Analysis of a diffusion-limited hollow fiber reactor for the measurement of effective substrate diffusivities

Mathematical analyses of a diffusion-limited hollow fiber reactor for the measurement of effective substrate diffusivities are presented. An analytical solution to the mathematical model with a first order substrate consumption rate is used to show that the procedure of Webster and Shuler(1) is incorrect. A rigorous analysis that requires numerical solution is also outlined for any form of the substrate consumption rate. These analyses allow for more accurate estimations of effective substrate diffusivities since they should be used in conjunction with integral reactor behavior.