MURPHREE AND VAPORIZATION EFFICIENCIES IN …

1 MURPHREE AND VAPORIZATION EFFICIENCIES IN multicomponent distillation A G MEDINA, ? N ASHTON and C MCDERMOTT Chemical Engmeermg Department, Umverslty of Birmmgham, Bummgham BlS, England (Recewed 19 Apnl 1977, accepted 14 June 1977) Abstract-A quantitative comparison between MURPHREE and vaponzatlon efficlencles IS presented based on ternary chstdlatlon data for the systems acetone/methanol/ethanol, acetone/benzene/chlorobenzene, benzene/toluene/m- xylene and n-hexanelmethylcyclopentanelbenzene The Influence of expenmental errors on calculated values of MURPHREE EFFICIENCIES IS also analysed It IS shown that the vaporlzatlon efficiency model fads to descnbe the hehavlour of dlstdlatlon plates and It IS suggested that MURPHREE s model grves a more useful representation of the behavlour of dlstdlatlon columns INTRODUCTION In the design of dlsdlation columns the knowledge of accurate values of plate EFFICIENCIES 1s very Important as they have a direct effect on the number of plates required and an mdrrect effect on the runnmg costs of the eqmp- ment MURPHREE s model[l7]

2 Was the first of several models leadmg to different efficiency defimttons Vapour phase MURPHREE efficiency for component I and plate n can be defined as %v,z= Ynr-Yn+lt Y2 I - Y"+i I (1) where y I and y,,+, 1 are the mole fractions of component I m the vapour leaving and entering plate n respectively and y* , IS the mole fraction of component I In the vapour m eqmhbrmm with the hqmd leaving plate R @us liquid 1s considered to be a saturated hquld) The ongmal Murpbree defimtlon was generahzed by Taylor[20] allowing for unsaturated llquld and vapour streams Holland [ 11 J defined the vaporlzatlon efficiency for component I and plate n as E y =- vn I (2) *t where Y,,, = K,,, A,, x,, IS the mole fraction of com- ponent 1 in the hqmd leavmg plate n and K,, IS the vapour-hqmd equllrbnum ratio evaluated at the actual temperature and pressure at which hqmd leaves plate n Naturally Y,, , = y*n I If the hquld leavmg the plate IS a saturated liquid Several papers were pubhshed recently dlscussmg the relative merits of MURPHREE and vaponzatlon efficlencles Holland and McMahon[12] attempted to show that m the dlstlllatlon of multlcomponent murtures, condltlons could exist m which the values of MURPHREE efficIencles were zero and mfimty while vaponzation efficlencles had finite, bounded values Their statements were later ques- tloned by Standart [ 191 ?]]

3 Present address, Centro de Engenhana Qmmwa, Faculdade de Engenhana, Porto, Portugal Expenmental values of vaporlzatlon efficlencles were pubhshed by Gucalp[lO] and M&m ef al [16] for the dlstlllatlon of the ternary system n-hexanelmethyl- cyclopentane/benzene in an Oldershaw column, it was shown that average ternary vaporlzatlon EFFICIENCIES were m close agreement with binary values obtamed m the same column Arguments m favour of the vaporlzatlon efficiency concept were also put forward by Castells Pique et al [3], pomtmg out that Its experlmental determmatlon 1s easier, above all for columns not operatmg at total reflux, and by Ellis and Boyes [6] Advantages of the use of vaporlzatlon efficlencles m dlstiatlon calculations were referred to by Holland [ 111, Yamada and Holland[24] and Yamada et al 1251 It 1s the purpose of the present work to present a quantltatlve comparison between MURPHREE and vaporlzatlon efficlencles using published ternary dls- tlllatlon data for the systems acetone/methanol/- ethanol [8], acetone/benzene/chlorobenzene [8]]

4 , benzenel- toluenelm-xylene[l81 and n-hexanelmethylcyclo- pentane/benzene [ 10,161 It IS important to emphasize that all the experlmental work was carried out m small laboratory columns m which the hquld m each plate could be consldered com- pletely mixed VAPOUR-LIQUID RQUlLLBRIlJM DATA The calculation of plate efficlencles requires the knowledge of accurate vapour-hquld equlhbrlum data As for each ternary system limited experimental mfor- matlon IS normally available, It 1s common practice to adopt correlating equations using the experlmental vapour-hquld equdlbrlum pomts to determme the con- stants m the equations For this purpose a computer program usmg the descent method of Davldon[5] for the mnumlzatlon of the differences between experlmental and predicted vapour mole fractions was prepared MarguIes three suffix equatlons[l3] were used to cor- relate hquld phase actlvlty coefficients The vapour phase was consldered to be ideal Pure component vapour pressures were evaluated m 332 A G MEDINA et ol terms of the Antoine equations wrltten as B hzmp.]]

