Module C1_BoreholeStresses I

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Module C -1:Stresses Around a Borehole - I

Argentina SPE 2005 Course on

Earth Stresses and Drilling Rock Mechanics

Maurice B. DusseaultUniversity of Waterloo and Geomec a.s



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: Young’s modulus, Poisson’s 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 usedare confusing and irritating

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

somewhat complex by natureThe 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? Asequivalent 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 arenatural earth stressesand pressures, genera-ted by gravity,tectonics…

Borehole stresses aregenerated by creationof an opening in anatural stress field

Far-field stresses:scale: 100’s of metres

Borehole stressesscale: 20-30 ri (i.e.

local- to small-scale)

Far-field stress

r q

s’r

s’q

r i

pw

shmin

sHMAX

po

Borehole stress



Important to Remember…

sq

is the tangential stress, also called thehoop stress, you will see it repeatedlyreferred to in these terms

sq lies parallel (tangential) to the wall trace

The magnitude of sq is affected by:In situ stressesMW and cake efficiencyTemperature and rock behavior

It is the most critical aspect of the stresscondition around a borehole… High sq values lead to rock failureLower sq values usually imply stability



Borehole Stability Analysis Concept

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

Δp, ΔT, 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 bypoor mud chemistry and behavior

If matrix stress exceeds strength, we say

the rock has yielded (or “failed”)



Plotting Stresses Around a Borehole

Usually, we plots

q,s

r values along one orthe 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 concentrationTwo- 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) FF

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” isgenerated 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 s’q

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 thanthe total stresses

Thus, the excessstress must be carried

by rock near the hole If the stresses now

exceed strength, theborehole wall can yield

However, “yield” is not

“collapse”! A boreholewith yielded rock canstill be stable…

shmin

circular

opening,

pw s H M A X



Arching of Stresses

archeslintels

load

stress arching



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

tmax = (s’1 - s’3)/2, or (s’q - s’r)/2 in the figure

Vertical

borehole

sr

sq

radius

s

pw = 0

Vertical borehole

smax

smin



Assumptions:

The simplest stress calculation approach isthe 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

r i2

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

ts s

q

q

q

q

max min max min

max min max min

max min

cos

cos

sin

.

r

q

sr

sq

r i

Symbols used

smin

smax

Far-field stress

pw = 0 Known as the “Kirsch” Equations



Comments

Note that the equations are written interms of effective stresses (sq, sr,s’min…), 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 criticalcondition is when s’hmin = s’HMAX = s’h s’q]max in this case = 2· s’h if pw = po

However, we can still get rock yield!

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

This means that the shear stresses are larger

around the borehole after it is drilledThis 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

σ ‛a

σ ‛r = σ ‛3

σ’a = σ ‛1

εa – axial strain σ ’ –

s t r e s

s ( σ ‛ 1 –

σ ‛ 3 )

E = Ds/De =Young’s modulus

Stress-strain plot



Lessons from the Elastic Model - I

Even in an isotropic stress field (e.g. shmin

sHMAX for a vertical hole in the GoM), shearstress concentration exists around the holeThis can lead to rock yield. How to counteract?

We can partly counteract with mud weightE.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 theshear stress, which reduces the risk of rock

yield, but increases LC risk, slows drlg…



Lessons from the Elastic Model - II

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

Fracture propagation is Ppropagation = shmin,

also taken to be PF (fracture pressure) forplanning of MW programsThis is often taken to be MW]max

MW is usually maintained to be less than shmin

In practice, it is often possible to use somemethods to “strengthen” the borehole

This allows drilling somewhat “overbalanced”,when pw > σ hmin, (this must be done carefully!)



Here, we plot the tangential stress, s’q

Higher stress difference is serious! Itgives rise to higher s’q values. Rupture??

