Material and heat transfer rate in the gas-lquid system

Transcription

1 Tatana osornac, aa Ivanovc-Kneevc, ateral and heat transfer rate n the gas-lqud system Tatana osornac, aa Ivanovc-Kneevc, Srdan Peanovc, 3 halo Peruncc, Nevenka Boskovc- Vragolovc Ol Refnary Pancevo,Spolnostarcevacka bb, 3 Pancevo, Serba, e-mal: Department of Chemcal Engneerng, Faculty of Technology and etallurgy, The Unversty of Belgrade, Karnegeva, Belgrade, Serba,emal: maa@tmf.bg.ac.rs, srdap@tmf.bg.ac.rs, 3 Faculty of Technology, Unversty of Nov Sad, Cara aara, Nov Sad,Serbae-mal:perun@uns.ac.rs Abstract:- In ths paper substance transfer rate n the multstage system was nvestgated. Substance transfer between lqud and gas phases n a dstllaton packed column wth packng was examned. Substance and heat transfer rate were examned and substance transfer coeffcents were determned. Effcency of substance transfer were examned by heght of transfer unts and volumetrc substance transfer coeffcents. Based on derved mathematcal model the total heght of transfer unts and ndvdual heght of transfer unts for the lqud and gas phases were determned. The nvestgaton was performed by computer smulaton and experments. Several correlaton models for heght of transfer unts and substance transfer coeffcents were studed. Keywords: ultstage system, heght of transfer unts, substance transfer coeffcent, bnary system, dstllaton column. I. INTRODUCTION as absorpton s operaton n whch one or more soluble components of a gas mxture are dssolved n a lqud. The reverse operaton called strppng or desorpton s employed to transfer one or more volatle components from a lqud mxture nto gas. There are three type broad steps n the separaton system desgn. Data on the vapor-lqud equlbrum relatons for the system are needed to determne to quantty of lqud necessary to absorb the requred amount of the soluble components from the gas, or the quantty necessary to strp the desred amount of the volatle components from the lqud. Data of the lqud and vapor capacty of equpment of the type beng consdered for use are needed to determne the necessary cross sectonal area and se of the equpment. Equlbrum data and materal balances are used n combnaton wth fundamental relatons percular to the absorpton-strppng process to calculate the number of equlbrum stages requred for the separaton desred. When the composton of a flud mxture vares from pont to another, each component has a tendency to flow n the drecton that wll reduce the local dfferences n concentraton. If the bulk flud s ether statonary or n lamnar flow n a drecton normal to the concentraton gradent, the materal transfer reducng the concentraton dfference occurs by a process of molecular dffuson. Ths mechansm, charactered by random movement of ndvdual molecules, contrasts wth the bulk transport by eddes whch occurs n a turbulent flud. The theory of molecular dffuson has been the subect of extensve nvestgaton because of ts close relatonshp to the knetc theory of gases. Detaled revews are avalable have provded a valuable crtcal comparson of the varous correlatons whch have been presented for the predcton of dffusvtes n gases and lquds, ncludng electrolytes and nonelectrolytes under a varety of condtons []-[]. Dfferent theoretcal approaches to the descrpton of dffuson n lquds have been made, dependng upon whether the systems are electrolyte or nonelectroltc. The avalable predcton procedures must therefore be dvded nto those sutable for nonelectrolytes and those sutable for electrolytes. ost studes have been denoted to the estmaton of dffusvtes n very dlute soluton, although some progress has been made towards allowance for the substantal varatons that occur wth ncreasng concentraton of the dffusng solute. ateral transfer phenomena where dffuson occurs through the lqud and gas nterface has been studed n dstllaton columns. A dfferent approaches to the modellng of the packed column, partcularly applcable to bnary and multcomponent dstllaton, were developed and appled n full-scale tests n papers[7]-[7]. They put forward the concept of substance transfer secton and defned vaporaton effcences to compensate the devaton of each secton from an deal stage. Ruckensten [3] solved the transport equatons n the lqud phase wthout usng the two-flm model. Ths was a smultaneous treatment of heat and mass transfer, but confned to the lqud phase. Dutka-Rukensten [] abandoned the dea of thermal dstllaton and modelled the packed column usng only overall mass transfer coeffcents. The mass transfer coeffcents and mass transfer effcency were nvestgated by Savkovc- Stevanovc et.al.