Transport Operations III Staged Operations
Transport Operations III Staged Operations CH E 307
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This 0 page Class Notes was uploaded by Blanche Quitzon on Sunday November 1, 2015. The Class Notes belongs to CH E 307 at New Mexico State University taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/233193/ch-e-307-new-mexico-state-university in Chemical Engineering at New Mexico State University.
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Date Created: 11/01/15
NEW MEXICO STATE UNIVERSITY Department of Chemical Engineering CHE 307 Transport Phenomena Ill Staged Operations Spring 2008 Exam 2 Open BookNotes Full Name please print SOLUTION Social Security Number By my signature I attest that the work contained Within this exam is a result of my own e orts I did not receive provide or supplicate assistancefrom anyone during the course of this examination Further I understand that If found guilty of ethical violations regarding my solution to this exam I will be punished to the maximum extent allowable described under quotAcademic Misconduct in the NMSU Student Handbook I understand the quotStudent Code of Conduct provides policies and procedures that will befollowed by thefaculty member administering this examination should an accusation be made by the exam proctor or afellow student Finally I accept and agree to fulfill my responsibility to report in writing to the supervising professor should I observe any solicitation for assistance or action that can be regarded as cheating Within 24 hours of the completion of the exam Date Examination Rules 0 Open Book amp Notes 0 Clearly state ALL assumptions AND indicate where they apply in the solution 0 All pages must be stapled together in proper order at the conclusion of the exam Any pages not stapled to the cover page will not be graded Ch E 307 Spring 2008 Exam 2 Problem 1 40 goints A distillation column operates at 1 atm and has a partial reboiler and a total condenser returning saturated liquid It is being used to separate a mixture of 123trimethylbenzene toluene and benzene A saturated vapor feed enters at 100 kmolhr at a molar composition of 40 benzene 30 toluene and 30 123trimethylbenzene Fractional molar recoveries of 95 of the toluene in the distillate and 95 of the 123trimethylbenzene in the bottoms are required Estimate a the number of equilibrium stages are required at total reflux b the recovery fraction of benzene in the distillate c the minimum reflux ratio d total number of equilibrium stages and optimum feed location for an actual reflux ratio of 10 Physical property data Wagner s equation Reid et al 1987 may be used to calculate vapor pressure 5 3 6 P AXBX1 5113 T In 1 M where X1I PC 1 T6 Component Th1atm K TEK Pcbar A B c D Toluene 3836 9 410 1 2834 2792 123 rimethylbenzene 4493 Benzene SOLUTION Assume CMO ideal solutions Raoult s law ideal gases ideal gas law In the analysis that follows the components are identified by subscripts as follows A E Toluene LK B E 123trimethylbenzene HK C E Benzene LNK Since liquid solutions are ideal and the gases are ideal the VLE can be described by Raoult s law The relative volatilities will be simply the ratio of the vapor pressures To estimate the relative volatilities we need an initial estimate of the conditions at the top and bottom of the column For a 95 recovery of the LK in the distillate we may assume a nondistributing LNK The bottoms is then pure HK and the reboiler temperature will be close to the normal boiling point ofthe HK 4493 K The overhead temperature is at the bubble point of a solution containing all of