Reconstructed porous media

Fig. 2. Types of computer representation of porous media—network diagrams (left) and solid-phase function of reconstructed porous media (right).

Experimental techniques commonly used to measure pore size distribution, such as mercury porosimetry or BET analysis (Gregg and Sing, 1982), yield pore size distribution data that are not uniquely related to the pore space morphology. They are generated by interpreting mercury intrusion-extrusion or sorption hysteresis curves on the basis of an equivalent cylindrical pore assumption. To make direct comparison with digitally reconstructed porous media possible, morphology characterization methods based on simulated mercury porosimetry or simulated capillary condensation (Stepanek et al., 1999) should be used. 

Calculation of Effective Transport Properties on Reconstructed Porous Media... 

Experimentally determined effective transport properties of porous bodies, e.g., effective diffusivity and permeability, can be compared with the respective effective transport properties of reconstructed porous media. Such a comparison was found to be satisfactory in the case of sandstones or other materials with relatively narrow pore size distribution (Bekri et al., 1995 Liang et al., 2000b Yeong and Torquato, 1998b). Critical verification studies of effective transport properties estimated by the concept of reconstructed porous media for porous catalysts with a broad pore size distribution and similar materials are scarce (Mourzenko et al., 2001). Let us employ the sample of the porous... 

As shovm in Fig. 1, the reconstructed porous media is placed into adiabatic boundary channel, there s a heat conduct plan at the top of the model with a constant heat flux q . We will survey and evaluate the permeability and heat conductivity coefficient of this model with different inlet velocities. 

Adler Pierre M., Jacquin Christian G., Thovert Jean Francois. 1992. The formation factor of reconstructed porous media. Water Resources Research, 28 (6) 1571-1576. 

Stepanek, F., Marek, M., Adler, P. M., 1999. Modeling capillary condensation hysteresis cycles in reconstructed porous media. 

Zhao X., Yao J. Yi Y Anew stochastic method of reconstructing porous media. Transp. Porous Media 69 (2007), pp. 1-11. 

Fig. 3. Procedure of the reconstruction of porous media SEM image of the porous silica-sup-ported catalyst particle, selection of rectangular box, binarization of SEM image, calculation of the autocorrelation function Mu), and reconstructed porous medium.

Fio. 9. Streamlines showing steady-state velocity profile during single-phase flow in a reconstructed porous medium. 

Fig. 12. Skeleton of the the solid phase of spatially 3D reconstructed porous medium obtained by conditional thinning and disconnection of the skeleton at the weak point (from Grof et al., 2003).

The capillary pressure response, a direct manifestation of the underlying pore morphology, can be evaluated from the two-phase LB drainage simulation and the corresponding transport relation as function of liquid water saturation can be devised as shown in Fig. 20 for the reconstructed CL micro structure.21 The overall shape of the capillary pressure curve agrees well with those reported in the literature for synthetic porous medium.55 The capillary... 

Let us consider an isotropic porous medium under the reconstruction described by a pore phase function fgk r) in the /cth iteration step of the simulated annealing algorithm and let the actual statistical characteristics of this phase function, i.e., the two-point correlation function, be Rgk u). The distance of from the target morphological characteristics Rgtarset(u) of the... 

Let us generate a spatially 3D isotropic porous medium fg r) with a given porosity s = fg(f) and a given correlation function Rg(u). The porous medium fg(r) is considered to be discretized into the grid of Nc x Nc x Nc voxels, each voxel of the same size h. The reconstructed cube of the porous medium is usually considered to have periodic boundary conditions. 

In this section we reconstruct the theory of consolidation by introducing the concept of a finite strain and a nominal stress rate, which are given in Chap. 2. Note that in Chap. 5 a mixture theory was developed for a porous medium with multiple... 

Ideally, a representative reconstruction of a porous medium in three dimensions should have the same correlation properties as those measured on a single two-dimensional section, expressed properly by the various moments of the phase fimction. In practice, matching of the first-two moments, that is, porosity and autocorrelation fimction, has been customarily pursued since the first application of the method [2]. 

For the detailed study of reaction-transport interactions in the porous catalytic layer, the spatially 3D model computer-reconstructed washcoat section can be employed (Koci et al., 2006, 2007a). The structure of porous catalyst support is controlled in the course of washcoat preparation on two levels (i) the level of macropores, influenced by mixing of wet supporting material particles with different sizes followed by specific thermal treatment and (ii) the level of meso-/ micropores, determined by the internal nanostructure of the used materials (e.g. alumina, zeolites) and sizes of noble metal crystallites. Information about the porous structure (pore size distribution, typical sizes of particles, etc.) on the micro- and nanoscale levels can be obtained from scanning electron microscopy (SEM), transmission electron microscopy ( ), or other high-resolution imaging techniques in combination with mercury porosimetry and BET adsorption isotherm data. This information can be used in computer reconstruction of porous catalytic medium. In the reconstructed catalyst, transport (diffusion, permeation, heat conduction) and combined reaction-transport processes can be simulated on detailed level (Kosek et al., 2005). 

An alternative to stochastic reconstruction of multiphase media is the reconstruction based on the direct simulation of processes by which the medium is physically formed, e.g., phase separation or agglomeration and sintering of particles to form a porous matrix. An advantage of this approach is that apart from generating a medium for the purpose of further computational experiments, the reconstruction procedure also yields information about the sequence of transformation steps and the processing conditions required in order to form the medium physically. It is thereby ensured that only physically realizable structures are generated, which is not necessarily the case when a stochastic reconstruction method such as simulated annealing is employed. 

SEM and TEM images give detailed information about the porous structure of a supported heterogeneous catalyst (pore size distribution, typical sizes of the particles, etc.). The information from SEM and TEM images can be used in the reconstruction of porous catalytic medium. In the digitally reconstructed catalyst, transport (diffusion, permeation), adsorption, reaction, and combined reaction-diffusion processes can be simulated (Stepanek et al., 2001a). Parametric studies can be performed, and the resulting dependencies can serve as a feedback for the catalyst development. 

The macro-porosity emacro and the correlation function corresponding to the macro-pore size distribution of the washcoat were evaluated from the SEM images of a typical three-way catalytic monolith, cf. Fig. 25. The reconstructed medium is represented by a 3D matrix and exhibits the same porosity and correlation function (distribution of macro-pores) as the original porous catalyst. It contains the information about the phase at each discretization point— either gas (macro-pore) or solid (meso-porous Pt/y-Al203 particle). In the first approximation, no difference is made between y-Al203 and Ce02 support, and the catalytic sites of only one type (Pt) are considered with uniform distribution. 

The analysis is based on averages of four realizations of reconstructions of two different porous media with c=0.42 and 8=0.355, respectively. Typical cross sections for each medium are shown in Fig. 2. A comparison between the experimental autocorrelation functions (SANS data) and the autocorrelation functions measured on the reconstructed media is presented in Fig. 3a and 3b. It is evident that the stochastic reconstructions exhibit nearly identical autocorrelation functions with the experimentally observed ones. This indicates that the reconstructed materials respect the basic statistical content of the actual porous materials. 

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