Models pore structure

The question of the constancy of the surface tension in porous media has been under consideration for many years and has been taken up again recently by Grown et al. (1997). Formerly, it was thought that for a concave liquid-vapour interface the surface tension should increase with increased curvature. The experimental findings that the hysteresis critical temperature is generally appreciably lower that the bulk critical temperature (see Section 7.5) is considered to be a strong indication that the surface tension of a capillary-condensate is reduced below the bulk value. More work on model pore structures is evidently required to settle this question. 

As indicated in Chapter 1, there is now considerable interest in the application of computer simulation (e.g. GCMC) and density functional theory (DFT) to physisorp-tion in model pore structures. It is already possible to predict the behaviour of some simple fluids in model micropores of well-defined size and shape and further progress is to be expected within the next few years. 

The goal of reconstruction methods is to build model pore structures that match experimental structure data (including surface chemistry data) for the real materials, at least in a quafitative way. For example, models can be constructed that match the experimental structure factor, S(q), or TEM data, by reverse Monte Carlo (RMC), off-lattice reconstruction, or other methods. 

Chatzis, I., and F.A.L. Dullien. 1977. Modelling pore structures by 2-d and 3-d networks with application to sandstones. Can. J. Petrol. Tech. 16 97-108. 

Due to the visualization of a porous medium as an ensemble of large dust molecules in the Dusty G ls Model pore structure properties such as porosity, tortuosity, and pore size distribution are not directly included. All information on pore structure characteristics is contained in the permeability constants Co, Ci, and Ca. Heteroporosity as originating from a wide pore size distribution is not accounted for specifically. On the other hand the Dusty Gas Model has the etdvantage to allow a separation of the influence of pore structure characteristics on the different transport mechanisms. The influence of the adsorbent material pore structure on gas phase mass transport is incorporated through the parameters Co, Ci, and C2 resp. They are determined by flux experiments for the specific adsorbent material (refs. 4, 6). The values for the different trstructural parameters such as representative pore diameter dp, porosity p, and tortuosity factor Tp by the expressions ... 

These models, though necessarily idealized, are sufficiently close to the actual systems found in practice to enable useful conclusions to be drawn from a given Type IV isotherm as to the pore structure of a solid adsorbent. To facilitate the discussion, it is convenient to simplify the Kelvin equation by putting yVJRT = K, and on occasion to use the exponential form ... 

Thus, while models may suggest optimal pore spuctures to maximize methane storage, they give no indication or suggestion as to how such a material might be produced. On the other hand, simple measurement of methane uptake from variously prepared adsorbents is not sufficient to elucidate the difference in the pore structure of adsorbents. Sosin and Quinn s method of determining a PSD directly from the supercritical methane isotherm provides an important and valuable link between theoretical models and the practical production of carbon adsorbents... 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

Coimectivity is a term that describes the arrangement and number of pore coimections. For monosize pores, coimectivity is the average number of pores per junction. The term represents a macroscopic measure of the number of pores at a junction. Connectivity correlates with permeability, but caimot be used alone to predict permeability except in certain limiting cases. Difficulties in conceptual simplifications result from replacing the real porous medium with macroscopic parameters that are averages and that relate to some idealized model of the medium. Tortuosity and connectivity are different features of the pore structure and are useful to interpret macroscopic flow properties, such as permeability, capillary pressure and dispersion. 

In a further study, Rill et al. [325] developed a model of gel permeation chromatography that included a bimodal pore stracture. The smallest mode in the pore-size distribution represents the basic background polyacrylamide pore structure of about 1-mn mean radius, and the second mode was around 5 nm, i.e., in the range of size of the molecular templates. The introduction of this second pore structure was found to substantially improve the peak resolution for molecules with molecular sizes in the range of the pore size. 

Models of regular structures, such as zeolites, have been extensively considered in the catalysis literature. Recently, Garces [124] has developed a simple model where the complex pore structure is represented by a single void with a shell formed by n-connected sites forming a net. This model was found to work well for zeolites. Since polymer gels consist of networks of polymers, other approaches, discussed later, have been developed to consider the nature of the structure of the gel. 

Figure 3. Possible model of the pore structure of ZSM-5 and Silicallte ("SIO2").

The simple pore structure shown in Figure 2.69 allows the use of some simplified models for mass transfer in the porous medium coupled with chemical reaction kinetics. An overview of corresponding modeling approaches is given in [194]. The reaction-diffusion dynamics inside a pore can be approximated by a one-dimensional equation... 

Illustration 6.2 indicates how void volume and surface area measurements can be combined in order to evaluate the parameters involved in the simplest model of catalyst pore structure. 

Scanning electron microscopy and other experimental methods indicate that the void spaces in a typical catalyst particle are not uniform in size, shape, or length. Moreover, they are often highly interconnected. Because of the complexities of most common pore structures, detailed mathematical descriptions of the void structure are not available. Moreover, because of other uncertainties involved in the design of catalytic reactors, the use of elaborate quantitative models of catalyst pore structures is not warranted. What is required, however, is a model that allows one to take into account the rates of diffusion of reactant and product species through the void spaces. Many of the models in common use simulate the void regions as cylindrical pores for such models a knowledge of the distribution of pore radii and the volumes associated therewith is required. 

This section is concerned with analyses of simultaneous reaction and mass transfer within porous catalysts under isothermal conditions. Several factors that influence the final equation for the catalyst effectiveness factor are discussed in the various subsections. The factors considered include different mathematical models of the catalyst pore structure, the gross catalyst geometry (i.e., its apparent shape), and the rate expression for the surface reaction. 

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