Bi-nonlinear vibration model of tubing string in oil & gas well and its experimental verification

Fluid-induced vibration (FIV) prediction is an important prerequisite work in wear and fatigue analysis of tubing string in oil & gas well. The finite element method, energy method and Hamiltonian principle are comprehensively used to establish a single nonlinear vibration model of pipe conveying fluid, taking into account the longitudinal/lateral coupled vibration. Based on the contact/impact theory of elastic/plastic body, the nonlinear contact-impact model of tubing-casing is established and introduced into the single nonlinear vibration model to form a bi-nonlinear vibration model of tubing string in oil & gas well. The bi-nonlinear model is numerically discretized by the finite element method, solved by Newmark− β method, and verified preliminarily by a classical contact/impact example in literature in which the influence of inflow is not taken into account temporarily. A similar experiment of tubing vibration is designed and completed to further test the validity of the bi-nonlinear vibration model by comparing the frequency-domain and time-domain responses of the experiment with those from the model. The analysis shows that the bi-nonlinear model has good calculation accuracy and the vibration response law is basically consistent with the experimental results, which can provide an effective theoretical analysis tool for FIV behavior of tubing string in oil & gas well.