where Pt is the probability of the yth category occurring, and is determined from Eq. (83). Once (/ ■ Re)/ and (/' ■ Re)c are obtained, the flow distribution at the shell side of the module can be determined by using the fractional flow WSj (Wsj = Fsj /Fs) at the shell side for the /th category [38]:

Because in this case there is no polydispersity of fiber inner diameter, the lumen side flowrate in a category is proportional to its membrane area (or number of fibers). Therefore, the fractional flow at the lumen side of the /th category, lVtJ (Wtj = FtJ / Ft), is:

Once the flowrates at the lumen and shell sides of the module for each category are known, Eqs. (72) - (75) can be used to describe each category. The total flux of the module and the outlet temperatures of the feed and permeate can also be derived from Eqs. (80) and (81), respectively.

5.2.6. Results and discussion

(1) The effect of the polydispersity of fiber inner diameter

A specific hollow fiber module is used as an example to study the effect of polydisperisty of fiber inner diameter. The characteristics of the module studied are listed in Table 7.

Table7

Characteristics of the module studied

Membrane area Packing fraction

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