Macroporous mass transfer

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

Air is commonly run with tube-side feed. The permeate is run countercurrent with the separating sldn in contact with the permeate. (The feed gas is in contact with the macroporous back side of the membrane.) This configuration has proven to be superior, since the permeate-side mass-transfer problem is reduced to a minimum, and the feed-side mass-transfer problem is not limiting. 

When the catalyst is expensive, the inaccessible internal surface is a liabihty, and in every case it makes for a larger reactor size. A more or less uniform pore diameter is desirable, but this is practically reahz-able only with molecular sieves. Those pellets that are extrudates of compacted masses of smaller particles have bimodal pore size distributions, between the particles and inside them. Micropores have diameters of 10 to 100 A, macropores of 1,000 to 10,000 A. The macropores provide rapid mass transfer into the interstices that lead to the micropores where the reaction takes place. 

Another recent trend focused on supports in the shape of monolithic columns having the goal to benefit from the high permeability and the improved mass transfer characteristics of such structures. With this goal in mind, Lubda and Lindner [75] prepared enantioselective silica monolith columns with tert-butylcarbamoylquinine surface modification. A commercial sol-gel-derived Chromolith Performance Si (100 X 4.6 mm ID) monolith (1.9 tim macropore diameter, 12.5 nm mesopore... 

Equation (9.15) was written for macro-pore diffusion. Recognize that the diffusion of sorbates in the zeoHte crystals has a similar or even identical form. The substitution of an appropriate diffusion model can be made at either the macropore, the micro-pore or at both scales. The analytical solutions that can be derived can become so complex that they yield Httle understanding of the underlying phenomena. In a seminal work that sought to bridge the gap between tractabUity and clarity, the work of Haynes and Sarma [10] stands out They took the approach of formulating the equations of continuity for the column, the macro-pores of the sorbent and the specific sorption sites in the sorbent. Each formulation was a pde with its appropriate initial and boundary conditions. They used the method of moments to derive the contributions of the three distinct mass transfer mechanisms to the overall mass transfer coefficient. The method of moments employs the solutions to all relevant pde s by use of a Laplace transform. While the solutions in Laplace domain are actually easy to obtain, those same solutions cannot be readily inverted to obtain a complete description of the system. The moments of the solutions in the Laplace domain can however be derived with relative ease. 

Diffusion in the macro-pores of a formed parhcle is generally speaking a very important mechanism. If we speak in terms of resistances to mass transfer macropore resistance is often the largest of the resistances to mass transfer. For transport in the macro-pores we must introduce two parameters that influence the transport. 

Reid, Sherwood and Prausnitz [11] provide a wide variety of models for calculation of molecular diffusion. Dr is the Knudsen diffusion coefficient. It has been given in several articles as 9700r(T/MW). Once we have both diffusion coefficients we can obtain an expression for the macro-pore diffusion coefficient 1/D = 1/Dk -i-1/Dm- We next obtain the pore diffusivity by inclusion of the tortuosity Dp = D/t, and finally the local molar flux J in the macro-pores is described by the famiUar relationship J = —e D dcjdz. Thus flux in the macro-pores of the adsorbent product is related to the term CpD/r. This last quantity may be thought of as the effective macro-pore diffusivity. The resistance to mass transfer that develops due to macropore diffusion has a length dependence of R]. 

It may not be obvious but driving selectivity to a high value is best done by driving N2 adsorption to some acceptably high value and then driving O2 to a minimum. This dramatically changes the volume of gas that must pass in and out of the macro-pore structure of the adsorbent In aU PSA separations it is the macropore diffusion that is the dominant resistance to mass transfer. 

Micropore mass transfer resistance of zeoUte crystals is quantified in units of time by r /Dc, where is the crystal radius and Dc is the intracrystalline diffusivity. In addition to micropore resistance, zeolitic catalysts may offer another type of resistance to mass transfer, that is resistance related to transport through the surface barrier at the outer layer of the zeoHte crystal. Finally, there is at least one additional resistance due to mass transfer, this time in mesopores and macropores Rp/Dp. Here Rp is the radius of the catalyst pellet and Dp is the effective mesopore and macropore diffusivity in the catalyst pellet [18]. 

Due to their defined monomodal macropore distribution (see Section 1.2.1), monolithic stationary phases, based on polymerization of organic precursors, are predestined for efficient and swift separation of macromolecules, like proteins, peptides, or nucleic acids, as their open-pore structure of account for enhanced mass transfer due to convection rather than diffusion. In fact, most of the applications of organic monolith introduced and investigated in literature are directed to analysis of biomolecule chromatography [29]. 

