Mass-transfer correlations for the shell-side mass-transfer coefficients in hollow-fiber membrane (HFM) modules have been published by several authors. The uneven distribution of shell-side flow is due to the random packing of fibers in the module. The results of different authors give apparently conflicting results. This work provides an approach to estimating empirical correlations for HFM shell-side mass transfer. This approach is then applied to explain several literature observations and to offer corrections to earlier published correlations. The dependence of the Sherwood number on both the Reynolds number and the packing fraction are considered. Further work on the packing fraction dependence is required.