The thermodynamics of alcohols-hydrocarbons mixtures

Transcription

1 MATEC Web of Conferences 3, (2013) DOI: / matecconf/ C Owned by the authors, publshed by EDP Scences, 2013 The thermodynamcs of alcohols-hydrocarbons mxtures R. Prvat 1, J.-N. Jaubert 1, and M. Molère 2 1 Laboratore Réactons et Géne des Procédés (LRGP), Unversté de Lorrane, Nancy 54000, France 2 GE Energy Products Europe, 20 Avenue du Maréchal Jun, BP 379, Belfort Cedex, France Alcohols/hydrocarbons blends represent mportant products n the ndustry and remarkable systems from the thermodynamc standpont, especally n presence of traces of water. In automotve applcatons, ethanol s ncorporated n ncreasng proportons nto car fuel formulatons for envronmental and economc reasons. From a thermodynamc vewpont, the strongly polar nature of ethanol versus the rather apolar character of hydrocarbons makes the study of such blends partcularly nterestng n terms of vapor pressure and mscblty behavor. A long term collaboraton between GE Energy- Europe (Belfort, France) and the Thermodynamcs Team of the LRGP laboratory (Nancy, France) has been conducted to mprove the knowledge of these systems, usng the UNIFAC thermodynamc theory. Frst, blends of anhydrous ethanol and naphtha class hydrocarbons have been studed n terms of volatlty: a strong lqud/vapor non-dealty effect has been put n evdence and numercally characterzed. In a further step, blends of hydrated ethanol and hydrocarbons featurng dverse compostons have been the matter of a thermodynamc modelng that confrmed the paramount role played by the mosture content of ethanol on the mscblty, usng the Maxmum Mscblty Temperature ( TMM ) concept; ths study also ponted out the non-neglgble nfluence of the PONA data and sulfur speces of the hydrocarbon cut. Later on, other alcohols namely methanol, sopropanol and n-butanol, that may play an mportant role n future green fuel formulatons, were ncluded n ths study that showed an nterestng chan length effect. Recently, the team has started a study of the effect of bodesel addtons on the TMM of hydrated alcoholhydrocarbon mxtures. Ths paper summarzes the methodology and the results of the mult-step, collaboratve modelng study developed n the feld of ethanol/hydrocarbon thermodynamcs. hydrocarbon car fuels and ncrease ther octane number (RON) whle mprovng vehcle emssons. Industral alcohols often contan a non-neglgble amount of water (that can reach 10 % n mass). From a thermodynamc pont of vew, the addton of an ndustral alcohol (even n small quanttes) to a gasolne or a gasol strongly mpacts on all phase equlbra. GE and the thermodynamc team of the LRGP are conductng a collaboratve, mult-year program amed at studyng these systems wth a specal emphass placed on the vapor pressure and the mscblty behavour. In 2009, the team carred out a frst study devoted to the change n vapor pressure caused by the ncorporaton of anhydrous ethanol nto a naphtha cut taken as surrogate for a commercal gasolne. In 2010, the thematc of the alcohols/gasol mscblty was tackled and led to study the nfluence of the type of alcohol and ts water content on ts mscblty wth selected gasol cuts featurng varous compostons (paraffn/ aromatcs/ naphthenes dstrbuton; sulphur compounds). Snce the openlterature contans very few expermental data n ths area, the strategy has been n favor of a theoretcal approach. Four ndustral alcohols (methanol, ethanol, sopropanol or 1-butanol) featurng varous water contents and four commercal gasol wth defned hydrocarbon dstrbutons were ncluded n ths study. 2 Vapor pressure of ethanol-naphtha blends The theoretcal approach s based on the 1978 verson of the Peng and Robnson equaton of state [1], noted PR78 n ths paper. More nformaton on the theoretcal model s avalable n [2]. Fgure 1 shows a plot of the vapour pressure data computed for blends contanng varable proportons of anhydrous ethanol and a naphtha consstng n 18% n- hexane and 82% n-heptane by weght. 1 Introducton In recent years, the quest for sustanable prmary energes has ncreased the potental nterest of bogenc/fossl fuels mxes. In ths context, lght alcohols are often used as gasolne extenders to both partly substtute for Ths s an Open Access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense 2. 0, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. Artcle avalable at or

