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Paul B Weisz - One of the best experts on this subject based on the ideXlab platform.
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Effective Diffusivities in zeolites 3 effects of polarity cation density and site occupancy in zsm 5
Journal of Catalysis, 1993Co-Authors: S F Garcia, Paul B WeiszAbstract:The Effective diffusivity that determines the catalytic reaction inhibition (utilization factor) in the steady-state process of catalysis, D[sub ss], differs from that derived from nonsteady-state sorption kinetics, D[sub ns] (e.g., uptake diffusivity'). D[sub ss] is obtainable from D[sub ns] by a transformation based on the equilibrium ratio C[sub T]/C[sub o] of the total sorbed concentration to the applied vapor phase concentration c[sub o][center dot]D[sub s] is several orders of magnitude larger than D[sub ns]. For o-xylene in siliceous ZSM-5 D[sub ss] was found to be virtually invariant with temperature. Introducing a polar NH[sub 2] substituent in place of CH[sub 3] does not alter the temperature independence, i.e., it does not introduce or alter activation energy'. In fact, a larger diffusively results, presumably from the slightly smaller Effective molecular size. Introducing a high sodium cation density in the zeolite structure creates a temperature dependence of D[sub ss]. However, it is shown to be a result of the high percentage of occupancy of transition (jump) sites by sorbed molecules which diminishes with increasing temperature. These several observations allow important conclusions to be drawn concerning the real or apparent nature of activated' diffusion in the zeolite. 18 refs., 8 figs.
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Effective Diffusivities in zeolites 2 experimental appraisal of Effective shape selective diffusivity in zsm 5 catalysis
Journal of Catalysis, 1993Co-Authors: S F Garcia, Paul B WeiszAbstract:Abstract A method is described for experimentally probing the molecular shape-sensitive diffusivity of a molecular species Effective during the steady-state process of catalysis in a zeolite. It does not require the use of catalyst samples of differing and known particle (i.e., crystallite) sizes but with otherwise identical properties. It can be carried out on a single catalyst sample. The method makes use of hydrogen-deuterium transfer as the catalytic reaction. Instead of comparing reaction rates on different crystallite sizes, it makes use of altering the magnitude of a pseudo-first-order reaction rate constant to probe for the effect of diffusion inhibition. The method is used here to examine the magnitude of the catalytically Effective diffusivity of ortho -xylene is ZSM-5, in comparison to the "uptake diffusivity" derived from sorption measurements.
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Effective Diffusivities in zeolites 1 aromatics in zsm 5 crystals
Journal of Catalysis, 1990Co-Authors: Sigfrido F Garcia, Paul B WeiszAbstract:Abstract Real or apparent inconsistenceis of up to several orders of magnitude exist in reported Diffusivities of zeolites. Some are caused by differences in definition, usage, and methodologies in their determination. Some result from operating conditions involving transport mechanisms deviating from a strictly stochastic process. Diffusivities Effective in non-steady-state methods of determination (e.g., uptake Diffusivities) can be translated into Diffusivities applicable to characterization of catalytic (i.e., to steady-state) behavior. For ortho -xylene and other aromatic molecules in ZSM-5, the magnitude of these Diffusivities follows the expectations of shape selectivity; i.e., they decrease systematically with increasing Effective minimum dimension of the molecules. These Diffusivities are found to be invariant in both temperature and for a 360-fold variation in applied concentration. A mechanistic model for activated zeolite diffusion, involving inernalized molecules of more than one type (energy level), is suggested to be useful in future considerations of the relationship of intrinsic and Effective Diffusivities and their activation energies to shape, structure, and molecular mechanism.
Stratis V Sotirchos - One of the best experts on this subject based on the ideXlab platform.
