Numerical Modeling of Liquid–Liquid Mass Transfer and the Influence of Mixing in Gas-Stirred Ladles

Abstract

Ladle refining plays a key role in the steelmaking process. During the refining, a bubbly gas stream is used for mixing and to enhance the rate of removal of impurities from the molten steel. A numerical model has been developed to understand mass transfer and mixing behavior in a three-phase gas-stirred ladle. A two-resistance approach was used for the liquid–liquid mass transfer, while the mass transfer coefficient was determined using the Small Eddy theory. The model was validated with experimental data, obtained from a water–oil physical model simulating an industrial ladle with a scale factor of 1/17, valid for axisymmetric gas injection. Three variables were included to study the mass transfer behavior, namely gas flow rate, Q, oil (slag) thickness, h, and oil (slag) viscosity, $$ \mu_{\text{o}} $$ . The gas flow rate ranged from 2.85 L/min to 8.56 L/min to meet industrial operating conditions. It was found that: (1) the volumetric mass transfer coefficient (ka) increases when the gas flow rate (Q) increases; and (2) increasing slag (oil) thickness has a positive influence on mass transfer as it considerably increases the interfacial area and promotes turbulence at the interface. At this range of gas flow rate, the effect of slag (oil) viscosity is limited. A general correlation was established: $$ {\text{ka}} = 0.058Q^{0.459} h^{0.612} $$ . Mixing time was studied within the same flow rate range to observe its influence on the mass transfer. Mixing in the ladle is accomplished in a much shorter time than interphase mass transfer, specifically by two orders of magnitude, which indicates that mass transfer is the rate-limiting step.