A Unique Computer Simulation Model Well Drilling: Part I—The Reza Drilling Model

ABSTRACT A new non-linear multidimensional, dimensionless mathematical drilling model for deep well applications, utilizing the Buckingham Pi theorem dimensional analysis technique, has been developed. The parameters included in the three equations of penetration rate, rate of bit dulling and rate of bearing wear are: the weight on bit, the rotary speed, the drilling fluid volumetric flow rate, the bit diameter, the bit nozzle diameter, the bearing diameter, the drilling fluid kinematic viscosity, the differential pressure, the temperature, and the heat transfer coefficient. The unknown exponents and proportionality constants were determined by using the statistical regressional curve fitting method utilizing actual field data from a 21,000 foot well within the Anadarko Basin located in Caddo County, Oklahoma. To generalize the model, a parametric study was performed for each of the exponents in each of the drilling equations. Also, a comparison between the derived model and the previously developed model which has been widely used by the industry was done. It was concluded that the derived model yields more realistic results in terms of factors affecting the deep well drilling process than the model compared in this study. This paper is only concerned with the development of the model and the determination or proportionality constants and unknown exponents. The remaining material will be presented in Part II of this series of two papers.