Correlation for fitting multicomponent vapor-liquid equilibria data and prediction of azeotropic behavior

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1 Al-khwarzm Engneerng Jurnal Al-Khwarzm Engneerng Jurnal, Vl.3, N, pp (7) Crrelatn fr fttng multcmpnent vapr-lqud equlbra data and predctn f azetrpc behavr Dr. Khald Farhd Chasb Al-Jbury Chemcal Engneerng Department Unversty f Technlgy ((Reeccee vveedd SSppt teembbeerr 66 ;; aacccceeppt teedd 44 Apprr ll 77)) Abstract Crrelatn equatns fr epressng the blng temperature as drect functn f lqud cmpstn have been tested successfully and appled fr predctng azetrpc behavr f multcmpnent mtures and the knd f azetrpe (mnmum, mamum and saddle type) usng mdfed crrelatn f Gbbs-Knvalv therem. Als, the bnary and ternary azetrpc pnt have been detected epermentally usng graphcal determnatn n the bass f epermental bnary and ternary vapr-lqud equlbrum data. In ths study, sbarc vapr-lqud equlbrum fr tw ternary systems: -Prpanl Heane Benzene and ts bnares -Prpanl Heane, Heane Benzene and -Prpanl Benzene and the ther ternary system s Tluene Cyclheane s-octane (,,4-Trmethyl-Pentane) and ts bnares Tluene Cyclheane, Cyclheane s-octane and Tluene s-octane have been measured at.35 KPa. The measurements were made n recrculatng equlbrum stll wth crculatn f bth the vapr and lqud phases. The ternary system -Prpanl Heane Benzene whch cntans plar cmpund (-Prpanl) and the tw bnary systems -Prpanl Heane and -Prpanl Benzene frm a mnmum azetrpe, the ther ternary system and the ther bnary systems d nt frm azetrpe. All the data passed successfully the test fr thermdynamc cnsstency usng McDermtt-Ells test methd (McDermtt and Ells, 965). The mamum lkelhd prncple s develped fr the determnatn f crrelatns parameters frm bnary and ternary vapr-lqud epermental data whch prvdes a mathematcal and cmputatnal guarantee f glbal ptmalty n parameters estmatn fr the case where all the measured varables are subject t errrs and the nn dealty f bth vapr and lqud phases fr the epermental data fr the ternary and bnary systems have been accunted. The agreement between predctn and epermental data s gd. The eact value shuld be determned epermentally by eplrng the cncentratn regn ndcated by the cmputed values. Keywrds: Vapr-Lqud Equlbra, Azetrpc Behavr, Multcmpnent system Ths page was created usng Ntr PDF tral sftware. Ô T purchase, g t

2 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) Intrductn The term azetrpe means nnblng by any means (Greek: a - nn, ze - bl, trps - way/mean), and dentes a mture f tw r mre cmpnents where the equlbrum vapr and lqud cmpstns are equal at a gven pressure and temperature. Systems whch d nt frm azetrpes are called zetrpc. Departures frm Rault s law frequently manfest themselves n the frmatn f azetrpes, azetrpes are lqud mtures ehbtng mamum r mnmum blng pnts that represent, respectvely, negatve r pstve devatns frm Rault s law. Als cnstantblng mtures are referred t as azetrpes. They ccur between certan cmbnatns f the cmpnents f the mture r mtures f clseblng speces f dfferent chemcal types. Azetrpes ccur frequently between cmpunds whse blng pnts dffer by less than abut 3 C. If the vapr and lqud are f the same cmpstn, the tw-phase mture s called a hmgeneus azetrpe. The cnstant-blng mtures that ccur wth a vapr and tw r mre dense phases are called hetergeneus azetrpes (Ths s because n rder t get the lqud t phase separate nt tw lqud phases the cmpnents must be hghly repulsve) (Hffman, 964). The y- curve crsses the y = lne (the 45 lne) at the azetrpc cmpstn, n the regn belw ths ntersectn wth the dagnal, the equlbrum vapr s rcher n ne cmpnent than the lqud, abve ths ntersectn, the vapr s prer n ths cmpnent than the crrespndng lqud frm whch t cmes. Fr the sbarc system the temperature versus cmpstn curves cncde at a mnmum at the azetrpc cmpstn. Such azetrpc systems frequently ccur when the tw cmpnents are dssmlar functnally and the blng pnts are nt greatly dfferent f abut 5 C fr mst systems, althugh much greater dfferences are nted n sme systems (mture n whch there s strng repulsn between the dfferent speces), because less thermal energy has t be ntrduced t get mlecules t enter the vapr phase t vercme the attractn n the lqud. A hgh-blng azetrpe dffers frm the lw-blng azetrpe n that the temperature versus cmpstn curves f the sbarc plt Ths page was created usng Ntr PDF tral sftware. Õ T purchase, g t ehbt mamum, the hgh-blng azetrpe s less cmmn than the lw-blng azetrpe, t generally ccurs between cmpnents whse mlecules are smewhat attracted t each ther (mture n whch there s strng attractn between the dfferent speces), because addtnal thermal energy has t be ntrduced t get mlecules t enter the vapr phase t vercme the attractn n the lqud. Fr the T--y dagrams f the dew and bubble curves tuch at sme ntermedate cmpstn where the cestng phases have the same cmpstn. Such a pnt s knwn as an azetrpe and althugh the tw phases cest there at the same temperature, pressure and cmpstn, t s dstngushed frm a crtcal pnt by a dfference n the densty f the phases (Harld, 97). An analyss f the structural prpertes f vapr-lqud equlbrum (VLE) dagrams prvdes a fundamental understandng f the hghly nndeal thermdynamc behavr f azetrpc mtures. The pssblty t graphcally represent the VLE depends n the number f cmpnents n the mture. Phase dagram analyss s an ecellent tl fr ganng nsghts nt the cmple behavr f nndeal ternary mtures. Ternary vapr-lqud equlbrum (VLE) dagrams prvde a graphcal tl t predct qualtatvely the feasble separatns fr multcmpnent azetrpc mtures befre detaled smulatn r epermental study f ther dstllatn (Walas, 985). The man dfference fr ternary and multcmpnent mtures s that an azetrpc pnt s nt necessarly an abslute etreme (mnmum r mamum pnt) f the blng temperature at sbarc cndtn, but t may be a lcal etreme (saddle). The tendency f a mture t frm an azetrpe depends n tw factrs: (a) The dfference n the pure cmpnent (b) blng pnts. The degree f nndealty. The clser the blng pnts f the pure cmpnents and the less deal mture, the greater the lkelhd f an azetrpe. The mprtant pnts abut azetrpes are: They lmt the separatn achevable by dstllatn because even wth nfnte trays,

