For two processes of large importance, catalysis and biocatalysis, were reported zones without reactants, so called dead zone (DZ). They results from diffusional transport limitations, when apparent reaction order is between (-1..1). Formation of DZ reduces effectiveness of catalyst and influence packed bed reactor productivity. For simple reaction kinetic model, a DZ width inside a pellet can be calculated analytically solving appropriate differential mass balance model. However, generally the analytical solution is unknown and only with using numerical method the position of DZ can be established. The problem with DZ appearance belongs to problems with moving boundaries. Its solution requires application of special numerical procedure and relatively long CPU time. In this work it was proposed a simple, very fast numerical method for calculation of DZ position inside pellet. The method proposed combined with orthogonal collocation on finite elements can be applied for analysis of work of packed bed reactor.

Applications of transfer function to derivation of a high precision model of tracer flow in a commercial measurement system is presented. A transfer function concept makes easier development of models of complex systems and consequently allows for obtaining a model that matches in the best way a physical system. The method has an additional profit viz. the same numerical algorithm i.e. inverse Laplace transform can be employed to solve the model both on the stage of precise model development (boundary value problem) and to find real model parameters (inverse boundary value problem). As a result of concept application, a very precise model of commercial measurement instrument was developed and, next, it was employed to determination of axial dispersion coefficients for empty tube and packed bed. Presented method is precise in wide range of operating conditions and faster comparing to other methods previously described in literature. The paper shows that mathematical modelling can be exploited to enhance measurements for a commercial measurement instrument i.e unlock the full potential of the commercial measurement system with no equipment design changes. The method is also a fast alternative to computational fluid dynamics for high precision calculations.