Three-dimensional simulation of multiphase flows in porous solid foam structures

1 Introduction
Ceramic foam packings, due to their high porosity, high specific surface area and low pressure drop are promising alternatives for packing internals used in chemical engineering processes. Photograph of the sponges can be seen in Figure 1. The applications of foam packing as burners and heat exchangers have been widely studied, but as catalyst carriers particularly for gas-liquid systems solid foam behaviour is not yet well understood. Due to its highly porous nature, it is very tough to understand the influence of hydrodynamics on the process performance. The long term goal of this work is to perform three dimensional Computational Fluid Dynamics (CFD) simulations of the evolving gas-liquid patterns considering ceramic foams as column internals and to validate them with experimental X-ray tomographic studies. It is noteworthy to mention that no 3D CFD simulations have been performed considering Ceramic foams as column internals in pilot scale. On the other hand, detailed studies are available considering spherical particles as internals in Trickle bed reactors. The closures will be modified according to the ceramic foam specifications.

2 Modeling Details
To simulate the column with ceramic foam as internals, there are two major requirements. One is the more precise information regarding the geometry and other is the appropriate closures.

The major challenge to grasp the ceramic foam packing as representative ‘porous body’ is to characterize the geometrical parameters such as pore diameter, strut diameter, pores per inch, porosity accurately and to understand the relationship with specific surface and pressure drop. Different empirical correlations are already available in the literature [2, 3]. Some of the correlations proposed in the literature will be used initially in this work.

A two phase Eulerian model is used considering the flow domain as porous. The influence of the liquid and gas drag is added as external source term to liquid and gas momentum equations separately. The drag force between the phases have been taken into account using relative permeability approach which was developed by Saez and Carbonell [4] for packed beds using capillary pressure and relative permeabilities of two phase flows.

As a first step, simulations are performed considering 2 mm spherical particles with porosity of 0.41 as column internals. Column has diameter of 0.3 m and height of 1.3 m. Air and Water is used as test substance. Single orifice with 25mm ID is used as inlet distributor. These simulation results are compared with experimental investigation studies of Marcandelli et. al. [5]. As next, this validated model is transferred to solid foams by mimicking high solid foam porosity of 0.93 with different ppi’s and to validate with in-house experiments performed using X-ray tomographic studies.

References
[1] Calvo. S., Beugre. D., Crine. M., Leonard. A., Marchot. P., Toye. D., Phase distribution measurements in metallic foam packing using X-ray radiography and micro-tomography, Chemical Engineering and Processing, Vol. 48, pp. no. 1030–1039, (2009).
[2] Dietrich, B., Pressure drop correlation for ceramic and metal sponges, Chemical Engineering Science, Vol. 74, pp. no. 192 – 199, (2012).
[3] Inayat, A., Freund,H., Zeiser, T., Schwieger, W., Determining the specific surface area of ceramic foams : The tetrakaidecahedron model revisited, Chemical Engineering Science, Vol. 66, pp. no. 1179 – 1188, (2011).
[4] Saez, A.E., Carbonell, R.G., Hydrodynamic Parameters for Gas-Liquid Cocurrent Flow in Packed Beds, AIChE Journal, Vol. 31, No.1, pp no. 52- 62, 1985.
[5] Marcandelli, C., Lamine, A.S., Bernard, J.R., Wild, G., Liquid Distribution in Trickle-Bed Reactor, Oil & Gas Science and Technology – Rev. IFP, Vol. 55, No.4, pp no. 407 - 415, 2000.

Acknowledgement
This work was funded by the Helmholtz Association within the frame of the Helmholtz Energy Alliance "Energy Efficient Chemical Multiphase Processes".