3 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) there s n thermdynamc drvng frce t separate beynd the azetrpe. The azetrpc pnt can be mved, fr eample by lwerng the pressure, s that the desred cmpstn may be btaned.. In fact, fr sme systems, the azetrpe mght nt even frm f the pressure s changed enugh and the azetrpe can be brken. Azetrpes can be used t help separatns. Addng a thrd cmpnent t a system whch frms a mnmum blng pnt azetrpe wth ne f the rgnal cmpnents can be used t entran that cmpnent, allwng fr t t be vaprzed away and recvered (Marc et al., 998). Thery f azetrpc predctns The ablty t predct azetrpc behavr becmes mre and mre mprtant and cmple when the number f cmpnents n the mture ncrease. Ths predctn s tested successfully by applyng the Gbbs-Knvalv therem (Malesnsk, 965). They develped crrelatn equatns fr epressng blng temperature f the vapr-lqud equlbra data, sbarc cndtns, as a functn f lqud cmpstn, where () N N N O T T j A j j B j Where T s the blng temperature f pure cmpnent n C, and N number f cmpnent n the mture. Ths equatn s useful fr btanng sthermals and fr eplrng the azetrpc behavr f bnary and ternary mtures. The ceffcent A j, B j, and C j are bnary r ternary parameters whch are determned drectly frm the bnary r ternary data. The ncrease n the number f parameters ncreases the predctn accuracy. And anther crrelatn fr predctn azetrpc behavr f the bnary and ternary mtures, and the knd f azetrpe (mnmum, mamum and saddle type), wll be dscussed belw: The Gbbs-Knvalv therem (Malesnsk, 965) fr multcmpnent systems states that the fllwng cndtns are fulflled at j C j j the azetrpc pnt where = y at cnstant pressure: T P, j =,,, N () The nde `j means that the relatnshp T s gven n terms f all mle fractns as ndependent varables, ecept j. The dfferentatn s carred ut by keepng all the mle fractns cnstant ecept. Fr a ternary mture, the applcatn f () namely T T t the ternary frm f 3 P, P, 3 () yeld that: Where O O T T 3.. (3) O O.(4) T T (5) k A k Fr (8) (9) j B j C j j j (6) 3 j 3Dj j 4Ej j Bj C j (7) K = : j = and =. K = : j = 3 and =. K = 3 : j = 3 and = () Equatns (3) and (4) are nnlnear equatns fr the unknwns and and f a ternary mture ehbts azetrpc behavr, the slutn fr and shuld le wthn -. Fr bnary mtures, ne btans frm T that: P, O O T T. () Ths page was created usng Ntr PDF tral sftware. Ö T purchase, g t

4 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) Equatn () s slved numercally and an azetrpe ests f slutn s wthn the nterval < <. The use f ptmzatn technque fr determnng the parameters f the crrelatn by means f sbarc vapr-lqud equlbra requres mnmzatn f an bjectve functn. The bjectve functn s: O. F m bs T T cal () In a multcmpnent mture under sbarc cndtns, there s a pssblty fr an azetrpe wth a mnmum blng pnt, wth a mamum blng pnt and a saddle pnt azetrpe. The thermdynamc cndtns determnng the knd f the multcmpnent azetrpe fr sbarc equlbra may be derved as fllws: () ndcates that the blng temperature f a multcmpnent mture may be epressed as a functn f the lqud cmpstn, namely, T(,,, N- ). Desgnatng by T and the crdnates f the azetrpc pnt and epandng T nt a Taylr seres arund the azetrpc pnt gves: mnrs f the determnant a N- are desgnated as fllws: a a a a a a a a3 ; a a a3 a a3 a3 a33 33 (5) On the bass f therems related t quadratc frms and by cnsderng (3), (4) and (5), the fllwngs can be cncluded cncernng the pssble knds f azetrpes (Table ): Table. Cndtns fr determnatn f knds f multcmpnent azetrpes Mnmum n T - a a a 33 a44... Mamum n T - a a a 33 a44... Plttng calbratn curves Nether mamum r mnmum n T, namely Saddle type behavr Nether ne f the cndtns n the tw left hand clumns s fulflled. (3) T T,, N T,, N j k j Where terms beynd the secnd dervatve were neglected and accrdng t () the frst dervatves vansh at the azetrpc pnt. Equatn (3) s knwn as the quadratc frm and the knd f azetrpe depends n the fllwng determnant: T T T T T T N N T N T a N a an, T N k j a a an, j k k a, N a, N an an, N (4) Where the dervatves are taken at the azetrpc pnt. Fr smplcty, the prncpal Ths page was created usng Ntr PDF tral sftware. T purchase, g t Refractve nde and densty measurements at 3 C were chsen as rapd and accurate methds fr analyss f equlbrum mtures. Calbratn curves analyses f all bnary systems are usually represented graphcally by plttng refractve nde aganst the cmpstns. Cmbnatn f refractve nde and densty measurements were emplyed fr the analyss f the ternary systems graphcally, f the cncentratn f ne f the cnsttuents s kept cnstant whle the ther tw are vared. Ths was dne by nterplatn f prevusly determned refractve nde-cmpstn and denstycmpstn charts. The schematc dagram f the calbratn curve f the ternary system -Prpanl Heane Benzene s llustrated n fgure.a, and the calbratn curve f the ternary system Tluene Cyclheane s-octane s llustrated n fgure.b, ths s a graphcal methd fr analyss f the ternary system. Anther very accurate methd used fr analyss s by the use f cmputer prgram desgned and develped by usng

