GB2138141A

GB2138141A - Borehole surveying

Info

Publication number: GB2138141A
Application number: GB08309704A
Authority: GB
Inventors: Anthony William Russell; Michael King Russell
Original assignee: Sperry Sun Inc; NL Sperry Sun Inc
Current assignee: Sperry Sun Inc; NL Sperry Sun Inc
Priority date: 1983-04-09
Filing date: 1983-04-09
Publication date: 1984-10-17

Abstract

Using a survey instrument having its longitudinal axis coincident with the axis of the borehole, the survey instrument is rotated about the borehole axis at a survey station, and the components of the earth's gravity and the earth's magnetic field (gOX, gOY, gOZ, BOX and BOY) are measured along two non-coincident axes (OX and OY) transverse to the axis of the borehole for at least three different orientations (O) of the survey instrument about the borehole axis. At least one error correction value is determined from the results of these measurements (gOX, gOY, gOZ, BOX, BOY). The azimuth and inclination of the borehole are then determined at a plurality of points along the length of the borehole by measuring the components of the earth's gravity and the earth's magnetic field (gOX, gOY, gOZ, BOX and BOY) along the transverse axes (OX and OY) and applying the previously determined error correction value to the measurements so obtained.

Description

SPECIFICATION Improvements in, or relating to, borehole surveying This invention relates to the surveying of boreholes such as are drilled when prospecting for oil, for example.

It is well known to monitor the direction of a borehole by making measurements of the earth's gravity and earth's magnetic field components at a plurality of survey stations as the survey instrument is moved along the borehole. An instrument making use of this survey method is described in Specification No. 1,240,830, for example. However, there are a number of sources of error associated with the measurement of the inclination 6 and the azimuth # of the borehole by this method. These include errors in the individual gravity and magnetic field transducers and errors due to non-alignment of the longitudinal axis of the instrument with the axis of the borehole (off-set axis errors).

It is an object of the invention to provide a method of surveying a borehole in which the major source of error associated with the OX and OY transducer datums may be eliminated and the offset axis errors may be reduced.

According to the invention there is provided a method of surveying a borehole using a survey instrument having its longitudinal axis coincident with the axis of the borehole, comprising rotating the survey instrument about the borehole axis at a survey station, measuring the components of the earth's gravity and the earth's magnetic field (gox, goy, goz, Box and Boy) along two non-coincident axes (OX and OY) transverse to the axis of the borehole for at least three different orientations () of the survey instrument about the borehole axis, determining at least one error correction value from the results of these measurements (gox, goy, 9OZ, Box, Boy), and determining the azimuth and inclination of the borehole at a plurality of points along its length by measuring the components of the earth's gravity and the earth's magnetic field (gox, goy, g, Box and Boy) along the transverse axes (OX and OY) and applying the previously determined error correction value to the measurements so obtained.

In order that the invention may be more fully understood, one form of the invention will now be described, by way of example, with reference to the accompanying drawings, in which: Figure 1 is a diagram showing a vector Vin a set of earth-fixed axes; Figure 2 is a two-dimensional plot of the measurements obtained from two transducers; and Figures 3 to 5are graphs illustrating the results of worst-case error calculations.

In Figure 1 an orthogonal set of earth-fixed axes OXYZ is shown with OZ lying along the borehole axis and OY and OZ lying perpendicular to one another in a plane perpendicular to OZ. The components of an earth-fixed vector V at a survey station (6,4') corresponding to the origin of this set of axes can be written as: Voxy = Foxy (V,O,+) in the OXY plane, and Voz = Foz (V,O,+) along the direction OZ where 0 and W are the inclination and azimuth of the borehole at this location.

If Voxymakes an angle # with the highside reference direction (see Figure 1) and OX makes an angle # with the highside reference direction then the components of V along the OX and OY directions can be written as: Vox = VOxy cos (E - 4) and Voy = VoXy-sin (g - +) where # is a function only of 6 and P.

Consider a set of axes OXmYmZm fixed with respect to a survey instrument disposed within the borehole at this location and generated from the set OXYZ by tilting the axis OZ through a small angle a in a fixed direction ss with respect to the axis OX. The components of"' in the OXm and OYm directions can be written as: VXM = VOX + AVOX and VYM = Voy + AVoy where AVox = fl Voz and AVoy = f2.VOZ are offset errors, and where fq and f2 are functions only of a and ,S.

If the instrument transducers used to measure VXM and VYM have fixed datum errors #VXD and AVYD respectively, then the outputs from these transducers can be written as:

where K is the transducer scale factor. Thus,

where A\Q'x = K. AVox and AVÓY = K. AVoy and the relationship between Sx and Sy may be written as::

where

Thus, if the pipe and hence also the survey instrument is rotated about the axis OZ at some survey station (6,4'), sets of (Sx,Sy) can be measured for various values of X, and a two-dimensional plot of (Sx,Sy) in a co-ordinate system OSxSy will yield a circle of radius K.Voxy centred at (a,b), as shown in Figure 2.

A minimum of three sets of (Sx,Sy) for three different values of + is theoretically sufficient to determine Voxy, the values of the combined errors due to datum and offset axis effects in the OX and OY transducers being obtained from a and b respectively. In practice, it is proposed that sets of (Sx,Sy) will be stored as the pipe is rotated with storage sets selected at defined values of calculated highside angle Xm or calculated magnetic steering angle m. Storage decision making calculations and the subsequent calculations to determine Voxy, a and b will be performed in the survey instrument.

Survey calculations The above described method may be used to determine the datum and offset axis errors associated with the instrument transducers used to measure the gravity and magnetic field components along the OX and OY directions, and this enables these errors to be eliminated during measurement of the inclination angle 6 and azimuth angle g at a plurality of survey stations along the length of the borehole.

