Wellbore stress analysis

The magnitude of Sv is equivalent to integration of rock densities from the
surface to the depth of interest, z. In other words,
Sv = ∫
z
0
ρ(z)gdz ≈ ρ′gz
where ρ(z) is the density as a function of depth, g is gravitational
acceleration and ρ′ is the mean overburden density (Jaeger and Cook,
1971). In offshore areas, correction for water depth is done
Sv = ρwgzw + ∫
z
zw
ρ(z)gdz ≈ ρwgzw + ρ′g(z − zw)

Figure. Dependence of rock
strength on the angle of weak
bedding or foliation planes.
(a) Rock samples can be tested
with the orientation of weak
planes at different angles, β, to
the maximum principal stress,
σ1. (b) The strength can be
defined in terms of the intact
rock strength (when the weak
planes do not affect failure) and
the strength of the weak planes.
(c) Prediction of rock strength
(normalized by the cohesion of
bedding planes) as function of
β.Modified from Donath (1966)
and Jaeger and Cook (1979).

Figure. When bedding planes dip
steeply, both the deviation and
azimuth of wells have a strong
effect on wellbore stability (similar
to Willson, Last et al. 1999). (a)
Wellbore stability diagram that
shows the case above a fault at
about 15,000 ft depth, where the
bedding plane orientation (the red
dot is the pole to the bedding
planes) was such that drilling a
near vertical well was quite
problematic. Drilling orthogonal to
the bedding planes (to offset the
effect of bedding on strength)
would require a steeply dipping
well to the northwest. (b) Below
the fault, the bedding orientation
changes such that a near-vertical
well is stable.

Figure . A pre-drill
well design, made
by assuming that
the pore pressure
and the fracture
gradient limit the
mud window. (After
Moos, Peska et al.
2003). Reprinted
with Permission of
Elsevier.

Figure . In this case study for an
offshore Gulf of Mexico well, near
vertical wells and those deviated
to the northwest or southeast
require unrealistically high mud
weights (i.e. in excess of the frac
gradient) to achieve an
acceptable degree of wellbore
stability. In contrast, wells that
are highly deviated to the
southwest or northeast are
relatively stable.

Figure. Two views of a well trajectory that takes advantage
of the principles demonstrated in Figure 10.5. By turning
the well to the southwest in the problematic area, wellbore
stability could be achieved with a mud weight less than the
fracture gradient. The colour indicates the mud weight (in
ppg) required to stabilize the well at a given depth.

Filter cake in shale and stress support

Effect of mud cake on well bore Stresses

Heating and cooling in the hole and thermal alteration of σ’θ

Effect of rock yield on σ’θ and
Ballooning

Figure. Schematic diagram
illustrating the effects of
reservoir depletion on
deformation surrounding the
reservoir and contours of the
stress changes resulting
from depletion in a reservoir
at unit depth and radius
(from Segall 1989). Note that
in compressional tectonic
settings, reverse
faulting is promoted above
and below the reservoir
whereas in extensional
tectonic settings, normal
faulting is promoted around
the edges of the reservoir.

The evolution of the least
principal stresses with
decreasing pore pressure
in the Tor reservoir of the
Valhall field in the North
Sea (after Zoback and
Zinke 2002).
Pore pressure history of Field X
(after Chan and Zoback 2002).

(c)A portion of the Arcabuz–Culebra field in Mexico in which the
current direction of maximum horizontal stress is at an oblique
angle to the predominant trend of normal faults in the region. (d) A
depleted section of the Arcabuz–Culebra field (near that shown in
c) where the direction of maximum horizontal stress appears to
follow the strike of the normal faults in the area. (c) and (d) are
modified from Wolhart, Berumen et al. (2000). C 2000 Society
Petroleum Engineers

Fig. showing the hydro fracturing in non
depleted and depleted reservoir.

Wellbore stress analysis

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