Modeling of Phase and Chemical Equilibria for Systems Involved in Biodiesel Production

Transcription

1 855 A publcaton of CHEMICAL ENGINEERING TRANSACTIONS VOL. 43, 205 Chef Edtors: Sauro Perucc, Jří J. Klemeš Copyrght 205, AIDIC Servz S.r.l., ISBN ; ISSN The Italan Assocaton of Chemcal Engneerng Onlne at DOI: /CET54330 Modelng of Phase and Chemcal Equlbra for Systems Involved n Bodesel Producton Larssa P. Cunco, Regnaldo Gurardello* School of Chemcal Engneerng, State Unversty of Campnas (UNICAMP), Av. Albert Ensten 500, Campnas- SP. Brazl gura@feq.uncamp.br In recent years, the nterest n the use of renewable energy has encouraged the growth of studes nto renewable sources, such as the producton of bofuels. Ths wor nvestgates the vapor-lqud equlbrum (VLE), vapor-lqud-lqud equlbrum (VLLE) and lqud-lqud equlbrum (LLE) of bnary, ternary, quaternary and pseudo-quaternary systems usng an optmzaton approach for components found n bodesel producton, whch conssts n vegetable ols, fatty acds, esters and alcohols. A methodology has been developed based on the Gbbs energy mnmzaton and the dscretzaton of the molar fracton doman, whch ncorporates a thermodynamc model to descrbe the phase equlbra. Ths wor used the Soave-Redlch- Kwong equaton of state (SRK-EOS) for phase equlbra calculaton, where the compressblty factor was used to determne the phase present n the system (lqud, vapor or supercrtcal flud). The chemcal and phase equlbrum problem s solved usng lnear programmng and satsfes the mass balance constrants. It was found that the proposed methodology adequately represents the selected expermental data, wth an average absolute devaton of.3 % obtaned.. Introducton The most used energy sources worldwde are stll non-renewable, such as ol, coal and natural gas. Factors such as envronmental problems encourage the growth of studes n renewable sources such as bofuels. In large development, bodesel has the man advantages: ) It s bodegradable and non-toxc; 2) It contrbutes to the reducton of greenhouse gases, emssons of partculate matter and acd ran. The bodesel producton nvolves a number of processng steps that requre nowledge of chemcal or phase equlbrum. When a system s n equlbrum, the Gbbs energy has a mnmum value for a gven pressure and temperature. The calculaton of the correct number of phases n equlbrum and ts composton can be dvded n two manly categores: through the equaton-solvng approach for searchng same fugacty or chemcal potental n all the present phases n equlbrum, or through the drect mnmzaton of the Gbbs energy (Teh and Rangaah, 2002). The frst approach solves the necessary condtons to guarantee chemcal equlbrum, but only one soluton mnmzes the Gbbs energy and satsfes the second law of thermodynamcs. Consderng the mnmzaton of Gbbs energy, a common problem observed s the convergence n a global soluton and a good estmate of the composton as a startng pont s requred. Ths wor presents a lnear program model formulaton for phase and chemcal equlbra calculaton n quaternary and pseudo-quaternary systems, based on a dscretzaton of the molar fracton doman. The proposed approach can be appled to any thermodynamc model such as equatons of state or excess Gbbs energy models. However, n ths wor, the equaton of state of Soave-Redlch-Kwong (SRK-EOS) wth the mxng rule of van der Waals two adjustable parameters (VDW-2) was employed. The use of ths equaton of state allows the calculaton of both vapor-lqud equlbrum n elevated condtons of pressure and temperature, vapor-lqud n lower condtons of pressure and temperature, and lqud-lqud equlbrum. In the second part of ths wor, the performance of the proposed method n predctng phase and chemcal Please cte ths artcle as: Cunco L., Gurardello R., 205, Modelng of phase and chemcal equlbra for systems nvolved n bodesel producton, Chemcal Engneerng Transactons, 43, DOI: /CET54330

