PLATE COLUMNS ABSORPTION: ALTERNATIVE METHODOLOGY TO GRAPHICAL METHODS

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1 2 d Mercosur Cogress o Chemcal geerg 4 th Mercosur Cogress o Process Sstems geerg PAT COUMNS ABSORPTION: ATRNATI MTHODOOGY TO GRAPHICA MTHODS O. C. Motta ma, J. M. Müller, M. A. S. D. Barros, A. H. Osterle & J.. Das Jr. State Uverst of Margá Chemcal geerg Departmet Abstract. Gas absorpto s a ver used ut operato dustral plats for the purfcato of both raw materals ad fal products. Fudametall, t s a recover process of oe or more compoets from a gaseous mture b a selectve lqud solvet. So, t s ver mportat that the solvet ad the orgal mture get touch for a suffcet tme to the desre compoet(s) absorpto, ad, due to the large dfferece of destes betwee the gas ad the lqud phases, the use of cotact devses to elarge phases teracto s ecessar. Idustrall, two tpes of absorpto colums (towers) are ofte used, based o dfferet phase cotact devses: packg/packed ad plate/stage colums. Isde ths cotet, ths work teds to mprove a alteratve methodolog to the usual hadmade graphcal methods, to reduce the tme ad the effort related to the desg ad aalss of absorpto processes dealg wth three compoets (gas, solute ad solvet) plate/stage colums. Furthermore, t s proposed the use of XC worksheets as the ddactc computatoal tool for the suggested methodolog mplemetato the calculus of plate/stage colums, cosderg, f desred, the cocept of plate (or stage) effcec. Thus, for eample, classroom cocepts ad absorpto problems could be better dscussed ad easl resolved b teachers ad ther studets, or the calculus of a plat egeer could be doe a cosderabl reduced tme. Ths work s part of a academc project of the Chemcal geerg Departmet (DQ/UM), for the use of computatoal tools Ut Operatos teachg, allowg the studets ther use ot ol classroom, but, thereafter, as professoal egeers. Kewords: Absorpto ; Plate Absorpto ; XC Program ; Plate ffcec ; Strppg.. Itroducto Gas absorpto s a ver used ut operato dustral plats for the purfcato of both raw materals ad fal products. Fudametall, t s a recover process of oe or more compoets from a gaseous mture b a selectve lqud solvet, ad s based o cocetrato ad solublt dffereces betwee the phases volved. So, t s ver mportat that the solvet ad the orgal mture get touch for a suffcet tme to the desre compoet(s) absorpto, ad, due to the large dfferece of destes betwee the gas ad the lqud phases, the use of cotact devses to elarge phases teracto s ecessar. Idustrall, two tpes of absorpto colums (towers) are ofte used, based o dfferet phase cotact devses: the oes wth a ert materal packed bed sde - packg/packed colums, ad the oes smlar to the tradtoall used dstllato - plate/stage colums, whch wll be the focus of ths work. There are several methods for determg the umber of deal stages for a plate absorber or, also, a strpper (Kremser, 930; Souders ad Brow, 932; Che, 964; Souders, 964); however, these methods are complcated. The covetoal graphcal techque s tedous ad tme-cosumg, especall f a large umber of plates are requred. Also, steppg off stages at the eds of the curves s mpractcal uless cosderable magfcato of the chart s made; however, such a process ofte lads to accuraces. To whom all correspodece should be addressed. Address: Colombo Aveue 5790, Bl. D-90, , Margá Brazl -mal: oswaldo@deq.uem.br

