Flat plate catalyst pellets

Develop expressions for the Thiele modulus and the concentration profile of A for the following reversible first-order reaction that takes place in a flat plate catalyst pellet ... 

Set up the equations necessary to calculate the effectiveness factor for a flat-plate catalyst pellet in which the following isothermal reaction takes place ... 

The porosity (i ) and tortuosity (t ) of the flat plate catalyst pellet are then used to calculate the ejfective diffusivities associated with each component according to ... 

To evaluate the effectiveness factor for a first-order, isobaric, nonisothermal, flat plate catalyst pellet, the material and energy balances must be solved simultaneously. As shown previously, the mole balance in a slab is given by ... 

Consider a first-order reaction occurring on a nonporous flat plate catalyst pellet. In Section 6.2, it was shown that the concentration of reactant A on the external surface of the catalyst is related to both the mass transfer coefficient, k, and the surface rate constant, ks. ... 

Now consider the first-order reaction in a porous flat plate catalyst pellet so that both external (interphase) and internal (intraphase) transport limitations are encountered. At steady state, the flux of A to the surface of the pellet is equal to the flux entering the pellet ... 

For example, an isothermal, first-order reaction in a flat plate catalyst pellet has individual effectiveness factors that are ... 

The isothermal, reversible, first-order reaction A = B occurs in a flat plate catalyst pellet. Plot the dimensionless concentration of A (Ca/C s) as a function of distance into the pellet for various values of the Thiele modulus and the equilibrium constant. To simplify the solution, let Cas = 0.9(Ca + Cg) for all cases. 

Fig. 11-8 Reactor for a single flat-plate catalyst pellet...

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 ... 

Derive the energy balance for a flat-plate catalyst pellet operating under nonisothermal conditions (first-order exothermic reaction). Give a plausible argument why the effectiveness factor can in this case exceed unity. 

If the flat plate model for the catalyst pellet as shown in Figure 3.2, Volume 3, is assumed, then a material balance gives ... 

The parameter ag= 1, 2, 3, for flat plate, cylindrical, or spherical geometry respectively. In the Thiele modulus, the character distance L = L (a half of thickness of catalyst pellet) for flat plate, L = r<, (the radius of catalyst pellet) for cylindrical, or spherical geometry. 

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. 

Pommersheim and Dixit (7 ) have developed models for poisoning occurring in the pores of flat plate and spherical catalyst pellets. 

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. 

---