Determination of activity coefficients of dimethyl ether in butyl acetate and 2-propanol

Transcription

1 Determnaton of actvty coeffcents of dmethyl ether n butyl acetate and 2-propanol Petar Petrov Determnaton of actvty coeefcents of dmethyl ether n butyl acetate and 2-propanol: The paper presents expermental setup, measurements data and approprate model for determnng the actvty coeffcents n bnary mxtures dmethyl ether butyl acetate and dmethyl ether 2 propanol at room temperature. Through a smple mathematcal model the actvty coeffcents are correlated to the composton of the mxtures, and two parameter Margules equatons are derved. The results could be used for predcton of vapour lqud equlbrum n the gven systems, and may brng sgnfcant support for the researchers dealng wth dmethyl ether applcatons and especally n the aerosol ndustry. Key words: Dmethyl ether, 2-propanol, butyl acetate, aerosol, actvty coeffcents, vapor-lqud equlbrum, Margules equaton, parameter estmaton NTRODUCTION The use of dmethyl ether (DME) n dfferent areas of ndustry grows constantly wthn last decades. The DME s a colorless, vrtual odorless and low vscosty substance, whch has a bolng pont ca. -25 C at 1 bar, and has a vapor pressure of 5.1 bar at 20 C. Due to ts hgh solvency power ths materal s used n hgh amounts n aerosol ndustry as a valuable component n aerosol formulatons whch contan substances that are dffcult to dssolve. The DME s an apprecated propellant (pressure makng lquefed gas) n many aerosol products for pharmaceutcals (.e. wart remover), personal care (.e. harsprays), home care (.e. ar fresheners), varety of techncal aerosols as spray pants and polyurethane foam. In many of these products t plays dual role (1) t creates the pressure needed for product use, sometmes together wth propane-butane, and (2) acts as solvent for the ncompatble components thus creatng one homogenous lqud phase n the aerosol can. It has an mportant role n the aerosol polyurethane foam producton where t ensures the good homogenzaton between the propane-butane whch s nonpolar materal and more polar components as amne catalyst, polyether dols and dphenylmethane-4 4'-dsocyanate. Besdes the use n the aerosol ndustry, the DME contnually attracts more and more nterest to become an alternatve fuel especally for desel engnes, ncludng DME derved by bomass converson [1], [2]. There are many measurements n relaton wth vapour-lqud equlbrum of DME and other materals water, alcohols, esters wthn broad range of temperatures and pressures [3]-[5]. Due to the practcal nterest of the aerosol ndustry we chose to examne the vapour-lqud equlbrum of the materal systems DME + butyl acetate and DME + 2-propanol. The second of these systems has been measured at hgher temperatures [4]. The methodology s qute dentcal wth the presented n [6] the pressure at dfferent overall DME concentraton s measured and through mass balance and equaton of state for the gas phase the actvty coeffcents of both components n the bnary mxture are determned. EXPERIMENTA METHOD As contaner for the pressure measurement was chosen a metal vessel wth full volume of 1000ml and burst pressure mn 15 bar. The lquds butyl acetate or 2-propanol were added manually n ths contaner and after ths t was sealed through a specal valve, smlar to ths used n aerosol products. The weght of added lqud was then determned, and after ths the DME was njected through the valve. The mxture was allowed to stay 24h for the full establshment of the vapor-lqud equlbrum and after ths the chosen temperature was adjusted n the water bath / thermostat wthn 0.1K accuracy. The pressure s recorded wth the dgtal manometer Wka D 10, accuracy 0.5%, through drect attachment to the valve of the metal contaner. Ths procedure was repeated for each of the compostons lsted below