5 = A - C,+T where pp IS the vapour pressure of component I (mm Hg), A,, B,, C, are the Antoine constants for component I and T IS the temperature ( C) Values of the Antoine constants used are presented in Table 1 Sources of ternary equlhbrmm data for the drfferent systems are hsted m Table 2 The system ben- zene/toluene/m-xylene can be considered as an Ideal one[18, 231 A summary of the fitted Margules constants IS presen- ted m Table 3 together with the numerical values of root mean square devlatlons (r m s d ) for the mole fraction of each component, the bodmg point temperature and the total pressure PtATE E%FIcIEW!IEs Computer programs were developed[l41 for the cal- culatlon of vapour phase plate efficlencles from expen- mental hquld composltlons and temperatures Neither Nord [18] nor Free and Hutchlson[8]]]

6 Measured liquid plate temperatures and so, m the treatment of their results, the liquid in each plate was assumed to be a saturated Ilqud Table 1 Antome constants component A B C Acetone 7 1171 1210 595 229 664 Benzene 6 90565 1211 033 220 790 Chlorobenzene 6 9781 1431 a53 217 55 Ethanol 8 1122 1592 864 226 184 n-Hexane 6 8778 1171 530 224 366 MCP 6 8628 1186 059 226 042 Methanol 8 0810 1582 271 239 726 Toluene 6 9580 1346 773 219 693 m-Xylene 7 0065 1460 183 214 a27 TabIe 2 Vapour-hqmd eqmhbrmm data system Author Reference Acetone/Methanol/Ethano~ Amer, Paxton and 1 Van Acetone/Benzene/Chlorobenzene Free and Hutchxon 7 n-Hexane/M C P /Benzene Eelknap and Weber 2. Benzene/Toluene/m-Xylene Ga-jewskl and Westephely 9,23 Table 3 Correlanon of vapour-llqmd equtibnum system Acetone <l)/ Acetone cl)/ n-Hexane (I)/ Methanol (2)/ Benzene <2)/ MCP (2)/ Ethanol (3) Chlorobenzene (3) Benzene (3) Margules M ( ) 0 6334 0 4708 0 1499 constants M (2,1> a 6283 0 2602 0 1695 M (1,3) a 5600 0 2456 0 1772 N (3,l) 0 3161 a 2530 0 2084 M (2,3) 0 0794 0 0125 0 00133 M (3,2) -0 a470 -a la53 0 01578 RHSD ye a 007 0 008 0 005 Y2 0 007 0 005 0 005 YS 0 006 0 009 0 007 temp (OC) 0 341 0 375 0 168 press (mm Hg)

7 9 531 8 471 4 012 MURPHREE and vaporlzatlon efficrenctes m multlcomponent disttllation 333 From the large number of results obtamed, those presented m Tables 47 were selected as typical exam- ples for the systems benzeneltoluenelm-xylene, acetone/methanol/ethanol, acetonelbenzenelchloroben- zene and n-hexanelmethylcylcopentanelbenzene respec- tlvely Plots of expernnental composltlon protiles and cal- culated values of MURPHREE and vaponzation efficlencles for the first three systems are presented m Figs l-3 Sumlar plots for the system n-hexane/methylcyclo- pentane/benzene were pubhshed elsewhere [ 10,161 INFLUENCE OF -AL. ERRORS ON CALCULATED VALUES OF - EFFIclENcm In order to assess the influence of experrmental errors, hquld composltlon errors (due to sampling and analysis) and vapour-liquid eqmhbnum errors, on calculated values of MURPHREE EFFICIENCIES , a computer program was wrttten[l4] to allow the defimtion of the possible extremes of calculated values of MURPHREE EFFICIENCIES The followmg experimental errors were assumed Liquid composlhon error4 001 (mole fraction) Vapour-liquid eqmhbnum error-0 005 (mole fraction)]

8 For any plate n two extreme situations were defined, as follows Sttuatton 1 Table 4 Companson between MURPHREE EFFICIENCIES and vapormtion efficlencles-system benzeneltoluenelm- xylene Plate number Component x EMV E 2 Benzene Toluene m-Xylene Benzene Toluene m-Xylene Benzene Toluene m-Xylene Benzene Toluene m-Xylene Benzene Toluene m-Xylene Benzene Toluene m-Xylene Benzene Toluene m-Xylene Benzene Toluene m-Xylene Benzene Toluene m-Xylene Benzene Toluene 10 11 0 926 0 058 0 016 0 906 0 066 0 028 0 968 0 027 0 005 0 963 0 030 0 007 0 957 0 034 0 009 0 952 0 036 0 012 0 947 0 040 0 013 0 940 0 044 0 016 0 322 0 207 0 512 0 239 0 122 0 380 0 960 2 12 3 52 0 808 0 071 0 041 0 941 2 21 4 12 0 868 0 079 0 224 0 928 0 177 2 09 0 272 4 58 0 a50 0 083 0 067 0 a35 0 089 0 076 0 814 0 097 0 089 0 786 0 104 0 110 0 176 0 086 0 253 0 134 0 121 0 144 0 166 0 150 0

