ZLC desorption curves

The analysis of the ZLC desorption curve involves solving Fickian diffusion equation with appropriate initial and boundary conditions (9). The solution of the desorption curve for spherical geometry is given as ... 

Figure ]. Effect of the nature of the purge gas on ZLC desorption curves for PFTBA on Al-MCM-41 sample (SiCVAfeO =19.7) at 100 °C.

This approach is illustrated in fig. 2 which shows a family of ZLC desorption curves for CO2 from a sample of a carbon monolith, measured over a wide range of flow rates. The isotherm is linear so at low flow rates (equilibrium control) the response is given by ... 

ZLC desorption curves were measured over a wide range of conditions for several different hydrocarbon sorbates in a range of different sizes of NaX and 5A zeolite crystals. In general He was used as the purge gas but numerous checks were made with an Ar purge to confirm the absence of any extracrystalline resistance. The form of the desorption curves was consistent with the theoretical model outlined above and consistent diffusivity values were obtained at different flowrates and with different crystal sizes. A few representative curves are shown in figure 1. 

Figure 1. Representative ZLC desorption curves for o-Xylene in different size 13X zeolite crystals at 200°C.

In bidisperse porous adsorbents such as zeolite pellets there are two diffusion mechanisms the macropore diffusion with time constant Rp /Dp and the micropore diffusion with time constant rc /Dc. Bidisperse porous models for ZLC desorption curves have been recently developed by Brandani [28] and Silva and Rodrigues [29]. In bidisperse porous adsorbents, it is important to carry out experiments in pellets with different sizes but with the same crystal size (different Rp, same rc) or pellets with the same size but with different crystals (same Rp, different rc). If macropore diffusion is controlling, time constants for diffusion should depend directly on pellet size and should be insensitive to crystal size changes. If micropore diffusion controls the reverse is true. The influence of temperature is also important when macropore diffusion is dominant the apparent time constant of diffusion defined by Rp2(H-K)/Dp is temperature dependent in the same order of K (directly related to the heat of adsorption) which is determined independently from the isotherm. The type of purge gas is... 

Figure 3. Effect of temperature on ZLC desorption curves in 5A zeolite pellets, a) System He/nCs. b) System He/nCe- Data of Silva and Rodrigues, [19], [20].

The reciprocal of the apparent time constants for diffusion Dp /Rp2(l+K) of nC.5 and nCe (calculated from ZLC desorption curves) plotted versus 1/T are shown in Figure 4. A strongly temperature dependence of time constants exists which is of the order of heat of adsorption. Time constants range from 0.002 s at 473K up to 0.03 s at 573K in the system He/nC.5, and from 0.00035 s at 473K up to 0.0053 s at 573K in the system He/nCe. 

Brandani, S., Analytical solution for ZLC desorption curves with bi-porous adsorbent particles, Chem. Eng. Sci., 51(12), 3283-3288 (1996). 

Fig. 9 Effect of sample quantity and nature of purge gas on ZLC response curves for benzene in 50- jim crystals of NaX zeolite at 250 °C. a Desorption curves. Note that when the sample is sufficiently small, desorption is rapid and the curves for He and N2 purge coincide, but for a larger sample we see slower desorption with a significant difference between the curves for He and N2, indicating the intrusion of external diffusional resistance. b Apparent diffusional time constants showing the variation with sample mass. Filled symbols denote He purge, open symbols denote N2 purge. Note that when the sample mass is sufficiently small, the time constants for He and N2 become coincident and independent of sample mass, showing the absence of external diffusional resistance. From Brandani et al. [55]...

The solution to the diffusion equation yields a series of exponentials and it is difficult from a single ZLC experiment to distinguish different mass transfer mechanisms, i.e. surface barriers vs internal diffusion. For linear systems the shape of the initial part of the desorption curves should be distinctive [3] and the analysis of the moments of the desorption curves can also provide a means to distinguish the two mechanisms [4]. 

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