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Effective Diffusivities and conductivities of random dispersions of nonoverlapping and partially overlapping unidirectional fibers
Journal of Chemical Physics, 1993Co-Authors: Manolis M Tomadakis, Stratis V SotirchosAbstract:Computer simulation results are presented for the Effective bulk, transition, and Knudsen diffusion coefficients in structures consisting of parallel nonoverlapping (impenetrable) or partially overlapping (penetrable) fibers. The numerical procedure is based on a discrete step‐by‐step random walk mechanism used to determine the mean square displacement of molecules traveling in the interior of the porous medium. The computed transition regime Diffusivities are compared with the predictions of the reciprocal additivity Effective diffusivity expression. The bulk diffusivity results are also expressed as formation factors describing other transport properties (e.g., thermal and electrical conductivity, magnetic permeability, and dielectric constant) of the fibrous structures or in general of the corresponding arrays of cylinders (either nonconducting or infinitely conducting with respect to the matrix phase). The formation factors of nonoverlapping cylinders are compared with variational bounds and analytica...
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steady state versus transient measurement of Effective Diffusivities in porous media using the diffusion cell method
Chemical Engineering Science, 1992Co-Authors: Stratis V SotirchosAbstract:Abstract The relation between the Effective Diffusivities of gases obtained from transient and steady-state mass transport experiments using the diffusion-cell method is investigated in this study. A simple structure of parallel pores, of some pore-size distribution, is used to represent the porous medium, and, in order to investigate the effects of pore interaction on the problem, the pores are assumed to communicate with each other at a number of equidistant points between the two ends of the porous slab. It is shown that matching the zero and first moments of the experimental (inhomogeneous model) response of the diffusion cell with the corresponding moments of the response of the homogeneous model yields the same Effective diffusion coefficient as steady-state diffusion-cell experiments. Time-domain parameter estimation schemes tend to produce larger, in general, Effective Diffusivities, but the difference between the time-domain responses of the homogeneous and inhomogeneous model, with the same first two moments, decreases sharply if the pores are allowed to interact in the interior of the porous pellet.
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Effective kundsen Diffusivities in structures of randomly overlapping fibers
Aiche Journal, 1991Co-Authors: Manolis M Tomadakis, Stratis V SotirchosAbstract:Effective Knudsen diffusion coefficients are presented for fibrous structures consisting of overlapping fibers. The fibers are distributed randomly in d (d=2 or 3) directions with their axes perpendicular to one direction (d=2) or in the three-dimensional space with no preferred orientation (d=3), or they are grouped into d (d=1, 2, or 3) mutually perpendicular bundles of parallel, randomly overlapping fibers. Effective Diffusivities are computed using a Monte Carlo simulation scheme to determine the mean square displacement of molecules traveling in the interior of the porous medium for large travel times. Our results show that structures with fibers distributed randomly in d directions have diffusion coefficients identical, within the accuracy of our simulation, to those of d-directional, parallel fiber structures. Effective Knudsen Diffusivities are strongly influenced only by the directionality of the fiber structure, with tridirectional or randomly oriented fiber structures presenting lower percolation thresholds (0.04 vs. 0.11) and higher Effective Diffusivities than bidirectional or random structures with their axes perpendicular to one direction. The tortuosity factor is in general found to decrease with increasing porosity, approaching for each case, as the porosity goes to unity, the corresponding lower bound that is derived using variational principles.
Petr Schneider - One of the best experts on this subject based on the ideXlab platform.
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Effective Diffusivities and pore transport characteristics of washcoated ceramic monolith for automotive catalytic converter
Chemical Engineering Science, 2006Co-Authors: Tomas Starý, Petr Schneider, Olga Solcova, Milos MarekAbstract:Abstract Using the chromatographic technique (carrier-gas: N2; tracer-gases: He, Ar) the Effective diffusivity in single-pellet string columns (SPSC) packed with porous slab particles was studied. Dispersion due to extra-column effects was eliminated via convolution of column responses for two lengths. The measurements were done for cordierite particles and for cordierite coated with alumina-based washcoat. The Effective diffusion coefficients for two tracer–carrier pairs were evaluated by fitting column response (chromatographic) peaks in time-domain. Mean transport parameters were evaluated for both types of porous particles. The obtained mean transport pore radii are in reasonable agreement with pore-size distribution from mercury porosimetry.
