Energy Balance in Rock Drilling
Authors: Simon R. 
Published: December 2007

SIMON, R., BATTELLE MEMORIAL INSTITUTE, COLUMBUS, OHIO

Abstract
The sources of energy dissipation for concentrated loadings on rock are considered in an attempt to account for the experimentally measured magnitude of the work required to break out a unit volume of rock from the free surface of an essentially semi-infinite medium. It is concluded that most of this work probably represents the elastic strain energy developed by the loading in a much larger volume of rock beneath the loaded region than the volume of the rock fragment broken out to the side of the loaded region. This strain energy is largely dissipated in the form of stress waves generated by the high rate of unloading produced by the propagating cracks. The energies associated with the formation of the new surfaces of the cracks and with the stress waves generated directly by the loading process are computed to be negligibly small.Possibilities for improving the utilization of energy to drill rock, subject to the geometrical limitations imposed by down-hole operation, are discussed. It is pointed out that any such possible improvements would probably have to be differential ones, since each rock configuration of more favorable loading geometry that can be created down the hole is accompanied by a complementary configuration of less favorable loading geometry.

Introduction
Dislodging each cubic inch of rock from the bottom of the hole by the action of a bit requires the expenditure of an amount of energy that varies from approximately 5,000 in.-lb to approximately 100,000 in.-lb, depending on the hardness of the rock, or, more technically, upon its fragmentation strength. In this paper we will discusswhy the energy expended in drilling is so large,what happens to this energy upon completion of the drilling process, andwhat are the possibilities for reducing the magnitude of the energy required to drill rock.

DETERMINATION OF ROCK DRILLING ENERGY
The volume of rock removed per unit time from the bottom of a hole of diameter D is evidently ( ), where R is the rate of penetration of the bit. If P is the rate at which work is done by the bit on the rock at the bottom of the hole, the energy required to break out a unit volume of rock is given by:
(1)
For rotary drilling, of either the rolling-cone or drag-bit variety, where L is the torque resistance to rotation at the bottom of the hole and N is the rate of rotation of the bit. L is essentially the same as the torque measured at the rotary table only when drilling in shallow holes. The energies expended in rotating the drill string against the frictional resistance of the walls of the hole and against the viscous drag of the drilling fluid are extraneous to the subject under consideration, although these may be much greater in magnitude than Ev when drilling in a deep hole.For percussion drilling, where f is the percussion frequency and E is the work done on the rock per impact. The latter quantity can be both computed and measured for a percussion drilling machine. 2 (Under satisfactory drilling conditions, defined in terms of ranges of numerical values of certain dimensionless parameters, E is only 30 to 50 per cent less than the impact energy of the striker.)Alternatively, Ev may be measured directly by dropping chisels shaped like bit edges, backed by rigid weights, onto the surfaces of laboratory rock samples of effectively semi-infinite extent. Under these circumstances, essentially all of the impact energy is converted to work done on the rock, and the relationships among volume of rock broken out, chisel shape, impact energy and indexing distances can be obtained.The values of the energy required to break out a unit volume of rock under favorable circumstances are substantially in agreement for rotary drilling, percussion drilling and drop testing at atmospheric pressure. The energy per unit volume is a quantity of the order of magnitude of roughly twice the compressive strength of the rock as measured by a uniaxial loading test.
SPEJ
P. 298^