Borehole Stresses if shmin sHMAX

Sing06.021

pw

2·σhmin

σ HMAX

σ hmin

= 1.0) (

σhmin

σHMAX

= 1.4) (

1.6·σ hmin

3.2·σ hmin

σ HMAX

σ hmin

σHMAX

Calculated from Kirsch equations,

along principal stress directions

2σhmin

σhmin

Far-field stresses, shmin, sHMAX, are: shmin – po, sHMAX – po

wellbore pressure pw assumed to be equal to po

pw



It gets worse in tectonic cases!

When shmin - sHMAX is large, the borehole wallin the sHMAX direction is in tension! Inducedfractures can be generated during pw surges

High sHMAX - shmin Cases (Tectonic)

Sing06.022

σ hmin pw

σ hmin

σ HMAX

sq ~ 5σ hmin

σ

hmin sq ~ 8σ hmin

= 2.0) ( σ HMAX

σ hmin

= 3.0) ( σ HMAX

σ hmin

σ HMAX

*Note: here, borehole pressure, pw, is assumed = po

pw



θ r w

0

+90°

-90°

Plot of the Tangential Stresses

σ HMAX

σ HMAX

Refer to paper by Grandi for details

Here, σ θ stresses at thewall (ri) are plotted as afunction of θ

Note the symmetry

σ θ(r i)



Borehole Wall Stresses (@r = ri)

Now, introduce effective stresses: e.g.symbols s for total, s for effective

Maximum stress at the borehole wall:σ q]max = 3·σ HMAX - σ hmin – po (total stresses)

sq]max = 3·σ’HMAX - σ’hmin (effective stresses)

Minimum stress at the borehole wall:

σ q]min = 3·σ hmin - σ HMAX - po (total stresses)

s’q]min = 3·σ ’hmin - σ ’HMAX (effective stresses) For a general 3-D solution for inclined

wellbores: use a software solution (big

equations!)



Preliminary Comments…

Creation of a borehole: high tangentialstresses (sq), low radial stresses (sr)

The larger sHMAX - shmin, the higher sq is(in the direction of shmin), the lower sq is

(in the direction of sHMAX) Radial effective stress (sr) is low near the

borehole wall, zero right at the wall

pw = 0

sr

sq

radius

s



More Preliminary Comments…

If both stresses are equal (sh) and MW =

po: at borehole wall: sq = 2sh, and sr = 0

If sHMAX – shmin is large, sq is increased,and sr doesn’t change too much

This greatly increases the shear stresses These shear stresses are responsible for

failure of the rock, breakouts, sloughing…

How do we control this?High effective mud weights reduce this

Mud cooling shrinks rock, reduces stresses

Avoid shale swelling, promote shale shrinkage



Mud Weight Effect (equal s case)

pw = 0.3s

sr

sq

pw = 0.8s

sr

sq

Here, we assume for simplicity that wehave “perfect” mud cake, and that the

pore pressure in the rock is zero

radius

s

radius

s

pw = 0

sr

sq

Assume sHMAX = shmin = s

radius

s



Let’s Include Pore Pressures…

pw = 0.6s

sr

sq Assume sHMAX = shmin = s

radius

s

Pore pressure - po

Positive support force = pw – po is applied in the case of a perfect mud cake:

this is a strong stabilizing force because it increases confining stress, this

will be discussed later, when we introduce rock strength

Mud

pressure -

pw

Much of what we do in mud chemistry and MW management is to try and

keep a positive support force right at the wall. This acts like a liner in a

tunnel, keeping the rock from deteriorating and reducing the shear stresses.

If it is lost by poor cake…, deterioration can be expected, especially in shale.

perfect cake



Filter Cake Efficiency

The better the filter cake, the better thesupport pressure on the borehole wallSupport pressure = pw - pi

If there is poor filter cake, supportpressure on a shale may be almost zero!

This support pressure is a true effectivestress that is acting in a radial outwarddirection, holding rock in place!

In WBM in shales, the support pressuretends to decay with time!Soon after increase in MW – good stabilityAfter some time (days, weeks), sloughing can

start again because support p decays



Horizontal vs. Vertical Wellbore?

