Diffusional regime effectiveness factor

After drying and reduction, the Pd-Ag/C catalysts are composed of bimetallic Eilloy nanoparticles ( 3 nm). CO chemisorption coupled to TEM and XRD analysis showed that that, for catalysts 1.5% wt. in each metal, the bulk composition of the alloy is close to 50% in each metal, whereas the surface is 90% in Ag and 10% in Pd [9]. Mass transfer limitations can be detected by testing the same catalyst with various pellet sizes [18]. Indeed, if the reactants diffusion is slow due to small pore sizes, the longer the distance between the pellet surface and the metal particle, the larger the influence of the difiusion rate on the apparent reaction rate. Pd-Ag catalysts with various pellet sizes were thus tested in hydrodechlorination of 1,2-dichloroethane. Results were compared to those obtained with a Pd-Ag/activated charcoal catalyst. Fig. 4 shows the evolution of the effectiveness factor of the catalysts, i.e. the ratio between the apparent reaction rate and the intrinsic reaction rate, as a function of the pellet size. The intrinsic reaction rate was considered equal to the reaction rate obtained with the smallest pellet size. When rf = 1, no diffusional limitations occur, and the catalyst works in chemical regime. When j < 1, the observed reaction rate is lower than the intrinsic reaction rate due to a slow diffusion of the reactants and products and the catalyst works in diffusional regime [18]. 

Effect of Diffusional Restrictions on Enzyme Reactor Design and Performance in Heterogeneous Systems. Determination of Effectiveness Factors. Batch Reactor Continuous Stirred Tank Reactor Under Complete Mixing Continuous Packed-Bed Reactor Under Plug Flow Regime... 

In this paper we will first review some basic concepts and apply them to the design of isothermal reactors working in the diffusional regime.Then we will concentrate our attention on the problem of intraparticle convection in large pore catalysts.Several aspects of this question will be dealt with - effectiveness factors for iso -thermal and nonisothermal catalysts, measurement of effective diffu-sivities and the implication of intraparticle convection effects on the design and operation of fixed bed catalytic reactors. 

For zero order reactions one should take into account that r=k only if c> 0 otherwise r=0. In a situation where the concentration reaches a zero value inside the particle at a point x=x we should replace the boundary condition (Ic) by f=0 and df/dx=0 at x=x, The effectiveness factor is now simply the ratio of the "utilized" particle volume and the total particle volume,i.e., r]=l-x. In the kinetic controlled regime ri-1 and in the pure diffusional regime n-yT/((), Again for any shape we get ... 

In general for irreversible nth order reactions the catalyst effectiveness factor in the diffusional regime is ... 

Operating in the diffusional regime (R2 rate controlling), an increase in catalyst concentration of a factor of 50 is necessary before any enhancement is observed. It is this effect that makes operation in the enhanced mode usually uneconomic. 

If the pressure at the downstream (permeate) side is in the transition or continuum regime and is not negligible, there is a back-diffusional flux into the membrane decreasing the value of a. Equation 9.38 gives the effect of back diffusion on the actual separation factor [23,24]. 

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