Physical aspects governing the design of hollow fiber modules

Abstract

For the design and use of hollow fiber membrane separation units, the engineer is in need of a quantitative or at least semi-quantitative description of the process, which will enable him to predict the effect of fiber length, fiber diameter, packing density, flow rates, etc. To this end, models are considered for which an approximate mathematical description can be developed. By way of illustration, two processes are discussed in particular: reverse osmosis and dialysis. In reverse osmosis, the relevant physical quantities for a given permeability are flow rates and pressure gradients. The model assumes a rate of permeation which is proportional to the pressure difference between the two sides of the membrane. Special attention is paid to the serious problem of polarisation. The dialysis process considered is one in which the shell-side flow is radial, volume changes due to permeation of solute are small, and the rate of permeation of solute is proportional to the concentration difference. The conditions to be fulfilled to neglect the role of diffusion are examined and, by way of illustration, corrections for diffusion are developed for the special case of axial flow of a solution through a fiber when the solute is removed by dialysis through the fiber wall.