σ v = 0.9 psi/ft, σ h = 0.6 psi/ft, p = 0.4 psi/ft

In non-tectonic systems (shmin ~

sHMAX) vertical holes are subjected

to lower shear stresses; they are

generally more stable thanhorizontal holes

sq = 1.3 psi/ft, sides

Horizontal Hole

Vertical Hole

sq = 0.1 psi/ft,

top, bottom

sv = 0.5 psi/ft

sh = 0.2 psi/ft

sh = 0.2 psi/ft

Stress State0.5

0.2

0.2

0.2

sq = 0.4 psi/ft



Tectonic Stress Conditions

Vertical effective stress = 0.5 psi/ft Min. horizontal effective stress = 0.3 psi/ft Max. horizontal effective stress = 1.0 psi/ft

Vertical well

0.1

2.7

0.1

2.7

This orientation is the

best one for this case,

showing the importanceof knowing the in situ

stresses

1.2

0.4 0.4

1.2

sv = 0.5 psi/ft

shmin = 0.3 psi/ft

sHMAX = 1.0 psi/ft

2.5

0.5

Horizontal well aligned with

minimum stress, shmin

0.5

2.5 Horizontal well aligned withminimum stress, sHMAX



TABLE 1

Maximum Stress Minimum Stress(σθ]min)

No.Hole

Configuration Gradient

( psi/ft)

Magnitude

( psi)

Gradient

( psi/ft)

Magnitude

( psi)

1 Vertical 2.7 13,500 -0.1 -500

2Parallel tominimum

horizontal stress2.5 12,500 0.5 2,500

3Parallel tomaximum

horizontal stress1.2 6,000 0.45 2,000

Stress at borehole wall (σ’θ) in a tectonically active area(Compressive stresses are +ve; Tensile stresses are -ve)

Depth of investigation is 5,000 ft

(σθ]MAX)



3-Dimensional Borehole Stresses

Effective stresses:

s1 = s1 - po s2 = s2 - po s3 = s3 - po

z

x

y

F Y

s1

s2

s3

po

F, Yare dip and dip direction

(wrt x) of the borehole axisx, y, z are coordinates oriented

parallel to s1, s2, s3

s1, s2, s3 are the principal totalstress magnitudes

po is the pore pressure

Borehole radial,

axial & tangentialstresses, sr , sa, sq

Almost always, principle stresses can be

taken as and to the earth’s surface



What About the Axial Stress??

Axial stress, sa

, acts parallel to thehole wall, to sr, sq

Usually ignored in borehole stability

However, if sa is very large compared

to sr & sq, it can also cause yield More sophisticated analysis req’d

Almost always, using the hole angle

and azimuth, we do the following:Determine maximum and minimum

stresses in the plane of the hole

Carry out a 2-D stability analysis

sr , sa, sq



The Best Well Orientation

In a relaxed (non-tectonic) basin, sv

> shmin

~sHMAX, vertical wells are the most stable

In a tectonic basin, an estimate of thestresses is essential; for example:

If sHMAX > sv > shmin, we still have to know thespecific values to decide the best trajectory

If sHMAX = 0.7, sv = 0.5, shmin = 0.4 psi/ft, ahorizontal well parallel to sHMAX is the best

If sHMAX = 0.7, sv = 0.6, shmin = 0.4 psi/ft, a wellparallel to shmin is likely the best

Careful Rock Mechanics analysis is best

+0ther factors: fissility, fractures…



Stresses and Drilling

sv >> sHMAX > shmin

shmin

sHMAX

sv

sHMAX >> sv > shmin

sHMAX ~ sv

>>shmin

sv

shmin

sHMAX

sv

shmin

sHMAX

To increase hole stability, thebest orientation is that whichminimizes the principal stressdifference normal to the axis

60-90° cone

Drill within a 60°cone(±30°) from the mostfavored direction

Favored holeorientation



“Showing” the Best Trajectory

This is a polar plot of

“ease of drilling” Related to magnitude of

shear stress on wall

This is based in situ

stress knowledge In this example, a

horizontal well, W to E,seems to be “easiest”