2 2 d Mercosur Cogress o Chemcal geerg 4 th Mercosur Cogress o Process Sstems geerg Isde ths cotet, ths work teds to mprove a alteratve methodolog to the usual hadmade graphcal methods, to reduce the tme/effort related to the desg ad aalss of absorpto (ad strppg) processes dealg wth three compoets (gas, solute ad solvet) plate/stage colums, Fgure. Ths methodolog s based the work of Ngue (979), who develop a geeralzed, smplfed method to determe the umber of actual plates, emplog the Murphree stage effcec. Ths approach has also bee used b the cted author to determe the actual umber of stages a costat-uderflow, coutercurret-leachg cascade (Ngue, 978). Fg. - Absorpto Plate Colum Furthermore, t s also proposed the use of XC worksheets as the ddactc computatoal tool for the suggested methodolog mplemetato the calculus of plate/stage colums, cosderg, f desred, the cocept of plate (or stage) effcec. Thus, for eample, classroom cocepts ad absorpto (strppg) problems could be better dscussed ad easl resolved b teachers ad ther studets, or the calculus of a plat egeer could be doe a cosderabl reduced tme. Ths work s also part of a academc project of the Chemcal geerg Departmet (DQ/UM), for the use of computatoal tools Ut Operatos teachg, allowg the studets ther use ot ol classroom, but, thereafter, as professoal egeers. 2. The Proposed Methodolog The methodolog proposed ad appled here s based o the work of Ngue (979), who develop smplfed equatos to calculate the umber of actual plates of absorbers ad strppers, usg the Murphree stage effcec. Compostos at each plate - deal ad/or actual - ca also be determed, ad the proposed equatos ofte are both more accurate tha tpcal graphcal meas ad easer to use tha most other formulas (Ngue, 979). 2.. Operatg le Cosder a coutercurret absorber havg plates. et G represet the total vapor flow of the carrer gas mole per ut tme of composto, ad let be the total moles per ut tme of the ert carrer-solvet flow of composto. 2

3 2 d Mercosur Cogress o Chemcal geerg 4 th Mercosur Cogress o Process Sstems geerg G The materal balace of the solute, amog the bottom of the colum ad a teral stage, s: G () Assumg costat molal overflow, q. () ma be rearraged to eld q. 2, whch s the equato for the operatg le wth a slope of /G. (2) G G 2.2. Desg equatos Assumg that the gas ad lqud leavg each plate are equlbrum ad that a lear relatoshp ests betwee ad, the: * m c (3) where * s the equlbrum cocetrato, m s the slope of equlbrum cocetrato, ad c s the -tercept. lmatg X q. (2) ad (3) elds: * c (4) G The vapor Murphree plate effcec s: Substtutg * from q. (6) to q. (4), ad the rearragg: m c (5,6) *, or: * (7) quato (7) s a lear dfferece equato, solved b Ngue (979). The: Ak m c ; m c Ak (8,9) Cacelg ad puttg the value of k : A m c (0) where A s a costat that s evaluated from boudar codtos. 3

4 2 d Mercosur Cogress o Chemcal geerg 4 th Mercosur Cogress o Process Sstems geerg Whe 0,, ad A s determed. The complete soluto for actual plates s: ( ) m c m c () Sce lqud composto at the bottom,, s ot ofte specfed, t ma be elmated from q. (). A materal balace of the solute for the etre colum elds: G G 2 2 (2) Combg qs. () ad (2), ad smplfg, elds the fal desg equato for actual plates: ß ) ( (3) where: ß ad: 2 ( m2 c) (4,5) quato (5) s used to compute actual composto at each plate. I addto, whe, the B /, the absorpto factor. B q. (3) ma be called the modfed absorpto factor. Furthermore, whe, q. (3) reduces to Che s equato for calculato umber of theoretcal plates absorpto (Che, 964). For calculatg the umber of actual plates (), ad the umber of deal plates ( ), q.(3) s rearraged as: ß ad (6,7) where: / (8) The overall effcec, 0, s calculated b q. (9), whch s the same as that gve b Trebal (955). 0 ß (9) 2.3. qud-phase equatos Smlarl, the Murphree plate effcec terms of the lqud phase s: * (20) 4

