NO813568L - APPARATUS AND PROCEDURES FOR Borehole Measurement - Google Patents

Description

This invention relates to an apparatus and a method for surveying a borehole or the like by measuring gravity components in order to obtain a representation of the borehole's path or route in relation to a known reference point, e.g. the ground 0 where the borehole begins.

Surveying a borehole or the like is often carried out with an instrument or probe that moves through the hole and measures inclination and azimuth angles at successive points.

The inclination, i.e. the angle by which the tangent of the borehole deviates from a vertical line can be measured with a pendulum or an accelerometer. Azimuth, or the direction angle of the borehole in relation to a reference direction such as north, can be measured with a magnetic or gyroscope compass. These angles, together with the distance in the borehole's longitudinal direction, are used to determine the coordinates of points along the borehole in relation to the reference point or ground 0.

A pendulum for measuring the inclination can be designed as

a linear servo accelerometer. which is sensitive to the earth-gravitas ion. Servo accelerometers are available that are small, sturdy and accurate. Measuring azimuth is more difficult. Magnetic compasses and other devices that respond to the Earth's magnetic field are subject to errors caused by magnetic irregularities in the Earth. The gyroscope compass has several disadvantages, such as size, bearing wear, sensitivity to shocks, operation and precession errors, as well as the requirement for a long setting time for stabilization when a measurement is carried out.

According to the present invention, there is an apparatus and a method with which the borehole route can be determined from gravity components measured with linear servo accelerometers as mentioned above, as well as from the distance in the longitudinal direction of the hole. The measurements are carried out by the probe, which is passed through the borehole, emitting a data signal from which the route of the hole is determined. The speed and accuracy of a survey based on servo-accelerometer measurements surpasses anything achieved with other instruments. In addition, a probe that uses accelerometers and does not need a compass for azimuth measurement can be mounted in a smaller housing, and is more robust.

One feature of this invention is a borehole measuring apparatus or a probe which uses a first bg and another pair of accelerometers where the input or input axis of each pair forms a measuring plane. The accelerometers are mounted so that they pass through the borehole with the two measuring planes a certain distance apart and perpendicular to the borehole's local tangent, respectively axis. The two pairs of accelerometers are connected by a flexible, torsionally rigid coupling to follow the trajectory of the borehole while maintaining a constant angular relationship between the pairs of accelerometers around the axis of the borehole. The apparatus further comprises a device for deriving from the accelerometer signals a representation of the borehole route.

One. another feature of the invention is that the probe has a first and a second section with a set of accelerometers in each section. The sections are connected by a connecting piece of pipe or

cable that is torsionally rigid around its longitudinal axis and flexible around axes perpendicular to the longitudinal direction. The coupling piece ensures that the distance between the probe sections is constant in the borehole's longitudinal direction, that the connection is torsionally rigid and that each accelerometer set follows the axis of the borehole and is free to rotate about it. More specifically, the two probe sections are connected by a cable or pipe which is flexible for bending about the axis of the borehole, but which is rigid with respect to torsion about the axis. The accelerometers can alternatively be mounted in a common housing which is flexible to follow the borehole's curves, but which is ionically rigid to resist twisting.

A further feature of the invention is the method for measuring the inclination and azimuth angles along the borehole,

p. a.'measurement of the earth's gravity (along orthogonal axes)

.in a plane across the axis of the borehole at a number of points along the borehole. This generates signals that represent ak s-e Ir . the eration,. and from the acceleration signals a representation of the borehole route is derived.

The inclination of the borehole at each measurement plane can be found from the vector sum of the two components of the earth's gravity measured at the corresponding pair of accelerometers. This has been known from before. A principle feature of this invention is that the change in the azimuth of the borehole between the two drilling planes can

is determined from the four signals from the two pairs of accelerometers and the distance between the measurement planes. The borehole route is expressed by

.inclination, azimuth and borehole length.

More specifically, while the probe is guided through the borehole, gravity measurements are taken from the accelerometer pairs and corresponding measurements of the distance in the borehole's longitudinal direction. From here, the course of the borehole is determined in three dimensions.

Further features and advantages of the invention appear from the following description and from the drawings, where Fig. 1 is a partial diagram of an apparatus where the invention is applied, and includes a section of a borehole showing the measuring probe. Fig. 2 is a block diagram of the accelerometers. and a circuit

for transmitting the acceleration signals to the surface..

