Analytical determination of optimum bit weight and rotary speed combinations

Abstract

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. These mathematical expressions contain constants which can he adjusted to represent actual drilling experience in any area, provided that field data on drilling rate and bit life expectancy are available. After the mathematical expressions are adapted to a particular area, then the optimum combinations of bit weight and rotary speed can be established. From the analysis based on simplifying assumptions it is concluded that optimum combinations of bit weight and rotary speed exist which minimize total drilling cost and that these optimum combinations can be calculated for any drilling condition Calculation of combinations of bit weight and rotary speed which are optimum for the conditions of the illustrative field example shows that at depth intervals from 1000 to 6000 ft high bit weights (i.e., in excess of 50,000 lb at 75 rpm) are necessary to approach minimum total drilling cost. Also, the optimum combinations of bit weight and rotary speed are strongly dependent on rig cost and bit life.