Phase equlbrum of the CO2/glycerol system: Expermental data by n stu FT-IR spectroscopy and thermodynamc modelng Yao Medna-Gonzalez, Therry Tassang, Séverne Camy, Jean-Stéphane Condoret To cte ths verson: Yao Medna-Gonzalez, Therry Tassang, Séverne Camy, Jean-Stéphane Condoret. Phase equlbrum of the CO2/glycerol system: Expermental data by n stu FT-IR spectroscopy and thermodynamc modelng. Journal of Supercrtcal Fluds, Elsever, 213, vol. 73, pp. 97-17. <1.116/j.supflu.212.11.12>. <hal-87768> HAL Id: hal-87768 https://hal.archves-ouvertes.fr/hal-87768 Submtted on 29 Oct 213 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.
Open Archve TOULOUSE Archve Ouverte (OATAO) OATAO s an open access repostory that collects the work of Toulouse researchers and makes t freely avalable over the web where possble. Ths s an author-deposted verson publshed n : http://oatao.unv-toulouse.fr/ Eprnts ID : 9936 To lnk to ths artcle : do:1.116/j.supflu.212.11.12 URL : http://dx.do.org/1.116/j.supflu.212.11.12 To cte ths verson : Medna-Gonzalez, Yao and Tassang, Therry and Camy, Séverne and Condoret, Jean-Stéphane Phase equlbrum of the CO2/glycerol system: Expermental data by n stu FT-IR spectroscopy and thermodynamc modelng. (213) The Journal of Supercrtcal Fluds, vol. 73. pp. 97-17. ISSN 896-8446 Any correspondance concernng ths servce should be sent to the repostory admnstrator: staff-oatao@lstes-dff.np-toulouse.fr
Phase equlbrum of the CO 2 /glycerol system: Expermental data by n stu FT-IR spectroscopy and thermodynamc modelng Y. Medna-Gonzalez a,b,c,1,2, T. Tassang c,, S. Camy a,b,1, J.-S. Condoret a,b, a Unversté de Toulouse, INPT, UPS, Laboratore de Géne Chmque UMR CNRS 3, 4, Allée Emle Monso, F-313 Toulouse, France b CNRS, Laboratore de Géne Chmque, F-31432 Toulouse, France c Insttut de Scences Moléculares, UMR CNRS, Unversté Bordeaux, 1, cours de la Lbératon, 334 Talence Cedex, France a b s t r a c t Keywords: Glycerol Supercrtcal CO 2 Bphasc system Phase equlbrum Infrared spectra Thermodynamc modelng Phase equlbrum ermental data for the CO 2 /glycerol system are reported n ths paper. The measurements were performed usng an n stu FT-IR method for temperatures rangng from 4 C to 2 C and pressures up to. MPa, allowng determnaton of the mutual solublty of both compounds. Concernng the CO 2 rch phase, t was observed that the glycerol solublty n CO 2 was extremely low (n the range of 1 n mole fracton) n the pressure and temperature domans nvestgated here. Conversely, the glycerol rch phase dssolved CO 2 at mole fractons up to.13. Neglgble swellng of the glycerol rch phase has been observed. Modelng of the phase equlbrum has been performed usng the Peng Robnson equaton of state ( EoS) wth classcal van der Waals one flud and EoS/G E based mxng rules (PSRK and MHV2). Satsfactory agreement was observed between modelng results and ermental measurements when PSRK mxng rules are used n combnaton wth UNIQUAC model, although UNIFAC predctve approach gves unsatsfactory representaton of ermental behavor. 1. Introducton Recently, nterest n bphasc systems, whch couple supercrtcal CO 2 and a conventonal lqud solvent have been hghlghted [1,2], as they can provde nnovatve reacton meda. The nterest of these bphasc systems s maxmum when the partner solvent s a bosourced solvent because such systems become then envronmentally frendly. Such bphasc systems are useful to overcome the lmted solvatng power of pure scco 2, especally n respect to homogeneous catalyss where n ths case catalysts can be more easly solublzed n the lqud solvent. They can also allevate the drawback of the conventonal use of bosourced solvents whose low volatlty usually handcaps easy recovery of the reacton products. Indeed, supercrtcal CO 2 can be used to recover the reacton products by extracton from the lqud phase. In addton, these bphasc systems can be consdered as ntensfed systems because, n ths case, reacton and separaton are operated n one sngle step. Correspondng author. Tel.: +33 4 28 92; fax: +33 4 84 2. Correspondng author at: Unversté de Toulouse, INPT, UPS, Laboratore de Géne Chmque UMR CNRS 3, 4, Allée Emle Monso, F-313 Toulouse, France. Tel.: +33 34 32 36 97; fax: +33 34 32 37 7. E-mal addresses: t.tassang@sm.u-bordeaux1.fr (T. Tassang), jeanstephane.condoret@ensacet.fr (J.-S. Condoret). 1 Tel.: +33 34 32 37 13; fax: +33 34 32 37 7. 2 Tel.: +33 34 32 36 7; fax: +33 34 32 36 97. Among the bosourced solvents, glycerol s of prme nterest as t s a byproduct n bodesel fabrcaton and t s therefore very easly avalable. Provded ts potental own chemcal reactvty s not problematc, glycerol can be proposed as an alternatve reacton medum for water, when water s not sutable due to ts hydrolytc power or n the case of dehydraton reactons for nstance. Glycerol has been shown to be an nterestng alternatve for dfferent organc synthess [3,4] as for nstance selectve reducton of aldehydes, ketones and -ketoesters wth NaBH 4 []. Several other examples have been gathered n a revew by Daz-Alvarez et al. [6]. Studes by Jérôme and Gu [7 9], have shown that, n some reactons, such as the Aza-Mchael reacton of p-ansdne and the