2 MATEC Web of Conferences Ths fgure demonstrates the hghly non-deal behavor of these blends: for nstance, for a blend contanng 17% ethanol, a calculaton assumng an deal behavour (Raoult s law) would lead to undervalue the vapour pressure by 51% (table 1). These results are very mportant from a safety standpont snce the Lower and Upper Flammablty Lmts depend on the vapour pressure; they are also relevant for the selecton of the rght naphtha cuts when one wshes to prepare ethanol/gasolnes blends havng sutable volatlty for cars (e.g. E10 ). Fgure 1. Vapor pressure devaton from dealty for a naphtha/ethanol blend. Table 1. Vapor pressure of tanks contanng () naphtha, () ethanol and () a gven naptha-ethanol blend (27 C, 70 % full tank). Lqud (% mass) () Naphtha: (18 %C %C 7 ) () 100% EtOH () 83 % napththa + 17 % EtOH Real (computed) Idealty hypothess Relatve dfference Vapor pressure (mbar) % 3 Alcohol-gasol mscblty study In ths paper, we wll use a pseudo-bnary system made by the hydrocarbon mxture consttutng the gasol, on one hand, and the alcohol/water mxture (also called hydrated alcohol or ndustral alcohol ), on another hand. To characterze the mscblty behavour of such gasol/alcohol/water systems, t s convenent to access to the so-called Mnmum Mscblty Temperature ( MMT ) whch s the lowest temperature at whch the fluds are fully mscble, regardless of the proporton of ndustral alcohol. For any temperature below the MMT, addton of ndustral alcohol to the gasol may gve rse to two lqud phases n equlbrum whle, for any temperature above the MMT, the mxture cannot unmx anymore, as llustrated n fgure 2. lqud phase s stable the lqud phase may unmx for a range of x values 1 lqud phase 1 lqud phase 2 lqud phases T/K MMT Mole fracton of ndustral alcohol x 1 The sketch of fgure 2 has large commonaltes wth classcal lqud-lqud phase dagrams of bnary systems n whch () the maxmum of the saturaton curve s actually a lqud-lqud crtcal pont (and s called UCST for upper crtcal soluton temperature, nstead of MMT) and () t s possble to draw a horzontal te-lne at a gven temperature. However, snce the pseudo-bnary gasol/ndustral alcohol systems nvolve many compounds, t s no longer possble to draw horzontal te-lnes; n addton, the maxmum of the saturaton curve s not a crtcal pont anymore (a crtcal pont may exst anywhere on the saturaton curve). The openlterature s very poor n MMT data for gasol/ndustral alcohols systems. For ths reason, we decded to use an effcent predctve thermodynamc model, called UNIFAC for representng the behavor of the fluds of nterest. Ths model reles on the group-contrbuton concept and s able to account for the effects of: () the nature of the alcohol and () addtons of small amounts of water n the alcohol. In studyng four gasols (noted GO1, GO2, GO3 and GO4) havng dfferent compostons, t s possble to nvestgate the nfluence of the paraffnc, aromatc, naphthenc and sulphur contents. The rough compostons of these four gasols are gven table 1. As we wll work wth condensed lqud phases, the pressure effect wll be neglected throughout ths study. 0.0 Fgure 2. Pseudo-bnary phase dagram for a mxture of gasol and ndustral alcohol. The bell s the boundary between the sngle lqud and the two-lqud felds (saturaton curve). MMT s the summt of the saturaton curve p.2

