Measuring and testing – Borehole or drilling
Reexamination Certificate
2000-06-05
2002-03-05
Williams, Hezron (Department: 2856)
Measuring and testing
Borehole or drilling
C073S152160, C073S597000, C073S784000, C367S027000, C367S031000, C367S086000, C702S006000, C702S011000, C702S018000
Reexamination Certificate
active
06351991
ABSTRACT:
TECHNICAL FIELD
The present invention relates to methods for determining stress parameters from sonic velocity measurements in an earth formation around a borehole.
BACKGROUND OF THE INVENTION
Formation stresses play an important role in geophysical prospecting and development of oil and gas reservoirs. Knowledge of both the direction and magnitude of these stresses is required to ensure borehole stability during directional drilling, to facilitate hydraulic fracturing for enhanced production, and to facilitate selective perforation for prevention of sanding during production. A detailed knowledge of formation stresses also helps producers manage reservoirs that are prone to subsidence caused by a significant reduction in pore fluid pressure (herein referred to as“pore pressure”) and an associated increase in the effective stress that exceeds the in-situ rock strength.
The formation stress state is characterized by the magnitude and direction of the three principal stresses. Generally, the overburden stress yields the principal stress in the vertical direction. The overburden stress (S
V
) is reliably obtained by integrating the formation mass density from the surface to the depth of interest. Accordingly, to fully characterize the formation stress state, it is necessary to determine the two principal stresses in the horizontal plane maximum and minimum horizontal stresses, S
H max
and S
h min
, respectively.
Existing techniques for estimating the maximum and minimum horizontal stresses are based on analyzing borehole breakouts and borehole pressure necessary to fracture the surrounding formation, respectively. Both borehole break-outs and hydraulic fracturing are destructive techniques that rely on assumed failure models. For example, a borehole breakout analysis can be used only in the presence of a compressive-shear failure and assumed cohesive strength and friction angle in the Mohr-Coulomb failure envelope (Gough and Bell, 1982; Zoback et al., 1985). The hydraulic fracturing technique for the estimation of S
H max
requires a reliable knowledge of the rock in-situ tensile strength that is difficult to obtain.
Hydraulic Fracturing and Wellbore Breakouts
The standard technique for determining in-situ formation stresses is based on hydraulic fracturing of surrounding formation between a sealed-off interval in a borehole. The technique includes applying increasing hydraulic pressure in the sealed-off interval to produce a radial fracture. The rock fractures when the circumferential stress produced by pressure and borehole-induced stress concentrations exceeds the tensile strength of rock. The effective circumferential (or hoop) stress at the borehole surface for an elastic deformation of a nonporous and impermeable formation is given by (Vernik and Zoback, 1992)
&sgr;
&thgr;&thgr;
=(S
H max
+S
h min
)-
2
COS
2
&thgr;(S
H max
−S
h min
)−P
w
, (1)
where &thgr; is the angle measured from the S
H max
direction; and P
W
is the wellbore pressure. Hydraulic fracturing applies a tensile failure model at &thgr;=0° and 180°, and wellbore breakouts uses a compressive-shear failure model at &thgr;=90° and 270° for the estimation of maximum and minimum horizontal stresses in the far-field. Hubbert and Willis proposed that if P
b
were the breakdown or fracture pressure in the borehole, the relationship between the maximum and minimum horizontal stresses is given by
S
H max
=
3
S
h min
−P
b
−P
p
+T
o
, (2)
where T
o
is the tensile strength at the borehole surface, P
P
is the formation pore pressure, and it is assumed that there is no fluid injection into the formation. This expression yields an upper bound on the breakdown pressure. If fluid injection occurs (i.e. mud penetrates the formation), there is a reduction in the breakdown pressure magnitude. In the presence of any plastic deformation at the borehole surface or borehole wall cooling during drilling (Moos and Zoback, 1990), the hoop stress at the borehole surface is appreciably reduced and this results in an overestimate of the maximum horizontal stress S
H max
magnitude.
Minimum horizontal stress S
h min
can be determined more reliably using hydraulic fracturing and a method proposed by Roegiers. After the fracture has propagated for a while, the hydraulic pumps are stopped and an instantaneous shut-in pressure is recorded. This pressure is only slightly above the minimum principal stress—assuming the influence of borehole to be negligibly small. Therefore, the instantaneous shut-in pressure is taken to be the minimum horizontal stress S
h min
(Roegiers, 1989).
After the formation has bled off, a second cycle of pressurization is started with the same pressurizing fluid and the same pumping rate as the first cycle. The pressure required to re-open the fractures, P
reopen
is recorded and subtracted from the breakdown pressure P
b
, to yield the tensile strength T
o
. However, estimation of the tensile strength is not very reliable.
Vernik and Zoback (1992) have shown from core analysis that there is a significant tensile and compressive strength anisotropy in rocks. They have suggested the use of an effective strength in the failure model used in the estimation of the maximum horizontal stress S
H max
magnitude from the wellbore breakout analysis. The S
H max
can be estimated from the following equation
S
H
max
=
C
ef
+
P
w
1
-
2
cos
(
π
-
2
φ
b
)
-
S
h
min
1
+
2
cos
(
π
-
2
φ
b
)
1
-
2
cos
(
π
-
2
φ
b
)
,
(
3
)
where 2&phgr;
b
is the breakout width, and P
W
is the wellbore pressure. This equation is derived from the effective stress with 2&thgr;=&pgr;/2−&phgr;
b
, and C
ef
is the effective compressive strength of the formation near the borehole surface.
Pore Pressure in Over-Pressured Formations
Existing techniques for determining pore pressure in an overpressured formation attempt to account for the potential source of pore pressure increase in terms of undercompaction (resulting in an increase in porosity) and/or pore fluid expansion caused by a variety of geological processes (Eaton, 1975; Bowers, 1994). Eaton (1975) proposed an empirical relationship between the measured compressional velocity V and the effective stress &sgr;
V=V
o
+C
&sgr;
⅓
(4)
where the empirical parameter C is obtained by fitting the velocity-effective stress data in a normally compacted zone. Below the top of overpressure in the velocity reversal zone, using the same empirical parameter C and the exponent ⅓ may lead to an underestimate of the pore pressure increase. Bower (U.S. Pat. No. 5,200,929, Apr. 6, 1993) has proposed to remedy the limitation of the Eaton's technique by assuming two different empirical relations between the measured compressional velocity and effective stress. These two different relations in a normally compacted and velocity-reversal zones are constructed to account for the undercompaction and pore-fluid expansion (that may be caused by temperature changes, hydrocarbon maturation, and clay diagenesis). Bower (SPE 27488, 1994) has proposed the following relationship between the measured compressional velocity and effective stress a in a normally compacted zone (also referred to as the virgin curve)
V=V
o
+A
&sgr;
B
(5)
where V
o
is the velocity at the beginning of the normal compaction zone; A and B are the empirical parameters obtained from velocity-effective stress data in a nearby offset well. The velocity-effective stress in a velocity-reversal zone attributable to a fluid-expansion effect and an associated hysteretic response is described by
V=V
o
+A
[
&sgr;MAX
(&sgr;/&sgr;MAX)
1/U
]
B
(6)
where A and B are the same as before, but U is a third parameter to be determined from the measured data in a nearby offset well. &sgr;
MAX
is defined by
σ
MAX
=
(
V
MAX
Batzer William B.
Lee John L.
Wiggins David J.
Williams Hezron
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