Fig (1) A Distillation column

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1 Iteratoal Joural of Egeerg Scece ad Iovatve Techolog (IJESIT) olue 5, Issue 5, Septeber 206 Maual deterato of the uber of theoretcal plates b MCCB-Thel ad b usg MTB KM. M. HMI, Prof. G.. GESMSEE, r. TIF BERHIM bstract: eterato of the uber of theoretcal stages stage wse dstllato s rather portat for the desg of a fractoator s colu. There are a graphcal ad eprcal correlatos for the deterato of the theoretcal stages, aog these ethods, s the graphcal ethod of MCcabe-thele whch s relable. I a recet work b Gaselsed G.. etal t s approved that McCabe-Thele ca be used for ult copoet fractoato, takg the lght ad heav kes as pseudo bar. McCabe-Thele ethod requres the codto of the feed, the equlbru data or relatoshp, the coposto of the feed, top ad botto products ol fractos as well as the q le. I ths paper the uber of theoretcal stage were plotted auall b McCabe-Thele ethod ad b software usg MTB. The results of the uber of stage were copared ad foud to b a agreeet. It s recoeded that MTB software progra has to be eteded for a coplete desg of the fractoato colu. Kewords: Bar, Pseudo sste, McCabe-Thele, Matlab. I. INTROUCTION stllato colus used to separate a ture of 2 lquds or ore depedg o ther relatve volatlt t s portat to estate the uber of the stages that eeded for pure dstllate. Fg () stllato colu II. ESTIMTION OF MINIMUM NUMBER OF STGES Feske Equato Feske (932) was the frst to derve a Equato to calculate the u uber of tras for ultcopoet dstllato at total reflu. The dervato was based o the assuptos that the stages are equlbru stages ad ca be wrtte as

2 Iteratoal Joural of Egeerg Scece ad Iovatve Techolog (IJESIT) olue 5, Issue 5, Septeber 206 k HK log HK destlate K btotto N () log K Where N s the u uber of stage at total reflu, cludg the reboler s the average K relatve volatlt of the copoet wth respect to referece copoet., the ole fracto of the k Hk lght ke ad heav ke respectvel top ad botto of the colu Pocho-Savart Method Backgroud Prcple s cocered wth the graphcal aalss of calculatg the theoretcal stages b ethalp balace requred for the desred separato b dstllato process (Hes ad Maddo, 984). I ths ethod, the ethalp balaces are corporated as a tegral part of the calculato, ths procedure cobes the ateral balace calculatos wth ethalp balace calculatos. Ths ethod also provdes the forato o the codeser ad reboler dutes. McCabe ad Thele graphcal Method The splfg assuptos of costat olar heat of vaporzato, o heat losses, ad o heat of g, lead to a costat olar reflu flow a secto of the colu. Usg these splfcatos, thus three was of deterg the equlbru relatoshp betwee lqud ad vapor phases whch are frst f a costat relatve volatlt, respectvel s assued, the vapor coposto b the relatoshp as flows:- ( ) B The two erchet equatos are obtaed: For rectfg secto d For strppg secto W w k / k ad k b are the volatlt of ad B B where kb B / b ca be detered at a gve lqud coposto McCabe-Thele poted out that, sce these equatos represet straght les coectg o, the ca be draw o the sae dagra wth ad wth as equlbru curve to gve a sple graphcal soluto for the uber of stages requred. Thus, f d equato (5) the d d d (2) (3) (4) (5) Ths equato represets straght le passg through the pot zero, the d, (6) (7) (8) (9) d. If s put equal to.gvg a secod easl detered pot. The top operatg le s therefore draw 2

3 Iteratoal Joural of Egeerg Scece ad Iovatve Techolog (IJESIT) olue 5, Issue 5, Septeber 206 through two pots coordates d, ), the w w w d ( ad d (0, ) c For the botto operatg le, w (0) Sce that s ( Fg (2) represet the tras of a dstllato colu. W, t follows that w. Thus the botto operatg le passes through the pot C,, w w ), ad has a slope of. the the two operatg les have bee draw the tersected at pot B together wth q-le whch s pass through the pot ( f, f ) ad have slope of q /( q).see fg(3) Secodl therodac odels ca used to detere the equlbru relatoshp. If the copoets ad B for a deal ture, ad the vapor pressure for the pure copouds. obtaed fro toe equato (2) sat B log P () t C Fel, the lqud ad vapor coposto, P sat ca be ad ca be drectl read fro actual data wth the lqud B ad ad vapor coposto equlbru ad equlbru carve s plotted. Where C are toe costat for copoet.these equatos are used to calculate the relato betwee the 3

