Approximations for unsteady state diffusion and adsorption with mass transfer resistance in both phases

A new approximate kinetic model, valid for both long and short duration of transient mass (or heat) transfer processes, was proposed. The presented model may be used in the cases of transient diffusion in bodies in the shape of infinite slab, infinite cylinder or sphere. The case where mass transfer resistance is both inside and outside a body (adsorbent pellet) has been considered. In the presented model Laplace transform for diffusion equation is used, the solution is transformed to the form of continued fractions and the resulting expression is truncated to obtain such a number of terms that ensures the required accuracy. This concept, which was presented by J. Lee and D.H. Kim (Chemical Engineering Journal, 2012) for systems without external mass transfer resistance, in this work has been extended on systems where such resistance exists. On the basis of calculations done in this work it was shown that values obtained with the approximate model are almost identical to values derived from the exact model. It is worth mentioning that such consistency refers to all considered shapes regardless of the magnitude of external mass or heat transfer resistance. The model can be used for modelling and design of cyclic adsorption–desorption processes.

► We present a new approximate kinetic model for transient mass transfer processes.
► The model can be used for cyclic adsorption–desorption processes.
► The model allows one to take into account external resistance to mass transfer.
► The model is valid for bodies in the shape of slab, cylinder and sphere.
► The proposed model was verified numerically.