5 2 d Mercosur Cogress o Chemcal geerg 4 th Mercosur Cogress o Process Sstems geerg 5 Combg q. (20) wth those equatos for the equlbrum ad operatg les, the followg dfferece equato s obtaed for a boudar codtos of: 2 at 0; at. m m 2 2 (2) As before, the fal desg equato for actual plates s: ) ( 2 ß (22) where: ß ad ( ) c G (23, 24) Therefore: ß 2 (25) Whe, q. (25) becomes: 2 (26) From the last two equatos: ß 0 (27) Ths s the same equato developed b Che (967). quatg q. (9) ad (27) gves the relatoshp betwee ad : (29) Sce: (30) Or, for /, the: ( ) (3) Ad:

6 2 d Mercosur Cogress o Chemcal geerg 4 th Mercosur Cogress o Process Sstems geerg ; ( ) ( ( ) ) ( ) (32,33) ( ) ( ) Ths equato s the same as that gve b Smth (963): ( ) (34) 3. XC Implemetato, Results ad Dscusso Two eamples are gve to show the XC mplemetato of the proposed methodolog, ad results are compared wth those from ther respectve lterature. 3.. ample Determe the umber of actual plates to remove ucracked NH 3 (3% b volume) from the resultg gas of a process for makg small amouts of hdroge b crackg ammoa at 2 atm ad 80 ºC, cosstg of hdroge ad troge (3: molar rato). Process data s provded from Trebal (955), ad s lsted below. XC scree, wth problem data ad absorpto results, s show o Fgure 2. The value of gve b Trebal (955) s 4. Data: G 0.45 lb-moles/s ; lb-moles/s ; qulbrum le: * (0.707) 2 0 ; ; 0.03 ; ample 2 2 m c G v 0,03 0,035 0, , ,322 0,45 0,575 lb-moles/s lb-moles/s lambda 3,40 alfa 8,4-06 beta v,6446 Theoretcal plates - ' 6,5 Actual plates - 4,4 Fg. 2 XC ample : NH3 Absorpto The umber of actual plates calculated here s agreemet wth Trebal (955), ad t s mportat to remd that, whe determg the requre stages the ver dlute or ver cocetrated regos at the tower eds - as ths eample -, a McCabe-Thele plot ca probabl lead to errors. Others methods, such as usg a logarthmc (Robso ad Glllad, 957; Horvath ad Schubert, 958) or probablt (oweste, 962) scale are tme-cosumg. The proposed equatos, plus XC mplemetato, ca advatageousl replace them ample 2 It s desred to desorb a solute from a soluto b usg a solute-free gas. The soluto eters a plate colum at 20 mole % of solute A ad leaves the bottom at 2 mole %. The slope of the operatg le s. ad the equlbrum le s gve b 0.02 (Che, 964). Determe the umber of theoretcal plates ad the 6

7 2 d Mercosur Cogress o Chemcal geerg 4 th Mercosur Cogress o Process Sstems geerg theoretcal vapor ad lqud cocetratos at each plate. Whe the Murphree plate effcec ( ) s 0.80, calculate the umber of actual plates ad ther compostos. XC scree, wth problem data ad strppg results, s show o Fgure 3, ad Tables ad 2 show a comparso amog the theoretcal vapor ad lqud compostos at each plate calculated b the proposed methodolog (provded drectl at the XC worksheet, Fgure 3) ad those b Che (964) ad, also, graphcall, from a McCabe-Thele dagram (Ngue, 979). Tables ad 2 also show the actual vapor ad lqud compostos calculated at the XC worksheet, Fgure 3. ample 2 2 m c G v 0 0,02 0,2 0,02, 0,8 2 0,980 plate - deal - actual - deal - actual lambda, 0,0400 0,0320 0,0200 0,020 alfa -0,44 2 0,0764 0,067 0,0564 0,047 beta v, ,094 0,0892 0,0894 0,0692 Theoretcal plates - ' 6,27 4 0,395 0,47 0,95 0,0947 Actual plates - 7,92 5 0,668 0,384 0,468 0,84 6 0,96 0,603 0,76 0, ,806 0, ,995 0,795 Fg. 3 XC ample 2: Solute Strppg XC - q. (7) Table. apor composto Theoretcal apor Composto Che (964) Graphcal Ngue (979) Actual Plates XC - q. (7) Table 2. qud composto Theoretcal qud Composto Che (964) Graphcal Ngue (979) Actual Plates

