This research aimed at developing a mathematical model for the prediction of NTU/HETS and the mass transfer coefficient for the VPE based on the agitation level of the plates (af – the product of frequency and amplitude of the plate reciprocation), the plate spacing, and the flow rates of the fluids, which will allow for the simplification in the design of this type of column.
The system chosen was the acetone-toluene-water system with the acetone in toluene forming the feed that is dispersed in the column and moves upward while the water moves as a continuous phase countercurrently down the column. This system is a standard test system for liquid extraction as stipulated by the European Federation of Chemical Engineering. The total throughput of the system was kept constant at 30 l/h while varying the individual flow rates to achieve the 1:2, 1:1 and 2:1 solvent to feed ratios.
The experimental part of the research was divided into two broad sections viz.
hydrodynamics and mass transfer. In attempting to develop the mathematical models, the following experimental investigations were examined: effects of agitation level and S/F ratio on drop size/distribution and holdup with and without mass transfer; effects of agitation level, S/F ratio and tray spacing on the extent of mass transfer, NTU and the efficiency;
effects of mass transfer on drop size/distribution and holdup.
In the operation of the equipment it was found that flow rates could not be measured accurately with rotameters because of fluctuations caused by the peristaltic pumps and the pressure changes at the bottom of the column caused by the vibration of the plates. Surge tanks were designed, built and installed in order to overcome this limitation. One surge tank was placed between the water inlet pump and rotameter which allowed for steady flows to be read off the rotameter. A second surge tank was installed between the feed inlet pump and rotameter in order to absorb the fluctuations of the pump while a third tank, placed between the rotameter and the feed sparger, reduced the effects of the pressure changes at the bottom of the column from affecting the rotameter reading.
Preliminary tests showed that a minimum of 45 minutes was required for an experimental run for the system to reach steady state before readings, photos or samples could be taken.
The holdup during mass transfer and in the absence of mass transfer decreased initially as the agitation level was increased (during the mixer-settler regime) until it reached a minimum at an agitation level of 3.75 mm/s (transition between mixer-settler and diffusion regimes) before having an increasing trend beyond this limit (for the diffusion and eventually emulsion regimes). The holdup decreased as the S/F ratio increased and since it was found that there was a weak relationship between continuous phase flow and holdup, it was concluded that the holdup decreased with a decrease in dispersed phase flow and was independent of continuous phase flow. The holdup during mass transfer was lower than that in the absence of mass transfer due to the solute being continuously removed from the dispersed phase resulting in there being lesser dispersed phase and a lower holdup during mass transfer.
Drop size analysis showed that there was a wide distribution of sizes at low agitation levels which became narrower as the agitation level was increased corresponding to a decrease in the Sauter mean diameter as the agitation level increased. During mass transfer there were a few large drops that were observed even at high agitation levels as a result of enhanced coalescence effects. When the tray spacing is increased, the distribution is wider resulting in a much higher Sauter mean diameter for all the agitation rates. This is due to the reduced coalescence and breakup of the drops which occur predominantly in the vicinity of the plates.
From the differences in the measurements during hydrodynamics and mass transfer (for the measurement of holdup and droplet size/distribution) it was concluded that the measurements during hydrodynamics cannot be used in correlations for the prediction of performance of the extractor since the process of mass transfer affects the hydrodynamics of the column (although the shape of the holdup and droplet size graphs were the same, the actual values were different).
The amount of acetone extracted during the mass transfer experiments gradually increased
smaller droplets were formed which increased the interfacial area available for mass transfer which improved the extent of acetone removal. As the S/F ratio increased, the concentration difference (driving force for mass transfer) was increased which increased the amount of acetone removal. With the increased plate spacing the extraction effectiveness is drastically reduced due to a fewer number of transfer units being present for the mass transfer to take place. The amount of energy dissipated to the fluids from the vibrating plates is also reduced due to the fewer plates, resulting in larger drops and lower holdup. This contributes to the poorer performance.
The ideal number of transfer units taking into account the backmixing of the phases was calculated graphically using the McCabe Thiele method. By plotting the operating line for the various cases the extent of backmixing was noticed. For the 1:1 flow ratio, the backmixing was minimal for the low agitation levels with evidence of the start of backmixing in the dispersed phase at the maximum agitation while there was no notice of backmixing in the continuous phase. For the 2:1 flow ratio, no backmixing was seen to occur in either phase. During the 1:2 flow ratio, there was backmixing for all the agitation levels in the dispersed phase while the start of backmixing in the continuous phase was seen.
Using the information of NTU calculations an empirical correlation was developed for the prediction of the measured NTU taking into account axial dispersion (Noxm). The data for the 1:1 flow ratio with both tray spacings was used to develop the correlation for the effects of agitation level, tray spacing and flow ratio. The correlation was tested with data for the other 2 flow ratios and showed reasonable accuracy with a maximum error of 6 %. The correlation was also adapted to calculate the HETS.
From the holdup and drop size data and the actual number of transfer units identified in the column, a correlation was developed for the prediction of mass transfer coefficient for the 1:1 flow ratio at both tray spacings as a function of agitation level and tray spacing. The correlation was tested for the other 2 flow ratios and showed reasonable accuracy with a maximum error of 13 %. The mass transfer coefficient was found to be independent of flow ratios.
The volumetric, overall and Murphree efficiency calculated was seen to remain constant in the mixer-settler regime and increase exponentially in the dispersion and emulsion regimes and decreased with an increase in flow ratio and tray spacing.
Recommendations and Future Work:
The flow rate through the feed pump was unstable and was dependent on the positioning and flexibility of the tube than ran through the pump and as a result it is highly recommended that a flow controller be installed in order to maintain a constant flow rate.
Additional experiments are required to test the models developed for tray spacing and amplitude changes.
More experiments are also required for agitation levels in the emulsion regime near the flooding point.