Bidisperse structure

A significant increase in catalytic activity as compared to the limiting values, shown in Figure 8.1, can be achieved by the use of bidisperse porous structures. Such catalyst pellets are formed by compressing, extruding or in some other manner compacting finely powdered mkroporous material into a pellet. Ideally the micropores are due to the porosity in the individual microparticles of catalyst. The macropores result from voids between the microparticles, after pelletization or extrusion. In such catalysts, most of the catalytic surface is contained in the micropores, since S llre. The bidisperse structure is illustrated in Figure 8.2 compared to monodisperse particle. 

A single effective diffusion coefficient cannot adequately characterize the mass transfer within a bidisperse-structured catalyst when the influence of the two individual systems is equally important. In a realistic model the separate identity of the macropore and micropore structures must be maintained, and the diffusion must be described in... 

A bidisperse structure can be advantageous because the effectiveness factor in the microparticles is often close to unity (their size being three to four orders of magnitude smaller than the usual size of the industrial catalysts). It is of interest to estimate the ratio of the conversion rates with mono- and bidisperse structures, having the same size, when the porous structure of the microparticles is identical to that of a monodisperse pellet. This ratio can easily be found when the micropore effectiveness factor is close to unity, as in the case for many industrial systems. Since the external surface area of the... 

The FR measurements have been carried out for several systems using bidispersed structured sorbents [64,76,77]. All the spectra, however, indicate that either micropore diffusion or macropore diffusion, with or without a surface resistance, was the rate-controlUng step for these systems. 

Do, D.D., Hierarchy of rate models for adsorption and desorption in bidispersed structured sorbents,... 

The same concept applies to the size distribution of microparticles in the case of adsorbents with bidisperse structures. 

In a particle having a bidispersed pore structure comprising spherical adsorptive subparticles of radius forming a macroporous aggregate, separate flux equations can be written for the macroporous network in terms of Eq. (16-64) and for the subparticles themselves in terms of Eq. (16-70) if solid diffusion occurs. 

For particles with a bidispersed pore structure, the mass-transfer parameter in the LDF approximation (column 2 in Table 16-12) can be approximated by the series-combination of resistances... 

In the same year, Fulda and Tieke [75] reported on Langmuir films of monodisperse, 0.5-pm spherical polymer particles with hydrophobic polystyrene cores and hydrophilic shells containing polyacrylic acid or polyacrylamide. Measurement of ir-A curves and scanning electron microscopy (SEM) were used to determine the structure of the monolayers. In subsequent work, Fulda et al. [76] studied a variety of particles with different hydrophilic shells for their ability to form Langmuir films. Fulda and Tieke [77] investigated the influence of subphase conditions (pH, ionic strength) on monolayer formation of cationic and anionic particles as well as the structure of films made from bidisperse mixtures of anionic latex particles. 

Fulda and Tieke [77] studied the effect of a bidisperse-size distribution of latex particles on the structure of the resulting LB monolayer. For this purpose, a mixed colloidal solution of particles la and lb was spread at the air-water interface. Particles la had a diameter of 434 nm, particles lb of 214 nm. The monolayer was compressed, transferred onto a solid substrate, and viewed in a scanning electron microscope (SEM). In Figure 10, SEM pictures of LB layers obtained from various bidisperse mixtures are shown. 

Figure 9.17 The basic schemes of (a) bidisperse (biporous) porous solid structure 1, nonporous primary particles, 2, aggregates of primary particles (secondary particles), 3, porous solid (granule, grain, pallet, etc.) (b) a bed of granules in a catalytic reactor 4.

The described treatment of mass transport presumes a simple, relatively uniform (monomodal) pore size distribution. As previously mentioned, many catalyst particles are formed by tableting or extruding finely powdered microporous materials and have a bidisperse porous structure. Mass transport in such catalysts is usually described in terms of two coefficients, a effective macropore diffusivity and an effective micropore diffusivity. 

The available transport models are not reliable enough for porous material with a complex pore structure and broad pore size distribution. As a result the values of the model par ameters may depend on the operating conditions. Many authors believe that the value of the effective diffusivity D, as determined in a Wicke-Kallenbach steady-state experiment, need not be equal to the value which characterizes the diffusive flux under reaction conditions. It is generally assumed that transient experiments provide more relevant data. One of the arguments is that dead-end pores, which do not influence steady state transport but which contribute under reaction conditions, are accounted for in dynamic experiments. Experimental data confirming or rejecting this opinion are scarce and contradictory [2]. Nevertheless, transient experiments provide important supplementary information and they are definitely required for bidisperse porous material where diffusion in micro- and macropores is described separately with different effective diffusivities. 

The method can be applied to investigate the bidisperse pore structures, which consist of small microporous particles formed into macroporous pellets with a clay binder. In such a structure there are three distinct resistances to mass transfer, associated with diffusion through the external fluid film, the pellet macropores, and the micropores. Haynes and Sarma [24] developed a suitable mathematical model for such a system. 

In the above considerations the total pressure should also be taken into account. With increasing pressure, the efficiency of a bidisperse catalyst decreases because diffusion in micropores turns from Knudsen to ordinary and the difference between Df n and Dejt disappears. At a pressure of 1-10 MPa, a uniform porous structure with a pore size close to the mean free path is the most favorable [6]. 

Cylindrical pellets of four industrial and laboratory prepared catalysts with mono- and bidisperse pore structure were tested. Selected pellets have different pore-size distribution with most frequent pore radii (rmax) in the range 8 - 2500 nm. Their textural properties were determined by mercury porosimetry and helium pycnometry (AutoPore III, AccuPyc 1330, Micromeritics, USA). Description, textural properties of catalysts pellets, diameters of (equivalent) spheres, 2R, (with the same volume to geometric surface ratio) and column void fractions, a, (calculated from the column volume and volume of packed pellets) are summarized in Table 1. Cylindrical brass pellets with the same height and diameter as porous catalysts were used as nonporous packing. 

Two porous catalysts in the form of cylindrical pellets were used industrial hydrogenation catalyst Cherox 42-00 with monodisperse pore structure (Chemopetrol Litvinov, Czech Rep. height x diameter = 4.9 x 5.0 mm) and laboratory prepared a-alumina, A5 (based on boehmite from Rural SB, Condea Chemie, Germany) with bidisperse pore structure (height x diameter = 3.45 x 3.45 mm). 

A final word should be said about the variety of porous materials. Porous catalysts cover a rather narrow range of possibilities. Perhaps the largest variation is between monodisperse and bidisperse pellets, but even these differences are small in comparison with materials such as freeze-dried beef, which is like an assembly of solid fibers, and freeze-dried fruit, which appears to have a structure like an assembly of ping-pong balls with holes in the surface to permit a continuous void phase. ... 

Technology of the reverse meniscus consists in imposition of micro-porous layer to the PIN-structure that provides high intensity of heat transfer. Using of bidisperse wick structure is also instrumental in intensification of heat transfer. 

The Wakao-Smith model has been found appropriate for bidisperse porous support where the effective diffusivity can be predicted from the porous structure of the particles. According to this model, the effective diffusivity can be evaluated using the relation ... 

---