8 2 d Mercosur Cogress o Chemcal geerg 4 th Mercosur Cogress o Process Sstems geerg Theoretcal vapor ad lqud compostos calculated at each plate totall agree wth those from cted lterature (Che, 964; Ngue, 979), ad, also, the calculated theoretcal ad actual umber of plates, Fgure 3, wth the McCabe-Thele dagram results from Ngue (979), 6 ad 8 plates, respectvel. 4. Coclusos From the above eamples, t s show that the XC work sheet s a terestg tool for the mplemetato of the proposed equatos ad that the methodolog ca successfull predct the umber of deal ad actual plates, ad the actual compostos at each plate, for ether absorpto or strppg plate colums. Furthermore, these equatos ca also be used to determe the colums effcec, provded that other parameters are specfed. Whe the equlbrum les are ot straght, the colums ca be cosdered to be composed of several short sectos wth lear equlbrum ad operatg les. Thus, the proposed methodolog would be used to calculate the umber of actual plates each secto, ad the total umber of plates of the colum would be the sum. Nomeclature A - costat q. (0), [see equato] c - tercept of equlbrum le, q. (3), [see equato] - Murphree plate effcec 0 G - Overall effcec - total vapor flow, [moles per ut tme] - total lqud overflow, [moles per ut tme] m - slope of equlbrum le, q. (3) - umber of actual plates - umber of theoretcal plates (stages) - mole fracto of solute lqud phase - mole fracto of solute vapor phase * - equlbrum mole fracto of solute vapor phase - as defed b q. (5) - as defed b q. (24) β - as defed b q. (23) β - as defed b q. (4) - / Subscrpts: - th plate of colum 2 - top of colum - bottom of colum - lqud - vapor Refereces Che, N. H. (964). Calculatg Actual Plates Absorbers or Strppers. Chem. g., ol. 7, No 0, Ma, 59. Che, N. H. (967). Basc quato Solves Ma Mass-Trasfer Problems. Chem. g., ol. 74, No., Ja 2., 93. Horvath, P. J., ad Schubert, R. F. (958). Fd Dstllato Stages Graphcall. Chem. g., ol. 65, No. 3, Feb. 0, 29. 8

9 2 d Mercosur Cogress o Chemcal geerg 4 th Mercosur Cogress o Process Sstems geerg Kremser, A. (930). Theoretcal Aalss of the Absorpto Process. Nat. Petrol. News, ol. 22, No 2, 48. oweste, J. G. (962). Dstllato Colum Desgg. Id. g. Chem., ol. 54. No., 6. Ngue, H. X. (978). Calculatg Actual Stages Coutercurret eachg. Chem. g., ol. 85, No. 25, Nov. 6, 2. Ngue, H. X. (979). Calculatg Actual Plates Absorbers ad Strppers. Chem. g., Aprl 9, 3. Robso, C. S. ad Glllad,. R. (985). Fd Dstllato Stages Graphcall. Chem. g., ol 65, No 3, Feb. 0, 29. Smth, B. D. (963). Desg of qulbrum Stage Processes. McGraw-Hll. New York, 599. Souders, M. (964) The Coutercurret Separato Process. Chem. g. Progr., ol 60, No. 2, Feb., 75. Souders, M., Brow, G. G. (932). Fudametal Desg of Absorbg ad Strppg Colums for Comple apors. Id. g. Chem., ol. 24, 59. Trebal, R.. (955). Mass Trasfer Operatos. McGraw-Hll. New York,