CALCULATION OF VAPOUR - LIQUID - LIQUID EQUILIBRIA

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1 Chemcal and Process Engneerng 202, 33 (3), DOI: /v CALCULATIO OF VAPOUR - LIQUID - LIQUID EQUILIBRIA I QUATERARY SYSTEMS Andrzej Wyczesany * Unversty of Technology, Insttute of Organc Chemstry and Technology, 3-55 Kraków, Poland A method of parameters fttng to the expermental vapour - lqud - lqud equlbrum (VLLE) data s presented for the RTL and the Unquac equatons for sx quaternary mxtures. The same equatons but wth coeffcents taken from the smulator Chemcad database were also used for calculaton of the VLLE for the same mxtures. The calculated equlbrum temperatures and compostons for all the three phases were compared wth the expermental data for these four cases. The nvestgated models were also appled for calculaton of the compostons and temperatures of ternary azeotropes occurrng n the consdered quaternary mxtures. The computed values were compared wth the expermental ones to apprecate the model's accuracy and to confrm whether the model correctly predcts the presence of homo- or heteroazeotrope. The RTL equaton wth coeffcents ftted to the VLLE data proved to be the most accurate model. For the mxtures contanng water, ethanol and two dfferent hydrocarbons ths model shows partcularly hgh accuracy. In three cases the mean devatons between the calculated and measured temperatures do not exceed 0.25 K, and for the fourth mxture the dfference equals Besdes, the mean devatons between the calculated and the measured concentratons n the gas and lqud phases, wth one excepton do not exceed mole %. Keywords: vapor lqud lqud equlbra, quaternary systems. ITRODUCTIO Mxtures water - ethanol - hydrocarbons are mportant n fuel ndustry because of ethanol contanng gasolnes. The presence of ethanol n gasolne ncreases ts octane ratng and promotes more complete combuston, reducng the content of harmful substances emtted wth the flue gas. However, a small amount of water n the mxture can lead to phase splttng, whch can cause troubles n the engne. For ths reason, ethanol must be dehydrated before mxng wth gasolne. Heterogeneous azeotropc dstllaton wth an addton of hydrocarbon s often used for ths purpose. Ths process can lead to pure ethanol or a "dry" mxture of ethanol wth the hydrocarbon whch can be drectly blended wth gasolne. A flow dagram of such a process can be analysed usng a professonal technologcal process smulator such as Chemcad. However, we should remember that the results of calculatons are strongly dependent on a properly chosen thermodynamc model, descrbng as accurately as possble both the vapor - lqud equlbrum (VLE) and the lqud - lqud equlbrum (LLE). In esterfcaton processes or durng regeneraton of mxed solvents such as alcohol - ketone, alcohol - ether, or ketone ester, whch often absorb water, heteroazeotropes other than water-alcoholhydrocarbon can also be formed. *Correspondng author, e-mal: awyczes@chema.pk.edu.pl Authentcated Download Date /8/2 7:09 PM 463

