One of the major challenges during drilling in hard-brittle formation in Tarim basin is to evaluate the rock drillability and to predict the rate of penetration (ROP) accurately. The aim of this article is to analyze the drilling resistance of rock breaking and to predict the ROP from a new angle. In this paper, the fractal characteristic of rock fragmentation and the problem of rock energy consumption in drilling process are studied based on the fractal theory through rock-breaking laboratory experiment by roller cone bit and rock cuttings screening experiment. A new prediction model of energy consumption on rock fragmentation is proposed based on size distribution of rock cuttings, fractal dimensions, and energy dissipation analysis. Also, the prediction equation of ROP is given based on the principle of energy conservation. The biggest advantage of this model is that the energy consumption on rock fragmentation and the ROP can be predicted entirely based on rock cuttings, fractal dimensions and drilling parameters. According to field data analysis, the consistency, is encouraging, with an average error below 15%.
In drilling process, to make an accurate evaluation of rock drillability is an important basis for optimizing drilling parameters and determining drilling measures. Currently, many investigators have evaluated the rock drillability and predicted the ROP mainly from the perspective of rock drillability test indoor or drilling rate equation [3-6]. However, these methods are not only costly but also takes a long time; the ROP predictions are complicated and infeasible in field application.
Fractal geometry was originally developed by Mandelbrot to describe the highly irregular and self-similar objects, and then the fractal theory was applied to many other science fields [1, 8, 9]. In the field of rock comminution, numerous studies show that rock fragmentation has fractal characteristic; the fractal characteristic of cuttings reflects the rock crushing mechanism and energy dissipation process [2, 7, 8, 9]. In this paper, the size distribution of cuttings and drilling parameters are combined based on fractal geometry to develop a fractal model for energy dissipation of rock crushing. This model can be applied to determine the required minimum energy for rock breaking. Meanwhile, according to the principle of energy conservation, we can use this model to predict drilling speed. Therefore, the establishment of this model provides a new method for optimizing drilling parameters and improving drilling efficiency.