Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2003-04-03
2004-11-30
Picard, Leo (Department: 2125)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C702S009000, C367S073000
Reexamination Certificate
active
06826486
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates broadly to the hydrocarbon industry. More particularly, this invention relates methods and apparatus for predicting pore and fracture pressures of a surface formation. The invention has particular application to the casing of wells undertaken during the drilling of the well, although the application is not limited thereto.
2. State of the Art
To safely drill a deep well for hydrocarbon exploration or production, it is necessary to prevent formation fluids from flowing into the well. This is typically done by adjusting the density of the drilling mud so that the wellbore pressure is at all depths above the pressure of formation fluids (the pore pressure). On the other hand, the mud density cannot be so great as to cause hydraulic fracturing of the formation (the fracture pressure). The pore pressure and the fracture pressure gradients thus provide minimum and maximum values for the mud weight that define a mud weight window (See, Burgoyne, A. T., Jr., Millheim, K. K., Chenevert, M. E., and Young, F. S., Jr., Applied Drilling Engineering, SPE Textbook Series, vol. 2, 1991).
In deep drilling, it is generally not possible to choose a mud weight that keeps the wellbore pressure within the bounds imposed by the pore and fracture pressures over the entire depth range of the well, and it is necessary to set a number of intermediate casing strings to hydraulically isolate the formation. As seen in
FIG. 1
, these casing strings are set at depths defined on the basis of the estimated pore and fracture pressure gradients. For safe and cost-effective drilling, it is then important to have a method to estimate pore and fracture pressures before drilling and to update these estimates as the well is being drilled and new information is acquired.
In current practice, estimates of the pore and fracture pressures can be obtained from information on the variation in compressional wave velocity with depth (in turn obtained from surface seismic data and borehole measurements). These estimates can then be calibrated with pressure data acquired during drilling. Although these pore and fracture pressure estimates are recognized to be inaccurate, a major limitation of current practice is that there is no quantification of their uncertainty.
An approach commonly used to estimate pore and fracture pressures is based on measurements of compressional wave velocities, formation resitivities, or drilling penetration rates. The fundamental assumption of this approach is that anomalies over a normal trend in depth of these measurements are related to corresponding anomalies in pore and fracture pressures. For example, if elevated pore pressures are due to undercompaction of shales, the sediment porosities will be anomalously high and velocities anomalously low. For purposes of simplicity, the description of the invention herein will focus on the use of compressional wave velocity to estimate pore and fracture pressures, because velocity estimates are typically available before drilling from the processing of surface seismic data (see, e.g., Sayers, C. M., Johnson, G. M., and Denyer, G., “Pore pressure prediction from seismic tomography”, paper
OTC
11984 presented at the 2000 Offshore Technology Conference, Houston, May 14, 2000) and can then be refined with measurements acquired while drilling such as sonic logs, vertical seismic profiles (VSPs), or seismic MWD (see, e.g., Esmersoy, C., Underhill, W., and Hawthorn, A., “Seismic measurement while drilling: conventional borehole seismics on LWD”, paper RR presented at the 2001 Annual Symposium of the Society of Professional Well Log Analysts, Houston, Jun. 17-20, 2001).
Most methods for pore and fracture pressure prediction start from Terzaghi's effective stress principle, which states that all effects of stress on measurable quantities (such as compressional wave velocities) are a function of the effective stress &sgr;
v
(z), defined as
&sgr;
v
(
z
)=
p
over
(
z
)−
p
pore
(
z
), (1)
where p
pore
(z) is the pore pressure at depth z, and p
over
(z) is the pressure due to the overburden. The pressure due to the overburden p
over
(z) is defined by
p
over
(
z
)=
g
∫&rgr;(
z′
)
dz′,
(2)
where g is the acceleration of gravity, &rgr;(z) is bulk density, and the integration is carried out from the surface to depth z. A commonly used formula to predict pore pressure is set forth in Eaton, B. A., “The equation for geopressure prediction from well logs”, paper
SPE
5544 presented at the 50
th
annual fall meeting of the Society of Petroleum Engineers, Dallas, Sept. 28-Oct. 1, 1975:
p
pore
(
z
)=
p
over
(
z
)−[
p
over
(
z
)−p
norm
(
z
)][&agr;(
z
)/&agr;
norm
(
z
)]”, (3)
where p
norm
(Z)=p
w
gz is the normal (hydrostatic) pore pressure (p
w
, is the water density), &agr;(z) the compressional wave velocity, and &agr;
norm
(z) the normal trend expected when there are no overpressures. As set forth in Sayers, C. M., Johnson, G. M., and Denyer, G., “Pore pressure prediction from seismic tomography”, paper
OTC
11984 presented at the 2000 Offshore Technology Conference, Houston, May 1-4, 2000, this normal trend can be taken to be a linear increase in velocity with depth:
&agr;
norm
(
z
)=&agr;
0
+b
&agr;
[z−z
0
] (4)
where &agr;
0
is the velocity at the mudline, b
&agr;
the velocity gradient in the normal trend, and z
0
the depth of the mudline.
Eaton's equation (3) essentially predicts that where the compressional wave velocity follows the normal trend, the pore pressure should be close to its normal, hydrostatic value. If the velocity becomes smaller than the normal trend, the pore pressure predicted by equation (3) increases from the hydrostatic value. To apply this method to any particular location, one should determine the variation of velocity and density in depth, the value of the coefficients as and b
&agr;
in the normal velocity trend, and the value of the exponent n in equation (3). Compressional wave velocity can be estimated from surface seismic data. Density can be estimated from a local trend (e.g., established from logs in nearby wells) or from a relationship between velocity and density such as Gardner's law (see, Gardner, G. H. F., Gardner, L. W., and Gregory, A. R., “Formation velocity and density: The diagnostic basis for stratigraphic traps”,
Geonhysics,
39, p. 770-780, 1974):
&rgr;(
z
)=
A &agr;
(
z
)
B
. (5)
The coefficients A and B in (5) can be obtained by fitting Gardner's law in a cross-plot of logged values of compressional velocity and density; an example of which is shown in FIG.
2
. Of course, the value of density cannot be exactly predicted by compressional velocity with Gardner's law as the density predicted from velocity using Gardner's law will have a residual uncertainty which is denoted by &Dgr;
p
and is typically a few percent of the density value.
The coefficients &agr;
0
and b
&agr;
in the normal velocity trend can be estimated from the velocity trend at depth intervals known or assumed to be in normal pressure conditions. Eaton originally suggested that the exponent n should be around 3. In Bowers, G. L., “Pore pressure estimation from velocity data: Accounting for overpressure mechanisms besides undercompaction”, SPE Drilling & Completion, p. 89-95, June 1995 (1995), however, it was noted that if overpressures are due to mechanisms other than undercompaction the appropriate value of n should be higher (up to about 5). The coefficients &agr;
0
and b
&agr;
and the exponent n can be calibrated by measurements of pore pressure or mud weights in the well being drilled (see, e.g., Bowers, 1995, and see Sayers et al., 2000, both cited above).
Widely used methods for fracture pressure predictions also start from Terzaghi's effective stress principle (equation 1 above). The most common stress state is one where the minimum effective stress &sgr;
h
(z) i
Batzer William B.
Gordon David P.
Kosowski Alexander J
Picard Leo
Ryberg John J.
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