Mixing of Miscible but Dissimilar Liquids in Serial Flow in a Pipeline

Abstract

New formulae for determining the length of an interface that occurs during consecutive flow of fluids through a single pipeline are deduced in this paper. They result from an analysis carried out using data obtained from pipes varying from 1/8 inch to 40 inches in diameter, and from a few feet to hundreds of miles in length. Whilst previous theory, that the volume of mixing varies to an extent with diameter of pipe and distance travelled by the interface, is confirmed, it is also shown that there are two distinct regions of commingling in turbulent flow for each pipe diameter. The transition from one region to the other occurs quite sharply at different Reynolds number for each diameter of pipe. Below these critical values for Reynolds number commingling will increase rapidly as the Reynolds number decreases, even though flow may nominally still be well within the turbulent range. An explanation for this phenomenon—which hitherto appears to have received little or no attention—is attempted. The work is of practical significance for the oil industry in the field of ‘products pipelines' design.