Mchael reacton of ndole, glycerol used as solvent s capable to acheve yelds up to 8% under catalyst-free condtons, these yelds beng hgher than those obtaned wth usual solvents. The same research group has developed a seres of catalysts combned wth sugarbased-surfactants of organc substrates whch favors mass transfer of organc substrates and lmts the undesred reactvty of glycerol [1]. However, drawbacks n the utlzaton of non-volatle solvents, such as glycerol, are stll the uneasy recovery of products and recyclng of catalysts. In ths context, bphasc systems usng supercrtcal CO 2 (scco 2 ) as a partner phase make t possble the solublzaton of the catalyst n the glycerol phase whle products are extracted by scco 2 [9,11,12]. In ths context, one prerequste for effectve desgn and control of such bphasc systems s the knowledge of the phase equlbrum http://dx.do.org/1.116/j.supflu.212.11.12
of the mxture. Also, understandng the effects of dssolved CO 2 on the physcochemcal propertes of the glycerol-rch phase s mportant for reacton desgn [13,14]. Indeed, CO 2 modfes the polarty of the solvent and, for nstance, from ths effect, ntally mscble compounds are lkely to become mmscble when the solvent s pressurzed wth CO 2, even at moderate pressures (. MPa) []. So, CO 2 can then act as a swtch to control the polarty and solvatng propertes of the partner solvent, allowng recovery of catalysts, products, byproducts, and so on. Despte ths recent growng nterest for scco 2 /glycerol system, phase equlbrum ermental data are scarce and not yet fully valdated. Only two studes upon ermental determnatons of solublty of glycerol n pressurzed CO 2 have been publshed [16,17] and ther results are not n coherence. To perform accurate measurements of concentratons of the phases n equlbrum, the technque of n stu FTIR spectroscopy can be proposed. Ths method has been prevously successfully appled n phase equlbrum studes for the determnaton of the CO 2 sorpton and swellng n lquds [18,19] and n polymers [2,21]. In partcular, we would lke to stress that molar absorpton coeffcents of CH stretchng vbratonal modes and combnaton bands are ected to exhbt lttle senstvty upon temperature and pressure condtons [2,22,23]. For example, Buback et al. [24] have shown that the molar absorpton coeffcent of combnaton bands of CO 2 were almost ndependent of the CO 2 densty. Therefore, IR spectroscopy allows determnng the concentraton of a gven spece n a mxture wth a statstcal error lower than 1%. Also, modelng of scco 2 glycerol phase equlbrum has been already proposed [] but the lack of ermental results dd not allow valdaton of the model. Such calculatons are useful but accurate predcton of CO 2 glycerol phase equlbrum has not been yet fully developed and compared wth ermental results. In ths context, the purpose of the present work s to ermentally determne the phase behavor of the CO 2 /glycerol system usng n stu FTIR spectroscopy and to propose an adequate thermodynamc modelng of the phase equlbrum data. 2. Expermental 2.1. Materals Dry glycerol wth purty of 99.% was purchased from Sgma Aldrch; water content was determned by ttraton wth a Mettler-Toledo DL38 Karl Fscher ttrator and found to be.4%. CO 2 N4 was obtaned from Ar Lqude. All chemcals were used wthout further purfcaton. A BoRad FTS-6A nterferometer equpped wth a globar as nfrared source, a KBr/Ge beamspltter and a DTGS (deuterated trglycne sulfate) detector has been employed to record sngle beam spectra n the range of 4 6 cm 1. Sngle beam spectra recorded wth 2 cm 1 resoluton were obtaned from the Fourer transformaton of 3 accumulated nterferograms. 2.2. Apparatus and procedure The hgh-pressure cell and the nfrared setup used for phase behavor determnaton erments have been descrbed thoroughly elsewhere [18]. Solublty of glycerol n CO 2 has been determned usng a cell wth an optcal path length of.3 mm and equpped wth germanum wndows, employng the followng procedure: bottom of the cell was flled wth dry glycerol and a magnetc bar was placed nsde. The cell was tghtly closed then placed nsde the nterferometer and thermostated at the desred temperature usng cartrdge heaters. CO 2 was pumped nsde the cell to the desred pressure and the system was agtated usng a magnetc strrer. After an equlbraton perod of at least 3 h, Table 1 Molar extncton coeffcents of glycerol and CO 2 for dfferent absorpton bands. Glycerol CO 2 Group frequency C H C H 2 2 + 3 Wave number (cm 1 ) 2933 2883 3696 ε (L mol 1 cm 1 ) 49.78 47.61 1.978 FT-IR spectra of the CO 2 rch phase were obtaned. Durng the stablzaton of the operatng condtons (weak decrease of the pressure between 1 and 1 bar that was compensated wth the manual pump), consecutve spectra were recorded every 3 mn. Equlbrum has been consdered as reached when at least three consecutve spectra spaced by 3 mn dd not show any sgnfcant absorbance dfference. Indeed, as a consequence of the hgh vscosty of glycerol, t has been observed that equlbraton perod was temperature dependent and decreased sharply wth temperature: at low temperatures (4 C) equlbraton needed about 12 h. Two seres of measurements have been performed