2 RESUTS AND CACUATIONS The expermental condtons allow that the gas phase s treated wth the deal gas law due to the relatve low pressures n the system, up to 6 bar. Consequently the devaton between deal and real gas treatment (cubc equaton of state) s comparable wth the expermental errors and the deal gas law s preferred. The other mportant pont consdered durng the experments s the presence of ar n the closed metal contaner, together wth DME and 2-propanol and butyl acetate. We dd a quanttatve estmaton of ths nfluence, consderng the bnary systems ar + dmethyl ether and ar + butyl acetate or 2-propanol at temperatures close to our reference temperature. For such system, assumng all components are presented n both phases, and usng Henry s law, the composton has been calculated usng also the mass balance lqud-gas phase and deal gas law. The Henry coeffcents of ntrogen and oxygen n the solvents consdered here were taken from lterature [7] [10]. The results show that the ar solublty n the lqud phase durng experments could be defntely neglected. Ths statement s also backed-up by the fact that the butyl acetate and 2-propanol are saturated wth ar, so no any addtonal ar penetraton n the lqud phase s expected. Consequently, the ar contrbutes to the overall pressure only through ts partal pressure n the gas mxture. In ths work we use the followng formulas n order to correlate the total measured pressure and the actvty coeffcents of DME and solvent. p = n R T V, = tot p = p ; p = γ.p sat (T).x, =1,2 n = n V = V = 1 + n, = 1,2 + V n x =, = 1,2 n1 + n 2 In total we have 11 equatons wth 11 unknown varables V, the two lqud molar parts x, the four mol amounts n both phases, the total pressure and the three partal pressures, where ndex 1 stands for DME, ndex 2 for solvent, and 3 for the ar. Before applyng the data regresson procedure for determnaton of actvty coeffcents, we checked the above mathematcal model usng parameter senstvty analyss. The purpose was to verfy the nfluence of the actvty coeffcents on the thermodynamc equlbrum and partcularly on the partal pressures n the system. The software used for solvng the above system [11] offers a possblty to obtan the partal dervatves of the soluton of the algebrac system wth respect to some chosen parameters, n our case the two actvty coeffcents γ. In general the parametrc senstvty analyss may be performed together wth the system soluton, and havng the values of Jacob matrx one may obtan also the needed dervatves wth respect to the parameters as a by-product of the man Newton method of soluton. The table 1and 2 present the dependency of the partal pressures of DME, butyl acetate or 2-propanol, ar, and ther sum from the actvty coeffcents n terms of ther dervatves, meanng the bgger the value s, the bgger s the dependency. The values of the dervatves for each actvty coeffcent γ 1 (DME n mxture DME/butyl acetate) and γ 2 (butyl acetate n mxture DME/butyl acetate), respectvely γ 1 (DME n mxture DME/2-propanol) and γ 2 (2-propanol n mxture DME/2-propanol) were calculated keepng both coeffcents fxed at three dfferent values 0.5, 1.0 and 1.5, whch represent a reasonable guesses for the lower and upper lmt of the actvty coeffcents. It s clear vsble tendency that the partal pressure of DME depends very strong on γ DME and almost doesn t depend on the actvty coeffcent of butyl acetate. Smlarly, the partal pressure of butyl acetate depends mostly on ts own actvty coeffcent, but ths dependency s much lower than of DME. Havng n mnd that the total pressure s sum of all three partal

3 pressures, respectvely the same apples for ther dependences on the actvty coeffcents, we see that the total pressure depends mostly on the value of the actvty coeffcent of DME, and ths s due to the fact that DME has very hgh saturated vapor pressure compared wth other speces. Same observaton s vald for the DME/2-propanol system, but here less strong dependency s vald, because the 2-propanol has sgnfcant hgh vapor pressure compared to butyl acetate. In general, for all three levels of actvty coeffcents nvestgated the dependency of the total pressure n the system on the actvty coeffcent of DME s about 500 tmes hgher than on actvty coeffcent of butyl acetate and about 60 tmes hgher than ths of 2-propanol.Fg.1 shows the smulated dependency of the total pressure as functon of each of the both actvty coeffcent, keepng the other one fxed. Fg. 1 Smulated pressure n system 160g DME and 411g 2-propanol at 22 C as functon of the actvty coeffcents, ndex 1 = DME, 2 = 2-propanol. Table 1. Dervatves of partal pressure wth respect to γ 1 (DME, 149g) and γ 2 (Butyl acetate, 324g) at 22 C, at three dfferent levels of γ. γ 1 = γ 2 =0.5 γ 1 = γ 2 =1.0 γ 1 = γ 2 =1.5 p/ γ 1 p/ γ 2 p/ γ 1 p/ γ 2 p/ γ 1 p/ γ 2 p DME 1.44E E E E E E+00 p solvent 1.07E E E E E E+02 p ar -6.53E E E E E E-02 p tot 1.44E E E E E E+02 Table 2. Dervatves of partal pressure wth respect to γ 1 (DME, 160g) and γ 2 (2- propanol, 411g) at 22 C, at three dfferent levels of γ. γ 1 = γ 2 =0.5 γ 1 = γ 2 =1.0 γ 1 = γ 2 =1.5 p/ γ 1 p/ γ 2 p/ γ 1 p/ γ 2 p/ γ 1 p/ γ 2 p DME 9.07E E E E E E+01 p solvent 1.34E E E E E E+03 p ar -5.24E E E E E E-02 p tot 9.02E E E E E E+03 The above dscussed features of both systems justfy the use of parameter estmaton technque for determnaton of the actvty coeffcents, and ther dependency on the composton. In the feld of chemcal thermodynamc exst many equatons connectng the system composton and actvty coeffcents, and for the case studed we chose the two parameter Margules equaton [12]: lnγ 1 = x 2 2.(A (A 21 A 12 ).x 1 ), lnγ 2 = x 1 2.(A (A 12 A 21 ).x 2 ), The physcal meanng of the actvty coeffcents s clearly vsble through ther connecton wth the excess bs energy of mxng of the two components 1 and 2:

4 E = R T x ln γ, where E s the devaton between actual and the bs energy n case of deal soluton, meanng there s no nteracton between the molecules. In ths way the actvty coeffcents are measure for the devaton between the real and deal state for the gven system, and are very useful for predcton of vapor lqud equlbrum n two-component non-deal systems. The procedure for determnng the coeffcents A 12 and A 21 for DME and butyl acetate or 2-propanol as a second component s as follows: The total pressure at gven temperatures n the correspondng mxtures was measured for several dfferent compostons. In general, the pressure n the system ncreases when addng more DME to the mxture due to ts hgh vapor pressure, but also because of the ncreased volume of the lqud phase, respectvely decreased gas phase volume and correspondng compresson of the ar n the metal vessel. The procedure of the non-lnear least squares s used wth objectve functon constructed as the square of the dfference between measured and predcted accordng to the above model total pressure. As a result of the soluton, one may obtan the values of A 12 and A 21 whch gves lowest devaton between calculated and measured pressure. The graphcal results of ths procedure are presented on Fg. 2 and Fg. 3 for the both materal systems respectvely. The R 2 values are 97% for both systems, and the mean devatons between calculated and measured pressures are 7.0% for DME/butyl acetate and 9.4% for DME/2-propanol. The actvty coeffcents for DME and solvents at temperature of 22 C and for concentratons up to 0.4 mol/mol DME may be calculated accordng to the above gven expressons havng the values A 12 =0.862, A 21 = for DME/butyl acetate, and A 12 =1.025, A 21 = Fg. 2 Parameter estmaton n system DME kg butyl acetate, 22 C. Fg. 3 Parameter Estmaton n system DME kg 2-propanol, 22 C. CONCUSIONS The artcle presents a smplfed expermental method for determnaton of actvty coeffcents n the lqud phase n two component system consstng of at least one lquefed gas dmethyl ether. Usng mass balance, known vapor pressures of the components and performng non-lnear parameter estmaton t s possble to estmate the concentraton dependence of the actvty coeffcents of the both components. The results may be helpful n predctng vapor-lqud equlbrum n systems contanng DME as for example n the aerosol ndustry

5 REFERENCES: [1] Semelsberger T., R.. Borup, H.. reene. Dmethyl ether (DME) as an alternatve fuel. Journal of Power Sources 156 (2006) [2] Arcoumans C., C. Bae, R. Crookes, E. Knoshta. The potental of d-methyl ether (DME) as an alternatve fuel for compresson-gnton engnes: A revew. Fuel 87 (2008) [3] Pozo M., W.B. Streett. Flud Phase Equlbra for the System Dmethyl Ether/Water from 50 to 220 C and Pressures to 50.9 MPa. J. Chem. Eng. Data 1984, 29, [4] Chang E., J. C.. Calado, W. B. Stroett. Vapor-qud Equlbrum n the System Dmethyl Ether/Methanol from 0 to 180 C and at Pressures to 6.7 MPa. J. Chem. Eng. Data 1982, 27, [5] Elbaccouch M., J. R. Ellott. Hgh-Pressure Vapor-qud Equlbrum for Dmethyl Ether + 2-Propanol and Dmethyl Ether + 2-Propanol + Water. J. Chem. Eng. Data, 2001, 46, [6] Daguj H., E. Hhara. Vapor-qud Equlbrum for Dmethyl Ether + Propyl Acetate.. Chem. Eng. Data, 2003, 48, [7] aursen T., P. Rasmussen, S.I. Andersen. VE and VE Measurements of Dmethyl Ether Contanng Systems, J. Chem. Eng. Data, 2002, 47, [8] Teodorescu M., P. Rasmussen. Hgh-Pressure Vapor-qud Equlbra n the Systems Ntrogen + Dmethyl Ether, Methanol + Dmethyl Ether, Carbon Doxde + Dmethyl Ether + Methanol, and Ntrogen + Dmethyl Ether + Methanol, J. Chem. Eng. Data, 2001, 46, [9] uha A., D. Panda. Solublty of Some Non-polar ases n Mxed Solvents, Int. J. Chem. Sc.: 6(3), 2008, [10] Jabłonec A., S. Horstmann, J. mehlng. Expermental Determnaton and Calculaton of as Solublty Data for Ntrogen n Dfferent Solvents, Ind. Eng. Chem. Res., 2007, 46, [11] Athena Vsual Studo, v. 12.3, and references there. [12] Polng B., J. Prausntz, J. O Connell, The Propertes of ases and quds, 5 th edton, Mcraw-Hll About the author: Ph.D. Petar Petrov, Intellgent Energy Systems, nes-bg@mal.bg, telephone ; Ths paper has been revewed