Fig. 3-12 are geometric diagrams illustrating the derivation of inclination and azimuth angles as well as the borehole position coordinates from acceleration and distance measurements. Fig. 13 is a development tree which graphically shows the derivation illustrated geometrically in fig. 3-12. Figs 14 and 15 are block diagrams illustrating a system and a method for deriving the borehole route from the acceleration measurements, where the distance between the measurement positions is equal. the distance between the accelerometer pairs.

The invention is described here in connection with a borehole, such as for an oil or gas well. However, it can also be used for other purposes, such as, e.g. surveying of mine shafts. When boreholes are referred to in the requirements, this must be interpreted in a broad sense, except when the context necessitates a different interpretation.. A representation of the borehole route can be obtained, e.g. in the form of three-dimensional j onal coordinates or a plotting of an existing borehole to determine its location. Trasé — the representation can also be derived while the hole is being drilled, to monitor the drilling operation and to help the drill operator guide the drill along a desired path. The invention is not intended for a specific route production.

In fig. 1 shows a borehole 20 which extends downwards from point 20a at the surface and is lined with a pipe 21. The measuring probe has a first section 22 and at a distance from this another section .23. The sections are connected by a cable or a pipe 24. The probe is lowered into the borehole by a hoisting cable 25 which also contains wires for. to supply the probe with electrical power and to transmit signals from the probe to circuits on the surface.

A pair of accelerometers (not shown in Fig. 1) are placed'

in the first probe section 22. The accelerometers preferably have their sensitive axes X, Y at right angles to each other and form

a measurement plane across the longitudinal axis of the probe section. The probe axis corresponds to the borehole axis. Likewise, a pair of accelerometers (not shown in Fig. 1) is placed in another probe section 23 where they. have their sensitive axes X, Y perpendicular to each other and form a measuring plane at right angles to the probe section 23 and the borehole's common axis.

As explained below will be. the borehole's position coordinates determined from the angle of inclination in relation to the gravity vector and an angular measure of each measurement plane's zenith. The angles are easily and precisely determined by measuring the gravity vectors with orthogonally placed accelerometers in a measuring plane at right angles to the axis of the borehole. Measuring the gravity vector with a. however, pairs of accelerometers whose axes are sensitive to independent vectors in a plane of known position in the borehole (ie the sensitive axes are neither collinear nor parallel) can be geometrically transformed into inclination and zenith angle measures.

In a typical probe, the diameter of the section housing is in the range 50-75 mm, and two servo accelerometers cannot be mounted next to each other. The accelerometers in a pair are therefore axially offset from each other (sections 22, 23), but are sufficiently close to each other compared to the distance between the pairs of accelerometers, to be considered to lie in the same plane.

A third accelerometer can be mounted with its sensitive axis perpendicular to the first two accelerometers in a pair as shown at Z, Z<1>. The third accelerometer offers improved precision, . and enables operation even if an X or Y accelerometer should fail.

The cable or pipe 24 is attached at each end to the probe six ions 22, 23 and serves to maintain a constant distance between the probe sections in the borehole 20. The cable 24 is flexible to be able to follow curves in the borehole, but resists torsional stresses for to prevent rotation of one section in relation to the other. This maintains a predetermined relationship between the accelerometer axes X, X' and Y, Y'. With the probe sections 22, 23 axially aligned, the axes X, X<1> should preferably be parallel and form a plane through the longitudinal axis of the probe. Likewise, the axes Y, Y<1> are parallel to each other and form another plane through the probe axis at right angles to the first. It is not required that the corresponding axes are parallel, only that they have a constant ratio. However, it is easier to treat. the acceleration signals when the sensitive axes are nominally parallel.

Each accelerometer is preferably a linear servo-accelerometer with an associated electronic circuit (not shown) which generates an analog signal where the amplitude represents the gravitational component along the sensitive axis of the accelerometer. US patent 3,702,073 shows such an accelerometer. An electronic circuit in the s.onden (described in more detail below) multiplexes the analog signals, converts them to digital form and connects

them through wires in the hoist cable 25 to circuits at the top of the well. The acceleration signals are connected to the data input of a data storage unit. 26. The output of the storage unit is connected to a data processing unit or processor 27 which derives a representation or production of the borehole route. A transducer 28 in connection with the hoist cable 25 ■ produces a signal AL to the unit or processor 27 and indicates the probe's position in the borehole.

