NPTEL Chemcal Mass Transfer Operaton 1 MOULE 5: ISTILLATION LECTURE NO. 8 5.3. Introducton to Multcomponent stllaton In ndustry, most of the dstllaton processes nvolve wth more than two components. The multcomponent separatons are carred out by usng the same type of dstllaton columns, rebolers, condensers, heat echangers and so on. However some fundamental dfferences are there whch s to be thoroughly understood by the desgner. These dfferences are from phase rule to specfy the thermodynamc condtons of a stream at equlbrum. In multcomponent systems, the same degree of freedom s not acheved because of the presence of other components. Nether the dstllate nor the bottoms composton s completely specfed. The components that have ther dstllate and bottoms fractonal recoveres specfed are called key components. The most volatle of the keys s called the lght key (LK) and the least volatle s called the heavy key (HK). The other components are called non-keys (NK). Lght no-key (LNK) s referred when non-key s more volatle than the lght key whereas heavy non-key (HNK) s less volatle than the heavy key. Proper selecton of key components s mportant f a multcomponent separaton s adequately specfed. Several short-cut methods are used for carryng out calculatons n multcomponent systems. These nvolve generally an estmaton of the mum number of trays, the estmaton of mum reflu rate and number of stages at fnte reflu for smple fractonators. Although rgorous computer methods are avalable to solve multcomponent separaton problems, appromate methods are used n practce. A wdely used appromate method s commonly referred to as the Fenske-Underwood-Gllland method. Jont ntatve of IITs and IISc Funded by MHR Page 1 of 1
NPTEL Chemcal Mass Transfer Operaton 1 5.3.1. Estmaton of Mnmum number of trays: Fenske Equaton Fenske (193) was the frst to derve an Equaton to calculate mum number of trays for multcomponent dstllaton at total reflu. The dervaton was based on the assumptons that the stages are equlbrum stages. Consder a multcomponent dstllaton column operatng at total reflu as shown n Fgure 5.4. Equlbrum relaton for the lght key component on the top tray s y (5.57) 1 K11 For total condenser, y 1 = then K (5.58) 1 1 An overall materal balance below the top tray and around the top of the column can be wrtten as: L 1 (5.59) Jont ntatve of IITs and IISc Funded by MHR Page of 1
NPTEL Chemcal Mass Transfer Operaton 1 Fgure 5.4: Multcomponent column at mum trays Under total reflu condton, = 0, thus, = L 1. The component materal balance for the lght key component around the frst plate and the top of the column s y L1 1 (5.60) Then under the condtons of the mum trays, the Equaton (5.60) yelds y = 1. The equlbrum relaton for plate s y (5.61) K The Equaton (5.61) becomes at y = 1 Jont ntatve of IITs and IISc Funded by MHR Page 3 of 1
NPTEL Chemcal Mass Transfer Operaton 1 (5.6) 1 K Substtutng Equaton (5.6) nto Equaton (5.58) yelds K (5.63) 1K Contnung ths calculaton for entre column, t can be wrtten as: K K... K K (5.64) 1 n In the same fashon, for the heavy key component, t can be wrtten as: KK... KK 1 n (5.65) Equaton (5.64) upon Equaton (5.65) gves K1K... K nk KK... K K 1 n (5.66) The rato of the K values s equal to the relatve volatlty, thus the Equaton (5.66) can be wrtten as... 1 n (5.67) If average value of the relatve volatlty apples for all trays and under condton of mum trays, the Equaton (5.67) can be wrtten as N avg (5.68) Solvng Equaton (5.68) for mum number of trays, N Jont ntatve of IITs and IISc Funded by MHR Page 4 of 1
