Mass-transfer zone

The required desiccant weight is a function of several factors the water removal requirements (mass/time), the cycle time, the equiUbrium loading of water on the desiccant at the feed conditions, the residual water loading on the desiccant after regeneration, and the size of the mass-transfer zone of the desiccant bed. These factors, in turn, depend on the flow rate, temperature, pressure, and water content of both the fluid being dried and the regeneration fluid (see Adsorption, gas separation). 

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). 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

There are data showing that at the same contact time, but different linear velocities, there is no difference in the performance of a carbon system. It is obvious then that the effect of linear velocity on the diffusion through the film around the particle and the ratio of the magnitude of the film diffusion to the pore diffusion are the factors that determine the effects, if any, that occur. Therefore, the linear velocity cannot be ignored completely when evaluating a system. Systems at the higher linear velocity (LV) treat more liquid per volume of carbon at low-concentration levels and the mass-transfer zone (MTZ) is shorter. 

For each component in the inlet gas stream, there will be a section of bed depth, from top to bottom, where the desiccant is saturated with that component and where the desiccant below is just starting to adsorb that component. The depth of bed from saturation to initial adsorption is known as the mass transfer zone. This is simply a zone or section of the bed where a component is transferring its mass from the gas stream to the surface of the desiccant. 

As the flow of gas continues, the mass transfer zones move dow nward through the bed and water displaces the previously adsorbed gases uniil... 

The shape of the breakthrough curve is depending on the behavior of the so called mass transfer zone (MTZ). Figure 242 shows schematically the MTZ within a packed bed of adsorbent. Within the MTZ the properties of the incoming air are changed to the outlet air properties. 

Washington, J.B. and Ong, S.K., Air sparging effectiveness laboratory characterization of air-channel mass transfer zone for VOC volatilization, J. Hazard. Mater., 87, 241-258, 2001. 

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

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. 

With that caveat the design proceeds in essentially the same manner as was outlined for water removal by 4A. We always do the dehydration design first, calculating the bed consumption for handling the water, allowing for a mass transfer zone and then factoring up the bed requirements in view of cyclic stability. 

Compound beds of alumina and zeolite X have been employed successfully in industrial dehydration by PSA. In both types of applications, the more favorable shape of the zeolite isotherms shorten the mass transfer zone and simultaneously allow for achievement of lower mole fractions of water or lower dew points for the product gas. 

This work prompted a flurry of activity in the mid- to late 1980s to find the type IM isotherm. A number of inventions can be found in which alumina, or silica gel are blended with zeolites type X or Y to mimic the shape of the isotherm that Collier defined. Mol Sieve type DDZ-70(g) is in fact one of only a few true type IM isotherms. This product and Engelhard s type ETS-10 both have the required isotherm shape for water and deliver the benefits expected, to wit excellent capacity for water, self-sharpening mass transfer zone and low energy investment required to regenerate. Mol Sieve type DDZ-70(g) is used commercially in rotors... 

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. 

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