2 A. Wyczesany, Chem. Process Eng., 202, 33 (3), The avalable models correlate the VLE very precsely, and only slghtly less accurately descrbe the LLE. Unfortunately, the parameters descrbng exactly one type of equlbrum very naccurately predct the equlbrum of the second type. Fttng of the parameters for the VLLE s stll nsuffcently nvestgated. Font et al. (2003) correlated the VLLE and the VLE data to obtan the parameters of the Unquac equaton for the system water ethanol sooctane. However, the mnmsed objectve functon was not gven. The same equaton was used by Asens et al. (2002) for the system water -propanol - pentanol. The objectve functon contaned the dfferences between the calculated and the expermental values of pressure, mole fractons n both lqud phases and actvty coeffcents. Ruz et al. (987) correlated the Unquac parameters for the system water ethanol 2-ethylhexanol. The objectve functon conssted of two terms. The frst one referred to the LLE data at 25 o C and the second one to the VLE data of two bnary systems (water ethanol and ethanol 2-ethylhexanol) at P =.03 bar. Hseh et al. (2006), Lee et al. (996) and Hseh et al. (2008) used the maxmum lkelhood prncple to correlate the RTL or Unquac equaton parameters for the followng systems: water propylene glycol monomethyl ether - propylene glycol methyl ether acetate, ethanol ethyl acetate water and water methyl acetate methyl proponate, respectvely. The mnmsed objectve functon used the dfferences between the expermental and calculated pressure, temperature, mole fractons n both lqud phases and mole fractons n the vapour phase. Kosuge and Iwakabe (2005) appled two objectve functons to correlate the parameters of Unquac or RTL equatons for the systems water ethanol -butanol and water ethanol 2-butanol. One functon used the VLE data and the second one the LLE data. Both methods were repeatedly used untl the mnmum values of the objectve functons were obtaned. Grgante et al. (2008) and Ye et al. (20) used the Peng Robnson equaton of state wth Wong Sandler mxng rule for descrpton of the VLLE at elevated pressures for the systems sopropanol water propylene and water methanol dmethyl ether carbon doxde, respectvely. Kundu and Banerjee (20) appled the COSMO-SAC model to calculate the actvty coeffcents used for predctng the VLLE of eght systems. The am of ths work was to develop computer programs fttng the model parameters to the expermental VLLE data avalable n the lterature for quaternary systems. The RTL (Renon and Prausntz, 968) and the Unquac equatons (Abrams and Prausntz, 975) were appled n the calculatons. For the quaternary systems the frst model s descrbed by 8 parameters, the Unquac equaton needs 2 coeffcents (the ternary systems are descrbed n a prevous artcle (Wyczesany, 200). The computed coeffcents were used for calculaton of the VLLE of consdered mxtures and for predcton of the compostons and temperatures of ternary azeotropes occurrng n these systems. The same values were calculated usng the RTL and the Unquac equatons, for whch the bnary parameters were taken from a professonal smulator Chemcad (Chemcad, 200). These parameters descrbe the VLE for bnary mxtures of completely mscble components and the LLE for the mxtures havng a mscblty gap (wth the excepton of a mxture water n-butyl acetate for the Unquac model). Any user performng smulaton calculatons for the process based on the VLLE must use these parameters as the other ones are not avalable. 2. THERMODYAMICS MODELS The actvty coeffcents n the lqud phase can be calculated by the RTL (Eq. ) and the Unquac (Eq. 3) equatons. lnγ = τ jg j x j j = Gl xl l = + x jgj Glj xl l = j = τ τ kjgkj xk k = j Glj xl l = τ A j j = G j = exp( α jτ j ) () T 464 Authentcated Download Date /8/2 7:09 PM

3 Calculaton of vapour - lqud - lqud equlbra n quaternary systems In the basc verson the RTL equaton has three adjustable parameters for each bnary mxture (A j, A j and α j ) ftted to the expermental equlbrum data. Such a form s appled n the present paper. For the LLE n Chemcad a more extended expresson for the parameter τ j (Eq. 2) s used by the RTL model. In ths case a bnary mxture s descrbed by 7 coeffcents. where: Bj τ j = Aj + + Cj ln(t) (2) T Φ θ jτ j ln γ = ln (3) θ Φ + + x 5q ln l x jl j q ln θ jτ j + q q ln Φ x j= j= j= k= θ τ k kj Φ = r x j= r j x j, q x θ, l 5( r q ) ( r ), = j= q j x j = A j τ j = exp (4) T Ths paper uses the basc verson of the Unquac equaton wth two adjustable parameters: A j and A j. For the LLE Chemcad uses also a more complcated expresson for the parameter τ j (Eq. 5). Such bnary mxture has sx parameters. Bj τ j = exp Aj + Cj ln( T) (5) RT 3. CALCULATIO OF THE RTL AD UIQUAC EQUATIOS PARAMETERS The parameters of correlaton equatons should allow to descrbe the VLLE as precsely as possble. To acheve the best precson the mnmsed objectve functon FC gven by Equaton (6) was formulated. The functon has a slghtly dfferent form than that used n the prevous work (Wyczesany, 200). FC = LLE 4 2 VLE 4 VLE xexp, k, j, xcal, k, j, ) + W( yexp, j, ycal, j, ) + W 2 ( Texp, Tcal, ) = j= k= = j= = ( (6) The objectve functon uses LLE expermental ponts for the LLE. The data may refer to the VLLE and the LLE for the gven quaternary system. The frst term of the functon FC refers to both (aqueous and organc) phases and four components. Therefore, the ndex k changes from to 2 and ndex j from to 4. The second term of the objectve functon ncludes VLE expermental ponts of the VLE and also relates to four components. The data may descrbe the VLLE and the VLE for the gven quaternary system. The last term of the mnmsed objectve functon apples to the dfferences between the expermental and calculated temperatures and s calculated for VLE expermental ponts. The values W and W2 are the weght parameters whch allow to ft better the calculated values (temperature or the composton of the gas phase or both lqud phases) to the expermental data. The calculated temperatures and mole fractons n both phases appearng n Eq. (6) represent the full VLLE. For addtonal expermental data referrng to the VLE or the LLE the calculated mole fractons descrbe approprate phase equlbrum. In the classcal approach the VLLE s calculated for known constant values of T, P and mole fractons z of the total mxture. Unfortunately, the appled expermental data do not gve the values z but only mole fractons of each component n all the three phases. Also, the temperature s dfferent for each Authentcated Download Date /8/2 7:09 PM 465