[]. any types of mass transfer operatons are carred out n ether contnuous or stage wse columns. These columns are usually packed wth Raschg rngs, Pall rngs, Berl saddles, essng rngs, or other types of packng, to promote ntmate contact between the two phases. Contnuous contact s therefore mantaned between the two countercurrent streams throughout the equpment, necesstatng a dfferental type of treatment. The preferred method of desgn nvolves determnaton of the number of transfer unt (NTU necessary to acheve the desred separaton. Evaluaton of the (NTU requres ISSN: 79-5 Issue, Volume, October

2 Tatana osornac, aa Ivanovc-Kneevc, prelmnary constructon of the equlbrum curve and the operatng lnes of the separaton process. ultstage and gas-lqud phase separaton modellng s gven n the recent paper [9 ]. Industral separaton processes nvolvng acetc acd contnue to be of consderable nterest. ass transfer between the lqud and vapor phase of the systems wth assocaton n a dstllaton column was studed [5]-[7]. The effects of assocaton on the (HTU n laboratory and plot-plant packed dstllaton columns are nvestgated n the papers []-[]. In ths paper the substance transfer coeffcents and heght of transfer unts are determned, usng effectve dffuson coeffcents for acetc acd -xylene. ethod for substance transfer coeffcents determnaton was derved by fttng operaton curve and vapor-lqud equlbrum curve to the expermental data.. SIUTANEOUS ATERIA AND HEAT TRANSFER IN THE UTISTAE AS-IQUID-SYSTE et assume, n a dstllaton packed column concentraton gradent s changed only n drecton elements,, 3,., n countng from the top to the bottom (Fg.. Phase equlbrum between vapor and lqud phases for component, at the same pont s: f E f ( V where E vaporaton effcency at the pont. Analogously, for any secton wll be: f E f ( V where E so called vaporaton effcency for any element. For equlbrum condtons when vapor and lqud phases pressure and temperatures are equal then, y V E x γ ( f / f (3 If the both vapor and lqud phases can be consdered as deal V soluton, then can be denoted wth K f / f. ateral balance for steady state condtons: ateral balance for the vapor phase of the element s, + N + d ( and for the lqud phase, N d (5 Energy balance for steady state condtons Energy balance for the vapor phase of the element s: + + H H + N d Q d ( Fg. Substance transfer n the gas-lqud sytem n packed bed Energy balance for the lqud phase whch ncludng lqud phase, lqud flm, nterphase and vapour flm and reacton heat of the element s: + h h N d + Q d (7 H+ H + NHd Q d d( U H dt + ( Energy balance for the lqud phase whch ncludng lqud phase, lqud flm, nterphase and vapour flm and reacton heat of the element s, h h + Nhd Q d d( U h dt (9 3.SUBSTANCE TRANSFER RATE Substance transfer drvng force between gas and lqud phase can be defned as: t t m m,, dc dt dc, dt where, ( * k a( c c ( k a( c c (,, /,, * k a( c c ( k a( c c ( c /,, / c /, and, mean concentraton n the phases borders and can be approxmated wth concentraton whch n equlbrum wth the exstng average concentraton of the lqud phase. The relatonshp between the overall and ndvdual substance transfer coeffcents s gven by the followng relaton:,, ISSN: Issue, Volume, October

