Deduction of 1D Models through the Transport of the Moments of the Age Distribution: Application to L-S Adsorption Columns

Leonel Fangueiro Gomes^1,2*, Frédéric Augier¹, Damien Leinekugel-Le-Cocq¹,

Ivana Vinkovic², Serge Simoëns²

¹ IFP Energies Nouvelles, BP3, 69360 Solaize, FRANCE

² Laboratory of Fluid Mechanics and Acoustics, CNRS UMR 5509, Ecole Centrale de Lyon, Ecully, FRANCE

* E-mail: leonel.fangueiro-gomes@ifpen.fr

Keywords: CFD, fixed beds, hydrodynamics, liquid-solid adsorption.

*

The p-xylene (PX) is produced in a mixture with its isomers that share close boiling points. In order to purify the PX for the manufacture of polyethylene terephthalate (PET) a setup of superposed fixed beds is used, filled with adsorbent, this process is called Simulated Moving Bed (SMB). Such process contains several hydrodynamic heterogeneities, such as pipes of the distribution and withdrawal system and beams that support the beds weight placed within the porous media, imperfect distribution systems and free media chambers between consecutive beds.

Augier et al. (2008) studied the impact of the obstacles placed inside the porous media on the dispersion of the concentration fronts, by measuring the resulting variance.

Knowing that CFD simulations of multicomponent adsorption (PX and its isomers) can take up to 72 hours to converge, for one single bed, it turns impossible the use of CFD for parameter fitting or optimization of a multi-bed process. It is then interesting to deduce 1D hydrodynamic models capable of accurately describe the flow of the SMB.

Until today, the poor performance of the adsorbent concerning the mass transfer between the liquid (xylenes) and the solid (adsorbent) has been provoking a considerable dispersion of the concentration fronts that advance throughout the SMB. In this scenario, the enchainment of the fixed beds has successfully been described by a simple 1D model where all the hydrodynamic heterogeneities described above are taken into account by adjusting an axial dispersion coefficient. However, with the development of new adsorbents with better mass transfer performances, the concentration fronts became steeper and the effect of the hydrodynamic heterogeneities became preponderant. With this the accuracy of the traditional 1D model decreases abruptly and a more representative way to describe the SMB hydrodynamic is needed.

In this work, the coupling between the standard k-e turbulence model (free media chambers) and the Brinkman-Fochheimer model (porous media) has been validated for further studies of the SMB hydrodynamic. Such goal was achieved by doing tracer tests in a cold mock-up representative of a slice of a SMB bed. A salty solution was injected in the inlet and with the aid conductivity sensors the concentration of the tracer was measured throughout the experimental setup.

Then, in order to study and characterize the hydrodynamic of a single SMB bed, the moments of the age distribution were transported by CFD as described by Liu and Tilton (2010). Knowing that for every given point of a vessel there is an associated age distribution, they showed that the moments of this distribution are transported by convection and diffusion. With this, it is possible to obtain the spatial distribution of these moments through stationary simulations that converge in seconds, showing a great contrast with the dynamic simulations of a tracer injections that can take up to 24 hours to converge. Liu (2012) also showed that by using the volume averages of the first two moments (mean age and variance) of such distribution it is possible to compute the degree of mixing proposed by Danckwerts (1958) and developed by Zwietering (1959).

In order to deduce new 1D models able to describe the SMB hydrodynamic regardless of the mass transfer performance of the adsorbent, the spatial distribution of the moments described above and the degree of mixing were used. The model proposed in this work consists in two parallel 1D models that are connected between themselves through multiple cross connections. Such model shows a much better accordance to the Residence Time Distributions (RTD) and adsorption separation of xylenes obtained through 2D CFD simulations than the traditional 1D model.

A methodology was established, allowing to instantly deduce a 1D model through the results of two stationary simulations: one to simulation the stationary flow in the turbulent free media and in the laminar porous regions, and a second one to transport the moments of the age distribution. With this, it is much faster and feasible to perform parametric studies and evaluate the variation of the process separation efficiency in function of the operational conditions.

Augier, F., Laroche, C. and Brehon, E., (2008), "Application of computational fluid dynamics to fixed bed adsorption calculations: effect of hydrodynamics at laboratory and industrial scale", Separation and Purification Technology 63.2, 466-474.

Danckwerts, P.V., (1958), "The effect of incomplete mixing on homogeneous reactions", Chemical Engineering Science 8.1, 93-102.

Liu, M., and Tilton, J.N., (2010), "Spatial distributions of mean age and higher moments in steady continuous flows", AIChE journal 56.10, 2561-2572.

Liu, M., (2012), "Age distribution and the degree of mixing in continuous flow stirred tank reactors", Chemical Engineering Science 69.1, 382-393.

Zwietering, Th.N., (1959), "The degree of mixing in continuous flow systems", Chemical Engineering Science 11.1, 1-15.