5 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) Mathcad sftware fr the purpse f fndng the cmpstns f the ternary r bnary systems at a gven refractve nde and densty HEXANE PROPANOL DENSITY REFRACTIVE INDEX BENZENE Fg..a. Trangular plt f Refractve nde Densty Cmpstn (Calbratn curve) f the ternary system -prpanl Heane Benzene at 3 C, n whch lnes f cnstant refractve nde and cnstant densty are pltted. Epermntal wrk Apparatus and prcedure The epermental determnatn f vaprlqud equlbrum data are perfrmed usng a crculatng equlbrum apparatus, Fg., n whch the gas and lqud phases f a mture are crculated cntnuusly at cnstant pressure. The apparatus used was an all-glass recrculatng stll. Ths equpment has a sde-heatng unt whch ensures cmplete mng f the lqud mture. The desgn als prevented lqud drp entranment and partal cndensatn n the vapr phase. The equlbrum temperature were measured by a dgtal thermmeter wth an accuracy f ±. C. In each eperment, the lqud mture was heated n a recrculatng stll at fed pressure f.3 KPa. Equlbrum was reached after h where the temperature f the lqud and vapr phases were cnstant (the blng pnt had becme stable) and ther dfference was wthn. C. Samples f the equlbrum phases were taken at small vlumes and were analyzed by measurng denstes and refractve ndces at 3 C. TOLUENE REFRACTIVE INDEX CYCLOHEXANE s-octane DENSITY Fg.. Flw dagram fr equlbrum apparatus. Fg..b. Trangular plt f Refractve nde Densty Cmpstn (Calbratn curve) f the ternary system Tluene Cyclheane-s-Octane at 3 C, n whch lnes f cnstant refractve nde and cnstant densty are pltted. system selectn Ternary system I Ths page was created usng Ntr PDF tral sftware. T purchase, g t The ternary system I cnssts f - Prpanl, Heane and Benzene and ts bnares. One f the prblems n the feld f etractve dstllatn s t fnd a quanttatve methd f assessng slvents, n term f the physcal prpertes f the cnsttuents, n rder t

6 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) select the mst effcent slvent fr a partcular prcess fr separatng clsely blng cmpunds. The system studed n ths wrk was cmpsed f Heane and Benzene. These hydrcarbns are dffcult t separate because f clseness f blng pnts. -Prpanl was used as a slvent, t determne epermentally the effect f plar cmpnents n the separatn f bnary systems. Als, these hydrcarbns havng dfferent structures cmes frm dfferent grups and frm nn-deal slutn, heane (straght chan) frm alkanes grup and benzene frm armatcs grup and -prpanl frm alchls grup. Ternary system II The ternary system II cnssts f Tluene, Cyclheane and s-octane (,,4-Trmethylpentane) and ts bnares. Armatc hydrcarbns have lng been knwn t shw nn-deal characterstcs when med wth ther type f hydrcarbns. In the cmmercal prductn f tluene frm petrleum, the tluene must be separated frm hydrcarbns havng abut the same blng pnt, thus the separatn f Tluene as a pure cmpund by rdnary fractnatn s very dffcult. Als, the mprtance f usng s-octane (,,4-Trmethyl-pentane) as the central cmpnent n an nvestgatn f rentatn effects n the pure lqud cmpnents. The system studed n ths wrk was cmpsed f Tluene, Cyclheane and s- Octane (,,4-Trmethyl-pentane). These hydrcarbns havng dfferent structures cme frm dfferent grups and frm nn-deal slutn, cyclheane and s-ctane frm alkanes grup and tluene frm armatcs grup. Publshed data fr cnsttuent bnary systems -prpanl heane, heane benzene, -prpanl benzene, and tluene cyclheane were reprted n the lterature (Hala et al., 968; Ohe, 989; Hrata et al., 975). T ur knwledge, n sbarc r sthermal VLE epermental data have been reprted prevusly n the lterature fr the bnary systems cyclheane s-ctane and tluene s-ctane, and fr the tw ternary systems -prpanl heane benzene, and tluene cyclheane s-ctane. Pssble epermental wrk errrs Systematc errrs n the eperments can be ruled ut snce all the analytcal methds were carefully cntrlled (recheckng the analytcal prcedure) and all the measurements were duplcated. The value f the epermental results depends n the care emplyed by the epermentalst n elmnatng surces f errr. Obtanng gd epermental data requres apprecable epermental skll, eperence and, patence. Pssble causes f the devatn were due t the fact that the mtures were nt deal mtures r due t naccuracy f refractmeter, thermmeter r barmeter r ncrrect readng ff f ther values. The lmt f errr n readng the refractmeter was ne n the ffth place, and dd nt vary ntceably fr varus mtures. The estmated precsn f the equlbrum mture cmpstn measurements was ±. mle fractn fr the lqud phase and ±.5 mle fractn fr the vapr phase. The estmated uncertantes n the equlbrum temperature and pressure were ±. C and.5 mmhg, respectvely. Care was taken t assure that equlbrum really ested, that the temperature and pressure were measured at the pstn where equlbrum ested, and that the takng f samples fr analyss dd nt dsturb the equlbrum apprecably. Thermdynamc cnsstency test One f the greatest arguments n favr f btanng redundant data s the ablty t assess the valdty f the data by means f a thermdynamc cnsstency test. The cnsstency f the epermental data was eamned t prvde nfrmatn n the thermdynamc plausblty r ncnsstency and t recgnze any devatns f the measured values. Accrdng t McDermtt-Ells test methd, tw epermental pnts a and b are thermdynamcally cnsstent f the fllwng cndtn s fulflled (McDermtt and Ells, 965): D < D ma (6) The lcal devatn D s gven by D N a b ln b ln a (7) Ths page was created usng Ntr PDF tral sftware. T purchase, g t