3 Tatana osornac, aa Ivanovc-Kneevc, k k O O m ' + (3 k k + ( k m ' k Substance rate between vapor and lqud phase can be defned as follow: dn dy dx (5 dn k a y y Sd k a( x x Sd ( ( / / Snce, nterphase y / and x / uncertan for gven locaton t s more conventon to use over all component transfer coeffcent as followng: * * dn k a( y y Sd k a( x x Sd (7 O and combnng eqs.(5-( s obtaned: y dy x dx d x * ( asy ( y k asx ( x y * ko By ntegraton between top and bottom of the column s determne total column heght Z. k as dy y O yd xd Z y * B x * B O y k OaS dx x x (9 Integrals n eq.(9 defnes NTU Number of Transfer Unt and Z/NTU s equal HTU-Heght of Transfer Unt. Relatonshps between overall and ndvdual heght of transfer unt are gven by eqs.(-(. m' ( HTU ( HTU + ( HTU O ( HTU O ( HTU + ( HTU m' ( ( where m/ and /m, (mk are absorpton and desorbton factors.. COPARISON OF EQUIIBRIU AND TRANSFER UNIT ETHOD The equlbrum stage method for charcteraton of the dffucty of separaton provdes an adequate measure of separablty for dstnct substance transfer elements n a counter current columns n a hghly effcent plate column. On the other hand, the transfer unt method s preferred when vapor and lqud are n contnuous contact, n packed columns and plate columns whch have an effcency wll below. The equlbrum stage method s used often n practce, because graphcal determnaton of the number of equlbrum steps on the y-x dagram s much easear than ntegraton wth respect to the drvng force. The equlbrum curve and the operatng lne can almost always be lneared n narrow concentraton ranges. The followng relatonshp s then obtaned m ' ln ( / ( NTU O n t m ' ( / ( In the specal case when m/(/ (NTU O n t. The heght equvalent of theoretcal plate (HETP can be defned. HETP Z/ n t. (3 5. PACKED COUNS Packed columns are often used for dstllaton and gas absorpton. In ths paper only dstllaton wll be consdered. In the gas lqud contact n a packed bed column, the lqud flows down the column over the packng surface and the gas or vapor, counter currently, up the column. In some gas-absorpton columns co-current flow s used. The performance of a packed s very dependent on the mantenance of good lqud and gas dstrbuton throughout the packed bed, and ths s an mportant consderaton n packed column desgn. The choce between a plate or packed column for a partcular applcaton can only be made wth complete assurance by costng each desgn. However, ths wll not always be worthwhle, necessary, and the choce can usually be made, on the bass of experence by consderng man advantages and dsadvantages of each type. Plate columns can be desgned to handle a wder range of lqud and gas flow rates than packed columns. The packed columns are not sutable for very low lqud rates. The effcency of plate can be predcted wth more certanty than the equvalent term for packng (HTU or (HETP. Plate columns can be desgned wth more assurance than packed columns. There s always some doubt that good lqud dstrbuton can be mantaned throughout a packed column under all operatng condtons, partcularly n large columns. It easer to make provson for the wthdrawal of sde streams from plate columns. If the lqud causes foulng, or contans solds, t s easer to make provson for cleanng a plate column, man ways can be nstalled on the plates. Wth small dameter columns t may be cheaper to use packng and replace the packng when t becomes fouled. For corrosve lquds a packed column wll usually be cheaper than the equvalent plate column. The lqud holdup s apprecably lower n a packed column than a plate column. Ths can be mportant when the nventory of toxc or flammable lquds needs to be kept as small as possble for safety reasons. The packed column are more sutable for handlng foamng systems. The pressure drop per equlbrum stage (HETP can be lower for packng than plates, and packng should be consdered for vacuum columns. Packng should always be consdered for small dameter columns, say less than.m, where plates would be dffcult to nstall, and expensve. The desgn of a packed column wll nvolve the followng steps: select the type and se of packng, determne the column ISSN: 79-5 Issue, Volume, October