Effects of polymer structure on reaction of phenylacetonitrile with excess 1-bromo-butane and 50% NaOH have been studied under conditions of constant particle size and 500 rpm stirring to prevent mass transfer limitations I03). All experiments used benzyltrimethylammonium ion catalysts 2 and addition of phenylacetonitrile before addition of 1-bromobutane as described earlier. With 16-17% RS the rate constant with a 10 % CL polymer was 0.033 times that with a 2 % CL polymer. Comparisons of 2 % CL catalysts with different % RS and Amberlyst macroporous ion exchange resins are in Table 6. The catalysts with at least 40% RS were more active that with 16 % RS, opposite to the relative activities in most nucleophilic displacement reactions. If the macroporous ion exchange resins were available in small particle sizes, they might be the most active catalysts available for alkylation of phenylacetonitrile. 

Prediction of the breakthrough performance of molecular sieve adsorption columns requires solution of the appropriate mass-transfer rate equation with boundary conditions imposed by the differential fluid phase mass balance. For systems which obey a Langmuir isotherm and for which the controlling resistance to mass transfer is macropore or zeolitic diffusion, the set of nonlinear equations must be solved numerically. Solutions have been obtained for saturation and regeneration of molecular sieve adsorption columns. Predicted breakthrough curves are compared with experimental data for sorption of ethane and ethylene on type A zeolite, and the model satisfactorily describes column performance. Under comparable conditions, column regeneration is slower than saturation. This is a consequence of non-linearities of the system and does not imply any difference in intrinsic rate constants. 

There are three distinct mass-transfer resistances (1) the external resistance of the fluid film surrounding the pellet, (2) the diffusional resistance of the macropores of the pellet, and (3) the diffusional resistance of the zeolite crystals. The external mass-transfer resistance may be estimated from well-established correlations (4, 5) and is generally negligible for molecular sieve adsorbers so that, under practical operating conditions, the rate of mass transfer is controlled by either macropore diffusion or zeolitic diffusion. In the present analysis we consider only systems in which one or other of these resistances is dominant. If both resistances are of comparable importance the analysis becomes more difficult. 

If zeolitic diffusion is sufficiently rapid so that the sorbate concentration through any particular crystal is essentially constant and in equilibrium with the macropore fluid just outside the crystal, the rate of mass transfer will be controlled by transport through the macropores of the pellet. Transport through the macropores may be assumed to occur by a diffusional process characterized by a constant pore diffusion coefficient Z)p. The relevant form of the diffusion equation, neglecting accumulation in the fluid phase within the macropores which is generally small in comparison with accumulation within the zeolite crystals, is... 

A new mathematical model based on moment techniques to describe micro- and macropore diffusion is used to study the mass-transfer resistances of Ci to C4 saturated hydrocarbons in H and Na mordenites between 127° C and 272° C. The intracrystalline diffusion coefficient decreases as the number of carbon atoms increases while the energy of activation increases with the number of carbons. The contribution from individual mass-transfer resistances to the overall mass-transfer processes is estimated. 

Results of these calculations for H mordenite are presented in Table IV. The macropore diffusion plays a role far from negligible even at high temperature and in some instances (e.g., low temperature and large particles) is the major contribution to the total mass-transfer resistance. No single step controls the overall mass-transfer process as no resistance has a relatively large enough contribution to dominate the process. In every... 

Mesostructured materials are granules containing individual platelets (crystals) associated in a fairly random manner. This type of configuration is always associated with a bi-porous structure, in which small particles (platelets) have pores, usually mesopores, different from the composite particle (secondary mesopores and macropores). The secondary pore structure controls access to the individual crystal mesoporosity. As a result, different mass transfer resistances to diffusion through bi-porous structures could be present. In order to evaluate the relative significance of both primary and secondary pore diffusion, usually two different particle sizes are employed in diffusion measurements. 

The first hypothesis seems unlikely to be true in view of the rather wide variation in the ratio of carbon dioxide s kinetic diameter to the diameter of the intracrystalline pores (about 0.87, 0.77 and 0.39 for 4A, 5A and 13X, respectively (1J2)). The alternative hypothesis, however, (additional dif-fusional modes through the macropore spaces) could be interpreted in terms of transport along the crystal surfaces comprising the "walls" of the macropore spaces. This surface diffusion would act in an additive manner to the effective Maxwell-Knudsen diffusion coefficient, thus reducing the overall resistance to mass transfer within the macropores. 

Using the computer programs discussed above, it is possible to extract from these breakthrough curves the effective local mass transfer coefficients as a function of CO2 concentration within the stable portion of the wave. These mass transfer coefficients are shown in Figure 15, along with the predicted values with and without the inclusion of the surface diffusion model. It is seen that without the surface diffusion model, very little change in the local mass transfer coefficient is predicted, whereas with surface diffusion effects included, a more than six-fold increase in diffusion rates is predicted over the concentrations measured and the predictions correspond very closely to those actually encountered in the breakthrough runs. Further, the experimentally derived results indicate that, for these runs, the assumption that micropore (intracrystalline) resistances are small relative to overall mass transfer resistance is justified, since the effective mass transfer coefficients for the two (1/8" and 1/4" pellets) runs scale approximately to the inverse of the square of the particle diameter, as would be expected when diffusive resistances in the particle macropores predominate. 

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