Stoichiometric front

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). 

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.

If the fluid solute concentration in the column propagates as a stoichiometric front (plug-flow), the position of the front would be Ls in Figure 7.5. This corresponds to the portion of the column from Ls to Ld as being unused. When La corresponds to the column length Lc, the length of the unused bed LUB) can be defined as... 

Defining 4 as the time that the stoichiometric front would arrive at the column exit, an analogous expression using the plot in Figure 7.4 is... 

This result indicates that the velocity of the solute front is inversely proportional to the slope of the isotherm. We can illustrate this result using a Type I isotherm (Figure 7.6). During the adsorption step, the direction is from the lower left to upper right portion of the curve. So, dg/dT is largest V is slowest) during the initial portion of sorption. This is the rate-limiting step so the entire front moves as a discontinuous wave (stoichiometric front). A balance across this wave shows that Aq/AY reduces to Aq/AY, the chord from the initial state to the saturated state in the column. 

Show that a mass transfer zone that propagates as a stoichiometric front would correspond to the shortest sorbent bed needed. 

In trying to model dynamic adsoiption mathematically and predict the shepe and size of the MTZ, assumptions must be made about the equiiibriam mndel, molecular diffusion, axial-flow dispersion, and isothermality. The simplest model is isothermal equilibrium operation with infinite diffusion rate nod negligible dispersion, that is. a stoichiometric front. 

FIGURE 5.21 Stable breakthrough curve in sorbent bed and position of the stoichiometric front (horizontal lines) relative to the stable mass-transfer front during dynamic adsorption. 

The key test data required for the estimation of LUB are the time required for breakthrough, tb, and the time required for the stoichiometric front to reach the end of the bed, t, in a system in which a stable mass transfer zone has developed- The equation for calculating LUB as given by Keller et al. (1987) is... 

In one simplified approach, the total bed is viewed as the sum of two sections the length of equivalent equilibrium section (LES) and the length of unused bed (LUB). LES is equivalent to the position of the stoichiometric front at breakthrough, while LUB is one-half the length of the MTZ. When breakthrough occurs, LUB is defined by equation 12-11 ... 

Where LUB = length equivalent to unused bed, ft L = total bed length, ft Lj = position of stoichiometric front in bed, ft... 

The position of the hypothetical stoichiometric front at any time is given by the following equation ... 

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