Breakout and Breakdown Pressures

Summary

A vertical well fails in two ways. If the mud pressure is too low, the hoop stress at the wall exceeds the rock's compressive strength and the wall breaks out; the pressure at which this starts is the Shear-failure mud pressure. If the mud pressure is too high, the hoop stress becomes tensile and a fracture opens; the pressure at which this starts is the Breakdown pressure. The two together bound the usable mud pressure.

Inputs and outputs

Equations

Use the wall stresses of the Kirsch solution and the failure criteria of the previous pages. All pressures are in psi; UCS in MPa is converted with \(1\ \text{MPa} = 145.04\) psi.

Shear failure (breakout). The wall is most highly stressed at the azimuth of the minimum horizontal stress, where the effective hoop stress is \(\gmSigThMax - \gmPp\) and the effective radial stress is \(\gmPw - \gmPp\). Mohr-Coulomb failure occurs when the larger exceeds the unconfined strength plus \(\gmQf\) times the smaller:

Solving for the wellbore pressure gives the lowest pressure that keeps the wall intact:

Tensile failure (breakdown). The wall is least stressed at the azimuth of the maximum horizontal stress. A fracture initiates when the effective hoop stress there falls to minus the tensile strength \(\gmT\):

For equal horizontal stresses this reduces to the Hubbert-Willis form \(2\gmSh - \gmPp + \gmT\). If the mud penetrates the rock, the pore pressure at the wall rises with the mud pressure. With the poroelastic factor \(\eta = \alpha(1 - 2\nu)/(2(1 - \nu))\) the breakdown pressure becomes \(\left(3\,\gmSh - \gmSHm + \gmT - 2\eta\,\gmPp\right)/\left(2\left(1 - \eta\right)\right)\), which is lower. In ppg, divide by \(0.052\) times the true vertical depth \(\zdepth\):

Single-value calculator

Behavior

The plot holds Shmin at 6000 psi and pore pressure at 4700 psi, with a UCS of 30 MPa, a friction angle of 30° (q = 3), a tensile strength of 400 psi and a depth of 10000 ft, and sweeps SHmax. At the default SHmax of 6700 psi the collapse pressure is 4787 psi (9.21 ppg), and the breakdown pressure 7000 psi (13.46 ppg). Raising SHmax pushes the two bounds together from both sides: collapse rises with 3 SHmax, and breakdown falls with SHmax. At 7000 psi the bounds are 9.64 and 12.88 ppg; at 8600 psi they are 11.95 and 9.81 ppg, so the window has closed, since the collapse pressure is above the breakdown pressure. Strength moves only the lower bound. At the default stresses, UCS of 10, 30 and 60 MPa give collapse pressures of 10.60, 9.21 and 7.11 ppg: raising UCS from 10 to 30 MPa lowers collapse by about 1.4 ppg at this depth. Check on the isotropic limit: with both horizontal stresses at 6000 psi, the collapse pressure is 4262 psi and the breakdown pressure is 7700 psi, which equal (2 x 6000 - 4351 + 2 x 4700)/4 (UCS 30 MPa is 4351 psi) and 2 x 6000 - 4700 + 400. The poroelastic form, with a Biot coefficient of 0.8 and Poisson's ratio of 0.25 (η = 0.267), lowers the default breakdown pressure from 7000 to 6268 psi.

Parameter guidance

Strength. UCS, friction angle and tensile strength come from UCS Correlations and Friction Angle, Biot Coefficient and Cohesion, calibrated to core. The result for the lower bound is sensitive to UCS and the friction angle: both enter directly. Run the calculation with a low and a high case.

Tensile strength. It is small and uncertain, from zero for rock with natural fractures or bedding planes to about a tenth of UCS for intact rock. A value of zero is the conservative choice for an upper bound that the mud must not exceed, but it puts the breakdown pressure at its lowest. Do not take it as a measured quantity unless core tests exist.

Stresses. From Horizontal Stress Methods and Vertical Stress. SHmax is the weakest input and has the largest effect on both bounds. Use a range.

Calibration with breakouts. Where caliper or image logs show breakouts in a section drilled at a known mud weight, the model must predict them. If it does not, strength is too high, SHmax too low, or the mud weight used was not what was recorded. Breakout width is a further constraint on SHmax, which this page does not cover.

Worked example

Collapse and breakdown pressures at 10000 ft for SHmax 6700 psi, Shmin 6000 psi, pore pressure 4700 psi, UCS 30 MPa, a friction angle of 30° and a tensile strength of 400 psi, with the isotropic check and the poroelastic breakdown:

