Wax deposition continues to be a relevant problem for petroleum production and transportation pipelines. This viscous and waxy flow is theoretically modelled with a simple conservation equation system, by expressing the wax layer thickness as function of time and duct length. The flow parameters are written, depending on these independent variables but also on the Reynolds and the Peclet numbers, where effect of latent heat on the wax layer thickness deposit is investigated. A numerical simulation of the flow, for two practical cases, is performed in order to predict the pipeline obstruction.
A dynamical study of a bubbly flows in a transversal varying section duct (Venturi), is modeled by the use of the mass and momentum phases equations, which are coupled with the Rayleigh-Plesset equation of the bubbles dynamics. The effects of the throat dimension and the upstream void fraction on flow parameters are investigated. The numerical resolution of the previous equations set let us found that the characteristics of the flow change dramatically with upstream void fraction. Two different flow regimes are obtained: a quasi-steady and a quasi-unsteady regimes. The former is characterized by a large spatial fluctuations downstream of the throat, which are induced by the pulsations of the cavitation bubbles. The quasi-unsteady regime corresponds to flashing flow in which occurs a bifurcation at the flow transition between these regimes. This transition occurs at R c 4.3 which corresponds to s 4.710-3. An analytical expression for the critical bubble size at the flashing flow point is also obtained and compared with theoretical data.
The transient vaporous and gaseous cavitation phenomena in an elastic pipeline are investigated for homogeneous liquid‐gas mixture flow. It has been shown, in the case of two components having the same velocity, that modelling is also possible by considering the continuous character of the medium, i.e. without any location of column separation. The governing equations have been solved by using two finite difference schemes: the Mac Cormack’s scheme and an improved new finite difference two‐time step scheme. Characteristics method is used at the boundaries. The theoretical results obtained are compared and found to correlate well with similar results.
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