American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
Abstract This paper presents a new approach in formulating and solving the optimal drilling problem. The approach is heuristic as it involves the interaction of raw data, regression and an optimization technique. From several bit runs regression equations were established for predicting penetration rate and bit life. Three control variables are accounted for: weight on bit, rotary speed and bit hydraulic horsepower. The equations for penetration rate and bit life are incorporated into a drilling cost equation and the cost function is minimized over the control variables. These variables then dictate the optimal drilling of the next bit run.
A uniform formation drilled with similar bits and an on-line optimization scheme for updates with each new bit run, is best suited for this approach. An application of the procedure to field data is given.
Introduction Numerous publications over the years have contributed to the complex subject of drilling optimization. Concentrating on some of the recent publications that offer a mathematical model for drilling, publications that offer a mathematical model for drilling, Reed devised a Monte Carlo technique to solve the variable weight-speed problem. He concluded that it offers very little advantage over the simpler constant weight-speed approach. He then presented a solution to the constant weight-speed problem based on the conjugate-gradient method. Reed used nearly the-same set of empirical equations Young proposed, as a set of differential constraints in the context of minimization. Interestingly we found no significant difference in comparing several examples reported by Reed with solutions by Young's formulation. Wilson and Bentsen applied several optimization techniques to minimize drilling costs. In their "Multi-interval Optimization", dynamic programming was used to optimize the intervals drilled and programming was used to optimize the intervals drilled and the minimum of the total cost function indicated where to change the bit. They have used the equations derived by Galle and Woods in their modeling. Some theoretical analysis that include the stress properties of the formations was carried out by properties of the formations was carried out by Wardlaw. Polynomial-type functions were derived from dimensionless groupings of variables according to categorized drilling conditions. Minimization of the drilling cost function was achieved by geometric programming. programming. There appear to be some drawbacks in common to each of these approaches. These can be listed as:Several formation and bit parameters must be known in advance. These are determined from analytical expressions, from previous data, field testing or from experience and judgement;
Only bit weight and rotary speed are fully accounted for as control variables.