The Efficacy of a Three-Dimensional Static Liquid–Vapor Interface Model to Calculate the Static Liquid Holdup of a Packed Bed

Abstract

When liquid flows in an operating packed bed, some volume of the liquid remains in the bed at any instant of time. This is known as total liquid holdup. When the liquid flow is stopped, some portion remains static in the bed and the rest drains out. The first portion of the total liquid holdup is known as the static liquid holdup. The extent of the static liquid holdup affects mass transfer, heat transfer, permeability, as well as productivity of a packed bed reactor. Experimental and fundamental research has been performed to calculate the extent of static liquid holdup for last several decades. Many empirical correlations have been developed and mathematical models have been made in pursuit of quantifying this. However, significant difference in the experimental observations and modeling results can still be seen in the literature. In this work, a fundamental building block of a packed bed, i.e., a two-sphere contact, has been taken as the investigation domain. Experiments have been performed to understand how liquid films are formed, their shapes and variation of maximum static film volume before dripping, with respect to inclination for specific contact angles. Dripping involves formation and draining of droplets, and a volume remaining at the contact after dripping; these are measured for various inclinations of the sphere contact axis. Notionally, static liquid holdup is the volume of the liquid that can be held at the two-sphere contacts due to the interplay between static forces namely the surface tension and gravitational force. Hence, the mathematical model incorporating only static forces to capture the three-dimensional liquid shape at the two-sphere contacts, developed in a previous work of our group, is used in this work, and it is shown that the maximum volume of liquid before the liquid dripping can be very well captured for various inclinations. On the other hand, the remaining volume calculated from the mathematical model, with the assumption of quasistatic droplet detachment, results in much underprediction. When the two-sphere experimental values are extended to packed bed situations, it can be shown that the static liquid holdup calculated from the remaining volume after dripping matches are closer to the packed bed experimental values, whereas static liquid holdup calculated from maximum volume leads to overprediction.