Wellbore stability: collapse pressure, breakouts and the mud weight

A shale that stood up in every vertical offset can fail in a deviated well drilled with the same mud. The rock has not changed; the stresses around the hole have. This article works through a 50° well in a Lower Cretaceous shale above a sandstone reservoir: the earth model from logs, the collapse pressure by hand and by engine, how it changes with inclination and azimuth, and the mud weight that keeps the hole in gauge.

Why holes collapse

Before the well, the rock at depth carries three stresses: the vertical stress from the weight of the rock above, S_v, and two horizontal stresses, the largest σ_H and the smallest σ_h. Drilling a hole removes the rock that carried part of that load, and the load flows round the hole. At the wall the stress around the circumference, the hoop stress, rises to several times the far-field stress on two opposite sides.

The mud pressure pushes back on the wall. If it is too low, the hoop stress exceeds the rock's strength and the wall fails in shear on those two sides. The failed rock falls in as angular cavings and leaves two breakouts, elongations of the hole aligned with σ_h. Narrow breakouts are often harmless. Wide ones join up, the hole enlarges all round, cuttings beds build in the washouts, and the string packs off. That is the lower limit of the mud weight, the collapse pressure, and in strong, normally pressured shale it often sits well above the pore pressure.

The upper limit is where the mud opens the rock. A tensile fracture starts when the hoop stress on the other two sides is pulled into tension (breakdown), and an existing fracture keeps taking mud once the pressure exceeds σ_h (loss). The safe window lies between the higher of pore pressure and collapse, and the lower of breakdown and loss. The pore-pressure and fracture-gradient side of that window is built in pore pressure, fracture gradient and the mud-weight window; this article adds the collapse side.

The method

The calculation has three steps: an earth model of stresses and strength from logs, the stresses at the wall for the well's direction, and a failure criterion solved for the mud pressure.

ν, E

static Poisson's ratio and Young's modulus, from the sonic and density logs

α, P_p

Biot's coefficient (1.0 here) and pore pressure

ε_h, ε_H

tectonic strains in the directions of σ_h and σ_H, calibrated to a leak-off test

P_w

wellbore (mud) pressure

σ′₁, σ′₃

largest and smallest effective stress at the wall; at the wall σ′₃ = P_w − P_p

UCS, φ

unconfined compressive strength and internal friction angle

The vertical-hole form is the one to check by hand. For a deviated hole the far-field stresses are first rotated into the hole's own frame, using its inclination, its azimuth and the azimuth of σ_H, and the full Kirsch solution then gives the hoop, axial and shear stresses at every point round the wall. The collapse pressure is the lowest P_w at which no point fails.

The criterion matters. Mohr–Coulomb ignores the intermediate principal stress and is the conservative choice. Mogi–Coulomb and the modified Lade criterion credit the intermediate stress with some strength and give lower collapse pressures, which often match field experience better in strong rock. Choose one, calibrate it against what offset wells actually did, and use it consistently.

The example well

The example is a deviated oil producer set in conditions typical of onshore Kuwait. Below Neogene sands, Eocene limestone and anhydrite, and a thick Upper Cretaceous carbonate section, it drills Aptian–Albian limestones, then 220 m of Lower Cretaceous shale over the target, a Lower Cretaceous sandstone. Pore pressure is hydrostatic for a strong brine, 1.07 SG, and 1.10 SG in the reservoir from offset tests. The regional maximum horizontal stress runs north-east.

The earth model takes Eaton's pore pressure from the shale sonic, the overburden from the density log, elastic properties from the sonic, and strength from published correlations: Horsrud's for shale UCS and Lal's for its friction angle. The tectonic strains were scaled, in a 4 : 1 ratio towards σ_H, until the model's σ_h at the 9⅝″ shoe matched the leak-off: 1.81 SG with ε_h = 0.0002 and ε_H = 0.0008.

