A-UNIFAC Modeling of Binary and Multicomponent Phase Equilibria of Fatty Esters+Water+Methanol+Glycerol
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1 -UNIFC Modelng of Bnary and Multcomponent Phase Equlbra of Fatty Esters+Water+Methanol+Glycerol N. Garrdo a, O. Ferrera b, R. Lugo c, J.-C. de Hemptnne c, M. E. Macedo a, S.B. Bottn d,* a Department of Chemcal Engneerng, FEUP, Unversty of Porto, Porto, Portugal b Departamento de Tecnologa Químca e Bológca - Insttuto Poltécnco de Bragança, Campus de Santa polóna, p Bragança, Portugal c Insttut Franças du Pétrole Drecton Chme et Physco-Chme pplquées, & 4 av de Bos Préau, Ruel Malmason, France d Planta Ploto de Ingenería Químca PLPIQUI, Unversdad Naconal del Sur, Camno La Carrndanga Km 7.5 CC 77, Bahía Blanca, rgentna Correspondng author: Tel.: ; fax: ; E-mal address: sbottn@plapqu.edu.ar (S.B. Bottn) Keywords: thermodynamc modelng, -UNIFC, bodesel bstract The producton of methyl and ethyl esters of fatty acds s of great ndustral nterest, consderng the drect applcaton of these esters as bodesel. Predcton of the phase behavour of mxtures contanng fatty esters, alcohols, glycerol and water s of utmost mportance for the desgn and optmzaton of bodesel purfcaton and by-products recovery processes. In ths wor we show the capablty of -UNIFC to correlate and predct the phase behavour of these mxtures. Ths G E model s an extenson of UNIFC that explctly ncludes assocaton effects between groups, based on the statstcal Werthem theory []. -UNIFC wth the fnal set of parameters s able to predct wth good agreement expermental data on bnary and ternary lqud-lqud equlbra of glycerol, methanol and fatty esters as well as nfnte dluton actvty coeffcent for these systems. ddtonally, satsfactory results are obtaned for the predcton of lqud-lqud equlbrum of bnary mxtures contanng water and fatty acd esters.. Introducton Bodesel can be prepared by transesterfcaton of trglycerdes wth an excess of alcohol, to produce methyl or ethyl esters of fatty acds and glycerol. fter reacton, several separaton processes are requred for the purfcaton of bodesel and the recovery of by-products. Knowledge of phase equlbra of the reactve mxture comprsng fatty esters, alcohols, glycerol and water s therefore essental for the desgn and optmzaton of these processes. Consderng the presence of several hydrogen bondng components, the assocatng - UNIFC actvty coeffcent model s appled to descrbe bnary and ternary lqud-lqud equlbra (LLE) of glycerol, methanol and fatty acd esters mxtures, as well as LLE of water and methyl esters. The parameterzaton methodology s descrbed n secton 3 and the results obtaned are shown and dscussed n secton 4. The man conclusons are fnally presented n secton UNIFC model
2 Mengarell et al. [] have proposed a modfed UNIFC model that taes nto account assocaton effects. Ths G E model adds a group-contrbuton assocaton term to the orgnal UNIFC combnatoral and resdual expressons (Fredenslund et al., 975). The assocaton term s based on Werthem s theory for fluds wth hghly drected attractve forces [2]. The general expresson for the assocaton contrbuton to the actvty coeffcent s a functon of the fracton of non-bonded stes n the soluton ( X ) and n pure-component ( X ):: lnγ assoc = NG X X X ν + + ln r ρ = X 2 2 () In ths equaton ν s the number of groups of type n a molecule of component, ρ represents the densty of assocatng group n the mxture and r represents the UNIQUC molecular volume of speces (evaluated from UNIFC group volume parameters R n the usual way;.e. summaton over all NG groups wthn molecule : NG r = ν R summaton n eq. () extends to all NG assocatng groups and assocatng stes. = ). The The fracton of non-bonded stes X s a functon of the assocatng group densty ρ and the assocaton strength B between ste of group and ste B of group. Ths fracton s gven by the followng expresson []: X = (2) NG B B + ρ X = B smlar equaton s appled