Residence Time Distributions for Turbulent, Critical, and Laminar Pipe Flow

Abstract

Longitudinal dispersion processes are often described by the advection dispersion equation (ADE), which is analogous to Fick’s law of diffusion, where the impulse response function of the spatial concentration distribution is assumed to be Gaussian. This paper assesses the validity of the assumption of a Gaussian impulse response function, using residence time distributions (RTDs) obtained from new laboratory data. Measured up- and downstream temporal concentration profiles have been deconvolved to numerically infer RTDs for a range of turbulent, critical, and laminar pipe flows. It is shown that the Gaussian impulse response function provides a good estimate of the system’s mixing characteristics for turbulent and critical flows, and an empirical equation to estimate the dispersion coefficient for the Reynolds number, R, between 3,000 and 20,000 is presented. For laminar flow, here identified as R<3,000, the RTDs do not conform to the Gaussian assumption because of insufficient available time for the solute to become cross-sectionally well mixed. For this situation, which occurs commonly in water distribution networks, a theoretical RTD for laminar flow that assumes no radial mixing is shown to provide a good approximation of the system’s mixing characteristics at short times after injection.