Mathematical modeling of a multitubular shell-side packed bed reactor

For a multitubular shell-side (MSS) packed catalytic reactor, two-dimensional models are developed to determine the spatial radial temperature and concentration distributions in the shell-side fixed bed. The whole packings along with the cooling tubes is approximated by a number of annular fixed beds. Different methods are adopted to take into account the effects of radial porosity changes, radial variations in the velocity and in the transport properties which all affect the performance of the reactor.;In the second approach the EA model is improved and further developed. Heat and mass balances are directly undertaken in the imaginary circular fixed bed (IM model), some alterations being made in the reaction intensity, in the heat and mass transport environment and in the heat transfer boundary condition in accordance with the conformal transform. The IM model is thus generated, by means of which we can solve for temperature and concentration distributions in the fixed bed as in a single circular tube.;By replacing the EA model with the IM model, the simulation of a MSS fixed bed reactor is greatly simplified and an approximate analytical solution of the radial temperature profile across fixed bed is possible. Within the range of an acceptable linearized reaction rate expression, it provides a more detailed picture of the radial temperature distribution either using a partial differential model (PDE model) or an ordinary differential model (ODE model). The PDE model gives an analytical solution which can demonstrate the axial and radial variations of the reaction temperature. For fast solutions of the radial temperature distribution in the industrial process, of the radial temperature distribution we develop a Waterloo model having the simplicity of Beek's model and the accuracy of the ODE model. In these calculations, the reaction heat effect and the enthalpy change resulting from the convective flux are explicitly and more conveniently accounted for in terms of the coolant temperature gradient. (Abstract shortened with permission of author.);In the first approach, a model of the heat and mass balance across the catalytic bed is established in the annular geometry (EA model). The correlation of flow rate is introduced by means of the conformal mapping skill based on the pioneering experimental and theoretical analyses in a circular fixed bed.