Collapse by hand at 2,301 m TVD

Take one depth in the middle of the shale, and first imagine the hole vertical.

1. Strength. The shale reads 89.0 µs/ft, so V_p = 304,800 / 89.0 = 3,424 m/s. Horsrud's 0.77 V_p^2.93 (km/s) gives UCS = 28.4 MPa, 4,113 psi. Lal's sin φ = (V_p − 1)/(V_p + 1) gives φ = 33.2°, so q = 3.421.
2. Stresses. One SG of mud at 2,301 m TVD is 22.58 MPa. The earth model gives S_v 54.38 MPa (2.41 SG), σ_H 43.74 MPa (1.94 SG), σ_h 37.82 MPa (1.68 SG) and P_p 24.64 MPa (1.09 SG): a normal-faulting regime.
3. Peak hoop stress. 3 × 43.74 − 37.82 = 93.39 MPa, less the mud pressure.
4. Collapse. Set 93.39 − P_w − 24.64 = 28.36 + 3.421 (P_w − 24.64). Then P_w = (93.39 − 28.36 + 2.421 × 24.64) / 4.421 = 28.20 MPa, or 1.249 SG.
5. Check the assumption. At that pressure the effective hoop stress is 40.55 MPa and the axial stress 32.35 MPa, so the hoop stress is the largest, as the closed form assumes.

DrillIQ's engine gives 1.247 SG for the vertical hole at the same depth. The 0.002 SG difference is the engine's resolution: it checks the wall every 10°, and here the hoop-stress peak falls between two of those points. The hand check makes the main point already. The collapse pressure, 1.25 SG, is 0.16 SG above the pore pressure, so in this shale the pore pressure does not set the lower limit at all.

The window along the well

Run along the 50° well, the collapse pressure through the shale is 1.34–1.41 SG, a median of 1.37, against 1.22 for a vertical hole in the same rock. Below the shale, in the sandstone, it falls under the pore pressure and stops mattering. The loss limit, σ_h, runs 1.62–1.69 SG in the shale; breakdown is above 2.7 SG and never governs.

With a 0.03 SG margin under collapse and 0.035 SG under the loss limit, the shale needs at least 1.44 SG and allows at most 1.59 SG. The planned 1.18 SG, the weight that worked in the vertical offsets, is 0.26 SG short. The offsets were not luckier; they were vertical.

Inclination and azimuth

At 2,301 m TVD, collapse rises from 1.25 SG vertical to 1.39 SG at the plan's 50° heading 315°, and to between 1.51 and 1.57 SG horizontal. The reason is the regime. Here the vertical stress is the largest. A vertical hole sees only the two horizontal stresses, which are close; an inclined hole brings S_v into the plane of its cross-section, and the hoop stress grows with the difference between the stresses in that plane.

Direction matters less than inclination, but it is not free. At 50° a hole heading along σ_H, 045°, needs 1.47 SG; heading along σ_h, the plan's 315°, needs 1.39 SG. The plan's azimuth was set by the reservoir, and it happens to be the most stable one; a well heading north-east to the same target would need 0.08 SG more. When the target allows a choice, the polar plot of collapse against inclination and azimuth belongs in the planning meeting, not after it.

How much breakout to accept

Collapse is defined as the first point of shear failure, but a hole can live with some breakouts. The engine also gives the width of each breakout at a given mud weight. At the planned 1.18 SG the 50° hole would have two breakouts each 150° wide, of a possible 180°, by Mohr–Coulomb: in practice the whole wall. A vertical hole at 1.18 SG gets breakouts 60° wide, consistent with what the offsets reported: some cavings, and a hole that stayed open.

