Two phase flows occur in many engineering problems, especially in the nuclear, gas and petroleum industries. In oil and gas applications, specifically, a mixture of oil and natural gas is transported in pipelines from offshore platforms to the continent. The prediction of how the flow behaves in time as it moves along the pipe is extremely important, mainly during the pipeline design stage or regular operation. This paper presents simulations for stratified gas-liquid two-phase flow in a horizontal pipeline that is subject to the temperature gradients that exist in the bottom of the ocean, and the resulting heat transfer process that may lead to wax formation and deposition. A one-dimensional two-fluid mathematical model was employed that includes conservation equations of mass and momentum for each fluid and one energy equation for the mixture of liquid and gas. The problem was formulated as an initial-boundary value problem of the hyperbolic type and it was solved using the Flux Corrected Transport (FCT) numerical method, which is second-order accurate in space, coupled with an explicit discretization in time that is first-order accurate. The FCT method is appropriate to solve problems characterized by hyperbolic equations that may contain discontinuities and shock waves, and it presents small dispersive effects. The results showed excellent accuracy results when compared to commercial software widely used in the oil and gas industry.

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