Magnetic induction based localization for wireless sensor networks in underground oil reservoirs

1. A method comprising:

measuring, by each of a plurality of sensors in a wireless underground sensor network (WUSN) in a hydrocarbon reservoir, corresponding received magnetic field strengths (RMFSs) on a plurality of respective magnetic induction (MI) links forming an MI network linking the plurality of sensors and at least two anchor devices to each other, wherein the plurality of sensors are disposed at respective sensor locations within the hydrocarbon reservoir, wherein the at least two anchor devices are disposed at respective anchor device locations on a dipole antenna inside the hydrocarbon reservoir, and wherein locations of the at least two anchor devices are known;

transmitting, by each of the plurality of sensors based on magnetic induction, the corresponding RMFSs to at least one anchor device over the MI network;

determining a set of distances from the received RMFSs, wherein the determined set of distances represents an estimate of distances between the respective sensor locations of the plurality of sensors and the respective anchor device locations of the at least two anchor devices in the WUSN;

establishing an MI-based localization framework by applying a sequence of algorithms to the determined set of distances and the known locations of the at least two anchor devices, wherein applying the sequence of algorithms comprises first applying a weighted maximum likelihood estimation (WMLE) and then applying a semi-definite programming (SDP) relaxation to the determined set of distances and the known locations of the at least two anchor devices;

after establishing the MI-based localization framework, determining a first set of sensor locations, wherein the determined first set of sensor locations represents a first estimate of locations of the respective sensor locations within the hydrocarbon reservoir; and

after determining the first set of sensor locations, determining a second set of sensor locations based on the determined first set of sensor locations, wherein the determined second set of sensor locations represents a second estimate of locations of the respective sensor locations within the hydrocarbon reservoir.

2. The method of claim 1 , wherein determining the first set of sensor locations comprises applying an alternating direction augmented Lagrangian method (ADM) to the established MI-based localization framework.

3. The method of claim 2 , wherein determining the second set of sensor locations comprises applying a conjugate gradient algorithm (CGA) to the determined first set of sensor locations.

4. The method of claim 1 , wherein the first estimate of locations is a coarse estimate while the second estimate of locations is a fine estimate.

5. The method of claim 1 , wherein the determined second set of sensor locations is more accurate than the determined first set of sensor locations.

6. The method of claim 1 , wherein the dipole antenna is disposed inside a drilling well on the hydrocarbon reservoir.

7. The method of claim 6 , wherein one anchor device is placed on top of the dipole antenna inside the hydrocarbon reservoir and another anchor is placed on bottom of the dipole antenna inside the hydrocarbon reservoir.

8. The method of claim 1 , wherein determining the set of distances from the received RMFSs is based on an MI-based communication channel model.

9. A computer-implemented method comprising:

determining, by one or more hardware processors, a set of distances between respective sensor locations of a plurality of sensors and respective anchor device locations of at least two anchor devices in a wireless underground sensor network (WUSN) in a hydrocarbon reservoir, wherein the plurality of sensors are disposed at the respective sensor locations within the hydrocarbon reservoir, wherein the at least two anchor devices are disposed at the respective anchor device locations on a dipole antenna inside the hydrocarbon reservoir, and wherein locations of the at least two anchor devices are known;

establishing, by the one or more hardware processors, an MI-based localization framework by applying a sequence of algorithms to the determined set of distances and the known locations of the at least two anchor devices, wherein applying the sequence of algorithms comprises first applying a weighted maximum likelihood estimation (WMLE) and then applying a semi-definite programming (SDP) relaxation to the determined set of distances and the known locations of the at least two anchor devices;

after establishing the MI-based localization framework, determining, by the one or more hardware processors, a first set of sensor locations, wherein the determined first set of sensor locations represents a first estimate of locations of the respective sensor locations within the hydrocarbon reservoir;

after determining the first set of sensor locations, determining, by the one or more hardware processors, a second set of sensor locations based on the determined first set of sensor locations, wherein the determined second set of sensor locations represents a second estimate of locations of the respective sensor locations within the hydrocarbon reservoir; and

generating, by the one or more hardware processors, a fracture map of the hydrocarbon reservoir based on at least the determined second set of sensor locations.

10. The method of claim 9 , wherein determining the first set of sensor locations comprises applying an alternating direction augmented Lagrangian method (ADM) to the established MI-based localization framework.

11. The method of claim 10 , wherein determining the second set of sensor locations comprises applying a conjugate gradient algorithm (CGA) to the determined first set of sensor locations.

