C

Fig. 53. Schematic representation of non-uniform distribution of hollow fibers in membrane module; adapted from the source [571.

Fig. 53. Schematic representation of non-uniform distribution of hollow fibers in membrane module; adapted from the source [571.

Fig. 54. Illustration of Voronoi tessellation of the module cross section.

Fig. 55. Cylinders arranged in triangular array.

where F(m3 h"') is the volume flowrate of the fluid. AP ! dz (Pa m" ) is the pressure gradient, and c is the porosity of the hollow fiber membrane module. Under the condition that (1) identical pressure drop in all cells; (2) the total mass flowrate is equal to the sum of the individual cell mass flowrate, the effective /-Re in the overall fiber bundle can be determined by

(/■Re), where (in) and Ac, (m2j is the wetted perimeter and the flow area of the ith polygonal cell, respectively; 7\v (m) and Ac (m2) is the total wetted perimeter and total cross-sectional area for flow in the overall bundle, respectively; ri{ is the total number of fibers in the overall bundle [34],

Like the lumen side, a histogram consisting of m categories to describe the distribution of the cells' area in the module is introduced. The effective / - Re is then given by

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