Liquid-Liquid Equilibria for Ternary Mixtures of (Water + Carboxylic Acid+ MIBK), Experimental, Simulation, and Optimization

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1 World Academy of Scece, Egeerg ad Techology teratoal Joural of Chemcal ad Molecular Egeerg Vol:7, No:6, 03 Lqud-Lqud Equlbra for Terary Mtures of (Water + Carboylc Acd+ MBK, Epermetal, Smulato, ad Optmzato D. Laad, A. Hassee, ad A. Merzougu Dgtal Ope Scece de, Chemcal ad Molecular Egeerg Vol:7, No:6, 03 waset.org/publcato/443 Abstract ths work, Epermetal te-le results ad solublty (bodal curves were obtaed for the terary systems (water + acetc acd + methyl sobutyl ketoe (MBK, (water + lactc acd+ methyl sobutyl ketoe at T = 94.5K ad atmospherc pressure. The cosstecy of the values of the epermetal te-les was determed through the Othmer-Tobas ad Hads correlatos. For the etracto effectveess of solvets, the dstrbuto ad selectvty curves were plotted. addto, these epermetal tele data were also correlated wth NRTL model. The teracto parameters for the NRTL model were retreved from the obtaed epermetal results by meas of a combato of the homotopy method ad the geetc algorthms. Keywords Lqud-lqud equlbra, homotopy methods, carboylc acd, NRTL. M. NTRODUCTON ANY attempts have bee made to descrbe the solvet etracto of carboylc acds from aqueous fermetato solutos. The (lqud lqud equlbrum (LLE measuremets ad phase behavour of terary systems cludg carboylc acds has bee the subject of much research recet years [] [5]. LLE data of the related systems are ot oly eeded for the desg of a effcet ad productve etracto system, but they are also dspesable calbrato ad verfcato of aalytcal models. the preset work, lqud lqud equlbrum data have bee obtaed for three dfferet systems, amely, (water + acetc acd + methyl sobutyl ketoe, (water + lactc acd+ methyl sobutyl ketoe at 94.5K ad at atmospherc pressure. The dstrbuto coeffcets ad separato factors were obtaed from epermetal results ad are also reported. The te les were determed ad were correlated by the methods of Othmer-Tobas ad Had o a mass-fracto bass. The epermetal results are compared wth values predcted by NRTL.. EPERMENTAL SECTON A. Chemcals Acetc acd, lactc acd, dchloromethae ad methyl sobutyl ketoe were purchased from Merck ad were of 99, 99, 98, ad 99% mass purty, respectvely. The chemcals were used wthout further purfcato. Deozed ad redstlled water was used throughout all epermets. B. Aalytcal Methods The Solublty curve was determed by the cloud pot method [6] usg a thermostated cell, equpped wth a magetc strrer ad sothermal flud jacket. The cell was kept a costat-temperature bath mataed at ±0. C. The cell was flled wth homogeeous water + carboylc acd mtures prepared by weghg, usg a Nahta YP40N balace wth a precso of 0 - g. The solvet was ttrated to the cell from a mcroburet wth a ucertaty of ±0.0cm 3. The ed pot was determed by observg the trasto from a homogeeous to a heterogeeous mture. Ths patter was coveet to provde the aqueous-rch sde of the curves. The data for orgac-rch sde of the curves were therefore obtaed by ttratg homogeeous solvet + carboylc acd bares wth water utl the turbdty had appeared. The mamum error the calculato of the compostos of the bmodal curve was estmated to be 0 -. Net, the refractve dees of these terary mtures are measured by usg a Nahta Modèle 690/ refractometer. Each measuremet was take o three occasos. For the te-le measuremet, a equlbrum cell was mmersed a thermostat cotrolled at the desred temperature (±0. o C. The pure compoets were added, ad the mture was strred for at least 3 h wth a magetc strrer. The twophase mture was allowed to settle for at least 3. Samples were take by syrge from the upper ad lower mtures. The refractve dees of both phases at equlbrum were measured to later determe ther compostos. D. Laad s wth the Departemet of dustral chemstry, Uversty Mohamed Khder Bskra, Algera (phoe: ,e-mal: ayadh_jm@yahoo.com A. Hassee s wth the Departemet of dustral chemstry, Uversty Mohamed Khder Bskra, Algera (e-mal: hasee@yahoo.fr A. Merzougu s wth the Departemet of dustral chemstry, Uversty Mohamed Khder Bskra, Algera (,e-mal: merzougukarm@yahoo.com. MODELS THERMODYNAMC The NRTL model was used to correlate the epermetal data ths work, the NRTL model was epressed by: teratoal Scholarly ad Scetfc Research & ovato 7(

