6. Pressure Drop—Empirical Methods

Void fraction is a quantity of primary importance in the design and analysis of two-phase systems. The pressure gradient in two-phase flow is present in the momentum conservation equation; at steady state, it has three components, the gravity, acceleration and friction terms. The first two can be computed in a straightforward way if the void fraction distribution in the duct is known. The frictional pressure gradient requires further modelling and the largest part of the chapter is devoted to this. Traditionally, the frictional pressure gradient (or frictional pressure drop) in two-phase flows has been obtained using a reference pressure gradient (based on the flow in the pipe of one of the phases alone) corrected for the presence of two-phase flow by a multiplier. Martinelli introduced this method that is still widely used today long time ago.

The simplest way to compute the pressure drop in two-phase flow is when one uses the homogeneous model but this is generally not sufficiently accurate. A number of the numerous correlation methods that have been proposed over the years for the frictional multiplier are reviewed and the most often used ones discussed. Comparisons about the quality of the predictions by various correlations are presented. At the end of the chapter, there is a special section devoted to the methods used in the petroleum industry for large pipes. There is also a brief general discussion on the pressure drop in piping singularities.