2 856 equlbrum was analyzed for eght types of vegetable ols (cotton, peanut, canola, coconut, sunflower, corn, palm and soybean) and ther respectve methyl and ethyl esters. 2. Methodology 2. Thermodynamc Equlbrum The chemcal and phase equlbra, n a multphase and multcomponent closed system, at constant pressure and temperature, can be calculated by the mnmzaton of the Gbbs energy n terms of fugacty: NP NC ˆf G= n μ + R T ln () = = f where n s the number of moles of each component at each phase, NC s the number of compounds and NP s the number of phases. In ths wor, the SRK equaton of state was consdered to represent both vapor and lqud phases. The mnmzaton of the Gbbs energy must satsfy some constrants: - the number of moles cannot be negatve, for any component n any phase: n 0 for =, 2,..., NC and =, 2,..., NP (2) - the molar balance for each component n the system: NP 0 n = n ν ξ for =, 2,..., NC (3) = where ν s the stochometrc coeffcent of each compound n the reacton and ξ s the extent of the reacton. If some compound does not react, then ν s zero. 2.2 Dscretzaton of the molar fracton doman The problem of mnmzng the Gbbs energy was formulated as a lnear programmng model through a dscretzaton of the molar fracton doman, as seen n Ross et al. (2009). However, n ths wor the methodology was extended to consder quaternary systems. The system s consdered to have a potental number of phases, each one wth molar fractons gven by: z = δ ( p ) for p =, 2,..., N + (4) ( ) δ ( ) z2 = z δ p2 for p2 =,2,..., p (5) z3 = z z2 p3 for p3 =, 2,..., p 2 (6) z = z z z (7) where δ s /N. At each pont n the molar fracton doman, all roots of the SRK equaton of state are calculated and for each possble real root a potental phase s assgned. In ths way, dscontnutes are consdered, snce for the same molar fracton t may exst a lqud or a vapour phase. 2.3 Dfferentaton of the phases The dfferentaton of the phases present n the system was performed consderng the root of the cubc equaton. When the cubc equaton has three real roots, more than one phase s present n the system. These roots were dealng wth the compressblty factors calculated by the algorthm. For SRK-EOS, the compressblty factors are calculated as: Z Z + ( A B B ) Z AB= 0 (8) where: amp bp m A =, B = (9) ( RT ) 2 RT The smallest root represents the lqud phase n the case of vapor-lqud equlbrum (VLE) systems. For lqudlqud equlbrum (LLE) systems, the values of the molar fractons should be observed to dfferentate the lqud phases. In the cases where the equaton does not have three real roots, but just one, the sothermal

3 857 compressblty was consdered to defne f the phase s lqud or vapour. The SRK-EOS equaton has the followng sothermal compressblty coeffcent: 2 2 ( b ) V V V β = = ( ) ( 2 )( ) V P T RTV V b a V b V b T 2 For pressures close to atmospherc, the Polng et al. (98) crteron for the phase defnton s: β < / atm, ndcates lqud phase () 0.9 / P < β < 3.0 / P, ndcates vapor phase (2) To dentfy whether the phase les n the crtcal regon, mxng rule were used for crtcal propertes of the mxture (temperature and pressure). If the temperature and pressure of the chosen system are above of the crtcal values calculated, the result ndcates a supercrtcal flud. 3. Results and Dscusson Not all physcal propertes of fatty acds, esters, ols and bodesel are avalable n the lterature. However, t s possble to use predctve methods such as group contrbuton methods to estmate these propertes. A detaled dscusson of the analyss of the estmaton of the propertes can be seen n our prevous wor (Cunco et al., 203). The values used for the compounds utlzed n ths wor can be seen n Table. Table : Pure component propertes consdered n the phase equlbrum calculatons. Component T c (K) P c (KPa) V c (cm 3 /mol) ω Δ H 0 f (J/mol) Δ G 0 f (J/mol-) 0 cp (J/mol.K) at 298 K Trolen a 334 a 3, ,0727-4, Methanol a 8,090 a 7 a a -200,940 a -62,320 a a Glycerol a 7,500 a 264 a 0.53 a -38,2 a -06,859 a 5.28 a Methyl oleate a,280 a,060 a.049 a -626,000 a -70,900 a a Methyl laurate 708.9, , , Methyl myrstate , , , Methyl lnoleate ,329, ,052-65, Ethyl laurate , ,449-24, Ethanol a 6,37 a a a -59,860 a -7,3860 a a Ethyl myrstate , ,07-23, Olec acd a,390 a, a.82 a -762,20 a -26,00 a a Hexane a 3,025 a 37 a 0.30 a -66,940 a -45,400 a 4.79 a Water a 22,055 a 55.9 a a -24,80 a -237,20 a a a Expermental values from DIADEM (2000) and NIST (n: 200). (0) The results of the proposed methodology and the compounds present n bodesel producton were compared wth expermental data found n lterature consderng the average absolute devaton - AAD (%): AAD (%) = 00 where NP NC = = lt x x NP NC wor (3) lt x refers to the value of the molar fracton found n the lterature and wor x ths wor. The problem of mnmzng the Gbbs energy, subject to the restrctons of molar balances and non negatvty of mol number, was solved usng the software GAMS (General Algebrac System Model) wth CPLEX as solver. The CPU tme was low (maxmum 6.68 seconds - Pentum III, 52MB, 900MHz, OS UNIX, parallel run). For bnary and ternary systems, δ was set to 0.002, and for quaternary systems t was set to 0.02.