2 World Academy of Scece, Egeerg ad Techology teratoal Joural of Chemcal ad Molecular Egeerg Vol:7, No:6, 03 Dgtal Ope Scece de, Chemcal ad Molecular Egeerg Vol:7, No:6, 03 waset.org/publcato/443 lγ = j= τ k= j j k j k j + j= jj τ j kj k k = ( α jτ j = k = τ = ep α j = α j The effectve teracto parameter τ g g R. T τ j j j = = j kj k j s defed by: The LLE epermetal data were used to determe the optmum NRTL bary teractos parameters. The thermodyamc model was ftted to epermetal data usg the Newto homotopy formulato [7]. V. HOMOTOPY CONTNUATON METHOD The phase equlbrum problem volves the separato of N C compoets of molar fractos z to two phases ad at a gve temperature T ad pressure P. The molar fractos of the compoets the two phases are deoted as, respectvely. these equatos; A T ( β z = 0 j ( ad β + (, Feed γ γ = 0 (3 = 0 (4 deote the mole fractos phases ad. β stads for the phase fracto of phase. The deotes the actvty coeffcets to be calculated by usg a approprate actvty coeffcet model such as the UNQUAC model whch s dscussed the prevous secto. ths work, a cove lear homotopy cotuato method s used; ths method s globally coverget method for the soluto of olear equatos;.e., ths method ca fd the soluto whle movg from a kow soluto or a startg pot to a ukow soluto. The homotopy fucto of a lear combato of two fuctos (, a easy fucto, ad F(, a dffcult fucto. γ H(,t = tf( + ( - t( (5 where t s a homotopy parameter that s gradually vared from 0 to as a path s tracked from ( (kow soluto to F( (ukow soluto ad s the vector of depedets varables, 0 s the tal of ad a soluto of (. For the Newto homotopy formulato, the fucto H(,t (4 wth (= F( - F( 0, ca takes a form as follows: H(, t = F( - ( - t F( 0 (6 Whe usg homotopy cotuato method, t s ot oly coveet but effectve as well, to talze the terary system wth pure methyl sobutyl ketoe ad water [7]. V. RESULTS AND DSCUSSON A. Epermetal Bodal ad Te-Le Measuremets The compostos defg the bodal curve of the terary systems, (water + acetc acd + methyl sobutyl ketoe, (water + lactc acd+ methyl sobutyl ketoe at 94.5K are lsted Table whch deotes the mass fracto of the th compoet. TABLE EPERMENTAL SOLUBLTY CURVE DATA Water ( + lactc Acd ( + MBK(3 Water ( + acetc Acd ( + MBK(3 ( ( (3 ( ( ( Table shows the epermetal te-le compostos of the equlbrum phases, for whch ad 3 refer to the mass fractos of the th compoet the aqueous ad solvet phases, respectvely. The bodal curves ad te-les are show Fgs. ad. TABLE EPERMENTAL TE-LNE RESULTS N MASS FRACTON FOR TERNARY SYSTEMS Water-rch phase (aqueous phase Solvet-rch phase (orgac phase (water 0,7666 0, ,597 0,5785 0, (solute (solvet (water (solute Water ( + Lactc Acd ( + MBK(3 0,9684 0, ,0366 0,044 0,8344 0,0598 0,053 0, ,354 0, , ,0308 0, , ,043 0,57 0,4595 0,0 0,0439 0,659 Water ( + Acetc Acd ( + MBK(3 0,034 0,043 0,0934 0,0376 0,095 0, ,0639 0,097 3 (solvet 0,944 0,8796 0,8604 0,8053 0,790 0,9543 0,9489 0,873 0,8449 0, , ,0796 0, 0,799 teratoal Scholarly ad Scetfc Research & ovato 7(