for a number of ponts n specfed condtons of temperature and pressure to check for the reproducblty of the measurements. CO 2 solublty n glycerol was determned usng the same system by fllng the cell wth dry glycerol. The optcal path length was fxed to.12 mm and sapphre wndows were used for ths determnaton. FT-IR spectra of the glycerol-rch phase have then been acqured. Solublty erments were performed at temperatures rangng from 4 to 2 C and pressures up to MPa. 2.3. Data processng for the determnaton of mutual solublty and phase equlbrum Beer Lambert law (A = ε L c, where A s the sample absorbance, ε the molar extncton coeffcent (L mol 1 cm 1 ), L the optcal path length (cm) and c the sample concentraton (mol L 1 )) was used to calculate the concentratons of glycerol and CO 2 n each phase. In order to determne the concentraton of glycerol n the CO 2 -rch phase, the absorbance of the two peaks centered at about 2933 and 2883 cm 1 assocated to the CH stretchng mode of glycerol was used. As baselne correcton can nduce large errors when peak ntegrated area s used for quantfcaton, peak heght was used for these determnatons n order to mnmze ths error. In order to determne the concentraton of glycerol (C glycerol ) n the CO 2 -rch phase, molar extncton coeffcents (ε) for two selected bands of glycerol were determned from spectra of aqueous solutons of glycerol at known concentratons (see Table 1). We emphasze that the sgnal of the FTIR spectrum of glycerol n the C H stretchng regon was the same n water and n CO 2 whch shows, as t s ected, that the C H stretchng vbratonal modes of glycerol are not senstve to the nature of the solvent. Thus, the concentratons were calculated from the average of the concentraton values estmated wth the two consdered CH peaks of glycerol (see Table 1). In order to determne the CO 2 concentraton (C CO2 ) n the glycerol-rch phase, the peak heght of the 2 2 + 3 band of CO 2 centered at 3696 cm 1 was used. Molar extncton coeffcent of ths band was determned by recordng the nfrared spectra of neat CO 2 at dfferent temperatures and pressures, the densty (concentraton) was then obtaned from lterature [26]. Table 1 shows the obtaned ε value. Mole fracton of glycerol n the CO 2 -rch phase has been calculated as: x glycerol = C glycerol C glycerol + C CO2 (1) where C glycerol s the concentraton of glycerol as determned by our FTIR measurements and C CO2 s calculated from the NIST data [26].
Table 2 Densty of pure glycerol at atmospherc pressure as functon of temperature. T ( C) Densty (kg/m 3 ) a Densty (kg/m 3 ) Relatve dfference c 4 1272.3 1248 b.19 6 1281.3 12 b.36 8 19.2 1223 b.29 1 129.3 129.27 b 2.E 12 1189.7 1194.46 c.4 14 1163.6 1179.1 c.13 16 1131. 1164.4 c.29 18 1116. 1148.64 c.28 2 183.1 1131.78 c.43 a Data from ths study (precson ±%). b Data from Ref. [27]. c Data from Ref. [48]. Calculated as obtaned value lterature value. lterature value Indeed, as the solublty of glycerol n the CO 2 rch phase s very low (see below), t has been consdered that the concentraton of CO 2 n the CO 2 rch phase was not affected by the presence of glycerol and equal to that of neat CO 2 under the same temperature pressure condtons. Mole fracton of CO 2 n the glycerol-rch phase was obtaned from: x CO2 = C CO2 C CO2 + C glycerol (2) where C CO2 s the concentraton of absorbed CO 2 n the glycerol rch-phase determned by our FTIR measurements and C glycerol s the concentraton of neat glycerol obtaned from FTIR measurement performed on neat glycerol as a functon of temperature (see below). Indeed, as t wll be evdenced below n Secton 3.2, sgnfcant swellng of the glycerol rch phase by scco 2 was not detected n the range of temperature and pressure nvestgated here. Therefore, t was assumed that the concentraton of glycerol n the glycerol rch phase was equal to that of neat glycerol under the same temperature condtons. Glycerol densty at atmospherc pressure has been calculated as a functon of temperature from pure glycerol spectra, by usng the peak centered at about 7 cm 1, whch was assgned to 2 C H. Thus, usng the Beer Lambert law, the concentraton (densty) of neat glycerol was calculated usng the peak heght of the band observed at 7 cm 1 assocated wth the 2 C H overtone. To determne the molar extncton coeffcent ε for ths mode, the spectrum measured at T = 1 C was used as a reference and the correspondng concentraton data reported n the lterature at the same temperature [27]. The concentraton (densty) values of neat glycerol calculated usng ths method are shown n Table 2 and good agreement wth values reported n the lterature [27] can be observed, relatve dfference between both values s presented as well. The present values of densty have then been used to calculate the concentraton of the glycerol-rch phase. Fnally, takng nto account all the source of errors assocated wth our methodology (baselne correcton, constant molar extncton coeffcent, spectrometer stablty), a maxmum relatve error of about ±% n the concentraton values has been estmated. We emphasze that the relablty of such methodology has already been demonstrated n prevous nvestgatons on the mutual solublty of epoxde wth CO 2 [19] and water wth CO 2 [23] where a satsfactory agreement wth lterature data was shown. 