Method and device for estimating downhole string variables

1. A method for estimating downhole speed and force variables at an arbitrary location of a moving drill string based on surface measurements of the speed and force variables, comprising:

a) using geometry and elastic properties of said drill string to calculate transfer functions describing frequency-dependent amplitude and phase relations between cross combinations of said speed and force variables at the surface (surface variables) and downhole;

b) selecting a base time period that is at least as long as a period of fundamental drill string resonance;

c) measuring surface speed and force variables, conditioning said measured data, and storing the conditioned data at least over a last elapsed base time period,

d) calculating the downhole variables in the frequency domain by applying an integral transform of the surface variables, multiplying results of the calculating with said transfer functions, applying an inverse integral transform to sums of coherent terms and picking points in said base time period to get time-delayed estimates of the downhole speed and force variables.

2. The method of claim 1 , further comprising estimating general variables representing one or more of the following pairs:

torque and rotation speed;

tension force and axial velocity;

pressure and flow rate.

3. The method of claim 1 , further comprising adding mean values to said estimates of the speed and force variables.

4. The method of claim 1 wherein step a) comprises approximating said drill string by a series of uniform sections.

5. The method of claim 1 , wherein step c) comprises storing data in circular buffers.

6. The method of claim 1 , wherein step c) further includes filtering out data from start-up of a drill string moving means.

7. The method of claim 6 , wherein the step of filtering out start-up data comprises setting the speed equal to zero until a mean force variable reaches a mean force measured prior to last stop of said drilling string moving means.

8. The method of claim 1 , wherein step b) comprises selecting a base time period representing an inverse of a fundamental frequency of a series of harmonic frequency components of said drill string.

9. The method of claim 1 , wherein step d) comprises picking points at or near a center of said base time period.

10. The method of claim 1 , wherein step a) further comprises calculating an effective characteristic impedance of a selected mode of said drill string.

11. The method of claim 10 , wherein the step of calculating said effective characteristic mechanical impedance of said drill string comprises adding a tool joint correction factor to a pipe impedance factor to account for pipe joints in said drill string.

12. The method of claim 11 , wherein said pipe joint correction factor is used to calculate a wave number of a pipe section in said drill string, and wherein a damping factor is added to said wave number to account for linear damping along said drill string.

13. The method of claim 12 , wherein accounting for said linear damping comprises adding a frequency-dependent and/or a frequency-independent damping factor.

14. The method of claim 2 , wherein step c) comprises measuring tension force and axial velocity in a deadline anchor and/or in a draw works drum, and accounting for inertia of moving mass prior to storing the data.