A new scale independent mass transfer correlation for liquid-in-shell cross-flow in hollow fiber membrane contactors and a new sizing model for degassing applications

Degassing of liquids using hollow fiber membrane contactors (HFMCs) operating in cross-flow liquid-in-shell configuration is modelled. Vacuum and excess sweep gas operation modes are considered assuming ideal liquid plug flow and uniform gas composition. The model allows to estimate mass transfer coefficients from recovery rate measurements. Based on these estimates carried out for commercial HFMCs of various sizes, a new mass transfer correlation linking a Sherwood number and a cross-flow Graetz number, defined for this purpose, is proposed. This is the first time that a Sherwood-Graetz correlation is developed for mass transfer in HFMC liquid shell-side cross-flow. It is demonstrated that the mass transfer efficiency can be expressed as a function of the fiber diameter, the diffusion coefficient of the stripped species, the liquid flow rate and the external membrane area. When expressed in this way and for the first time in literature, both the efficiency and the Sherwood number fall on a single curve, no matter the size of the device. The independence of the correlations to the system size permits to use them for upscaling HFMCs.