4 Tatana osornac, aa Ivanovc-Kneevc, heght requred for the specfed separaton, determne the column dameter, capacty, to handle the lqud and vapor flow rates, select and desgn the column nternal features packng support, lqud dstrbutor, redstrbutors. The prncpal requrements of a packng are that t should: provde a large surface area (a hgh nterfacal area between the gas and lqud, have an open structure, low resstance to gas flow, promote unform lqud dstrbuton on the packng surface, promote unform vapor gas flow across the column cross secton. Wth contnuous contactors, stagewse contactors utle ntermtten contact between the phases. The stages often take the form of horontal plates of vared desgn, arranged vertcally above each other n the column. The two phases enter a stage from opposte drectons n countercurrent flow, mx together to facltate transfer and then separate and leave the stage. When two phases leave n a state of equlbrum the stage s sad to be an deal or theoretcal one. Ths concept has been extended to packed columns by defnng the heght, of packng, equvalent to a theoretcal stage such that the streams leavng ths secton are n equlbrum. The number of theoretcal stages to whch ths packed column s equvalent s gven by the broken-lne stepwse constructon between the operatng and equlbrum curves.. EXPERIENTA SECTION The expermental setup has shown n Fg.. The expermental data were obtaned n a ordnary glass Normag dstllaton column wth a packng heght of mm and a dameter of 33 mm. The average dameter of packng partcle Rashg rngs.x. cm. The bed vod fracton was., and the specfc surface of packng.9 cm / cm 3. The batch dstllaton unt s controlled by the acquston block. Normatron was connected for reflux flow rate control over mcroprocessor. Sensor for pressure drop and temperature sensors Pt- were used. The experments were carred out by batchwse dstllaton operaton and were sem-contnuous n adabatc condtons. The compostons of the dstllate and the bottom product were determned by refractometer. The dstllaton was carred out at the atmospherc pressure. The charge conssted of 9mol% acetc acd and mol% p-xylene. Holdup on each stage was. mole, for total condenser and reboler moles. The dstllaton was performed at dfferent flow rates through the column. The hydrodynamc characterstcs wth Rashg rngs were determned and shown n Fg.3. The optmal flow rate through the column was establshed at.5 m/s. The ntegrals n equaton (9 are evaluated by numercal ntegraton. Informaton for ths procedure s obtaned from the equlbrum curve-operatng lne plot on x,y coordonates. It s often nconvenent to determne nterfacal compostons (y*, x* correspondng to each pont on the operatng lne, so overall (NTU values are frequently determned n preference to the ndvdual ones. The evaluaton could be performed by numercal ntegraton. Ths would requre equatons for the equlbrum and operatng curves. Numercal ntegraton was relaed usng Smpon s rule. An algorthm was derved and program module was developed n Fortran programmng language. Fg.(a Scheme of the laboratory dstllaton column wth temperature and pressure acquston system Fg. (b Fg.(b Expermental set up NTU s gven by the ares under the curve betwee lmts of ntegraton. Expermental set up ISSN: Issue, Volume, October

5 Tatana osornac, aa Ivanovc-Kneevc, p/,m/s 3 7.PACKED CONTACTOR PARAETERS AND VARIABES In separaton processes need to defne mxture varables and packed tower varables. The best fttng of those varables gves the optmal process condton. Fg. 5 represents optmal correlated dervng procedure. Substance transfer effcency f (column and packng propertes, system propertes ( HTU f(, D, d, H f ( µ,, D, σ (5 c p HETP f(, Dc, d p, H f( k, α, µ,, D, σ ( The conflct resoluton between f and f functons has gven the optmal values for HTU and HETP. START - w,m/s Fg.3 Pressure drop vs. gas velocty Fg. shows dependence dstllate qualty of vapor velocty through the column under nfnte reflux rato R. Input data (,D c,d p,h,µ,,σ,d,α,k, condtons Correlatons for HTU and HETP - defnton f and f x, mol/mol.55 f ~ f yes Output HTU,HETP no STOP.55.5 Fg.3 Press - w,m/s Fg. Top xylene composton versus gas velocty for the ntal charge mxture %mol xylene and 9mol% acetc acd (R Fg.5 Correlaton modellng. (HTU and (HTU CORREATION ODES Several correlatons for packed dstllaton columns were studed []-[]. The expermental values (HTU O and (HTU O were determned usng eq.