Inferring Orientation Parameters of A Steering System for Use with A Drill String

A method to steer a drill bit of a rotary steerable system within a wellbore, the method comprising:

• introducing the rotary steerable system into the wellbore, the rotary steerable system comprising:
• an upper portion coupled to a drill string;
• a lower portion coupled to the upper portion via a flexible collar, the lower portion having the drill bit coupled thereto;
• a first survey instrument package and a second survey instrument package disposed within the upper portion, wherein the second survey instrument package is axially offset from the first survey instrument package;
• and
• a third survey instrument package disposed within the lower portion, wherein the third survey instrument package is axially offset from the drill bit;
• establishing a magnetic model associated with the drill bit with an initial source position;
• measuring a respective plurality of magnetic field parameters at the first, second, and third survey instrument packages;
• solving an initial tool-face angle, an initial bend angle, and an initial azimuth based on the magnetic field parameters with respect to the magnetic model;
• determining a magnetic gradient tensor based on the magnetic field parameters of the first, and second survey instrument packages;
• solving for a calculated tool-face angle, a calculated bend angle, and a calculated azimuth with respect to the magnetic model based on the magnetic gradient tensor, the initial tool-face angle, the initial bend angle, and the initial azimuth;
• and
• steering the drill bit via the rotary steerable system based on the calculated tool-face angle, the calculated bend angle, and the calculated azimuth.

A drill string control system, comprising:

• an upper portion coupled to a drill string;
• a lower portion coupled to the upper portion via a flexible collar, the lower portion having a drill bit coupled thereto;
• a first survey instrument package and a second survey instrument package disposed within the upper portion, wherein the second survey instrument package is axially offset from the first survey instrument package;
• a third survey instrument package disposed within the lower portion, wherein the third survey instrument package is axially offset from the drill bit;
• and
• a controller including a processor and a non-transitory computer readable medium, the drill string control system communicatively coupled to the controller, wherein the computer readable medium stores a computer readable program code that, when executed by the processor, configures the processor to perform a method comprising:
• establishing a magnetic model associated with the drill bit with an initial source position;
• measuring a respective plurality of magnetic field parameters at the first, second, and third survey instrument packages;
• determining an initial azimuth of the magnetic model based on the plurality of magnetic field parameters of the third survey instrument package;
• determining a magnetic gradient tensor based on the magnetic field parameters of the first, and second survey instrument packages;
• solving for a calculated tool-face angle, a calculated bend angle, and a calculated azimuth with respect to the magnetic model based on the magnetic gradient tensor, the initial azimuth and the initial source position;
• and
• directing a rotary steerable system based on the calculated tool-face angle, the calculated bend angle, and the calculated azimuth.