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determination of Effective Diffusivities and transport parameters of porous solids in the single pellet string column
Catalysis Today, 1997Co-Authors: Olga Solcova, Vladimír Hejtmánek, Petr SchneiderAbstract:Abstract The chromatographic technique which employs SPSC and takes into account the extra-column effects of the measuring system can provide consistent transport characteristics of porous solids. These characteristics are independent of the kind of gases which are transported through pores, as well of temperature and pressure. Dispersion of the tracer band in the interparticle spaces of the SPSC increases at higher carrier gas velocities when the non-porous column packing is replaced by a porous one. This points to some additional mechanism of band spreading caused by the presence of interface gas-porous solid.
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Effective Diffusivities from dynamic diffusion cell the general moments analysis
Chemical Engineering Science, 1994Co-Authors: Daniel Arnost, Petr SchneiderAbstract:Abstract Expressions for the first absolute moment, μ′ 1 , and the second central moment, μm 2 , of the impulse response of the dynamic version of the Wicke-Kallenbach diffusion cell were derived for the general case of bidisperse porous medium and adsorbable tracer gas. The significance of individual terms in these expressions is discussed. All previously published results issue from the general expressions as special cases. The use of adsorbable tracers is suggested as a means of increasing the confidence of Effective diffusion coefficients evaluated from experimental cell responses.
Sebastian C. Reyes - One of the best experts on this subject based on the ideXlab platform.
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A simple correlation for predicting Effective Diffusivities in immobilized cell systems.
Biotechnology and Bioengineering, 2010Co-Authors: Mark R. Riley, Fernando J. Muzzio, Helen M. Buettner, Sebastian C. ReyesAbstract:A simple correlation method has been developed to predict Effective Diffusivities of small molecules in heterogeneous materials such as immobilized cell systems. This correlation uses a single diffusivity measurement at one cell volume fraction to predict Diffusivities for any other volume fraction of cell. The method has been applied to 20 sets of published diffusivity measurements in immobilized cell systems and accurately predicts affective Diffusivities of molecules for the full range of cell fractions. It may also be used to predict Effective Diffusivities in heterogeneous materials in which the diffusivity of a molecule in each phase and the volume fraction of each phase are known. © 1996 John Wiley & Sons, Inc.
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calculation of Effective Diffusivities and reactivities in immobilized cell systems using finite difference methods
Computers & Chemical Engineering, 1998Co-Authors: Mark R. Riley, Fernando J. Muzzio, Sebastian C. ReyesAbstract:Abstract Immobilized cell systems typically consist of a single cell type encased in a semi-rigid polymer support. The rates at which nutrient molecules diffuse and react in these materials determine the feasible longevity and the amount of desirable product generated by the cells. Finite difference techniques were developed to calculate Effective Diffusivities and rates of reaction of small molecules in such immobilized cell systems. The structures analyzed consist of multiple cellular inclusions distributed in a continuous phase where molecules diffuse more slowly in the cells than in the continuous phase. Diffusivities are in excellent agreement with available theoretical bounds. Under typical reactive conditions, the depth to which oxygen can penetrate ranges from 24–200 μm, depending on the cell volume fraction, oxygen supply, and cellular uptake kinetics. Increases in the cell fraction beyond 0.55 yield minimal increases in the oxygen consumption rate, suggesting that such materials are limited by the diffusive supply of oxygen.
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Effective Diffusivities in catalyst pellets new model porous structures and transport simulation techniques
Journal of Catalysis, 1991Co-Authors: Sebastian C. Reyes, Enrique IglesiaAbstract:Compressed and sintered porous solids are simulated by random-loose aggregates of spheres that are distributed in size and partially overlapped to achieve the required porosity. The resulting porous networks closely capture the morphological details of diffusing channels within granular materials commonly used as catalyst supports. Effective Diffusivities in these model solids are calculated by Monte Carlo techniques that allow the probing of representative regions of the void space throughout the Knudsen, transition, and molecular diffusion regimes. Simulated Diffusivities and tortuosity factors are in excellent agreement with experimental observations. These simulations also allow the calculation of accurate pore-size distributions and of transition-region Diffusivities, previously estimated by simple geometric arguments and by the Bosanquet approximation, respectively. Mean pore radii calculated from surface area (S) and porosity ({Phi}{sup A}) data ({bar r}{sub p} = 2 {Phi}{sup A}/S) closely resemble the exact values obtained in our simulations for compressed solids but less so for sintered materials. The simulations show that tortuosity factors, when properly defined and calculated, are intrinsic properties of porous solids, and identical in the Knudsen and molecular diffusion regimes.
