# US 11,905,816 B2 · Casing thickness estimation by frequency correlation

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- Number: US 11,905,816 B2
- Document ID: US11905816B2
- Status: Granted
- Kind: B2
- Application number: 16/062,051
- Filed: 2016-03-03
- Published: 2018-12-20
- Granted: 2024-02-20
- Earliest claimed: 2016-03-03
- Assignees: Halliburton Energy Services, Inc.
- Applicants: Halliburton Energy Services, Inc.
- Inventors: Zhijuan Zhang; Nazareth Bedrossian
- Web page: https://patentgrep.com/patent/US11905816B2

## CPC

- E21B 47/00: Survey of boreholes or wells (monitoring pressure or flow of drilling fluid E21B21/08)
- E21B 47/005: Monitoring or checking of cementation quality or level
- E21B 47/007: Measuring stresses in a pipe string or casing (for locating blocked portions of pipes E21B47/09)
- G01V 1/282: {Application of seismic models, synthetic seismograms}
- G01V 1/284: {Application of the shear wave component and/or several components of the seismic signal}
- G01V 1/50: Analysing data
- G01V 2210/1299: Subsurface, e.g. in borehole or below weathering layer or mud line
- G01V 2210/1429: Subsurface, e.g. in borehole or below weathering layer or mud line
- G01V 2210/43: Spectral
- G01V 2210/614: Synthetically generated data
- 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

The thickness of borehole casing can be determined by ultrasound logging in conjunction with simulations of ultrasonic plane-wave echo waveforms across a range of frequencies for a plurality of casing thicknesses and correlation of synthetic frequency spectra derived from the simulated plane-wave echo waveforms for the various casing thicknesses against the frequency spectrum of a measured pulse-echo waveform. In accordance with various embodiments, a portion of the measured pulse-echo waveform that corresponds to the first reflection off the interface between the borehole casing and the borehole fluid is used as a driving pulse to weight the simulated plane-wave echo waveforms in the synthetic frequency spectrum.

## Claims

### Claim 1

A method comprising:
measuring a pulse-echo waveform with an ultrasonic logging tool disposed interior to a borehole casing;
extracting, from the measured pulse-echo waveform, a reflection portion corresponding to a reflection off an interface between the borehole casing and a borehole fluid contained within the borehole casing;
computing, for each of a plurality of casing thicknesses, a synthetic frequency spectrum as a weighted sum of plane-wave echo waveforms simulated for the respective casing thickness across a range of frequencies, using the reflection portion extracted from the measured pulse-echo waveform as a driving pulse to weight the simulated plane-wave echo waveforms;
correlating a frequency spectrum of the measured pulse-echo waveform with the synthetic frequency spectra computed for the plurality of casing thicknesses to obtain a correlation coefficient as a function of casing thickness; and
determining a thickness of the borehole casing based on a maximum of the correlation coefficient.

### Claim 2 (depends on 1)

The method of claim 1, further comprising simulating the plane-wave echo waveforms for the plurality of casing thicknesses and across the range of frequencies.

### Claim 3 (depends on 2)

The method of claim 2, further comprising measuring a velocity of sound in the borehole fluid with a mud cell disposed interior to the borehole casing.

### Claim 4 (depends on 3)

The method of claim 3, wherein the measured velocity of sound in the borehole fluid is used in simulating the plane-wave echo waveforms.

### Claim 5 (depends on 2)

The method of claim 2, wherein the plane-wave echo waveforms are simulated based on a three-layer model of the borehole fluid, the borehole casing, and cement surrounding the borehole casing.

### Claim 6 (depends on 1)

The method of claim 1, wherein the frequency spectrum of the measured pulse-echo waveform is derived from the measured pulse-echo waveform by Fourier transform.

### Claim 7 (depends on 1)

The method of claim 1, wherein the thickness of the borehole casing exceeds 0.7″ and is determined with a margin of error of less than 0.05″.