(. The (NTU O and (NTU O are gven by the area under the curve between lmts of ntegraton and by numercal ntegraton were determned. Heght of transfer unts were correlated by Sherwood-Holloway and Zuderweg correlaton models eqs.(-(5[7]-[]. Substance transfer coeffcents were modelled by Sherwood- Holloway and Onda-Takeuch-Okumoto correlaton models []- [3] eqs.(5-(9. ISSN: 79-5 Issue, Volume, October

6 Tatana osornac, aa Ivanovc-Kneevc, Heght of transfer unt: Sherwood-Holloway: n.5 HTU B ( / µ Sc ( (.3.33 ( B ( / HTU (3 Zuderweg: ( HTU CW d p D g ( ( HTU ( C Re Sc W 9. SUBSTANCE TRANSFER COEFFICIENTS ODEIN any correlaton models for mass transfer coeffcents n packed columns are reported n the lteratue [9]-[]. any authors were correlated own expermental data. Some authors correlated expermental data from lterature by dfferent correlaton models. In ths paper Sherwood-Holloway and Onda - Takeuch - Okumoto correlaton models were used. Sherwood-Holloway: n.5 ( k a / D ( Sc B µ where a S p / V ( ε. p Onda-Takeuch and Okumoto: /3 /3.5. ( k / ct ( / µ g C3 ( / awµ ( µ / D ( at Dp ( k DRT/ p ( ( 7.7 /3.. C ( / at ( µ / D ( at Dp µ ( ( aw / at exp[.5( g / σ Re Fr We where We / σ Fr at / Re / a µ t a t., g, σ (9 µ s vscosty, and s densty for the lqud and gas phase were determned by equatons for low pressure ( see Appendx, C s packng constant, C, C 3 are constants. Dffusvtes D were calculated accordng to the equatons Fuller et. al for the gas phase and effler Cullnan[]-[7] and Savkovc-Stevanovc for the lqud phase[](see Appendx. Vapor pressure, densty and vscosty were calculated accordng to expressons gven n the Appendx. Dffusvty was determned accordng to expressons gven n the Appendx.. ETHOD FOR PRAETERS DETERINATION The parameters of the nvestgated correlaton models were obtaned by mnmaton method based on least squares []- []. The obectve functons for heght of transfer unt and heght of equvalent theoretcal plate were defned as: [(HTU Oexp. - (HTU Ocal.] mn (3 [(HTU Oexp. - (HTU Ocal.] mn ( [(HETPexp - (HETPcal ] mn (9 The obectve functons substance transfer coeffcents were defned as: [k Oexp. - k Ocal.] mn ( [k Oexp. -k Ocal.] mn ( The obtaned parameters have shown n Table and Table. For parameters determnaton n correlaton models based on least squares method an algorthm was derved and correspondng program modules were developed. The parameters values n correlaton models for (HTU are gven n Table. The parameters for substance transfer coeffcent correlatons are gven n Table.. RESUTS AND DISCIUSION The obtaned results for heght of transfer unts and substance transfer coeffcents are presented n Fgs. and 7 and Tables and. The pressure drop vs. vapor velocty has shown n Fg.3. The optmal flow rate for the examned column was w5.m/s. The expermental data were gven under total reflux ( R. Table. The parameters values for the examned correlatons for HTU Correlaton as phase qud phase Sherwood Holloway B.5 B9. n.5 Zuderweg C.5E- C.95E- Table. Parameters values for substance transfer coeffcents for the examned correlatons Correlaton as phase qud phase Sherwood- Holloway - B. n.5 Onda-Takeuch- Okumoto C 3.5 C. ISSN: Issue, Volume, October

7 Tatana osornac, aa Ivanovc-Kneevc, The obtaned results for heght transfer unts for varety flow rate through the column are gven n Fg.. Fg. shows the expermental values for overall (HTU for acetc acd p-xylene n the both lqud and gas phases vs. lqud flow rate. The expermental values of the substance transfer coeffcents n the lqud and vapor phase are shown n Fg. 7. The comparson of expermental and calculated values for (HTU O has shown n Fg.. Fg. 9 shows the comparson of expermental and calculated values for substance transfer coeffcent for the lqud phase. 