NPTEL Chemcal Mass Transfer Operaton 1 N ln ln (5.70) ave The Equaton (5.70) s a form of the Fenske Equaton. In ths Equaton, N s the number of equlbrum trays requred at total reflu ncludng the partal reboler. An alternatve form of the Fenske Equaton can be easly derved for mult-component calculatons whch can be wrtten as N (5.71) ( )( ) ln ( )( ) ln ave The amount of lght key recovered n the dstllate s ( ). Ths s equal to the fractonal recovery of lght key n the dstllate say FR tmes the amount of lght key n the feed whch can be epressed as: ( FR ) F (5.7) LK From the defnton of the fractonal recovery one can wrte ( 1 FR ) F (5.73) LK Substtutng Equatons (5.7) and (5.73) and the correspondng Equatons for heavy key nto Equaton (5.71) yelds N ( FR )( FR ) ln (1 FR )(1 FR ) ln (5.74) ave Once the mum number of theoretcal trays, N s known, the fractonal recovery of the non-keys can be found by wrtng Equaton (5.74) for a non-key component and ether the lght or heavy key. Then solve the Equaton for FR NK, or FR NK,. If the key component s chosen as lght key, then FR NK, can be epressed as Jont ntatve of IITs and IISc Funded by MHR Page 5 of 1
NPTEL Chemcal Mass Transfer Operaton 1 FR NK, N NKLK FR 1 FR N NKLK (5.75) 4.3.. Mnmum Reflu: Underwood Equatons For mult-component systems, f one or more of the components appear n only one of the products, there occur separate pnch ponts n both the strppng and rectfyng sectons. In ths case, Underwood developed an alternatve analyss to fnd the mum reflu rato (Wankat, 1988). The presence of non-dstrbutng heavy non-keys results a pnch pont of constant composton at mum reflu n the rectfyng secton whereas the presence of non-dstrbutng lght non-keys, a pnch pont wll occur n the strppng secton. Let us consder the pnch pont s n the rectfyng secton. The mass balance for component around the top porton of the rectfyng secton as llustrated n Fgure 5.4 s y, n 1 L, n, (5.76) The compostons are constant at the pnch pont then, n1, n, n1 (5.77) and y y y (5.78), n1, n, n1 The equlbrum relaton can be wrtten as y m (5.79), n1, n1 From the Equatons (5.76) to (5.79) a balance n the regon of constant composton can be wrtten as L (5.80) y, n 1 y, n1, m efnng the relatve volatlty α =m /m HK and substtutng n Equaton (5.80) one can epress after rearrangng as Jont ntatve of IITs and IISc Funded by MHR Page 6 of 1
NPTEL Chemcal Mass Transfer Operaton 1 y, n1, L m HK (5.81) The total vapor flow n the rectfyng secton at mum reflu can be obtaned by sumg Equaton (5.81) over all components as: y, n1, L m Smlarly after analyss for the strppng secton, one can get st, efnng m HK, st, st L st,, st, m HK, st HK (5.8) (5.83) L 1 and Lst, (5.84) st, mhk, st Equatons (5.8) and (5.83) then become, 1 (5.85) and st,, (5.86) For constant molar overflow and constant relatve volatltes, both Equatons (5.86). The change n vapor flow at the feed stage ( as by addng the Equatons (5.86) F st,,, 1 that satsfes F ) s then wrtten (5.87) Combnng (5.87) wth the overall column mass balance for component can be epressed as F f, F (5.88) Jont ntatve of IITs and IISc Funded by MHR Page 7 of 1
NPTEL Chemcal Mass Transfer Operaton 1 Agan f the fracton q s known, the change n vapor flow at the feed stage can be epressed as F ( 1 q) (5.89) F Comparng Equaton (5.88) and (5.89), f ( 1 q) (5.90) Equaton (5.90) s known as the frst Underwood Equaton whch s used to calculate approprate values of λ. whereas Equaton (5.86) s known as the second Underwood Equaton whch s used to calculate m. From the mass balance L m can be calculated as L (5.91) 4.3.3. Estmaton of Numbers of Stages at Fnte Reflu: Gllland Correlaton Gllland (1940) developed an emprcal correlaton to relate the number of stages N at a fnte reflu rato L/ to the mum number of stages and to the mum reflu rato. Gllland represented correlaton graphcally wth ( N N ) /( N 1) as y-as and ( R R ) /( R 1) as -as. Later Molokanov et al. (197) represented the Gllland correlaton as: ( N N N 1 ) 1 54.4( R R 1 ep 11117.( R R ) /( R 1) ( R R ) /( R 1) [( R R ) /( R 1) 1 0.5 ) /( R 1)] (5.9) Accordng to Seader and Henley (1998), an appromate optmum feed-stage locaton, can be obtaned by usng the emprcal Equaton of Krkbrde (1944) as N N R S HK, F LK, F LK, HK, 0.06 (5.93) where N R and N S are the number of stages n the rectfyng and strppng sectons, respectvely. Jont ntatve of IITs and IISc Funded by MHR Page 8 of 1