7 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) In ths methd, t s recmmended the use f a fed value f. fr D ma f the accuracy n the measurement f the vapr and the lqud mle fractn s wthn.. The lcal mamum devatn, D ma, due t epermental errrs, s nt cnstant, and s gven by D System I ma N N a b a y a b y b y N N P ln bln a a b P (8) a b t ta tb table. Results f Thermdynamc Cnsstency Test. System D D ma Cnsstency Thermdynamc Test -Prpanl Heane.43.6 Pass Heane Benzene.6. Pass -Prpanl Benzene.74.9 Pass the Mean Overall Devatn and Average Abslute Devatn. The Mean Overall Devatn mean D % s a mre tangble element ndcatng the verall gdness f the ft f the data by the crrelatn and t reads: mean D % n bsd calcd M M bsd M Average Abslute Devatn AAD n bsd n calcd. (9) M M () AAD n where M s an ntensve prperty and n s the number f data pnt. These equatns are used t calculate Mean Overall Devatn mean D% and Average Abslute Devatn AAD f epermental results f bnary and ternary systems. Azetrpc predctns System II -Prpanl Heane Benzene Tluene Cyclheane Cyclheane s- Octane Tluene s- Octane Tluene Cyclheane s- Octane.3.35 Pass.96.3 Pass.53.8 Pass.78.4 Pass.46.6 Pass The cnclusn can be drawn that all the data are thermdynamcally cnsstency Statstcal measurement and analyss f dspersn T knw the applcablty and accuracy f any prpsed crrelatn t s very mprtant t knw hw ths crrelatn fts the epermental data whch s dne by cmparng the btaned results frm the prpsed crrelatn wth the epermental data. The varus measurement f dspersn r varatn are avalable, the mst cmmn beng Ths page was created usng Ntr PDF tral sftware. Ð T purchase, g t The wde cncentratn feld whch must be nvestgated epermentally n rder t detect an azetrpe n the ternary mtures, reflects the mprtance f the crrelatn t be able t predct azetrpc behavr. The blng temperature f the mture was crrelated wth the lqud cmpstn by the fllwng equatn: T N T O N N j j A j B j j C j j () Where T s the blng temperature f pure cmpnent n C, and N number f cmpnent n the mture. Ths equatn s useful fr btanng sthermals and fr eplrng the azetrpc behavr f bnary and ternary mtures. The ceffcent A j, B j, and C j are bnary r ternary parameters whch are determned drectly frm the bnary r ternary data. The ncrease n the number f parameters ncreases the predctn accuracy. Fr eplrng the azetrpc behavr f bnary and ternary mtures equatn () was slved smultaneusly wth equatns 3. An

