Shortcut Design Method for Multistage Binary Distillation via MS-Excel

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1 RESERCH RTICE OPEN CCESS Shortcut Desgn Method for Multstage Bnary Dstllaton a MS-Excel Mr. S. B. Dongare a, Mr..C.Shende a, Dr.V.N.Ganr a, Dr. G.M.Deshmukh a a axmnarayan Insttute of Technology, Rashtrasant Tukadoj Maharaj Nagpur Unersty, Nagpur , Inda. BSTRCT Multstage dstllaton s most wdely used ndustral method for separatng chemcal mxtures wth hgh energy consumptons especally when relate olatlty of key components s lower than 1.5. The McCabe Thele s consdered to be the smplest and perhaps most nstructe method for the conceptual desgn of bnary dstllaton column whch s stll wdely used, manly for quck prelmnary calculatons. In ths present work, we prode a numercal soluton to a McCabe-Thele method to fnd out theoretcal number of stages for deal and non-deal bnary system, reflux rato, condenser duty, reboler duty, each plate composton nsde the column. Each and eery pont related to McCabe-Thele n MS-Excel to ge quck column dmensons are dscussed n detals. Keywords: Multstage dstllaton; McCabe-Thele Method; Non-deal System; Relate olatlty I. INTRODUCTION More than 90 years ago, McCabe-Thele deeloped a create graphcal soluton technque based on ews assumptons of constant molar oerflow for the ratonal desgn of dstllaton column. [1] There are two ways to do dstllaton calculatons by McCabe-Thele method. One s graphcal method (by hand and tme consumng), and other way s by usng any other commercal smulaton software. It s costly and requre lcense. thrd alternate s presented here: Mergng the graphcal and manual computatonal methods so that the naccuraces of the former are compensated for by the speed of the computatons. The calculatons can be run by any spreadsheet program, such as Mcrosoft Excel, elmnatng the need for employng expense smulaton software and for laborng oer hand calculatons. Further, the tme noled from a programmer s pont of ew s no more (or consderably less) than that requred to learn how to use a commercal smulaton package. The method presented here s easy to learn, and offers a quck way to make prelmnary estmates of the tower dameter and heght, number of stages, energy consumpton, and reflux rato. lthough the calculaton procedure s ntended for bnary systems, ternary systems can also be modeled f the thrd component s less than 10% by olume and ts olatlty s not drastcally dfferent from the those of the remanng two components. II. SPREDSHEET CCUTION PROCEDURE Whle performng the dstllaton desgn calculaton, t s necessary to do mass balance around the dstllaton column (.e. by knowng feed, dstllate and resdue condtons), s determnng the apor/lqud equlbrum (VE) data. Raoult s law s used to calculate the saturaton pressure for the pure components [2]. Snce most systems are non-deal, the Wlson equaton s then appled to determne the lqud and apor compostons [3]. Ths equaton ncludes the actty coeffcents for a mxture, makng t sutable for non-deal systems. water/cetc cd system s used to llustrate the oerall method. III. PPY ROUT S W ND THE WISON EQUTION Use Raoult s law to fnd the saturated apor pressure for each component. Publshed data are aalable for arous compounds. The saturated apor pressure of each component s expressed as: ln P s B C T (1) where, P 1sat s the saturated apor pressure of component 1 (Pa), T s the temperature (K), and, B, and C are the Raoult s law constants for each compound [4]. The correspondng parameter alues for cetc cd and water are gen n Table 1. To calculate the saturaton pressure of a 6 P a g e