A keyboard and a screen 30 are connected to the processor: 27. A representation of the borehole's route can be expressed by coordinate dimensions in a three-axis system. The keyboard allows for operator input and control. The production of the borehole route can be printed or saved for future use. . Devices for performing these functions are known and are not illustrated in the drawings.

The measuring probe's sections 22, 23 have cylindrical, pressure-resistant housings. Resilient centering pieces 31 on the outside of the housing are in contact with the inside of the borehole lining 21, and hold the probe housings in position so that their longitudinal axis essentially coincides with that of the borehole. The probe's lower section 23 has its housing divided into two parts, 32, 33. The cable 24 is attached to the upper end of the part 32 which contains the accelerometers X', Y'. The housing part 33 of the probe section 23 has the centering pieces 31 and is long enough to be kept in line with the borehole. The housing parts 32, 33 are connected by a swivel (not shown) which allows the part 32 to rotate freely relative to the part 33 and to maintain the desired alignment with the probe section 22.

The borehole survey is carried out by passing the probe through the hole from end to end, in one direction or the other, while data is collected and processed. The survey can be carried out while the probe is lowered into the borehole or while it is raised from the bottom. One can improve the precision by collecting data in both directions and using the average of the measurements.

The azimuth of the borehole is referred to the outside world by

establish an exit azimuth -for. the probe at the surface. The probe can e.g. is aligned with a fixed mark, and the direction is confirmed with a surveying instrument 35.

Fig. 2 schematically illustrates accelerometers and signal circuits in the probe. Upper probe section contains X, Y and Z accelerometers which have analog signals ax, a^ and az. Lower probe section 23 has X', Y' and Z' with analog signals ax', a^' and

Power from the power source 37 on the surface is. connected through, the hoist cable 25 with the power supply unit 38 inside the probe.

The analog accelerometer signals are connected to the "sample and hold" circuits 39, 39' and are multiplexed through analog-to-digital converters 40, 40' to the signal control 41 through which they are transmitted to the surface. The signal control circuit 41 provides timing control for the sample and hold circuits 39, 39' and the A/D converters 40 and 40'. Signals from the cable length transducer 28 are compared with the accelerometer signals to identify the point in the borehole where each set of measurements is taken.

A possible source of error in the measurement can be minimized by placing temperature sensors 42, 42' in each probe section together with temperature controls 43, 43', thus keeping the temperature in sensitive elements within desired limits. Samples of analogue temperature signals t and t' are sent to the surface together with the acceleration signals. The temperature signals are used in the temperature compensation circuit 26' to further minimize temperature errors.

The probe sections 22 and 23 must be long enough to maintain direction between the section axes and the borehole axis. The maximum length is limited by the smallest bending radius in the borehole lining. Within these limits, a typical probe section is between 6 and 60 meters long. The distance between the accelerometer pairs should be at least 3 to 5 meters. A typical probe is between 15<p>g and 50 meters long.

Fig. 3 -: 12' illustrates the geometrical conditions underlying the derivation of the borehole's trajectory from the two accelerometer pairs of gravity component signals. Fig. 13 shows some of the conditions in diagram form. Below is a table of symbols and terminology used in the drawings and the following discussion.

Fig. 3 is a three-dimensional diagram in a rectangular coordinate system MEG with origin at reference ground 0. The borehole's curve C extends downward under the north-east quadrant. Curve C is the borehole's projection onto the earth's surface.

The coordinates NE. describes a horizontal plane at the earth's surface.

G extends downwards at right angles to the ground plane and represents the direction of gravity. The circles Cn and Cn' represent. unit circles centered on the borehole curve at 0 n and J 0 n'. The plane of the circles is perpendicular to the borehole's curve and is a distance from one another. This distance is equal to the distance between the accelerometer pairs in the measuring probe. It is assumed that the borehole's curve between 0 n and " 0 r. 1 describes a circular arc with radius r n about a center Q n , fig J. 4.

