# US 9,752,428 B2 · Methods and apparatus to acquire compensated signals for determination of formation parameters

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- Number: US 9,752,428 B2
- Document ID: US9752428B2
- Status: Granted
- Kind: B2
- Application number: 14/431,887
- Filed: 2012-12-18
- Published: 2015-08-27
- Granted: 2017-09-05
- Earliest claimed: 2012-12-18
- Assignees: Halliburton Energy Services, Inc.
- Applicants: Halliburton Energy Services, Inc.
- Inventors: Hsu-Hsiang Wu; Burkay Donderici
- Web page: https://patentgrep.com/patent/US9752428B2

## CPC

- E21B 47/13: by electromagnetic energy, e.g. radio frequency
- E21B 49/00: Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
- G01V 3/28: using induction coils
- G01V 3/34: Transmitting data to recording or processing apparatus; Recording data
- G01V 3/38: Processing data, e.g. for analysis, for interpretation, for correction
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02)

## Abstract

Various embodiments include apparatus and methods to operate a measurement process in a borehole that uses a symmetric sensor structure or a sensor structure operable to mimic a symmetric sensor structure to provide structural compensation. Apparatus and methods can include a data processing unit to generate compensated signals based on the measurement signals and to determine formation parameters using the compensated signals. Additional apparatus, systems, and methods are disclosed.

## Claims

### Claim 1

A method comprising:
making signal measurements using a symmetric sensor tool, wherein the symmetric sensor tool includes a tool structure on which an upper crossed sensor structure, a lower crossed sensor structure, an upper tilted sensor, and a lower tilted sensor are disposed in a symmetric arrangement with respect to a longitudinal axis of the tool structure such that the upper crossed sensor structure and the upper tilted sensor are spaced apart by a distance at which the lower crossed sensor structure and the lower tilted sensor are spaced apart, the upper crossed sensor structure formed by two co-located tilted sensors and the lower crossed sensor structure formed by two co-located tilted sensors;
generating ZZ, XZ, ZX, and XX coupling components of a relationship between transmitted signals and received signals relative to a formation from the signal measurements;
generating a set of compensated signals from the coupling components; and
performing an inversion operation using the set of compensated signals to determine one or more formation parameters.

### Claim 2 (depends on 1)

The method of claim 1, wherein the upper tilted sensor and the lower tilted sensor are tilted antenna transmitters and the upper crossed sensor structure and the lower crossed sensor structure are tilted receiver antennas with the upper crossed sensor structure and the lower crossed sensor structure disposed between the upper tilted sensor and the lower tilted sensor.

### Claim 3 (depends on 2)

The method of claim 2, wherein making signal measurements includes firing the upper tilted sensor and collecting signals at each of the tilted antenna receivers of the upper crossed sensor structure in response to firing the upper tilted sensor and the lower crossed sensor structure, and firing the lower tilted sensor and collecting signals at each of the tilted antenna receivers of the upper crossed sensor structure and the lower crossed sensor structure in response to firing the upper tilted sensor and the lower crossed sensor structure.

### Claim 4 (depends on 2)

The method of claim 2, wherein generating the set of compensated signals includes generating
SignalijComp≡√{square root over (VT1-R1R2R3R4ij×VT2-R1R2R3R4ij)},
where i and j indicate different coupling components, VT1-R1R2R3R4ij is a coupling component derived from receiving a signal in each of antenna receivers R1, R2, R3, R4, in response to firing antenna transmitter T1, and VT2-R1R2R3R4ij is a coupling component derived from receiving a signal in each of antenna receivers R1, R2, R3, R4 in response to firing antenna transmitter T2, antenna transmitter T1 being the upper tilted sensor, antenna transmitter T2 being the lower tilted sensor, R1 and R2 forming the upper crossed sensor structure, R3 and R4 forming the lower crossed sensor structure.

### Claim 5 (depends on 1)

The method of claim 1, wherein generating the set of compensated signals from the coupling components includes generating compensated signals as
SignaliComp≡√{square root over (SignaliTup×SignaliTdn)}; i=1, 2, 3, 4, or 5,
with T up being the upper tilted sensor and SignaliTup based on coupling components generated with respect to firing the upper tilted sensor, and Tdn being the lower tilted sensor and SignaliTdn based on coupling components generated with respect to firing the lower tilted sensor.