9 178 0 193 0 126 0 0 537 0 171 0 647 0 912 2 18 4 59 0 a97 2 11 5 03 0 888 2 03 4 76 0 931 0 048 0 021 0 874 2 01 4 37 0 664 0 891 0 113 0 061 0 223 0 048 0 882 1 72 2 28 0 46s 0 792 0 609 0 839 0 129 0 090 0 410 1 26 0 406 0 iia 0 636 1 89 0 252 0 596 0 619 0 780 0 132 0 133 2 77 0 969 m-Xylene 0 616 0 271 0 608 1 50 334 A G MEDINA et al Table 5 Companson between MURPHREE efficrencles and VAPORIZATION efficlencres-system acetouel- methanol/ethanol Plate Component x Y+ %V E number " Acetone 0 420 Methanol 0 464 Ethanol 0 116 Acetone 0 351 0 495 0 481 0 849 Methanol 0 495 0 435 0 517 1 07 Ethanol 0 154 0 070 0 454 1 65 Acetone Methanol Ethanol 0 262 0 519 0 219 Acetone 0 201 Methanol 0 526 Ethanol 0 273 0 419 0 473 0 log 0 500 0 144 0 566 0 522 0 584 105 1 43 0 393 0 735 0 268 1 04 0 418 1 52 Acetone Methanol Ethanol 0 272 0 481 0 738 0 528 0 829 0 997 0 200 0 501 1 36 Acetone Methanol Ethanol 0 170 0 541 0 289 0 117 0 499 0 384 0 637 0 793 0 616 0 960 1 20 Acetone "lethanol Ethanol 0 135 0 519 0 346 0 073 0 464 0 443 0 046 0 4J_4 0 540 0 361 0 625 0 821 0 969 0 622 1 15 Table 6 Comparison between MURPHREE efficlencles and vapomatlon efficlencles-system acetone/ben- zenelchlorobenzene Plate + Component x Y E number YV E" 1 Acetone 0 404 Benzene 0 574 Chlorobenzene 0 022 2 Acetone Benzene Chlorobenzene Acetone Benzene Chlorobenzene Acetone Benzene Chlorobenzene Acetone Benzene Chlorobenzene Acetone Benzene Chlorobenzene 7 Acetone Benzene Chlorobenzene 0 263 0 491 0 684 0 503 0 053 0 006 0 134 0 333 0 750 0 650 0 116 0 017 0 062 0 199 0 713 0 756 0 225 0 045 0 020 0 084 0 570 0 795 0 410 0 121 0 008

10 0 041 0 408 0 723 0 564 0 236 0 002 0 013 0 212 0 520 0 786 0 467 0 620 0 824 0 608 1 14 0 664 3 47 0 650 0 791 0 660 1 05 0 640 3 02 0 526 0 673 0 866 0 992 0 607 2 55 0 655 0 737 0 637 0 898 0 641 1 85 0 362 0 486 0 514 0 788 0 500 1 74 0 529 0 599 0 636 0 785 0 632 1 25 MURPHREE and vaponzatlon EFFICIENCIES in multicomponent distdlation Table 7 Comparison between MURPHREE efficlencles and vaponzatton efficlencles-system n-hexanelmethylcyclo- pentane (M C P )/benzene 335 Plate Component x Y number =MV E" 10 11 12 13 14 15 1 n-Hexane 0 476 0 505 0 577 0 977 MCP 0 305 0 293 1 07 0 977 Benzene 0 219 0 204 0 126 1 07 2 n-Hexane MCP Benzene 3 n-Hexane MCP 0 449 0 480 0 905 0 994 0 313 0 302 0 672 1 01 0 238 0 220 0 988 1 00 0 431 0 464 0 570 0 318 0 308 0 470 0 251 0 231 0 6011 4 !-l-HeXaIle 0 396 0 431 1 02 MCP 0 334 0 326 1 92 Benzene 0 270 0 246 0 778 0 971 1 02 1 04 1 00 0 976 1 07 5 n-Hexane 0 382 0 416 0 417 0 953 YCP 0 331 0 323 -0 359 1 04 0 287 0 258 0 580 1 05 6 II-Hexane 0 353 0 392 0 744 0 974 MCP 0 346 0 343 5 61 0 964 Aenzene 0 301 0 272 0 487 1 05 0 326 0 369 0 622 0 956 0 349 0 352 -0 933 0 982 0 325 0 294 0 770 1 02 0 282 0 324 1 05 1 00 0 357 0 363 -1 31 0 961 0 361 0 320 0 878 1 02 Il-HeXane MCP Benzene n-Hexane MCP Benzene 0 249 0 298 0 667 0 944 0 332 0 350 1 36 1 02 0 419 0 369 1 17 0 977 0 214 0 263 0 713 0 946 0 308 0 331 104 1 00 0 478 0 411 0 876 1 02 n-HeXaTIe 0 178 0 231 0 674 0 925 MCP 0 279 0 315 0 807 0 970 BeKl2ene 0 543 0 467 0 850 1 02 I-l-HeXane 0 132 0 180 0 956 0 988 MCP 0 238 0 279 0 994 0 999 Benzene 0 630 0 525 0 831 1 03 n-Hexane 0 097 0