In the oil industry the localization of a leak that occurs in a pipeline is an important piece of information that needs to be obtained before mitigating actions can be taken to remedy the leak effects. In this paper we are particularly interested in testing a leak localization model for two-phase flows based upon the intersection of the hydraulic grade lines emanating from the pipeline ends. This methodology is commonly applied to single-phase-flows. In two-phase flows, the flow-pattern that develops along the entire pipeline upstream and downstream of the leak strongly affects the pressure gradient and has significant influence on the location of the leak. We consider this two-phase flow to be steady and to occur in a nearly horizontal pipeline characterized by the stratified-flow pattern. We also assume that the flow is isothermal with a compressible gas phase and an incompressible liquid phase. The results of the numerical simulations allow the model sensitivity to be studied by changing the leak location, for a given leak magnitude. From this analysis, we may observe how these parameters affect the pressure gradients along the pipeline that develop upstream and downstream of the leak and the model’s ability to predict the leak location.
Two-phase flows in pipelines occur in a variety of processes in the nuclear, petroleum and gas industries. Because of the practical importance of accurately predicting steady and unsteady flows along the line, one-dimensional two-fluid flow models have been extensively employed in numerical simulations. These models are usually written as a system of non-linear hyperbolic partial-differential equations, but some of the available formulations are physically inconsistent due to a loss of the hyperbolicity property. In these cases, the associated eigenvalues become complex numbers and the model loses physical meaning locally. This paper presents a numerical study of a one-dimensional single-pressure four-equation two-fluid model for an isothermal stratified flow that occurs in a horizontal pipeline. The diameter, pressure and volume fraction are kept constant, whereas the liquid and gas velocities are varied to cover the entire range of superficial velocities in the stratified region. For each point, the eigenvalues are numerically computed to verify whether they are real numbers and to assess their signs. The results show that hyperbolicity is lost near the boundaries of the stratified pattern and in a vast area of the region itself. Moreover, the eigenvalue signs alternate, which has implications on the prescription of numerical boundary conditions.
To maintain efficiency and high productivity in pipeline operations, it is necessary to keep an updated maintenance program. To accomplish this goal, the use of pigs is a very common task, but not a simple one, since there are uncertainties and risks associated to their passage, especially inside long pipelines. For these reasons, it is important to understand how the motion of the pig impacts the line operation and vice-versa. Therefore, it becomes crucial to accurately predict the pig motion and the fluid flow within the pipeline. To do so, numerical simulations are the easiest and cost-effective way to address such a problem. This paper presents a mechanical model, along with a numerical scheme, to obtain approximate solutions to the resulting initial-boundary-value problem that describes the pig movement in a transient two-phase flow inside a pipeline. The model is discretized using the Flux-Corrected Transport (FCT) method along with the Petzold-Gear method. A numerical simulation was carried out for a foam pig travelling in a typical stratified-pattern two-phase flow in a gas pipeline and the obtained results were compared with the well-known commercial software OLGA.
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