If the team accepts breakouts up to 60° wide, Mohr–Coulomb asks for 1.35 SG instead of 1.40 SG at this depth. Mogi–Coulomb asks for less again: along the whole shale its collapse peaks at 1.33 SG, and the modified Lade criterion at 1.29 SG, against 1.41 SG for Mohr–Coulomb. The 0.12 SG between the criteria is larger than either safety margin, which is why the criterion is a calibration, not a preference. Here the vertical offsets give one: their 1.18 SG produced cavings but no collapse, and any criterion that predicts a collapsed vertical hole at that weight is too pessimistic for this shale.

Choosing the mud weight

The conservative answer, Mohr–Coulomb with full margins, is 1.44 SG for the shale. That leaves 0.14 SG below the loss limit for the circulating density and surge, enough for an 8½″ hole if the flow rate is held and pipe is run with care; the check is the subject of hydraulics and ECD.

The reservoir changes the picture. With 1.44 SG mud, the sandstone at 2,400 m TVD sees (1.44 − 1.10) × 0.0981 × 2,400 = 80 bar of overbalance: enough to stick pipe against it and damage it. With 1.18 SG it would see 19 bar. So the plan changes to two mud weights: drill the shale at 1.44 SG, set the 7″ liner at its base, and drill the reservoir in 6″ hole with the lighter mud. The alternative, accepting 60° breakouts at about 1.35 SG and one string fewer, needs good hole cleaning and inhibitive mud, and a team that watches the shakers for cavings, because a time-dependent shale gets weaker the longer it is open.

A checklist for the rig team

• Check whether the offset wells that set the mud weight were vertical; deviated wells need their own collapse calculation.
• Calibrate the horizontal stresses to the leak-off at the shoe above the shale.
• Check one depth by hand before trusting the model along the well.
• Compare collapse from at least two criteria, and calibrate the choice against offset experience.
• Look at collapse against inclination and azimuth before the azimuth is fixed.
• Agree an acceptable breakout width, and the mud weight it implies, before spud.
• Check the overbalance on the reservoir below the shale, and set casing between them if it is too high.
• While drilling, watch cavings shape and volume, torque and drag, and pack-offs; angular cavings mean breakouts.

How DrillIQ handles it

DrillIQ's Pore Pressure & Geomechanics module builds a mechanical earth model from the well's sonic, density and gamma-ray logs: elastic properties, rock strength by lithology, and the three stresses with tectonic strains. Its wellbore-stability engine rotates the stresses into the well's own frame along the survey, solves for the collapse pressure with Mohr–Coulomb, Mogi–Coulomb or the modified Lade criterion, adds breakdown and loss limits, and gives the breakout width at any mud weight. Click a depth and it draws the polar plot of collapse by inclination and azimuth. Collapse feeds the mud-weight window, the casing seats and the mud programme by section, and while drilling it is checked against the ECD at the bit. The numbers above come from that engine and the hand check shown.

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References

1. Kirsch, G. Die Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre. Zeitschrift des Vereines deutscher Ingenieure 42, 1898.
2. Fjær, E., Holt, R.M., Horsrud, P., Raaen, A.M. and Risnes, R. Petroleum Related Rock Mechanics, 2nd ed. Elsevier, 2008.
3. Zoback, M.D. Reservoir Geomechanics. Cambridge University Press, 2007.
4. Horsrud, P. Estimating Mechanical Properties of Shale From Empirical Correlations. SPE Drilling & Completion, SPE 56017, 2001.
5. Al-Ajmi, A.M. and Zimmerman, R.W. Stability analysis of vertical boreholes using the Mogi–Coulomb failure criterion. International Journal of Rock Mechanics and Mining Sciences 43, 2006.
6. Ewy, R.T. Wellbore-Stability Predictions by Use of a Modified Lade Criterion. SPE Drilling & Completion, SPE 56862, 1999.
7. Castagna, J.P., Batzle, M.L. and Eastwood, R.L. Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks. Geophysics 50, 1985.

About this example. The well in this article is a representative scenario set in typical onshore Kuwait conditions and worked through with DrillIQ's engines. It is not a client's well, and its figures are not field results.