A method for real-time identification and control of downhole dynamics in a drilling system (40), the method performed by a processor (24) and comprising:
- receiving, by the processor (24), a plurality of acceleration measurements (112) corresponding to a plurality of locations in a first two-dimensional reference frame, the first two-dimensional reference frame being a moving reference frame fixed to and defined by the orientation of drill string (12), the first two-dimensional reference frame coincident with a plane orthogonal to a rotational axis (54) of the drilling system (40) and based on a position of the drilling system (40) in the plane, the plurality of acceleration measurements (112) comprising measurements in a plurality of non-parallel directions lying in the plane;
- determining, by the processor (24), a rotational position (132) of the drilling system (40) in the first two-dimensional reference frame based on the plurality of acceleration measurements, the rotational position (132) represented as a rotational angle (58) and describing rotation of the drilling system (40) in the plane about the rotational axis (54), wherein the rotational angle (58) is the drill string's (12) rotation about the rotational axis of the drill string;
- converting, by the processor (24), a first location of the plurality of locations to a corresponding second location of the drilling system (40) in a second two-dimensional reference frame based on the plurality of acceleration measurements, the second two-dimensional reference frame being a static reference frame which is coincident with the plane and invariant with the position of the drilling system (40) in the plane;
- determining, by the processor (24), a revolution position (152) of the drilling system (40) in the second two-dimensional reference frame based on the rotational position (132) and the second location, the revolution position (152) describing revolution of the drilling system (40) in the plane about a revolution axis (52);
- and
- identifying, by the processor (24), a whirl dynamic of the drilling system (40) based on the revolution position (152);
- determining, by the processor (24), a rotational velocity of the drilling system (40) in the first two-dimensional reference frame based on the plurality of acceleration measurements;
- and
- determining, by the processor (24), the rotational position (132) based on the rotational velocity;
- wherein the first location comprises a first sensor location of the first sensor (22A), a first measurement subset of the plurality of acceleration measurements are sensed by the first sensor (22A), the first sensor location spaced apart from the rotational axis (54) by a first radius RA;
- and
- wherein a second measurement subset of the plurality of acceleration measurements are sensed by a second sensor (22B), the second sensor (22B) having a second sensor location spaced apart from the rotational axis (54) by a second radius RB and spaced apart from the first sensor location.