Concentric buttons of different sizes for imaging and standoff correction
A method of estimating standoff in a borehole through an earth formation, includes: disposing a sensor including a plurality of return electrodes and at least one transmitter electrode disposed in a concentric arrangement into the borehole; injecting current, I, into the formation by applying at least two frequencies of alternating current (AC) voltage between at least two of the electrodes; measuring impedance, Z, for each of the frequencies; and using a predetermined relationship between impedance, Z, and standoff, estimating the standoff. A system and a computer program product are provided.
1. A method of estimating a property of an earth formation traversed by a borehole, the method comprising:
disposing into the borehole a sensor comprising a plurality of return electrodes and at least one transmitter electrode disposed in a concentric arrangement;
injecting a first current, I 1 , of a first frequency, f 1 , into the formation by applying an alternating current (AC) voltage between first selected ones of the plurality of return electrodes and the at least one transmitter electrode;
injecting a second current, I 2 , of a first frequency, f 2 , into the formation by applying an alternating current (AC) voltage between second selected ones of the plurality of return electrodes and the at least one transmitter electrode;
measuring effective impedance, Z e , for each of the currents; and
using a predetermined relationship between at least one of the effective impedance, Z e , and standoff, to estimate the standoff between the sensor and the borehole.
2. The method as in claim 1 , wherein the first selected ones and the second selected ones are selected to vary an apparent size of the sensor.
3. The method as in claim 1 , further comprising determining a resistivity of a gap, R g , between the sensor and the formation.
4. The method as in claim 1 , further comprising determining a resistivity of the formation, R f .
5. The method as in claim 1 , further comprising determining a capacitance, C, between the formation and an electrode injecting at least one of the first current, I 1 , and the second current, I 2 .
6. The method as in claim 1 , further comprising fitting a curve to the effective impedance measurements.
7. The method as in claim 1 , further comprising selecting the selected ones to modify an effective size of at least one of the return electrode and the transmitter electrode.
8. The method as in claim 7 , wherein the selecting comprises performing switching between the electrodes.
9. The method as in claim 1 , further comprising determining a geometric factor, G, for the sensor.
10. The method as in claim 1 , further comprising determining an imaginary part of the effective impedance, Z e .
11. The method as in claim 1 , wherein the predetermined relationship comprises at least one of a graph, a table of values, and a mathematical function.
12. A system for correcting imaging of an earth formation traversed by a borehole, the system comprising:
a sensor disposed into the borehole, the sensor comprising a plurality of return electrodes and at least one transmitter electrode disposed in a concentric arrangement;
a processor coupled to the sensor and a power supply, the processor comprising machine executable instructions stored therein for imaging the formation by:
injecting a first current, I 1 , of a first frequency, f 1 , into the formation by applying an alternating current (AC) voltage between first selected ones of the plurality of return electrodes and the at least one transmitter electrode;
injecting a second current, I 2 , of a second frequency, f 2 , into the formation by applying an alternating current (AC) voltage between second selected ones of the plurality of return electrodes and the at least one transmitter electrode;
measuring effective impedance, Z e , for each of the currents;
using a predetermined relationship between standoff and at least one of effective impedance, Z e , and a geometric factor, G, to estimate the standoff, S, between the sensor and the borehole; and
correcting the imaging according to the standoff, S.
13. The system as in claim 12 , wherein the geometric factor, G, is estimated according to a relationship comprising:
G·Re ( Ż )= R f ;
where Re(Ż) represents a real part of measured impedance and R f represents a resistivity of the formation.
14. The system as in claim 12 , wherein effective impedance, Z e , is estimated according to a relationship comprising:
Z
e
=
Z
T
+
Z
G
+
R
f
=
U
I
;
where I represents the current for a selected frequency, U represents the voltage for the selected frequency, Z g represents an impedance in a gap between the sensor and the formation, Z T represents an impedance of the sensor; and R f represents a resistivity of the formation.
15. The system as in claim 12 , wherein the geometric factor, G, is estimated according to a relationship comprising:
B
1
ω
1
-
B
2
ω
2
A
1
-
A
2
=
G
=
Cr
;
where A 1 , A 2 and B 1 , B 2 correspond to a real part of the impedances and an imaginary part of the impedances for the effective impedance at the first frequency, Z e1 , and the effective impedance at the second frequency, Z e2 .
16. The system as in claim 12 , further comprising estimating a resistivity of the formation, R f , according to a relationship comprising:
R
f
=
A
1
-
(
ω
1
C
)
2
r
r
2
+
(
ω
1
C
)
2
=
A
2
-
(
ω
2
C
)
2
r
r
2
+
(
ω
2
C
)
2
where A 1 , A 2 correspond to a real part of the impedance for the first frequency and the second frequency, respectively, and C represents capacitance between an electrode and the formation.
17. The system as in claim 12 , wherein a resistivity of the gap, R g , may be estimated according to a relationship comprising:
R
g
=
(
A
1
-
A
2
)
/
(
1
1
+
(
ω
1
G
)
2
-
1
1
+
(
ω
2
G
)
2
)
where A 1 , A 2 correspond to a real part of the impedance for the first frequency and the second frequency, respectively.
18. The system as in claim 12 , wherein an image of the formation is generated using measurements from electrodes that satisfy the condition B/S is greater than or equal to 3, where B and S denote an effective size of the electrode and a value of the standoff, respectively.
19. A computer program product comprising machine readable instructions stored on machine readable media, the instructions for imaging an earth formation using a sensor comprising a plurality of return electrodes and at least one transmitter electrode disposed in a concentric arrangement, by implementing instructions for:
injecting a first current, I 1 , of a first frequency, f 1 , into the formation by applying an alternating current (AC) voltage between first selected ones of the plurality of return electrodes and the at least one transmitter electrode;
injecting a second current, I 2 , of a second frequency, f 2 , into the formation by applying an alternating current (AC) voltage between second selected ones of the plurality of return electrodes and the at least one transmitter electrode;
measuring effective impedance, Z e , for each of the currents;
using a predetermined relationship between standoff and at least one of effective impedance, Z e , and a geometric factor, G, estimating the standoff, S; and
correcting the imaging according to the standoff, S.