2 component, smply substtute the alue of the temperature. In these calculatons, 1 refers to Water and 2 s for cetc cd. Table 1- Raoults aw constants for Water & cetc cd Compound B C Water cetc cd The lqud and apor mole fractons of Water (x and y 1, respectely) are found 1 usng the total system pressure, P total : x = P 1 1sat /(P 1sat + P 2sat ) (2) y = (x 1 1 P 1sat )/P total (3) For an deal system, these equatons wll determne the VE data needed to estmate the column dmensons. When a lqud contans dssmlar polar speces, partcularly those that can form or break hydrogen bonds, the deal lqud soluton assumpton s almost always nald and the regular soluton theory s not applcable. Non deal soluton effects can be ncorporated nto K-alue formulatons, therefore VE calculatons are carred out by usng the actty coeffcents for the lqud whch are calculated to correct the equlbrum constant. t present there are at least four dfferent types of correlaton for the predcaton of actty coeffcents n chemcal E g x ln ( x x ) ( x x ) RT The ctty coeffcents dered from ths equatons are ln ln ln x x x x x x x systems that are normally used: Wlson, NRT, UNIQUC and UNIFC. [3] For non-deal mxture or azeotropc mxture addtonal arable γ (actty coeffcent) appears n apor-lqud equlbrum equaton. P sat y =γ X (4) Ptotal Where represents degree of deaton from realty. When γ =1, the mxture s sad to be deal whch smplfes the equaton to Raoult s law. For non-deal mxture γ 1, exhbts ether poste deaton from Raoult s law (γ > 1), or negate deaton from Raoult s law (γ < 1). The predcton of lqud phase actty coeffcent s most mportant for desgn calculaton of non-deal dstllaton. Before calculatng aporlqud equlbrum of non-deal mxture, the actty coeffcent of each component must be calculated. There s seeral excess energy models to calculate the actty coeffcent for multcomponent systems, the most mportant models are of (Wlson, NRT, UNIFC, and UNIQUC). In all these models, the model parameters are determned by fttng the expermental data of bnary mxtures. Each one of these models has adantages and dsadantages. There s no general model whch has a good representaton of all azeotropc mxtures. The selecton of approprate model for a gen mxture s based on three characterstcs, whch are temperature, pressure and composton. If napproprate model s selected, the desgn and smulaton of the process wll not work well. Based on molecular consderatons, Wlson (1964) presented the followng expresson for the excess Gbbs energy of a bnary soluton: ln x x x x x x x (10).(11) (12) In Eq. (10) the excess Gbbs energy s defned wth reference to an deal soluton n the sense of Raoults aw; Eq(10) obeys the boundary condtons that g E anshes as ether x 1 or x 2 becomes zero. [2] Wlson s equaton has two adjustable parameters. 12 and 21. n Wlson s deraton, these are related to the pure-component molar olumes and to characterstcs energy dfferences by ex p R T..(13) 7 P a g e

3 21 Where ex p R T (14) s the molar lqud olume of j pure component and are energes of nteracton between the molecules desgnated n the subscrpts. To a far approxmaton, the dfferences n the characterstc energes are ndependent of temperature, at least oer modest temperature nterals. Therefore, Wlson s equaton ges not only an expresson for the actty coeffcents wth temperature. Ths may prode a practcal adantage n sobarc calculatons where the temperature ares as the composton changes. For accurate work, ) and s B ln P T C should be consdered temperature-dependent but n many cases ths dependence can be neglected wthout serous error. Wlson s equaton appears to prode a good representaton of excess Gbbs energes for a arety of mscble mxtures. Table 3-Spreadsheet for the tabulaton of VE data Temp Vapor Pressure Partal Pressure Sum Water Mole cetc cd Mole ( 0 C) (mm Hg) Pressures Pp/Ptotal (mm Hg) Fractons Fractons Water cetc cd Water cetc cd x1 y1 x2 y E E E IV. CCUTE VE DT Table 3 presents the spreadsheet for the water/cetc cd bnary system (only the begnnng, mddle and endng sectons are shown). The program also ncludes cells for the Wlson coeffcents and those for Raoult s law, whch are not shown n Table 3. The temperature alues between bolng ranges of components are chosen by the programmer. The number of these alues chosen determnes, of course, the number of data ponts. ll other entres n the table are ether constants, or functons of constants and the nputted temperature. To fnd the partal pressures of both components (Columns 4 and 5), the saturated apor pressures are needed at a gen temperature (Columns 2 and 3). The saturated apor pressures are calculated usng Raoult s law and the partal pressures by applyng the Wlson equatons. Snce the total pressure s predetermned, a test column s set up n whch the total pressure (the sum of the partal pressures) s dded by the actual total pressure at that stage (Column 6). When ths alue n Column 6 approaches unty (wthn a gen tolerance) the correct temperature has been found. Thus, once alues of x1 are chosen, the only arable s the temperature (Column 1). Table 4- Spreadsheet of Input detals 8 P a g e

