Numerical Solution of the Column Reactor Model

Mathematically, the system consists of parabolic PDEs, which were solved numerically by discretization of the spatial derivatives with finite differences and by solving the ODEs thus created with respect to time (Appendix 2). Typically, 3-5-point difference formulae were used in the spatial discretization. The first derivatives of the concentrations originating from a plug flow (Equations 9.1 through 9.3) were approximated with BD formulae, whereas the first and second derivatives originating from axial dispersion in the bulk phases and diffusion inside the catalyst particles were approximated by central difference formulae. Some simple backward (Equation 9.14) and central difference (Equation 9.15) formulae are shown here as examples  

FIGURE 9.5 Contour plot of concentration (Fe ) in the column reactor (4.7bar oxygen, 120°C). 

FIGURE 9.6 Concentration of oxygen (left) and FeS04 (right) inside a catalyst particle at different reaction times (60°C, 6bar). 

---