Note: Descriptions are shown in the official language in which they were submitted.
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METHOD OF DETERMINING AZIMUTH OF A BOREHOLE
The present invention relates to a method of
determining an azimuth angle of a borehole formed in an
earth formation using magnetometer tool arranged in a
drill string extending longitudinally in the borehole.
During drilling of a borehole in an earth formation it is
generally desirable to check the borehole course by
measuring the inclination and azimuth of the borehole at
regular intervals. The borehole inclination can be
determined using accelerometer measurements in the
borehole and the Earth gravity field as a reference. The
borehole azimuth is determined using a package of
magnetometers included in the Bottom Hole Assembly (BHA)
of the drill string. The magnetometers are operated to
measure the components of the local magnetic field from
which the borehole azimuth is determined using the Earth
magnetic field as a reference. In many instances however
the measured local magnetic field includes, apart from
the Earth magnetic field components, components
attributable to drill string magnetisation. In order to
obtain sufficiently accurate azimuth data it is required
that such drill string magnetisation effects are taken
into account.
EP-A-0 193 230 discloses a method of determining
azimuth of a borehole formed in an earth formation using
a magnetometer package included in a drill string
extending into the borehole, wherein the effect of drill
string magnetisation is taken into account by first
eliminating the effect of cross-axial drill string
magnetisation prior to eliminating the influence of axial
drill string magnetisation. The cross-axial drill string
magnetisation is eliminated by taking so-called
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rotational shots, i.e. by measuring the local magnetic field
at different rotational locations of the magnetometer tool
and determining the cross-axial drill string magnetisation
from the magnetic field data thus obtained. The axial drill
string magnetisation is computed from the measured magnetic
field and from the Earth magnetic field. Once the measured
magnetic field has been corrected for cross-axial and axial
drill string magnetisation, the borehole azimuth is
determined from the corrected field and from the Earth
magnetic field which is generally known for most places on
Earth. The computed azimuth however is very sensitive to
inaccuracies in the Earth magnetic field data, especially in
case of highly inclined boreholes extending substantially in
east or west direction.
It is an object of the invention to provide an
improved method of determining azimuth of a borehole, which
method is less sensitive to inaccuracies in the Earth
magnetic field data even for highly inclined boreholes
extending substantially in east or west direction.
In accordance with the invention there is provided
a method of determining an azimuth angle of a borehole
formed in an earth formation using a magnetometer tool
arranged in a drill string extending in the borehole, the
magnetometer tool having a selected orientation relative to
the drill string, the method comprising: a) selecting at
least two locations along the borehole at which the borehole
has selected different borehole inclinations; b) for each
selected location, arranging the drill string in the
borehole such that the magnetometer tool is positioned at
the selected location and operating the magnetometer tool so
as to measure a component of a local magnetic field along an
axis having a selected orientation relative to the
magnetometer tool, the local magnetic field including the
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earth magnetic field and a drill string magnetisation field;
c) determining from the measurements and from the selected
borehole inclinations, a contribution from the drill string
magnetisation field to the measured components; d)
correcting the measurements for said contribution from the
drill string magnetisation field; and e) determining from
the corrected measurements, the borehole azimuth, wherein
said component of the local magnetic field is the axial
component of the local magnetic field, wherein for a
borehole inclination at a first one of said locations being
less than 45 , step c) comprises determining the
contribution from axial component of the drill string
magnetisation from the relationship:
Cz (cos 12 - COS Ii) = BHSel sin II - Bz1 cos II - BHSe2 sin 12 +
Bz2 cos 12
as defined hereinbefore.
The contribution from the Earth magnetic field to
each measured component along the axis of selected
orientation is different for the different borehole
locations because the drill string, and therefore also said
axis, is oriented differently relative to the earth magnetic
field at the different locations. On the other hand, the
contribution from the drill string magnetisation field to
the measured component is the same for the different
borehole locations because the orientation of said axis
relative to the drill string magnetisation field does not
change. Since the orientation of said axis is directly
related to the orientation of the drill string and therefore
to the borehole inclination, the contribution from the drill
string magnetisation field to the measured component can be
determined from the difference between the measured
components at the different locations and from the different
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borehole inclinations at the different locations. An
example of such determination is presented in the detailed
description below.
