**2. Experimental**

The NMR imaging technique, the sample-holder bulb containing the liquid phase in equilibrium with the gas phase, and the narrow zone monitored by the detector have been described in [1–3], respectively.

The upper face of the cylindrical bed of zeolite crystallites is exposed to a constant pressure of each gas (**Figure 1**). The diffusion of the two gases is axial in

**Figure 1.** *Distribution of the layers (left) and corresponding parameters (right).*

*Competitive Adsorption and Diffusion of Gases in a Microporous Solid DOI: http://dx.doi.org/10.5772/intechopen.88138*

the macropores of the inter-crystallite space (z direction along the height, *l*, of the bed) and radial in the micropores of the zeolite. According to the experimental conditions, the zeolite bed consists of a large number, N, of very thin layers of solid, of thickness Δ*lk* ¼ *lk* � *lk*�1, perpendicular to the propagation of the gas in the z direction. The corresponding coefficients of inter- and intra-crystallite space are *Dinter,k* and *Dintra,k*, respectively.

## **3. Experimental results: gaseous benzene and hexane adsorption curves**

The experimental results have been summarized in [4]: the spectrum of each gas at every instant and every level of the solid and the benzene and hexane concentrations along the sample, for each diffusion time. Here we shall only use the evolution, as a function of time, of the benzene and hexane concentrations at different levels of the sample, on which the calculations of the diffusion coefficients and the instantaneous inter- and intra-crystallite concentrations are based [8]. **Figure 2** shows clearly that, under the chosen experimental conditions, benzene hinders the diffusion of hexane, and this at every moment. Moreover, it can be noticed that, at equilibrium, the amount of benzene within the zeolite is twice that of hexane, indicating quantitatively the relative affinity to the two adsorbates.

These curves display modulations as a function of time, which must be averaged for all subsequent mathematical representations. These modulations are weak at the lower layers of the tube and can be due to errors in the measurement of small amounts. Those closer to the arrival of the gas are greater and are similar for the two gases. We suggested that these fluctuations may be due to the fact that intercrystallite adsorption at levels close to the gas phase is fast compared to the liquid-gas equilibrium, which is not as instantaneous for a mixture as for a single component [8]. Each slight decrease of the gas pressure could correspond a slight fast desorption.

**Figure 2.**

imaging technique, named slice selection procedure, to follow the diffusion and adsorption of a gas in a microporous bed [1–3]. The sample is displaced vertically, stepby-step, relative to a very thin coil detector during the adsorption of the gas. The bed is assumed to consist of *N* very thin layers of solid, and the region probed is limited to each layer, so that the variation of the concentration of gas absorbed at the level of each layer is obtained as a function of time. An interesting feature of this technique is its ability to visualize directly the co-diffusion of several gases. Indeed, the NMR signals are quantitatively characteristic of the adsorbed gases. They can therefore provide directly, at every moment and at every level of the bed, the distribution of several gases competing in diffusion and adsorption. We have presented in a previous paper the experimental results of the co-diffusion of benzene and hexane through a silicalite bed [4]. In [5, 6] we have developed a mathematical methodology for efficient linearization of similar models. Using Heaviside's operational method and Laplace's integral transformation method, we have built solutions allowing fast calculations for twocomponent co-adsorption in a heterogeneous zeolite bed and for the dehydration of natural gas [7]. In this chapter we have improved the methods previously used to compute the diffusion coefficients against time, increasing the accuracy and speed of calculations by significantly reducing the iteration number. This made it possible to use them for the co-adsorption of several gases diffusing along such a column.

The NMR imaging technique, the sample-holder bulb containing the liquid phase in equilibrium with the gas phase, and the narrow zone monitored by the

The upper face of the cylindrical bed of zeolite crystallites is exposed to a constant pressure of each gas (**Figure 1**). The diffusion of the two gases is axial in

detector have been described in [1–3], respectively.

*Distribution of the layers (left) and corresponding parameters (right).*

**2. Experimental**

*Zeolites - New Challenges*

**Figure 1.**

**14**

*Evolution vs. time of the benzene and hexane concentrations (arbitrary units) at different levels of the sample (*continuous*, experimental curves;* dotted*, their approximations used for simulation) [from Ref. [8], reprinted with permission from ACS].*
