Computational Geometry as An Aid to Data Analysis of Drilling Data

Abstract

Abstract As the amount of real time data collected during drilling continues to rise, sophisticated methods for analyzing and displaying data are needed to make sense out of large volumes of data. This paper describes a novel use of the concepts of computational geometry to analyze and display data from a downhole drilling data tool. The use of a mathematical transformation called a convex hull allows one to create a boundary around a set (cloud) of data points. This is most easily visualized in two dimensions as putting a rubber band around the set of points. Imagine that the rubber band is such that it will be tightly stretched when it is around all the points, so that certain points in the data cloud dictate the resulting outline. A convex hull software routine, the best known of which is the"qhull" program from the University of Minnesota, fits line segments around a cloud of points in up to nine dimensions. Utilizing the convex hull output one can calculate the volume in 3-D or area in 2-D described by data clouds. The result is used as an indicator of bit and drill string behavior.