Mechanical caliper system for a logging while drilling (LWD) borehole caliper
A logging while drilling (LWD) caliper includes a drill collar, at least one movable pad, a hinge coupler, a power transmitter and a power receiver. The hinge coupler couples the movable pad to the drill collar in such a way that the movable pad can move between an open position and a closed position. The power transmitter is coupled to the drill collar in such a way that the power transmitter receives power from the drill collar. The power receiver is coupled to the movable pad in such a way that the power receiver provides power to the movable pad. Also, the power transmitter is coupled to the drill collar and the power receiver is coupled to the movable pad is such a way that power is transmitted from the power transmitter to the power receiver.
1. A method comprising:
providing a first coil within a drill collar;
providing a second coil in the moveable member;
coupling the first and second coils with a coupling coefficient, k, wherein, k=M/√{square root over (L 1 L 2 )}≦0.9, M is a mutual inductance between the first and second coils, L 1 is a first self-inductance of the first coil, and L 2 is a second self-inductance of the second coil; and
resonantly tuning the first coil at a first frequency, f 1 , with a first capacitance, C 1 , and the second coil at a second frequency, f 2 , with a second capacitance, C 2 , wherein f 1 is approximately equal to f 2 ,
f
1
=
1
2
π
L
1
C
1
and
f
2
=
1
2
π
L
2
C
2
;
wherein the first and second coils have a figure of merit, U, wherein
U
=
k
Q
1
Q
2
≥
3
,
Q
1
=
2
π
f
1
L
1
R
1
,
Q
2
=
2
π
f
2
L
2
R
2
,
Q 1 and Q 2 comprise respective quality factors associated with the first and second coils, and R 1 and R 2 comprise respective resistances of the first and second coils.
2. The method as recited in claim 1 , further comprising:
approximately matching a source impedance of the first coil, R S , with a load impedance of the second coil, R 1 , wherein R S ≈R 1 √{square root over (1+k 2 Q 1 Q 2 )}.
3. The method as recited in claim 1 , further comprising:
approximately matching a load impedance of the second coil, R 1 , with a source impedance of the first coil, R S , wherein R L ≈R 2 √{square root over (1+k 2 Q 1 Q 2 )}.
4. The method as recited in claim 1 , wherein the moveable member measures a borehole diameter.
5. The method as recited in claim 1 , wherein the moveable member includes at least one of an electromagnetic measurement sensor, a nuclear measurement sensor, and an acoustic measurement sensor.
6. The method as recited in claim 1 , wherein the moveable member is a moveable caliper arm or a moveable pad.
7. The method as recited in claim 1 , wherein the moveable member is an under-reamer arm.
8. The method as recited in claim 1 , wherein the first coil is coupled to the drill collar and the second coil is coupled to the movable member so that power is transmitted from the first coil to the second coil as a function of a distance between the movable member and the drill collar.
9. The method as recited in claim 1 , wherein the moveable member comprises a plurality of movable members each coupled to the drill collar, wherein each of the plurality of movable members has a second coil coupled thereto and each second coil has a corresponding first coil coupled to the drill collar, and wherein each first coil transmits power to a corresponding second coil whereby the corresponding movable member moves between an open position and a closed position.
10. The method as recited in claim 1 , further comprising monitoring the position of the movable member relative to the drill collar.
11. A logging while drilling apparatus, comprising:
a drill collar;
a moveable member coupled to the drill collar;
a first coil coupled within the drill collar;
a second coil coupled within the moveable member;
wherein the first and second coils are coupled with a coupling coefficient, k, wherein, k=M/√{square root over (L 1 L 2 )}≦0.9, M is a mutual inductance between the first and second coils, L 1 is a first self-inductance of the first coil, and L 2 is a second self-inductance of the second coil, and
wherein the first coil is resonantly tuned at a first frequency, f 1 , with a first capacitance, C 1 ,
wherein the second coil is resonantly tuned at a second frequency, f 2 , with a second capacitance, C 2 , wherein f 1 is approximately equal to f 2 ,
f
1
=
1
2
π
L
1
C
1
and
f
2
=
1
2
π
L
2
C
2
,
and wherein the first and second coils have a figure of merit, U, wherein
U
=
k
Q
1
Q
2
≥
3
,
Q
1
=
2
π
f
1
L
1
R
1
,
Q
2
=
2
π
f
2
L
2
R
2
,
Q 1 and Q 2 comprise respective quality factors associated with the first and second coils, and R 1 and R 2 comprise respective resistances of the first and second coils.
12. The apparatus as recited in claim 11 , wherein a source impedance of the first coil, R S is approximately matched with a load impedance of the second coil, R 1 , wherein R S ≈R 1 √{square root over (1+k 2 Q 1 Q 2 )}.
13. The apparatus as recited in claim 11 , wherein a load impedance of the second coil, R 1 , is approximately matched with a source impedance of the first coil, R S , wherein R L ≈R 2 √{square root over (1+k 2 Q 1 Q 2 )}.
14. The apparatus as recited in claim 11 , wherein the moveable member measures a borehole diameter.
15. The apparatus as recited in claim 11 , wherein the moveable member includes at least one of an electromagnetic measurement sensor, a nuclear measurement sensor, and an acoustic measurement sensor.
16. The apparatus as recited in claim 11 , wherein the moveable member is a caliper arm.
17. The apparatus as recited in claim 11 , wherein the moveable member is an under-reamer blade.
18. The apparatus as recited in claim 11 , wherein the moveable member is a moveable pad.
19. The apparatus as recited in claim 11 , wherein the moveable member is coupled to the drill collar in such a way that the movable member is urged in the open position.
20. The apparatus as recited in claim 11 , wherein the first coil comprises a multi-turn coil wrapped on a ferrite core, wherein the second coil comprises a multi-turn coil wrapped on a ferrite core, and wherein the first coil is coupled to the drill collar and the second coil is coupled to the movable member such that magnetic poles of the first coil and the magnetic poles of the second coil are aligned with an axis of the drill collar.
21. The apparatus as recited in claim 11 , wherein the moveable member comprises a plurality of movable members each coupled to the drill collar, wherein each of the plurality of movable members has a second coil coupled thereto and each second coil has a corresponding first coil coupled to the drill collar, and wherein each first coil transmits power to a corresponding second coil whereby the corresponding movable member moves between an open position and a closed position.