Geology Reference
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Drill collar
Displacement source drillbit model
x = 0, Rock-bit interaction,
Mechanical impedance model
Figure 4.2.3.
Downhole model near the bit.
4.2.4.4 Empirical notes on rock-bit interaction.
Penetration rate into a formation depends upon the entire drillstring
dynamics: the same bit drilling the same rock will penetrate differently with
different drillstring lengths. The dynamics is controlled by local interactions at
the bottom of the hole. This is clear to any home carpenter who has drilled with
new versus dull bits. In vibrations modeling, we view the simulation problem as
the result of two sub-problems. The first is
macroscopic;
this includes the
governing partial differential equation and the surface boundary condition. Its
description is determined by rig, drillpipe and bottomhole assembly details. The
second is a
microscopic
view related to events at the bottom x = 0. These
details, known as rock-bit interactions, are empirical: they depend on drillbit
geometry, bit and bearing wear, and formation hardness. What we seek is an
“absolute” statement about local interactions which can be used to show how
different drillstrings drill differently with bit and formation held constant. If this
statement is inferred from laboratory rig tests, the final result must be carefully
expressed in a manner relating bit and rock only. The effects of the drilling
assembly must be removed (or,
deconvolved
) so that the boundary condition can
be used with other drilling assemblies.
Laboratory drillbit data.
It is difficult to obtain true rock-bit boundary
conditions if the dynamics of the drilling assembly (i.e., the system transfer
function) cannot be characterized accurately. Controlled drilling where
vibration isolates the bit from reverberant oscillations is ideally desired. At least
in principle, information along these lines does appear in the drilling literature.
For example, Rowley, Howe and Deily (1960) performed laboratory drilling
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