Module C-2: Stresses Around a Borehole - II Argentina SPE 2005 Course on Earth Stresses and Drilling Rock Mechanics Maurice B. Dusseault University of.

Module C-2: Module C-2: Stresses Around a Borehole - IIStresses Around a Borehole - II

Argentina SPE 2005 Course on Earth Stresses and Drilling Rock Mechanics

Maurice B. DusseaultUniversity of Waterloo and Geomec a.s.

Stress TrajectoriesStress Trajectories

circularopening,

pw

stress trajectories arelines which representthe “flow” of stresses

through the solid body

HMAX

v

v

HMAX

shear stresses cannot pass through a fluid,

however, compressive stresses can (i.e. a fluid pressure in a borehole)

on the boundary of the opening, is zero and

r = pw (pressure)

Example of a horizontal well

Stress TrajectoriesStress Trajectories

These are plots of how the principal stresses “flow” around a hole or reservoir

If the trajectories are closely spaced, the compressive stresses are large

If they are sparse, stresses are lower They provide a good visualization of how

the stresses are distributed For more detail and analysis, we plot them

along a radial line from the borehole (see previous Module for examples)

Typical Borehole Instability Typical Borehole Instability IssuesIssues 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 BoreholeYield of Rock Around a Borehole

Borehole pressure= pw = MW z

HMAX

hmin

Axial borehole fractures develop during drilling when MW is higher than (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

High

Shear yieldTensile yield

Borehole Stability and Rock Borehole Stability and Rock FailureFailure

The rock can yield somewhat around a borehole but drilling can continue. Why?

The yield process relieves high stresses, so the yield zone stops propagating

If we can still trip and drill ahead, the borehole fulfils its function: it has not “failed”

But, the rock around the borehole has yielded and lost its cohesive strength

This distinction is very important:Rock yield does not mean borehole lossMud support pressure can sustain the hole, even

if the hole is surrounded by yielded (fragmented) rock

Cat-Scan of Hole YieldCat-Scan of Hole Yield

This is a tomographic reconstruction of a hollow cylinder test

The dark lines are higher-porosity shear bands around the hole

The central part of the hole is filled with spalled rubble

This is evidence of typical borehole yield in a symmetrical stress field

Intact portion

Sheared region

Equal far-field stresses - h

Are Breakouts Serious?Are Breakouts Serious?

MAX

min

Breakouts are evidence that there is a stress difference in the plane normal to the hole. They also indicate that the rock in the breakout area has surpassed its strength. However, they are not a sign of impending full collapse unless they grow in an uncontrolled manner.

Rock mechanics analysis can predict the onset of breakouts and yield, but less successful in predicting complete opening collapse. Collapse is a complex structural response affected by many factors including stresses, strength, fabric of the rock, drilling and tripping practices, and so on…

Geochemical EffectsGeochemical Effects Swelling or shrinkage can occur because of

geochemical effects in shalesGeochemical changes lead to swelling or

shrinkage!This ΔV changes the tangential stresses (Δσ’θ)

Swelling always leads to problems:Rock yield from high hoop stressesDeterioration of cohesion from chemistry changes

and small volume changesSqueezing of borehole, mudrings, poor mud…

Shrinkage can also reduce strength because any ΔV helps degrade grain-to-grain cohesion

Modest shrinkage or no shrinkage are best

What is a Washout?What is a Washout? When shale yields (high ), it weakens

and tends to fragment If filter cake is poor, r is low (no support

for the shale fragments) sloughing Washouts develop all around the borehole,

roughly symmetric (made worse by fissility)

gage

gage = ri

hmin

HMAX

Stresses “flow” around borehole

breakouts

Washouts, no strong orientation

yielded shale

Borehole Wall Features & FailureBorehole Wall Features & Failure Axial fractures (high

MW) are not rock failure and deterioration

Breakouts are evidence of rock shear failure

Large washouts as well, leading to problems…

Natural fractures are not usually a problem, except if they are high-angle and can slip

This case is more common than thought

0 90 180 270 360

washout

breakouts

axial fractures

Natural fracture traces

Sandstone Mudcake, Sandstone Mudcake, p Supportp Support

borehole

p(r), steady-state, no mud-cake

mudcake

limited solidsinvasion depth

p across mudcake

p(r) with mudcake

pressure

po

pw

distance (r)

sandstone

Excellent supportMW

HMAX

hm

in

Filter Cake in SandstonesFilter Cake in Sandstones

Filter cake is made of clays, polymers, etc.

