An Empirical Boundary Layer Based Model to Predict Contamination in Multiproduct Refined Petroleum Pipelines

Theoretical convective diffusion models predict interfacial mixing volumes in refined petroleum pipelines using the square root of the travel/pipe length. This is an idealized case obtained by assuming the universal velocity profile and it has been shown to not being able to predict transmix volumes to the required degree of accuracy. This lack of prediction accuracy has been attributed to the presence of pipe fittings, entrance effects and other unaccounted factors.  Viable methods have not been developed to account for these factors and hence, empirical models are a popular choice for industrial applications. The empirical models available in literature suggest a variety of exponent values to replace the ideal square root relationship.  Values ranging from 0.38 to 0.62 can be commonly found in literature. This work intends to suggest a revised empirical relation for flow through straight pipes, with the power law exponent varying based on the physical properties of the system under consideration. The work also offers a phenomenological context to the development of the empirical model. It is argued that the viscous sub-layer has a major role in the formation of transmix and can be employed as a parameter to estimate the extent of contamination. The effects of bends and other pipe fittings have been accounted for by employing the technique of equivalent lengths that is conventionally know to apply to pressure drop predictions in pipe flows. A comparison of the predictions against literature data validates the improved accuracy of the present work.