2.4. Phase equlbrum modelng Thermodynamc modelng was performed usng the wellknown Peng Robnson equaton of state ( EoS) [28],.e., wth a dfferent resson of the m term for compounds wth acentrc factor greater that the one of n-decane (.491) [29], as t s the case for glycerol. In a frst approach, Peng Robnson EoS has been Table 3 Characterstc parameters of pure compounds used n EoS. Compound T c (K) P c (MPa) ω M (kg kmol 1 ) CO 2 [49] 34.21 7.38.2236 44.1 Glycerol [] 8 7..16 92.9 used wth the classcal van der Waals one-flud mxng rule (vdw1f) for a and b parameters. Classcal combnng rules,.e., geometrc mean rule wth k j bnary nteracton coeffcent for a j parameter, and arthmetc mean rule, wthout any nteracton coeffcent, for b j parameter have been used. Fnally, a and b parameters of the mxture are obtaned from the followng equatons: n n a(t) = z z j a a j (1 k j ) (3) b = wth =1 j=1 n z b (4) =1 a =.47229 R2 T 2 c, P c, (T) () b =.77796739 RT c, P c, (6) The computaton procedure for the parameter (T) depends on the temperature and acentrc factor values of the compound. For compounds above ther crtcal temperature, (T) s calculated as recommended by Boston and Mathas [3]: (T) = [[c (1 T d r, )]]2 (7) wth d = 1 + m 2 c = 1 1 d (9) f ω.491 then m =.37464 + 1.4226ω.26992ω 2 f ω >.491 then m =.379642 + 1.483ω (8) (1).164423ω 2 +.16666ω 3 (11) Else, f T < T c,, the conventonal resson of (T) for Peng Robnson s used: (T) = [1 + (.37464 + 1.4226ω.26992ω 2 )(1 T r, )] 2 f ω.491 (12) (T) = [1 + (.379642 + 1.483ω.164423ω 2 +.16666ω 3 2 )(1 T r, )] f ω >.491 (13) Pure component propertes of CO 2 and glycerol necessary for these calculatons are presented n Table 3. Carbon doxde and glycerol exhbt very dfferent polarty and the so-called EoS/G E approach s then ected to be more approprate to model hgh-pressure flud phase equlbra of ths system. Indeed, ths knd of mxng rules enlarges the feld of applcaton of
Table 4 Summary of the models used n ths work to represent CO 2 glycerol phase equlbrum. Name of the global model Equaton of state Mxng rule Actvty coeffcent model Bnary nteracton coeffcents Conventonal k j = f(t) PSRK UNIFAC PSRK PSRK UNIQUAC A j = f(t)/a j = f(t) MHV2-UNIFAC MHV-2 UNIFAC Lyngby MHV-2 UNIQUAC A j = f(t)/a j = f(t) cubc equaton of state to polar compounds at hgh pressure. Ths s done va the ncorporaton of the excess Gbbs energy (G E ) n the calculaton of the energy parameter, a, of the EoS. The excess Gbbs energy s calculated usng an actvty coeffcent model. Huron and Vdal [31] were the frst to propose ths approach, and several models based on ths concept have then been developed, such as Wong-Sandler, MHV1, MHV2, PSRK...and were successfully appled to descrbe hgh pressure flud phase equlbra of mxtures contanng polar compounds ([32,33] as examples). A complete revew of EoS/G E mxng rules and ther range of applcaton can be found n the recent book of Kontogeorgs and Folas [34]. For the purpose of ths study PSRK [] and MHV2 [36,37] mxng rules have been chosen, n addton to classcal vdwf1 mxng rules. Ther ablty to model the CO 2 glycerol thermodynamc behavor has been compared. For both PSRK and MHV2 mxng rules, Peng Robnson has been used as the equaton of state and Eqs. (4) (13) have been used to evaluate pure component parameters and to calculate mxture parameter b of the EoS. For PSRK and MHV2, mxture parameters are obtaned from: ) ( ) + q2 q 1 ( z = a brt = a b RT 2 z 2 = ge RT + ( b ) z ln b (14) () (16) wth a, b and b obtaned from (), (6) and (4) respectvely. In the case of Peng Robnson equaton of state, q 1 =.64663 and q 2 = for PSRK model (lct calculaton of ) and q 1 =.4347 and q 2 =.364 for MHV2 model (mplct calculaton of ). Then an actvty coeffcent model has to be chosen to determne the value of the excess Gbbs energy at zero pressure (reference pressure) g E. At ther ntal development, authors of PSRK, so as MHV mxng rules, coupled the SRK or equaton of state wth the UNIFAC predctve actvty coeffcent model, leadng to a predctve way to use cubc equatons of state. In the present study, PSRK mxng rule has been used wth the PSRK verson of UNIFAC model proposed by Fredenslund et al. [38] and modfed n such a way that bnary nteracton coeffcents between functonal groups depend on temperature [,39] and wth UNIQUAC actvty coeffcent model [4,41]. In a same way, MHV2 mxng rule s used wth the Lngby verson of UNIFAC [42]. When UNIQUAC model s used n the mxng rule, two bnary nteracton coeffcents (A j and A j ) have to be ftted on ermental data. In the present study, because of the large range of nvestgated temperatures, bnary nteracton coeffcents have been shown to be lnearly temperature dependent. Flud phase equlbra calculatons have been performed usng Excel (Mcrosoft) coupled wth Smuls Thermodynamcs software (ProSm S.A, France). Smuls Thermodynamcs contans the dfferent models summarzed n Table 4. Relatve absolute average devaton (ressed n percentage, %AAD) was calculated to evaluate ablty of the model to represent ermental data for CO 2 mole fracton n lqud phase (x CO2 ) and glycerol mole fracton n the vapor phase (y glycerol ). %AAD for a varable z s defned as: %AADz = 1 N p N p =1 z z z calc 1 (17) where N p s the number of ermental values. 