3 k O k O k O k O HTU,cm - (HTU O (HTU O w, m/s 5 Fg.7 The expermental values of the volumetrc substance transfer coeffcents for acetc acd p-xylene n the both lqud and gas phases vs. flow rate (R (HTU O,cm (calculated...5. w, m/s 5 3 (HTU O (HTU O Fg. The values of overall HTU for acetc acd p-xylene n the both lqud and gas phases vs. lqud flow rate (R In Fg. the comparson of expermental and calculated values for substance transfer coeffcents n the vapor phase. The results of modellng of the mass transfer coeffcents demonstrate that the expermental values of the coeffcents are n a good agreement wth the calculated ones. Onda et al. gves better agreement n comparson wth Sherwood- Holloway (HTU O,cm (expermental Zuderweg Sherwood- Holloway Fg. Comparson of the expermental and calculated values for ( HTU O ISSN: 79-5 Issue, Volume, October

8 Tatana osornac, aa Ivanovc-Kneevc, k O, mol/cm s (calculated Fg. 9 Comparson of the expermental and calcultaed values for substance transfer coeffcents n the lqud phase k O, mol/cm s (calculated Onda et al. Sherwood-Holloway Onda k O, mol/cm s (expermental k O, mol/cm s (expermental Fg. Comparson of the expermental and calcultaed values for substance transfer coeffcents n the vapor phase.concusion The substance and heat transfer rate and heght of transfer unts are examned, usng effectve dffuson coeffcents. The substance transfer dffuson coeffcents were determned. The substance transfer coeffcents determnaton method was derved by fttng workng curve and vapor-lqud equlbrum curve to the expermental data. Effcency of the substance transfer by (HTU/(NTU methods for bnary systems were nvestgated. The overall, ndvdual and component transfer coeffcents were determned. Scherwood-Holloway and Zuderweg correlaton models for (HTU/(NTU and Scherwood-Holloway and Onda- Takeuch-Okumoto models for substance transfer coeffcents were studed. The obtaned results show good agreement between expermental and calculated results. The obtaned results n ths paper can be appled n others multstage, multphase doman. Acknowledgement. The authors wsh to express ther grattude to the Fund of Serba for Fnancal Support. Appendx Vapour pressure determnes accordng to equaton: B lg P A (A. ( C + t where for acetc acd A 5.99, B., C 9.9, and for p-xylene: A.995, B53.3,C5.37 at atmospherc pressure. Vscosty can determne accordng to equaton: A ( B + t µ (A. n where for acetc acd A7., B.7, n.9, for xylene A 9.395, B5., n.. Vscosty of the mxture acetc acd-p-xylene has calculated accordng to followng equaton: µ x (A.3 µ / 3 / 3 x µ + µ x µ mx (A. x + µ Densty of the pure component n dependent of temperature: 3 [ s + α( t ts + where for acetc acd: β( t t s γ( t t ] + (A. 3 s.7 g / cm,t s C, α.9, β.5, γ.,. 3 for p-xylene: s.5 g / cm, t s C, α.55, β.9, γ.73,.5, and t s temperature C. s ISSN: Issue, Volume, October

9 Tatana osornac, aa Ivanovc-Kneevc, For the mxture acetc acd p-xylene equaton for determnaton of the densty of bnary mxtures at low pressure were used.: x mx (A.5 x + T ( y y.t + (A. Appendx Dffusvty was D calculated accordng to equatons of ( D effler-cullnan et.al.[],[9]. Dffusvtes D and D were calculated by the equaton of uss-ratclff. D µ T ( D [.5 x x ( D ( + ( A v ( / 3 d ln γ d ln x v (. ( v ( / 3 v + ]( A. v where v s mole fracton and T s temperature. Actvty coeffcents for bnary systems of the Λ Λ lnγ ln( x +Λx + x( ( A x +Λ x Λ x + x mxtures were calculated by Wlson's correlaton:.. examned where γ actvty coeffcents, Λ Wlson's parameters for bnary systems acetc acd-p-xylene whch were ftted from expermental data are Λ.99 Λ.77. Notaton a- nterfacal surface per unt volume, cm /cm 3 a t -total surface area of packng per unt volume, cm /cm 3 B,B -constants C T,C,C, C 3,C -constants D-flud dffusvty, cm /s d c column dameter, cm D, D -dffusvty of the lqud and gas phase, respectvely, cm /s D p -dameter of packng, cm E-vaporaton effcency f-fugacty -gas flow rate, mole/s g-gravtatonal acceleraton, cm/s H-enthalpy of the lqud phase, J/mole h- enthalpy of the vapour phase, J/mole HTU- Heght of transfer unt, cm (HTU, (HTU - heght of transfer unt over the lqud and gas phase, respectvely, cm K- equlbrum constant.3 k k, ndvdual transfer coeffcent for the lqud and the gas phase, respectvely, mol/cm 3 s k O, k O, overall substance transfer coeffcent,mol/cm 3 s -lqud flow rate, mole/s -total number of component m - equlbrum phase rato( α /[ + ( α x] m t -amount of substance transfer N- total number of molecules n-constant n t.