Piezometric diffusion measurements

Measurement of the transient adsorption or desorption curve for a sample of zeolite crystals exposed to a step change in ambient sorbate concentration (pressure) provides, in principle, a simple and direct method of measuring the intracrystalline diffusivity (D). Such measurements are conveniently carried out by gravimetric, volumetric or piezometric methods. The... 

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or piezometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

Fig. 18. Self-diffusion coefficients of benzene in NaX at 458 K PFG NMR, O (97) and (92) (JENS, A (13) deduced from NMR lineshape analysis, (10). Comparison with nonequilibrium measurements T, sorption uptake with piezometric control (93) , zero-length column method (96) o, frequency-response and single-step frequency-response technique (98). The region of the results of gravimetric measurements with different specimens (92) is indicated by the hatched areas. Asterisked symbols represent data obtained by extrapolation from lower temperatures with an activation energy confirmed by NMR measurements.

The intracrystalline diffusivities of the hydrocarbons were measured under the conditions of the temperature range of 373-773 K and the pressure range of 0-1.33 kPa by the constant volume method [9]. The apparatus and the procedure are the same as employed by Hashimoto et al. [4,5]. Change in the total pressure caused by adsorption was recorded by use of a piezometric sensor with a transducer, the response of which is first enough to measure accurately the pressure change. To eliminate the influence of several factors (such as mass conductivity between the sorbate and the pressure sensor) on the pressure change, the blank tests were conducted without zeolites. Comparing these data obtained with those with zeolites, an uptake curve of the amount adsorbed was obtained. 

The piezometric method involves following the pressure response in a dosing cell connected to an uptake cell containing a sample of the adsorbent. According to the results reported in the hterature, the piezometric method can be used to accurately measure intracrystalline diffusivities for fast diffusing and strongly adsorbed species such as benzene on NaX [15,16]. Furthermore, it is also claimed to provide the required accuracy needed to study combined intracrystalline processes such as diffusion and first-order reaction [17]. 

We conclude that the piezometric technique is capable of yielding reliable diffusivity data provided that the pressures are monitored in the uptake cell and the limitations imposed by the time constant of the valve and finite heat dissipation rates are respected. For strongly adsorbed species theses restrictions limit the applicability to relatively slow processes (half times of at least several seconds). For weakly adsorbed species somewhat faster diffusion processes can be measured. A detailed assessment of the range of validity of this method, as a function of the system variables, has been presented by Schumacher and Karge [19]. In reviewing earlier reported piezometric diffusivity data, the values derived from measuring only the pressure in the dosing cell should not be accepted without further detailed analysis. 

Fig. 5 Loading dependence of corrected diffusivities (Do) for ethylbenzene in H-ZSM-5 at various temperatures, measured by piezometric technique. From Schumacher et al. [20] with permission...

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