Flat plate catalyst pellets diffusion/reaction

We consider the situation depicted in Figure 4.5, involving transport through a gas film to a liquid interface, followed by diffusion and reaction in the liquid film. The difference element over which the mass balance is taken is the same as that for the flat-plate catalyst pellet, and leads to the same differential equation and the same boxmdary conditions ... 

To keep the mathematics as simple as possible, we treat the catalyst pellet as an infinitely flat plate (b = 0 in eq 139). The solution of eq 139 depends on whether the reactant concentration will drop to zero at some point Xo inside the pellet, in the case that the reaction rate is strongly influenced by diffusion, or will be finite everywhere in the pellet interior, if there is only a moderate effect of diffusion. This is a general feature of zero-order reactions which arises from the assumption that the reaction will proceed at a constant rate until the reactant is completely exhausted. 

You saw how the equations governing energy transfer, mass transfer, and fluid flow were similar, and examples were given for one-drmensional problems. Examples included heat conduction, both steady and transient, reaction and diffusion in a catalyst pellet, flow in pipes and between flat plates of Newtonian or non-Newtonian fluids. The last two examples illustrated an adsorption column, in one case with a linear isotherm and slow mass transfer and in the other case with a nonlinear isotherm and fast mass transfer. Specific techniques you demonstrated included parametric solutions when the solution was desired for several values of one parameter, and the use of artificial diffusion to smooth time-dependent solutions which had steep fronts and large gradients. 

When the rate is measured for a catalyst pellet and for small particles, and the diffusivity is also measured or predicted, it is possible to obtain both an experimental and a calculated result for rj. For example, for a first-order reaction Eq. (11-67) gives directly. Then the rate measured for the small particles can be used in Eq. (11-66) to obtain k. Provided is known, d) can be evaluated from Eq. (11-50) for a spherical pellet or from Eq. (11-56) for a fiat plate of.catalyst. Then 7caic is obtained from the proper curve in Fig. 11-7. Comparison of the experimental and calculated values is an overall measure of the accuracy of the rate data, effective diffusivity, and the assumption that the intrinsic rate of reaction (or catalyst activity) is the same for the pellet and the small particles. Example 11-8 illustrates the calculations and results for a flat-plate pellet of NiO catalyst, on an alumina carrier, used for the ortho-para-hydrogen conversion. 

Problem 9-1 (Level 1) The reaction A B is taking place at steady state in a catalyst particle that can be represented as an infinite flat plate of thickness 2L. Internal temperature gradients are negligible. The effective diffusivities of A and B are equal. The concentrations of A and B at the pellet surface are Ca,s and Cb,s, respectively. The reaction rate is strongly influenced by pore diffusion, such that 0 is large. 

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