A horizontal well N to Sis the worst (all otherfactors being equal)

shmin

sHMAX

sv



Typical Troublesome Hole (GoM)

8.00

9.00

10.00

11.00

12.00

13.00

14.00

15.00

16.00

3000’ 4000’ 5000’ 6000’ 7000’ 8000’ 9000’

PP

Sh

Sv

Planned Casing

Actual Casing

Drill MW

MW to Keep Hole Open

Increase MW to

get out of hole

Pore pressureMWmin Ladeshmin

sv

Planned Csg Actual Csg

Drill MW

MW to keep

hole open

4960 Stuck Pipe: no

rotation, no circulation

Hole tight with pumps off

Losing 300 bbl.hr (ballooning?)

17½” x 20 ” 17½” x 20 ” 16 ” Liner 16 ” Liner 13 3/8 ” 13 3/8 ” 14¾” x 17½” 14¾” x 17½”

Pack-off

S t r e s s , p r e s s u r e i n p p g

Depth in feet



The Plan … The Reality

Hole planned from offset wells (sv

, shmin

,log correlations to strength data, po…)

Jagged line is a prediction of MW tosustain reasonable borehole stability

Brown line: chosen MW program fromstability calculation (using “Lade” criterion)

Red line was the actual mud weight neededto cope with a series of problems

The casings were set higher than expectedand an extra string was eventually needed



How do We Sustain Stability?

MW control (up or down)

Mud properties control (reduce ECD)

Trip and connection policy (speed, surge…)

Inhibitive WBM: minimize chemical effects

OBM: eliminate chemical effects

Air or foam UB drilling (shallow, strong rx)

Use fn-gr LCM, gilsonite in fractured shale

Cool the drilling mud to reduce sq,reducing the chances of rock failure

When all else fails, sidetrack, set casing



Well Design and Cost Optimization

High risks are mainly

related to low MW, rapiddrilling, increased wellblowout risks… Low costif successful.

Low risks are mainlyassociated with slowdrilling and high MW, butdrillings time is long…Generally costly…

In between, there is alevel of acceptable riskswith a lower cost factor

Well Design Costs

A c t u a l ( L i k e l y ) W

e l l C o s t s

High Risk Low Risk



Borehole Cost Optimization

Affected by drilling speed, casing stringcosts, cleaning problems, cost of drillingmud, risks, trip problems…

Optimizing this in “real time” is the

challenging task of the Drilling Engineer

Mud Weight

S t r e s s t o S t r e n

g t h r a t i o1.0

0.8

0.6

F l u i d

i n f l u x

S h e a r f a i l u r e

s l o u g h i n g

Safe Lost

circulation

“ B a l l o

o n i n g ”

The shape of the

cost curve changes,

depending on the

stresses and where

we are in the hole!



Borehole Stability and Hydraulics

Borehole management is not only stresses,rock strength, MW and mud properties!

It is also dependent on hydraulics:Pumping strategy and cleaning capabilities

Gel strength, viscosity, mud densityBHA design, ECD, even tripping policy



How do We Predict RM Stability?

We need to know the rock stresses in situ

Vertical, horizontal usually, sv, shmin

Pore pressures (especially overpressure cases)

We need to know the rock strength

Lab testing of coreCorrelations to geophysical log data bases

Testing of drill chips (penetrometers, sonic…)

Then, we make predictions of stability MW

This is an indicator only!Careful monitoring on the active well

Improvement of our “calibrations”, ECD…



Lessons Learned

Stress concentrations arise naturally whena hole is drilled

The tangential stress sq is criticalAffected by stress, tectonics, rock behavior…

Borehole cake and mud support are critical We can calculate stresses, but rock

parameters are (E, n, Y, Co, T o…) needed

We can reduce the effects of high sqMW, lower T, better cake, OBM…

We can use log data and correlations topredict the MW for stability

Module C1_BoreholeStresses I

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