Effectiveness, intraparticle

Aguwa, A.A.. Patterson, J.W., Haas. C.N., and Noll, K.E. Estimation of effective intraparticle diffusion coefficients with differential reactor columns./. Water PoMut Control Fed., 56(5) 442-448,1984. 

Where V is the volume of aqueous metal solution, is the amount of resin, Ig is the density of the dry ion exchange resin, R is the radius of the spherical resin, B is the adsorption capacity of resin, in g-mole-metal-ion/g-resin, t is the adsorption time, is the effective intraparticle diffusion of heavy ion metals through resins, Xf is the removal fraction of heavy metal ions by ion exchange resins. 

In industrial practice, the most convenient way of accounting for mass-transfer effects is to view the penetrable catalyst particle as a pseudo-homogeneous phase. Obstruction of mass transfer by the solid material in the particle then is reflected by an "effective" intraparticle mass-transfer or diffusion coefficient that is appropriately lower than in the contacting fluid. If this approach is taken, two fundamentally different mass-transfer situations appear Mass transfer to and from the particle across an adherent boundary layer is affected by the reaction only in that the latter sets the boundary condition at the particle. Here, mass transfer and reaction are sequential and occur in different parts of the system, and the slower of the two is the bottleneck and dictates the overall rate and its temperature dependence. Within the particle, however, mass transfer and reaction occur simultaneously and in the same volume element. Here, the reaction introduces a source-or-sink term into the basic differential material balance. If the reaction is slow, it alone controls the overall rate and its temperature dependence. If mass transfer is slow, both reaction and mass transfer affect the rate, and the apparent reaction order and activation energy are the arithmetic means of those of reaction and mass transfer. 

The method has the advantage that it depends on a steady-state measurement and it is not affected by finite heat transfer. Effective intraparticle diffusivities determined in this way are commonly somewhat smaller than the values derived for the same adsorbent under simitar conditions from transient uptake rate measurements. This is because blind pores, which contribute to the flux in a transient measurement, make no contribution in a Wicke-Kallenbach system. 

Intraparticle mass transport resistance can lead to disguises in selectivity. If a series reaction A — B — C takes place in a porous catalyst particle with a small effectiveness factor, the observed conversion to the intermediate B is less than what would be observed in the absence of a significant mass transport influence. This happens because as the resistance to transport of B in the pores increases, B is more likely to be converted to C rather than to be transported from the catalyst interior to the external surface. This result has important consequences in processes such as selective oxidations, in which the desired product is an intermediate and not the total oxidation product CO2. 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

The ratio of the observed reaction rate to the rate in the absence of intraparticle mass and heat transfer resistance is defined as the elFectiveness factor. When the effectiveness factor is ignored, simulation results for catalytic reactors can be inaccurate. Since it is used extensively for simulation of large reaction systems, its fast computation is required to accelerate the simulation time and enhance the simulation accuracy. This problem is to solve the dimensionless equation describing the mass transport of the key component in a porous catalyst[l,2]... 

Rijnaarts HHM, A Bachmann, JC Jumelet, AJB Zehnder (1990) Effect of desorption and intraparticle mass transfer on the aerobic biomineralization of alpha-hexachlorocyclohexane in a contaminated calcareous soil. Environ Sci Technol 24 1349-1354. 

Application of the Balzhinimaev model requires assumptions about the reactor and its operation so that the necessary heat and material balances can be constructed and the initial and boundary conditions formulated. Intraparticle dynamics are usually neglected by introducing a mean effectiveness factor however, transport between the particle and the gas phase is considered. This means that two heat balances are required. A material balance is needed for each reactive species (S02, 02) and the product (SO3), but only in the gas phase. Kinetic expressions for the Balzhinimaev model are given in Table IV. 

Effect of fragmentation on catalyst utilization when intraparticle diffusion is rate controlling (shaded areas represent regions of the catalyst with insignificant concentrations of reactants). 

In this case the reaction rate will depend not only on the system temperature and pressure but also on the properties of the catalyst. It should be noted that the reaction rate term must include the effects of external and intraparticle heat and mass transfer limitations on the rate. Chapter 12 treats these subjects and indicates how equation 8.2.12 can be used in the analysis of packed bed reactors. 

One often finds that either external or intraparticle mass transfer effects are significant in reactors of this type. Although the treatments... 

The term in brackets is a dimensionless group that plays a key role in determining the limitations that intraparticle diffusion places on observed reaction rates and the effectiveness with which the catalyst surface area is utilized. We define the Thiele modulus hT as... 

J.5.2 Implications of the Effectiveness Factor Concept for Kinetic Parameters Measured in the Laboratory. It is useful at this point to discuss the effects of intraparticle diffusion on the kinetic parameters that are observed experimentally. Unless we are aware that intraparticle diffusion may obscure or disguise the... 

Schematic representation of shift in activation energy when intraparticle mass transfer effects become significant.

The Consequences of Intraparticle Temperature Gradients For Catalyst Effectiveness Factors... 

In this equation the entire exterior surface of the catalyst is assumed to be uniformly accessible. Because equimolar counterdiffusion takes place for stoichiometry of the form of equation 12.4.18, there is no net molar transport normal to the surface. Hence there is no convective transport contribution to equation 12.4.21. Let us now consider two limiting conditions for steady-state operation. First, suppose that the intrinsic reaction as modified by intraparticle diffusion effects is extremely rapid. In this case PA ES will approach zero, and equation 12.4.21 indicates that the observed rate per unit mass of catalyst becomes... 

To illustrate the masking effects that arise from intraparticle and external mass transfer effects, consider a surface reaction whose intrinsic kinetics are second-order in species A. For this rate expression, equation 12.4.20 can be written as... 

At this point it is instructive to consider the possible presence of intraparticle and external mass and heat transfer limitations using the methods developed in Chapter 12. In order to evaluate the catalyst effectiveness factor we first need to know the combined diffusivity for use... 

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