The measuring probe is passed through the borehole, and measurements are taken from the two pairs of accelerometers at successive positions with a space l, which is equal to the distance between pairs of accelerometers. As explained below, the inclination of the borehole at each accelerometer position and the change in azimuth angle between the positions can be determined from the accelerometer signals. If the measurements begin at ground reference 0, and the azimuth is known at this point, the azimuth at any point along the borehole can be found by adding the increments from point to point. The measurements can start at reference ground 0 and continue to the bottom of the borehole, or they can start at the bottom and continue up to the reference ground.

In the latter case, the azimuth of the borehole at the individual measurement points cannot be determined before the survey is completed, and all azimuth measurements can be summed up, with the azimuth at the base reference.

Inclination and azimuth angles as well as the distance along the borehole can be used to identify each point in the borehole in the rectangular coordinate system NEG.

The acceleration signals ax and a^ from a pair of orthogonal accelerometers determine the inclination I of the plane of the accelerometers as well as the orientation angle between the zenith of the unit circle and the sensitive axis of the X-accelerometer. In fig. 6 is unit circle C. horizontal, and Cner tipped about the diameter jn, ~jn>

Fig. 7 is a further detail of fig. 6, where one sees perpendicularly

on the vector X . It can be seen that

■ n

Since the accelerometer signals a and a are known, both

n n

'tø and I- are determined. These calculations have been made for the unit circles Cn and CR'. From. this information as well as the assumption that the borehole follows a circular arc between positions n and n<1>, the change in azimuth from n to n' can also be determined.

More specifically,

This gives the borehole inclination at 0n. The inclination of

0n1 is calculated in the same way. This is represented by step 43, (fig. 13).

In fig. 8, three concentric circles are shown:

The circle CH is -horizontal or parallel to the earth's surface.

The circle C is at right angles to the borehole at 0, has zenith Z

n n n

and is tipped relative to C about an axis defined by j and~jn-The circle Cn<1>is perpendicular to the borehole at n<1>, has zenith Zn', and J is found by rotating' the circle C n about V n and 3 -V nwith an angle 26. Circle C intersects circle CT7 at j ' and --j„1 . The turning point on Cner- 90 from Vnog ~Vn. In accordance with the angular rotation 20, the point Tn on CR is moved to'-U on Cn 1 .

Thus both T and U are 90° from V . In fig. 8 is the a angle

between Z and T„, and 6 the angle between Z ' and U '.

n-n 3 n^n

Fig-. 10 shows the circles C and .C .' superimposed, while.

one looks along the axis of the borehole..

In fig. 8 and 10 can be seen.at

Hence the zenith shift

(after rotating the right angle /Zn0jn clockwise with /y)

n = a - o

The spherical triangle in fig. 9 lies on the right side of the circles in fig. 8. In this triangle:

sin a sin I n .= sin In' (sin a cos, y - cos a sin y) sin a (sin I - sin I cos y) = -cos a sin y sin In'

Therefore:

Then y - ^-w^1 are'all the quantities on. right side of the equation known from the four accelerometer signals, and tan a and a can be calculated.

■Also with reference to the spherical triangle in fig. 9, the bending angle 3. can be calculated as follows when using; of the law of spherical triangles:

Since all the quantities on the right side of the equation are known,

the angle 3 can be calculated.

The three quantities 5 , a and B, step 44, (fig. 13) are known.

The geometric meaning of a, which is the direction angle for the lower probe center 0 1 when looking down along the borehole's tangent at the upper probe center 0 , is illustrated in fig. 5. The bending angle 23 is illustrated in Figures 3 and 4, and shows how much the borehole cross-section Cn<1> has fluctuated in relation to the cross-section Cfl.

The position of the vectors i, j and k (fig. 3 and 8) can be connected with successive circles by coordinate transformation matrices as follows:

The matrix M has already been found in a previous measurement and calculation. It is necessary only to derive the matrix M<1>. Based on the three-circle image (Fig. 8) is the expression for the vectors

(U , V , k ') expressed by (i ', j ', k ):

.. n n' nJn'Jnn

The coordinate transformation M , which connects the two vectors (in, jn, kn). and (<i>n',<j>n', kn') in fig. 8 is found via the symbols"(Un, V , kn).