import math
SH, Sh, Pp, tvd = 6700.0, 6000.0, 4700.0, 10000.0
ucs_mpa, ifa, T = 30.0, 30.0, 400.0
ucs = ucs_mpa * 145.038
q = (1 + math.sin(math.radians(ifa))) / (1 - math.sin(math.radians(ifa)))
def collapse(SH, Sh):
    return (3 * SH - Sh - ucs + (q - 1) * Pp) / (1 + q)
def breakdown(SH, Sh):
    return 3 * Sh - SH - Pp + T
ppg = lambda p: p / (0.052 * tvd)
print(f"q = {q:.3f}, UCS = {ucs:.0f} psi")
print(f"collapse  = {collapse(SH, Sh):.0f} psi = {ppg(collapse(SH, Sh)):.2f} ppg")
print(f"breakdown = {breakdown(SH, Sh):.0f} psi = {ppg(breakdown(SH, Sh)):.2f} ppg")
print(f"pore pressure = {ppg(Pp):.2f} ppg, Shmin = {ppg(Sh):.2f} ppg")
# check: at the collapse pressure the Mohr-Coulomb margin is zero
pw = collapse(SH, Sh)
margin = (3 * SH - Sh - pw - Pp) - (ucs + q * (pw - Pp))
print(f"MC margin at collapse pressure = {margin:.6f} psi")
# isotropic limit and poroelastic breakdown
print(f"isotropic 6000/6000: breakdown = {breakdown(6000.0, 6000.0):.0f} psi = 2 x 6000 - Pp + T = {2 * 6000 - Pp + T:.0f}")
nu, alpha = 0.25, 0.8
eta = alpha * (1 - 2 * nu) / (2 * (1 - nu))
pb = (3 * Sh - SH + T - 2 * eta * Pp) / (2 * (1 - eta))
print(f"poroelastic breakdown: eta = {eta:.3f}, Pb = {pb:.0f} psi = {ppg(pb):.2f} ppg")

Output

q = 3.000, UCS = 4351 psi
collapse  = 4787 psi = 9.21 ppg
breakdown = 7000 psi = 13.46 ppg
pore pressure = 9.04 ppg, Shmin = 11.54 ppg
MC margin at collapse pressure = -0.000000 psi
isotropic 6000/6000: breakdown = 7700 psi = 2 x 6000 - Pp + T = 7700
poroelastic breakdown: eta = 0.267, Pb = 6268 psi = 12.05 ppg

Assumptions and limitations

• A vertical well, with the Kirsch wall stresses, and the principal stresses (vertical and the two horizontal) as inputs. Deviated wells need the general transformed solution.
• The most highly stressed azimuth is the one where the hoop stress is largest, and the hoop and radial stresses are the extreme principal stresses at the wall. If the axial stress exceeds the hoop stress, the criterion has to be applied with the axial stress as the largest, which happens in some strike-slip and reverse states.
• Linear Mohr-Coulomb strength with the intermediate principal stress ignored. This tends to give a conservative (too high) collapse pressure compared with criteria that use all three stresses, and with the observation that a wellbore can tolerate some breakout.
• Initiation of failure, not extent. The collapse pressure is where the wall first fails; a limited breakout is often tolerable and a mud weight below it does not necessarily mean the hole is lost. The breakdown pressure is where a fracture starts, not where it propagates.
• Tensile strength is a constant. Natural fractures and bedding planes can reduce it to zero.
• Pore pressure at the wall is the far-field value (an impermeable wall) in the basic formulas.
• No time dependence: shale swelling, chemical effects and thermal changes can all lower the strength with time.

QC checks

• The Mohr-Coulomb margin is zero at the collapse pressure. Check by evaluating the criterion at the pressure from the formula (done in the worked example).
• Isotropic limit: with equal horizontal stresses the breakdown pressure is 2 Sh - Pp + T.
• Collapse rises with SHmax and falls with strength. Breakdown falls with SHmax and rises with Shmin and tensile strength. A model that behaves otherwise is coded wrongly.
• Predicted breakouts are consistent with the caliper, image logs and drilling events (tight hole, cavings, pack-offs) in offset wells. Breakouts at a mud weight above the predicted collapse mean the model is too optimistic.
• Breakdown is consistent with leak-off, extended leak-off and lost-circulation events. Breakdown pressure is generally above the leak-off pressure, which is controlled by closure of existing fractures.
• The window width is not negative at the mud weights that were actually used. If it is, the stresses or strengths are wrong, or the wells were drilled with stability problems that should show in the logs.

Going Deeper

The collapse and breakdown formulas are the two simplest results of wellbore stability theory. Their appeal is that they need only five numbers, but each number is uncertain, and the structure of the answer is more reliable than its value: the lower bound rises with the stress anisotropy and falls with strength, the upper bound falls with anisotropy. Practical analyses make several refinements. Mohr-Coulomb ignores the intermediate stress, and criteria such as Mogi-Coulomb or Drucker-Prager that include it give lower collapse pressures in many cases. Where the wall is permeable and the mud filtrate invades, the poroelastic stresses change both bounds. Thermal stresses and chemical interaction between the shale and the mud lower the effective strength with time. And allowing a limited breakout, with the wall failing over a stated angle, lowers the minimum mud weight needed. The choice of the criterion and of the allowed breakout is an engineering decision as much as a rock mechanics one.

References

1. Zoback, M.D., 2007. Reservoir Geomechanics. Cambridge University Press.
2. Fjær, E., Holt, R.M., Horsrud, P., Raaen, A.M. and Risnes, R., 2008. Petroleum Related Rock Mechanics, 2nd edition. Elsevier.
3. Hubbert, M.K. and Willis, D.G., 1957. Mechanics of hydraulic fracturing. Transactions of the AIME, 210, 153–168.
4. Haimson, B. and Fairhurst, C., 1967. Initiation and extension of hydraulic fractures in rocks. Society of Petroleum Engineers Journal, 7(3), 310–318.
5. Moos, D., Peska, P., Zoback, M.D. et al., 2003. Comprehensive wellbore stability analysis utilizing quantitative risk assessment. Journal of Petroleum Science and Engineering, 38(3–4), 97–109.

Python reference implementation

Related methods

• Vertical Stress
• Horizontal Stress Methods
• Near-Wellbore Stress State
• Mud Weight Window
• Pore Pressure
• UCS Correlations
• Friction Angle, Biot Coefficient and Cohesion