Effects of shell-side non-ideal flow in hollow fibre membrane contactors operating in cross-flow

Abstract

Hollow fibre membrane contactors are very common today in many areas of separation process technology. The main applications include, but are not limited, to membrane distillation, reverse osmosis, ultrafiltration, gas separation, blood oxygenation and haemodialysis. In some applications (e.g., membrane distillation, haemodialysis) two fluids occupy two separate compartments, the lumen- and the shell-side, whereas in others (e.g., reverse osmosis, ultrafiltration) it is the portion of the feed crossing the membrane that passes from one compartment to another. The cylindrical shell housing includes bundles of several thousand hollow fibres, made of semipermeable membranes allowing for the selective passage of some species from a fluid to another. A common issue of these systems is the management of non-ideal effects on the shell-side fluid dynamics. The main relevant phenomenon, known in the literature as channelling, causes the fluid to flow mainly along preferential passages while some regions of the contactor are essentially stagnant. It is typical of axial, cross- and mixed flow across non-uniform bundle distributions, as already observed, among others, by Bao and Lipscomb [1-2]. Recently, several authors have dealt with it. Sun et al. [3] studied the effects on the module’s performance of the radial non-uniformity of the porosity between the core and peripheral regions of the bundle. Also Cancilla et al. [4] investigated the effects of a non-uniform porosity on shell-side axial flow by means of CFD. The computational domain was a chequerboard arrangement of alternately high and low porosity regions, between which the fluid was free to move. The authors showed that non-uniformity causes a significant increase of the Darcy permeability and an even larger drop of the mass transfer coefficient. In the present work, numerical simulations around non-uniform fibre bundle distributions under creeping cross flow conditions were performed to assess the influence of non-ideal shell-side flow. Both random and chequerboard configurations were investigated. Fig. 1 reports the dimensionless mean normal permeability knorm as a function of the mean porosity ε for random 20-fibre configurations (for example, the random fibre arrangement for ε=0.5 is shown in Fig. 2(a)). For comparison purposes, results by Sangani and Mo [5] for 64-fibre random configurations, and by Cancilla et al. [6] for regular square and hexagonal arrays are also reported. At ε=0.5-0.6, the present results are above those in [5] and lie below the values of for both regular arrays. At ε=0.8-0.9, Sangani and Mo predicted values larger than those for regular arrays (~1.35 times larger for ε=0.9), while the present results practically coincide with those for regular arrays (i.e., for isolated fibres), which, in their turn, tend to become independent of the type of lattice (i.e., square vs. hexagonal). Fig. 2 shows false colour maps of the velocity module and superimposed vector plots for ε=0.5 and 0.9 and a flow attack angle of 0°. For ε=0.5, the flow field exhibits a strong interaction between any particular fibre and the neighbouring ones. On the contrary, for ε=0.9, as better shown in the inset of Fig. 2(b), the flow field around any given fibre is almost unaffected by the presence of the adjacent fibres.