4 Table 5 Calculated Vapor-qud VE data V. FOW DIGRM OF MS-EXCE SPREDSHEET- Fg. 1 shows the stepwse calculaton procedure for ths spreadsheet. Spreadsheet snapshot of nput alues such as Relate Volatlty, Mole fracton of feed, Dstllate & Resdue and calculates VE data s shown n Table 4 & 5 reply. Fg. 1- Flow dagram of Excel Spreadsheet VI. DETERMINE THE THEORETIC NUMBER OF STGES - The theoretcal number of stages s calculated usng the McCabe- Thele method (Fg. 2). The followng algorthm s used to generate the approprate data ponts and construct the dagram (xd s the dstllate composton): 1. Start at the y = x lne for the dstllate condtons (x, y) = (x D, x D ). 2. Follow the constant y lne to the VE lne pont (x, y) = (x VE, x D ). 3. There are two optons. For total reflux, follow the constant x VE lne to the y = x lne for total reflux to the pont (x, y) = (x VE, x VE ). lternately, follow the x VE lne to the mnmum or optmum reflux lne: y = mx + b to the pont (x, y) = (x VE, m x VE + b). 4. Repeat the algorthm for the new data pont set defned n Step 3. 9 P a g e

5 Fg 2-McCabe-Thele dagram for determnng the number of stages n the rectfyng and strppng sectons of a dstllaton column VII. COUMN SPECIFICTIONS Table 4 presents the feed, dstllate and bottom specfcatons for the column, as well as other operatng parameters. reflux rato of 1.5 tmes the mnmum reflux raton was chosen arbtrarly. Table 4 calculates the flow condtons, based on the mass balance of the system. Water s referred to as the graphed component to dfferentate t from the other component (cetc cd) used n the calculatons. These three tables (Tables 4, and 5) contan all the data needed to defne the system, now that the VE data are determned. Next, calculatons are performed to fnd the mnmum number of stages. Mnmum number of stages The mnmum number of deal stages, whch occurs at total reflux, s calculated usng the algorthm presented before. Table presents the results for the water/cetc cd system. The alues for the frst row (x, y) are (x D, y D ), and for all subsequent rows are (x VE, y VE ), based on the preous x and y alues, whch are calculated usng the equatons.. Ths spreadsheet was set up to calculate compostons for 15 stages. Ths number s usually more than suffcent to accommodate most dstllaton columns. The calculatons generated a alue of x = 0.90 for Stage 1, whch s a bottoms of essentally equal to zero as shown n fg.3. Fg 3- Spreadsheet of McCabe-Thele dagram for determnng the number of stages n the rectfyng and strppng sectons of a dstllaton column 10 P a g e

6 Slope of mnmum reflux rato operatng lne - Now the mnmum reflux must be calculated. Ths s done by fndng the ntersecton of the q-lne (the qualty of the lqud) wth that of the operatng lne and the VE cure. Based on the dstllate, ths pont occurs at: m q-lne = (y VE y F )/(x VE x F ) The subscrpt F refers to the feed. ll of the aboe alues are known except x VE, and y VE. The cells used for ths calculaton are shown n Table 6. For a saturated lqud whose q-lne s ertcal, a ery large slope s calculated (see the upper part of Table 6). The lower part of Table 6 shows the slope of the operatng lne for mnmum reflux: m Rmn = (x D y VE )/(x x VE ) (15) Table 6- Strppng and rectfyng operatng lnes calculatons Optmum operatng condtons Once the mnmum reflux condtons are set, m Rmn s multpled by the predefned optmum reflux multpler. The optmum reflux rato, R, s now defned by the slope of the upper or rectfyng operatng lne. To fully defne the system, the pont of ntersecton of the operatng lne and the q-lne must be known, after whch the slope of the lower (strppng) operatng lne can be calculated easly. Usng the operatng lne slope, m R, the followng equatons are employed to fnd the ntersecton of the operatng lne wth the q-lne at (x, y). Based on the upper or rectfyng lne the equaton s: y = m R (x x D )/x F Ths equaton has two unknowns, thus, an expresson for x s formulated from the strppng lne: x = [(x F + m R )/m q-lne x F ]/(m R /x D* m q-lne 1) When the ntersecton s found, then the slopes of all the operatng lnes are calculated by smple algebra,. Usng the lower and upper operatng lnes, the preously mentoned algorthm for the Mc- Cabe Thele dagram s employed to calculate each stage s equlbrum alues. Use of condtonal statement - Throughout all of the calculatons, ncorporatng the upper and lower segmentaton lnes s accomplshed by the usng the f condtonal statement. Ths statement s crucal n calculatng the VE data for the constant y segment of the calculaton. Further, an addtonal f statement s necessary at the transton of the strppng and rectfyng lnes when calculatng beyond the alues at the ntersectons of the lnes. When the x alue of ntersecton of the operatng lnes s passed, the spreadsheet uses the strppng operatng lne to calculate the y alues. Ths s why the segmentaton sheet of Table 3 must determne the segmentaton transton alue of x, as well as that of y. To fnd the number of equlbrum stages, note the stage at whch the requred bottoms condtons are met. For ths case, assume that a bottoms x B alue of approxmately 0.05 meets the process requrements. The alue for Stage 14 s about 0.08, whle that for Stage 15 s about 0.05, so there are 15 equlbrum stages. Further calculatons are made to fnd the number of actual stages, the column heght, the energy transferred n the reboler and condenser, and the column dameter (based on the calculated apor flowrates). These calculatons use methods found n standard references, are relately straghtforward, and wll only be summarzed here. Column heght and flowrates - The heght s smply the number of actual stages multpled by the tray spacng or packng equalent heght. The flowrates are calculated a mass balances. The equatons are taken from Treybal ((4), pp ). Spreadsheets are easly created to perform all of these calculatons and conert the results nto dfferent systems of unts, when desrable. Reboler and condenser dutes Calculatons of the energy rates of the reboler and the condenser are made usng latent heats and specfc heats (when needed). [7] The calculatons are as thus performed pecewse, usng each chemcal speces and ts respecte latent and specfc heats. For example, the bottoms s consdered to be made up of 100% cetc cd, so ts heat duty would be the flowrate of the cetc cd apor rsng up from ths stage (at 118 C), multpled by the latent heat of cetc cd to create the apor. Column dameter - method descrbed by Kster ((5), pp ) determnes the upper and lower column dameters. Calculatons are based on the floodng elocty, the propertes of the lquds and apors, 11 P a g e