3 World Academy of Scece, Egeerg ad Techology teratoal Joural of Chemcal ad Molecular Egeerg Vol:7, No:6, 03 0, ,6884 0,689 0,585 0,884 0,39 0,706 0, , ,0884 0,05 0,0955 0,3 0,3 0,5 0,497 0,8 0,048 0,4 48 0,7056 0,67 0,656 where D ad D are the dstrbuto coeffcets of water ad carboylc acd, respectvely. The dstrbuto coeffcets, D, for water ( = ad carboylc acd ( = were calculated as follows: Dgtal Ope Scece de, Chemcal ad Molecular Egeerg Vol:7, No:6, 03 waset.org/publcato/443 acetc acd,00,00,00 MBK water Fg. Terary dagram for LLE of {water ( + Acetc acd ( + MBK (3} at T = 94.5 K; epermetal solublty curve; epermetal te-le data; * epermetal te-le data at K [8] Lacc Lactc acd acd,00,00,00 MBK water Fg. Terary dagram for LLE of {water ( + lactc acd ( + MBK (3} at T = 94.5 K; epermetal solublty curve; epermetal te-le data B. Dstrbuto Coeffcet ad Separato Factor The effectveess of etracto of carboylc acd by the solvet s gve by ts separato factor (S, whch s a dcato of the ablty of the solvet to separate carboylc acd from water. (7 where ad 3 D = (8 3 are the mass fractos of compoet the solvet-rch ad water-rch phases, respectvely. The dstrbuto coeffcets ad separato factors for each system are gve Table. Separato factors are greater tha for the systems reported here, whch meas that etracto of the studed carboylc acds from water wth MBK s possble. The separato factor s ot costat over the whole two-phase rego. Selectvty dagrams o a solvetfree bass are obtaed by plottg, 3 / 3 3 ( + ( versus / + for each carboylc acd Fg. 3 The selectvty dagram dcated that the performace of the MBK for etracto of acetc acd s hgher tha lactc acd. TABLE DSTRBUTON COEFFCENTS FOR WATER (D AND CARBOYLC ACD (D, AND SEPARATON FACTORS (S D D S Water ( + Lactc Acd ( + MBK(3 0,078 0,0505 0, ,074 0, ,007 0,0746 0,0958 0, 0,4943 0,788 0,408 0, , ,443 0,3538 Water ( + acetc Acd ( + MBK(3,046,07 0, , , ,976,043 6,0039 5, , , , ,74 0,076 7, ,6648 5,343 0,4398 0,8653 3,535 0,30584,0354 3, /(3 +3 0,80 0,78 0,76 0,74 0,7 0,70 0,68 0,66 0,64 0,6 0,60 acetc lactque 0,0788 0,0975 0,895 0,6495 0, ,3 /( + Fg. 3 Solvet-free bass selectvty dagram of systems for ( Water-Lactc acd-mbk, ( Water-Acetc acd-mbk C. Othmer Tobas ad Had Correlatos ths study Othmer-Tobas [9], Had [0], correlatos were used to ascerta the relablty of the epermetal teratoal Scholarly ad Scetfc Research & ovato 7(

4 World Academy of Scece, Egeerg ad Techology teratoal Joural of Chemcal ad Molecular Egeerg Vol:7, No:6, 03 Dgtal Ope Scece de, Chemcal ad Molecular Egeerg Vol:7, No:6, 03 waset.org/publcato/443 results for each system, where, mass fracto of water the aqueous phase; 3 ad, mass fracto of carboylc acd orgac ad aqueous phases, respectvely;, mass fracto of solvets orgac phase; a, b, a, ad b, the parameters of the Othme-Tobas correlato ad the Had correlato, respectvely, The Othmer-Tobas correlato s: l ( The Had correlato s l = a + bl = a' + b' l 3 (9 (0 The correlatos are gve Fgs. 4, 5, ad the costats of the correlatos are also gve Table V. The correlato factor (R beg appromately uty ad the learty of the plots dcate the degree of cosstecy of the measured LLE values ths study. TABLE V THE CORRELATON COEFFCENTS AND CORRELATON FACTORS FOR THE OTHMER-TOBAS AND HAND CORRELATONS System Othmer Tobas correlato Had correlato a b R a b R Water-Acetc 0,774,004 0,9935,3764 0,996 0,9943 acd-mbk Water-Lactc acd-mbk,3764,0898 0,9406 0,5993 0,675 0,967 L((- / 0,4 0,0-0,4-0,8 -, -,6 -,0 -,4 -,8-3, L((- / Fg. 4 Othmer Tobas plots of: ( Water-Acetc acd-mbk ad ( Water-Lactc acd-mbk terary systems L( / 0,0-0,5 -,0 -,5 -,0 -,5-3,0-3,5-4,0-4,0-3,6-3, -,8 -,4 -,0 -,6 -, -0,8-0,4 0,0 L( 3 / Fg. 5 Had plots of: ( Water-Acetc acd-mbk ad ( Water- Lactc acd-mbk terary systems V. OPTMZATON PROCEDURE The NRTL model was used to correlate the raw epermetal LLE values. the preset work, the value of the o-radomess parameter of the NRTL equato, α, was fed at 0.. The objectve fucto developed by Sorese [] was used to optmze the equlbrum models. The objectve fucto s the sum of the squares of the dfferece betwee the epermetal ad calculated data. The objectve fucto ca be defed as: mf m j = wk( k= j= = cal k ( j ep k ( j ( The observed results were used to determe the optmum NRTL ( g bary teracto eergy betwee a j par of j molecules or betwee each par of compouds (tables 5. The teracto parameters values obtaed wth geetc algorthm (A. The qualty of the correlato s measured by the root-mea square devato (RMSD. The RMSD value was calculated from the dfferece betwee the epermetal ad calculated mole fractos accordg to the followg equato: RMSD= 6 ( 3 k = j = = jk jk ( where s the umber of te-les, dcates the epermetal mole fracto, s the calculated mole fracto, ad the subscrpt dees compoets, j dees phases ad k =,,..., (te-les. The RMSD values the correlato by NRTL models for the systems studed at T = 394.5K are lsted Table V. teratoal Scholarly ad Scetfc Research & ovato 7(

