Drilling rate of penetration prediction and optimization using response surface methodology and bat algorithm

Abstract

Rate of penetration (ROP) prediction is crucial for drilling optimization because of its role in minimizing drilling costs. There are many factors, which determine the drilling rate of penetration. Typical factors include formation properties, mud rheology, weight on bit, bit rotation speed, type of bit, wellbore inclination, and bit hydraulics.In this paper, first, the simultaneous effect of six variables on penetration rate using real field drilling data has been investigated. Response surface methodology (RSM) was used to develop a mathematical relation between penetration rate and six factors. The important variables include well depth (D), weight on bit (WOB), bit rotation speed (N), bit jet impact force (IF), yield point to plastic viscosity ratio (Yp/PV), 10 min to 10 s gel strength ratio (10MGS/10SGS). Next, bat algorithm (BA) was used to identify optimal range of factors in order to maximize drilling rate of penetration.Results indicate that the derived statistical model provides an efficient tool for estimation of ROP and determining optimum drilling conditions. Sensitivity study using analysis of variance shows that well depth, yield point to plastic viscosity ratio, weight on bit, bit rotation speed, bit jet impact force, and 10 min to 10 s gel strength ratio have the greatest effect on ROP variation respectively. Cumulative probability distribution of predicted ROP shows that the penetration rate can be estimated accurately at 95% confidence interval. In addition, study shows that by increasing well depth, there is an uncertainty in selecting the jet impact force as the best objective function to determine the effect of hydraulics on penetration rate.