12. The method of claim 9 , wherein the first estimate of locations is a coarse estimate while the second estimate of locations is a fine estimate.

13. The method of claim 9 , wherein the determined second set of sensor locations is more accurate than the determined first set of sensor locations.

14. The method of claim 9 , wherein the dipole antenna is disposed inside a drilling well on the hydrocarbon reservoir.

15. The method of claim 14 , wherein one anchor device is placed on top of the dipole antenna inside the hydrocarbon reservoir and another anchor is placed on bottom of the dipole antenna inside the hydrocarbon reservoir.

16. The method of claim 9 , wherein the determined set of distances is based on a magnetic induction (MI) communication channel model.

17. A non-transitory computer-readable medium storing instructions executable by a computer system to perform operations comprising:

determining a set of distances between respective sensor locations of a plurality of sensors and respective anchor device locations of at least two anchor devices in a wireless underground sensor network (WUSN) in a hydrocarbon reservoir, wherein the plurality of sensors are disposed at the respective sensor locations within the hydrocarbon reservoir, wherein the at least two anchor devices are disposed at the respective anchor device locations on a dipole antenna inside the hydrocarbon reservoir, and wherein locations of the at least two anchor devices are known;

establishing an MI-based localization framework by applying a sequence of algorithms to the determined set of distances and the known locations of the at least two anchor devices, wherein applying the sequence of algorithms comprises first applying a weighted maximum likelihood estimation (WMLE) and then applying a semi-definite programming (SDP) relaxation to the determined set of distances and the known locations of the at least two anchor devices;

after establishing the MI-based localization framework, determining a first set of sensor locations, wherein the determined first set of sensor locations represents a first estimate of locations of the respective sensor locations within the hydrocarbon reservoir;

after determining the first set of sensor locations, determining a second set of sensor locations based on the determined first set of sensor locations, wherein the determined second set of sensor locations represents a second estimate of locations of the respective sensor locations within the hydrocarbon reservoir; and

generating a fracture map of the hydrocarbon reservoir based on at least the determined second set of sensor locations.

18. The computer-readable medium of claim 17 , wherein determining the first set of sensor locations comprises applying an alternating direction augmented Lagrangian method (ADM) to the established MI-based localization framework.

19. The computer-readable medium of claim 18 , wherein determining the second set of sensor locations comprises applying a conjugate gradient algorithm (CGA) to the determined first set of sensor locations.

20. A system comprising:

a plurality of sensors disposed at respective sensor locations in a wireless underground sensor network (WUSN) in a hydrocarbon reservoir, the plurality of sensors configured to:

measure, by each of the plurality of sensors, corresponding received magnetic field strengths (RMFSs) on a plurality of respective magnetic induction (MI) links forming an MI network linking the plurality of sensors and at least two anchor devices to each other; and

transmit, by each of the plurality of sensors based on magnetic induction, the corresponding RMFSs to at least one anchor device over the MI network;

the at least two anchor devices disposed at respective anchor device locations on a dipole antenna inside the hydrocarbon reservoir, wherein locations of the at least two anchor devices are known, the at least two anchor devices configured to receive the corresponding RMFSs from the plurality of sensors over the MI network; and

a data processing apparatus configured to:

determine a set of distances between the respective sensor locations of the plurality of sensors and the respective anchor device locations of the at least two anchor devices in the WUSN in the hydrocarbon reservoir;

establish an MI-based localization framework by applying a sequence of algorithms to the determined set of distances and the known locations of the at least two anchor devices, wherein applying the sequence of algorithms comprises first applying a weighted maximum likelihood estimation (WMLE) and then applying a semi-definite programming (SDP) relaxation to the determined set of distances and the known locations of the at least two anchor devices;

after establishing the MI-based localization framework, determine a first set of sensor locations, wherein the determined first set of sensor locations represents a first estimate of locations of the respective sensor locations within the hydrocarbon reservoir; and

after determining the first set of sensor locations, determines a second set of sensor locations based on the determined first set of sensor locations, wherein the determined second set of sensor locations represents a second estimate of locations of the respective sensor locations within the hydrocarbon reservoir.

21. The system of claim 20 , wherein determining the first set of sensor locations comprises applying an alternating direction augmented Lagrangian method (ADM) to the established MI-based localization framework.

22. The system of claim 21 , wherein determining the second set of sensor locations comprises applying a conjugate gradient algorithm (CGA) to the determined first set of sensor locations.