Numerical simulation of non-isothermal two-phase flow in pipelines using a two-fluid model

The analysis of two-phase flows through numerical simulations is a very useful tool to design and operate long pipelines. It is also important for monitoring the flow during adverse situations, such as the formation of hydrates and wax deposition that may occur due to temperature variations in the fluids along the pipe. The present work aims to validate a model along with a numerical technique for analyzing non-isothermal stratified-pattern two-phase flows that occur in typical gas-gathering offshore pipelines. The mathematical model is one-dimensional and based on a two-fluid model that comprises two mass and two momentum conservation equations, one for each phase, along with one energy conservation equation for the mixture. The system of equations is discretized in a conservative form within a finite-difference framework and is solved by the flux-corrected transport (FCT) numerical method. Because an ill-posed mathematical problem is obtained if the system of equations is not hyperbolic, a hyperbolicity analysis is performed for all cases simulated in this work, which also indicates how to impose the boundary conditions adequately and avoids the production of non-physical output. The results obtained for the distribution of pressure, fluid velocities, holdup and temperature along the pipeline demonstrated that even relatively small temperature differences between the fluids and the external environment at the pipe inlet cause significant thermal effects on the entire flow. The simulations also predicted results in good agreement with those of a commercial software used for comparison, for steady-state regime, and significantly different results from those produced by an isothermal-flow model, which emphasizes the importance of considering the heat transfer in the problem. In summary, the results showed that the mathematical model and the numerical method form together a reliable tool of second-order accuracy in space that perform accurate numerical simulations of two-phase flows in long pipelines that are subject to non-isothermal conditions.