Substance and heat transfer in multistage systems

Transcription

1 aa Ivanovc-Kneevc Internatonal Journal of Appled Physcs Substance and heat transfer n multstage systems AJA IVANOVIC-KNEZEVIC Faculty of Technology and etallurgy, The Unversty of Belgrade, Karnegeva,000 Belgrade, Serba,emal: maa@tmf.bg.ac.rs Abstract:- In ths paper smultaneously substance and heat transfer n the multstage system was nvestgated. Substance transfer between lqud and gas phases n a dstllaton packed column was consdered. 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 heght of the equlbrum stages. 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 examnaton was performed by computer smulaton and experments. Keywords: ateral and heat transfer, heght of transfer unt, heght of equlbrum plate, substance transfer coeffcent, bnary system, dstllaton column. Introducton 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 conons. 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 the papers[]-[0]. 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 [7] 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 [8] 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.[9]. 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 ISSN: Volume, 07

2 aa Ivanovc-Kneevc Internatonal Journal of Appled Physcs 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 prelmnary constructon of the equlbrum curve and the operatng lnes of the separaton process. 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 [9]-[0]. 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. Smultaneous materal and heat transfer n the staged gas-lqud system 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 Energy balance for steady state conons: Energy balance for the vapor phase of the element s, H H N d Q d 0 ( Δ Fg. Substance transfer n the gas-lqud system n packed bed Energy balance for the lqud phase of the element s, h h N d Q d 0 (7 Energy balance for the vapor phase whch ncludng vapor phase, nterphase and vapor flm and reacton heat of the element s: where E so called vaporaton effcency for any element. For equlbrum conons when vapor and lqud phases pressure and temperatures are equal then, y V E x ( f / f (3 If the both vapor and lqud phases can be consdered as V deal soluton, then can be denoted wth K f / f. ateral balance for steady state conons: ateral balance for the vapor phase of the element s: N d ( and for the lqud phase, N d 0 (5 0 H H NHd Q d d( U H (8 Energy balance for the lqud phase whch ncludng lqud phase, lqud flm, nterphase and vapor flm and reacton heat of the element s, d( U h h h Nhd Q d (9 3 Substance transfer rate Substance transfer drvng force between gas and lqud phase can be defned as: t t m m dc (0 k a( c c ( k a( c c ( / ISSN: Volume, 07

3 aa Ivanovc-Kneevc Internatonal Journal of Appled Physcs dc where 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: 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 Sdk 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: 0 y dy x dx d x (8 as( y y k as( x x y ko By ntegraton between top and bottom of the column s determne total column heght Z. k as O dy xd dx (9 x y k as B x x yd Z y B O y O 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.(0-(. m' ( HTU ( HTU ( HTU ( HTU O ( HTU ( HTU m' O (0 ( where m / and /m, (m =K are absorpton and desorbton factors. Equlbrum stage method and transfer unt method comparson The equlbrum stage method for characteraton of the dffculty 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 easer than ntegraton wth respect to the drvng force. The equlbrum curve and the operatng lne can almost always be lnear 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 Columns wth packng 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 ISSN: Volume, 07

4 aa Ivanovc-Kneevc Internatonal Journal of Appled Physcs 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 conons, 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 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 0. 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 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, stage wse 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. Expermental secton The expermental setup has shown n Fg.. The expermental data were obtaned n a ordnary glass dstllaton column wth a packng heght of 000 mm and a dameter of 33 mm. The average dameter of packng partcle Rashg rngs 0. x 0. cm. The bed vod fracton was 0.0, and the specfc surface of packng 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-00 were used. The experments were carred out by batchwse dstllaton operaton and were sem-contnuous n adabatc Fg.(a Scheme of the laboratory dstllaton column wth temperature and pressure acquston system conons. 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 90mol% acetc acd and 0mol% p-xylene. Holdup on each stage was 0. 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 ISSN: Volume, 07

5 aa Ivanovc-Kneevc Internatonal Journal of Appled Physcs determned and shown n Fg.. The optmal flow rate through the column was establshed at 0.5 m/s. Fg. 3 shows dependence dstllate qualty of vapor velocty, through the column under nfnte reflux rato R=, and optmal hydrodynamc regon. Fg.(b Expermental set up NTU s gven by the ares under the curve betwee lmts of ntegraton. x, mol/mol Fg. (b Expermental set up Fg.3 Press w,m/s Fg.3 Top xylene composton versus gas velocty for the ntal charge mxture 0%mol xylene and 90mol% acetc acd (R= p/,m/s w,m/s Fg. Pressure drop vs. gas velocty 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 coordnates 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 realed usng Smpon s rule. An algorthm was derved and program module was developed n Fortran programmng language. Fg. shows the substance transfer dffuson coeffcents vs. vapor velocty. 7 Concluson 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. ISSN: Volume, 07

6 aa Ivanovc-Kneevc Internatonal Journal of Appled Physcs k O k O k O k O T-temperature, K U-hold up, mol y- vapor composton y - equlbrum composton x-lqud phase composton V-volume,cm 3 w-gas phase velocty, cm/s - column heght, cm 0-8 Subscrpt -gas -lqud O-overall lqud phase O-overall gas phase reek Symbol -relatve volatlty w, m/s Fg. The expermental values of the volumetrc substance transfer coeffcents for acetc acd xylene n the both lqud and gas phases vs. flow rate (R= Notaton c-concentraton, mol/ cm 3 E-vaporaton effcency f-fugacty -gas flow rate, mol/s g-gravtatonal acceleraton, cm/s H-enthalpy of the lqud phase, J/mol h- enthalpy of the vapor phase, J/mol HETP-Heght of equvalent theoretcal plate, cm HTU- Heght of transfer unt, cm (HTU, (HTU - heght of transfer unt over the lqud and gas phase, respectvely, cm K- equlbrum constant 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, mol/s -total number of component m - equlbrum phase rato(= /[ ( 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 S-radal column surface, cm References [] T.osornac, J.Savkovc-Stevanovc, A multstage, multphase and multcomponent process system modellng, Internatonal Journal of athematcal odels and ethods n Appled Scence,5(-,0. []Bassyon A.A., cdanel R., Holland C.D.,Chem. Eng.Sc. 5(970 p.37. [3] 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 (970 p.33. [5] cdanel R.,Holland C.D., Chem. Eng.Sc. 5 (970p.83. [] Rubac R.E., cdanel R., Holland C.D., Chem Eng. Sc. 5(970p.383. [7] Rukensten E.,AIChE J, (970 p.. [8] Dutka E.,Rukensten E., Cheme et Industre ene Chmque 0(97 p.35. [9] 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.85. [0] Savkovc-Stevanovc J.,HETP n packed dstllaton column wth assocated systems, Chem.-Ing.-Techn. 57 (985 p.38.. ISSN: Volume, 07