This means that the coordinate transformation matrix Mn (step 45, Fig. 13) can be constructed: In practice, the processor will store the coordinate transformation matrix from previous local coordinates (i, j, k) in the global coordinate system NEG. It means that . the computer already knows the matrix'M, where

To update the transformation matrix Mntil Mn+]_> which transforms the local coordinates (i n 1, j J n , k n1) to the global coordinate system NEG, the matrix product is calculated

See fig. 13, step 46.

In fig. 11, when looking along the borehole in the direction of vector +kfi, (fig. 3, 4 and 5), it is assumed that the borehole from 0n to 0' has a clockwise direction an degrees from the zenith Z';

and that the borehole is bent along a circular line through an arc 2Bn-

If i is the borehole length from 0 to 0', the local position vector 0n0n1 from 0n to 0n' (step 47, Fig. 13) can be expressed

To write the column vector 0n0n' in the ■NEG coordinate system:

where 00n is stored from previous calculations. The position of 0n1 in relation to basic reference 0 is thus determined.

With the vector 00^ pointing towards position 0n', the azimuth An1 (see fig. 3) can be expressed:

where (Nn', En<1>, Gn') are the coordinates of the vector 0Qni the NEG system with the base 5 as reference (step 49, Fig. 13).

The derivation of the borehole route from the gravity vector signals is preferably carried out by a programmed digital processor. Figures 14 and 15 are schematic maps illustrating the derivation of a representation of the borehole route in NEG coordinates. The illustrations and description assume that the accelerometer signals. are from measurements taken. at intervals along the borehole.

The scalar inputs to.fig. 14' are the digital gravity vector signals a , a ■ and a ' ,' a ' . Each block in the diagram tells algebraically or in words which function

■ which is performed. The program will be described in general terms and refer to certain geometrical explanations given above.

In step 50, a and a^, combined with the gravity g, become

and an arcsin function is used in step 51 to find the inclination angle I for a position in the borehole. Likewise, in steps 52 and 53, a' and ay' are used to derive I<1>, which is the angle of inclination at the second point in the borehole. In step 54, the ratio a^ to a^ is taken; and in step '55 are the tangent gives a further measure of the angle.co, see fig. 3, 6 and 8. On

similarly, a 1 - and -a ' are combined at steps 56, 57

x y

to provide a signal representing the angle in' . At step 58, the difference w-to' gives the angle y, which is the displacement in zenith between subsequent positions along the borehole, see fig. 10. The inclination angles i, I<1> and the zenith offset angle y are combined in steps 60 and 61 to calculate the angle a which represents the course of the borehole between successive positions.

In steps 62 and 63, a is combined with the inclination angles

I and 1<1> as well as the displacement angle y to derive the bending angle 3.

The numerical quantities a, 3, Y and I provide input for the matrix/vector program which is illustrated schematically in fig. 15. In the character system used in fig. 15, M represents a borehole's local coordinate transformation matrix from (i, j, k)' n<1> to (i, j, k)n, and M 1 is the global coordinate transformation matrix from (i, j, k)' ' to(N, E, G).

The original azimuth Aq for the probe is determined by et. surveying instrument 35, and this information is given as input to the system through the keyboard 30<1>. At step 70, the starting position of the probe is defined by a global matrix MQ(Ao, IQ The form of the matrix M is indicated in the footnote in Fig. 15. For the first measurement position, or n=0, the matrix Mq from step 70 is connected through the street 61 with the matrix multiplier 12.

The angles a and y are subtracted at step 73 to give the angle 6 which is further combined with a and 3 at step 74 to give the matrix Mn which has a form as indicated in the footnote jti to fig. 15. The matrix Mn is multiplied by matrix Mnved 75,. and gives a transformed global matrix Mn_]_ for lower position along the borehole. This matrix is delayed at step 76 and coupled through gate 77 to matrix multiplier 72 when n is 1 or greater, becoming Mn for subsequent measurement.

and a are combined in step 78 to give the vector 0 0

r ^ nn which is multiplied by the matrix Mni step 72, see fig. 11 and 12. The product of this multiplication °n0n<1> is connected with

a vector addition unit 80 where it is summed with the NEG coordinates for the point '0. At the first measurement location (the borehole at the ground surface), these coordinates are 000. The result of the vector addition is NEG coordinates which represent a point on the borehole. This result is also fed or connected through a delay circuit (unit delayer)

at step 81, as input to the vector addition unit 80 for the next measurement position. The successive sets of NEG coordinates developed from successive accelerometer measurements provide a representation of the borehole trajectory.

