A packed bed catalytic reactor consists of catalyst particles, usually spherical, randomly arranged and held in position within a cylindrical vessel or tube. The reactants are passed over the bed and undergo chemical transformation. The reactants are transported to the surface of the particles and adsorbed before the chemical reaction occurs accompanied by associated heat release or consumption. Products are then desorbed and diffuse back into the flow. The catalyst is not consumed and is used repeatedly in a continuous process.The approach adopted in a CFD model is to treat the packed bed as a lumped parameter model and define each of the processes above with respect to this model. Thus, rather than modelling the individual catalyst particles, the interaction of the particles in terms of heat, mass and momentum transfer is defined with a series of sub-models as follows:
The objective of these sub-models is to translate the design/process information regarding the packed reactor into a CFD simulation that includes much more than just flow.
- A surface reactions model to include adsorption, surface reactions and desorption;
- A momentum loss associated with the packing of the bed particles and the ability to simulate anisotropy and variation in packing density;
- A heat exchange model to represent the heat transfer between the bed particles and the surrounding gases and account for non-equilibrium between bed and gas temperatures;
- Anisotropic thermal conductivity within catalyst bed;
- Representation of the dispersion effects (of heat and species) in the gas due to the presence of the particles.
As an example, consider an in-line packed bed catalytic reactor.
It is impossible and impractical to model each individual sphere so the first step of the modelling procedure is to represent the particles with a lumped parameter model. For the flow calculations, the lumped parameter model must represent the pressure drop and porosity of the bed.
In this example, there are only a small number of particles across the radius and in this situation it is well known that the packing will be non-uniform and their distribution can be described by Moallemi's correlation. Empirical expressions for the pressure drop characteristics are available from standard reference literature and are utilised by the lumped parameter model.
The predicted flow velocities show the flow channelling effect due to the higher porosity bands that exist due to the nature of the packing near the walls. From this pattern, it is obvious that the feed of reactant to the bed will be non-uniform, but it is not possible from this to understand how this affects the temperature of the bed or the reaction rates and overall efficiency of the process.
The next step is therefore to introduce simulation of the catalyst particle temperatures. The thermal model solves for the separate temperature distributions of the gas and the catalyst particles and uses an empirical heat transfer coefficient to estimate the heat transfer between them. In this case, the predicted catalyst bed temperature shows that the flow channelling results in a high flow rate and heat transfer coefficient so that particles in those regions get hotter more quickly.
The final step in the model development is the introduction of the catalysed reactions. First, the steps in the reaction are defined including the adsorption, surface reactions and desorption stages. Setting up the appropriate reactions is non-trivial and requires a detailed knowledge of the system under consideration.
For a fairly simple system there will be several gas species involved, maybe 10 or more surface species and possible 30 or more surface reactions to define. The reaction rates are then calculated based on the reaction mechanisms, the species concentrations, the gas and particle temperatures and the surface area of the particles. Finally, the appropriate heat and mass sources and sinks are computed and included in the flow and thermal models.
The output from the simulations comes in the form of numerical results as well as graphical illustrations. The key results that can be obtained might be the overall conversion rates for the process, maximum and minimum gas and catalyst temperatures and other parameters that characterise the efficiency. Graphical output can provide detailed insight into the flow patterns, temperature distributions, concentrations and reaction rates.
One of the key benefits of this approach is the prediction of the key performance indicators and the ability to investigate the reasons for good and bad performance. You can start by modelling your current process and then look for improvements using a series of models to try out your own improvement ideas based on the model results and your own engineering intuition.
Dr. David Kinnear is Chemical & Process Team Leader with Fluent Europe.