Real-Time Inference and Uncertainty Quantification of Friction for Coiled Tubing Operations

Abstract

Abstract For many years, tubing force models (TFMs) have been used to predict coiled tubing (CT) reach in the wellbore, de-risk interventions, and track CT pipe life. Several input parameters, for example, the friction coefficient, the stripper friction, and the fluid viscosity, are difficult to obtain before an operation. They are typically fitted later during the operation or once the operation is completed. A method is presented here to infer those parameters iteratively in real time during the job. The method is based on the unscented Kalman filter (UKF). A TFM predicts the surface weight from input parameters. The UKF solves the "inverse problem" by observing the noisy surface weight measurement and infers the unknown parameters in a probabilistic way. Unlike the fitting-based optimization methods, UKF is an iterative method and makes an incremental update to the parameters from each measurement. Moreover, based on probabilistic theories, the UKF computes rigorously the uncertainty bounds of the inferred parameters. We implemented a UKF framework in Simulink. To test the model, a synthetic dataset with well-defined ground truth friction and well trajectory was first created. This synthetic well had a vertical section of 2 km (6,562 ft) below the surface, followed by a 2-km deviated section of constant dogleg severity where the well changes from vertical to horizontal, followed by a last horizontal section of 2 km. An analytic solution for the surface weight was derived for this specific well, and Gaussian noise was added to the solution to mimic the measurement noise. The noisy synthetic data were fed into the customized UKF framework with a wrong initial guess of the friction. The UKF framework incrementally and correctly adjusted the friction to the ground truth friction value in a few hundred iterations at 0.1 Hz. In real operations, if there is a sudden condition change, one expects the UKF to take similar steps to adapt to the change. Next, actual data from a previous job were replayed iteratively into the UKF framework. No ground-truth friction value existed for that dataset. But with the real-time inferred friction, the model was observed to provide a much better surface weight prediction compared to a legacy model without parameter inference. To the knowledge of the author, this is the first time UKF is reported to perform parameter inference for CT operations. It provides clear advantages compared to the legacy fitting-based method because (1) it can easily handle multiparameter inference; (2) it is straightforward to quantify the uncertainty of the inference; (3) the filter can incorporate any prior knowledge about the parameters; and (4) the method can be applied iteratively, continuously, and automatically.