Scope and Method of Study:

Understanding the processes governing axial dispersion of contaminants in a flowing system is one of the unsolved classical problems in fluid mechanics. Taylor (1953; 1954) provided a robust methodology to model such systems in their ideal laminar and turbulent flow conditions. The current study reveals that both laminar and turbulent conditions need to be considered simultaneously in order to accurately model axial dispersion in real systems. The analyses presented in this work provide a physical backing to Taylor's theory, while providing new conceptual visualizations of the processes governing axial dispersion. Theoretical and phenomenological analyses are carried out to show that the viscous sublayer has a significant role in axial dispersion under turbulent flow conditions. The current study reveals that both viscous and turbulent aspects need to be considered simultaneously in order to accurately model axial dispersion in real systems. Theoretical and phenomenological analyses are carried out to show that the viscous sublayer, long believed to be a major influence on axial dispersion, has a significant role in the axial dispersion phenomenon. The axial dispersion model proposed in the current study has been validated using laboratory, pilot, and field experimental data. The higher mixing rates at lower Reynolds number turbulent flows have been explained by the effects of the viscous sublayer. A straight forward technique to incorporate the influence of bends has also been included in this work.

Findings and Conclusions:

A robust phenomenological model has been developed for estimating the axial dispersion coefficient for flow of liquids through straight pipes. The proposed model employs the viscous sublayer thickness as a parameter to combine the convective-diffusion equation with the boundary layer theory. The mathematical formulations developed using Reynolds analogy, in concurrence with the characteristic turbulent bursting events observed in the near-wall regions of the flow, have been shown to be applicable even for non-ideal low Reynolds number turbulent flow conditions. This hints at the possibility of a universal theory governing all mass, momentum, and heat transport processes. Furthermore, theoretical and empirical concepts used in pressure drop estimations for flow through straight and bent pipes have been demonstrated to be applicable to axial dispersion estimations. The axial dispersion models proposed in the current study have been validated using laboratory, pilot, and field experimental data. The proposed concepts could be used in identifying novel techniques to help reduce interfacial contamination in petroleum pipelines and other similarly affected processes. This work is also expected to lead to improved models and theories that broaden our understanding of the axial dispersion process.