Wellbore Stability (1D Geomechanical Model)

Purpose

Wellbore stability asks how much pressure a well needs to stay open. The answer is a range, the mud weight window: low enough that the mud does not fracture the formation or lose fluid into it, and high enough that the wall does not collapse and the formation fluid does not flow in. The range comes from a one-dimensional geomechanical model, a set of curves along the well for the three principal stresses, pore pressure and rock strength. This step builds the stress state and the failure analysis; the rock properties it depends on are in Geomechanics.

Position in the workflow

Upstream. The model needs four sets of inputs. Pore pressure comes from Pore Pressure. Static Poisson's ratio and Young's modulus come from the dynamic moduli and the static conversion, which need a shear log, measured or modelled with Shear Log Modeling. UCS, friction angle and Biot coefficient come from the strength pages. The density log provides the overburden.

Downstream. The window is used to select mud weights and casing points, to explain drilling events, and, with the stress state, to design completions: the minimum horizontal stress contrast between layers is a primary control on fracture height.

Error propagation. Pore pressure errors act directly on the lower bound and, through effective stress, on every stress. A 1 ppg error in pore pressure at 10000 ft is 520 psi. Poisson's ratio errors act on Shmin: a change of 0.05 near 0.25 changes the factor ν/(1-ν) by about 0.09, so Shmin by about 0.09 times the effective vertical stress: roughly 450 psi, or 0.9 ppg at 10000 ft with an effective vertical stress of 5100 psi. Strength errors change the lower bound, and SHmax errors change both.

Key concepts

Three principal stresses. The vertical stress is the weight of the rock above. The minimum and maximum horizontal stresses are the smallest and largest stresses in the horizontal plane. Their ordering sets the regime: normal faulting when the vertical stress is the largest, strike-slip when it is the middle one, reverse when it is the smallest. See Vertical Stress and Horizontal Stress Methods.

Effective stress. Total stress minus the Biot coefficient times pore pressure. Rock deforms and fails according to effective stress.

Stress concentration. Drilling the hole concentrates stress at the wall. For a vertical well the hoop stress is 3 SHmax minus Shmin minus the mud pressure at one azimuth, and 3 Shmin minus SHmax minus the mud pressure at the other. See Near-Wellbore Stress State. The page covers the vertical well and states that deviated wells need the general transformation.

Two failure modes. Shear failure, in compression, produces breakouts and sets a lower bound on mud pressure. Tensile failure sets an upper bound. See Breakout and Breakdown Pressures.

Window. The range between the bounds, in ppg. See Mud Weight Window. The unit conversion is psi divided by 0.052 times true vertical depth in feet.

Calibration. The only way to trust the model is to compare it with what happened in nearby wells: leak-off tests for the minimum horizontal stress, breakouts and drilling events for strength and the maximum horizontal stress.

Method selection guide

Page	Inputs	Use when	Strengths	Weaknesses
Vertical Stress	Density log, extrapolated trend, water depth	Always, first	Best-constrained stress; direct from logs	Needs a shallow density assumption; biases from bad density accumulate
Horizontal Stress Methods	Sv, pore pressure, Poisson's ratio, Biot coefficient, tectonic strain, friction	Always. Pick the method by what can be calibrated	Several levels of complexity, from simple to calibrated	Large uncertainty; SHmax is only bounded; tectonic strain is a tuning parameter
Near-Wellbore Stress State	The three stresses, pore pressure, mud pressure	To understand where the wall fails and to build the failure formulas	Exact for the elastic vertical well	Vertical well only; no thermal or poroelastic terms
Breakout and Breakdown Pressures	Wall stresses, UCS, friction angle, tensile strength	To get the lower and upper pressure bounds	Closed-form, easy to check	Linear Mohr-Coulomb is conservative; tensile strength is poorly known
Mud Weight Window	All of the above	To plan mud weights and casing points	The result drilling uses; testable against events	Differences of large numbers; magnifies input errors

Decision guidance

For Shmin, use Eaton's uniaxial strain with a static Poisson's ratio as the baseline, and the poroelastic form where a Biot coefficient is known. Add tectonic strain only if leak-off or minifrac data exist to calibrate it.
Use Hubbert-Willis only as a rough bracket or a regional rule, not as the primary method in overpressured or consolidated rock.
For SHmax, use an upper frictional bound and a lower bound at Shmin, and narrow it with breakout or tensile fracture observations when they exist. Show the range.
For a deviated or horizontal well, do not apply the vertical-well formulas directly; use the full 3D wall stress.