the LK and LNK for which xA 0429 and xC 0571 See calculation sheet for relative volatility calculation from vapor pressures and use of Fenske Equations to answer a and b 03 3836 591 410 toluene z 03 pr 4493 Tc 6645 Pc 345 123 trimethylbenzene 04 3532 5622 489 define the Wagner Equa on for calculating vapor pressures benzene 77286 1381 72834 72792 A 78442 B 2922 C 75667 D 2281 76983 1332 72629 73333 T T 1 7 Tc A TlB T1395lc T3lD T6l 17 T gt gt gt PVPT Pcexp Ch E 307 Spring 2008 Exam 2 assuming nondistributing non key components 7 1 7 1 XDitoluene Zl39zl Z3 039429 XDibenzcne Z339Zl Z3 0571 Estimate temperature ofdistillate bubble point calc and bottoms pure B boiling pt TD 370 Given PvpTD1xDim1uene PVPTD3xDibenz ne 1 TD FindTD 362894 T T 4493 B bp2 calculate vapor pressures and relative volatilities of distillate and bottoms 1 1 3 053 8583 W PD P P T 0062 1 D vp D D D FRD LK 095 1348 2 21 573 FR 095 4782W P 4 719W 1341K B PB 1 PvpTB 1013 B 1 g 1 AB D B 6364 9566 2 944 1 1 f 14271 CB D3 B3 1 FRDiLK FRB7111lt 1 FRDiLK 1 FRBiHK N 3182 mm 1 AB N CB assumption ofnondistributing FRD LNK 0996 2 FR N components Is acceptable Bj i t CB 1 FRB7111lt F 100 I ABz1 1z2 CBz3 I 2 Gwen 1 F1nd 3258 AB 1 CB DXDA FzlFRDiLK 285 DXDB Fzzl 4 FRB K 15 DXDC Fz3FRD7LNK 39839 D DXDA DXDB DXDC 69839 AB39DXDA 1 39DXDB CB39DXDC min 109343 AB 1 CB RRactual 1 Ch E 307 Spring 2008 Exam 2 Liddle fit of Gilliland Correlation 0002743 y2X2 0545827 7 0591422x2 X RRactual 7 RRmin absolssa 0217 ordinate y2abscissa 043 RRactual 1 N 7 Nmin N 5 leen ordlnate N 1 N FindN 6337 C XNKdist 057 DXDB DX XPKdist D 0021 XLKdist A 0408 LKiHK AB 6364 ZLK z1 ZHK 22 1 XLKdist ZHKW n X z N Nme K W 9 NF NE 1 N LKK mm 3168 Ch E 307 Spring 2008 Exam 2 Problem 2 30 points A liquid mixture containing 50 mol nheptane and 50 mol noctane at 30 C is subjected to a batch distillation at 1 atm pressure until 60 mol of the feed has been distilled What will be the composition of the distillate and residue The following equilibrium data are provided T C Pc7 mmHg Pca mmHg Xc7 Yc7 984 760 333 10 10 105 940 417 0655 0810 110 1050 484 0487 0674 115 1200 561 0312 0492 120 1350 650 01571 0279 1256 1540 760 0 0 SOLUTION F 100 molx 05 D 60 mol W40 mol 0 0 01571 0279 0312 0492 Xd 0487 y 0674 M csplinexdy fx inIeIp txdyx 0655 0810 1 1 F100 W 40 DF7W60 11171 adjust xandn until integration yields 0916 W dx w apply Raleigh Eqn ln nal 7W lu 70916 foinal XD XW F 1 X005 X0001 X for 161n1 yfx 1 ye x x lt x x 1 171 x X Trapezoid rulefor integration 1quot 0quotn a1quot Elli 11H Za 0914 XWfina1 Xn 0329 xF x0 05 initialize yDavg 06 apply overall material balance given FxF Wwajnal DyDavg ndyDavg 0614 Hand solution will not use as many intervalsfor trapezoid rule step size of004 is sufficient One could also note that relative volatility is approximately constant at216 rangingfrom 228 to 202 and could use the appropriate E05 to describe y fX Ch E 307 Spring 2008 Exam 2 Problem 3 25 gointsl It is proposed to separate a mixture of 40 mol water and 60 mol butyl acetate using the twocolumn system shown Using the binary xy diagram for this system provided sketch a McCabeThiele construction to design the butyl acetate column assuming constant molal overflow Take butyl acetate as a 99 mol pure saturated liquid bottoms product and assume the reboil ratio is 15 times the minimum reboil ratio the minimum reboil ratio is found by drawing a line from x5 through the point representing the butyl acetaterich composition of the binary heterogeneous azeotrope Assume the phases in the decanter are in liquidliquid equilibrium at their bubble point Erichphax a How many stages are required in each