Porous systems

Interestingly, a general thermodynamic relationship allows the surface area of a porous system (without ink bottles) to be calculated from porosimetry data, note Section XVII-16B. The equation is [45]... 

The detailed consideration of these equations is due largely to Kozeny [50] the reader is also referred to Collins [51]. However, it is apparent that, subject to assumptions concerning the topology of the porous system, the determination of K provides an estimate of Ao- It should be remembered that Ao will be the external area of the particles and will not include internal area due to pores (note Ref. 52). Somewhat similar equations apply in the case of gas flow the reader is referred to Barrer [53] and Kraus and co-workers [54]. 

J. G. Powles, M. Pogoda. A flexible model for the simulation of fluids in infinite porous systems. Mol Phys 75 757, 1993. 

Quintard, M, Diffusion in Isotropic and Anisotropic Porous Systems Three-Dimensional Cal-cnlations. Transport in Porons Media 11, 187, 1993. 

Mass transport may constitute another problem. Since many catalysts are porous systems, diffusion of gases in and out of the pores may not be fast enough in comparison to the rate of reaction on the catalytic site. In such cases diffusion limits the rate of the overall process. 

The following is a description of the experimental, set-up and conditions used for the investigation of porous systems. 

In this chapter, a number of transport phenomena with entirely different natures are compared for liquids filling porous systems. Here transport can refer to flow, diffusion, electric current or heat transport. Corresponding NMR measuring techniques will be described. Applications to porous model objects will be juxtaposed to computational fluid dynamics simulations. 

Equations (85) and (86) and the data shown in Figure 22 represent experimental results for flow in smooth straight tubes. Experimental data for complex porous systems sometimes differ slightly from the results given by Figure 22 in the region between the low pressure limit and a L 1. 

The analysis of the literature data shows that zeolites modified with nobel metals are among perspective catalysts for this process. The main drawbacks related to these catalysts are rather low efficiency and selectivity. The low efficiency is connected with intracrystalline diffusion limitations in zeolitic porous system. Thus, the effectiveness factor for transformation of n-alkanes over mordenite calculated basing on Thiele model pointed that only 30% of zeolitic pore system are involved in the catalytic reaction [1], On the other hand, lower selectivity in the case of longer alkanes is due to their easier cracking in comparison to shorter alkanes. 

Here, following the works of J.H. De Boer (Delft, The Netherlands, see elsewhere [1,2]), by texture one means the individual geometrical structure of catalysts, supports, and other porous systems (PSs) at the level of pores, particles and their ensembles (i.e., on a supramolecular level scale of 1 nm and larger). In a more complete interpretation, texture includes morphology of porous space and the skeleton of a condensed (solid or sometimes liquid) phase, the shape, size, interconnectivity, and distribution of individual supramolecular elements of the system particles and pores (or voids) between particles, various phases, etc. In turn, texturology also involves general laws of texture formation and methods for its characterization [3],... 

Porous systems of the type shown in Figure 9.25b are of practical interest since they have an interconnected system of large pores that decreases the diffusion resistance in mass transfer processes. The pores between aggregates play the role of transport channels, while the majority of the surface and catalytically active species are located inside the aggregates. This explains the wide use of systems with this type of structure. 

The main focus of the following considerations is on catalysis using inorganic materials. Similar considerations come into play for catalysis with molecular compounds as catalytic components of course, issues related to diffusion in porous systems are not applicable there as molecular catalysts, unless bound or attached to a solid material or contained in a polymeric entity, lack a porous system which could restrict mass transport to the active center. It is evident that the basic considerations for mass transport-related phenomena are also valid for liquid and liquid-gas-phase catalysis with inorganic materials. 

Step one is, oxygen diffusion in the porous system of the particle inwards to the char combustion front and the reaction site, (2) adsorption of oxygen to the active sites on the intraparticle char phase, (3) oxidation reaction with carbon, and (4) desorption of... 

The water is transported from the intraparticle phase to the interstitial gas phase. It is then further transported through the porous system of the bed towards the bed surface by means of forced convection. 

C. Equations describing the paramagnetic relaxivity enhancement caused by Gd(III)-loaded, porous systems... 

C. Equations Describing the Paramagnetic Relaxivity Enhancement Caused by Gd(IH)-LoADED, Porous Systems... 

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