Design Expert-Based RMS for Optimization of Oil Drilling Mechanical Parameters Based on the Penetration Rate Model: Mathematical Modeling and Statistical Analysis

Abstract In modern times, many manufacturing processes and laboratory experiments are becoming increasingly intricate as they rely on a multitude of variables that are hard to intuitively manipulate. To make sense of and model such complex phenomena, the design of experiments methodology is one of the most effective approaches. In the current report, the Surface Response Method (RSM) was adopted to assess how different drilling mechanical parameters affect the Rate of Penetration (ROP). The main goal is to explore the behavior of ROP when various mechanical drilling parameters, including weight on the bit (WOB), rotational speed of the bit (RPM), and cutting angle (β), are altered. The investigation covers two types of limestone rocks, and the gathered data is statistically analyzed using ANOVA to develop a mathematical model that explains the relationship between the different parameters and the rate of advancement, using the Response Surface Method (RSM). The results demonstrate that the WOB factor has the most significant influence on ROP development for both rock types, compared to other factors. Applying an optimization method is likely to control the optimal parameters for the drill's rational operation regime. The model developed in this study accurately fits the data and is therefore valuable in predicting the response. The technical reason that prompted us to conduct this scientific research is the excessive and continuous alteration of mechanical parameters in the drilling machine WOB (80,120,160 kgf), RPM (118, 135, 152 rpm), β (3°, 8°, 45°), aimed at maintaining an advanced drilling rate and ensuring the safety of its components. Therefore, it is aimed to reduce this continuous alteration while achieving the same or better results. Each parameter can be limited to a single level to achieve the same or better results. For the first rock A, the parameters are (WOB = 80.632, RPM = 118.959rpm, β = 23.016°) and for the second rock B, the parameters are (WOB = 136.418kgf, RPM = 147.911rpm, β = 40.911°).