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 set of equations governing an isothermal compressible fluid flow is analytically and numerically analyzed. The obtained equations are written in characteristic form and resolved by a predictorcorrector lambda scheme for the interior mesh points. The method of characteristics (MOC) is used for the boundaries. Advantages of explicit form of these schemes and the flexibility of the MOC are used for an isothermal fast transient gas flow in short pipeline. The results, obtained for a simple practical application agree with those of other methods.
A study on the upslope flow of heated petroleum paraffin was conducted based on motion equations and heat transfer, which were rewritten in a completely dimensionless form to analyze the influence of temperature on the position of the deposit point and its change over time. A numerical resolution of the new equation system, based on the Runge-Kutta 4th order method, was performed for two current practical cases to avoid the line obstruction problem.Uneétude sur l'écoulement ascendant de pétrole, chauffé et chargé en paraffine, est menée sur la base deséquations du mouvement et du transfert de chaleur. Ces dernières sont réécrites sous une forme adimensionnelle complète, afin d'analyser l'influence de la température sur la position du point de déposition et sonévolution en fonction du temps. Une résolution numérique du nouveau système d'équations, basée sur la méthode de Runge-Kutta d'ordre quatre, est réalisée pour deux cas pratiques courants afin de prévenir le problème d'obstruction des conduites.
In the present work, the bubbly cavitating flow phenomena after passing through the converging nozzle is numerically investigated. The dynamic of the cavitating bubbles is modeled by the use of the mass and momentum phase's equations, which are coupled with the Rayleigh-Plesset equation of the N bubbles dynamics. However, assuming that the same initial conditions of all bubbles are identical and that all bubbles are equi-distant from each other simplifies the governing equations. Equation set is numerically resolved by the use of a fourth order Runge-Kutta scheme. The numerical resolution of the previous equations set let us found that the bubble radius distribution, fluid velocity and fluid pressure change dramatically with upstream void fraction and an instability appeared just after the passing the converging nozzle for both cases one bubble N=1 and two bubbles N=2. Indeed, for the case of one bubble N=1, the flashing flow phenomena occurs for an upstream void fraction α s =11.2x10 -3 , which corresponds to a critical bubble radius R c =1.8. Whereas, for bubble number N=2, the same phenomenon occurs for α s = 8.9x10 -3 , with R c =2. This difference is due to the bubble interaction. Also, we found that, the bubble number N strongly affect the bubble frequency. However, with increase the bubble number, the maximum size of the bubbles increases and bubble frequency oscillation decrease.
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