Very low permeability Sand k is much larger

than cake k… Allowing the pressure

difference to give a direct support stress

Therefore: sands almost never slough, but:

Differential sticking is an issue in sandstones

pw

The positive support pressure in a sandstone is usually close to pw – po because permeability is high

po

Damaged rock held in place by +ve

mud support

Filter cake

Shale Mudcake, Shale Mudcake, p Supportp Support

borehole

p(r), steady-state, @ t = ∞ now, no more mud-cake effect!

mudcake?

p(r) initially, @ t = 0. This is an excellent support condition

pressure

po

pw

distance (r)

shale

MW

shale

Because no mudcake can form on a shale, slow pressure penetration takes place, and the support pressure effect is slowly destroyed

This is a time-dependent process

HMAX

hm

in

Filter Cake in ShalesFilter Cake in Shales

Intact shale k is much lower than cake k…

A true filter cake cannot form on the borehole wall

Initially, support is good But, with t, it decays… Rock yields =

microfissures pw penetrates more fully

into the damaged region p support is lost leading

to sloughing, breakouts… A time-dependent

process!

pw

The support pressure in shale is a function of time

po

Damaged rock is not held in place by mud pressure and high k

Support lost with time

Cake Efficiency ManagementCake Efficiency Management

Using OBM in intact shale gives excellent efficiency, good p support, reducing the shear stresses in the borehole wall

In fractured shale, OBM often ineffective:Filtrate penetrates the small fracturesNo p across wall can be sustained (no cake)These shales easily slough on trips,

connections When using WBM

Gilsonite, dispersed glycol, fn.-gr. solids can help plug small induced microfissures

This helps maintain good p across the wallBut! Geochemical effects can take place.

Damage Effect on Damage Effect on p Supportp Support

pressure

po

pw

distance (r)

pressure gradient drops with time

low permeability shale, no mudcake

A(intact borehole)

B(damaged borehole)

no p for wall support

shale

transientpressurecurves

mud pressure

formation pressure

p(r) curves with time

High leads to rock damage. This permits pressure penetration, loss of radial mud support. It is time-dependent, and reduces stability.

borehole

Thermal DestabilizationThermal Destabilization

shear stress

normalstress

r

r

T + T

po

+

To

mudsupport

Shear strength criterion for the rock around the borehole

initialconditions

i,j

heating leads to borehole destabilization

When the stress state semicircle “touches” the strength criterion, it is assumed that this is the onset of rock deterioration (not necessarily borehole collapse…)

Y

Thermal Alterations of Thermal Alterations of

Kirsch elastic solutionthermoelastic heating (convection)thermoelastic cooling (convection)

(r) for cooling

radius

max

Tw

Except for heating, mostprocesses reduce the ]max

value at the borehole wall

These curves show the hoop stress calculated using an assumption of heating and an assumption of cooling. Clearly, heating a borehole increases the magnitude of the stress, and leads to hole problems. Cooling the borehole is generally always beneficial to stability.

tangential stress -

(r) for heating

To

Initialh

borehole

What Happens with Hot Mud?What Happens with Hot Mud?

