An Approach for Modeling the Field Drilling Data
Authors: Xu Hong , Tochikawa Tetsuro , Hatakeyama Takashi , Ota Hitoshi 
Published: December 2007

Abstract
It is well-known that even a small percentage of reduction in bit-related cost can result in significant savings. Improving bit performance is an effective approach to cost reduction and modeling bit performance is a scientific approach to optimizing of bit performance. However modeling bit performance has long been diminished, since to develop a model under experimental conditions is usually costly and few models from experimental or theoretical conditions have been practically utilizable.
Following up the success in developing a practical method for modeling ROP using logging data from the North Sea area, this paper explains the developed method further with a series of case studies including modeling ROP for a combination of bit runs, individual bit runs, short section under dynamic drilling conditions. The data were from 46 insert-tricone-bit-run of the 12-1/4" section of an onshore exploration well in Japan. The data were measured at surface with conventional logging equipment. The mud is water-based Lignosulphonate system and the formation is namely Hiuchiyama including variegated sequence of sedimentary and igneous rocks. The developed model succinctly explain about 80% of the ROP variations and the median of the normalized ROP residuals (NReROP) is around 10 to 15%. The essence of the developed method is by grouping data to improve the suitability of data for modeling and still retain the information representing the intrinsic relations between the variables. The nature of the presented method are discussed and the utilizability and limitation of the models are addressed. Now that this method consistently appears to be physically valid and practically utilizable, it is intended for application in routine drilling practice in conjunction with further improvement and modification.

Introduction
As the investment in an exploration well amounts to millions of dollars and the bit-related cost is a major proportion of it, so even a small percentage of reduction in this area can result in significant savings. It has been recognized that improving bit performance is an effective approach to achieve cost reduction and there exist many models in literature.
However, under real drilling conditions, it is difficult to apply the models from experimental conditions or theoretical analysis, because a model is simply a mathematical representation of a physical process, its utility depends on the similarity between the conditions in which it was derived and those in which it is to be applied. In fact the real drilling conditions almost always differ radically from the experimentally or theoretically presumed conditions.
Logging data closely represent the real drilling conditions and usually readily available from exploration wells, therefore it is desirable to develop drilling models from such data. However, due to lacking in systematic method for manipulating the apparently erratic raw data, people usually fail to develop reliable and then resort to upgrading the logging equipment or to correcting the data based on some assumptions, e.g. the effect of temperature on ROP etc.
Since conventionally the measurement interval for ROP measurement is 1-foot or 1-meter, the effects of gravity force and temperature on ROP are trivial within it and even within a bit run the effects of gravity force and temperature vary little and can be negligible. In fact few apparently erratic ROP data correspond to the usually assumed sources of erratic measurement, e.g. severe variations of WOB. Even under Even closely controlled drilling conditions in laboratory, e.g. using homogeneous rock samples, maintaining constant drilling parameters and minimizing compliance of drill string, it is still very difficult, if not impossible, to explain the variations of ROP samplings from tiny interval.
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