Abstract
With several limiting assumptions, a mathematical model of the diamond-bit drilling, process has been developed. The model represented by an instantaneous rate-of-penetration equation takes into account the reduction in penetration rate during drilling resulting from bit wear. The model has been tested both under laboratory and under field conditions. The comparison of the theoretical and experimental results has shown reasonable agreement. A method for estimating rock properties also has been established. Using this method, we can find the so-called index of rock strength and the index of rock abrasiveness.
Introduction
Several published studies concerned with diamond-bit drilling report on rock properties and drillability. drilling fluid additives, diamond wear, and drilling performance theories. Among the factors, that affect diamond-bit drilling performance, the type of formation to be drilled is of utmost importance since it significantly affects the type of bit, the drilling practices. and subsequently the rate of penetration and the drilling cost. The nature of the formation is also one of the main factors in planning deep wells, fracture jobs, mud and cement technologies, etc.
For rock properties evaluation as well as for selection of proper drilling practices, several descriptions of the diamond-bit drilling process have been developed. The relevant literature is extensive and is not reviewed in this paper.
The objective of this paper is to describe the diamondbit drilling model for surface-set diamond core bits and its application to determining the index of formation strength and the index of formation abrasiveness. The main difference between our model and the models known in literature is that we consider the effect of friction between the diamond cutting surfaces and the rock. A decrease in penetration rate is observed if the drilling parameters, are constant and if the formation is macroscopohomogeneous.
Drilling Model
The drilling model for a surface-set diamond core bit is subjected to the following limiting assumptions.Rock behavior during cutting with a single diamond may be approximated by a rigid Coulomb plastic material.The active surface of the bit is flat, and diamonds are spherical with diameter. d.The cross-sectional area of the chip formed by a single diamond is equal to the diamond cutting surface and can be established by geometry.During drilling, the neighboring diamonds work together to make a uniform depth of cut (Fig. 1).A number of diamonds forming one equivalent blade have to provide it uniform depth of cut from the inner to the outer diameter of the diamond core bit. so the bit is modeled to be a combination of several equivalent blades (Fig. 2).The diamond distribution technique provides uniform radial coverage that results in equally loaded cutting diamonds.Individual cutting diamonds perform some work that results from the friction between the rock and the diamond.Bit wear is assumed to be gradual while drilling is in progress.
Under the preceding assumptions we may state that the drilling rate of the surface-set diamond core bit is a function only of weight on bit (WOB), rotary speed, average density of the diamonds on the bit's active surface, diamond size, core-bit diameters, rock properties, and degree of diamond dullness. The effects of flow rate, differential pressure, hydraulic lift, drilling fluid properties. and drillstring dynamics are ignored.
According to Peterson, the penetration rate of the diamond bit, after some modifications, can be described by the following simplified equation.
(1)
This equation does not include the effect of diamond wear and hence pertains to unworn bits or to when bit dullness is negligible.
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