column section of column 1 b What is the distillate to feed ratio of column 1 Do not design the column to treat the aqueousrich composition from the decanter Recall the relationship 7 I7B I7B1 L between vapor and liquid flow rates below the feed state ofa CMO column 5 V 78 1 VWater Ch E 307 Spring 2008 Exam 2 VWater zF xE 02 2D x 07 D 052 F DB I 1533 0 01 02 03 04 05 06 07 08 09 xwater Retlux ratio can be estimated from sloge ot tog ogerating line as 022l theretore VZF can be calculated to be about 042 ow E3EI7 SprngDUE Exam 2 Prablem A 25 g nu emanm 39 curve dwagram DEM ow E3EI7 SprngDUE Exam 2 ethano DEM NEW MEXICO STATE UNIVERSITY Department of Chemical Engineering Ch E 307 Transport Phenomena Ill Staged Operations Spring 2009 Exam 1 Open BookNotes Full Name please print SOLUTION NMSU ID Number By my signature I attest that the work contained Within this exam is a result of my own e orts I did not receive provide or supplicate assistancefrom anyone during the course of this examination Further I understand that If found guilty of ethical violations regarding my solution to this exam I will be punished to the maximum extent allowable described under quotAcademic Misconduct in the NMSU Student Handbook I understand the quotStudent Code of Conduct provides policies and procedures that will befollowed by thefaculty member administering this examination should an accusation be made by the exam proctor or afellow student Finally I accept and agree to fulfill my responsibility to report in writing Within 24 hours of the completion of the exam to the course professorshould l observe any solicitationfor assistance or action that can be regarded as cheating Date Examination Rules 0 Open Book amp Notes 0 Clearly state ALL assumptions AND indicate where they apply in the solution 0 All pages must be stapled together in proper order at the conclusion of the exam 0 Computers may not be used during this exam Calculators or slide rules are acceptable Ch E 307 Spring 2009 Exam 1 Problem 1 30 gointsl A mixture of nhexane 25 mol noctane 40 mol and nnonane 35 mol is fed at 25 kmolhr to a flash drum operating at 304 kPa and 180 C Determine the flow rate and composition of both the liquid and vapor effluents SOLUTION multicomponent ash known drum temperature 1 13 j 16 T 81567 p146763 nC6 71778901 0 696783 7084634 0 0 a 0 7764681641 1248457 7073152 0 0 C8 42551040 0 569313 7067818 0 0 C9 K 7 am a12 1 a5 aural K 72977 17exp 2 T a133a1 4np 2 p 17 T p a a a a 21 22 25 26 K2exp 2Ta23a2341np 2 T K271406 T p 7 a31 a32 1 a35 a36 K 7 0493 K37exp 2 T a333a3 4np 2 p 37 T 025 3 mol 2 040 F 2510 hr 035 Ki ll39zi Initialize VOF 05 Gwen E W 0 VOF F1ndVOF 0834 7 o 39 1 1 Z 009 0281W 1 x x 0299 x1 Kx 042 1 1 1Ki 139OF l0607l Z YI 1 1 y l0299l 2y 103m01 V VoFF 20858T L F 7 V 4142 Ch E 307 Spring 2009 Exam 1 Problem 2 20 goints The feed to a distillation column is at a rate of 2000 lb molhr and 30 C and contains 30 mol npentane and 70 mol nhexane The column operates at 1 atm with a total condenser operating with an external reflux ratio of 275 saturated liquid The distillate product is 998 mol npentane while the bottoms product is 999 mol nhexane What is the heat load on the reboiler QR Latent heat at normal boiling point of component in Btulbmol Mg 11369 Amos 13572 heat capacities in units of calg mol C and temperatures evaluated in units of C cpmg 397 cwO6 517 cpmg 2745 008148 T 4538gtlt10395 TZ 10lgtlt 10399 T3 cwO6 3285 009763 T 5716gtlt10395 TZ 1378gtlt10399 T3 SOLUTION mol 5 mol Z 03 XB 0001 XD 0998 F 2000454 F 908 gtlt 10 hr hr 5 mol 5 mol 2723gtlt 10 BF7D63S7X 10 LoD 275 hr hI 11369 BTU cal C 397 C5 454 mol pLCS