Rate of Penetration Prediction Using Quantile Regression Deep Neural Networks

Abstract As the petroleum industry makes strides towards meeting the energy efficiency and low emissions goals required to tackle ongoing climate challenges, there is an increasing need for optimizing drilling operations. A central aspect of drilling optimization lies in the ability to select the drilling parameters that improve the rate of penetration (ROP) for the rock formations being drilled. Optimization algorithms require an efficient predictive model of the ROP as a function of key drilling parameters and formation properties. Over the past decades, various mathematical ROP models have been developed. The use of machine learning and artificial intelligence for ROP modeling has become quite common, as indicated by the quickly expanding literature on this topic in recent years. Most of these modeling efforts have focused on providing single-point forecasts of ROP without any indication of the uncertainty surrounding the predictions. However, different factors, such as bit wear or foundering may severely limit the achievable ROP. Without including such uncertainty in the predictions, the reliability of ROP models for optimization and decision-making can be difficult to evaluate. To address this issue, we present the application of quantile regression deep neural networks (QRDNN) to the ROP prediction problem. In our work, quantile regression models perform probabilistic forecasts of ROP for a given range of drilling parameters and formation properties available from logging while drilling measurements or offset well logs. The model outputs consist of estimated values for different quantiles, such as the P10, P50, and P90 estimates, and associated confidence intervals. Several such models with different input features and neural network architectures, including fully connected, convolutional, and dropout layers, are trained and validated on publicly available field data spanning 12 hole sections from 7 wells drilled in the Volve field in the North Sea. The results indicate that the QRDNN achieves good prediction accuracy within the projected confidence intervals. These results highlight the advantages of combining deep learning with quantile regression compared to using machine learning models which only generate single-point predictions for the ROP.