Online analysis and prediction of torque and drag (T&D) during drilling provides critical information for down-hole condition monitoring and drilling parameters optimization. It's difficult for traditional soft or stiff string methods to incorporate amounts of friction test data because of the complex string motion state in real wellbores and limited considering factors in physical model. Machine learning features in high dimensional process modelling and large volume of data processing, it's possible to increase the accuracy of T&D prediction during drilling by combining of traditional physical model and modern machine learning methods.

Combining the robustness and continuity of soft-string model and the nonlinear mapping capacity of machine learning method, a hybrid method is proposed to increase T&D prediction accuracy: (1) a soft string model is fitted by friction test observations (pick-up weight, slack-off weight, free rotating weight and torque) and predicts profiles of observations, (2) a machine learning model is designed to model the residual error between physical model predictions and real observations, considering additional influence factors (such as fluid properties, string moving velocity and acceleration), (3) a online learning algorithm is designed to describe the T&D changing trend and support prediction ahead of bit.

The hybrid method is tested in an ultra-deep well (depth is over 8000m) and a horizontal well and the performance is compared with physical model and machine learning model respectively. It's shown that the prediction error of hybrid method is 23.19% lower than physical model and the hybrid method is more stable than pure machine learning model, with prediction variance decreased by 11.06%. The hybrid method is helpful to predict down-hole weight on bit and diagnose abnormal down-hole conditions during drilling.

It's the first time that physical model and machine learning method are combined to analysis T&D based on literature review, providing a reasonable way to apply modern data science method in drilling engineering.

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