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

Stress Trajectories sv sHMAX sHMAX sv Example of a horizontal well stress trajectories are lines which represent the “flow” of stresses through the solid body circular opening, pw sHMAX shear stresses cannot pass through a fluid, however, compressive stresses can (i.e. a fluid pressure in a borehole) sHMAX on the boundary of the opening, t is zero and sr = pw (pressure) sv Example of a horizontal well

Stress 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 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 sHMAX 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 shmin Borehole pressure = pw = MW  z High sq Low sq Shear yield Tensile yield

Borehole Stability and Rock Failure 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 loss Mud support pressure can sustain the hole, even if the hole is surrounded by yielded (fragmented) rock

Cat-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 Equal far-field stresses - sh Intact portion Sheared region

Are Breakouts Serious? sMAX smin 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… sMAX smin

Geochemical Effects Swelling or shrinkage can occur because of geochemical effects in shales Geochemical changes lead to swelling or shrinkage! This ΔV changes the tangential stresses (Δσ’θ) Swelling always leads to problems: Rock yield from high hoop stresses Deterioration of cohesion from chemistry changes and small volume changes Squeezing 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? When shale yields (high sq), it weakens and tends to fragment If filter cake is poor, sr is low (no support for the shale fragments)  sloughing Washouts develop all around the borehole, roughly symmetric (made worse by fissility) gage = ri Washouts, no strong orientation Stresses “flow” around borehole gage shmin breakouts yielded shale sHMAX

Borehole Wall Features & Failure 90 180 270 360 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 axial fractures breakouts washout Natural fracture traces

Sandstone Mudcake, p Support pressure Excellent support pw MW p(r), steady-state, no mud-cake Dp across mudcake po borehole p(r) with mudcake distance (r) mudcake sandstone limited solids invasion depth

Filter Cake in Sandstones sHMAX 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 po Filter cake shmin pw Damaged rock held in place by +ve mud support The positive support pressure in a sandstone is usually close to pw – po because permeability is high

Shale Mudcake, p Support pressure pw MW p(r), steady-state, @ t = ∞ now, no more mud-cake effect! shale mudcake? This is a time-dependent process po p(r) initially, @ t = 0. This is an excellent support condition borehole distance (r) Because no mudcake can form on a shale, slow pressure penetration takes place, and the support pressure effect is slowly destroyed shale

Damaged rock is not held in place by mud pressure and high k Filter Cake in Shales sHMAX 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 Dp support is lost leading to sloughing, breakouts… A time-dependent process! po Support lost with time shmin pw Damaged rock is not held in place by mud pressure and high k The support pressure in shale is a function of time

Cake Efficiency Management Using OBM in intact shale gives excellent efficiency, good Dp support, reducing the shear stresses in the borehole wall In fractured shale, OBM often ineffective: Filtrate penetrates the small fractures No Dp 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 Dp across the wall But! Geochemical effects can take place.

Damage Effect on p Support pressure no Dp for wall support mud pressure pw B(damaged borehole) A(intact borehole) transient pressure curves p(r) curves with time po formation pressure pressure gradient drops with time borehole distance (r) shale low permeability shale, no mudcake High sq leads to rock damage. This permits pressure penetration, loss of radial mud support. It is time-dependent, and reduces stability.

Thermal Destabilization shear stress Shear strength criterion for the rock around the borehole initial conditions heating leads to borehole destabilization Y sr To po sq mud support i,j T + DT Dsq normal stress sq sr sq + Dsq When the stress state semicircle “touches” the strength criterion, it is assumed that this is the onset of rock deterioration (not necessarily borehole collapse…)

Thermal Alterations of  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 - sq Except for heating, most processes reduce the sq]max value at the borehole wall sq (r) for heating sq]max sq (r) for cooling Initial sh Kirsch elastic solution thermoelastic heating (convection) thermoelastic cooling (convection) To Tw radius borehole

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 Hole in tanks 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 sq, often promoting failure and sloughing. At the bit, cooling, shrinkage, both of which enhance stability. Commercial software exists to draw these curves mud up annulus casing heating geothermal temperature shoe open hole +T mud down pipe drill pipe mud temperature BHA -T cooling depth bit

