Use of slopelimiter techniques in traditional numerical methods for multi-phase flow in pipelines and wells

Abstract

The aim of this paper is to show how simple and traditional methods for simulating multi-phase flow can be improved by introducing higher order accuracy. Numerical diffusion is reduced to a minimum by using slopelimiter techniques, and better predictions of flow rates and pressure are obtained. Slopelimiter techniques, originally developed to achieve higher order of accuracy in Godunov's method, is applied to a method following a finite element approach and a predictor–corrector shooting technique. These methods are tested and compared to a Godunov-type scheme recently developed for multi-phase flow. Implementation of Godunov-type schemes for multi-phase flow tends to be a complicated and challenging task. Introducing the slopelimiter techniques in the finite element approach and the predictor–corrector shooting technique is however simple, and provides an overall reduction of the numerical diffusion. The focus is on using these techniques to improve the mass transport description, since this is the main concern in the applications needed. The presented schemes represent different semi-implicit approaches for simulating multi-phase flow. An evaluation of higher order extensions, as well as a comparison by itself, is of large interest. We present a model for two-phase flow in pipelines and wells, and an outline of the numerical methods and the extensions to second order spatial accuracy. Several examples motivated by applications in underbalanced drilling are presented, and the advantages of using higher order schemes are illustrated. Copyright © 2005 John Wiley & Sons, Ltd.