Conditions Along the Membrane

As a consequence of the permeate flux, the pressure gradient as well as the mean velocity and concentration will vary along the membrane surface-in principle at the feed side as well as at the product side. Depending on module design, this has to be taken into account for one or both sides. If, for example, the membrane is of tubular design with feed-flow inside, the following has to be expected along the tube-axis  

For these reasons, the overall permeation rate and the product quality of a membrane channel have to be calculated by integrating over the length elements employing, in addition to the equations discussed above, 

The equations necessary for the calculation of tubular RO-membrane channels (flow of permeate unhindered, no influence of the porous support-layer) are  

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Figures 6.2 and 6.3 indicate the order of magnitude of concentration polarization for laminar and turbulent flows through tubular membranes. The diagrams illustrate the dependence of the concentration boundary layer on flow conditions along the membrane (Re) and on the permeation flux (Pew).

The module, i.e., the industrial configuration of membranes, has to meet a variety of requirements which are sometimes even contradictory. Points of major importance are (1) flow conditions along the membranes, (2) ratio of membrane area to pressurized vessel volume, (3) price of module and (4) the possibility of cleaning the membrane. 

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