Simplified 1D Incompressible Two-Fluid Model with Artificial Diffusion for Slug Flow Capturing in Horizontal and Nearly Horizontal Pipes

This article proposes a numerical resolution of a one-dimensional (1D), transient, simplified two-fluid model regularized with an artificial diffusion term for modeling stratified, wavy and slug flow in horizontal and nearly horizontal pipes. Artificial diffusion is introduced to prevent the unbounded growth of instabilities where the 1D two-fluid model is ill-posed. We propose a method to set the artificial diffusion case by case to obtain the desired cut-off at short wavelengths by combining the choice of the spatial discretisation and the amplification factors obtained by the linear stability analysis of the model. A proper criterion to simulate two-phase to single-phase flow transition, which occurs during slug formation, is also developed. Flow pattern transitions have been numerically computed and compared against theoretical transition boundaries and experimental observations. Moreover, we showed that the developed code computes slug initiation and slug characteristics, in a reasonably accurate way considering the simplicity of the model, comparing numerical results with well-known empirical correlations and experimental data. Furthermore, the model simplicity leads to a computationally-inexpensive numerical resolution; this can be useful in engineering applications where obtaining fast numerical results is fundamental, such as applications involving automated control for two-phase flows.