8 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) azetrpe ested f slutn s wthn the nterval < <. If the cmputatns dd nt yeld a slutn whch crrespnds t a true azetrpe, the system wuld nt ehbt azetrpc behavr. The fllwng eperment was perfrmed n rder t check the valdty f the predcted values. Ternary slutns wth the calculated cmpstns were prepared and ntrduced n the recrculatng stll. The system was bled untl equlbrum was acheved. The analyss yelded the equlbrum cmpstns f the vapr and lqud. It was seen that the lqud cmpstn devated very small frm the vapr cmpstn, the cmputed values dd nt crrespnd t true azetrpes. On the ther hand, the true value f the azetrpc pnt was dentcal t the slutn r was lcated n ther vcnty. It was bserved that the azetrpc blng temperature was very accurately predcted than the cmpstn. The reasn fr ths behavr s due t the fact that varatns n the temperatures n the vcnty f the azetrpc pnt are usually relatvely small n cmparsn t the cncentratn (Andersn et al., 978). dscussn f results In rder t assess the relablty f epermental results, the equlbrum curves were pltted and cmpared wth thse frm lterature (Hala et al., 968; Ohe, 989; Hrata et al., 975), as shwn n fgures 3 t 8. It may be seen that there s gd agreement between the epermental data f ths wrk and the epermental data frm lterature and cnfrms the relablty f ths wrk. The fact that the equlbrum curves fr bth bnares - Prpanl Heane and - Prpanl Benzene crss the 45 lne ndcates that they frm azetrpes. Mle Fractn f Heane n Vapr Equlbrum Curve Epermental data Lterature data Mle Fractn f Heane n Lqud Fg. 3. Vapr - Lqud equlbrum Dagram n Bnary system f - Prpanl Heane. Mle Fractn f Heane n Vapr Equlbrum Curve Epermental data Lterature data Mle Fractn f Heane n Lqud Fg. 4. Vapr - Lqud Equlbrum Dagram n Bnary system f Heane Benzene. Ths page was created usng Ntr PDF tral sftware. Ñ T purchase, g t

9 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) Mle Fractn f Benzene n Vapr Equlbrum Curve Epermental data Lterature data Mle Fractn f Cyclheane n Vapr Equlbrum Curve Epermental data Mle Fractn f Benzene n Lqud Mle Fractn f Cyclheane n Lqud Fg. 5. Vapr - Lqud Equlbrum Dagram n Bnary System f - Prpanl Benzene. Fg. 7. Vapr Lqud Equlbrum Dagram n Bnary system f Cyclheane - s- Octane...9 Mle Fractn f Cyclheane n Vapr Equlbrum Curve Epermental data Lterature data Mle Fractn f Cyclheane n Lqud Fg. 6. Vapr - Lqud equlbrum Dagram n Bnary system f Tluene Cyclheane. Mle Fractn f s-octane n Vapr Equlbrum Curve Epermental data Mle Fractn f s-octane n Lqud Fg. 8. Vapr - Lqud Equlbrum Dagram n Bnary System f Tluene - s-octane. The T--y dagrams were pltted at sbarc cndtn, fgures 9 t 4. All thse epermental results were cmpared wth lterature. It may be seen that there s gd agreement between the epermental data f ths wrk and the data frm lterature. The bnary mtures f tluene cyclheane and tluene s-ctane are nearly deal slutn. The ther bnary mtures shwed pstve devatns. Ths page was created usng Ntr PDF tral sftware. Ò T purchase, g t

10 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) T--y Curves TEMPERATURE, C T--y Curves Lqud phase epermental data Lqud phase lterature data Vapr phase epermental data Vapr phase lterature data TEMPERATURE, C Lqud phase epermental data Lqud phase lterature data Vapr phase epermental data Vapr phase lterature data Mle Fractn f Heane Mle Fractn f Benzene Fg. 9. Blng Pnt - Cmpstn Curve fr - Prpanl Heane at 76 mmhg. Fg.. Blng Pnt - Cmpstn Curve fr - Prpanl Benzene at 76 mmhg T--y Curves Lqud phase epermental data Lqud phase lterature data Vapr phase epermental data Vapr phase lterature data 5 T--y Curves Lqud phase epermental data Lqud phase lterature data Vapr phase epermental data Vapr phase lterature data TEMPERATURE, C TEMPERATURE, C Mle Fractn f Heane Mle Fractn f Cyclheane Fg.. Blng Pnt - Cmpstn Curve fr Heane Benzene at 76 mmhg. Fg.. Blng Pnt - Cmpstn Curve fr Tluene Cyclheane at 76 mmhg. Ths page was created usng Ntr PDF tral sftware. Ó T purchase, g t

11 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) TEMPERATURE, C T--y Curves Lqud phase epermental data Vapr phase epermental data Mle Fractn f Cyclheane Fg. 3. Blng Pnt - Cmpstn Curve fr Cyclheane - s-octane at 76 mmhg. TEMPERATURE, C T--y Curves Lqud phase epermental data Vapr phase epermental data Mle Fractn f s-octane Fg. 4. Blng Pnt - Cmpstn Curve fr Tluene - s-octane at 76 mmhg. accuracy (the estmated precsn f the equlbrum mture cmpstn measurements was ±. mle fractn fr the lqud phase and ±.5 mle fractn fr the vapr phase. The estmated uncertantes n the equlbrum temperature was ±. C). The average scatter f the epermental pnts frm the best lne s less than that f the prevus nvestgatns n the lterature. Fr system I the epermental data fr all the three bnares shw that they are nn-deal n nature. When studyng the equlbrum f heanebenzene, the bservatn made n ths nvestgatn was that n separatn btanable at cncentratn abve 97 mle % heane. The - prpanl-heane and -prpanl-benzene systems shw mnmum blng azetrpes. Fr system II the tluene-cyclheane system des nt frm an azetrpe, but t seems that there s a tendency tward azetrpe frmatn at hgh cyclheane cncentratn (at lw-blng ends f the T--y dagram). The cyclheane s-ctane system shws nearly deal behavr. The tluene s-ctane system des nt frm an azetrpe, but t seems that there s a tendency tward azetrpe frmatn at hgh s-ctane cncentratn. Table 5 ndcates the azetrpc cmpstn and temperature f these bnares. The dstrbutn f the epermental vaprlqud equlbrum data fr ternary systems n the cmpstn trangle dagram may be readly apprecated. These dstrbutns were presented n fgures 5 and 6. Each equlbrum cmpstn s shwn n fgures 5 and 6 by an arrw, wth the flght end representng the cmpstn f the lqud phase and the arrwhead that f the vapr phase. The epermental data fr bnary system were fund t be n clse agreement wth the reprted values f the lterature. There was n evdence f errneus data at the entre cncentratn range because n scatterng pnts were bserved and all the pnts f data fall n smth curves, shwng the epermental values t be cnsstent. The dfference between the epermental pnts and the smthng curves are wthn the analytcal Ths page was created usng Ntr PDF tral sftware. Ô T purchase, g t