If the above-mentioned earth-fixed vector V is considered as the earth's gravity vector, then the inclination angle 6 can be determined from: sin 6 = goxy cos6 gOZ Since datum and offset axis errors can be effectively eliminated from goxy, then these types of errors will only impact on the value of the inclination angle 6 through their effect on SoZ. It will be appreciated that these errors will have the most significant effect at larger values of inclination 6.

If the vector V is considered as the earth's magnetic field vector B, then the azimuth angle + can be determined from

where Bv is the vertical component ofBand + is the highside angle calculated from sin + = 9ox cos gOy Thus, since datum and offset axis errors can be eliminated from gox, goy, Box and Boyt considerable improvement in the calculation of the azimuth angle is to be expected.

Error calculation A worst-case error calculation was performed assuming the following systems errors: (i) scale factor transducer errors, (ii) datum transducer errors, (iii) offset axis errors, and (1v) errors in the value of Bv The calculation assumed that measured data sets are taken at equal rotational angle increments of 45 from 0" to 360 of the instrument about the axis OZ.

in Figures 3 to 5, the results of these calculations are plotted as comparisons between the worst-value set using the multiple-reading approach of the invention and the worst-value obtained using a single-reading set. Inclination, azimuth and highside errors are compared at (i), (ii) and (iii) respectively, and the errors obtained by the multiple-reading method are projected into displacement error components which are also plotted at (iv) for various values of inclination.The displacement error components plotted are as follows: Error in Horizontal Plane Projection transverse to the borehole azimuth direction: Horizontal (Transverse) = 1000*sinO Error in Horizontal Plane Projection in-line with the borehole azimuth direction: Horizontal (in-line) = 1000*cos6.A6 Error in the Vertical Projection (TVD): Vertical Projection = 1000*sin6.A6 Figure 3 indicates the results obtained using a survey instrument having errors similar to those of a conventional SST probe and the calculations are performed with zero offset axis error. Figure 4 assumes a similar instrument error set with the exception of an improved gz transducer. Figure 5 indicates the results obtained when an offset axis error of 0.2 degrees is included.

The results indicate that, if an operational procedure to implement the rotational multiple-reading method of the invention is carried out, then considerable advantages in the 0 to 30 inclination range can be obtained.

In particular, the highside and inclination readings are greatly improved and this is also reflected in a much improved azimuth reading. A survey instrument using this method would be capable of yielding displacement error results in the 0 to 30 inclination range better than 3 feet per thousand feet drilled, with considerably better results than this figure in near-vertical situations. At higher inclinations, displacement errors are effectively determined by the azimuth error.

An example of a conventional SST probe is disclosed in Specification No. 1,578,053.

Claims

CLAIMS 1. A method of surveying a borehole using a survey instrument having its longitudinal axis coincident with the axis of the borehole, comprising rotating the survey instrument about the borehole axis at a survey station, measuring the components of the earth's gravity and the earth's magnetic field (gox, goy, goz, Box and Boy) along two non-coincident axes (OX and OY) transverse to the axis of the borehole for at least three different orientations () of the survey instrument about the borehole axis, determining at least one error correction value from the results of these measurements (gox, goy, goz, Box, Boy), and determining the azimuth and inclination of the borehole at a plurality of points along its length by measuring the components of the earth's gravity and the earth's magnetic field (gox, goy, goz, Box and Boy) along the transverse axes (OX and OY) and applying the previously determined error correction value to the measurements so obtained. 2. A method of surveying a borehole, substantially as hereinbefore described with reference to the accompanying drawings. 3. Apparatus for carrying out the method of claim 1 or claim 2. Superseded claims 1 to 3 New claims:

1. A method of surveying a borehole using a survey instrument having its longitudinal axis coincident with the axis of the borehole, comprising rotating the survey instrument about the borehole axis at a survey station, measuring the components of the earth's gravity and the earth's magnetic field (gox, goy, goz, Box and Boy) along two non-coincident axes (OX and OY) transverse to the axis of the borehole for at least three different orientations () of the survey instrument about the borehole axis, determining at least one error correction value from the results of these measurements (gox, goy, goz, Box, Boy) and determining the azimuth and inclination of the borehole at a plurality of points along its length by measuring the components of the earth's gravity and the earth's magnetic field (Sox, goy, goz, Box and Boy) along the transverse axes (OX and OY) and applying the previously determined error correction value to the measurements so obtained.

2. A method according to claim 1, wherein for each measurement of the components of the earth's gravity and the earth's magnetic field at a respective one of said three different orientations of the survey instrument, a respective set of measurement signals (Sx,Sy) is outputted by the transducers within the survey instrument and stored.

3. A method according to claim 2, wherein a calculation is performed on the three sets of measurement signals (Sx, Sy) obtained in order to determine the resultant vector VOXY.

4. Apparatus for surveying a borehole using a survey instrument having its longitudinal axis coincident with the axis of the borehole, comprising means for measuring the components of the earth's gravity and the earth's magnetic field (gox, goy, goz, Box and Boy) along two non-coincident axes (OX and OY) transverse to the axis of the borehole for at least three different orientations () of the survey instrument about the borehole axis at a survey station, means for determining at least one error correction value from the results of these measurements (gox, goy, goz, Box, Boy), and means for determining the azimuth and inclination of the borehole at a plurality of points along its length by meauring the components of the earth's gravity and the earth's magnetic field (gox, g0, goz, Box and Boy) along the transverse axes (OX and OY) and applying the previously determined error correction value to the measurements so obtained.

5. A method of surveying a borehole substantially as hereinbefore described with reference to the accompanying drawings.

6. Apparatus for carryng out the method of claim 1,2,3 or 5.