Expansion and Borehole Stresses See Module C This is the standard elastic case of borehole stress redistribution “lost” s “elastic” rocks resistribute the “lost” stress D High sq near the hole This is the case of rock heating when the mud is hotter than the formation “elastic” rocks redistribute thermal stresses as well expanding “rocks”

Thermal Stresses Around Boreholes Heat transfer: conductive or convective Conductive: low permeability rock – shale, salt Convective: high permeability rocks – sandstone The stress distributions are different for these cases, and conduction is much slower Heating increases σθ, 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  These curves show sq 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. tangential stress - sq Except for heating, most processes reduce the sq]max value at the borehole wall sq (r) sq]max Initial sh Kirsch elastic solution Yield solution A Yield solution B radius

Rock Yield and Borehole Stresses 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 Fractures shift of peak stress site stress reduction in sq]min sq, damaged sq sq, intact sr damaged zone po fractures are propagated during drilling and trips when effective mud pressures exceed sq borehole, pw σHMAX radius limited depth fractures σhmin

Induced Axial Fractures Near the borehole, yield causes a reduction in the hoop stress, sq The MW may exceed sq near the wall When this happens, a short hydraulic fracture opens up, but it terminates against the zone of higher sq 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 Displacement Vincent Maury (1987, Elf-Aquitaine) High angle faults, fractures can slip and cause pipe pinching Near-slip earth stresses condition High MW causes pw charging Reduction in sn leads to slip BHA 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… sn pw

Lessons 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 cooling Rock damage effects, breakouts Axial fractures are related to stresses Even slip of old fault planes or joints

Additional Material Relevant to Stresses Around a Borehole

Review of Stresses and Boreholes In situ stresses: σv (Vertical/overburden stress) (or Sv) σh (Two horizontal stresses),, shmin and sHMAX (sometimes you will see Sh, Shmin, SHMAX (sh - po) = K·(sv - po) In other words… h = K·v K = ƒ [n/(1- n)] if no tectonics… But, n is not constant; it varies with f (depth) Fracture gradients (shale vs. sand) Eaton’s curve Ballooning/fracturing (clean sand fractures first in most stress regimes!)

MORE REVIEW Depleted sands Stress concentration around a wellbore Fracture gradient is lower than expected A “hesitation squeeze” can increase PF LCM injection, drilling with LCM + solids Stress concentration around a wellbore Gravity dominated stress system - GoM Tectonic system – high compression or extension (Rocky Mtn. Foreland, North Sea Central Graben) Borehole breakouts are evidence of large differences in stresses – Ds is large Breakouts vs. hole washouts: not the same These issues should be well understood

In RM, We Can Calculate Strength Rock Strength (next Modules) Failure in shear Failure in tension Borehole stability calculations (example…) Minimum pressure for hole collapse: Pw=[(3.shmax-shmin)/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 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 Dp: less yield We do the best we can, but there is much uncertainty.

E Q U A T I O N S Effective () vs. Total stress (S or s)  = (S - po) or (s - po) Pore press. = po Gravity dominated basin: Sv or v  Overburden weight (known) h = v·[n/(1- n)] (estimate) [Sh - po] = [n/(1- n)]·[Sv - po] Here, n is Poisson’s ratio, see next section Remember that this is just an estimate; measurements are always preferred…

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 derived Sv-> Overburden total stress = sv Sh-> Minimum horizontal total stress = shmin (Also called fracture gradient, PF) SHMAX = sHMAX ~ Shmin in “relaxed” basins Different in tectonically stressed cases

E Q U A T I O N S (Contd.) The General Stress System v = (Sv - po) or (sv - po) HMAX = (SHMAX - po) or (sHMAX - po) hmin = (Shmin - po) or (shmin - po) Tangential stress at the borehole wall: Vertical well case (best direction for drlg in a relaxed basin or offshore continental margin case where sHMAX ~ shmin < sv) Parallel to vertical wellbore (assuming pw = po) q]max = 3HMAX - hmin q]min = 3hmin - HMAX

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: q]max = 3v - hmin q]min = 3hmin - v Well parallel to minimum horizontal direction: q]max = 3HMAX - v q]min = 3v - HMAX

E Q U A T I O N S (Contd.) Borehole Stability (Contd.): Pressure for vertical borehole fracture breakdown: pw = (3shmin) - sHMAX - 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…