The rock in the borehole wall is heated Thermal expansion takes place This “attracts” stress to the expanding

zone around the well The peak stress rises right at the

borehole wall, and yield and sloughing is likely

For cooling, the rock shrinks; this allows the stress concentration to be displaced away from the borehole, helping stability

Cooling occurs at and above the bit Heating occurs farther uphole

Heating and Cooling in the HoleHeating and Cooling in the Hole

depth

T

casing

geothermaltemperature

bit

cooling

heating

mudtemperature

shoe

+T

-T

muddownpipe

mud upannulus

coolingin tanks

BHA

drillpipe

openhole

Heating occurs uphole, cooling downhole. The heating effect can be large, exceptionally 30-35°C in long open-hole sections in areas with high T gradients.

Heating is most serious at the last shoe. The shale expands, and this increases , often promoting failure and sloughing.

At the bit, cooling, shrinkage, both of which enhance stability.

Commercial software exists to draw these curves

Expansion and Borehole Expansion and Borehole StressesStresses

“lost”

“elastic” rocks resistribute the “lost” stress

D

“elastic” rocks redistribute thermal stresses as well

expanding “rocks”

High near the hole

This is the standard elastic case of borehole stress redistribution

This is the case of rock heating when the mud is hotter than the formation

DSee Module C

Thermal Stresses Around Thermal Stresses Around BoreholesBoreholes Heat transfer: conductive or convective

Conductive: low permeability rock – shale, saltConvective: high permeability rocks –

sandstone The stress distributions are different for

these cases, and conduction is much slower

Heating increases σθ, and shear failure is more likely (= sloughing)

Cooling reduces hoop stresses, and short axial fracturing is more likely

In general, the effects of axial fracturing on stability are not substantial

Effect of Rock Yield on Effect of Rock Yield on

Kirsch elastic solutionYield solution AYield solution B

(r)

radius

max

Except for heating, mostprocesses reduce the ]max

value at the borehole wall

These curves show calculated assuming that rock yield occurs once a limit stress has been exceeded. One curve is for a very simple model of yield, the other for a more complex case. In all yield cases, the stress concentration is reduced, and the peak pushed away from the borehole.

Initial h

tangential stress -

Rock Yield and Borehole Rock Yield and Borehole StressesStresses When rock yields, it loses some of its load

carrying capacity, thus “shedding” stress This stress is pushed out into the rock

mass, and may cause adjacent rock to fail This reduces the magnitude of the hoop

stresses around the hole Therefore, yield is evidence of the rock

trying to find a stable equilibrium If the damaged (weakened) rock can be

held in place, the hole becomes stable If not, sloughing occurs & yield propagates

Drilling-Induced FracturesDrilling-Induced Fractures

r

po

radius

stress

reduction in ]min

damaged zone

borehole,pw

limited depth fractures

, intact

, damaged

shift of peak stress site

fractures are propagatedduring drilling and trips

when effective mudpressures exceed

σhmin

σHMAX

Induced Axial FracturesInduced Axial Fractures

Near the borehole, yield causes a reduction in the hoop stress,

The MW may exceed near the wall When this happens, a short hydraulic

fracture opens up, but it terminates against the zone of higher

This can be exacerbated by high surges, high ECD, etc.

If this is significant, it leads to “ballooning” or “breathing” of the well

Borehole Shear DisplacementBorehole Shear Displacement

Vincent Maury (1987, Elf-Aquitaine) High angle faults, fractures can slip and

cause pipe pinchingNear-slip earth stresses conditionHigh MW causes pw charging

Reduction in n leads to slipBHA gets stuck on trip out

Probably more common than we realize: we never check for it, its effect is subtle on logs because drilling destroys “evidence”

Raising MW makes it worse! Lower MW…

npw

Lessons LearnedLessons Learned

The hoop stress around the borehole can be counteracted by good MW support

In sands, no problem, in shales, problems Stresses around the borehole can be

affected by a number of factors:Geochemical effects that lead to shrinkage,

swelling, loss of cohesion…Thermal effects of heating or coolingRock damage effects, breakouts

Axial fractures are related to stresses Even slip of old fault planes or joints

Additional Material Relevant to Additional Material Relevant to Stresses Around a BoreholeStresses Around a Borehole

Review of Stresses and Boreholes Review of Stresses and Boreholes

In situ stresses:σv (Vertical/overburden stress) (or Sv)

σh (Two horizontal stresses),, hmin and HMAX

(sometimes you will see Sh, Shmin, SHMAX

(h - po) = K·(v - po) In other words… h = K·v K ƒ [/(1- )] if no tectonics…But, is not constant; it varies with (depth)

Fracture gradients (shale vs. sand) Eaton’s curve Ballooning/fracturing (clean sand

fractures first in most stress regimes!)

