In this paper, the dependence of the drilling specific energy on the virgin pore pressure po is examined by analyzing the mechanics of a PDC cutter. On the basis of a simple failure mechanism involving a single shear plane, it is first established that the specific energy depends linearly on the difference between the bottom-hole pressure ph and the average pore pressure pb on the shear plane. The relationship between pb and po is then determined by considering fluid mass balance across the shear plane. It is shown that the drilling conditions for a shale is in the high-speed regime, while for a permeable sandstone it is typically in the low speed regime.
It is generally accepted in the Drilling Industry that the specific energy (the amount of energy required to drill a unit volume of rock), depends on the differential pressure, i.e. the difference between the bottom-hole pressure ph and the virgin pore pressure po. This commonly held assertion is based on the results of drilling experiments on permeable rocks that were undertaken in the late fifties (e.g. Eckel 1958, Cunningham and Eenink 1959). These results have been rationalized on the ground that (i) most of the pressure drop between the mud pressure and the far-field pore pressure takes place across the filter cake, (ii) the pore pressure in the failed rock regions is close to the virgin pore pressure due to the high permeability of the rock, and (iii) the strength of rock depends on the difference between confining (bottom-hole) and pore pressure. However, it has also been recognized early on (Handin 1959, Robinson and Holland 1969) that this conceptual model is probably not applicable to low permeability rocks because fluid cannot be supplied rapidly enough to the dilatant failed regions, causing the pore pressure in the failed zones to drop or even vanish. This view is supported by results of cutting experiments with a single PDC cutter on Mancos shale (Zijsling 1987) and drilling experiments with a milled tooth bit on an over consolidated Jurassic II shale (Gray Stephens et al 1991). These experiments indeed indicate that the specific energy depends on the bottom-hole pressure and not on the virgin pore pressure, thus implying that cavitation takes place in the failed regions. This paper addresses the issue of the dependence of the drilling response on the virgin pore pressure within the restricted context of a drag (PDC) bit and on the assumption that the rock dilates during failure.
The factors influencing the mechanical response of PDC bits can be analyzed by focusing on the mechanics of failure induced by the motion of a single cutter. Figure 1 shows a cutter removing material over a constant depth of cut £, at a constant velocity v. A mud pressure ph is applied on the free surface of the rock. Also illustrated in this figure is the simple flow mechanism considered by Merchant (1944, 1945) for the machining of metals.