Dynamic rate-based and equilibrium models for a packed reactive distillation column

Dynamic rate-based and equilibrium models were developed for a packed reactive distillation column for the production of tert-amyl methyl ether (TAME). The two types of models, consisting of differential algebraic equations, were implemented in gPROMS and dynamic simulations were carried out to study the dynamic behaviour of reactive distillation of the TAME system. The dynamic responses predicted by the two types of models are similar in general, with some differences in steady-state values. The influence of manipulated variables, such as distillate flow rate, reflux ratio, and reboiler duty, on the dynamic responses of the controlled variables (reactant conversion and product purity) was studied. The dynamic response of reactant conversion is very nonlinear and unconventional, but the response of product purity is well approximated by a linear first-order differential equation. The CPU time required to complete a dynamic simulation of the rate-based model is at least an order of magnitude higher than that for the equilibrium model. Therefore, the dynamic rate-based model is much more complicated than the equilibrium model, and simplification of the rate-based model is necessary for the implementation of model-based control. A new approach was proposed to simplify the dynamic rate-based model by assuming that the mass transfer coefficients are time invariant. This approach was demonstrated to be superior to the conventional simplification methods. It can reduce the number of equations by up to two-thirds and still accurately predicts the dynamic behaviour.     

Pilot plant synthesis of n-propyl propionate via reactive distillation with decanter separator for reactant recovery. Experimental model validation and simulation studies

Successful process intensification (PI) stories applied broadly are the reactive distillation (RD) processes used in esterification syntheses. One application is developed here with the heterogeneously catalyzed synthesis of n  -propyl propionate (ProPro) from 1-propanol (ProOH) and propionic acid (ProAc). In this investigation, conventional RD of ProPro was further improved. With the objective to recover product and reactant, an experimental column set-up was equipped with a decanter on top enabling to separate the distillate product into two main streams. The aqueous phase was discharged and part of the organic phase was refluxed back to the column. Experimental results comprising temperature and composition column profiles were obtained in a pilot-scale column (DN-50), equipped with structured packings (Sulzer BX and Katapak-SP 11 with Amberlyst 46™ for the reactive part). For simulation studies a non-equilibrium stage model (NEQ model) was applied which shows satisfactory agreement with the performed experiments. Further theoretical investigations of relevant operating parameters (total feed, molar feed ratio, reflux ratio and heat duty) and their effect on the overall process performance were realized. Studies with the given column configuration showed that product purity in the bottom stream could be increased to wProPro,bottom=91.0%$w_{\text{ProPro,bottom}}=91.0\%$ and maximum ProAc conversions to X_ProAc = 94.5%.     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28]). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.