Diffusion macropore control

Understanding the adsorption, diffusivities and transport limitations of hydrocarbons inside zeolites is important for tailoring zeolites for desired applications. Knowledge about diffusion coefficients of hydrocarbons inside the micropores of zeolites is important in discriminating whether the transport process is micropore or macropore controlled. For example, if the diffusion rate is slow inside zeolite micropores, one can modify the post-synthesis treatment of zeolites such as calcination, steaming or acid leaching to create mesopores to enhance intracrystalline diffusion rates [223]. The connectivity of micro- and mesopores then becomes an... 

Curves calculated in this way for macropore control and zeolitic diffusion control are compared in Figure 3 for one particular value of X. Also shown in this figure is the theoretical curve for zeolitic diffusion control with a constant diffusivity. Differences between the shapes of these curves are not large although the case of zeolitic diffusion control with a constant diffusivity leads to substantially greater tailing. 

Based upon the results shown in Figure 6 and the surface diffusion model given by equation (21), the values of ( Dos/is) which best fit the three systems were computed, both from the standpoint of assuming complete macropore control and from that of assuming the existence of micropore resistance as well, in the amount predicted from Figure 6. These values are given in Table III. 

Although the systems investigated here exhibited predominantly macropore control (at least those with pellet diameters exceeding 1/8" or 0.32 cm), there is no reason to believe that surface diffusion effects would not be exhibited in systems in which micropore (intracrystalline) resistances are important as well. In fact, this apparent surface diffusion effect may be responsible for the differences in zeolitic diffusion coefficients obtained by different methods of analysis (13). However, due to the complex interaction of various factors in the anlaysis of mass transport in zeolitic media, including instabilities due to heat effects, the presence of multimodal pore size distribution in pelleted media, and the uncertainties involved in the measurement of diffusion coefficients in multi-component systems, further research is necessary to effect a resolution of these discrepancies. 

The measured surface area consists of both external and internal area where internal surface area includes all cracks or connected pores that are deeper than they are wide, varying from subatomic defects to pores of extreme size (Gregg and Sing, 1982). For example, micropores are dehned as pores with radius <2 nm, mesopores as pores with radius from 2 nm to 50 nm, and macropores as those with pores of diameter >50 nm. The main distinction between internal and external surface is that advection can control transport to and away from external surface while diffusion must control transport for internal pore space (Hochella and Banheld, 1995). Porosity may be related to crystallization or replacement processes (Putnis, 2002). 

This technique may also be used to measure effective macropore diffusivities in biporous adsorbent pellets [13,14]. For such a system with a linear equilibrium isotherm and assuming rapid intracrystalhne diffusion, the governing diffusion equation is of the same form as for micropore control. The solution is identical to Eq. 1 except that R now refers to the particle radius and the diffusivity D is replaced by the effective diffusivity De = Dp p/(ep + (1 - p)fC). Since the equilibrium constant (K) is generally large and varies with temperature according to the van t Hoff equation (K = it is clear that a macropore-controlled system will gener-... 

The solution given in eq. (10.4-1 la) reduces to simple solutions when either the macropore or micropore diffusion is the controlling mechanism, that is when y is less than unity, that is the time scale for the diffusion in the macropore is much smaller than that in the micropore, we would then expect the micropore diffusion would control the overall adsorption kinetics. In this case, we have the following half time... 

Figure 10.4-3 shows the plot of y versus T and we see that the demarcation temperature is about 300K. For temperature greater than 400K, micropore diffusions controls the uptake while for temperature less than 200K, macropore diffusion controls. For temperatures between 200 and 400 K, both diffusion mechanisms control the uptake. 

The only parameter that could be affected by the total pressure is the pore diffusivity Dp. If the macropore diffusion is controlled purely by the Knudsen diffusion mechanism, the pore diffusivity is and hence it is independent of total pressure, implying that the parameter y is independent of pressure. However, if the macropore diffusion is governed by molecular-molecular collision, then the pore diffusivity is inversely proportional to the total pressure, meaning that the parameter Y increases linearly with the total pressure. This means that the system is moving toward macropore diffusion control as the total pressure increases. 

In the case of irreversible isotherm, the higher is the temperature, the larger is the value of y while for the case of linear isotherm as discussed earlier, the higher is the temperature the smaller is the value of y. Thus, macropore diffusion controls at high temperature for irreversible isotherm, while the micropore diffusion will control the uptake at high temperature in the case of linear isotherm. 

The appropriate form of the diffusion equation for a macropore-controlled system may be obtained from a differential mass balance on a spherical shell element ... 

