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Unformatted text preview: quation, with CF2 = CF ,
Raffinate, R2 = F1/CF2, P2 = AJ2, R1 = P2 + R2, and CF1 = F1/R1, P1 = AJ1, and back-calculated
F1 = P1 + R1. If the back-calculated F1 is not equal to the actual value of 5,882 gal/h, then a new
value of CF is assumed. The following values are calculated with the assumptions of A = 4,500
ft2 and CF = 30:
CF2 = CF = 30, R2 = 5,882/30 = 196 gal/h, P2 = 4,500(0.411) = 1,851gal/h, R1 = 1,851 + 196 =
2,047 gal/h, and CF1 = 5,882/2,047 = 2.873, P1 = 4,500(0.929) = 4,182 gal/h, and backcalculated F1 = 4,182 + 2,047 = 6,229 gal/h. Since this is not the required value of 5,882, the
Solver function, used with a spreadsheet gives CF = 36.487. However, the assumed area of
4,500 ft2 for each stage is not correct if it does not achieve the required value of 55 wt% (dry
basis) for TP + NPN in the retentate from stage 2. To check this, the following calculations are
made using the given values of the rejection factor, defined by (14-81), with the following form
( wt% i ) Fn CFn
( wt% i ) Rn =
CFn (1 − σi ) + σi
For example, for TP in stage 1, with a wt% of 0.6 in the feed, σ = 0.97, and for A = 4,500 ft2 and
CF1 = 2.873, Exercise 14.25 (continued)
Analysis: (continued) ( wt% i )R n = 0.6 ( 2.873) 2.873 (1 − 0.97 ) + 0.97 = 1.63 The resulting wt% TP + NPN (dry basis) is not 55 wt%, even for CF = 36.487. Therefore, the
assumed area is not correct.
From the double trial and error, the following results are obtained in an effort to obtain
the required value of 55 wt%: Assumed A, ft2 CF from Solver Wt% TP+NPN (dry basis) 4,500
55.00 The last result in the table gives the following material balance in lb/day, and % overall yield: Component
1,000,000 Stage 1
393,472 Stage 2
57,136 % Overall Yield
100.0 The area per stage = 3,730 ft2 or a total of 7,460 ft2. The number of cartridges per stage = 141 or
a total of 282 cartridges. Exercise 14.26
Subject: Section 2, involving diafiltration, of a cheese whey filtration process to obtain a dry
powder of combined TP and NPN as in Example 14.13, wherein section 3 is eliminated.
Given: Conditions of Example 14.13, including a whey feed of 1,000,000 lb/.day with the same
composition and solute retention factors. Feed to the diafiltration section 2 is the 55 wt%
concentrate from the 4-stage ultrafiltration section 1 of Example 14.13. The diafiltration section
is to achieve 85 wt% concentrate (dry basis) of combined TP and NPN.
Assumption: Assume 4 stages of diafiltration, as in Example 14.13.
Find: A suitable set of operating conditions for section 2.
Analysis: From the results of Example 14.13, the component flow rates in the concentrate
leaving section 1 and feeding the diafiltration section is as follows in lb/day:
Water Feed rate t...
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