-number of theoretcal plate NTU-Number of transfer unt Q-heat R-reflux rato R -gas constant Re- Reynolds number ( d c w / µ Sc- Schmdt number ( µ / rd Sh- Sherwood number ( kd c /D S-radal column surface, cm S p - packng surface, cm T-temperature, K y- vapor composton y * - equlbrum composton x-lqud phase composton V-volume,cm 3 w-gas phase velocty, cm/s - column heght, cm reek symbols α- relatve volatlty µ flud vscosty, Pas -densty, g/cm 3 σ surface tenson, N / m ε bedvod fracton Subscrpt -gas -lqud O-overall lqud phase O-overall gas phase p-packng References [] C.O.Bennett, J.E.ayers, omentum, Heat and ass Transfer, craw Hll, p.3-5,9. [] R.B.Brd, Advanced n ChemcalEngneerng, Vol. T.B.Drew, J.W. Hoopes,Eds., Academc Press New York, p.7-73,95. [3] R.B.Brd, W.E. Stewart, E.N.ghtfoot, Transport Phenomena,Wley New York, p. 9-5, 9. [] J. Crank, The athematcs of Dffuson, Clarendon Press, Oxford,95. [5] A.S.Foust,.A.Wenel, C.W.Clump,.aus,.B.Andersen, Prncples of Unt Operatons, Wley, New York, 9. [] E.D.Olver, Dffusonal Separaton Processes,Wley New York, 9. [7] T.osornac, J.Savkovc-Stevanovc, A multstage, multphase and multcomponent process system modellng, Internatonal Journal of athematcal odels and ethods n Appled Scence,5(,. []Bassyon A.A., cdanel R., Holland C.D.,Chem. Eng.Sc. 5(97 p.37. [9] Holland C.D.,Hutton A.E., Pendon C.P., Chem. Eng. Sc. (97 p.7. [] cdanel R.,Basyon A.A.,Holland C.D., Chem. Eng.Sc. 5 (97 p.33. ISSN: 79-5 Issue, Volume, October

10 Tatana osornac, aa Ivanovc-Kneevc, [] cdanel R.,Holland C.D., Chem. Eng.Sc. 5 (97p.3. [] Rubac R.E., cdanel R., Holland C.D., Chem Eng. Sc. 5(97p.33. [3] Rukensten E.,AIChE J, (97 p.. [] Dutka E.,Rukensten E., Cheme et Industre ene Chmque (97 p.35. [5] Savkovc-Stevanovc J., Smonovc D., Popovc.:Untersuhung der emprschen gleshungen ur bestmmung des HETP wertes ener dstllaton fullkorper kollone, Chem.-Eng.-Tech.9, (977 p.5. [] Savkovc-Stevanovc J., Smonovć D., The Refractve Indces and Denstes of Ternary xtures of Benene - Toluene - Xylene, Journal of Chem. and Eng. Data,, 5-59,97. [7] Savkovc-Stevanovc J.,HETP n packed dstllaton column wth assocated systems, Chem.-Ing.-Techn. 57 (95 p.3. [] Savkovc-Stevanovc J.,odellng of the mass transfer phenomena of the assocated systems n packed dstllaton column, Chem.Eng.Technol.5(99p [9] T.ošornac,J.Savkovc-Stevanovc, A multstage, multphase and multcomponent process stem modellng, Inter, Journal of ath. odels and ethods n Appled Scences, 5 (, -,. [] Sherwood T.K., Holloway, F.Al., Trans. Am.Inst.Chem Eng. 3 (9 p.. [] Zuderweg,F.J.,De Berechnung des Wrkungsgrades von Fullkopersaulen fur Dstllaton, Absorpton and Abreten, Technshe Hogeschool Delft, Nederlande,97. [] Cornell D., Knapp H.,Close J.R.,Far J.R., Chem.Eng.Prog. 5, No.(9 p.. [3] Onda K,Takeuch H.,Okumoto,Y., J.Chem. Eng. Japan, (9p.5 []Savkovc-Stevanovc J.,.Ivanovć-Kneževć, ass transfer coeffcents modellng n multphase, multcomponent and multstage dstllaton wth reacton esterfcaton, CHISA- 7 th Internatonal Congress on Chemcal and Process Engneerng, CD-RO, p., C.,pages, 7-3 Aug.,Prague,. [5] Ivanovć -Kneževć.,Substance transfer modellng n multstage, multcomponent reactve dstllaton, Comput. Ecol. Eng., (p.-. [] Fuller E.N., P.D.Schetter, J.C.ddngs, Ind.Eng.Chem.5,(9 p.9. [7uss.A.,.A.Ratclff, Can. J. Chem. Eng. (9 35. []effler J., H.T Cullnan, Varaton of lqud dffuson coeffcents wth composton-bnary systems, Ind. Eng.Chem. Fundamentals, 9(97p.3-. [9] effler J., H.T.Cullnan, Varaton of lqud dffuson coeffcents wth composton-dlute ternary systems, Ind. Eng.Chem. Fundamentals, 9(97p.-93. ISSN: 79-5 Issue, Volume, October