The described measuring instrument, which uses serv<p->accelerometers, gives reliable results as long as the borehole is not within approx. 1 degree from true vertical or horizontal direction. Under such conditions, the accelerometer measurements should be supplemented with other measurements of the borehole route.

Claims (14)

1. Borehole surveying apparatus comprising a measuring probe with an accelerometer device for generating gravity-based signals, characterized in that the sensitive probe includes a first pair of accelerometers whose sensitive axes form a first plane; another pair of accelerometers whose sensitive axes form another plane; a device carrying both pairs of accelerometers to be passed through the borehole with the accelerometer planes spaced apart and with the angle device between the two pairs of accelerometers about the borehole axis constant relative to each other; a device, for deriving from each accelerometer a signal representing the gravitational component along each accelerometer's sensitive axis. 2. Apparatus according to claim 1, characterized in that the sensitive probe contains a device for deriving from the accelerometer signals, in positions, at intervals along the borehole, a signal representing the borehole's inclination angle at each position; and a device for deriving from the accelerometer signals a signal representing a change in the azimuth angle of the borehole between the positions. 3. Apparatus according to claim 1, characterized in that the sensitive probe contains a device for deriving a signal representing each position's distance from a given reference; and a device for deriving from the accelerometer and distance signals the position coordinates of the borehole in relation to said reference. 4.. Borehole measuring device. which comprises a measuring probe that can be passed through the borehole, and where the probe has an accelerometer device that generates gravity-based signals, characterized in that the probe comprises a first section with an axis along the axis of the borehole, a second section located at a distance from the first section and with an axis along borehole axis; a device that connects the two sections and keeps them at a fixed distance from each other, where the connection is flexible so that it bends along the axis of the borehole when. first and second sections change position in relation to each other as resulting from changed inclination and/or' azimuth while counteracting rotation of one section relative to the other about the borehole axis, and maintaining angular alignment between the' sections; a first axis-elerometer pair in said first section, with their sensitive axes at right angles so as to form a measurement plane across the axis of the borehole; another pair of accelerometers in said second section, with their sensitive axes at right angles so as to form a measurement plane at right angles to the axis of the borehole; and a device for deriving from each accelerometer a signal representing the gravitational component along the sensitive axis of the accelerometer. 5. Apparatus according to claim 4, characterized in that when. the measuring probe is aligned, the sensitive axis of each accelerometer of the first pair lies in the same plane as the sensitive axis of the corresponding accelerometer of the second pair. 6. Apparatus according to requirements. 4, characterized in that. the measuring probe comprises a third accelerometer in each section with its sensitive axis along the axis of the probe section. 7. Apparatus according to claim 4, characterized by that the measuring probe comprises one housing for each section, and a device for centering the housings in the borehole. 8. Apparatus according to claim 7, characterized in that the probe housings are free to rotate in the borehole. 9. Apparatus according to claim 7, characterized in that the device that connects the sections is a coupling piece attached with one end to each of the section housings, which coupling piece has an axis that follows that of the borehole, and the coupling piece is rigid with regard to rotation about its own axis and flexible with regard to bending along the axis of the borehole when section the housings change position relative to each other in different positions along the borehole. 10. Apparatus according to claim 4, characterized in that the measuring probe comprises a device for deriving from the accelerometer signals. a representation of the borehole route., 11. Procedure for measuring a borehole, where a measuring probe is passed through the borehole to collect gravity-based signals, characterized by these steps: measuring the acceleration of the Earth's gravity along different axes at successive pairs of points along the borehole, the axes at each point of a pair having a known ratio; generating signals representing said acceleration; measuring the distance along the borehole for the said points; and from the acceleration and distance signals derivation of a representation of the borehole route. 12. Method according to claim 11, characterized in that the orthogonal axes at each point describe a plane at right angles to the axis of the borehole. 13. Method according to claim 11, characterized in that the production of the borehole route is expressed as coordinates in relation to a reference point. . 14. Method according to claim 11, characterized in that two sets of accelerometers spaced apart are passed through the borehole, and successive measurements are taken by sampling signals from the accelerometers.