Effect of intraparticle convection on the transient behavior of fixed-bed reactors: Finite differences and collocation methods for solving unidimensional models

Abstract

The effect of intraparticle convective flow inside large-pore catalysts (e.g. selective oxidation catalysts) on the transient behavior of fixed-bed catalytic reactors is analysed by using three different transient reactor models: the 1-D, heterogeneous, intraparticle diffusion/convection model, the 1-D, heterogeneous, intraparticle diffusion model and the pseudo-homogeneous model as a reference model. Results from these 1-D models were compared with those obtained in a previous paper when radial dispersion was taken into account. The process start-up analysis was achieved by feeding the reactor when heated at the wall temperature. The high capacity of the catalytic bed leads to a faster propagation of the transient concentration waves than of the thermal ones, developing sharp concentration fronts during the so-called pseudo-isothermal behavior of the reactor. When the transient regime inside the solid is considered these shock waves are smeared out showing different velocities associated with the intraparticle diffusive and convective transports. Higher reactant conversions are achieved when intraparticle convection is allowed. Besides being centered on the transient responses of large-pore systems, this paper also addresses numerical studies to allow a good representation of the dynamic features referred to above. The numerical solution for the model equations was obtained through the lines method. The performance of two different methods used on the space variables discretization, orthogonal collocation on finite elements and finite differences is discussed. A strategy of dividing the bed length into sections solved one after the other to avoid large dimension problems was also implemented. Important reductions in computing times can be obtatined by using the pseudo steady-state approximation for the intraparticle concentration profile and taking as initial condition the axial concentration profile corresponding to the pseudo-steady-state isothermal solution. Moreover, accounting for the axial dispersion on the model equations, the numerical integration becomes easier to perform with significative reductions in the CPU times.