Estimation of High-Frequency Vibration Loads in Deep Drilling Systems Using Augmented Kalman Filters

Deep drilling operations are primarily used to produce oil, gas, and geothermal heat from reservoirs in the earth’s crust. Today’s drilling technology allows to drill holes up to several thousand feet of true vertical depth and through long horizontal reservoir sections. A drill string, built of thread-connected components, is used to transfer mechanical energy from a drill rig at the surface to the drill bit at the bottom end. The lowest part of a drill string is called bottom-hole assembly (BHA) and contains sophisticated subassemblies for process and trajectory control, formation evaluation, surface communication, power generation, and system diagnostics. To maximize the design space for moving parts and electronics, the BHA has a greater diameter and greater stiffness than the rest of the drill string. As a consequence, the BHA can experience critical vibration without indication further up the string. These vibrations need to be closely monitored for process control, fatigue management, and design feedback.

Leading-edge measurement tools provide a sufficient sampling rate to acquire and store high-frequency stress and acceleration data for one sensor position. However, the associated mode shapes are characterized by short wavelengths, i.e., critically and negligibly loaded sections in close proximity. Even in high-end BHAs, the number of sensors is too small to provide reliable indication of loads on all critical components of the drill string. Adding sensors to each component, is currently neither economically nor technically viable.

This paper presents the application of Kalman Filters merging information from available sensors and dynamic models to obtain state estimates for all components of the BHA. The dynamics of drill strings can be described analytically, experimentally, e.g., using experimental and operational modal analysis or numerically, e.g., using the finite element method (FEM). Obtained dynamic models describe motion and stresses of the drill string over time, enabling interpretation of state estimates in terms of deflection, velocity, acceleration, internal forces or stresses.

A thorough analysis of load extrapolation based on test load measurement data is presented. Existing Kalman Filter types are considered for the task of load extrapolation from a minimal set of sensors to any component of the BHA. The expected accuracy and limitations are discussed for varying numbers and qualities of sensors. Results of load extrapolation are confirmed by comparison with measurements proofing the concept under inaccurately defined interaction with a downhole environment. The conclusion is that, using Augmented Kalman Filters, it is possible to evaluate the loads on BHA components caused by high-frequency vibration using minimal available measurement equipment.