12 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) HEXANE PROPANOL BENZENE frm the epermental data by graphcal nterplatn. - Prpanl ( 97. C ) C C 79.6 C C Fg. 5. Cmpstn dagram fr the ternary mture - Prpanl + Heane + Benzene flght end f arrws ( ) ndcate equlbrum cncentratns f the lqud phase at 76 mmhg and the arrwheads ( ) crrespndng vapr phase cmpstns. Heane ( 68.7 C ) C 7.37 C 7.45 C C 75. C C C Benzene ( 8. C ) Fg. 7. Cmpstn dagram fr the lqud phase f the ternary mture Prpanl + Heane + Benzene, shwng cnstant blng temperature cnturs at 76 mmhg. CYCLOHEXANE TOLUENE s - OCTANE Fg. 6. Cmpstn dagram fr the ternary mture Tluene + Cyclheane + s- Octane flght end f arrws ( ) ndcate equlbrum cncentratns f the lqud phase at 76 mmhg and the arrwheads ( ) crrespndng vapr phase cmpstns. Fgure 7 shws equlbrum stherms n the lqud phase cmpstn dagram btaned Fgure 7 shws a sharp temperature drp ccurs frm the heane benzene bnary as small amunts f -prpanl are added. The drp s less severe at hgh heane cncentratns. The nterr f the surface s nearly flat at pnts reasnably remved frm the pure substances. The flat nterr als rses rapdly as pure -prpanl s reached. A trugh wth nly slght curvature cnnectng the tw bnary azetrpes (-prpanl heane and -prpanl benzene). The surfaces rsng frm the trugh tward pure -prpanl and als tward the heane benzene bnary shw slghtly utward curvature. The ternary system I shwn n fgure 8 ehbts a ternary azetrpe. The azetrpc cmpstn and temperature f the tw bnares are shwn n the same fgure. In ths system, hwever, there s a pnt,, where blng temperature s lwer than any f the blng temperatures f the three pure cmpunds. Ths cmpstn s knwn as the ternary azetrpe. The lnes f cnstant blng temperature surrundng the azetrpc cmpstn, and as ne prceeds away frm the successve Ths page was created usng Ntr PDF tral sftware. Õ T purchase, g t

13 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) stherms that are ntersected represent ncreasng blng temperatures. Fg. 9. Spatal plt f the ternary system shws the regn f the ternary azetrpe C Heane ( 68.7 C ) 67. C 67.9 C 68. C 68.5 C -Prpanl ( 97. C ) 76 C Benzene ( 8. C ) Fg. 8. Cmpstn dagram fr the lqud phase f the Ternary mture Prpanl + Heane + Benzene, shwng cnstant blng temperature cnturs and the lcatn f the ternary and bnary azetrpe at 76 mmhg. N ternary azetrpe was detected epermentally n the ternary system II as shwn n fgures and, and the predctn methd dd nt dscver any mamum r mnmum wth the nterr f the phase surface, hence, the system des nt cntan ternary azetrpe. Als, the shape f curves ndcates that the system des nt ehbt azetrpc behavr. Isthermals fr bth ternary systems were btaned as shwn n fgures 7 and. The prmnent fact whch may be cncluded frm the behavr f the sthermals n fgure 7 s the estence f a ternary mnmum blng pnt azetrpe n the - Prpanl + Heane + Benzene system. On the ther hand, t may be cncluded frm fgure that the system Tluene + Cyclheane + s-octane des nt ehbt a ternary azetrpe. Tluene (.9 C ) In rder t determne the crdnates f the ternary azetrpe, fgure 9 was drawn. It s a spatal plt f the regn where the azetrpc pnt mght be lcated (a crater-lke shape r valley) C 3.5 C.59 C 98.5 C C C C C C 94.9 C C 89.7 C 87.9 C C C 8.86 C 84.4 C 8. C Cyclheane ( 8.4 C ) s-octane ( 99 C ) Temperature C 97. C 68.7 C Fg.. Cmpstn dagram fr the lqud phase f the ternary mture Tluene + Cyclheane + s-octane, shwng cnstant blng temperature cnturs at 76 mmhg. -Prpanl 67. C Heane Ths page was created usng Ntr PDF tral sftware. Ö T purchase, g t