4 Case Studes - Phase Equlbrum Phase equlbrum data sets avalable n lterature were chosen to analyze the proposed methodology. Representatve bnary and ternary expermental data of phase equlbrum for systems contanng components present n bodesel producton were selected to valdate the methodology. For quaternary systems, Tzvar et al. (2008) wor was consdered for compounds used n the process of purfcaton of the bodesel, where water s commonly used n the wash step of the bodesel. The wor of Felce et al. (2008) was consdered for compounds combned wth an organc solvent, as hexane. Fgure brngs an example of the model representaton of bnary system consderng the proposed methodology, whle the dfference observed for the phase calculatons by the methodology can be seen n Fgure 2 for ternary systems. Pressure 0 2 (KPa) Molar fracton (x) Fgure.VLE of bnary system: methyl myrstate () and methanol (2). Expermental data (Shmoyama et al., 2007): T= 493K, * T= 523K andn T= 543K, Calculated: SRK-EOS, The approach consderng SRK-EOS equaton of state showed good agreement wth expermental data. The absolute average devaton (% mole fracton) does not exceed 2.2 % and s less than % for some of the systems. Good representaton of expermental data was also obtaned for VLE and bnary system. Both sothermal and sobarc data could be ftted consderng the proposed methodology. It was observed better representaton by the methodology for the glycerol phase data n comparson wth the same methodology for the bodesel phase, whch can be explaned by the dffculty of some models n representng systems contanng major carbonc chans components. Note that some of the systems had the pure component propertes, such as crtcal temperature ( T c ), estmated by group contrbuton method. In those systems, there was a hgher devaton n the phase equlbrum data representaton. Fgure 2: LLE of ternary system: Olec acd, ethanol and water. Expermental data (Zhang and Hll, 99): T= K, T= K and T= K, Calculated usng SRK-EOS For some of the systems where the values of the bnary parameter ( j ) were not avalable n lterature, the relatonshp of Chueh and Prausntz (967) was consdered. The average absolute devaton and computatonal tme n seconds (s) for the proposed methodology and quaternary systems can be seen n Table 2.

5 859 Table 2: Average absolute devaton and computatonal tme for quaternary systems Systems AAD (%) CPU tme (s) Methyl oleate-methanol-glycerol-hexane Methyl oleate-methanol-glycerol-water Case Studes - Chemcal Equlbrum In ths part of the wor, combned chemcal and phase equlbra calculatons are presented. The molar balances n the Gbbs mnmzaton consders the stochometrc coeffcents. Expermental data of molar ratos (ol: alcohol) and ts converson n bodesel found n lterature were compared wth the calculated values. Dfferent operatng condtons (temperature, pressure, molar rato of ol: alcohol) were consdered to see how they affect the converson nto bodesel. All physcal propertes of pseudo-components (vegetable ols and esters) necessary n the modelng were calculated usng group contrbuton methods. Frst, the calculated values were compared wth avalable data for bodesel converson found n lterature, as can be seen n Table 3. Then, calculated values obtaned for a molar rato of alcohol equal to :6 and usng the proposed method were compared for both methanol and ethanol, and the results are presented n Table 4. Table 3: Converson n bodesel at 0.3 KPa usng the proposed methodology and comparson wth expermental values Temperature(K) Vegetable Ol Calculated (%) Expermental (%) Soybean (Santos et al., 203) Coconut (Rbero et al., 202) A good agreement was observed between expermental data and calculated chemcal and phase equlbra, wth smlar conversons n bodesel as showed n Noureddn and Zhu (2009) whch consdered the netcs reacton and presented values close to 90 to 00% of converson n bodesel for the molar rato ol: methanol equal to :6. Table 4: Bodesel converson obtaned for each vegetable ol (molar rato of ol: alcohol :6) at 0.3 KPa. Temperature (K) Vegetable Ol Wth Methanol Wth Ethanol Coconut Palm Cottonseed Soybean Corn Sunflower Canola Peanut Coconut Palm Cottonseed Soybean Corn Sunflower Canola Peanut It s mportant to hghlght that n the pseudo-components, just the tracylglycerols (TAGS) were consdered, snce TAGS represent around 95 % of vegetable ols total composton. For vegetable ols, pure fatty acd propertes were used to estmate the probable tracylglycerols (TAGS) composton accordng to Ceran (2005); for bodesels, the composton n methyl and ethyl esters followed the fatty acd composton reported by Ceran (2005). Propertes of these mxtures were consdered as smple molar averages of the ndvdual propertes of each component.