3. Results and dscusson 3.1. Solublty of glycerol n the CO 2 -rch phase Fg. 1a shows the evoluton of the nfrared spectra n the spectral range 28 cm 1 of glycerol solublzed n the CO 2 -rch phase wth an ncrease of pressure from 1. to. MPa at 12 C. a progressve ncrease of the peaks centered at 2883 cm 1 and 2933 cm 1 assgned to CH of glycerol can be observed, resultng from the ncrease of glycerol concentraton. From the ntensty of both peaks, the evoluton of the solublty of glycerol n the CO 2 -rch phase as a functon of CO 2 densty at dfferent temperatures (see Fg. 1b) has been calculated. As t can be observed, the values of solublty are very low, and ncrement of the CO 2 densty ncreases the solublty of glycerol at a gven temperature. In fact, glycerol s barely soluble n CO 2 at low temperatures and at constant densty; a slght ncrement n temperature nduces a sgnfcant ncrease of solublty. Our results are ntermedate between the ermental results prevously publshed by Sovova and Khachaturyan [17] and by Elsser and Fredrch [16], whch presented a dfference of two orders of magntude between them. The authors have attrbuted ths dfference to a.37 wt% dfference n the glycerol water content. However, t can be ponted out that the methods used n both studes can nduce systematc errors, prncpally when solute solublty s small (as n the case of glycerol). In both publcatons, several ponts are not provded n detals, such as analyss methods and equlbraton tme justfcaton. Table shows the calculated mole fracton of glycerol n the CO 2 -rch phase (y glycerol ) obtaned from ermental results of the solublty presented n Fg. 1b. As can be concluded from these values, a major advantage of the ermental method used n ths study les n ts ablty to measure very low values of concentraton wth an acceptable precson. 3.2. Solublty of CO 2 and swellng of glycerol n the glycerol-rch phase As an example, Fg. 2 shows the spectral changes of the glycerolrch phase occurrng wth an ncrease of temperature from 4 to 2 C at 1. MPa as a result of the change n CO 2 concentraton n that phase. The peak at 3696 cm 1, assgned to the combnaton mode 2 2 + 3 of the CO 2, decreases wth temperature, whch results from a decrease of CO 2 concentraton n the glycerol-rch phase when temperature ncreases from 4 to 2 C. The peak detected at 474 cm 1, assgned to the combnaton of the (OH) + ı(oh) mode of the assocated OH of glycerol, presents a shft towards 486 cm 1 (dashed lnes) when temperature ncreases,
Fgure 1. (a) Spectral changes of the CO 2-rch phase wth the pressure at 12 C. (b) Solublty of glycerol as a functon of CO 2 molar densty at temperatures between 4 C and 14 C. Lnes have been added to gude the eye. Error bars represent the % of relatve error allowed by our method. Table CO 2-rch phase equlbrum ermental data. S = solublty of glycerol n CO 2. 4 C 6 C 8 C P (MPa) y glycerol S (kmol/m 3 ) P (MPa) y glycerol S (kmol/m 3 ) P (MPa) y glycerol S (kmol/m 3 ) 1 4.9 1.7 1 3 1 4.7 1 3.6 1 4 1 7.41 1 3.73 1 4 13 6.96 1 1.17 1 3 13 4.7 1.4 1 4 13 6.8 1.22 1 4 7.84 1 1.39 1 3 7.29 1 1. 1 3 9.33 1 9.3 1 4 2 1.12 1 4 2.14 1 3 2 1.22 1 4 2. 1 3 2 1.63 1 4 2.2 1 3 1.36 1 4 2.72 1 3 1.73 1 4 3.9 1 3 2.16 1 4 3.37 1 3 3 1.49 1 4 3.7 1 3 3 2.19 1 4 4.12 1 3 3 2.64 1 4 4.47 1 3 1.8 1 4 3.83 1 3 2.3 1 4 4.96 1 3 3.9 1 4.4 1 3 1 C 12 C 14 C P (MPa) y glycerol S (kmol/m 3 ) P (MPa) y glycerol S (kmol/m 3 ) P (MPa) y glycerol S (kmol/m 3 ) 1 2.41 1 1.6 1 4 1 4.18 1 1.9 1 4 1 6.93 1 2.39 1 4 13 1.93 1 1.2 1 4 13. 1 2.78 1 4 13 1. 1 4 4.97 1 4 1.8 1 1.22 1 4 7.61 1 4.8 1 4 1.3 1 4 8.9 1 4 2 1.21 1 4 1.33 1 3 2 2.2 1 4 2. 1 3 2 3.44 1 4 2.71 1 3 2.37 1 4 3.17 1 3 3.93 1 4 4.1 1 3. 1 4.2 1 3 3 3.46 1 4.21 1 3 3.31 1 4 7.7 1 3 3 7.83 1 4 9.26 1 3 4.44 1 4 7.22 1 3 6.66 1 4 9.77 1 3 9.6 1 4 1.27 1 2 whch results from a progressve breakng of the hydrogen bond network of glycerol molecules, as prevously reported for other alcohols [22]. In fact, glycerol s a hghly flexble molecule formng both ntra- and nter-molecular hydrogen bonds; molecular dynamcs smulatons on ths molecule have shown that the number of nter-molecular hydrogen bonds decreases when temperature s ncreased [43,44]. The ntensty of the peak at 4 cm 1 assocated to a combnaton mode (CH) + ı(ch) decreases wth temperature, as a result of the glycerol densty decrease. No glycerol swellng, as a result of CO 2 solublzaton, was observed durng our erments wthn the ±% accuracy of our methodology as t s shown n Fg. 3. Indeed, no changes n the ntensty of characterstc bands of glycerol are observed (bands around 4 cm 1 and 437 cm 1 ) although an ncrease of the characterstc band of CO 2 (3696 cm 1 ) wth pressure s clearly present. The solublty of CO 2 n the glycerol-rch phase s reported n kmol/m 3 n Fg. 4 as a functon of the pressure. Table 6 presents the CO 2 mole fracton n the glycerol rch phase (x CO2 ) deduced Fgure 2. Spectral changes of the glycerol-rch phase wth temperature at 1 MPa.