4 A. Wyczesany, Chem. Process Eng., 202, 33 (3), expermental pont. Therefore, the calculatons of the VLLE were performed wth the method descrbed below. The known values are represented by the pressure and mole fractons z of the total lqud phase. The z values correspond to the arthmetc mean values of the expermental concentratons of ndvdual components n both lqud phases. The expermental temperature s treated n calculatons as the ntal one. For such defned values z and T the LLE s calculated accordng to Equatons (7) - (8). L aq β =, L = x x = γ γ = org, x org, z γ + β γ = 0 = = org, γ γ org, γ = (7), x org, x γ org, γ z γ org, γ + β γ We search for such a value β for whch the sums of the mole fractons n both phases equal. The problem s reduced to one Equaton (8) wth one unknown β and the equaton s solved n an teratve process. Subsequently, for a known value of P and the mole fractons of both lqud phases (aqueous x and organc x org, ) the two VLE are calculated. For ths type of equlbrum the bolng temperature and the mole fractons y of the gas phase are computed. The last ones are defned by Eq. (9) n whch s the saturated vapour pressure of pure component P s calculated from the Antone equaton and the actvty coeffcents γ from Eqs. () or (3). y s org, (8) γ P x = (9) P If n the frst step the y sum s less than, the temperature ncreases by 2%. In the opposte case t decreases by 2%. For a the new temperature the values γ, P, y and the y sum are calculated. If the last one s not suffcently close to, the next teratons are performed wth the ewton method accordng to Eq. (0). The teratons are contnued tll the dfference between and the y sum s smaller than 0-6. y s T Told slope =, T new = T slope ( y ) (0) y old In the next step the temperatures calculated for both lqud phases are compared. If the dfference between them s hgher than 0.00 K, the temperature of the organc phase s taken as the new one for further calculatons. Subsequently the LLE and the VLE for both lqud phases are computed. The teratons are performed untl the dfference between the temperatures n both gas phases s lower than 0.00 K. In the next step algorthm checks whether the dfferences between the mole fractons y computed for both lqud phases exceed the value for the same components. If so, the new temperature s assumed as the arthmetc mean of the values obtaned for both lqud phases and the algorthm returns to the LLE and the VLE calculatons for both lqud phases. If not, the VLLE s computed. A smlar procedure of the VLLE calculatons was appled by Lu and co-workers (Lu et al., 993). However, they used two dfferent sets of the RTL equaton parameters for the calculaton of the LLE and the VLE. They also assumed that equlbrum s reached when the dfference n bolng ponts 466 Authentcated Download Date /8/2 7:09 PM