3 39 th JEEP 19 th - 21 st March 2013 Nancy Table 2. Compostons of the four studed gasols Compounds GO1 GO2 GO3 GO4 Paraffnc 16 % 10.5 % 84 % 90 % Aromatc 84 % 82 % 16 % 8 % Naphthenc % Sulphur % The Group-Contrbuton concept 4.1 General aspects The group-contrbuton (GC) approach s a relatvely recent concept [1-17] whch orgnally amed at predctng the physcal propertes of pure molecules startng from ther chemcal structures. The applcaton of the GC concept to mxtures s actually an extenson of the GC concept for sngle molecules [3, 18]. The basc dea of any group-contrbuton method s that, whereas there are thousands of chemcal molecules, the number of functonal groups that consttute them s very lmted. Assumng that a physcal property of a flud s the sum of contrbutons made by the molecule s functonal groups, one can use a GC method to correlate the propertes of a very large number of fluds based on a much smaller number of parameters. These GC parameters characterze the contrbutons of ndvdual groups n the propertes. In ths paper, a predctve thermodynamc model based on the GC concept, named UNIFAC, s used for calculatng lqud-lqud phase equlbra of complex gasol/alcohol/water mxtures. 4.2 Outlnes of the UNIFAC method Ths model enables the estmaton of the complete sets of actvty coeffcents of all the components n a mxture, wthout fttng any model parameter from lqud-lqud expermental data. The mere knowledge of the chemcal structure of all the compounds n the mxture s enough to predct phase equlbra. Based on the mathematcal formulaton of the non-predctve UNIQUAC model, the UNIFAC model can be seen as a predctve verson of ths last model. The UNIQUAC equaton often gves good representatons of vapor-lqud and lqud-lqud equlbra for bnary and multcomponent mxtures contanng a varety of non-electrolytes, such as for nstance hydrocarbons and alcohols. The molecular actvty coeffcent s break down nto two parts: one part provdes the contrbuton due to dfferences n molecular sze and shape ( the combnatoral part ), and the other provdes the contrbuton due to molecular nteractons ( the resdual part ). In a multcomponent mxture, the UNIFAC equaton for the actvty coeffcent of component wrtes: comb res ln ln ln (1) res The calculaton of ln requres the knowledge of energy group-nteracton parameters a mn, the values of whch were estmated from phase equlbrum data regresson by Fredenslund et al. [18]. Note however that some amn values were reftted by ths team n prevous works (GT and GT ) for selected chemcal groups nvolved n gasol/alcohol mxtures; more detals about the UNIFAC model are avalable n these references. 5 Lqud-lqud phase dagrams for multcomponent systems Due to the hgh number of compounds contaned n gasol/ndustral alcohol mxtures (between 30 and 50 n the present case), the calculaton of the saturaton curve s a much more complcated and tme-consumng task than for actual bnary systems. Ths secton s thus devoted to explan the optons used to perform fast and relable calculatons of saturaton curves n a reasonable tme. 5.1 Drect calculaton of the saturaton curve In ths secton, the gasol composton s assumed to be known. Let us defne a system resultng from the mxng of a gven amount of ndustral alcohol (fully defned n terms of composton) wth a gven amount of gasol. The overall mole fracton vector z of such a system s thus completely characterzed; let us also denote z alcohol, the overall composton of the ndustral alcohol. The system s a sngle, stable lqud phase at hgh temperature and gves rse to a lqud-lqud equlbrum at low temperature. The saturaton pont s defned as the transton state between the sngle-lqud state and the lqud-lqud equlbrum state. Let us denote T* the saturaton temperature. The calculaton of a saturaton pont (.e. a pont of the saturaton curve) s llustrated n fgure 3. Fgure 3. Drect calculaton of the saturaton pont at a fxed overall composton z p.3

4 MATEC Web of Conferences A saturaton pont corresponds to two lqud phases n equlbrum, the frst one havng a known composton z and the second one havng an unknown composton x. The unknown varables T* and x can be determned by solvng the followng set of equatons: N 1 * * z a (T, ) a (T, x), for all 1;...; N x 1 (2) where a s the actvty of component calculated from the UNIFAC model and N s the total number of compounds contaned n the mxture. The frst lne of the equaton set (2) s obtaned by equatng the chemcal potental of component n the two lqud phases, whch expresses the lqud-lqud equlbrum condton). The second lne expresses the normalzaton of the molar fractons. To facltate the resoluton of the equaton set (2), one can rewrte t as an optmzaton problem, e.g.: * T, x * * z Mn a (T, ) - a (T, x) under the constrant x = 1 N =1 2 (3) Dong so, classcal optmzaton procedures (such as e.g. quas-newton methods) can be appled to determne T* and x. In the present case, the SLSQP (Sequental Least Squares Quadratc Programmng), optmzaton algorthm was used and led generally to satsfactorly results. Of course, when drawng the complete saturaton lne, the calculaton of a gven saturaton pont can be easly ntalzed from varables T* and x of the prevous saturaton pont. However, the ntalzaton procedure of the frst calculated saturaton pont remans an entre problem. Despte generally satsfactory results, t was observed that the resoluton of eq. (3) usng the SLSQP procedure was lkely to fal when: - the saturaton pont to be calculated s very close to a lqud-lqud crtcal pont (such that the two lqud phases n equlbrum have the same composton,.e. x = z) - several lqud-lqud equlbra exst at a gven overall composton z; when ths stuaton occurs, one lqud-lqud equlbra s declared stable (the one assocated to the lowest Gbbs energy value) and the other ones are declared non-stable. Each tme a drect calculaton of a saturaton pont faled, another procedure based on a flash algorthm calculaton was run. Such a combnaton of these two procedures allowed us to successfully plot the saturaton curves of all the consdered gasol/ndustral alcohol systems wthn a reasonable tme (less than 1 mnute for each curve contanng 150 ponts). Note that the flash algorthm can also be used to ntalze the frst calculated pont of the saturaton curve. 5.2 Indrect calculaton of the saturaton curve usng a flash-calculaton based procedure A lqud-lqud flash calculaton s a classcal algorthm amed at determnng whether a multcomponent lqud mxture gves rse to a lqud-lqud equlbrum at a gven temperature and overall composton z. If so, the flash calculaton provdes the composton of the phases as well as ther proportons. As llustrated n fgure 4, t s possble to use ths knd of calculaton to determne the saturaton temperature T*. Fgure 4. Indrect calculaton of the saturaton pont at a fxed overall composton z. To do so, t s necessary to perform a seres of flash calculatons n order to determne two temperatures T (1) and T (2) such that: T (2) < T* < T (1) where T (1) s a temperature at whch the system conssts of a sngle lqud phase and T (2) s a temperature at whch the system conssts of two lqud phases n equlbrum. The saturaton temperature T*, whch s the transton temperature between a 2-phase and a 1-phase system, can be accurately calculated usng, for nstance, a dchotomc procedure. 5.3 Flash calculaton Let us consder an N-component system havng an overall composton z and gvng rse to a lqud-lqud equlbrum (the two lqud phases n equlbrum are denoted and β). To perform a flash calculaton, a set of (2N + 2) equatons has to be solved: a (T, x ) a (T, x ), 1;...;N,, N 1 N 1,, α z x x, 1;...;N x 1 x 1 β (4) p.4