In bidisperse porous adsorbents such as zeolite pellets there are two diffusion mechanisms the macropore diffusion with time constant Rp /Dp and the micropore diffusion with time constant rc /Dc. Bidisperse porous models for ZLC desorption curves have been recently developed by Brandani [28] and Silva and Rodrigues [29]. In bidisperse porous adsorbents, it is important to carry out experiments in pellets with different sizes but with the same crystal size (different Rp, same rc) or pellets with the same size but with different crystals (same Rp, different rc). If macropore diffusion is controlling, time constants for diffusion should depend directly on pellet size and should be insensitive to crystal size changes. If micropore diffusion controls the reverse is true. The influence of temperature is also important when macropore diffusion is dominant the apparent time constant of diffusion defined by Rp2(H-K)/Dp is temperature dependent in the same order of K (directly related to the heat of adsorption) which is determined independently from the isotherm. The type of purge gas is... 

The analytical solution given by Ruckenstein et al. (1971) expresses the dimensionless uptake of adsorbate mt/m as a function of time. The solution is complex and Involves two parameters defined by c = DJrc)t DpIR ) and = 3a (1 - gp) qo/epCo- When the resistance to diffusion is controlled by diffusion in the micropores (j3 -> 0), the system is described by equations (4.17) to (4.21) inclusive, the uptake of adsorbate being represented by equation (4.22). When, on the other hand, macropore resistance dominates the diffusion process (/ -v oo), then equations (4.27) to (4.30) inclusive apply and the condition (4.18) is redundant because the concentration throughout the crystal is uniform. The solution is then identical to equation (4.22) with rp and Dp replacing rc and Dc, respectively. 

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...

The etch rate is further increased if H202 is added to the solution, as shown in Fig. 2.5 b. At such low rates the reaction is controlled by the kinetics of the reaction at the interface and not by diffusion in the solution. This etching solution is therefore found to be perfect to remove micro- and mesoporous silicon selectively from a bulk silicon substrate or to increase the diameter of meso- or macropores in an well-controlled, isotropic manner [Sa3],... 

The electrotransfer of proteins onto (non-specific) binding membranous sheets is named Western hlot in contrast to the transfer of DNA (Southern hlot) and of RNA (Northern hlot). The main advantage of blotting procedures lies in the immobilization and presentation of macromolecules on the surface of a solid planar material. This presentation leads to an easy access of reactants in the opposite to the diffusion-controlled motion of reaction partners within gels or macroporous spheres. 

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). 

The rate of n-paraffin desorption generally controls the overall production rate (18, 19). The diffusion of n-paraffins in commercial 5A molecular sieves is reported to be controlled by either micropore diffusion or macropore diffusion, or both, depending on the molecular sieve crytal size and macropore size distribution of the adsorbent (20). A 5A molecular sieve adsorbent with smaller crystal size and optimum macropore size distribution would have a faster adsorption-desorption rate and, therefore, a higher effective capacity. 

Purification of Air Prior to Liquefaction. Separation of air by cryogenic fractionation processes requires removal of water vapor and carbon dioxide to avoid heat exchanger freeze-up. Many plants today are using a 13X (Na-X) molecular sieve adsorbent to remove both water vapor and carbon dioxide from air in one adsorption step. Since there is no necessity for size selective adsorption, 13X molecular sieves are generally preferred over type A molecular sieves. The 13X molecular sieves have not only higher adsorptive capacities but also faster rates of C02 adsorption than type A molecular sieves. The rate of C02 adsorption in a commercial 13X molecular sieve seems to be controlled by macropore diffusion 37). The optimum operating temperature for C02 removal by 13X molecular sieve is reported as 160-190°K 38). 

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... 

The breakthrough curve for the case of macropore diffusion control may thus be obtained from the solution of Equations 2-4 and 13-17. 

Figure 2. Theoretical breakthrough curves for macropore diffusion control at X = 1.0 saturation (----------------------), regeneration (------)...

Figure S. Comparison of asymptotic constant pattern saturation breakthrough curves for X = 0.1 5 (1) zeolitic diffusion control with Dz independent of concentration, (2) zeolitic diffusion control, (8) macropore diffusion control...

Also shown in Table I are the estimated values of the time constant for macropore diffusion based on estimated macropore diffusivities. From the ratio of the time constants for macropore diffusion and zeolitic diffusion, it is clear that the assumption of zeolitic diffusion control is a valid approximation for these systems. 

In the experimental systems considered here, the controlling resistance was in each case zeolitic diffusion, but systems in which macropore resistance is dominant are equally common. As examples one may cite the sorption of light hydrocarbons in the Davison 5A molecular sieves which contain much smaller zeolite crystals and correspondingly smaller macropores than the equivalent Linde products (18). 

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 transport properties across an MIP membrane are controlled by both a sieving effect due to the membrane pore structure and a selective absorption effect due to the imprinted cavities [199, 200]. Therefore, different selective transport mechanisms across MIP membranes could be distinguished according to the porous structure of the polymeric material. Meso- and microporous imprinted membranes facilitate template transport through the membrane, in that preferential absorption of the template promotes its diffusion, whereas macroporous membranes act rather as membrane absorbers, in which selective template binding causes a diffusion delay. As a consequence, the separation performance depends not only on the efficiency of molecular recognition but also on the membrane morphology, especially on the barrier pore size and the thickness of the membrane. 

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