Physics-Informed Neural Network to Estimate Downhole Torsional Vibrations and Friction Coefficients

Abstract This paper introduces a method to estimate bit rotation speed and friction parameters in torsional drilling systems using Physics-Informed Neural Networks (PINNs). The proposed approach is versatile and applicable in the general setting of parameter estimation for nonlinear differential equations with partial measurements. The method is validated on both simulated and field data, making, to the best of our knowledge, the first application of PINNs for parameter estimation of a dynamical system using industrial data. The approach successfully predicts downhole bit rotation speed ωBit, and identifies friction coefficients along the drill string based solely on 1Hz surface measurements. Furthermore, it is generalizable, allowing it to be utilized for any well without restrictions, thereby addressing the limitations inherent in data-based models. Unlike physical models that require friction coefficients as input to estimate ωBit, this approach relies solely on surface measurements to predict both ωBit and friction coefficients. A transfer learning technique is incorporated to expedite the training process when transitioning between different sequences of surface data. This strategy proves highly effective, both in accurately estimating the friction coefficients and in reducing training time by nearly sixfold, thereby enabling the PINN's practical application in real-time scenarios. The calibrated friction coefficients and predicted bit rotation speed, obtained over the full drilling duration, provide valuable insights for drilling engineers, enabling enhanced control and optimization of critical parameters like weight-on-bit and rate-of-penetration, thereby improving drilling performance and efficiency.