to caculate the fracton of non-bonded stes n pure component : X = (3) NG B B + ( ρ ) X In these equatons ) = B ρ and ( ρ represent the densty of assocatng group n the mxture and n pure assocatng component, respectvely, evaluated through the value of the UNIQUC molecular volume of spece : NC = ν x = ρ = NC (4) r x ν ( ρ ) = (5) r where x s the mole fracton of component n the mxture. The denstes calculated by the last equatons are dmensonless and characterze the concentraton of assocatng group n the soluton and n pure component. The assocaton strength B s a functon of two assocaton parameters: the energy ( B ε ) and volume ( B κ ) of assocaton. B B B = κ [exp( ε / T ) ] (6)
3 3. Model Parameterzaton 3. ssocaton parameters ssocaton effects n methanol, water and glycerol are represented by the same hydrogenbondng hydroxyl group (OH) havng two assocatng stes (one electronegatve O and one electropostve H). There s one assocatng group n methanol and water and three n glycerol. Group CCOO n fatty esters can cross-assocate wth the electropostve ste of the hydroxyl OH group. The values for the hydroxyl (OH) and ester (CCOO) self- and cross-assocaton parameters were already avalable [3] and are presented n Table. Table. Energy / and volume assocaton parameters for the -UNIFC model [3] / (K) Self-assocaton OH Cross-assocaton OH CCOO κ 3.2 Resdual nteracton parameters The ntroducton of an assocaton contrbuton to the actvty coeffcent, maes t necessary to determne a new set of parameters for the nteracton between assocatng and nonassocatng functonal groups. The resdual parameters for the nteractons between water and ester functonal groups were prevously estmated usng low-pressure VLE data and nfnte dluton actvty coeffcenta γ n bnary mxtures of esters and water [3]. For the quantfcaton of the resdual non-dealtes, both methanol and glycerol molecules are represented by the molecular groups CH 3 OH and C 3 H 8 O 3. The resdual nteracton parameters between CH 3 OH and C 3 H 8 O 3 were obtaned by fttng sothermal lqud-lqud equlbrum data on the ternary system dodecanoc acd methyl ester-methanol glycerol [4]. The glycerol/paraffn (C 3 H 8 O 3 /CH 2 ) and glycerol/ester (C 3 H 8 O 3 /CCOO) nteracton parameters were estmated from expermental data on lqud-lqud equlbra and γ of the bnary systems dodecanoc acd methyl ester (DME)-glycerol and hexanoc acd methyl ester (HME)-glycerol n the range of 320 K to 438 K [4]. The resdual group nteracton parameters used n ths wor are reported n Table 2. Table 2. Resdual group nteracton parameters a m,n (K) for the -UNIFC model n m CH 2 C 3 H 8 O 3 CH 3 OH CCOO H 2 O CH c 22.7 b 232. a b C 3 H 8 O c e c n.a. CH 3 OH b e d b CCOO 4.8 a 20.0 c 8.49 d b H 2 O 36.8 b n.a b 50.3 b 0.0 a: orgnal UNIFC parameters [5]; b: [3]; c: [6]; d: [7]; e: ths wor; n.a.: not avalable.
4 4. Results and dscusson In ths secton several correlaton and predcton results are presented. 4. Bnary systems of esters and water n mportant bofuel qualty parameter s ts maxmum water content. Thus, the correct descrpton of the solublty of water n fatty acd esters s of maor mportance durng producton and storage of bodesel. The -UNIFC model has been prevously appled to descrbe low pressure VLE data and γ of bnary systems of water and short-chan esters [3]. In ths wor the same assocaton and resdual parameters are used to predct lqud-lqud equlbrum of water and several fatty acd esters. Fgures and 2 show that -UNIFC predctons are n good agreement wth the expermental nformaton avalable E+00 2.E-05 3.E-05 5.E-05 x ester x ester Fgure. Lqud-lqud equlbrum of octanoc acd methyl ester + water: -UNIFC predctons (sold lnes) and expermental data (symbols) [4]. x water methyl hexanoate methyl heptanoate methyl octanoate methyl tetradecanoate methyl octadecanoate methyl dodecanoate Fgure 2. Water solublty n several fatty methyl esters: -UNIFC predctons (sold lnes) and expermental data (symbols) [8].
