received by the International Bureau on 23 October 2020 (23.10.2020)

What is claimed is

1. A method for determining mechanical specific energy of a drill bit drilling a subsurface formation, the drill bit rotated by a drilling motor in a drilling assembly, the method comprising: measuring a parameter related to torque applied to the drill bit;

measuring a parameter related to rotational speed of the drill bit using a measurement made in a bottom hole assembly (BHA) on a side of the drilling motor opposite to the drill bit; determining a volumetric rate of penetration of the drill bit through the subsurface formation; and

calculating the mechanical specific energy from the parameter related to torque, the parameter related to rotational speed and the volumetric rate of penetration.

2. The method of claim 1 further comprising using the calculated mechanical specific energy to adjust a trajectory of a wellbore created by the drilling.

3. The method of claim 1 wherein the parameter related to rotational speed comprises magnetic field amplitude.

4. The method of claim 1 wherein the parameter related to rotational speed comprises acceleration.

5. The method of claim 1 wherein the parameter related to torque comprises torsional strain.

6. A method for determining power of a drill bit drilling a subsurface formation, the drill bit rotated by a drilling motor in a drilling assembly, the method comprising:

measuring a parameter related to torque applied to the drill bit;

measuring a parameter related to rotational speed of the drill bit using a measurement made in a bottom hole assembly (BHA) on a side of the drilling motor opposite to the drill bit; and

calculating the power from the parameter related to torque and the parameter related to rotational speed. REPLACEMENT SHEET

7. The method of claim 6 further comprising using the calculated power to adjust a trajectory of a wellbore created by the drilling.

8. The method of claim 6 wherein the parameter related to rotational speed comprises magnetic field amplitude.

9. The method of claim 6 wherein the parameter related to rotational speed comprises acceleration.

10. The method of claim 6 wherein the parameter related to torque comprises torsional strain.

11. A method for predicting a lithology-related parameter of a formation at a drill bit during drilling a wellbore, comprising:

measuring a parameter related to power expended at the drill bit made in a bottom hole assembly (BHA) during the drilling;

measuring a parameter related to vibration energy in a drilling assembly made in the bottom hole assembly (BHA) during drilling; and

using the measured parameter related to power and the measured parameter related to vibration energy as a control parameter to trajectory of the well during drilling.

12. The method of claim 11 wherein the parameter related to power comprises torque at the drill bit and rotational speed of the drill bit.

13. The method of claim 11 wherein the parameter related to rotational speed comprises magnetic field amplitude.

14. The method of claim 11 wherein the parameter related to rotational speed comprises acceleration.

15. The method of claim 11 wherein the parameter related to torque comprises torsional strain.

27 REPLACEMENT SHEET

16. The method of claim 11 wherein the parameter related to vibration comprises axial acceleration, lateral acceleration and rotational acceleration.

17. The method of claim 11 wherein the lithology-related parameter comprises at least one of density, neutron porosity, gamma ray radiation, resistivity and acoustic velocity.

18. The method of claim 11 wherein the corresponding measurements are made by at least one sensor disposed on the drilling assembly on a side of a drilling motor opposed to a side thereof on which the drill bit is disposed.

19. The method of claim 11 wherein the corresponding measurements are made by at least one sensor disposed on the drilling assembly between a drilling motor thereon and the drill bit.

20. The method of claim 11 further comprising:

using the measured parameter related to power and the measured parameter related to vibration energy, and corresponding measurements of the lithology-related parameter as input to train a machine learning model; and

using the measured parameter related to power and the measured parameter related to vibration energy in the trained machine learning model to predict a value of the lithology-related parameter at the drill bit.

21. The method of claim 11 further comprising determining rotary orientation of the BHA during drilling and measuring the parameter related to power expended at the drill bit and vibration energy, and assigning the measured parameters to bins corresponding to the rotary orientation.

28