Shared parameter picking

Pore pressure. One pore pressure curve, from Pore Pressure, in every stress and failure calculation.

Poisson's ratio and Biot coefficient. One static Poisson's ratio and one Biot coefficient, chosen on the Geomechanics pages, in the horizontal stress and wall stress calculations.

Strength. UCS, friction angle and tensile strength, one set, calibrated to core and breakout observations.

Overburden. One vertical stress curve, which must also be the one used in the pore pressure calculation.

Units. Stresses in psi, strengths converted from MPa with 145.04, and mud weights in ppg using 0.052 and true vertical depth. State the depth datum (rotary table or sea level) for offshore wells.

Friction coefficient. 0.6 for frictional limits unless data suggest otherwise.

Recommended default approach

Absent other information, a careful generalist would:

Build the vertical stress by integrating the repaired density log, with a documented extrapolation above the log and the water column offshore.
Take pore pressure from the pore pressure model and check it against measured pressures and kicks.
Estimate Shmin with the poroelastic uniaxial-strain relation, then calibrate it to leak-off or minifrac closure pressures with a tectonic strain term. If there is nothing to calibrate against, show Eaton and Hubbert-Willis as a bracket.
Estimate SHmax between Shmin and the frictional limit of the regime, and narrow it with breakouts and tensile fractures from image logs if available.
Compute the wall stresses and the collapse and breakdown pressures with UCS, friction angle and tensile strength calibrated to core.
Assemble the window, overlay the mud weights and events from offset wells, and adjust strength and SHmax until the model reproduces them.
Present low, mid and high cases, and flag where the window is narrower than the uncertainty.

Combining methods

The stress methods are not alternatives to be averaged; they differ in what they assume, and a calibrated one should win. The sensible combination is a bracket: the lowest credible Shmin (for example the poroelastic estimate) and the highest (for example the frictional limit or a leak-off-calibrated value) give a range for the upper bound of the window. Where several estimates of pore pressure or strength exist, carry them as scenarios through the whole calculation and compare the resulting windows rather than averaging the inputs. The window itself is a combination: the lower limit is the maximum of two bounds and the upper limit the minimum of two.

QC of results

A good model:

has Sv > Shmin > Pp in a normal regime, and SHmax between Shmin and a credible frictional limit,
satisfies the frictional limits in every interval, or explains why not,
matches leak-off and minifrac closure pressures in the offsets,
predicts breakouts and tight hole where they occurred and not where the hole stayed in gauge, and
has a window that agrees with the mud weights actually used and the events they produced.

Signs of a bad model: a window that is negative in intervals drilled without trouble, a predicted collapse that is far above the mud weights used, stress steps that follow log noise, and a stress state inconsistent with the geological regime.

Common pitfalls

Using dynamic Poisson's ratio or Young's modulus without a decision about conversion.
Treating the maximum horizontal stress as known. It is a range.
Using strength correlations without calibration to core and breakout observations.
Mixing psi, MPa and ppg, or applying 0.052 with measured instead of true vertical depth.
Using an overburden different from the one used in the pore pressure model.
Applying vertical-well results to a deviated or horizontal well.
Using the static mud weight and ignoring equivalent circulating density and surge pressure.
Presenting a single window line with no uncertainty.

Going Deeper

The one-dimensional model is a deliberate simplification: it assumes a laterally uniform earth with vertical and horizontal principal stresses and treats each depth independently. It works well in layered basins and fails near salt, faults and in tectonically complex areas, where a three-dimensional geomechanical model is needed. The methods here are also all elastic and short-term. Real rocks creep, shales interact with the mud over days, and depletion changes stresses over the life of a field. The strongest argument for the 1D model is that it is the only one that is cheap enough to build and calibrate for every well, and that it can be checked against drilling events, which makes it a rare part of the workflow whose results are routinely tested against what actually happened.