System for determination of measured depth (MD) in wellbores from downhole pressure sensors using time of arrival techniques

1. A system for estimating measured depth of a borehole, the system comprising:

a drilling fluid pulse telemetry system positioned in a borehole, the drilling fluid pulse telemetry system comprising an environmental sensor package and a drilling fluid pulser; and

one or more processors and a non-transitory computer-readable medium having executable instructions, which when executed, cause the one or more processors to perform operations of:

continuously obtaining time series measurements from the environmental sensor package, the times series measurements comprising source signals and reflected signals;

determining initial estimates of a time delay and path attenuation amplitude from the time series measurements;

determining an L2 error for the initial estimates of the time delay and the path attenuation amplitude;

performing iterative minimization of the L2 error until a set of source signal parameters converge, resulting in a least squares estimate of the source signal and the reflected signals;

using the least squares estimate to obtain time delay values; and

using the time delay values to continuously generate an estimate of a measured depth of the borehole.

2. The system as set forth in claim 1 , wherein the environmental sensor package comprises a drilling fluid pressure transducer and a drilling fluid temperature sensor.

3. The system as set forth in claim 2 , wherein the time delay values represent a time of flight between acoustic pulses generated by the drilling fluid pulser as measured by the drilling fluid pressure transducer and a received surface echo.

4. The system as set forth in claim 1 , wherein the time delay values are directly correlated with the estimated measured depth of the borehole.

5. The system as set forth in claim 1 , wherein the one or more processors further perform an operation of estimating arrival times of overlapping signals from a noisy received waveform.

6. The system as set forth in claim 1 , wherein the generated estimate is used to guide a downhole tool to a positional target.

7. A computer implemented method for estimating measured depth of a borehole, comprising an act of causing one or more processors to execute instructions stored on a non-transitory memory such that upon execution, the one or more processors perform operations of:

continuously obtaining time series measurements from an environmental sensor package, the times series measurements comprising source signals and reflected signals;

determining initial estimates of a time delay and path attenuation amplitude from the time series measurements;

determining an L2 error for the initial estimates of the time delay and the path attenuation amplitude;

performing iterative minimization of the L2 error until a set of source signal parameters converge, resulting in a least squares estimate of the source signal and the reflected signals;

using the least squares estimate to obtain time delay values; and

using the time delay values, continuously generating an estimate of a measured depth of the borehole.

8. The method as set forth in claim 7 , wherein the environmental sensor package comprises a drilling fluid pressure transducer and a drilling fluid temperature sensor.

9. The method as set forth in claim 8 , wherein the time delay values represent a time of flight between acoustic pulses generated by the drilling fluid pulser as measured by the drilling fluid pressure transducer and a received surface echo.

10. The method as set forth in claim 7 , wherein the time delay values are directly correlated with the estimated measured depth of the borehole.

11. The method as set forth in claim 7 , wherein the one or more processors further perform an operation of estimating arrival times of overlapping signals from a noisy received waveform.

12. The method as set forth in claim 7 , wherein the generated estimate is used to guide a downhole tool to a positional target.

13. A computer program product for estimating measured depth of a borehole, the computer program product comprising:

computer-readable instructions stored on a non-transitory computer-readable medium that are executable by a computer having one or more processors for causing the processor to perform operations of:

continuously obtaining time series measurements from an environmental sensor package, the times series measurements comprising source signals and reflected signals;

determining initial estimates of a time delay and path attenuation amplitude from the time series measurements;

determining an L2 error for the initial estimates of the time delay and the path attenuation amplitude;

performing iterative minimization of the L2 error until a set of source signal parameters converge, resulting in a least squares estimate of the source signal and the reflected signals;

using the least squares estimate to obtain time delay values; and

using the time delay values, continuously generating an estimate of a measured depth of the borehole.

14. The computer program product as set forth in claim 13 , wherein the environmental sensor package comprises a drilling fluid pressure transducer and a drilling fluid temperature sensor.

15. The computer program product as set forth in claim 14 , wherein the time delay values represent a time of flight between acoustic pulses generated by the drilling fluid pulser as measured by the drilling fluid pressure transducer and a received surface echo.

16. The computer program product as set forth in claim 13 , wherein the time delay values are directly correlated with the estimated measured depth of the borehole.

17. The computer program product as set forth in claim 13 , further comprising instructions for causing the one or more processors to further perform an operation of estimating arrival times of overlapping signals from a noisy received waveform.