In order to provide the drilling engineer with a generalized drillability equation that is portable, an analysis of the interaction of the rotating bit, circulation system and rock properties will be made. Many equations are in use in rotary properties will be made. Many equations are in use in rotary drilling. These are so numerous that handbooks must be used to classify them. Dimensional analysis can be used to simplify this situation, so that a generalized equation for all rock bits can be formulated.


Drillability will be defined as the rate at which a given rock may be penetrated, in distance/time units, with a given bit configuration and specified drilling fluid medium. The specified conditions for both fluid and rock must include pressure, temperature and composition. Penetration rate is the measurement term for drillability, in velocity units (usually feet/hour, but also meters/hour).

Penetration rate, Rp = ft/hour, in English units = (hole volume/hour)

On an energy basis,

Rp = (V/energy absorbed)(energy/hour)



Using triangular teeth with rectangular bases, which is appropriate for narrow rolling cutters, and for tooth height, ht, and base area, At,



Noticing that one tooth of height, ht, makes one depth penetration of ht and that the force absorbed is the net bit weight applied to the borehole bottom, W.


The bit tooth is labeled as follows.

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