NPTEL Chemcal Mass Transfer Operaton 1 Eample problem 5.4: A feed 100 kmoles/h of saturated lqud contanng 10 mole % LNK, 55 mole % LK, and 35 mole % HK and s to be separated n a dstllaton column. The reflu rato s 1. the mum. It s desred to have 99.5 % recovery of the lght key n the dstllate. The mole fracton of the lght key n the dstllate should be 0.75. Equlbrum data: LNK = 4.0, LK = 1.0, HK = 0.75. Fnd () Mnmum number of stages requred by Fenske method () Mnmum reflu rato by Underwood method () Number of deal stages at R = 1. R by Gllland method (v) Also fnd the number of deal stages at rectfyng secton and the strppng secton at the operatng reflu rato and locaton of feed stage. Soluton 5.4: () Feed F = 100 kmol/s, LNK,F = 0.1, LK,F = 0.55, HK,F = 0.35, LK, = 0.75, FR LK, = 0.995, HK = 0.75, LNK = 4.0, LK = 1.0. From the materal balance F. LK, F FR LK, LK, 7.967kmole/h Therefore W = F- = 7.033 kmole/h The amount of kmoles of dfferent component n dstllate: n LN = F. LNK,F.FR LK, = 54.75 kmole/h n LNK, = F. LNK,F = 10 kmole/h n HK, = - n LK, n LNK, = 8.4 kmole/h The amount of klo moles of dfferent component n bottoms: n LK, = F. LK,F (1- FR LK, ) = 0.75 kmole/h n LNK, = 0 n HK, = -n LK, n LNK, = 6.758 kmole/h = 1/ HK HK, = n HK, / = 0.113 LK, = n LK,/ = 0.010 Then as per Equaton (5.71) Jont ntatve of IITs and IISc Funded by MHR Page 9 of 1
NPTEL Chemcal Mass Transfer Operaton 1 N =.50 () To fnd the mum reflu at the condton of saturated lqud, q = 1, 1 = =, usng Equaton (5.90) (4.0)(0.1) (1.0)(0.55) (0.75)(0.35) 0 4.0 1.0 0.75 gves = 0.83 Then from Equaton (5.85) = 53.5 kmole/h And L = = 180.53 kmole/h R = L / =.47 () Now usng the Gllland correlaton (Equaton (5.9) to detere number of deal stages at R = 1. R =.97 one can get N = 48.89 (v) Usng Krkbrde Equaton N N R S HK, F LK, F LK, HK, Agan N R + N S = N = 48.89 0.06 0.75 So by solvng the above two Equatons one get N R = 10.56 and N S = 38.34 and feed at stage 11 Nomenclature Moles of bottoms PC ubble pont curve Moles of dstllate PC ew pont curve Eo Overall tray effcency E mv E ml Tray effcency based on vapor phase Tray effcency based on lqud phase F Moles of feed f Molal fracton of feed H Enthalpy K Equlbrum constant L Moles of lqud L Moles of lqud n strppng secton N, n Number of tray P Pressure, Pnch pont Q Rate of heat transfer Jont ntatve of IITs and IISc Funded by MHR Page 10 of 1
NPTEL Chemcal Mass Transfer Operaton 1 R Reflu rato Moles of vapor Moles of vapor n strppng secton mole fractons n lqud y mole fractons n vapor T Temperature Relatve volatlty µ scosty Subscrpts ottom C Condenser stllate F Feed HK Heavy key 1,, 3,., n L Lqud LK Lght key Mnmum NK Non key R Rectfyng secton S Strppng secton apor Jont ntatve of IITs and IISc Funded by MHR Page 11 of 1
NPTEL Chemcal Mass Transfer Operaton 1 References Ghosal, S.K., Sanyal, S.K. and utta, S., Introducton to Chemcal Engneerng, Tata McGraw Hll ook Co. (004). Gllland, E. R., Multcomponent Rectfcaton: estmaton of number of theoretcal plates as a functon of reflu rato, Ind. Eng. Chem., 3, 10-13 (1940). Hnes, A. L.; Maddo, R. N., Mass Transfer: Fundamentals and Applcatons, Prentce Hall; 1 Edton (1984). Krkbrde, C. G., Petroleum Refner 3(9), 31 (1944). McCabe, W. L., Thele, E. W., Graphcal esgn of Fractonatng Columns, Ind. Eng. Chem. 17, 605 (195). McCabe, W. L. and Smth, J. C., Unt Operatons of Chemcal Engneerng, (3rd ed.), McGraw-Hll (1976). Molokanov, Y. K., Korablne, T. R., Mazurana, N. I. And Nkforov, G. A., An Appromate Method for Calculatng the asc Parameters of Multcomponent Fractonaton, Internatonal Chemcal Engneerng, 1(), 09 (197). Seader, J.. and Henley, E.J., Separaton Process Prncples, Wley, New York (1998). Treybal R.E, Mass Transfer Operatons, McGraw Hll Internatonal Edton, 3rd Ed., (1981). Wankat, P. C., Equlbrum Staged Separatons: Separatons for Chemcal Engneers, Elsever (1988). Jont ntatve of IITs and IISc Funded by MHR Page 1 of 1