Geomechanics

Purpose

Geomechanics turns the logs into the mechanical properties of the rock: how stiff it is, how strong it is, how it fails and how it responds to pore pressure. These are the inputs for two decisions. In drilling they set how much mud pressure a well needs to stay open, which is the subject of the next topic, Wellbore Stability. In completions they help to choose where to fracture and where the barriers are. This step covers the rock properties; the stress state and the failure analysis built on them are on the Wellbore Stability pages.

Position in the workflow

Upstream. Dynamic moduli need compressional and shear slowness and a good density log, so the Stage 1 repairs, the depth matching and the washout flags all matter. Shear slowness is often missing, in which case it is modelled: see Shear Log Modeling. Mineral volumes from mineral inversion feed the brittleness and Biot calculations, and porosity feeds the strength correlations.

Downstream. The outputs go to the 1D mechanical earth model:

the static Poisson's ratio and the Biot coefficient go into the horizontal stress calculations,
UCS, friction angle and cohesion go into the breakout (shear failure) and mud weight window calculations, and
the brittleness index goes to completion design.

Error propagation. Strength errors act directly on the lower bound of the mud weight window. Modulus errors act on the horizontal stress, and therefore on the upper bound, through Poisson's ratio. A 10 percent error in UCS is not 10 percent in mud weight, but it is often 0.1 to 0.3 ppg, which is larger than the usual safety margin.

Key concepts

Dynamic and static. Logs measure dynamic moduli with small, fast waves. Drilling and fracturing deform the rock slowly and by much more, and the static moduli that describe that are lower. Every property here is either measured on core in the static condition or is an empirical estimate calibrated to it. See Static vs Dynamic Moduli.

Moduli. Two independent elastic constants describe an isotropic rock. Logs give them through Vp and Vs and density; Young's modulus and Poisson's ratio are the usual pair, and Poisson's ratio is the one that drives horizontal stress.

Strength. UCS is the strength with no confinement. With the friction angle it defines the Mohr-Coulomb envelope, which gives strength under confinement and the cohesion. See UCS Correlations and Friction Angle, Biot Coefficient and Cohesion.

Effective stress. Pore pressure carries part of the load. The Biot coefficient says how much, and it enters every stress calculation.

Brittleness. A ranking of how readily the rock fractures. There are many definitions, none of them a physical property, and they should be used to compare intervals, not as a number with a meaning of its own. See Brittleness Indices.

Empirical relations are local. Almost every strength and static modulus relation here was fitted to a specific lithology and region. The pages give the form and the range it was derived for, never as a general law.

Method selection guide

Page	Inputs	Use when	Strengths	Weaknesses
Dynamic Elastic Moduli	Vp and Vs slowness, density	Always, as the first step. A measured or modelled shear log is required	Exact for isotropic elastic rock, no parameters	Dynamic, not static; isotropic assumption; needs a good shear log
Brittleness Indices	Static E and Poisson's ratio, or mineral volumes	Screening frac targets and barriers in unconventional plays	Cheap, continuous, easy to explain	Many contested definitions; relative only; bounds are a choice
Static vs Dynamic Moduli	Dynamic Young's modulus; calibration to core	Before any strength or stress calculation that wants static values	Brings log moduli closer to the loading the rock sees	Relations differ by a factor of two; core calibration is needed
UCS Correlations	Slowness, porosity or static modulus	Whenever strength is needed and core is sparse	Gives a continuous strength curve	Lithology- and region-specific; scatter of 20 to 40 percent
Friction Angle, Biot Coefficient and Cohesion	UCS, Vp or porosity, frame and grain moduli	When the Mohr-Coulomb envelope and effective stress are needed	Closes the strength model; exact link between UCS, cohesion and angle	Friction angle and Biot values are the weakest inputs

Decision guidance

Compute dynamic moduli first, then decide how to make them static. Do not feed dynamic Young's modulus into a stress model unconverted.
For UCS, choose the relation for your lithology and then scale it to core. If you have no core, run the downstream calculation with at least two relations and show the spread.
Use the modulus-based brittleness index when you have static moduli and the mineral index when you have a reliable mineral inversion; compare them.
Where strength tests are available, use measured friction angle and cohesion in preference to anything computed from logs.