MORE REVIEWMORE REVIEW

Depleted sandsFracture gradient is lower than expectedA “hesitation squeeze” can increase PFLCM injection, drilling with LCM + solids

Stress concentration around a wellboreGravity dominated stress system - GoMTectonic system – high compression or

extension (Rocky Mtn. Foreland, North Sea Central Graben)

Borehole breakouts are evidence of large differences in stresses – is large

Breakouts vs. hole washouts: not the same These issues should be well understood

In RM, We Can Calculate In RM, We Can Calculate StrengthStrength Rock Strength (next Modules)

Failure in shear Failure in tension

Borehole stability calculations (example…)Minimum pressure for hole collapse:Pw=[(3.hmax-hmin)/2](1 - sin) + Pres·sin

- So.cos Co = 2·So·tan (45+ /2) (shear strength)

We want to calculate stability, and use logs, etc. to make assessments, predictions

Borehole Stability PhilosophyBorehole Stability Philosophy

Calculate stresses, compare to strengths Check for yield (rock failure) In many cases we must live with yield

Breakouts, sloughing, etc.Careful surveillance to manage it

If we avoid yielding the rock it is stronger If we reduce the hoop stress: less yield If we increase support p: less yield We do the best we can, but there is

much uncertainty.

E Q U A T I O N SE Q U A T I O N S

Effective () vs. Total stress (S or ) = (S - po) or ( - po) Pore press.

= po

Gravity dominated basin:Sv or v Overburden weight (known)

h = v·[/(1- )] (estimate)

[Sh - po] = [/(1- )]·[Sv - po]Here, is Poisson’s ratio, see next sectionRemember that this is just an estimate;

measurements are always preferred…

E Q U A T I O N S (Contd.)E Q U A T I O N S (Contd.)

Eaton & Pilkington’s Correlation to estimate stresses, developed for the GoM[Sh - po] = K[Sv - po]

K-> Stress Factor, empirically derivedSv-> Overburden total stress = v

Sh-> Minimum horizontal total stress = hmin

(Also called fracture gradient, PF)

SHMAX = HMAX ~ Shmin in “relaxed” basins

Different in tectonically stressed cases

E Q U A T I O N S (Contd.)E Q U A T I O N S (Contd.)

The General Stress System v = (Sv - po) or (v - po)

HMAX = (SHMAX - po) or (HMAX - po)

hmin = (Shmin - po) or (hmin - po)

Tangential stress at the borehole wall: Vertical well case (best direction for drlg

in a relaxed basin or offshore continental margin case where HMAX ~ hmin < v)Parallel to vertical wellbore (assuming pw = po)

]max = 3HMAX - hmin

]min = 3hmin - HMAX

E Q U A T I O N S (Contd.)E Q U A T I O N S (Contd.)

Stress at the borehole wall (Contd.): Horizontal well cases

Well parallel to maximum horizontal direction: ]max = 3v - hmin

]min = 3hmin - v

Well parallel to minimum horizontal direction:

]max = 3HMAX - v

]min = 3v - HMAX

E Q U A T I O N S (Contd.)E Q U A T I O N S (Contd.)

Borehole Stability (Contd.):Pressure for vertical borehole fracture

breakdown:

pw = (3hmin) - HMAX - po +To

To - Rock tensile strength, psi

We have to try to estimate and measure these rock parameters, but going from lab to field in this case seems not possible…