Table 6 Glycerol-rch phase equlbrum ermental data. S = solublty of CO 2 n glycerol. 4 C 6 C 8 C P (MPa) x CO2 S (kmol/m 3 ) P (MPa) x CO2 S (kmol/m 3 ) P (MPa) x CO2 S (kmol/m 3 ).834 1..68 1.1 1.87 1.2 7.8.168 1.64 1.981 1.49.967 1.47 1.117 1.82.16 1.63 2.1 1..19 1.97 2.1114 1.72 3.12 1.89 2.128 2.1 24.9.121 1.88 3.13 2.11 3.12 1.89 1 C 12 C 14 C P (MPa) x CO2 S (kmol/m 3 ) P (MPa) x CO2 S (kmol/m 3 ) P (MPa) x CO2 S (kmol/m 3 ) 1.631.92 1.2.38.78 1.428.61.73 1.11.646.9.39.78 2.9 1.36 2.816 1.22 2.674.99 3.1183 1.84 24.8.92 1.44.922 1.39 3.1132 1.7 3. 1.61 16 C 18 C 2 C P (MPa) x CO2 S (kmol/m 3 ) P (MPa) x CO2 S (kmol/m 3 ) P (MPa) x CO2 S (kmol/m 3 ) 1.334.47 1.246. 1.2.23.28.442.63.369.2.242.34 2.77.84 2.47.68 2.2.383..821 1.23.677.99 3.87 3.966 1.46 3.87 1.31 from ermental data of solublty. In all cases, at a gven temperature, solublty ncreases wth pressure. Nevertheless, at low temperature (T = 4 C), there s a strong ncrease of the solublty when pressure s ncreased, up to 1 MPa. For greater pressures, ths effect s leveled off. As temperatures ncreases, a more mportant effect of pressure has been observed, and at T = 2 C, ths effect s maxmal. In all cases, temperature has a negatve effect on solublty of CO 2 n glycerol n the temperature and pressure ranges studed. It can be observed that the shape of the curves of CO 2 solublty as a functon of the pressure s dfferent above 14 C. Ths behavor may be the consequence of a sgnfcant weakenng of the hydrogen bonded structure of glycerol above ths temperature. 3.3. Phase dagram of the scco 2 /glycerol system 3.3.1. Expermental results Phase dagram for the CO 2 glycerol system has been obtaned from solublty measurements for temperatures rangng from 4 C to 2 C and pressures up to MPa and s presented n Fg. a. As descrbed above, qute low mutual solublty s observed between CO 2 and glycerol n the pressure and temperature ranges studed here. In the case of the glycerol-rch phase, low quanttes of CO 2 can be dssolved. However, at 3 MPa and 4 C, a CO 2 mole fracton of up to.13 (Fg. b) can be obtaned. Concernng the CO 2 -rch phase, whatever the temperature, the quas-vertcal lne reveals the low solublty of glycerol n CO 2 ; a closer look on Fg. c ndcates an mportant effect of temperature on glycerol solublty. Ths behavor s typcal for bnary systems wth compounds of wdely dfferent molar mass and/or crtcal temperatures, such as CO 2 /water or CO 2 /glycol systems. Such systems exhbt a lqud lqud mmscblty zone at low temperatures and belong to type III of the classfcaton of Scott and Konynenburg [4,46]. The low solublty of glycerol n the CO 2 rch phase s an mportant characterstc n respect to the development of bphasc reactve systems usng glycerol as the catalytc phase and scco 2 as the reactants and products carrer [12]. Indeed, ths nsures that low amounts of glycerol are extracted by scco 2 durng the separaton step. 3.3.2. Phase equlbrum modelng Models of Table 4 have been used to descrbe flud phase equlbrum of the CO 2 /glycerol system. As prevously mentoned, Fgure 3. Spectral changes of the glycerol-rch phase wth pressure at 4 C. Fgure 4. Solublty of CO 2 n glycerol as a functon of pressure at T = 4 2 C. Lnes have been added to gude the eye. Error bars represent the % of relatve error allowed by our method.
