A Study of the Distribution of Formation Drillability

This study presents a method to generate the distribution of drillability in a cross section for formation simulation. According to data derived from well loggings and results from laboratory microbit tests on 32 rock samples in Daqing, a mathematic model for describing the correlation of sonic logs with the formation drillability for different lithology types is established by regression analysis. Rescaled (R/S) analysis indicates that sonic logs have a fractal character. Fractal theory can be used to describe formation heterogeneity. Successive random additions (SRA) is a fractal interpolation technique to generate distribution of values between two data points. Combining techniques of fine strata correlation and depth normalization, this article puts forward a method of random four-well fractal interpolation that suggests that this method should be improved from linear two-well interpolation to planar four-well interpolation. An accurate distribution field of acoustic log has been built up and a cross-sectional model of drillability is developed to represent the distribution of interwell drillability according to the established mathematic model. The practice shows that simulations of process performance can effectively quantitatively assess the influence of formation heterogeneity on drillability.