An Experimental Study Of Drag-Bit Drilling Using Dimensional Analysis
Authors: Kim Y.S. , Hartman Howard L. 
Published: December 2007

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Abstract
One aspect of rock penetration which has received attention in the Rock Mechanics Laboratory at Penn State has been drag-bit drilling, a subject of some interest to the petroleum. industry. This paper presents the results of the second research investigation conducted in this area.
Experimental design and interpretation of the findings were conducted with the aid of dimensional analysis, programmed for solution on an IBM 7074 digital computer. Certain groups of dimensionless parameters were developed which permitted the effect and the interaction of several operational variables to be analyzed with a limited number of laboratory experiments. These parameters related such factors as rotary speed, bit weight, distance drilled, bit clearance angle, circulation rate, bit wear, bit temperature and penetration rate—which were then investigated on a laboratory drill press using a drag bit of one-half-inch cutting edge drilling in Pennsylvania slate.
The experiments were concerned principally with two independent variables in separate tests: bit clearance angle and fluid circulation rate. Over a range of 5, 15 and 25-degree clearance angles, the following conclusions were drawn:Penetration rate varies directly with bit clearance angle and with thrust.Bit wear measured by weight loss varies directly with clearance angle but, measured by width of flat, varies inversely.
Over a range of circulation rates of 2 to 4 cu ft/ min and. 1/2 to 2 gal/min water, these findings were obtained for bits of various hard-metal compositions.Bit temperature increases as the flow rate decreases, accompanied by a corresponding increase in bit wear and decrease in penetration rate.An attempt to correlate this effect with the physico-thermal properties of the bits failed to yield significant results.For a given circulation rate, the temperature gradient across the cutting edge of a drag bit increases with penetration rate.
Certain observations are also reported regarding the nature of cutting action, rock failure and bit wear in drag-bit drilling.

Introduction
Penetration rate and bit wear, the factors on which the successful performance and economy of a drilling operation essentially depend, have long been the object of improvement through drilling research and development. Two of the more important factors known to influence drilling performance are bit geometry and the flushing or circulation system. The present research was devoted primarily to an investigation of the effects of bit clearance angle and bit temperature, as affected by flushing medium and flow rate, in rock drilling employing drag-bit cutting. This form of mechanical attack is attracting increased attention in both mining and petroleum circles, although drag-bit drilling has as yet been little researched.
In the mining literature, bit clearance angle has been the subject in several studies of the effect of bit geometry on penetration rate and bit wear. Fairhurst derived a general formula for the minimum clearance angle as
where is clearance angle, p is penetration per revolution, and r is distance from the axis of rotation.