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monte carlo simulations of Effective Diffusivities in three dimensional pore structures
MRS Proceedings, 1990Co-Authors: Sebastian C. Reyes, Enrique Iglesia, Yee C ChiewAbstract:A hybrid discrete/continuum Monte Carlo technique combining random walk simulations with first passage time (FPT) concepts is developed here in order to estimate diffusion properties of randomly-assembled sintered porous structures. This work combines the creation of realistic porous solid structures with controlled pore size, shape, and tortuosity features with the application of an efficient algorithm for calculating Effective Diffusivities in all diffusion regimes (Knudsen, transition, and molecular). The hybrid simulation technique consists of creating a “protective” boundary layer surrounding solid surfaces within which discrete random motion simulations are performed while continuum FPT results are used in the remaining pore space. The boundary layer thickness reflects a characteristic length scale, of the order of a few mean free paths, over which the FPT approximation breaks down. This procedure significantly reduces the computations required to cover statistically representative regions of the porous structure,a serious shortcoming in previous studies of gas diffusion through porous solids; it leads to Effective diffusivity estimates that are in excellent agreement with experimental measurements.
Enrique Iglesia - One of the best experts on this subject based on the ideXlab platform.
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Effective Diffusivities in catalyst pellets new model porous structures and transport simulation techniques
Journal of Catalysis, 1991Co-Authors: Sebastian C. Reyes, Enrique IglesiaAbstract:Compressed and sintered porous solids are simulated by random-loose aggregates of spheres that are distributed in size and partially overlapped to achieve the required porosity. The resulting porous networks closely capture the morphological details of diffusing channels within granular materials commonly used as catalyst supports. Effective Diffusivities in these model solids are calculated by Monte Carlo techniques that allow the probing of representative regions of the void space throughout the Knudsen, transition, and molecular diffusion regimes. Simulated Diffusivities and tortuosity factors are in excellent agreement with experimental observations. These simulations also allow the calculation of accurate pore-size distributions and of transition-region Diffusivities, previously estimated by simple geometric arguments and by the Bosanquet approximation, respectively. Mean pore radii calculated from surface area (S) and porosity ({Phi}{sup A}) data ({bar r}{sub p} = 2 {Phi}{sup A}/S) closely resemble the exact values obtained in our simulations for compressed solids but less so for sintered materials. The simulations show that tortuosity factors, when properly defined and calculated, are intrinsic properties of porous solids, and identical in the Knudsen and molecular diffusion regimes.
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monte carlo simulations of Effective Diffusivities in three dimensional pore structures
MRS Proceedings, 1990Co-Authors: Sebastian C. Reyes, Enrique Iglesia, Yee C ChiewAbstract:A hybrid discrete/continuum Monte Carlo technique combining random walk simulations with first passage time (FPT) concepts is developed here in order to estimate diffusion properties of randomly-assembled sintered porous structures. This work combines the creation of realistic porous solid structures with controlled pore size, shape, and tortuosity features with the application of an efficient algorithm for calculating Effective Diffusivities in all diffusion regimes (Knudsen, transition, and molecular). The hybrid simulation technique consists of creating a “protective” boundary layer surrounding solid surfaces within which discrete random motion simulations are performed while continuum FPT results are used in the remaining pore space. The boundary layer thickness reflects a characteristic length scale, of the order of a few mean free paths, over which the FPT approximation breaks down. This procedure significantly reduces the computations required to cover statistically representative regions of the porous structure,a serious shortcoming in previous studies of gas diffusion through porous solids; it leads to Effective diffusivity estimates that are in excellent agreement with experimental measurements.