Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 THE SOLID-GAS INTERFACE 229implications. The effectiveness factor will approach unity as the pellet size orintrinsic reaction rate coefficient decrease, or as the effective diffusivity increases.It is not always possible to determine the modulus q5L directly, because theintrinsic rate constant kv is not known. Weisz and Prater'93 have suggested amethod for the determination of q which does not require a knowledge of kv.The observed reaction rate - dn/dt can be expressed as follows-dn/dt = kv V, CMq mole . sec- 'where V, is the actual volume of catalyst [also V, = V,(~-E) where V, is thereactor volume and E is the void fraction]. Eliminating kV by using the equationfor the diffusion modulus and rearranging givesThe terms on the left hand side can all be measured or calculated, and the effectivenessfactor obtained from a prepared graph of q against 4tq. For q < 0.5, q =l/& and the effectiveness factor can be determined directly. Other methods forthe determination of q are given in references 187 and 193.So far only the case of an isothermal reaction without volume change has beenconsidered. A volume change during reaction (isothermal case) has no effect on r).if only Knudsen diffusion is operative but has a small effect if bulk diffusion is1 2 3 4 5OO6,Fig. 27. Dependence of effectiveness factor on the parameter 4 ~ Curves . A, B, C are for diffusioninto a flat plate of thickness L and sealed on one side and on the ends. Curve D is for diffusioninto a porous sphere, first order reaction. From ref. 184.References pp. 270-278