5 World Academy of Scece, Egeerg ad Techology teratoal Joural of Chemcal ad Molecular Egeerg Vol:7, No:6, 03 TABLE V NRTL ( α =0. BNARY NTERACTON PARAMETERS ( g j AND g j AND RMSD VALUES FOR LLE DATA OF THE TERNARY SYSTEMS AT T=94.5 K -j gj g j RMSD Water ( + Lactc Acd ( + MBK( Water ( + Acetc Acd ( + MBK( Dgtal Ope Scece de, Chemcal ad Molecular Egeerg Vol:7, No:6, 03 waset.org/publcato/443 V. CONCLUSONS The epermetal te-le data of, (water + acetc acd + methyl sobutyl ketoe ad (water + lactc acd+ methyl sobutyl ketoe at T = 94.5K ad atmospherc pressure. The NRTL model was used to correlate the epermetal data. The RMSD values betwee observed ad calculated mass percets for the systems water-lactc-mbk, water-acetc acd- MBK were 4.657%, 8.580% respectvely t s apparet from the separato factors ad epermetal te-les that MBK s foud to be preferable solvet for separato of acetc ad lactc acd from aqueous solutos. The combg Homotopy cotuato ad eetc algorthms ca be appled to predct lqud-lqud equlbrum ad bary teracto parameters, respectvely for other lqud lqud systems as well as vapor lqud systems. REFERENCES [] M. Blg, Ş.Đ. Kırbaşlar,Ö. Ö zca, U. Dramur, J. Chem. Thermody. 37, , 005. [] S.Çehrel, Flud Phase Equlbra, 48, 4-8, 006. [3] L.Wag, Y.Cheg, L, J. Chem. Eg.Data, 5, 7-73, 007. [4] S. Şah, Ş. Đsmal Kırbaşlar, M.Blg, J. Chem. Thermody, 4, 97-0, 009. [5] H. haadzadeh, A. haadzadeh la, Kh. Bahrpama, R. Sarr, J. Chem. Thermody, 4, 67 73, 00. [6] J. J.Otero, J. F.Comesaňa, J. M.Correa, A.Correa, J. Chem. Eg. Data, 45, , 000. [7] J.W. Kovach, W.D.Seder, Comput. Chem. Eg.,, , 987. [8] M. ovdaraja, PL. Sabaratham ; Flud Phase Equlbra, 08, 69-9, 995. [9] T.F.Othmer, P.E.Tobas, d. Eg. Chem., 34, , 94. [0] D. B.Had, J. Phys. Chem., 34, , 930. [] J.M. Sorese, Ph.D. Thess, Techcal Uversty of Demark, Lygby, Demark, 980. teratoal Scholarly ad Scetfc Research & ovato 7(

PREDICTION OF VAPOR-LIQUID EQUILIBRIA OF BINARY MIXTURES USING QUANTUM CALCULATIONS AND ACTIVITY COEFFICIENT MODELS

PREDICTION OF VAPOR-LIQUID EQUILIBRIA OF BINARY MIXTURES USING QUANTUM CALCULATIONS AND ACTIVITY COEFFICIENT MODELS Joural of Chemstry, Vol. 47 (5), P. 547-55, 9 PREDICTIO OF VAPOR-LIQUID EQUILIBRIA OF BIARY MIXTURES USIG QUATUM CALCULATIOS AD ACTIVITY COEFFICIET MODELS Receved May 8 PHAM VA TAT Departmet of Chemstry,