molK TF1 30 C 3 cal cal T 00C 631gtlt 10 C 517 ref C5 mol ch molK condenser balances 7 BTU 9 cal Qc 7 7 C5DLoD 1 772557x 10 T Q0776444x 10 E distillate is at SF of pure nC5 KC5 1 on DePriester Chart TD 3608 C bottoms is at SF of pure n06 KC6 1 on DePriester Chart TB 6875 C CpF ZCch5 1 Z39CpL06 4839139 hF chTF 7 Tref 1443 x 1031 hF 2396 X 103 45134301 1113 CPL35m 7 Tref 1432 x 103n aol1 hD 2581 X 103 451 hB cpl36733 7 Tref 3554x mag a hB 63940 103 4511301 9 cal 7 BTU QR DhD BhB 7FhF7Qc7783x 10 E QR3089X 10 Y Ch E 307 Spring 2009 Exam 1 Problem 3 15 goints Derive relationships based on overall balances to calculate D B Q and LD for an open steam heating distillation column as shown in the diagram Assume the column is adiabatic SOLUTION overall mass balance F S D B 1 morevolatile component balance FZSy5 DxDBxB 2 where y5 0 overall energy balance FhFSH5QC DhD Bh3 3 condenser mass balance V1 L0 D 4 condenser energy balance V1H1 Qc L0 DhD l5 solve 1 and 2 for Das W D 6 XD XB Substitute 6 into 1 to find B Solve 4 and 5 for Qc as L QC D 1 3quot hi H1 7 Substitute 7 into 3 L0 DhDSF7DhB ithisHs 1 8 D 1 30m 411 Use 8 in 7 to find Qc Ch E 307 Spring 2009 Exam 1 Problem 4 35 gointsl A distillation column has a partial condenser and total reboiler t processes 200 kmolhr ofa saturated mixture 80 liquid that contains acetone 40 mol and ethanol The column produces a distillate vapor that is 85 mol acetone and a bottoms product that is 5 mol acetone Column is operating at 1 atm with an external reflux ratio of 325 Assume constant molal overflow is valid Determine a the total number of equilibrium stages in the column and b the optimum feed location Equilibrium data can be found in problem 4D7 of the text SOLUTION 0 0 XD 085 KB 005 yD XD 010 0262 ZF 015 0348 ZF 04 q 08 RR 325 yfx 1 X 1 q a a q 020 0417 025 0478 r R 1 RR 7 x y KT 1 RR KT 1 RR D 030 0524 035 0566 1 XA 7 040 yA7 0605 we csp1neXAyA yexe 7 1nte1pwXAyAxe 03950 039674 y1 05 X11 05 given 060 0739 Z 070 0802 amp 1amp q F yI1RRXI 1RR XD yI 4X1 17 080 0865 q q 090 0929 XI 0378 yI 7 xB n X m 100 100 yI d I yI 0489 bOm m XI 7 KB initialize Xe 04 y1 xD yslxs mbottom39xs mbotmm ll39XB Given yexe Given yex Given ye Given yexe y4 X4 Findxe 0452 y5 yrx4 Given ye Given ye Given yexe y7 X7 Findx Given yexe y8 X8 Find Ch E 307 Spring 2009 Exam 1 yt 1 StaCkXD7XDy2y2Y3Y3Y4Y4Y5Y5y6ay6Y7Y7YgYgY9 xt stackxDx1xlx2x2x3x3x4x4x5x5x6x6x7x7x8XS I I I I YA first stage is the O O 0 8 partial condenser yex 39 column therefore has x 7 plates plus partial y 0639 condenser total of 8 r xf equililbrium stages y X f f04 feed stage is 5 fourth ysxs plate In the column yt 02 39 I I I I 0 02 04 06 08 XAXXXrXfXSXt NEW MEXICO STATE UNIVERSITY Department of Chemical Engineering CHE 307 Transport Phenomena Ill Staged Operations Spring 2008 Exam 1 Open BookNotes Full Name please print SOLUTION Social Security Number By my signature I attest that the work contained Within this exam is a result of my own e orts I did not receive provide or supplicate assistancefrom anyone during the course of this examination Further I understand that If found guilty of ethical violations regarding my solution to this exam I will be punished to the maximum extent allowable described under quotAcademic Misconduct in the NMSU Student Handbook I understand the quotStudent Code of Conduct provides policies and procedures that will befollowed by thefaculty member administering this examination should an accusation be made by the exam proctor or afellow student Finally I accept and agree to fulfill my responsibility to report in writing to the supervising professor should I observe any solicitation for