Another parameter that should be considered in evaluation of a column is the average residence time of the fluid in the column. Based on principles of probability, the average residence time of a fluid element is given according to Hill as follows:. According to Barros et al.
Mass Transfer and Kinetics of Ion Exchange (Nato Science Series E:)
Values of parameter R close to zero indicate that the operational conditions imposed are near the ideal condition, i. Therefore, this difference may contribute to the choice of best operational conditions in the column design Barros et al.
With the average residence time it is also possible to evaluate the variance in the breakthrough curve Hill, , which is given by. Finally, the dimensionless variance should be calculated as.
Determination of this parameter is useful to estimate the axial dispersion in the packed bed. Values of dimensionless variance close to zero mean that the behavior of the packed bed is close to that of an ideal plug-flow reactor with negligible axial dispersion. Finally, the competition for zeolitic sites is well evidenced by the dynamic capacity of the column.
Integration of areas under the breakthrough curve gives the amount of metal not recovered by the zeolite; based upon the difference in the quantity of metal fed into the column, this value permits determination of the amount retained by the exchanger Valdman et al. In order to compare systems with different cation exchange capacities, as in the case of single and competitive systems, was divided by the value of CEC for each column. Figures 2 shows the chromium breakthrough results for the NaY and NaX zeolite columns.
Both curves can be considered to be step curves, indicating minimum mass transfer resistances, as already discussed in Barros et al.
Moreover, it was observed that the breakpoint for the NaY zeolite packed bed occurred earlier, but as both zeolite columns had the same mass contents but not the same cation exchange capacity, it was not possible to draw any conclusions based on column efficiency, only on the breakthrough curves. Quantitative results from data presented shown in Table 1 will be discussed later. The binary-ion-exchange breakthrough curves generated during the ion exchange of the parent NaY and NaX zeolites are shown in Figures 3 to 5.
Different curvature profiles can be seen as a consequence of the affinity of the zeolites for each in-going cation in a competitive system. It can be seen from these figures that the removal of chromium was qualitatively almost the same. It was observed that in all breakthrough curves for NaY zeolite packed beds, the competing cations started exiting the column ealier than the chromium ions, which indicates that this zeolite has a more dynamic affinity for the trivalent cation. On the other hand, only potassium was released much earlier from the NaX zeolite column.
Therefore, it was possible to be assured that the NaX zeolite preferred the chromium to the potassium cations. Therefore, it was not possible to draw conclusions about the dynamic selectivity only based on the breakthrough curves. Although NaX and NaY zeolites are isomorphs, dense sites produced by high aluminum contents in the framework, may alter the interaction of each in-going cation with the zeolitic framework Rupp, The competing in-going ions can alter the ion-exchange mechanism as they may interact with chromium ions, and more importantly to considere that they can be exchanged at the available sites, decreasing chromium uptake.
When the available sites were saturated, chromium ions seemed to displace the competing cations already located in the zeolite, releasing them to the fluid phase. This phenomenon had already been observed in NaA zeolite Arroyo et al. Therefore, this sequential ion exchange is also a reasonable explanation for the chromium uptake in X and Y zeolites. The sequential ion exchange probably occurred due to two main factors: the selectivity of the ion exchanger itself and the operational conditions used in the packed bed. Depending on the cation-framework interaction, which takes into account the charge and the hydration energy of the cation and also the CEC of the zeolite, it may prefer one cation over another.
Thus, the process parameters were optimized for chromium uptake Barros et al.
- Account Options.
- Severe Convective Storms and Tornadoes: Observations and Dynamics?
- Ion-exchange reaction - Ion-exchange procedures | inmarkelaca.ml.
- Confessions of a Radical Industrialist: How Interface proved that you can build a successful business without destroying the planet.
