Using a Genetic Algorithm to Estimate Bingham Equation Parameters for Rate of Penetration Prediction

Abstract Bingham rate of penetration (ROP) model offers a reasonably accurate and easy-to-compute equation for ROP prediction. However, the model requires estimating the local empirical parameters varying by region and formation encountered. This requirement may cripple the effective utilization of the model when new entrants drill in a location. The standard method for estimating these empirical parameters is by iterations to find the optimum values. This work presents a methodology for estimating localized modified Bingham equation parameters using the Genetic Algorithm (GA). The case study was conducted on a large dataset collected from 260 wells covering the range of formations in the Western Desert of Egypt. The dataset provides more than 390,000 records for twenty-eight different formations in two different geological basins in the Egyptian Western Desert. The data was pre-analyzed by two different data processing techniques prior to its introduction to GA. The parameters of the modified Bingham model for every formation were determined using the entire dataset. The outcome range of the dataset prediction error ranges between 5.3 m/hr and 26.1 m/hr, with an average error of 13.91 m/hr for all 28 formations. In addition, it was observed that the model had increased accuracy with depth despite some anomalies that could be found in a few formations. The resultant empirical parameters for the modified Bingham ROP model of the case study can be used for any Egyptian Western Desert ROP prediction application, while the introduced algorithm can be applied elsewhere to find the value of its local empirical parameters.