5 Calculaton of vapour - lqud - lqud equlbra n quaternary systems calculated for the two lqud phases s less than 0.7 K and f the dfferences between the mole fractons y for the correspondng components calculated for the two lqud phases are less than For quaternary mxtures and the RTL equaton the mnmsed objectve functon has 8 parameters (A 2, A 2, A 3, A 3, A 4, A 4, A 23, A 32, A 24, A 42, A 34, A 43, α 2, α 3, α 4, α 23, α 24 α 34 ) and for the Unquac equaton 2 coeffcents (A 2, A 2, A 3, A 3, A 4, A 4, A 23, A 32, A 24, A 42, A 34, A 43 ). The problem s very dffcult to solve from the computatonal pont of vew, snce the mnmum value of the objectve functon strongly depends on the startng values of such a large number of unknowns. In practce the number of unknowns was reduced twce accordng to the followng reasonng: Quaternary mxtures consdered n the work can be classfed nto two types. The frst one contans: water, ethanol, and two hydrocarbons (cyclohexane + sooctane, cyclohexane + toluene, cyclohexane + n-heptane or n-hexane + toluene), whle the second one: water, ethanol, acetone and methyl ethyl ketone (MEK) or n-butyl acetate as the forth component. The systems water - hydrocarbon, water - MEK and water - n-butyl acetate are bnary mxtures wth the mscblty gap. The coeffcents of the RTL and the Unquac equatons were presented n a prevous work (Wyczesany, 200) for the ternary mxtures water - ethanol - hydrocarbon (for each of the above hydrocarbons) and water - ethanol - MEK, water - acetone - MEK, water - ethanol - n -butyl acetate and water - acetone - n-butyl acetate. In ths stuaton, t was assumed that for the quaternary system water - ethanol - cyclohexane - sooctane the bnary parameters of the ternary mxture water - ethanol cyclohexane (A 2, A 2, A 3, A 3, A 23, A 32, α 2, α 3, α 23 ) are known and the ftted parameters refer only to the bnary mxtures of sooctane wth the rest of components (A 4, A 4, A 24, A 42, A 34, A 43, α 4, α 24, α 34 ). We can also assume that the bnary parameters of the ternary mxture water ethanol sooctane are known and we should ft the coeffcents for bnary mxtures of cyclohexane wth the remanng three components. The stuaton s smlar for mxtures contanng water and MEK or water and n-butyl acetate. We can assume that we know the bnary coeffcents for the ternary system contanng two mmscble substances and ethanol or acetone. The sze of devatons between the measured and calculated values of the VLLE for quaternary mxture determnes whch the ternary system should be selected as the mxture wth the known bnary parameters. Mnmsaton of the objectve functon FC was performed usng the procedure MIUIT (James, 967). It should be noted that computaton of the optmal values of nne or sx parameters s stll a dffcult task and requres a very careful selecton of the startng pont. However, reducng by half the number of parameters makes the task much easer. Calculaton of the parameters by the above methodology dffers from that descrbed n the prevous paper (Wyczesany, 200) and gves better results for both ternary and quaternary mxtures. Therefore, for the ternary mxtures used n ths paper the bnary coeffcents were ftted by the method descrbed above. The computed parameters were appled as sets of known coeffcents for calculaton of the bnary parameters for the quaternary systems. The parameters calculated n the prevous work were used n the same manner. In most cases a better ft was obtaned for the new coeffcents. The set of parameters obtaned n ths way was treated as a carefully selected startng pont for calculaton of all the 8 coeffcents for the RTL equaton and 2 coeffcents for the equaton Unquac. Such procedure allows of better ft these parameters, although the ncrease n accuracy s rather small. 4. RESULTS OF CALCULATIO AD THEIR DISCUSSIO The followng values are the accuracy crtera of correlaton and predcton of VLLE: Δx and Δy - absolute mean devatons between expermental and calculated equlbrum compostons n the lqud and vapour phases, respectvely, and ΔT absolute mean dfference between expermental and calculated equlbrum temperatures. Addtonally, two mean devatons ΔX and ΔY were defned (Eq. (2)). The frst one refers to all the four components n both lqud phases, the second one to four components n the gas phase. Authentcated Download Date /8/2 7:09 PM 467

6 A. Wyczesany, Chem. Process Eng., 202, 33 (3), Δx = LLE = x exp, x cal, VLE, Δy = y = j= = exp, y cal, VLE, ΔT = T,exp T cal =, () ΔX = Δx j,, ΔY = Δy (2) 8 4 = Table presents the values LLE and VLE as well as the expermental temperature ranges for the systems consdered n the paper. All the data are sobarc. The calculated values of the parameters for both consdered equatons are presented n Tables 2 and 3. Table. Values of LLE, VLE, expermental temperature ranges and pressure for all the consdered mxtures (water + ethanol + comp. 3 + comp. 4) o. comp. 3 comp. 4 LLE VLE T [K] P [bar] Ref. cyclohexane sooctane Pequenn et al., cyclohexane toluene Pequenn et al., 20 a 3 cyclohexane n-heptane Pequenn et al., 20 b 4 n-hexane toluene Pequenn et al., 20 c 5 acetone MEK Youns et al., acetone n-butyl acetate Youns et al., acetone n-butyl acetate Youns et al., acetone n-butyl acetate Youns et al., 2007 Table 2. Coeffcents of the RTL equaton System A A A A A A A A A A A A α α α α α α Authentcated Download Date /8/2 7:09 PM