6 Concluson The proposed methodology was able to fnd the chemcal and phase equlbrum usng an approxmaton of the Gbbs energy based on the dscretzaton of the molar fracton doman. Snce the problem s formulated as a lnear programmng model, the soluton s easy to fnd. The methodology proposed does not restrct the use of any thermodynamc model, although n ths wor t focused on the SRK equatons of state. The use of a cubc EOS allows the model to consder dscontnutes such as a lqud and vapour phase for the same molar fracton. The number of phases n equlbrum and the number of moles of each compound n each phase were satsfactorly calculated and compared wth avalable expermental data n lterature, wth devatons often less than % and not exceedng 2.5 %. The computatonal tme was low (maxmum 6.68 seconds), even for the more complex systems, as the ones wth four compounds. The estmate of the physcal propertes of pure compounds present n the producton of bodesel, as for fatty acds, methyl and ethyl esters, was satsfactorly calculated usng group contrbuton methods. The predcton of chemcal equlbrum and phase for eght dfferent types of ols (peanut, cotton, canola, coconut, sunflower, corn, palm and soybean) was performed satsfactorly for systems contanng methanol and ethanol. The converson observed (90 or 00%) nto bodesel reached the results expected n the lterature, even though the results n lterature consder reacton netcs. Acnowledgements The authors gratefully acnowledge the fnancal support from CAPES and CNPq. References Ceran R., 2005, Computatonal Processes of Desacfcaton and Deodorzaton of Vegetable Ol, D.Sc. Thess, Unversty of Campnas, Campnas, Brazl. Chue P.L., Prausntz J.M., 967, Vapor-Lqud Equlbra at Hgh Pressures: Calculaton of Partal Molar Volumes n Nonpolar Lqud Mxtures, AIChE J. 3, Cunco L.P., Ceran R., Gurardello R., 203, Estmaton of Physcal Propertes of Vegetable Ols and Bodesel usng Group Contrbuton Methods, Chem. Eng. Trans. 32, DIADEM, 2000, Publc v..2 - DIPPR Informaton and Data Evaluaton Manager. Felce R.D., Faver D.D., Andres P., Ottonello P., 2008, Component Dstrbuton between Lght and Heavy Phases n Bodesel Processes, Ind. Eng. Chem. Res. 47, NIST - Natonal Insttute Search Technology. <webboo.nst.gov>. Accessed Noureddn H., Bandlamud S.R. P., Guthre E.A., 2009, A novel method for the producton of bodesel from the whole stllage-extracted corn ol, J. Am. Ol Soc. 86, Polng B.E. Grens E.A., Prausntz J.M., 98, Thermodynamc Propertes from a Cubc Equaton of State, Avodng Trval Roots and Spurous Dervatves, Ind. Eng. Chem. Process Des. Dev. 7, Rbero L.M.O., Santos B.C. da S., Almeda R.M.R.G, 202, Studes on reacton parameters nfluence on ethanolc producton of coconut ol bodesel usng mmoblzed lpase as a catalyst, Bomass Boenerg. 47, Ross C.C.R.S., Cardozo-Flho L., Gurardello R., 2009, Gbbs free energy mnmzaton for the calculaton of chemcal and phase equlbrum usng lnear programmng, Flud Phase Equl. 278, Shmoyama Y., Iwa Y., Jn B.J., Hraya T., Ara Y., 2007, Measurement and correlaton of vapor lqud equlbra for methanol + methyl laurate and ethanol + methyl myrstate systems near crtcal temperature of methanol, Flud Phase Equl., 257, Santos R.C.R., Vera R.B., Valentn A., 203, Montorng the converson of soybean ol to methyl or ethyl esters usng the refractve ndex wth correlaton gas chromatography, Mcrochemcal J., 09, Teh Y.S., Rangaah G.P., 2002, A study of equaton-solvng and gbbs free energy mnmzaton methods for phase equlbrum calculatons, Trans IChemE 80, Tvzar R., Mclean D.D., Kates M., Dube M.A., 2008, Lqud Lqud Equlbra of the Methyl Oleate Glycerol Hexane Methanol System, Ind. Eng. Chem. Res. 47, Zhang Z., Hll G.A, 99, Ternary Lqud-Lqud Equlbra of Water, Ethanol, and Olec Acd, J. Chem. Eng. Data 36,