Pores overall pore length

To get a better picture of the pore dimensions, it is interesting to calculate the mean pore diameter dpore.mean and the (hypothetical) overall pore length Lpore- Topic 4.5.1 shows that for a catalyst with 1000 m g internal surface area we get impressive values of dpore.mean of Only 2 nm and of Lpore of 160 X lO kmg. Thus the overall pore length of only 1 g of catalyst is equivalent to the distance between the earth from the sun (150 million km ). 

Topic 4.5.1 Pore diameter and overall pore length of a porous solid (catalyst)... 

Figure 2 summarises the situation the chain has partially entered into the pore (over a length F >D). It can be pictured as a sequence of blobs, each of size D and of monomer number gD=(D/a)5/3 (theFlory law). The confinement energy per blob is of the order kT [13] and the overall confinement energy is thus kT f/D ( /D being the number of squeezed blobs. The force tending to pull the chain out of the pore is thus kT/D. 

The equations for simultaneous pore diffusion and reaction were solved independently by Thiele and by Zeldovitch [16,17]. They assumed a straight cylindrical pore with a first-order reaction on the surface, and they showed how pore length, diffusivity, and rate constant influenced the overall reaction rate. Their solution cannot be directly adapted to a catalyst pellet, since the number of pores decreases going toward the center and assuming an average pore length would introduce some error. The approach used here is that of Wheeler [18] and Weisz [19], who considered reactions in a porous sphere and related the diffusion flux to the effective diffusivity, Z). The basic equation is a material balance on a thin shell within the sphere. The difference between the steady-state flux of reactant into and out of the shell is the amount consumed by reaction. 

Fischer et al, [122] proposed a model to predict the adsorption isotherm of krypton in porous material at supercritical temperature. In their study, a model pore of infinite length is formed by concentric cylindrical surfaces on which the centers of solid atoms are located. The interaction between an adsorbate and an individual center on the pore wall is described by the LJ 12-6 theory, and the overall potential is the integral of this interaction over the entire pore surface. With thermodynamic relations, Fischer et al. obtained the functional dependence of the saturation adsorption excess and the Henry s law constant on the pore structure. The isotherm was then produced by the interpolation between Henry s law range and saturation range. They tested their theory with the adsorption of krypton on activated carbon. It was shown that, with information on the surface area of the adsorbent and thermodynamic properties of the adso bate, their model gives more than quantitative agreement with experimental data. If a few experimental data such as the Henry s law constant at one temperature are available, the isotherms for all temperatures and pressures can be predicted with good quality. 

The overall length of the ion pore is 45 A and its diameter varies along its length (Figure 12.11). As expected for a channel, there is a surplus of... 

Tortuosity t is basically a correction factor applied to the Kozeny equation to account for the fact that in a real medium the pores are not straight (i.e., the length of the most probable flow path is longer than the overall length of the porous medium) ... 

Another approach of the problem has been proposed recently (9). Based on a comprehensive experimental study, it considers that wormholes have an almost infinite conductivity in comparison with the original pores of the rock. Consequently, a fair approximation of the permeability profile of an acidized piece of rock of length L is a step function. From its inlet up to almost the tip of the wormholes, the permeability is infinite. In the rest of the rock, it is equal to the original one, i.e. ko, and the overall permeability of this core becomes ... 

Completely solid packings produce no mass transfer effects related to solute movement into and out of tortuous pore structures. The principal limitation of solid packings is low total surface area and consequent limited sample capacity. Even with very small particles, the overall surface area generated per unit length of the column is still low compared to the porous materials with mean pore sizes in the 60 to 300 A range. Figures 13.5 A and B show a comparison of surface areas of... 

Catalyst deactivation was first identified as a percolation-type process by Sahimi and Tsotsis (2,3,41). The process studied by these authors was relatively simple. A porous catalyst, inside a differential isothermal reactor (with the catalytic active material uniformly distributed in its pores at an initial concentration CQ) is reacting while simultaneously undergoing slow deactivation. The overall reaction rate r in a single pore of radius R and length L is given by... 

---