14 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7).9 C 8 8 Temperature C 99 C T ( C ) calc Tluene s-octane C Cyclheane Fg.. Spatal plt f the ternary system Tluene + Cyclheane + s-octane T ept. ( C ) Fg.. Cmparsn f calculated and epermental temperature results fr Heane Benzene system A cmparsn f calculated and epermental temperature results usng equatn s gven n fgure, the ther results f bnary and ternary systems are llustrated n fgures 3 t 9. If there s cmplete agreement between epermental and predcted temperature values, all the pnts wuld fall n the 45-degree lne. It seem frm fgure that the equatn s useful fr btanng sthermals and fr eplrng the azetrpc behavr fr bnary and ternary system because the devatn f all the pnts frm the 45 lne s small. The cmparsn wth epermental temperature values ndcates that the calculatns shw rather gd agreement wth the data as llustrated n fgures t 9. The value f the parameter f equatn and cmparsn between epermental and calculated temperature fr bnary systems are llustrated n table 3. And, The value f the parameter f equatn and cmparsn between epermental and calculated temperature fr ternary systems are llustrated n table 4. T ( C ) calc T ept. ( C ) Fg. 3. Cmparsn f calculated and epermental temperature results fr - Prpanl Heane system. Ths page was created usng Ntr PDF tral sftware. T purchase, g t

15 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) T ( C ) calc. 85 T ( C ) calc T ept. ( C ) Fg. 4. Cmparsn f calculated and epermental temperature results fr - Prpanl Benzene system T ept. ( C ) Fg. 6. Cmparsn f calculated and epermental temperature results fr Cyclheane s-octane system T ( C ) calc. 96 T ( C ) calc T ept. ( C ) Fg. 5. Cmparsn f calculated and epermental temperature results fr Tluene Cyclheane system T ept. ( C ) Fg. 7. Cmparsn f calculated and epermental temperature results fr Tluene s-octane system. Ths page was created usng Ntr PDF tral sftware. T purchase, g t

16 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) T ( C ) calc T ept. ( C ) Fg. 8. Cmparsn f calculated and epermental temperature results fr - Prpanl Heane Benzene system 5 devatns fr all tw ternary systems f.78 and.959 respectvely, fr 56 data pnts. Cmparsn between epermental and lterature [9] and calculated values usng equatn and equatns 3 t f the azetrpc pnt fr the bnary systems are llustrated n table 5, and fr the ternary systems were llustrated n table 6. It seems frm tables 5 and 6 that the calculated temperature and cmpstn f azetrpc pnt f bnary and ternary systems and detectng the type f azetrpc pnt by usng equatn wth equatns 3 t gves gd results cmparng wth the epermental and lterature data. Table 3. The value f the parameter f equatn () and cmparsn between epermental and calculated temperature fr bnary systems. T ( C ) calc T ept. ( C ) Fg. 9. Cmparsn f calculated and Epermental temperature results fr Tluene Cyclheane s-octane system As the table 3 ndcates that the equatn gves values that have an verall average abslute devatns (AAD) and verall percentage mean devatns fr all s bnary systems f.7 and.33 respectvely, fr 38 data pnts. As the table 4 ndcates that the equatn gves values that have an verall average abslute devatns (AAD) and verall percentage mean Ths page was created usng Ntr PDF tral sftware. T purchase, g t

17 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) Table 4. The value f the parameter f equatn () and cmparsn between epermental and calculated temperature fr ternary systems System I System II Parameters -Prpanl + Tluene + Heane + Cyclheane Benzene + s-octane A A A B B B C C C D D D E E E N. f data pnts Overall Errr Mean D % AAD Cnclusn Based n ths study, the fllwng cnclusns can be made:. The recrculatng apparatus used wth all accessres prved t be very sutable fr btanng VLE data.. All the data btaned are thermdynamcally cnsstent because they passed the thermdynamc cnsstency test f McDermtt-Ells test methd. 3. A bnary azetrpe s an etremal pnt f the bnary mture temperature functns. Whle a ternary azetrpe s nt necessary a glbal temperature etreme fr the ternary mture, thus beng a saddle pnt f the temperature surface. 4. Ternary mtures may ehbt dstnctly dfferent stherm maps dependng n the estence f azetrpes, ther type (mnmum-, mamum- r saddle blng), ther lcatn, and the relatve rder f the blng pnts f the pure cmpnents. 5. Equatn whch s a mdfed crrelatn f Gbbs-Knvalv therem s very mprtant fr btanng sthermals and fr eplrng the azetrpc behavr f bnary and ternary systems. (a) Usng equatn fr the s bnary systems f 38 data pnt gve an verall average abslute devatns (AAD) and an verall percentage mean devatns f.7 and.33 respectvely. (b) Usng equatn fr the tw ternary systems f 56 data pnt gve an verall average abslute devatns (AAD) and an verall percentage mean devatns f.78 and.959 respectvely. Table 5. Cmparsn between epermental and lterature and calculated values f the azetrpc pnt fr the bnary systems Epermental Lterature Bnary system Temperature C -Prpanl() + Heane() System I Heane() + Benzene() -Prpanl() + Benzene() Tluene()+ Cyclheane() Ths page was created usng Ntr PDF tral sftware. Ð T purchase, g t System II Cyclheane()+ s-octane() Tluene() + s-octane() Temperature C Temperature C Calculated Azetrpc type Mnmum N Mnmum N N N blng azetrpy blng azetrpy azetrpy azetrpy

18 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) Table 6. Cmparsn between epermental and lterature and calculated values f the azetrpc pnt fr the ternary systems Ternary system Epermental Lterature Calculated System I -Prpanl () + Heane () + Benzene (3) System II Tluene()+ Cyclheane() + s-octane(3) Temperature C Temperature C 3 Temperature C N data N data Azetrpc type Mnmum Blng Azetrpy N azetrpy Ths page was created usng Ntr PDF tral sftware. Ñ T purchase, g t

