Mass transfer zone length

The expression for the effective gas phase coefficient that would account for axial dispersion and hence give a proper mass transfer zone length is ... 

Experimental studies for the removal of dissolved TBP in aqueous solutions by adsorbing on a fixed bed containing Amberlite XAD-4 resin were conducted. Break through curves were established for different flow rates and feed concentrations of TBP in aqueous solutions. Break through capacity, saturation capacity and mass transfer zone length (MTZ) were estimated and the MTZ length was correlated. The distribution data of TBP on resin were measured and the equilibrium data were fitted to Freundlich isotherm model. 

The critical bed depth is the theoretical depth of adsorbent that is just sufficient to prevent the effluent concentration from exceeding Cb at zero time and clearly is equal to the mass transfer zone length MTZL described above. The critical bed depth may be calculated by substituting r = 0 into equation (6.55) ... 

Mass-transfer zone Design based on stoichiometry and experience Isothermal MTZ length largely empirical Regeneration often empirical... 

FIG. 16-3 Bed profiles (top and middle) and hreakthroiigh curve (hottom). The Led profiles show the mass-transfer zone (MTZ) and eqiiilihriiim section at hreakthroiigh. The stoichiometric front divides the MTZ into two parts with contrihiitions to the length of equivalent eqiiihhriiim section (LES) and the length of equivalent unused hed (LUB). 

Working from substitution of Eq. (9.17) into Eq. (9.10) we can with a little mathematical manipulation obtain an expression for the length of the mass transfer zone without resorting to the solution of the pde. 

The distinction here is that the kK calculated from Eq. (9.19) would be used in a linear driving force model for the actual uptake rate expression and an axial dispersion coefficient would be substituted into the pde. If however one simply desires to match the adsorption response or breakthrough curves then the kK calculated according to Eq. (9.20) would provide very satisfactory results for estimation of the length of the mass transfer zone. 

The rest of the terms in Eq. (9.18) are readily obtained from the literature and then the resulting value of the overall mass transfer coefficient kK can then be substituted into Eq. (9.18). We now have the required added length of the mass transfer zone and the bed sizing is complete. 

Since this time does not consider the length of the mass-transfer-zone or unsteady-state periods, the real will longer - maybe 10-20 % longer. 

Figure 15.9. Concentrations in adsorption beds as a function of position and of effluent as a function of time, (a) Progress of a stable mass transfer front through an adsorption bed and of the effluent concentration (Lukchis, 1973). (b) The mass transfer zone (MTZ), the length of unused bed (LUB), stoichiometric front, and profile of effluent concentration after breakthrough.

In the case of an unfavorable isotherm (or equally for desorption with a favorable isotherm) a different type of behavior is observed. The concentration front or mass transfer zone, as it is sometimes called, broadens continuously as it progresses through the column, and in a sufficiently long column the spread of the profile becomes directly proportional to column length (proportionate pattern behavior). The difference between these two limiting types of behavior can be understood in terms of the relative positions of the gas, solid, and equilibrium profiles for favorable and unfavorable isotherms (Fig. 7). 

The reactor has a cross-sectional area, S, column length, D, and adsorbent mass in the bed, M (see Figure 6.23). The adsorbent bed in the PFAR can be divided in three zones I, the equilibrium zone II, mass transfer zone (MTZ) with a length, D0 and III, the unused zone [100,105,106], In addition, the length of the MTZ, D0, can be calculated with the following expression (see Figure 6.24) [106] ... 

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