5 39 th JEEP 19 th - 21 st March 2013 Nancy where and are the proportons of the lqud phases and β and the compostons of these two lqud phases are noted x and x β. To solve the set of equatons (4), the well-known Rce-Rachford procedure can be appled. 6 nfluence of the alcohol and the water content on the MMT In ths study, four real commercal gasols (GO1, GO2, GO3 and GO4) were selected; ther detaled compostons are gven n table 3. These types of gasols were taken because they contan dfferent amounts of paraffnc, aromatc, naphthenc and sulphur compounds. The frst gasol (GO1) contans 84 % of aromatc compounds, 16 % of paraffnc compounds and no sulphur speces. GO2 s smlar to GO1 but contans 7.5 % of sulphur compounds. On the contrary, GO3 and GO4 contan large amounts of paraffnc compounds (more than 80 %), and small quanttes of aromatcs. GO4 has the partcularty to contan a small amount of naphthenc hydrocarbons. It s thus possble to evaluate how these chemcal famles mpact on the MMT value of gasol/ndustral alcohol mxtures. The frst task s the calculaton of the lqud-lqud phase dagram usng the UNIFAC model. 6.1 Addton of four dfferent ndustral alcohols n gasol GO1 The hghest temperature at whch the phase splt occurs.e. the MMT has been calculated. The correspondng phase dagrams are shown n fgure 5 and the correspondng MMT are gven n table 4. Table 4. MMT values for gasol GO1 mxed wth the four alcohols havng varous H2O contents. % H 2 O (mass) methanol ethanol sopropanol butanol Fgure 5. Phase dagrams for GO1 mxed wth 4 alcohols contanng from 1 to 10 % water (n abscssa: mole fracton of hydrated alcohol). For any alcohol content, one observes that: - the MMT systematcally ncreases wth the proporton of water n the alcohol - the heaver the alcohol, the stronger ths ncrease; thus, when the water percent goes from 1 to 10 %, the MMT (n K) s multpled by: 1.3 for the methanol; 2.1 for the ethanol; 2.7 for the sopropanol and for 1- butanol. The changes of MMT wth the alcohol mass water contents are represented n fgure 6. As t can be observed, the smallest MMT values are obtaned wth heavy alcohols havng small water contents p.5

