Optimization Techniques For Weight-On-Bit And Rotary Speed Part II. Multi-Interval Optimization
Authors: Bentsen Ramon G. , Wilson David C. 
Published: March 2010

Abstract
Currently available techniques for optimizing weight-on-bit and rotary speed are somewhat limited in scope. They determine optimum policy in the light of a part of the drilling process, rather than in the light of the entire drilling process. The object of this two-part investigation was to develop techniques which are les8 limited in scope, and to demonstrate the importance of optimizing the drilling process as a whole, rather than optimizing separate parts of that process.
Three optimization methods have been developed. The methods differ primarily in the scope over which the optimization takes place. That is7 the first method seeks to minimize the cost per foot drilled during a given bit run, the second method minimizes the cost of a. selected interval and the third method minimizes the cost over a series of intervals. The methods are listed in order of increasing scope and complexity, the first two being examined in Part I, and the third treated in Part II. Results and conclusions regarding all three methods are to be found in Part II.
It was found that each of the methods gave a worthwhile cost saving, and that the saving increased as the scope and complexity of the method increased. The need for better data also increases as the scope and complexity of the method increases. Hence, the method used should be chosen according to the amount and quality of the data available.

Introduction
IN THE FIRST INSTALLMENT of this paper, attention was given to modifying and extending the drilling optimization techniques of researchers such as Galle and Woods(1,2), Young(3), Reed(4) and others. The so called "basic-point" method of Galle and Woods, which develops an optimal drilling policy for each bit used in a single lithological interval, was modified to yield an optimal policy over a group of lithological intervals. This approach was termed the "modified-point" method. In addition, a method called the "interval" technique was developed which optimizes each lithological interval separately; but, unlike the basic-point technique, which seeks to minimize the cost of each bit run, the interval method seeks to minimize the cost of drilling the section as a whole. Attention will now be focused on the third optimization technique examined.

"Multi-Interval" Optimization
Just as there is a similarity between the basic-point and interval methods, which both optimize the costs associated with drilling a single lithological interval, so are modified-point and multi-interval optimization similar in that each seeks to minimize drilling costs over a series of intervals, rather than over just one interval. The approach taken to achieve this end differs considerably, however. The modified-point method minimizes the cost of each bit run. In contrast, themulti-interval technique minimizes the cost of drilling the series of intervals as a whole.
The multi-interval optimization procedure involves the problem of deciding where the optimal point is for changing the bit. That is, it belongs to a general class of problems known as replacement problems. In particular, it is analogous to the catalyst replacement problem described by Roberts(5).