### Claim 8

A system comprising:
an ultrasonic logging tool to measure a pulse-echo waveform in a borehole casing; and
circuitry to process the measured pulse-echo waveform by
extracting, from the measured pulse-echo waveform, a reflection portion corresponding to a reflection off an interface between the borehole casing and a borehole fluid contained within the borehole casing;
computing, for each of a plurality of casing thicknesses, a synthetic frequency spectrum as a weighted sum of plane-wave echo waveforms simulated for the respective casing thickness across a range of frequencies, using the reflection portion extracted from the measured pulse-echo waveform as a driving pulse to weight the simulated plane-wave echo waveforms;
correlating a frequency spectrum of the measured pulse-echo waveform with the synthetic frequency spectra computed for the plurality of casing thicknesses to obtain a correlation coefficient as a function of casing thickness; and
determining a thickness of the borehole casing based on a maximum of the correlation coefficient.

### Claim 9 (depends on 8)

The system of claim 8, wherein the ultrasonic logging tool comprises a rotating ultrasonic transducer.

### Claim 10 (depends on 8)

The system of claim 8, wherein the ultrasonic logging tool comprises a mud cell for measuring a velocity of sound in the borehole fluid.

### Claim 11 (depends on 8)

The system of claim 8, wherein the circuitry is further configured to simulate the plane-wave echo waveforms.

### Claim 12 (depends on 11)

The system of claim 11, wherein the circuitry is configured to simulate the plane-wave echo waveforms based on a three-layer model of the borehole fluid, the borehole casing, and cement surrounding the borehole casing.

### Claim 13 (depends on 8)

The system of claim 8, wherein the circuitry comprises memory storing the simulated plane-wave echo waveforms for the plurality of casing thicknesses across the range of frequencies.

### Claim 14 (depends on 8)

The system of claim 8, wherein the circuitry is implemented in a surface logging facility.

### Claim 15

A machine-readable medium storing instructions for processing pulse-echo waveforms measured in a borehole casing to determine a thickness of the borehole casing, the instructions, when executed by one or more processors, cause the one or more processors to
extract, from the measured pulse-echo waveform, a reflection portion corresponding to a reflection off an interface between the borehole casing and a borehole fluid contained within the borehole casing;
compute, for each of a plurality of casing thicknesses, a synthetic frequency spectrum as a weighted sum of plane-wave echo waveforms simulated for the respective casing thickness across a range of frequencies, using the reflection portion extracted from the measured pulse-echo waveform as a driving pulse to weight the simulated plane-wave echo waveforms;
correlate a frequency spectrum of the measured pulse-echo waveform with the synthetic frequency spectra computed for the plurality of casing thicknesses to obtain a correlation coefficient as a function of casing thickness; and
determine a thickness of the borehole casing based on a maximum of the correlation coefficient.

### Claim 16 (depends on 15)

The machine-readable medium of claim 15, wherein the instructions, when executed by the one or more processors, further cause the one or more processors to simulate the plane-wave echo waveforms for the plurality of casing thicknesses and across the range of frequencies.

### Claim 17 (depends on 16)

The machine-readable medium of claim 16, wherein the instructions, when executed by the one or more processors, further cause the one or more processors to use a measured velocity of sound in the borehole fluid when simulating the plane-wave echo waveforms.

### Claim 18 (depends on 15)

The machine-readable medium of claim 15, wherein the instructions, when executed by the one or more processors, further cause the one or more processors to simulate the plane-wave echo waveforms based on a three-layer model of the borehole fluid, the borehole casing, and cement surrounding the borehole casing.

### Claim 19 (depends on 15)

The machine-readable medium of claim 15, wherein the instructions, when executed by the one or more processors, further cause the one or more processors to derive the frequency spectrum of the measured pulse-echo waveform from the measured pulse-echo waveform by Fourier transform.

### Claim 20 (depends on 15)

The machine-readable medium of claim 15, wherein the instructions, when executed by the one or more processors, cause the one or more processors to determine the thickness of the borehole casing with a margin of error of less than 0.05″.