6 MATEC Web of Conferences Table 3. Specated analyses of the four gasols. Components GO1 GO2 GO3 GO4 1,4-dmethyl benzene (para-xylene) ethyl-3-methyl benzene ,2,3-trmethyl benzene benzocyclopentane (ndane) methyl-1-propyl benzene ethyl-1,2-dmethyl benzene ,2,4,5-tetramethyl benzene methyl-4-(2-propenyl) benzene methyl-1-butyl Benzene Naphthalene ,3-dhydro-1,2-dmethyl 1H-ndene methyl naphthalene ethyl naphthalene 2.9 1,2-dmethyl naphthalene ,4-dhydro-1,4-methano naphthalene ,3,6-trmethyl naphthalene 15.7 n-pentadecane fluorene methyl-1-ethyl naphthalene methyl bphenyle n-hexadecane ethyl-1,4-dethyl azulene ,2-dmethyl bphenyle n-heptadecane phenanthrene n-octadecane methyl phenanthrene n-nonadecane ,10-dmethyl anthracene n-ecosane n-henecosane n-docosane n-trcosane n-tetracosane (n-pentacosane) (0.3) 0.9 2,3-dhydro-1-methyl ndene 0.6 para-dsopropyl benzene 0.5 n-octane 6.25 n-nonane n-decane n-undecane n-dodecane (n-trdecane) 9.8 (8.6) n-tetradecane n-hexacosane (n-heptacosane) 0.3 (0.3) 1-methylethyl cyclohexane 0.6 octyl cyclohexane 0.6 decyl cyclohexane 0.5 benzothophene 0.5 methyl benzothophene 0.9 dmethyl benzothophene 3.0 dbenzo thophene 0.9 thoxanthene p.6

7 39 th JEEP 19 th - 21 st March 2013 Nancy As prevously, for any alcohol content, one observes that: - the MMT ncreases wth the proporton of water n the alcohol, - the heaver the alcohol, the hgher ths ncrease; thus, when the water percentage goes from 1 to 10 %, the MMT (n K) s multpled by: 1.2 for methanol; 2.0 for ethanol; 2.5 for sopropanol and 2.7 for the 1- butanol. The change of MMT wth mass water contents the varous alcohol s represented n fgure 8. Fgure 6. Change of the MMT of the four GO1/alcohols wth the water content of the alcohol. 6.2 Addton of four dfferent ndustral alcohols n gasol GO2 The MMT data are gven n table 5 and the correspondng phase dagrams can be seen n fgure 7. Table 5. MMT values for gasol GO2 mxed wth the four alcohols havng varous H 2 O contents. % H 2 O (mass) methanol ethanol sopropanol butanol Fgure 8. Change of the MMT of the four GO 2/alcohols systems wth the water content of the alcohol. Here, the conclusons are exactly the same as wth gasol GO1. Due to the dfferent compostons of the gasol, the MMT values are however hgher than wth gasol GO1. Fgure 7. Phase dagrams for GO2 mxed wth 4 alcohols contanng from 1 to 10 % water (n abscssa: mole fracton of hydrated alcohol) p.7

8 MATEC Web of Conferences 6.3 Addton of four dfferent ndustral alcohols n gasol GO3 The phase dagrams can be seen n fgures 9 and 10 and the correspondng MMT are gven n table 6. Table 6. MMT values for gasol GO3 mxed wth the four alcohols havng varous H2O contents. % H 2 O (mass) methanol ethanol sopropanol 1-butanol Conclusons are the same as wth GO1 and GO2. When the water percent goes from 1 to 10 %, the MMT (n K) s multpled by: 1.5 for methanol; 2.6 for the ethanol; 3.3 for sopropanol and 3.4 for 1-butanol. Fgure 10. Change of the MMT of the four GO 3/alcohols systems wth the water content of the alcohol. Fgure 9. Phase dagrams for GO3 mxed wth 4 alcohols contanng from 1 to 10 % water (n abscssa: mole fracton of hydrated alcohol). 6.4 Addton of dfferent ndustral alcohols n gasol GO4 Phase dagrams can be seen n fgures 11 and 12 and the correspondng MMT are gven n table 7. Conclusons are the same as wth GO1, GO2 and GO3. When the water percent goes from 1 to 10 %, the MMT (n K) s multpled by: 1.6 for methanol; 2.7 for ethanol; 3.6 for sopropanol and 4.9 for 1-butanol p.8

9 39 th JEEP 19 th - 21 st March 2013 Nancy Fgure 11. Phase dagrams for GO4 mxed wth 4 alcohols contanng from 1 to 10 % water (n abscssa: mole fracton of hydrated alcohol). 7 nfluence of gasol composton on the MMT From the results above, t s possble to draw the nfluence of gasol compostons on the MMT, for a gven alcohol. It s remembered that these compostons are summarzed n tables 1 and 2. Results are syntheszed n fgure 13 and are dscussed n the concluson. Fgure 12. Change of the MMT of the four GO 4/alcohols systems wth the water content of the alcohol. Table 7. MMT values for gasol GO4 mxed wth the four alcohols havng varous H2O contents. % H 2 O (mass) methanol ethanol sopropanol Butanol Fgure 13. Results summary; Legend: PAR: paraffns; Aro: aromatcs; Nap: naphthenes; S: sulphur; Uppercases: major compounds; n parentheses: mnor compounds p.9