The sequential ion exchange observed in the breakthrough curves led us to conclude that all sites available to the competing cation were also available to chromium ions. Finally, Figures 3-a , 4-a and 5-a show a more pronounced sequential ion exchange for NaY breakthrough curves than for the respective NaX breakthrough curves shown in Figures 3-b , 4-b and 5-b. Therefore, it may be concluded that NaY zeolite has a greater affinity for chromium in competitive systems. The mass transfer parameters estimated from the breakthrough data are given in Table 1. Comparing the performance of the NaY and NaX zeolite columns, it can be observed from Table 1 that the length of unused bed as well as the overall mass transfer coefficient for the NaX zeolite columns was more favorable than for NaY zeolite beds in single or competitive systems.
The dimensionless variance for both systems generated similar values, which shows that axial dispersion was not strongly affected by the nature of the zeolite or the in-going ions. On the other hand, the operational ratio and mainly the dynamic selectivity show that inclusion of a competing cation altered the exchange mechanism, mainly for the NaX zeolite columns. It may be observed that there are only small differences in the length of unused bed for the single and competitive breakthrough curves for NaY zeolite columns. Therefore, it may be assumed that the chromium breakthrough was more strongly affected by the presence of a competing cation in NaX zeolite columns.
In column design for ion exchange large changes in H UNB values are not recommended because this increases the operating costs. Nevertheless, the values obtained reflected the competition for zeolite sites, which cannot be avoided. The striking feature of Table 1 is that some K c a values for competitive systems are higher than the ones obtained for single exchanges in NaY zeolite columns and lower in NaX zeolite columns. Therefore, it may be assumed that interaction of both in-going ions may alter in different ways the cation diffusion through the film and into the particle of NaY or NaX zeolites.
The parameter R for both zeolite columns is greater for competitive systems than for single runs, which clearly indicates the influence of a competitive cation in the ion exchange mechanism. The dimensionless variance becomes slightly different for single and competitive runs. This feature emphasizes changes in the uptake mechanism of chromium ions.
Potassium ions are much smaller than trivalent chromium cations Nightingale, , which may favor some interaction between them. In fact, the addition of calcium or magnesium to a chromium solution does not significantly alter the velocity profile, as could be expected due to their similar hydration radii Nightingale, and hydration energy Rupp, The amount of chromium retained in NaY zeolites in competitive systems is slightly smaller than in single ion-exchange systems. On the other hand, a large decrease in chromium uptake was observed in NaX zeolite. Therefore, it may be concluded that NaX zeolite is not as selective for chromium ions as the zeolite NaY.
In this work, trivalent chromium uptake by NaY and NaX zeolites in binary systems was studied. Extension of this phenomenon depended on the nature of the competitive cation and also on the selectivity of the zeolite. For single runs NaY or NaX zeolite could be used as it retained the same amount of chromium ions with negligible values of operational ratio and dimensionless variance. Differences in length of unused bed and overall mass transfer coefficient did not contradict earlier conclusions.
For competitive runs, the length of unused bed and the operational ratio were influenced much more by competitive systems for NaX zeolite, and neither the overall mass transfer coefficient nor the dimensionless variance was strongly affected. The presence of potassium ions interfered more in the axial dispersion of the fluid than the presence of calcium or magnesium, probably due to some interaction with chromium ions.
Ion Exchange Adsorption Kinetics of Miglitol by D Resins
Chromium uptake decreased significantly in competitive systems in NaX zeolite beds, but only small differences were observed in NaY zeolite. Concentration in the fluid relative to that in the feed. Weight fraction of the effluent of an age less than t. Chromium uptake up to the chromium breakpoint time meq. Competing ion uptake up to the chromium breakpoint time meq. It is important to correlate all these phenomena so as to avoid a very large number of unnec- essary measurements.
Such correlation is often possible [Meares, ] since all these phenomena are determined by the ease of migration of the different species across the membrane. Important correlations have been made and summar- ized even before high-capacity ion-exchange membranes became commercially available [Sollner, , iJ. Read more Read less. No customer reviews. Share your thoughts with other customers. Write a customer review. Discover the best of shopping and entertainment with Amazon Prime. Prime members enjoy FREE Delivery on millions of eligible domestic and international items, in addition to exclusive access to movies, TV shows, and more.