geomechanics · wellbore stability
Critical Mud Weight (Wellbore Breakout)
Pw_crit = [3SH − Sh − Pp(1−Nφ) − 2C0√Nφ] / (1+Nφ)
click formula to derive ↑
Inputs
psi
psi
psi
psi
°
ft
Description
Computes the minimum wellbore (mud) pressure required to avoid shear failure (breakout) at the wall of a vertical wellbore, combining Kirsch's (1898) elastic stress-concentration solution with the Mohr-Coulomb failure criterion. This is the LOWER bound of the safe mud-weight window — the companion upper bound, where mud weight becomes high enough to fracture the formation, comes from the Fracture Gradient (Eaton 1969), Formation Integrity/LOT EMW, or MAASP calcs.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Pw_crit | psi | Critical Mud Pressure |
| MW_crit | lb/gal | Critical Mud Weight (EMW) |
| SH | psi | Maximum horizontal stress — typically the upper bound from the SHmax (Stress Polygon) calc, or an independently known/measured value. |
| Sh | psi | Minimum horizontal stress — typically the Shmin output of the Fracture Gradient (Eaton 1969) calc. |
| Pp | psi | Pore pressure at the depth of interest. |
| C0 | psi | Intrinsic shear strength of the intact rock at the wellbore wall, from triaxial testing or log-derived rock-strength correlations. |
| φ | ° | Angle of internal friction of the rock at the wellbore wall. |
| TVD | ft | True vertical depth of the point of interest, used only to express the result as an equivalent mud weight. |
Assumptions
- Vertical wellbore, with the wellbore axis aligned with Sv (one of the three principal stress directions) — no stress-tensor rotation is needed
- Linear elastic rock behavior up to the point of failure (Kirsch's solution assumes elasticity)
- Mohr-Coulomb-valid intact rock at the wellbore wall, with cohesion and friction angle representative of that interval
Limitations
- Vertical-well case only — a deviated or horizontal wellbore requires resolving the full 3D stress tensor into the borehole's local coordinate system before applying Kirsch's solution (Peska & Zoback 1995), which is not included here
- Assumes purely elastic rock behavior up to failure — does not capture plastic yielding, time-dependent (creep) failure in shale, or chemical/osmotic effects from mud-shale interaction
- Predicts onset of breakout, not breakout progression or stability over time — does not address borehole enlargement growth or hole-cleaning consequences once breakout begins
- Does not include thermal stresses from mud/formation temperature differences, which can meaningfully shift the critical mud weight in HPHT wells
Use Cases
- → Defining the safe mud-weight window: Pair this lower (shear-failure) bound against the upper (fracture) bound from Fracture Gradient (Eaton 1969), LOT EMW, or MAASP to define the full safe mud-weight window for a casing section.
- → Pre-drill wellbore stability screening: Check whether a planned mud weight program stays above the breakout threshold before spudding a section, especially in weak or highly anisotropic-stress intervals.
- → Diagnosing observed breakout: If breakout is observed on image logs at a known mud weight, compare against this calc's prediction to back-check the assumed stress state or rock strength inputs.
Related Calculations
Region Notes
Permian Basin
Wolfcamp shale intervals with both significant stress anisotropy (SH notably greater than Sh) and moderate rock strength are common locations for breakout-driven hole problems in long laterals — checking this lower bound against planned mud weight is standard practice before committing to a casing/mud program.
Global
Breakout risk is highest in intervals combining high stress anisotropy (SH≫Sh) with low rock strength (low C0/φ) — weak shales are disproportionately represented in reported wellbore-stability failures.
References
Primary source
Need geoscience support? BauerCalc is just one of the tools we build. If you're looking for independent expertise in well planning, geosteering, reservoir characterization, or opportunity evaluation, visit BauerSubsurface.com.