### Claim 6 (depends on 5)

The method of claim 5, wherein generating SignaliTup and SignaliTdn includes generating, for Tup and Tdn, one or more of
Signal1T=Vzz(d1)/Vzz(d2), T=Tup, Tdn
Signal2T=SQRT(Vxx(d1)/Vzz(d1)×Vxx(d2)/Vzz(d2)), T=Tup, Tdn
Signal3T=SQRT(Vyy(d1)/Vzz(d1)×Vyy(d2)/Vzz(d2)), T=Tup, Tdn
Signal4T=SQRT(Vxx(d1)/Vyy(d1)×Vxx(d2)/Vyy(d2)), T=Tup, Tdn
Signal5T=SQRT((1+[(Vxz(d1)+Vzx(d1))/(½Vxx(d1)+½Vyy(d1)+Vzz(d1))])×(1+[(Vxz(d2) +Vzx(d2))/(½Vxx(d2)+½Vyy(d2)+Vzz(d2))])), T=Tup, Tdn,
Vzz, Vxx, Vzz, Vxz, and Vzx being coupling components, d1 and d2 being separation distances of the symmetric sensor tool.

### Claim 7 (depends on 1)

The method of claim 1, wherein the upper tilted sensor and the lower tilted sensor are tilted antenna receivers and the upper crossed sensor structure and the lower crossed sensor structure are tilted transmitter antennas with the upper tilted sensor and the lower tilted sensor disposed between the upper crossed sensor structure and the lower crossed sensor structure.

### Claim 8 (depends on 1)

The method of claim 1, wherein performing the inversion operation includes performing zero dimension inversion.

### Claim 9 (depends on 8)

The method of claim 8, wherein the method includes using results from the zero dimension inversion to construct an initial formation model in higher-order dimensional inversion.

### Claim 10 (depends on 1)

The method of claim 1, wherein the method includes determining formation vertical resistivity or a ratio of formation vertical resistivity to formation horizontal resistivity.

### Claim 11 (depends on 1)

The method of claim 1, wherein the method includes determining formation parameters in a formation having multiple layers.

### Claim 12

A method comprising:
operating a tool in a borehole, the tool having an asymmetric sensor structure;
making signal measurements, using the asymmetric sensor structure, corresponding to a symmetric sensor tool, the signal measurements collected by shifting the asymmetric sensor structure and taking measurements at the shifted locations such that the asymmetric sensor structure mimics the symmetric sensor tool;
generating ZZ, XZ, ZX, and XX coupling components of a relationship between transmitted signals and received signals relative to a formation from the signal measurements;
generating a set of compensated signals from the coupling components including generating compensated signals as
SignaliComp≡√{square root over (SignaliTup×SignaliTdn)}; i=1, 2, 3, 4, or 5,
with Tup being an upper tilted sensor of an asymmetric antenna and SignaliTupbased on coupling components generated with respect to firing the upper tilted sensor, and Tdn being a lower tilted sensor of the asymmetric antenna and SignaliTdn n based on coupling components generated with respect to firing the lower tilted sensor; and
performing an inversion operation using the set of compensated signals to determine one or more formation parameters.

### Claim 13 (depends on 12)

The method of claim 12, wherein generating the set of compensated signals includes generating
SignalijComp≡√{square root over (VT1-R1R2R3R4ij×VT2-R1R2R3R4ij)},
where i and j indicate different coupling components, R1, R2, R3, and R4 correspond to mimicked receivers in shifting the asymmetric sensor structure, VT1-R1R2R3R4ij is a coupling component derived from receiving a signal in each of mimicked antenna receivers R1, R2, R3, and R4 in response to firing antenna transmitter T1, and VT2-R1R2R3R4ij is a coupling component derived from receiving a signal in each of mimicked antenna receivers R1, R2, R3, and R4 in response to firing antenna transmitter T2.

### Claim 14 (depends on 12)

The method of claim 12, wherein generating SignaliTup and SignaliTdn includes generating, for Tup and Tdn, one or more of,
Signal1T=Vzz(d1)/Vzz(d2), T=Tup, Tdn
Signal2T=SQRT(Vxx(d1)/Vzz(d1)×Vxx(d2)/Vzz(d2)), T=Tup, Tdn
Signal3T=SQRT(Vyy(d1)/Vzz(d1)×Vyy(d2)/Vzz(d2)), T=Tup, Tdn
Signal4T=SQRT(Vxx(d1)/Vyy(d1)×Vxx(d2)/Vyy(d2)), T=Tup, Tdn
Signal5T=SQRT((1+[(Vxz(d1)+Vzx(d1))/(½Vxx(d1)+½Vyy(d1)+Vzz(d1))])×(1+[(Vxz(d2) +Vzx(d2))/(½Vxx(d2)+½Vyy(d2)+Vzz(d2))])), T=Tup, Tdn,
Vzz, Vxx, Vzz, Vxz, and Vzx being coupling components, d1 and d2 being separation distances of the symmetric sensor tool.

### Claim 15 (depends on 12)

The method of claim 12, wherein performing the inversion operation includes performing zero dimension inversion.

### Claim 16 (depends on 12)

The method of claim 12, wherein the method includes determining formation vertical resistivity or a ratio of formation vertical resistivity to formation horizontal resistivity.