Shared parameter picking

Static conversion. The relation chosen on the static-dynamic page feeds the brittleness, strength (modulus-based) and stress calculations. Choose it once for a formation and use it everywhere.

Lithology. Every strength and friction relation has a lithology it was derived for. Define the lithology flags (sand, shale, carbonate) once, from the mineral inversion or the clay volume, and use them to switch relations.

Poisson's ratio. One value (static, or dynamic if no conversion is made) is used for the stress calculation and the brittleness index. The same choice must hold in both places.

Core calibration. Strength, static modulus and friction angle are all scaled or fitted to the same core tests. Keep a table of the tests, with depth, lithology, confining stress and test type, and refer to it from every page.

Units. GPa for moduli, MPa for strength, degrees for angles, g/cm³ for density and µs/ft or µs/m for slowness. Stress calculations on the following pages are done in psi and ppg, and the conversion is 1 MPa = 145.04 psi.

Recommended default approach

Absent other information, a careful generalist would:

Build the dynamic moduli from the best compressional and shear slowness and the repaired density, and mask washouts.
Convert Young's modulus to static with a relation that suits the rock, calibrated to core where possible. Where there is no core, show results at two or three plausible conversions. Take static Poisson's ratio equal to the dynamic value unless core says otherwise.
Pick a UCS relation for the lithology and scale it to core strength tests. Without core, bracket the answer with two relations.
Take the friction angle from triaxial tests, or from a lithology-appropriate log relation, and compute cohesion from UCS and the angle.
Set the Biot coefficient from measurements or a stated assumption, and use the same value in every stress calculation.
If brittleness is needed, compute the modulus-based and mineral-based indices, and compare them with any observed fracture behaviour.
Record every constant, its source, and the lithology and range it applies to.

Combining methods

Where two relations for the same property are available, such as two UCS correlations, do not average them without thinking. First scale each to core. If they still disagree, the gap is the uncertainty, and the stability calculation should be run with both and shown as a range. A lithology-switched curve, with one relation for sandstone and another for shale and a transition at a clay cutoff, is a legitimate combination, but the transition should be checked for a step in strength at the boundary. For brittleness, there is no principled way to combine definitions; display them side by side.

QC of results

A good result:

has moduli and strength that follow lithology and porosity, with no spikes at washouts,
has a static Young's modulus below the dynamic one, and a Poisson's ratio between 0.1 and 0.4,
compares with core strength and static modulus with no systematic bias,
has cohesion positive and below UCS/2, and a friction angle that is lower in shale than in sandstone, and
has a Biot coefficient between 0 and 1, higher in softer rock.

Signs of a bad result: a Vp/Vs ratio outside 1.4 to 2.5, a negative bulk modulus, a strength that rises with porosity, a sudden step at a lithology switch, or a downstream breakout prediction that contradicts the caliper and image log.

Common pitfalls

Using dynamic Young's modulus where a static one is needed, which overstates stiffness and, through Poisson's ratio effects, can shift stress.
Mixing slowness units between the compressional and the shear logs.
Applying a strength relation outside the lithology and the units it was derived for.
Treating an uncalibrated empirical curve as a measurement.
Reading the brittleness index as an absolute property, or comparing indices normalised to different bounds.
Using a saturated dynamic bulk modulus in place of the drained frame modulus for Biot's coefficient.
Combining a UCS from one source with a friction angle from another and accepting a cohesion that makes no sense.
Using log values in a washed-out or invaded interval without a flag.

Going Deeper

The central difficulty is that the quantities that matter for decisions, static moduli and strength under confinement, are measured on a few centimetres of core in a lab, while the logs that cover the whole well measure something different. Everything in this step is a bridge between the two, built from empirical relations that carry their origin with them. Three open areas deserve mention. Anisotropy is ignored by the isotropic formulas but is large in shales and changes both the moduli and the stress calculation. Rock strength in a real wellbore is often controlled by weak bedding planes and natural fractures that no intact-rock relation sees. And scale effects mean that lab strength can differ from the strength of the rock mass. The usual response is to calibrate and to keep the uncertainty visible, which is why the stability pages that follow work with ranges.