19 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) References Andersn, T. F., Abrams, D. S., Grens, E. A., Evaluatn f parameters fr Nnlnear Thermdynamc Mdels, AIChE J., 4,, 978. Hala, E., Pck, J., Fred, V., and Vlm O., Vapr-Lqud Equlbrum, nd ed., Pergamn press, Lndn, 968. Harld, R. N., Phase Equlbrum n Prcess Desgn, Wley-Interscence Publsher, New Yrk, 97. Hrata, M., Hen, S., and Nagahama, K., Cmputer Aded Data Bk f Vapr-Lqud Equlbra, Kdansha Lmted, Tky, 975. Hffman, E. J., Azetrpc and Etractve Dstllatn, Interscence Publsher, New Yrk, 964. Malesnsk, W., Azetrpy and ther Theretcal Prblems f Vapr-Lqud Equlbrum, Interscence, PWN, New Yrk, 965. Marc, J. A., Martn, J. P. and Thamas, F. T., Thermphyscal Prpertes f Flud, An ntrductn t ther predctn, Imperal Cllege Press, frst reprnt, 998. McDermtt, C., Ells, S. R. M., A Multcmpnent Cnsstency Test, Chem. Eng. Sc.,, 93, 965. Ohe, S., Vapr-Lqud Equlbra Data Bk, Elsever Scentfc Publshng Cmpany, Netherlands, 989. Walas, S. M., Phase Equlbra n Chemcal Engneerng, Butterwrth Publshers, Lndn, 985. Ths page was created usng Ntr PDF tral sftware. Ò T purchase, g t

20 Dr. Khald Farhd Chasb Al-Jbury /Al-khwarzm Engneerng Jurnal,Vl.3, N. PP67 86 (7) علاقات ریاضیة لتمثیل بیانات توازن بخار ساي ل للا نظمة المتعددة وللتنبو بحالة الا یزوتروب د. خالد فرھود قسم الھندسة الكیمیاویة الجامعة التكنولوجیة الخلاصة: علاقات ریاضیة للتعبیر عن درجة حرارة غلیان الخلاي ط للا نظمة المتعددة كدالة مباشرة لتركیز الساي ل تم اختبارھا بنجاح وطبقت للتنبو بحالة الا یزوتروب للخلاي ط المتعددة وكذلك لایجاد نوع الا یزوتروب (أقل درجة حرارة أعلى درجة حرارة نوع ثابت درجة الحرارة) باستخدام العلاقات المطورة لنظریة ) - Gbbs (Knvalv كذلك نقطة الا یزوتروب للا نظمة الثناي یة و الثلاثیة تم التحقق منھا بصورة عملیة باستخدام التعیین البیاني على أساس البیانات العملیة لتوازن بخار ساي ل للا نظمة الثناي یة والثلاثیة. في ھذه الدراسة تم قیاس توازن بخار ساي ل بثبوت الضغط الجوي لا ثنین من الا نظمة الثلاثیة وھي" ١ - بروبانول - ھكسان بنزین" وكذلك الا نظمة الثناي یة التابعة لھ وھي " ١ -بروبانول ھكسان ھكسان بنزین و ١ -بروبانول بنزین"وكذلك للنظام الثلاثي الا خر وھو "تلوین ھكسان حلقي ایزو أوكتان (٢ ٢ ٤ ثلاثي مثیل بنتان)" وكذلك الا نظمة الثناي یة التابعة لھ وھي (تلوین ھكسان حلقي ھكسان حلقي ایزو أوكتان و تلوین ایزو أوكتان) تم قیاسھا جمیعا في ظروف ١٠١.٣٢٥ كیلوباسكال. القیاسات تمت في برج التوازن الدوار الذي یتم من خلالھ تدویر كلا الطورین البخار والساي ل. النظام الثلاثي " ١ -بروبانول - ھكسان بنزین" الذي یحتوي مركب قطبي وھو " ١ -بروبانول" وكذلك اثنین من الا نظمة الثناي یة وھي " ١ -بروبانول ھكسان و ١ -بروبانول بنزین" تكون حالة الا یزوتروب نوع أقل درجة حرارة. النظام الثلاثي الا خر وكذلك الا نظمة الثناي یة الباقیة لا تكون حالة الا یزوتروب. كل النتاي ج العملیة اجتازت بنجاح اختبار الصحة والدقة من الناحیة الثرمودینامیكیة باستخدام طریقة الاختبار ل.(McDermtt-Ells) طریقة الاختیار الا فضل المسماة Prncple) (Mamum Lkelhd استخدمت لا یجاد ثوابت العلاقات باستخدام البیانات العملیة لتوازن البخار ساي ل للا نظمة الثناي یة والثلاثیة وھذه الطریقة تضمن من الناحیة الریاضیة والحسابیة الاختیار الا فضل لقیم الثوابت في العلاقات حیث إنھا تعمل في حالة كل المتغیرات المقاسة تكون معرضھ للخطا وكذلك عندما تكون حالة اللا مثالیة في كلا الطورین البخار والساي ل للا نظمة الثلاثیة والثناي یة. التقارب بالقیم جید بین البیانات المتنبا بھا والتي تم قیاسھا عملیا. القیم الصحیحة یجب أن تعین تجریبیا بواسطة استكشاف منطقة التركیز التي یتم حسابھا بواسطة النتاي ج المحسوبة من ھذه العلاقات الریاضیة. Ths page was created usng Ntr PDF tral sftware. Ó T purchase, g t