Borehole stress

  • Important to Remember

    sq is the tangential stress, also called the hoop stress, you will see it repeatedly referred to in these terms

    sq lies parallel (tangential) to the wall trace The magnitude of sq is affected by:

    In situ stresses MW and cake efficiency Temperature and rock behavior

    It is the most critical aspect of the stress condition around a borehole High sq values lead to rock failure Lower sq values usually imply stability

  • Borehole Stability Analysis Concept

    First, we need stresses around the borehole In situ stresses are vital

    p, T, chemistry affect these stresses

    Mud cake efficiency

    In some cases, rock properties are also needed

    Then, we must compare the maximum shear stress with the rock strength We need to know the rock strength

    We need to know if the rock has been weakened by poor mud chemistry and behavior

    If matrix stress exceeds strength, we say the rock has yielded (or failed)

  • Plotting Stresses Around a Borehole

    Usually, we plot sq, sr values along one or the other of the principal stress directions

    Vertical

    borehole

    sr

    sq

    radius

    s

    pw = 0

    smin

    smax

    Far-field stresses

    Vertical borehole

    smax smin

  • Stresses Around a Borehole One Dimensional Case:

    A borehole induces a stress concentration

    Two- and three-dimensional cases are more complicated (discussion deferred)

    Stress lost must be redistributed to the borehole flanks (i.e.: s concentration)

    F (F/A =

    stress) F F

    Initial stress

    High sq near

    the borehole,

    but low sr!

    (F/A)

    (2F/A) F

    F = force, A = Area, F/A = stress

  • Stress Redistribution

    Around the borehole, a stress arch is generated to redistribute earth stresses

    elastic rocks have rigidity (stiffness)

    lost s

    elastic rocks resistribute the lost stress

    Everyone carries an equal

    load (theoretical socialism)

    In reality, some carry more

    load than others (higher sq near the borehole wall)

    Far away (~5D): ~no effect

    These guys may yield if they are overstressed

    D

  • Stresses Arch Around Borehole

    The pore pressure in the hole is less than the total stresses

    Thus, the excess stress must be carried by rock near the hole

    If the stresses now exceed strength, the borehole wall can yield

    However, yield is not collapse! A borehole with yielded rock can still be stable

    shmin

    circular

    opening,

    pw s H

    MA

    X

  • Arching of Stresses

    arches lintels

    load

    stress arching

  • Typical Borehole Instability Issues

    Pack-offs

    Excessive tripping and reaming time

    Excessive mud losses (fracturing losses)

    Stuck pipe and stuck or wedged BHAs

    Loss of equipment and costly fishing trips

    Sidetracks, often several in the same hole

    Cannot get casing to bottom

    Poor logging conditions, cleaning trips

    Poor cementing conditions, large washouts

    These are all related in some way to rock failure and sloughing

  • Yield of Rock Around a Borehole

    Borehole pressure

    = pw = MW z

    sHMAX

    shmin

    Axial borehole fractures develop

    during drilling when MW is higher

    than sq (surges, yield). (This is

    related to ballooning as well.)

    Swelling or other geochemical filtrate

    effects (strength deterioration,

    cohesion loss) lead to rock yield

    High shear stresses cause shear

    yield, destroying cohesion

    (cementation), weakening the rock

    Low sq

    High sq

    Shear yield

    Tensile yield

  • Shear Stresses

    Shear stress is the cause of shear failure

    The maximum shear stress at a point is half the difference of s1 and s3

    max = (s1 - s3)/2, or (sq - sr)/2 in the figure

    Vertical

    borehole

    sr

    sq

    radius

    s

    pw = 0

    Vertical borehole

    smax smin

  • Assumptions:

    The simplest stress calculation approach is the Linear Elastic rock behavior model

    This behavior model is very instructive

    It leads to (relatively) simple equations

    r

    i2

    2

    i2

    2

    i4

    4

    i2

    2

    i4

    4

    ri2

    2

    i4

    4

    i

    = ( + )

    2(1-

    r

    r) +

    ( - )

    2(1-

    4 r

    r+

    3r

    r) 2

    = ( + )

    2(1 +

    r

    r) -

    ( - )

    2(1 +

    3r

    r) 2

    = -( - )

    2(1 +

    2 r

    r-

    3r

    r) 2

    in all cases, r r , is taken CCW from reference

    ss s s s

    q

    ss s s s

    q

    s s

    q

    q

    q

    q

    max min max min

    max min max min

    max min

    cos

    cos

    sin

    .

    r

    q

    sr

    sq

    ri

    Symbols used

    smin

    smax Far-field stress

    pw = 0 Known as the Kirsch Equations

  • Comments

    Note that the equations are written in terms of effective stresses (sq, sr, smin), with no pore pressure in the hole

    Far-field effective stresses are the earth stresses, and they have fixed directions

    sq, sr can be calculated for any specific point (r, q) around the borehole, for r ri

    Later, one may introduce more complexity: T, p(r), non-elastic behavior, and so on

    These require software for calculations; various commercial programs are available

  • Calculations with In Situ Stresses

    For a vertical borehole, the least critical condition is when shmin = sHMAX = sh sq]max in this case = 2 sh if pw = po However, we can still get rock yield!

    However, in most cases, especially in tectonic regions and near faults The stresses are not the same!

    This means that the shear stresses are larger around the borehole after it is drilled

    This means that rock yield is more likely!

    Borehole stability issues are more severe

    Lost circulation more critical

  • What is a Linear Elastic Model?

    The simplest rock behavior model we use Strains are reversible, no yield (failure) occurs

    Linear relationship between stress & strain

    Rock properties are the same in all directions

    a

    r = 3

    a = 1

    a axial strain

    str

    ess ( 1

    3

    )

    E = Ds/De =

    Youngs modulus

    Stress-strain plot

  • From The Elastic Model

    Even in an isotropic stress field (e.g. shmin sHMAX for a vertical hole), shear stress concentration exists around the hole This can lead to rock yield. How to counteract?

    We can partly counteract with mud weight E.g.: if pw = shmin = sHMAX = sh (i.e.: MW = sh/z)

    If the filter cake is perfect (no Dp near hole)

    In practice, this is not done: if MW = sh/z, we are at fracture pressure & drilling is slower!

    Higher MW reduces the magnitude of the shear stress, which reduces the risk of rock yield, but increases LC risk, slows drlg

  • From The Elastic Model

    Fracture breakdown pressure is calculated to be Pbreakdown = 3hmin - HMAX + po In practice, this is not used for design