4 Iteratoal Joural of Egeerg Scece ad Iovatve Techolog (IJESIT) olue 5, Issue 5, Septeber 206 coposto of the lqud o a plate ad the coposto of the vapor rsg to that plate.b a ethod of those three, drawg equlbru curve ad operatg les, the uber of stages requred abe foud b a draw a horzotal le fro, ) to the equlbru curve ( b - rop a vertcal le to the operatg le c Repeat a ad b utl reach b Fg (3) McCabe-Thele dagra The operatg les rectfg ad strppg secto tersected the sae pot together wth the q-le ad the q-le jots the pot ( f, f ) le 45 wth the tersecto of operatg les wth slope of q/( q ) as show fg (4) whch represet the q-le wth dfferet values of q. the above s the theoretcal sde of the a progra dea. et s a proble for testg the progra. III. PROBEM a cotuous fractoatg colu s to be desged to separate 30000kg/h of a ture of 40%beezee ad 60% toluee to a over head product cotag 97%beezee ad a botto product cotag 98%toluee. These percetages are b weght. a reflu rato of 3.5 s used.bezee a toluee for a deal sste wth a relatve volatlt of a bout 2.5 ; the feed s saturated lqud at t s bolg pot at pressure of oe at. etere the uber of deal plates ad the posto of feed plate. I. SOUTION The olecular weght of bezee s78 ad that for toluee s 92. the cocetrato of feed( f ), overhead( ), ad botto( B ) respectvel ole fracto of bezee are:- f , B

5 Iteratoal Joural of Egeerg Scece ad Iovatve Techolog (IJESIT) olue 5, Issue 5, Septeber 206 The feed codto saturated lqud at t s bolg pot so q = relatve volatlt s gve ad equal to 2.5.the Reflu rato s =3.5 so we feed these data o the progra the uber of deal plates s foud to be 2 ad feed plate s uber 6 fro top see fg(5) bellow. CONCUSION It s cocluded that the uber of theoretcal plates for both bar ad ult copoet sstes ca cofdetl be detered usg McCabe-Thele graphcal ethod. s the graphcal ethod ca be serted to a coputer progra to obta the copostos profle, a progra was developed usg MTB. The progra requres the equlbru data as well the coposto of the feed, top ad botto ol fractos wth the q-le value ad the reflu rato.the ethod copared qute well ad the results usg the progra ad aual techque are ver good agreeet. The progra ca further be eteded to detere the coplete desg paraeters of a fractoal colu. The code s avalable upo request fro the authors. CKNOWEGEMENT The authors ackowledge the graduate collage of l-eela Uverst ad Nala Uverst for ther support of ths work for the degree of the Ph checal egeerg. REFERENCES [] Bra R.Hut Roald. psa Joatha M. Roseberg Gude to MTB for Begers ad Epereced users (Cabrdge 2 d ed. [2] McCabe,W.. Sth J.C. ad Harrott, P., Ut Operato of Checal Egeerg (McGraw Hll, 6 th ed 2000). [3] Eest E.udwg, ppled process desg for checal ad petrochecal, 999 Gulf Publshg Copa, Housto, TX. [4] J.R. Backhurst, J. H.Harker ad J. F. Rchardso, Checal Egeerg volue 2 5 th ed 2002, Butterworth Heea. [5] J. M. Coulso ad J. F. Rcharso, Checal Egeerg volue 5 Solutos to the Proble Checal Egeerg olue2. UTHOR BIOGRPHY KM. M. HMI, facult of graduate collage l-eela Uverst Prof. G.. GESMSEE, epartet of leather techolog, collage of appled ad dustral scece, uverst of Bahar, Khartou Suda P.O. Bo 660 r. TIF BERHI assocated Prof Checal egeerg feld of research checal ketc ad catalsts l-eela Uverst. PPENIX Fg (4) operatg les ad feed le tersected at a, b, c, d ad e wth dfferet values of q 5

6 Iteratoal Joural of Egeerg Scece ad Iovatve Techolog (IJESIT) olue 5, Issue 5, Septeber 206 Fg (5) q=, N =2 progra output for proble above Table soe oeclature F B f olar flow rate of feed, kol/hr olar flow rate of dstllate, kol/hr Molar flow rate of botto kl/hr ole fracto of lght copoet feed X w R R ole fracto of lght copoet stllate Mole fracto of lght copoet botto olar flow rate of lqud stage, kol/hr olar flow rate of vapor stage, kol/hr actual reflu rato u reflu rato 6