A CFD-based analysis on the effects of bundle porosity in regularly packed hollow fiber membrane contactors

Hollow Fiber Membrane (HFM) contactors are very common today in many applications of membrane separation processes, e.g. in the biomedical field, in gas separation treatments, in water treatment and desalination processes but also in gas-liquid or liquid-liquid extraction. HFM contactors are cylindrically shaped devices with two separate compartments (lumen and shell), which guarantee the fluids segregation. While the analysis of the lumen side flow is fairly simple and it is usually modelled by the Hagen Poiseuille law and by semi-empirical correlations providing information on the mass transport, the analysis on the shell side is very complex since it depends on many parameters and involves complex flow fields formation. This work aims to investigate by means of CFD the influence of the porosity ε on fluid flow around bundles of straight fibers, arranged in regular square and hexagonal lattices. In the range of low Reynolds number (Re) studied, the fluid flows across the bundle following the Darcy’s law. Purely axial (Rez=10, Ret=0), purely transverse (Rez=0, 10-3<30) and mixed (Rez=100, 10-3<30) flows are investigated in steady laminar and fully developed conditions. Simulations use the unit cell approach, in which the periodic computational domain includes a single fiber with the associated fluid. Both in purely axial and in purely transverse flow, the axial and the transverse permeabilities Kz and Kt increase strongly with ε, especially for ε>0.8. In mixed flow, Kz is not affected by Rez (as expected for a Darcy medium), but for Ret>1 Kz decreases significantly with Ret. For both lattices, Kt is not affected by Rez. For Ret<10, Kt is not affected either by Ret (Darcian medium) or by the angle θ between the applied pressure gradient and the x axis (isotropic medium). In purely axial flow, the mass transfer coefficient vs ε curve exhibits a bell-shaped behaviour. In purely transverse flow, Sherwood number (Sh) strongly depends on θ even at Ret<0.01, denoting a strong anisotropy. For both lattices, the mass transfer coefficient exhibits minima at θ corresponding to directions of symmetry, while it is much larger at intermediate angles. In mixed flow, the axial flow causes Sh to increase in a complex dependence on geometry (square vs hexagonal), ε and Ret.