5 4.2 Bnary systems of esters and glycerol Fgures 3-8 compare expermental data [4] wth -UNIFC correlaton of lqud-lqud equlbrum and nfnte dluton actvty coeffcents of the system ester / glycerol Fgure 3. Comparson between -UNIFC correlated (sold lnes) and expermental (symbols) solublty of glycerol n HME Fgure 4. Comparson between -UNIFC correlated (sold lnes) and expermental (symbols) solublty of HME n glycerol Fgure 5. Comparson between -UNIFC correlated (sold lnes) and expermental (symbols) solublty of glycerol n DME γ Fgure 7. Comparson between -UNIFC correlated (sold lnes) and expermental (symbols) nfnte dluton actvty coeffcents of DME n glycerol Fgure 6. Comparson between -UNIFC correlated (sold lnes) and expermental (symbols) solublty of DME n glycerol γ Fgure 8. Comparson between -UNIFC correlated (sold lnes) and expermental (symbols) nfnte dluton actvty coeffcents of glycerol n DME. 4.3 Ternary systems of esters, methanol and glycerol
6 The -UNIFC model wth the parameters lsted n Tables and 2 was used to calculate the flud phase equlbrum boundares of fatty acd methyl ester-methanol-glycerol mxtures at several temperatures [4,6]. Table 3 reports the mean standard devatons n the calculaton of methanol dstrbuton coeffcents by the -UNIFC model. The dstrbuton coeffcent was defned as the rato between the methanol mole fracton n the fatty acd methyl ester and glycerol phases. Table 4 gves the mean and maxmum absolute dfferences between calculated and expermental molar fractons of glycerol n the fatty ester phase and molar fractons of fatty ester n the glycerol Table 3. Mean standard devatons n the calculaton of methanol dstrbuton coeffcents by the -UNIFC model System Standard Devatons % (*) HME glycerol methanol 2.73 DME glycerol methanol 6.3 Methyl oleate (MO) glycerol methanol 6.36 (*) = 2 00 [ ( ) ] ; NP = number of expermental ponts Table 4. bsolute devatons between calculated and expermental mole fractons of dluted components usng -UNIFC System Mol fracton of glycerol n the fatty ester rch phase Mean dfference Maxmum dfference Mol fracton of fatty ester n the glycerol phase Mean dfference Maxmum dfference HME + methanol + glycerol DME + methanol + glycerol MO + methanol + glycerol Fgures 9 to 2 compare expermental data wth -UNIFC calculatons. x X methanol Methanol T=333.5K X Glycerol x X HME Kmethanol K T=333.5K T=352.8K x methanol X n HME phase phase
7 Fgure 9. Comparson between -UNIFC predcted (sold lnes) and expermental (dashed lnes) [4] te-lnes of the ternary system HME-methanol-glycerol at K. Fgure 0. Comparson between -UNIFC predcted (sold lnes) and expermental (symbols) [4] dstrbuton coeffcents of methanol n ternary system HMEmethanol-glycerol. x X methanol Methanol T=33.5K x X glycerol Glycerol x X MO Kmethanol K methanol T=33K T=333KC T=353K x methanol X n MO MO phase phase Fgure. Comparson between -UNIFC predcted (sold lnes) and expermental (symbols) [6] dstrbuton coeffcents of methanol n ternary system MO-methanolglycerol at 33.5 K. Fgure 2. Comparson between -UNIFC predcted (sold lnes) and expermental (symbols) [6] dstrbuton coeffcents of methanol n ternary system MO-methanolglycerol. 5. Conclusons The -UNIFC model gves a good representaton of the lqud-lqud equlbra of mxtures contanng glycerol, methanol and fatty esters as well as nfnte dluton actvty coeffcents n these systems. Ths group-contrbuton model can be further extended to descrbe the phase equlbra of multcomponent mxtures of nterest n bodesel producton. References [].C. Mengarell, E.. Brgnole, S.B. Bottn, Flud Phase Equlb. 63 (999) Fredenslund, R.L. Jones, J.M. Prausntz, IChE. J. 2 (975) [2] M. Werthem, J. Stat. Phys. 35 (984) 9. [3] O. Ferrera, E.. Macedo, S.B. Bottn, Flud Phase Equlbra 227 (2005) [4] F.M. Korgtzsch, Study of Phase Equlbra as a Fundament for the Refnement of Vegetable and nmal Fats and Ols. Ph.D. Dssertaton, TU Berln, 993. [5] J. Gmehlng, P. Rasmussen,. Fredenslund, Ind. Eng. Chem. Process Des. Dev. 2 (982) [6].E. ndreatta, L.M. Casás, P. Hegel, S.B. Bottn, E.. Brgnole, Ind. Eng. Chem. Res. 47 (2008) [7] L.M. Casás, B. Orge, O. Ferrera, J. Chem. Eng. Data 53 (2008) [8] M.B. Olvera, F.R. Varanda, I.M. Marrucho,.J. Quemada, J..P. Coutnho, Ind. Eng. Chem. Res. 47 (2008)
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