BOREHOLE STRESSES

James A. Craig Omega 2011

Stresses Around Borehole

Borehole Failure Criteria› Vertical Hole› Deviated Hole› Poroelastic Formation

STRESSES AROUND BOREHOLE

In drilling, stressed solid material is removed and replaced with a fluid under pressure (drilling fluid).

The well fluid pressure does not match exactly the stress state which the removed solid exerted.

There will be stress alteration around the well. Large alteration may lead to failure.

Stresses around borehole are:› σr: Radial stress

› σθ: Tangential stress

› σz: Axial stress

The largest deviations from the initial stress state are found at the borehole wall.

In a downhole situation:› σri → Pw = well pressure

› Ri → R = borehole radius

› Ri → ∞; Note: Ri = reservoir extent (radius)

› σro → σh = horizontal stress

› σz is a constant, independent of r.

› σz = σv for all r > R.

2

2r h h w

RP

r

2

2h h w

RP

r

BOREHOLE FAILURE CRITERIA

Borehole failure criteria are the boundary conditions for which borehole failure occurs.

This happens when the stress deviation in the formation close to the borehole exceeds the failure criterion of the rock.

Consequences of failure are normally borehole deformations of some kind.

BOREHOLE FAILURE CRITERION

Vertical Hole

In a linear elastic formation, the largest stress differences occur at the wall.

In isotropic horizontal stress (σH = σh) state, the principal stresses at the borehole wall are:

2r w

h w

z v

P

P

Shear Failure Criterion› Failure depends on the relative magnitude

between the principal stresses.› Where σθ > σz > σr :

› Failure criterion:› Failure occurs when:

› Where σr > σz > σθ :

› Failure criterion:› Failure occurs when:

2tano rC

2

12

tan 1w h oP C

2tanr oC

22

12 tan

tan 1w h oP C

Tensile Failure Criterion› σθ at the borehole wall becomes negative when Pw

is sufficiently large.› Where σθ < To :

› Failure occurs when: › To = tensile strength of the material

2w h oP T

Deviated Hole

Linear elastic formation with anisotropic horizontal stress (σH ≠ σh).

Shear Failure Criterion› Failure occurs when:

Tensile Failure Criterion› Failure occurs when:

2

13

tan 1w H h oP C

3w h H oP T

Poroelastic Formation

Borehole is vertical and the horizontal stress is isotropic.

Effective stress concept is introduced.

Shear Failure Criterion

22

12 tan 1

tan 1w h f oP P C

2

1

tanw v f o fP P C P

2

12

tanw h v f o fP P C P

2 22

12 tan tan 1

tan 1w h f oP P C

2 2tan tan 1w v f oP P C

2 22 tan tan 1w h v f oP P C

Condition Failure occurs if:

:z r

:z r

:z r

:r z

:r z

:r z

Tensile Failure Criterion Tensile failure occurs if Pw is sufficiently large

to make σθ negative. Failure occurs if:

2w h f oP P T