Abstract
Two classical geometries for wellbore hydraulics are the pipe and the plane channel, (often approximating an annulus). The technical literature is full of semi-empirical methodologies for computing frictional pressure losses and flow regimes in these geometries and there is much confusion about both the validity and physical basis of many of these phenomenological criteria.
In this paper we examine phenomenological criteria for transition, in the context of newly derived theoretical results on stability of these flows. We examine five transitional criteria commonly used in the petroleum industry and are able to rigorously demonstrate that only one of the five criteria can possibly be correct over the full range of Bingham numbers. We then examine a more limited, but relevant, range of Bingham numbers and show that enormous discrepancies exist between these criteria. We conclude by discussing implications for current practice.