Fgure. (a) Pressure versus CO 2 mole fracton dagram for the scco 2/glycerol system. (b) Glycerol-rch phase and (c) CO 2-rch phase. Lnes have been added to gude the eye. and MHV2-UNIFAC models are predctve, whle for and models bnary nteracton parameters have to be ftted from ermental data. Values of global absolute average devatons, %AAD xco2 and %AAD yglycerol (Eq. (17)), obtaned for each model, together wth ressons of ftted bnary nteracton parameters are gven n Table 7. The fttng of ermental data has been done mnmzng an objectve functon (least square method) and results are presented n Table 7 where t s frst notceable that, whatever the model used, the %AAD on both phases are not very good, none of them beng below %. Ths shows that, on a global pont of vew, EoS fals to accurately represent ermental behavor of that system, even wth EoS/G E mxng rules. For the EoS wth classcal mxng rule, t has not been possble to use an objectve functon smultaneously nvolvng composton of lqud phase and composton of the vapor phase n the same resoluton, because n that case, t led to globally poor descrpton for both phases. Especally, the very low ermental mole fractons of glycerol n the CO 2 rch phase were systematcally largely overestmated. Thus for model wth classcal mxng rule, the optmzaton method was done frstly wth the least square method appled to x CO2 values only (entry 1), that lans the rather bnary nterac on coeffcent k CO2-glycerol..3..2..1. F ed on y k =.7T +.8 F ed on x kj=.9t -.24 F ed on x kj =.T -.8827 3 32 34 36 38 4 42 44 46 48 T /K Fgure 6. Influence of the temperature on bnary nteracton coeffcents of Peng Robnson equaton of state ftted on x CO2 or y glycerol. satsfactory value of %AAD (7.7) for the glycerol rch phase n that case; Then the fttng was done on y glycerol only (entry 2), gvng acceptable %AAD for the vapor phase (61.1, stll overestmatng the Table 7 Values of bnary nteracton coeffcents and correspondng values of the relatve absolute average devatons (%AAD) for CO 2 lqud mole fracton and glycerol vapor mole fracton for each model. Entry Global model Bnary nteracton parameters %AAD xco2 %AAD yglycerol 1 ftted on x CO2 only k CO2 glycerol =.9T/K.27 for T 413 K 7.7 34 k CO2 glycerol =.T/K.8827 for T > 413 K 2 ftted on y glycerol only k CO2 glycerol =.7T/K +.8 62.2 61.1 3 ftted on both x CO2 and y glycerol A CO2 glycerol/cal mol 1 = 3.T/K + 23.31 18.4 7.2 A glycerol CO 2 /cal mol 1 = 3.84T/K 6.7 4 71.3 297.1 ftted on both x CO2 and y glycerol A CO2 glycerol/cal mol 1 = 7, 698.7T/K + 8.3 19. 97. A glycerol CO 2 /cal mol 1 = 2.81T/K + 219.18 6 MHV2-UNIFAC 28.3 8.7
4 3 4 3 2 2 1 (a)..1..2..3 x CO2 1 (b).99.996.997.998.999 1 y CO2 4 3 4 3 2 2 1 1 (c)..1..2..3 x CO2 (d).99.996.997.998.999 1 y CO2 4 3 4 3 2 2 1 (e)..1..2..3 x CO2 1 (f).99.996.997.998.999 1 y CO2 4 3 2 1 (g)..1..2..3 x CO2 Fgure 7. P-x,y data for the CO 2/glycerol system, ermental data and modelng results. (a and b) 4 C, (c and d) 8 C, (e and f) 12 C, (g) 2 C (k j for EoS s from Table 7, entry 1).
glycerol mole fracton), but, n ths case worse predctons were correlatvely found for the lqud phase (62.2). In the case of EoS, a detaled study of the nfluence of temperature upon bnary nteracton coeffcents has been done and results are plotted n Fg. 6. When fttng was realzed on x CO2 only, two lnear correlatons have been evdenced, dependng on the temperature range. Whatever the temperature, the k j value of the EoS s postve for ths system, as t s often the case because of overestmaton of nteracton between molecules ssued from the use of geometrc mxng rule (Eq. (3)). Moreover, the value of k j ncreases wth temperature, reflectng the decrease of the solublty of CO 2 nto the glycerol rch phase and the ncrease of solublty of glycerol nto CO 2 rch phase, because self-assocaton of glycerol by hydrogen bondng s weaker at hgh temperature, as prevously mentoned. As can be seen n Fg. 6, nfluence of temperature on k j s more mportant above 14 C and ths s presumably a consequence of the observed change of the mxture behavor above 14 C, as t s clearly observable n Fg. 4, where a change of concavty occurs when solublty of CO 2 n glycerol rch phase versus pressure s plotted. The smlar analyss on k j ftted on y glycerol shows that, at a same temperature, k j value s hgher, and the same tendency s observed as a functon of the temperature (Fg. 6). Note that ermental vapor phase compostons have been determned for T < 14 C only. For the purpose of the targeted applcaton of the CO 2 glycerol system as a bphasc medum to perform reactons, nformaton upon the amount of CO 2 solublzed n glycerol s of prme nterest because of the consequences upon physco-chemcal propertes or reactvty n the glycerol rch phase. Inaccurate predcton of the traces of glycerol n the CO 2 rch phase would not handcap the development of such bphasc systems. Thus, n the followng, the results wth EoS and k j ftted on x CO2 only have been retaned. The approach whch prvleges the vapor phase descrpton could be proposed n the context of an applcaton where an accurate calculaton of the vapor phase composton s needed. However, as can be seen n Table 7, when a descrpton for both phases smultaneously s needed the