Measurement and correlation of axial dispersion coefficient in a bubble column with a non-Newtonian liquid phase

Abstract

Hydrodynamic characteristics (gas holdup, friction factor, and mixing in the liquid phase) in a bubble column with a non-Newtonian liquid phase (aqueous solutions of carboxymethylcellulose, or CMC, at different concentrations) were measured and correlated. A three-step strategy for this novel approach was devised: first, the rigorous characterization of the rheology of CMC aqueous solutions was conducted to obtain the rheological parameters; second, the hydrodynamic characteristics were measured experimentally; and third, the variables measured were correlated in terms of the rheological parameters of the liquid phase. The rheological characterization of the aqueous CMC solutions was conducted in a StressTech Rheometer; the power-law model offered an excellent fit of the data and more complex models did not provide substantial improvement to justify their use. Changes in CMC concentrations, sample temperature, and the time of dissolution of the CMC powder in water affected the rheology of these solutions. Additionally, dynamic tests showed a viscoelastic behavior of CMC solutions. Experiments in a 0.2-m diameter, 2.4-m-high bubble column were carried out to determine pressure drop, gas holdup, and degree of mixing in the liquid phase at various gas and liquid flow rates. The pressure drop, measured with a differential pressure transducer, allowed the calculation of the two-phase friction factor and gas holdup. The gas holdup was also obtained by the disengagement technique. Residence-time distribution experiments were carried out by methylene-blue impulses to characterize the mixing of the liquid phase in two operating modes: batch and continuous. At the superficial velocities selected, two flow regimes were observed: heterogeneous bubbling flow and heterogeneous churn turbulent flow, and they were identified through the slope changes in the plots of pressure drop and gas holdup. The pressure drop did not seem to be affected by the superficial liquid velocity and it increased as the superficial gas velocity decreased or the CMC concentrations increased. Both techniques used for gas holdup gave similar values (within ±10%). Gas holdup was not affected by the superficial liquid velocity and increased as superficial gas velocity increased. With respect to mixing, two models were used to interpret the experimental data: the axial dispersion model was used in the two operating modes, batch and continuous, and the tanks-in-series model was used just in the case of continuous mode. The axial dispersion model with closed-closed boundary conditions fit experimental data quite well and thus was used to estimate the axial dispersion coefficient. This parameter was higher in batch mode than in continuous mode, and its trend was to increase as superficial gas velocity increased. The flow behavior and consistency indices of the power-law model, among other standard variables, were used in correlations for the pressure drop, two-phase friction factor, gas holdup, and axial dispersion coefficient in the liquid phase. Inasmuch as possible, dimensionless numbers were used in these correlations. Excellent agreement between predicted and experimental values was obtained. The proposed correlations compared favorably to expressions proposed by other authors. In summary, a creative and novel approach, holistic in nature, has been pursued. All aspects including rheology, careful experimentation, and rigorous mathematical analysis were taken into account. The results of this work provided an important tool to design bubble column reactors in applications such as fermentation and three-phase catalytic reactions where a powdered catalyst is a suspended in a liquid showing a nonNewtonian behavior. Therefore, this work constitutes a significant contribution to the field of heterogeneous reactor modeling.