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

# Find the difference in degrees of freedom analysis

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Unformatted text preview: bles below could be specified. Analysis: (a) Condenser heat duty might be substituted for the reflux ratio if the maximum heat duty of the condenser in an existing tower were known. (b) Stage temperature might be substituted for the recovery of a light or heavy component if there was a limit on the temperature of the cooling or heating medium in the condenser or reboiler. (c) Intermediate stage vapor rate might be substituted for reflux ratio for an existing tower diameter with a limiting vapor velocity to prevent flooding. (d) Reboiler heat load might be substituted for reflux ratio in the case of an existing reboiler area to prevent transition to film boiling. Exercise 5.32 Subject: Difference in degrees of freedom between a distillation column with a total condenser and one with a partial condenser. Given: A difference of 3 provided that only a vapor distillate leaves the partial condenser. Find: The difference in degrees of freedom Analysis: From Eq. (5-70), N D unit = ND all elements e − NR C + 2 + N A For a total condenser plus reflux divider, NR = 1 and NA = 0 Therefore, Eq. (1) becomes, N D unit = N D e − (C + 2) (1) (2) all elements Using the values of ND for the elements in Table 5.3: Total condenser C+4 Reflux divider C+5 Therefore, N D unit = (C + 4) + (C + 5) − (C + 2) = C + 7 For a partial condenser, NR = 0 and NA = 0, and using Table 5.3, N D unit = (C + 4) Therefore, the difference = (C + 7) - (C + 4) = 3 degrees of freedom Exercise 5.33 Subject: Replacement of a partial reboiler with live steam injection. Given: Operation (b) in Table 5.4 for distillation with a total condenser and partial reboiler. A column without the reboiler, but with steam injection and design variables listed below. Assumptions: Injection of steam will not cause the formation of a second liquid phase. Find: (a) The number of degrees of freedom = number of design variables. (b) The additional design specifications needed. Analysis: (a) Table 5.4, Operation (b), ND = 2N + C + 9. If the partial reboiler is eliminated, then from Eq. (5-70), N D unit = ND e − NR C + 2 + N A (1) NR = 7 and NA = 0 Therefore, Eq. (1) becomes, N D unit = (2) all elements ND all elements e − 7 ( C + 2) Let N1 = number of rectifying stages N2 = number of stripping stages Using the values of ND for the elements in Table 5.1: 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 N D e = 2(N1 + N2 ) + 9C + 27 (3) all elements Substituting Eq. (3) into (2), N D unit = 2 N 1 + N 2 + 9C + 27 − 7 C + 2 = 2 N 1 + N 2 + 2C + 13 (4) However, if the feed stage is counted in the total N stages, then N1 + N2 = N - 1. Substituting this into Eq. (4), gives (5) ( N D )unit = 2( N − 1) + 2C + 13 = 2 N + 2C + 11 (b) The specifications are: Pressures at all stages + condenser + divider = N + 3 Heat transfer rate for all stages + divider = N + 1 Feed conditions = C + 2 Alcohol concentration in distillate = 1 Stripping steam composition = C - 1 This totals 2N + 2C + 6. Therefore, 5 additional specifications are needed. Might also specify: Temperature and pressure of stripping steam, sa...
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