Magnetic induction based localization for wireless sensor networks in underground oil reservoirs
Example computer-implemented methods, computer-readable media, and computer systems are described for accurate localization of wireless sensor devices in underground oil reservoirs. In some aspects, every sensor measures respective received magnetic field strengths (RMFSs) on a plurality of respective magnetic induction (MI) links and transmits the measured respective RMFSs to at least one anchor devices. A set of distances is determined from the measured respective RMFSs. The set of distances is processed through an ordered sequence of algorithms, namely weighted maximum likelihood estimation (WMLE), semi-definite programming (SDP) relaxation, alternating direction augmented Lagrangian method (ADM), and conjugate gradient algorithm (CGA), to generate accurate localization of the wireless sensor devices in underground oil reservoirs.
1. A method comprising:
obtaining a set of distances, wherein the set of distances represents an estimate of distances between a plurality of sensors and at least two anchor devices in a wireless underground sensor network (WUSN) in a hydrocarbon reservoir, and locations of the at least two anchor devices are known;
establishing an MI-based localization framework by first applying a weighted maximum likelihood estimation (WMLE) and then applying a semi-definite programming (SDP) relaxation to the 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 plurality of sensors; 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 plurality of sensors.
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, and the determined second set of sensor locations is more accurate than the determined first set of sensor locations.
5. The method of claim 1 , wherein the plurality of sensors are disposed at respective sensor locations within the hydrocarbon reservoir, and the at least two anchor devices are disposed at respective anchor device locations on a dipole antenna inside the hydrocarbon reservoir.
6. The method of claim 5 , wherein the dipole antenna is disposed inside a drilling well on the hydrocarbon reservoir, one anchor device is placed on top of the dipole antenna inside the hydrocarbon reservoir, and another anchor device is placed on bottom of the dipole antenna inside the hydrocarbon reservoir.
7. The method of claim 1 , further comprising generating a fracture map of the hydrocarbon reservoir based on at least the determined second set of sensor locations.
8. A non-transitory computer-readable medium storing instructions executable by a computer system to perform operations comprising:
obtaining a set of distances, wherein the set of distances represents an estimate of distances between a plurality of sensors and at least two anchor devices in a wireless underground sensor network (WUSN) in a hydrocarbon reservoir, and locations of the at least two anchor devices are known;
establishing an MI-based localization framework by first applying a weighted maximum likelihood estimation (WMLE) and then applying a semi-definite programming (SDP) relaxation to the 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 plurality of sensors; 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 plurality of sensors.
9. The non-transitory computer-readable medium of claim 8 , wherein determining the first set of sensor locations comprises applying an alternating direction augmented Lagrangian method (ADM) to the established MI-based localization framework.
10. The non-transitory computer-readable medium of claim 9 , wherein determining the second set of sensor locations comprises applying a conjugate gradient algorithm (CGA) to the determined first set of sensor locations.
11. The non-transitory computer-readable medium of claim 8 , wherein the first estimate of locations is a coarse estimate while the second estimate of locations is a fine estimate, and the determined second set of sensor locations is more accurate than the determined first set of sensor locations.
12. The non-transitory computer-readable medium of claim 8 , wherein the plurality of sensors are disposed at respective sensor locations within the hydrocarbon reservoir, and the at least two anchor devices are disposed at respective anchor device locations on a dipole antenna inside the hydrocarbon reservoir.
13. The non-transitory computer-readable medium of claim 12 , wherein the dipole antenna is disposed inside a drilling well on the hydrocarbon reservoir, one anchor device is placed on top of the dipole antenna inside the hydrocarbon reservoir, and another anchor device is placed on bottom of the dipole antenna inside the hydrocarbon reservoir.
14. The non-transitory computer-readable medium of claim 8 , the operations further comprising generating a fracture map of the hydrocarbon reservoir based on at least the determined second set of sensor locations.
15. A device comprising:
a memory; and
a processing unit that is arranged to perform operations including:
obtaining a set of distances, wherein the set of distances represents an estimate of distances between a plurality of sensors and at least two anchor devices in a wireless underground sensor network (WUSN) in a hydrocarbon reservoir, and locations of the at least two anchor devices are known;
establishing an MI-based localization framework by first applying a weighted maximum likelihood estimation (WMLE) and then applying a semi-definite programming (SDP) relaxation to the 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 plurality of sensors; 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 plurality of sensors.
16. The device of claim 15 , wherein determining the first set of sensor locations comprises applying an alternating direction augmented Lagrangian method (ADM) to the established MI-based localization framework.
17. The device of claim 16 , wherein determining the second set of sensor locations comprises applying a conjugate gradient algorithm (CGA) to the determined first set of sensor locations.
18. The device of claim 15 , wherein the first estimate of locations is a coarse estimate while the second estimate of locations is a fine estimate, and the determined second set of sensor locations is more accurate than the determined first set of sensor locations.
19. The device of claim 15 , wherein the plurality of sensors are disposed at respective sensor locations within the hydrocarbon reservoir, and the at least two anchor devices are disposed at respective anchor device locations on a dipole antenna inside the hydrocarbon reservoir.
20. The device of claim 19 , wherein the dipole antenna is disposed inside a drilling well on the hydrocarbon reservoir, one anchor device is placed on top of the dipole antenna inside the hydrocarbon reservoir, and another anchor device is placed on bottom of the dipole antenna inside the hydrocarbon reservoir.