Systems and methods to utilize sensors to provide spatial resolution in downhole leak detection

1. A method of downhole leak detection, comprising:

positioning a physical sensor in a wellbore;

wherein the physical sensor consists of only a hydrophone, electromagnetic sensor, or chemical sensor;

moving the physical sensor along the wellbore;

recording a plurality of samples of physical signals detected by the physical sensor while moving the physical sensor along the wellbore;

identifying frames of correlated sequences observed in the plurality of samples provided by the physical sensor;

performing a coherent sequence extraction operation on the physical signals of the physical sensor to obtain a plurality of virtual signals associated with an array of virtual sensors;

constructing a covariance matrix based on the correlated sequences and the plurality of virtual signals;

computing a spatial spectrum that indicates a location of a leak in the wellbore based on the covariance matrix; and

utilizing a beamforming technique to determine a localized peak of the spatial spectrum, wherein the localized peak is indicative of the location of the leak.

2. The method of claim 1 , further comprising determining an approximate radial distance of the leak relative to the at least one physical sensor, wherein the location of the leak is expressed by the approximate radial distance.

3. The method of claim 2 , wherein the approximate radial distance comprises two components along two perpendicular axes that form a plane along which the first physical sensor is displaced, and wherein determining the approximate radial distance comprises determining a distance along a first component (x-axis) and a distance along a second component (y-axis).

4. The method of claim 3 , wherein the radial distance comprises a third component along an axis (z-axis) normal to the plane along which the first physical sensor is displaced, and wherein determining the approximate radial distance comprises determining a distance along the third component.

5. The method of claim 1 , further comprising:

determining a temporal correction factor of the virtual signals corresponding to the array of virtual sensors;

determining a modeled transfer function of the virtual signals corresponding to the array of virtual sensors;

calculating a virtual weight of the array of virtual sensors relative to the first physical sensor based on the temporal correction factor and the modeled transfer function; and

applying the virtual weight to one or more values of the covariance matrix that represent the virtual signals corresponding to the array of virtual sensors.

6. The method of claim 1 , wherein the covariance matrix based on the correlated sequences comprises a source component, a temporal delay component, and a propagation and attenuation component.

7. The method of claim 1 , wherein the physical sensor is traveling along the wellbore at an approximately constant velocity.

8. The method of claim 1 , wherein a processor is communicatively coupled to the physical sensor; and wherein the recording a plurality of samples of physical signals is performed by the processor.

9. The method of claim 8 , wherein the processor is a component of a surface-based electronic device.

10. The method of claim 8 , wherein the physical sensor and the processor are components of a leak detector and wherein the processor is disposed inside a casing of the leak detector.

11. A downhole leak detection system comprising:

a leak detector having a physical sensor, the physical sensor operable to travel along a wellbore and to detect physical signals that indicate a leak proximate the physical sensor; wherein the physical sensor consists of only a hydrophone, electromagnetic sensor, or chemical sensor; and

a processor communicatively coupled to the leak detector and operable to:

record a plurality of samples of physical signals detected by the physical sensor while traveling along the wellbore;

identify frames of correlated sequences observed in the plurality of samples provided by the physical sensor;

performing a coherent sequence extraction operation on the physical signals of the physical sensor to obtain a plurality of virtual signals associated with an array of virtual sensors;

construct a covariance matrix based on the correlated sequences and the plurality of virtual signals;

compute a spatial spectrum that indicates a location of a leak in the wellbore based on the covariance matrix; and

utilize a beamforming technique to determine a localized peak of the spatial spectrum, wherein the localized peak indicates the location of the leak.

12. The downhole leak detection system of claim 11 , wherein the processor is further operable to:

determine a temporal correction factor of the virtual signals corresponding to the array of virtual sensors;

determine a modeled transfer function of the virtual signals corresponding to the array of virtual sensors;

calculate a virtual weight of the array of virtual sensors relative to the physical sensor based on the temporal correction factor and the modeled transfer function; and

apply the virtual weight to one or more values of the covariance matrix that represent the virtual signals corresponding to the virtual sensor.

13. The downhole leak detection system of claim 11 , wherein the processor is a component of the leak detector and is disposed inside a casing of the leak detector.

14. The downhole leak detection system of claim 11 , wherein the processor is a component of a surface-based electronic device.

15. The downhole leak detection system of claim 11 , wherein the covariance matrix based on the correlated sequences comprises a source component, a temporal delay component, and a propagation and attenuation component.

16. The downhole leak detection system of claim 11 , wherein the physical sensor is traveling along the wellbore at an approximately constant velocity.

17. A non-transitory machine-readable medium comprising instructions stored therein, for execution by a processor, which when executed by the processor, causes the processor to perform operations comprising:

recording a plurality of samples of physical signals detected by a physical sensor traveling along a wellbore; wherein the physical sensor consists of only a hydrophone, electromagnetic sensor, or chemical sensor;

identifying frames of correlated sequences observed in the plurality of samples provided by the physical sensor;

performing a coherent sequence extraction operation on the physical signals of the physical sensor to obtain a plurality of virtual signals associated with an array of virtual sensors;

constructing a covariance matrix based on the correlated sequences and the plurality of virtual signals;

computing a spatial spectrum that indicates a location of a leak in the wellbore based on the covariance matrix; and

utilizing a beamforming technique to determine a localized peak of the spatial spectrum, wherein the localized peak indicates the location of the leak.

18. The non-transitory machine-readable medium of claim 17 , further comprising instructions stored therein, which when executed by the processor, causes the processor to perform operations comprising:

determining a temporal correction factor of the virtual signals corresponding to the array of virtual sensors;

determining a modeled transfer function of the virtual signals corresponding to the array of virtual sensors;

calculating a virtual weight of the array of virtual sensors relative to the physical sensor based on the temporal correction factor and the modeled transfer function;

determining a true steering vector of the virtual signals corresponding to a virtual sensor of the array of virtual sensors; and

applying the true steering vector and the virtual weight to one or more values of the covariance matrix that represent the virtual signals corresponding to the virtual sensor.

19. The non-transitory machine-readable medium of claim 17 , wherein detecting the correlated sequences from the physical signals comprises:

determining correlated sequences of the physical signals detected by the physical sensor; and

concatenating the correlated sequences into a multichannel representation of the correlated sequences.

20. The non-transitory machine-readable medium of claim 19 , wherein the multichannel representation of the correlated sequences comprises a source component, a temporal delay component, and a propagation and attenuation component.