10 MATEC Web of Conferences 8 Concluson Ths collaboratve, multstep study was ntended to progress n the thermodynamc descrpton of alcoholhydrocarbons mxtures n presence or absence of water. In a frst step, we have ponted out the strongly non-deal behavor of ethanol-naphtha blends n terms of vapor pressure. The second step was devoted to provdng general gudelnes for preparng mxtures of gasols wth ndustral alcohols dsplayng low Mnmum Mscblty Temperature (MMT) data. It must be stressed that the MMT values computed n the present paper are sometmes qute hgh and above the stablty temperature of the related alcohols; ths ponts out the essentally theoretcal reach of the present study, whch owes ts man nterest to the man trends observed: 1- wth slghtly hydrated alcohols: t s preferable to use heavy alcohols. As the alcohol molecules gets close, n sze, to the hydrocarbons contaned n the gasols, they are better solublzed. It s also preferable to use a gasol featurng a hghly aromatc character and substantal sulphur content n order to prevent any lqud-lqud phase splt. Naphthenc compounds should be dscarded. The mxtures of 1-butanol wth GO4 llustrate well these nferences. 2- wth strongly hydrated alcohols: ths tme, t s preferable to select lght alcohols (methanol or ethanol) n order the alcohol molecule sze becomes closer to that of the water molecule. Then, water gets more easly solublzed n the alcohol. Here agan, t s preferable to take gasols havng substantal aromatc contents and some sulphur contanng molecules havng more affnty wth polar speces (water and ethanol) than paraffnc compounds. Once agan, naphthenc compounds have to be dscarded. The mxtures of ethanol wth GO1 llustrate well these nferences. As next steps, ths study wll be followed by () an expermental work devoted to the verfcaton of these man theoretcal results and () a further study of the effect of ntroducng alkyl esters n the gasols/hydrated alcohols blends. 2. L. Constantnou, R. Gan, AIChE J. 40(10) 1697 (1994) 3. J.N. Jaubert, F. Mutelet, Flud Phase Equlbra (2004) 4. J.N. Jaubert, S. Vtu, F. Mutelet, J.P. Corrou, Flud Phase Equlbra (2005) 5. S. Vtu, J.N. Jaubert, F. Mutelet, Flud Phase Equlbra (2006) 6. S. Vtu, R. Prvat, J.N. Jaubert, F. Mutelet, Journal of Supercrtcal Fluds 45 1 (2008) 7. R. Prvat, J.N. Jaubert, F. Mutelet, Industral & Engneerng Chemstry Research (2008) 8. R. Prvat, J.N. Jaubert, F. Mutelet, Industral & Engneerng Chemstry Research (2008) 9. R. Prvat, J.N. Jaubert, F. Mutelet, Journal of Chemcal Thermodynamcs (2008) 10. R. Prvat, F. Mutelet, J.N. Jaubert, Industral & Engneerng Chemstry Research (2008) 11. J.N. Jaubert, R. Prvat, F. Mutelet, AIChE Journal (2010) 12. R. Prvat, J.N. Jaubert, F. Garca, M. Molere, Journal of Engneerng for Gas Turbnes and Power 132 art. no (2010) 13. J.N. Jaubert, L. Conglo, F. Denet, Industral & Engneerng Chemstry Research (1999) 14. J.N. Jaubert, L. Conglo, Industral & Engneerng Chemstry Research (1999) 15. J.N. Jaubert, P. Borg, L. Conglo, D. Barth, Journal of Supercrtcal Fluds (2001) 16. R. Gan, P. M. Harper, M. Hostrup, Industral & Engneerng Chemstry Research (2005) 17. R. Prvat, J.N. Jaubert, Global Journal of Physcal Chemstry (2010) 18. A. Fredenslund, R. L. Jones, J.M. Prausntz, AIChE Journal (1975) Nomenclature GO: gasol MMT: mnmum mscblty temperature. x : mole fracton of component n a gven phase. z : overall mole fracton of component. : actvty coeffcent of component. comb : combnatoral part of the actvty coeffcent. res : resdual part of the actvty coeffcent. k : molar proporton of lqud phase k. References 1. B.E. Polng, J.M. Prausntz, J.P. O'Connell, The propertes of gases and lquds, 5th edton, Mc Graw Hll, p.10