Preferably said component of the local magnetic
field is the axial component of the local magnetic field,
which is the component in axial direction of the drill
string. It is to be understood that the contribution from
the drill string magnetisation field to the cross-axial
component (if any at all) of magnetic field generally is an
order of magnitude smaller than the axial contribution.
Therefore, for most applications it is sufficiently accurate
to disregard such cross-axial contribution. Alternatively,
the measured magnetic field can be corrected for a cross-
axial contribution from the drill string magnetisation field
prior to step c).
The method can suitably be applied for a borehole
of which the longitudinal axis at the selected locations is
substantially located in a vertical plane.
For most applications it is sufficient to select
two said locations of different borehole inclination.
For enhanced accuracy in applying the method of
the invention, the borehole inclinations at at least two of
said locations differ from each other by an angle of at
least 40 .
If furthermore the drill string magnetisation at
the first location is different than at a second one of the
locations, e.g. due to different Bottom Hole Assemblies, the
borehole inclination angle at the second location is
suitably between 80 -100 .
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In the case where the wellbore inclination at the
first location exceeds 45 it is preferred to determine the
contribution to the axial components attributable to drill
string magnetisation from the horizontal component of the
Earth magnetic field. If furthermore the drill string
magnetisation at the first location is different than at the
second location, the borehole inclination
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angle at the second location is suitably between 00 and
+100.
The invention will be described further in more
detail and by way of example with reference to the
accompanying drawings in which
Fig. 1 shows a horizontal plane of the (N,E,V)
coordinate system;
Fig. 2 shows a vertical plane through line H of the
coordinate system of Fig. 1;
Fig. 3 shows a borehole-fixed coordinate system (HS,
HSR, z) and a tool-fixed coordinate system (x,y,z).
In Fig. 1 is shown the horizontal N-E plane of the
North (N), East (E), Vertical (V) coordinate system,
wherein line H is a projection in the N-E plane of the
longitudinal axis of a borehole 10 (Fig. 3) and angle A
indicates the borehole azimuth. It is to be understood
that angle A may vary along the length of the borehole.
BN represents the horizontal vector component of the
earth magnetic field.
In Fig. 2 is shown a vertical plane through line H.
Line T represents the longitudinal axis of the borehole
and angle I the borehole inclination which varies along
the length of the borehole. Bv represents the vertical
vector component of the earth magnetic field and Bn.cos A
is the projection of the horizontal component of the
earth magnetic field on line H.
In Fig. 3 is shown a cross-sectional view of the
borehole 10, a co-ordinate system (HS, HSR, z) fixed to
the borehole 10 and a co-ordinate system (x, y, z) fixed
to a magnetometer tool (not shown) for measuring the
components of a local magnetic field B in the (x, y, z)
co-ordinate system. The magnetometer tool is fixedly
arranged in a drill string (not shown) extending through
the borehole, therefore the (x, y, z) co-ordinate system
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can be thought of as being fixed to the drill string. The
HS-, HSR-, x-, and y-axes extend in the transverse plane
of the borehole at point P whereby the x-, y-axes are
rotated relative to the HS-, HSR-axes about an angle a
which is referred to as the tool-face angle. The z-axis
extends in longitudinal direction of the borehole 10. The
drill string is furthermore provided with an accelero-
meter tool (not shown) for measuring the components of
the earth gravity field G in the (x, y, z) co-ordinate
system.
During normal operation the magnetometer tool
measures the components Bx, By, Bz of the local magnetic
field vector B and the accelerometer tool measures the
components Gx, Gy, Gz of the gravity field vector G while
the drill string is kept stationary. The tool-face angle
a and the inclination angle I are determined from the
equations:
GHS = Gxcos a Gysin a (1)
Gv = Gzcos I GHgsin I (2)
Gzsin I+GHScos I = 0 (3)
wherein
GHS is the component of G in HS-direction;
Gv is the (known) component of G in V-direction.
