An analytical development of a new mechanistic drilling model for polycrystalline diamond compact (PDC) bits is presented. The derivation accounts for static balance of forces acting on a single PDC cutter and is based on assumed similarity between bit and cutter. The model is fully explicit with physical meanings given to all constants and functions. Three equations constitute the mathematical model: torque, drilling rate, and bit life. The equations comprise cutter’s geometry, rock properties drilling parameters, and four empirical constants. The constants are used to match the model to a PDC drilling process. Also presented are qualitative and predictive verifications of the model. Qualitative verification shows that the model’s response to drilling process variables is similar to the behavior of full-size PDC bits. However, accuracy of the model’s predictions of PDC bit performance is limited primarily by imprecision of bit-dull evaluation. The verification study is based upon the reported laboratory drilling and field drilling tests as well as field data collected by the authors.
This paper presents an advanced concept in drilling optimization—the dynamic drilling strategy. The dynamic drilling strategy is a new methodology of drilling process planning and control; it combines theory of single-bit control with an optimal multi-bit drilling program for a well. In the simulation study, the dynamic drilling strategy was compared to conventional drilling optimization and typical field practices; the considerable cost-saving potential of 25 and 60 percent, respectively, was estimated. The method also appeared to be the most cost-effective for expensive and long-lasting PDC bits through better utilization of their performance and reduction in the number of bits needed for the hole.
This paper presents a simulation study to evaluate the combined effect of cutting depth (drilling rate) and wear (bit dull) on the thermal response of polycrystalline diamond compact (PDC) cutters under downhole drilling conditions. A new understanding of frictionally generated heat between rock and PDC cutter is introduced from the analysis of forces active on the wearflat and the cutting (leading) surfaces of a cutter. Then this new concept is used to predict PDC bit performance with the controlled temperature of its cutters. Previous concepts, largely based on the laboratory drilling tests (with low drilling rate and under atmospheric conditions), recognize only one source of heat—the wearflat surface. However, this study, using field data, shows that the heat generated at the cutting surface may significantly contribute to the total heat flux in the cutter. As a result, the distribution of temperature within the cutter is changed, which particularly affects the maximum value of temperature at the cutting edge. A simplified 2-D finite difference numerical code is used to quantify the difference in cutter wearflat temperatures calculated with and without the additional heat flux generated at the cutting surface. The numerical analysis reveals that neglecting the cutting surface effect results in underestimation of the actual wearflat temperature by 10 to 530 percent, depending upon bit dull and downhole hydraulics. Also demonstrated is the actual impact of these findings on field drilling practices. The example comparison is made by calculating the optimal-control procedures for PDC bit with and without the effect of cutting surface. In these procedures, wearflat temperature becomes a mathematical constraint which limits weight on bit and rotational speed. The comparison includes calculation of the maximum bit performance curves which represent maximum drilling rate attainable for a bit to drill a predetermined length of a borehole (footage). The curves show an up to 18 percent reduction of drilling rate when the new and more rigorous temperature limitation is used. In addition, the example calculations show that the actual temperature of the bit cutters can be 460°C (860°F), and exceeds by almost 30 percent its maximum acceptable value of 350°C (660°F). For practical applications, the study reveals that many field failures of PDC bits may have been caused by lack of understanding of operational limits imposed by heat considerations.
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