Dynamic analysis of a pipe conveying a two-phase fluid considering uncertainties in the flow parameters

This paper is interested in the dynamics of a horizontal pipe conveying a two-phase fluid (gas and liquid), which is a problem of great regard for the oil and gas industry. The purpose of this paper is twofold. First, it introduces dimensionless coefficients that carry the information of the two-phase flow, allowing the dynamic equation to be written analogously to the equation of a single-phase fluid. Second, a probabilistic model is developed considering uncertainties in three flow parameters, (1) the flow profile factor, (2) the slip ratio and (3) the vapour quality, in order to analyse the influence of these parameters on the dynamic stability and on the frequency response of the system. The pipe is described using the linear elastic Euler-Bernoulli beam theory, and the fluid is modelled taking into account a constant tangential velocity of the flow. The coupled system is discretized by means of the finite element method, and the stochastic problem is approximated using the Monte Carlo method. The flow parameters affect greatly the system response, and different values of the critical flow velocity are obtained, depending on the level of uncertainty of the parameters.