An Analytical Approach to Calculate the One-Dimensional Drift Velocity in Bubble Columns

Abstract

The design and scale-up of a bubble column reactor require a complete understanding of its complex hydrodynamics, which is influenced by the physical properties of the phases, the operating variables, and the design parameters. Current design procedures for bubble columns involve several steps of pilot-plant experimentation, which is expensive and time-consuming. One of the critical unknown parameters involved in designing any gas-liquid system is the gas holdup. The gas holdup distribution varies dramatically throughout the flow regimes and determining its magnitude from input conditions in a given pipe is complicated as a result of the relative motion between the gas and the liquid phases. One of the most practical and accurate models for calculating the gas holdup is known as the drift-flux theory. This model considers the influence of non-uniformity in the flow as well as the local relative motion between phases, which are known as distribution parameter and drift velocity, respectively. Several constitutive equations to determine the drift-flux model coefficients have been proposed. But owing to the complexity and lack of understanding of the basic underlying physics of the problem, the majority of the analyses are more inclined towards empirical correlations. In view of the practical importance of the drift-flux model, this study has focused on developing an analytical approach to calculate the drift velocity. The constitutive equation that specifies the drift velocity was derived by considering an axially symmetric flow through a circular duct and the flow and gas holdup distribution were estimated by power-law profiles. The results predicted by the analysis were compared with experimental data available in the literature over a wide range of column diameters and flow conditions. The proposed correlations are in satisfactory agreement with experimental data for the large diameter bubble columns, but they cannot predict the values of the small columns very well.