Simple high-order approximations for unsteady-state diffusion, adsorption and reaction in catalyst: A unified method by a continued fraction

For unsteady-state diffusion, adsorption and a first-order reaction in a slab, cylinder and sphere catalyst, high-order approximations are developed. A continued fraction is developed as a function of the shape factor and the Thiele modulus in Laplace domain to unify the exact transfer functions of the three catalyst geometries. Inversion of the continued fraction to the time domain results in the approximation, the accuracy of which depends on the order of approximation and improves very quickly with each increment in the order. Construction of the proposed time-domain approximation is easy and systematic for any approximation order.