A macroscopic mass transfer model based on the unsteady‐state liquid film mass transfer mechanism for a single spherical bubble was formulated. Analytical solution of the model equation was obtained in Laplace transform using surface renewal rates based on Danckwerts' surface age distribution function. The mass transfer coefficient, kL, in a slurry bubble column under different operating conditions of temperature, pressure, gas flow rate, and solid concentration has been simulated using a program code “BUBBLESIM” in MATLAB®, developed by the authors. The proposed model has been validated using secondary data for a slurry system under a wide range of operating conditions. The predicted values of kL show very good agreement with the experimental data within an average deviation of ±2%. The results show that the mass transfer coefficient, kL, increased with increasing superficial gas velocity and temperature and decreased with increase in slurry concentration, while it changed slightly with pressure. Based on the present work, empirical correlations have been proposed for the prediction of δ in terms of dimensionless groups for H2–, CO–, and CO2–paraffin–quartz sand systems under elevated temperatures (298–423 K) and elevated pressures (1–3 MPa) in a slurry bubble column.
AbstractGas holdup is one of the most important parameters for characterizing the hydrodynamics of bubble columns. Modeling and design of bubble columns require empirical correlations for precise estimation of gas holdup. Empirical correlations available for prediction of gas holdup (εG) in various non-Newtonian systems for both gas-liquid and gas-liquid-solid bubble columns have been presented in this review. Critical analysis of correlations presented by different researchers has been made considering the findings and pitfalls. As the magnitude of gas holdup depends on many factors, such as physicochemical properties of gas and/or liquid, column geometry, type and design of gas distributors, operating conditions, phase properties, and rheological properties, etc., all of these have been discussed and examined. In order to emphasize the significance, relative importance of parameters such as flow behavior index, consistency index, column diameter, gas flow rate, and density of aqueous carboxymethylcellulose (CMC) solution on gas holdup has been quantified using artificial neural network and Garson’s algorithm for an experimental data set of air-CMC solution from the literature. Besides, potential areas for research encompassing operating conditions, column geometry, physical properties, modeling and simulation, rheological properties, flow regime, etc., have been underlined, and the need for developing newer correlations for gas holdup has been outlined. The review may be useful for the modeling and design of bubble columns.
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