assistance or action that can be regarded as cheating Within 24 hours of the completion of the exam Date Examination Rules 0 Open Book amp Notes 0 Clearly state ALL assumptions AND indicate where they apply in the solution 0 All pages must be stapled together in proper order at the conclusion of the exam Any pages not stapled to the cover page will not be graded Ch E 307 Spring 2008 Exam 1 Problem 1 gointsl A liquid mixture containing 50 mol nheptane and 50 mol noctane at 30 C is to be continuously flashed at 1 atm pressure to vaporize 60 mol of the feed What will the composition of the vapor and liquid and the temperature in the separator for an equilibrium stage Equilibrium data are provided in the vectors below where T is the temperature of the saturated mixture Pi is the vapor pressure of component i at T x and y are the liquid and vapor mole fraction of the more volatile component respectively 984 760 333 1 1 105 940 417 0655 0810 110 1050 484 0487 0674 T 115 PC7 1200 chl 561 X 0312 y 0492 1111 1121 15231 1013711 10391 SOLUTION 2282y 2254 calculate the relative volatility at each T and find about constant pC7 2169 which suggest constant a model is acceptable 7 P 7 2139 x C8 eq mean 2158 y X 2077 all 1 1 xeq 71 2026 L F F 100 v 60 L F7 v 40 zF 05 y0px0p TlXopd VzF X11 05 yI 05 find intersection of equilibrium line and operating line G 39XI L F X11 f 0386 1ven X z 1n X yI 1 xI 41 yI v I v F LyIJ dllyI 0576 YI Y3 112304 Interpolate flash temperature T ash T2 T3 7 T2 y2 7 y3 Ch E 307 Spring 2008 Exam 1 0 yeqXeqo Xeq 0 0 y 000 0 y0pX0po 10 Y 0 000 0 0 00 0 01 02 03 04 05 06 07 08 09 1 XeqXeqXXOpXIX 3 lb Ch E 307 Spring 2008 Exam 1 Problem 2 gointsl A distillation column operating at 1 atm is to be designed to continuously distill 200 kmolhr of a binary mixture of 60 mol benzene and 40 mol toluene at 298 K A liquid distillate and a liquid bottoms product of 95 mol and 5 mol benzene respectively are to be produced Before entering the column the feed is flashed at 1 atm producing an equimolal vaporliquid mixture VFF LFF 05 A reflux ratio 30 larger than the minimum is specified Calculate product flow rates minimum number of theoretical stages to achieve the separation at total reflux minimum reflux ratio d number of equilibrium stages and the optimum location of the feed stage for the reflux ratio specified e condenser reboiler and feed preheater duties Benzene B Toluene T AB 339 kJmol CDLIB 0147 kJmoIK CpVIB 0094 kJmoIK 371 E latent heat of vaporization avg liquid heat capacity avg gas heat capacity SOLUTION mol z 06 F 200000 hr ini alize solve block D 05F B 05F D Given zszBBxDD FBD BermdDB xD 095 xB 005 7LT 380 kJmol cmT 0174 kJmoIK CWT 0118 kJmoIK P 1013 33951 21605 six equilibrium stages and a reboiler at total re ux 1 mol 5 Ch E 307 Spring 2008 Exam 1 C yr0 0457 d 13equilibrium plates and a partial reboiler Ch E 307 Spring 2008 Exam 1 e TF 350 yF 05 XF 05 Given iyYF Z y PATF 17y PBTFI17 L XF 7 Z F P XF F P XF XF 0523 yF FindxFyFTF 0732 TF TFK TF 364689 71 v 33900 J 71 7 38000 J BI mol T I mol J J T 298K c 147 c 174 0 pLB molK pLT molK J HF 0 J J mol c 94 c 118 pVB molK pvr molK hLF XFCPLB 17 xFCPLT TF 7 To10663 HVF yFCPVB 17 yFvar TF 7 To yFAB 17 yF71T 695 energy balance on preheater LF E VF E 2 2 Texl 356811 QF VFHVF LFhLF 7 FHF 1454kW HVy1CPVB 17 y1CPLT TexDK7 To ylAB 17 y1 T 3969 x 104 hLx1CPLB 17 x1CPLT TexDK 7 To 8559 x 103 QC VHV7 hL 2539 x 106w HVb y14CPLB 17 y14CPLTTexl4K 7 To y14AB 17 y1471T 5217 x 104 hLb x13CPLB 17 x13CPLT Tex13K 7 To 1435 x 104 hLB X14CPLB 17 x14CPLT Tex14K 7 To 1458 x 104 QR VbHVb BhLB7 LbhLb 204 x 106w
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