From the measured magnitudes of Bx, By, Bz and from the
tool face angle a, the components of B in the (HS, HSR,
z) co-ordinate system are determined thus yielding the
local magnetic field vector (BHS, BHSR, Bz)= These
components include contributions from the earth magnetic
field and from drill string magnetisation. Denoting the
earth magnetic field vector by (BHSe, BHSRe, Bze) and the
drill string magnetisation vector by (CHS, CHSR, Cz) the
local magnetic field vector is
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(BHS, BHSR, Bz) = (BHSe- BHSRe- Bze) +
(CHS, CHSR, Cz) (4)
The cross-axial contributions from drill string
magnetisation are then determined and eliminated from the
magnetic field vector, for example by means of a
"rotational shot" whereby a number*of surveys are taken
at various rotational angles of the magnetometer tool in
the borehole as described in EP-A-0 193 230. After such
elimination the local magnetic field vector is
(BHS, BHSR, Bz) =(BHSe, BHSR e, Bze + Cz) (5)
The sum of the vertical components of BHSe and Bze is
equal to the vertical component Bv of the magnetic field
(BHSRe has no vertical component), thus yielding
Bv = -BHSe sin I+ Bze cos I
and from eq. (5)
Bv --BHSe sin I+(Bz - Cz) cos I (6)
By operating the magnetometer tool at two borehole
locations with different inclinations Il and 12 two local
magnetic field vectors (BHS1, BHSR1, BzI) and (BHS2,
BHSR2, Bz2) are obtained, and from eq. (6) it follows
Bv =-BHSe1 sin I1 +(Bz1 - Czl) cos Il (7)
Bv =-BHSe2 sin 12 +(Bz2 - Cz2) cos 12 (8)
Axial drill string magnetisation depends primarily on the
magnetic properties of the BHA, not on borehole
inclination. Therefore it is considered that at least as
long as the BHA is not changed:
Czl = Cz2 = Cz (9)
Equations (7), (8), (9) contain the unknowns Bv, Cz1 and
Cz2. The inclinations I1 and 12 are known from
measurements using one or more accelerometer meters
included in the drill string. It is found that
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Cz(cos 12 - COS I1) = BHSel sin II - Bzl cos Ii -
BHSe2 sin 12 + Bz2 cos 12 (10)
from which Cz is determined.
The local magnetic field at each point can now be
corrected for axial drill string magnetisation.
The above approach is preferred for low borehole
inclinations, i.e. inclinations less than 45 , because Cz
then is relatively insensitive to variations in borehole
inclination.
For borehole inclinations beyond 45 the following
approach is preferred.
The sum of the components of BHSe and Bze in
direction H is equal to the component of the earth
magnetic field in direction H, thus yielding
Bn cos A = BHSe cos I + B z e sin I (11)
or
Bn cos A = BHSe cos I+(Bz - Cz) sin I (12)
For two points with respective inclinations 11, 12 and
azimuth A1, A2 it follows that
Bn cos A1 = BHSel cos I1 +(Bzl - Czl) sin IZ (13)
Bn cos A2 = BHSe2 cos 12 + (Bz2 - Cz2) sin 12 (14)
The HSR components of the local magnetic field, corrected
for cross-axial drill string magnetisation as described
above, for the two points are
BHSRe1 = -Bn sin AI (15)
BHSRe2 = -Bn sin A2 (16)
From eqs. (13) - (16), and with Czl = Cz2 = Cz (e.g. for
unchanged BHA), it follows that
(BHSRe1)2 + (BHSe1 cos I1 + (Bzl - Cz) sin II))2 -
(BHSRe2)2 + (BHSe2 cos 12 + (Bz2 -
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Cz) sin 12) )2 = 0 (17)
Eq. (17) is a quadratic expression in Cz with
generally two solutions for Cz. The solution which gives
a horizontal magnetic field component closest to the
expected horizontal magnetic field component is to be
selected from the two. The local magnetic field at each
point can then be corrected for axial drill string
magnetisation.
If different BHA's are used during the measurements
at the different survey points Czl is generally not equal
to Cz2. Therefore it is preferred that for the low
inclination mode, i.e. when using eq. (10), at least one
survey point is at a borehole inclination between
80 -100 , preferably about 90 , because then one of the
components Czl cos 11 or Cz2 cos 12 in eqs. (7), (8)
substantially vanishes.
Similarly, it is preferred that for the high
inclination mode, i.e. when using eq. (17), at least one
survey point is at a borehole inclination between 0 and
+10 , preferably about 0 , because then either Cz1 sin Il
or Cz2 sin 12 in eq. (17) substantially vanishes.
Instead of using two survey points as described
above, more than two survey points can be used to correct
for axial drill string magnetisation.
