Specific Energy as a Criterion for Bit Selection
Authors: Rabia Hussain 
Published: December 2007

Summary
A simplified approach to bit selection that uses the principle of specific energy is presented. Comparison of bit selection, based on both cost per foot and specific energy, is made. The potential application of specific energy in development and exploration wells is discussed.

Introduction
The criterion for bit selection is normally based on cost per foot, which is determined by the following equation:
(1)
where C is in $/ft. Eq. 1 shows that cost per foot is controlled by five variables. For a given bit cost, and hole section, cost per foot will be highly sensitive to changes in rig cost per hour, trip time, and rotating time,. The trip time may not always be easy to determine unless a straight running in and pulling out of hole is made. If the bit is pulled out for some reason-say, to casing shoe for a wiper trip-such duration, if added, will influence the total trip time and, in turn, cost per foot. Bit performance, therefore, has been changed by some arbitrary factor. Rotation time is straightforward and is directly proportional to cost per foot, assuming that other variables remain constant. The rig cost will greatly influence the value of cost per foot. For a given hole section in a field that is drilled by different rigs having different values of, the same bit will produce different values of cost per foot, assuming that the same rotating hours are used in all rigs. It should be pointed out that, if the value of is taken as arbitrary (say $900/hr), then Eq. 1 will yield equivalent values of cost per foot for all rigs. The value of cost per foot in this case is not a per foot for all rigs. The value of cost per foot in this case is not a real value and does not relate to actual or planned expenditure. Performance of a bit in the different parts of a given hole section can be Performance of a bit in the different parts of a given hole section can be determined from the cumulative cost per foot (CCF). In this method, Eq. 1 is used to determine cost per foot for, e.g., every 10 ft [3.1 m], by assuming a reasonable figure for round-trip time . When the CCF value starts increasing, Ref. 1 suggests that it is time to pull the current bit out of hole. In other words, the CCF is being used as a criterion for determining the depth at which the current bit becomes uneconomical. The drawbacks with the use of the CCF method are thataccurate measurement and prediction of, and are necessary; andthe CCF may have suddenly increased as a result of drilling a hard streak of formation and may decrease once the bit has passed this streak.
Because of these uncertainties, pulling a bit out on the evidence of one CCF value may prove to be premature. Vargo suggests the determination of several increasing values of CCF and of the corresponding incremental cost per foot (ICF) for each, say, 10-ft [3.1-m] interval. A probabilistic test for trend then is performed on the difference between ICF and CCF to confirm that there is an upward trend for CCF. A simpler and more practical method, therefore, is required, whereby the performance of a bit can be quantified in each portion (or formation type) of the section it drills. This performance must be capable of being correlated with cost per foot to simplify the analysis of well cost. The aim of this paper is to provide drilling personnel with an on-site method for analyzing bit performance. The method uses a term referred to as "specific energy."
Definition of Specific Energy
Specific energy ( ) may be defined as the energy required to remove a unit volume of rock; it may use any consistent set of units. It has been shown that for rotary drilling may be calculated from the following equation:
............................(2)
in in.-lbf/cu in., and in metric units, MJ/m3,
where = weight on bit, lbf [N], = rotary speed, rev/min, = diameter of bit, in. [mm], and = penetration rate, ft/hr [m/h].
JPT
p. 1225