A Dynamic Model with Friction for Comprehensive Tubular Stress Analysis

Abstract

A new model technique is described for comprehensive dynamic stress and displacement analysis of wellbore tubulars including friction loads. A dynamic model of tubing forces is necessary to predict local pipe velocity which in turn determines the magnitude and direction of localized frictional contact. By tracking dynamic changes in axial force starting from the initial running state, a complete load history may be simulated through the life of the well. The dynamic friction model subdivides the string joint by joint and uses an elastic pipe momentum balance. Pipe velocity is related to axial force by the elasticity equation. Dynamically determined velocity is necessary to predict magnitude and orientation of local node friction vectors. Damping for the dynamic analysis is provided by annular fluid viscosity. The elastic equations are solved as a set of algebraic equations in terms of past and future values of pipe axial force and velocity. Key model inputs such as pressure, temperature, fluid and wellbore friction coefficients can be changed at each successive load step. Running loads and packer setting with slack-off or pick-up loads determine the initial string configuration. Given the initial configuration, each subsequent load case is calculated starting from the prior load and resultant friction state, allowing for full history dependence. The surface velocity profile of running individual stands is a key input. Unexpected magnitudes of downhole transfer of surface load are demonstrated. Change in operation load sequence is shown to produce significant differences in tubular axial loads, indicating that special attention to load history should be considered when performing tubular stress analysis. For slack-off, overpull, or packer setting events the model can track dynamic load response at downhole points such as a packer or cement top. An example well with deviated profile and planned sequence of life-cycle operations including stimulation, production and shut-in was simulated for a variety of load sequences. The model has been validated against field data using the actual hook load plot during installation of a single-trip, multi-zone intelligent completion in an offshore highly-deviated ERD well. Example calculations are given for an HPHT subsea well and a horizontal unconventional well. The dynamic friction model allows for seamless integration of running loads with friction into a fully sequential stress analysis of subsequent well life-cycle loads for landed strings. Current industry models separate installation state from the in-service life envelope. From comparison with appropriate static analytic solutions and industry standard drag and stress models, dynamics were found to affect friction force directions and magnitudes, suggesting that tubular dynamics cannot be neglected.