Separation Process Principles- 2n - Seader &amp; Henley - Solutions Manual

1 becomes n d unit nd all elements let n1 number of

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Unformatted text preview: er Pressure at reflux divider outlet Pressure at total condenser outlet Heat transfer rate for each stage, except reboiler Heat transfer rate for divider Feed mole fractions (only count C - 1) Reflux rate Mole fraction of component in distillate Mole fraction of component in bottoms Total Need 5 more specifications, which might be: Feed rate Feed temperature Feed pressure Optimal feed location Saturated liquid leaving condenser N 1 1 N-1 1 1 1 1 1 ______ 2N + 6 Exercise 5.28 Subject: Verification of numbers of degrees of freedom for 3 operations, and effect of adding another feed. Given: Degrees of freedom for operations (b), (c), and (g) in Table 5.4. Find: Verify values of ND and determine effect of adding another feed. Analysis: Operation (b), distillation with total condenser and partial reboiler: From Eq. (5-70), ND unit = ND all elements e − NR C + 2 + N A (1) e −9 C+2 (2) NR = 9 and NA = 0 Therefore, Eq. (1) becomes, N D unit = ND all elements Let N1 = number of rectifying stages and N2 = number of stripping stages. Using the values of ND for the elements in Table 5.3: C+4 Total condenser Reflux divider C+5 Rectifying section 2N 1 + 2C + 5 Feed stage with heat transfer 3C + 8 Stripping section 2N 2 + 2C + 5 C+4 Partial reboiler N D e = 2(N1 + N2) + 10C + 31 (3) all elements Substituting Eq. (3) into (2), N D unit = 2 N 1 + N 2 + 10C + 31 − 9 C + 2 = 2 N1 + N 2 + C + 13 (4) However, in Operation (b) of Table 5.4, the feed stage and the partial reboiler are counted in N. Therefore, N1 + N2 = N - 1 - 1 = N - 2. Substituting this into Eq. (4), gives ( N D )unit = 2( N − 2) + C + 13 = 2 N + C − 9 which verifies the result given in Table 5.4. (5) Exercise 5.28 (continued) If a second feed is added, we add C + 2 degrees of freedom for the feed variables and for feed location. Then, ( N D )2 feeds = ( N D )1 feed + C + 3 = 2 N + 2C + 12 Operation (c), distillation with a partial condenser and partial reboiler: With a partial condenser instead of a total condenser, there are only 8 redundant streams and no reflux divider. Therefore, Eq. (4) becomes: ( N D )unit = 2 N + C + 9 + (C + 2) − (C + 5) = 2 N + C + 6 (6) which verifies the result given in Table 5.4. With two feeds, ( N D )2 feeds = ( N D )1 feed + C + 3 = 2 N + 2C + 9 Operation (g), distillation with a partial reboiler and a mixed condenser that produces both vapor distillate and liquid distillate: With a mixed condenser, we can modify Operation (c), by adding a reflux divider and one redundant stream. Therefore, Eq. (6) becomes: ( N D )unit = 2 N + C + 6 + (C + 5) − (C + 2) = 2 N + C + 9 which verifies the result given in Table 5.4. With two feeds, ( N D ) 2 feeds = ( N D )1 feed + C + 3 = 2 N + 2C + 12 Exercise 5.29 Subject: Verification of numbers of degrees of freedom for 2 operations, and effect of adding a vapor sidestream.. Given: Degrees of freedom for operations (e) and (f) in Table 5.4. Find: Verify values of ND and determine effect of adding a vapor stream Analysis: Operation (e), reboiled absorber: From Eq. (5-70), ND unit = unit = ND all elements e − NR C + 2 + N A (1) e − 6(C + 2...
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