7 and the fractonal hole area n the trays, among other factors. The calculaton s straghtforward and s not ncluded here. VIII. CONCUSION By usng arous mathematcal tools n Excel spreadsheet, the numercal soluton to a McCabe-Thele dagram to fnd the theoretcal number of stages for bnary and pseudo-bnary systems s presented, also the spreadsheet automatcally calculates the actual number of stages, reflux rato and column dmensons and each plate composton. Once, such spreadsheet created, t s ery easy to sole another dstllaton desgn problems by aryng Feed Condtons, Temperature profle and other parameters to ge answers quckly. Nomenclature -,B,C = constants for Raoult s law, dmensonless r 1, r 2, q 1, q 2, a 12, a 21 = constants n Unquac equaton, dmensonless n = number of data ponts P = pressure, Pa q = qualty of lqud T = temperature, K x = lqud mole fracton y = apor mole fracton Greek letters: α = relate olatlty γ = actty coeffcent Subscrpts: 1, 2 = component 1 or 2 B = bottoms D = dstllate F = feed = data pont l = mxture sat = saturated R = reflux VE = at apor/lqud equlbru [5]. Paul M. Mathas, Vsualzng the McCabe Thele Dagram, meracan Insttute of Chemcal engneers,cep, [6]. Jake Jerc, Muhammad E. Fayed, Shortcut Dstllaton Calculatons a Spreadsheets, meracan Insttute of Chemcal engneers,cep, [7]. Prncples of Mass Transfer and Separaton Processes, Prentce Hall Inda Pt. mted, Eastern Economy Edton, 2007, by Bnay K. Dutta. [8]. Chemcal Engneerng, Butterworth- Henemann Publcaton, Vol. 2, Ffth Edton, 2002, by J.M.Coulson and J.R.Rchardson. [9]. Burns, M.., and J. C. Sung, Desgn of Separaton Unts Usng Spreadsheets," Chem. Eng. Educaton, 30, pp (1996). [10]. Ea Sorensen, Prncples of Bnary Sepearton, Department of Chemcal Engneerng, UC, ondon, UK, Chapetr 4, [11]. Treybal, R. E., Mass Transfer Operatons, McGraw Hll, New York (1987). [12]. Kster, H. Z., Dstllaton Desgn, McGraw-Hll, New York (1992). ITERTURE CITED [1]. McCabe, W.., and E. W. Thele, Graphcal Desgn of Fractonatng Columns, Ind. Eng. Chem., 17, pp (1925). [2]. Van Wnkle, M., Dstllaton, McGraw Hll, New York, Toronto (1967). [3]. Molecular Thermodynamcs of Flud- Phase Equlbra, 3 rd ed., Prentce Hall Internatonal Seres by John M. Prausntz. [4]. Perry, R. H., and D. W. Green, eds., Perry s Chemcal Eng- neers Handbook, 7 th ed., McGraw Hll, New York, p (1997). 12 P a g e