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This paper presents an analytical method for the selection of optimum combinations of rotary speed and bit weight to minimize total drilling cost. A mathematical analysis of the cost to drill any depth interval is the basis of the method. In the analysis, it is assumed that the total drilling cost can be expressed as the sum of rig cost for making round trips, rig cost for drilling, and bit cost. It is further assumed that bit life is limited by bearing failure, that bit weight is not limited by considerations such as hole deviation, and that drilling hydraulics are adequate. Based on these assumptions, the following important question is proposed: Do optimum combinations of bit weight and rotary speed exist which will minimize the cost to drill specified depth intervals? This question is understood more specifically through a consideration of the following facts. When either bit weight or rotary speed is increased, the rig cost for drilling becomes less because penetration rate is increased. However, when greater bit weight and/or faster rotary speed is used, both rig cost for making round trips and bit cost become greater because bit life is decreased. Whether or not a change in bit weight (or rotary speed) will increase or decrease drilling cost is determined by a mathematical analysis. To perform the analysis, the results of past field experience are used to derive empirical mathematical expressions for bit life expectancy and for drilling rate as a function of depth, rotary speed, and bit weight.

Analytical Determination of Optimum Bit Weight and Rotary Speed Combinations