A Dynamic Model with Friction for Comprehensive Tubular-Stress Analysis
Authors: Mitchell Robert F. , McSpadden Albert R. , Goodman Malcolm A. , Trevisan Ruggero , Watts Rick D. , Zwarich Nola R. 
Published: March 2020

A new model technique is described for comprehensive dynamic stress and displacement analysis of wellbore-completion tubulars, including friction loads with history. 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 can be simulated for the installed casing and tubing through the service life of the well.

The dynamic friction model subdivides the casing or tubing 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 the 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 slackoff or pickup loads determine the initial tubing-stress 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. A change in the 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 a tubular-stress analysis. For slackoff, 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 a deviated profile and a 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 hookload plot during installation of a single-trip, multizone intelligent completion in an offshore highly deviated extended-reach-drilling (ERD) well. Example calculations are given for a high-pressure/high-temperature (HP/HT) subsea well and a horizontal unconventional well.

The dynamic friction model allows for the seamless integration of running loads with friction into a fully sequential stress analysis of subsequent well life-cycle loads for landed completion strings. Although dynamic analysis has been extensively applied to complex drilling phenomena such as drillstring vibration or bottomhole-assembly design, current industry models for completion tubulars such as casing and tubing separate the installation state from the in-service life envelope or attempt to solve the problem with a static analysis. This represents a critical deficiency in the current industry state of the art for completion tubulars, which the present work proposed herein strives to address. From a 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.