Lecture_21

Lecture_21 - M4 am Gama(30M 0“ mmfim gu‘kto...

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Unformatted text preview: M4; am Gama-(30M +0“ mmfim gu‘kto We»; (2&3qu kWh-1 ? MM‘H—u I. SCHSN) Q E acewtm - & 4x‘JL3TIQB ' NE: 2¢+1 (MWB . .‘.N=Z‘+(o WADE) \Wb ' . 6 Mb, ' W4 UM ins-90¢qu «we ~1-«EMWHfM’ 6:4.)- kJ- N L 4C+ 1'5) — EZw-ngC-HA +— N‘ T 3 w... tmim M = 7u+ zuc +2c+‘| (19.5w) N‘s! ——_.._..._. chc-r'n - 200—13 SNi- put-+7. i102 N. .lvm. N thuJ-c‘imemLSCo-‘g N 2W i L (xicc3l I L.“- “ $414.“... T l. l S w-FZQ'F Mo. ml % #611... a cmétl“ Ha. m M 014.. Qan— . m 44.3-0- M . Equations ' Number of Equations . Pressure equality _ , 1 PVOUT _ PLOUT TVOUT = TLOUT ' Phase equilibrium relationships, C (yavom = K£(xi)LOUT Component material balances, C — 1 LIN(xi)Lm + VIN(yi).V|N = LOUT(xE)LOUT + VOUT(yi)VOUT Total material balance, 1 -LIN + VIN = Low + Vour Energy balance, 1 Q + hLmLIN + hVINVIN = hLOUTLOUT + hVOUTVOUT Mole fraction constraints in entering and exiting streams 4 C e.g., (ya-hm = 19 " NE = 2C + 7 ND=(4C+13)—(2C+7)=2C+6 —Variable Specification Number of Variables Component mole fractions, (x,)LIN - C — 1 Total flow rate, LIN 1 Component mole fractions, (yaym C — 1 Total flow rate, VIN 1 Temperature and pressure of LIN Temperature and pressure of VIN Stage pressure (PVOUT or PLOW) Heat transfer rate, Q 1 . N922C+6 I—lNN Specification of these (2C + 6) variables permits calculation of the unknown variables Low, VOUT, (xc)Lm, (ydvm, all (x;)LOUT, TOUT, and all (y,)V0UT, where C denotes the missing mole fractions in the two entering streams. VIN LOUT Figure 5.17 An N-stage cascade. Variable Specification Number of Variables Heat transfer rate for each stage (or adiabaticity) N Stage pressures N Stream VIN variables C .+ 2 Stream LIN variables - C + 2 Number of stages 1 2N + 2C + 5 auubv (2N + C + 6) 1. Recovery of 1. Number of Partial light key com- stages above ponent feed stage ' ' ' ' “~wa 2. "Recovery of “2. NTiii-Daefot‘ (CHI) 2:; ’ F" 1". .3; heavy key com- stages below 9 — Q .. M ponent I feed stage- ‘ 1 “' 3. Reflux ratio 3. Reflux ratio (> minimum) 4. Distillate flow 4. Optimum feed rate stageb ‘-"Reboi|er Figure 5.18 Complex distillation unit. . Element or Unit (N 1;)‘ (NE), Total condenser (2C + 7) (C + 3) Reflux divider (3C + 10) _ _ _ __ _ __ _' (2C + 5) _ (N 3'3) stages [7(N — S) + 2(N — S)C + 2C + 7] [SUV — S) + 2(N — .S')C + 2] Side-stream stage (5C + 16) (3C + 9) (S—1)—Fstages [7(S—l-F)+2(S—1—F)C [5(S—1—F)+2(S—1-F)C + 2C + 7] + 2] Feed stage (5C + 16) (2C + 8) (F— 1) — 1 stages [7(F — 2) + 2(F — 2)C + 2C + 7] [5(F -— 2) + 2(F - 2)C + 2] Partial reboiler (3C + 10) (2C + 6) 2(NV), = 7N + ZNC + 18C + 59 ZONE): = SN + 2NC + 4C + 22 Subtracting (C + 3) redundant variables for 13 interconnecting streams, according to_ (5-68), with NA = 0 (no unspecified repetitions), gives (Nam = 2 (NE), w 13(C + 3) = 7N + me + 5C + 20 Subtracting the corresponding 13 redundant mole-fraction constraints, according to (5-69), (Na-hm. = 2 (NE), a 13 = 5N + 2N0 + 4c + 9 Therefore, from (5-71), ND=(7N+2NC+5C+20)—(5N+2NC+4C+9)=2N+C+11 A set of feasible design variable specifications is Variable Specification Number of Variables 1. Pressure at each stage (including partial reboiler) N Pressure at reflux divider outlet 1 Pressure at total condenser outlet 1 Heat transfer rate for each stage (excluding partial reboiler) (N — 1) Heat transfer rate for divider Feed mole fractions and total feed rate Feed temperature Feed pressure Condensate temperature (e.g., saturated liquid) Total number of stages, N 11. Feed stage location 12. Sidestream stage location 13. Sidestream total flow rate, S 14. Total distillate flow rate, D or DEF 15. Reflux flow rate, LR, or reflux ratio, I.ng i—n PEOP'JTJP‘E-"PPP D—lr—lr—‘Fdl-II-iI-il-il—‘nb—K ND = (2N + c+11) In most separation operations, variables related to feed conditions, stage heat transfer rates. and stage pressure are known or set. Remaining specifications have proxies, provided that the variables are mathematically independent of each other and of those already known. Thus. in the above list, the first 9 entries are almost always known or specified. Variables 10 to 15, however, have surrogates. Some of these are 16. Condenser heat duty, QC. 17. Reboiler heat duty, QR 18. Recovery or mole fraction of one component in bottoms 19. Recovery or mole fraction of one component in distillate ...
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This note was uploaded on 01/13/2010 for the course CHEM 1 taught by Professor Pines during the Winter '08 term at Berkeley.

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Lecture_21 - M4 am Gama(30M 0“ mmfim gu‘kto...

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