LUMEN MASS-TRANSFER IN HOLLOW-FIBER MEMBRANE PROCESSES WITH NONLINEARBOUNDARY-CONDITIONS

Hollow-fiber membrane separation or reaction processes, with a nonline ar boundary condition at the lumen interface, are analyzed numerically Sixteen different nonlinear boundary conditions in the literature wer e simplified to four dimensionless boundary conditions, in which only two parameters are needed to incorporate the effect on mass transport of membrane and shell resistances, lumen inlet concentration, shell co ncentration, phase and/or chemical equilibria, and interface reaction kinetics. The lumen mass-transfer coefficients were obtained by solvin g the continuity mass-conservation equation with the corresponding bou ndary conditions. The calculated results demonstrate that the lumen ma ss-transfer coefficient is a function of lumen-inlet concentration and shell concentration, as opposed to the case when a linear boundary co ndition occurs at the lumen interface. By using the empirical correlat ions of the lumen local mass-transfer coefficient, an ordinary differe ntial equation substituting a partial differential equation can be app lied to obtain the lumen dimensionless mixed-cup concentration with an absolute error of less than 0.005 in most cases, thus making it possi ble to design and evaluate the hollow-fiber membrane separation or rea ction processes.