should be preferred (entry 3) because t gves acceptable %AAD (18.4 and 7.2 for x CO2 and y glycerol respectvely) although there s a loss of accuracy for the lqud phase n comparson to entry 1. Vsual assessment of calculated and ermental CO 2 mole fractons n the glycerol rch phase can be done n Fg. 7(a), (c), (e) and (g), and n the CO 2 rch phase n Fg. 7(b), (d) and (f), at 4, 8, 12 and 2 C. Among mxng rules based on EoS/G E approach, t appears clearly that PSRK mxng rule wth UNIQUAC actvty model provdes the best results n terms of both lqud and vapor compostons, followed by MHV2 mxng rule wth UNIQUAC (entry ), that gves worse results. Although the devatons obtaned wth are stll rather hgh, ths result confrms that these mxng rules are the most adequate to predct ermental behavor of such complex mxtures, as compared to classcal vdw1f mxng rules. Essentally, the hgh values of devatons may be laned by the large dfference of CO 2 and glycerol crtcal volumes (94 cm 3 mol 1 and 264 cm 3 mol 1, respectvely). Indeed, the CO 2 glycerol mxture could be classfed as a sze-asymmetrc system, for whch t has been shown that ths knd of model s actually somewhat unsutable [47], due to the dfference between the combnatoral term of the actvty coeffcent model and the one of the equaton of state. Ths dfference ncreases as the dfference n molecule sze ncreases [47]. To better nvestgate the ablty of the models to represent global ermental behavor of the lqud phase of the CO 2 /glycerol system on the wde range of temperature, t s nterestng to consder varatons of %AADx obtaned wth the dfferent models wth the temperature (Fg. 8) (Note: MHV2-UNIFAC s not consdered because %AADx s very hgh, whatever the temperature). Fgure 8. Influence of the temperature on %AAD for x CO2 obtaned wth dfferent models. Several tendences can be observed from Fgs. 7 and 8. Frstly, as prevously ponted out, whatever the temperature, non-predctve models wth ftted bnary nteracton parameters are the most sutable. Of course, ths result was ected, consderng the fact that for these models four coeffcents are ftted to ermental data n order to mnmze global average devaton. It s shown n Fg. 8 that devatons are hgher at hgh temperature, where the ermental curves show a change n concavty and where ermental ponts are scarce. Essentally, predctve models,.e., models usng UNIFAC n mxng rules, yelded poor representaton of ermental results, partcularly MHV2-UNIFAC (Table 7, entry 6). approach s satsfactory at low temperature, but devaton sharply ncreases wth temperature to reach about 2% at 2 C (Fg. 8). Concernng ths last model, ths result was ected consderng the fact that, for the functonal groups of our database used to descrbe the CO 2 /glycerol system (.e., CO 2, OH and CH 2 functonal groups), bnary nteracton parameters wthn these groups are provded as temperature ndependent. PSRK mxng rule was found here superor to MHV2, whatever the actvty coeffcent model, UNIFAC or UNIQUAC, chosen n the mxng rule. Ths result s somewhat surprsng, because MHV2 mxng rule provdes generally a better match of ermental results. The thermodynamc behavor of CO 2 /glycerol system s obvously governed by self-nteracton of glycerol. For such a system, an mprovement n phase equlbrum modelng could be acheved by usng advanced models based on assocaton theores, such as SAFT (Statstcal Assocatng Flud Theory) or CPA (Cubc Plus Assocaton) models. Although grounded on a more complex theoretcal bass, these models have been proved to be partcularly sutable for assocatng compounds [34]. 4. Conclusons In ths work, the mutual solublty of CO 2 and glycerol has been studed at temperatures rangng from 4 C to 2 C and pressures up to. MPa. Ths has been done usng the FT-IR technque whch proved to gve access to very low values of equlbrum concentratons wth a good accuracy. Concernng the CO 2 rch phase, t was observed that the glycerol solublty n CO 2 was extremely low (n the range of 1 n mole fracton) n the pressure and temperature domans nvestgated here. Conversely, the glycerol rch phase dssolved CO 2 at mole fractons up to.13. Neglgble swellng of the glycerol rch phase has been observed, whch ndcates that glycerol behaves as a class I Gas Expanded Lqud (GXL)
accordng to the classfcaton of Jessop et al. [1],.e., a system where the andng gas has a qute low solublty n the lqud, whch consequently does not exhbt large anson. Although the solublty of CO 2 n glycerol s largely hgher than the one of CO 2 n water, the thermodynamc behavor of ths system s rather smlar to that of CO 2 /water bnary mxture, whch s a class I GXL. Concernng the modelng of the CO 2 /glycerol system, the sutablty of EoS wth PSRK mxng rule and UNIQUAC model, has been hghlghted. Evoluton wth pressure of the composton of both phases n the 4 2 C range of temperature s qute well descrbed by ths model, provded that sutable values of bnary nteracton coeffcents are used. Conversely, predctve approaches proved to be non satsfactory. Smpler approach wth Peng Robnson equaton of state wth vdw1f mxng rule dd not allow computng accurately both lqud and vapor phases wth the same value of bnary nteracton coeffcent. 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