7 Calculaton of vapour - lqud - lqud equlbra n quaternary systems Table 3. Coeffcents of the Unquac equaton System A A A A A , A A A A A A A Table 4. Mean devatons of VLLE predcton for water ethanol cyclohexane sooctane system RTL- Unquac- Chemcad Chemcad RTL-VLL Unquac-VLL Δx Δx Δx Δx Δx org, Δx org, Δx org, Δx org, Δy Δy Δy Δy ΔX ΔY ΔT Tables 4-7 present the mean devatons n predctng the VLLE for all the systems. For mxtures contanng water ethanol cyclohexane sooctane and water ethanol cyclohexane toluene all the devatons Δx, Δy, ΔX, ΔY and ΔT are shown whereas for the remanng systems only the values ΔX, ΔY and ΔT are gven. The followng conclusons can be drawn. In almost every case the devatons are sgnfcantly smaller for the models n whch the coeffcents were ftted to the VLLE data (RTL-VLL and Unquac-VLL). The RTL-VLL model s much more precse. For the three mxtures consstng of water - ethanol - hydrocarbons the mean devaton between the calculated and measured temperatures does not exceed 0.25 K, for the fourth mxture t equals 0.33 K. Also, the mean devatons between the calculated and the measured concentratons n the gas phase and the lqud phases, wth one excepton do not exceed mole %. In the case of VLLE such an accuracy s really very hgh. The RTL-VLL model s also the most precse one for mxtures contanng MEK or n-butyl acetate n addton to water, ethanol and acetone, although the accuracy s no longer as good as n the case of water ethanol hydrocarbons mxtures. For the system contanng MEK ΔT equals 0.5 and for mxtures contanng n- Authentcated Download Date /8/2 7:09 PM 469

8 A. Wyczesany, Chem. Process Eng., 202, 33 (3), butyl acetate ths value s close to K. Devatons ΔX are generally less than mole % and the values ΔY exceed %. The models wth coeffcents taken from the Chemcad database (RTL-Chemcad and Unquac-Chemcad) gve much poorer accuracy n spte of the fact that some of the bnary mxtures are descrbed by a larger number of parameters (Eq. (2) or (5)). Also n ths case the RTL model shows hgher accuracy than the Unquac equaton. For systems contanng MEK or n-butyl acetate the bnary parameters for mxtures of these components and water taken from Chemcad related to the VLE nstead of LLE. The devatons ΔX, ΔY and ΔT were smaller for ths type of coeffcents. Sample fgures show pseudoternary representatons of the VLLE. In Fgures - 2 two hydrocarbons were combned n one pseudocomponent whereas n Fgures 3-4 the pseudocomponents represent the sums of ethanol and acetone mole fractons. The expermental data of systems contanng two hydrocarbons were measured for the four mxtures of a defned ntal rato M = x 4 /(x 3 +x 4 ) (M = 0.2, 0.4, 0.6 and 0.8). The expermental data of systems contanng ethanol and acetone also referred to four mxtures havng the same values of the ntal rato M. However, n ths case, the defnton of M was as follows: M = x acetone /(x ethanol +x acetone ). In order to make the graphs clear, only the lnes representng the expermental data and the models RTL-VLL and RTL-Chemcad were placed on them. In all the fgures we can observe a sgnfcant advantage of the model for whch the coeffcents were ftted to the VLLE data. Lower accuracy obtaned for the systems wth MEK or n- butyl acetate wth the models RTL-VLL and Unquac-VLL can be partly explaned by the qualty of the expermental data. Fgure 4 shows that the expermental ponts representng the composton of the lqud organc phase are not lyng on smooth but hghly corrugated curves. Table 5. Mean devatons of VLLE predcton for water ethanol cyclohexane toluene system RTL- Chemcad Unquac- Chemcad RTL-VLL Unquac-VLL Δx Δx Δx Δx Δx org, Δx org, Δx org, Δx org, Δy Δy Δy Δy ΔX ΔY ΔT An accurate predcton of temperature and concentratons of azeotropes s an mportant feature of a model. Accordng to the expermental data quaternary azeotropes are not formed n the consdered mxtures. However, we can observe the formaton of ternary azeotropes lsted n Table 8. The frst four are heteroazeotropes, and the last two are homoazeotropes. A comparson of the expermental and calculated compostons and temperatures for azeotropes presented n Table 8 leads to the concluson that agan these models n whch the coeffcents were ftted to the VLLE data show hgher precson. 470 Authentcated Download Date /8/2 7:09 PM

9 Calculaton of vapour - lqud - lqud equlbra n quaternary systems The RTL-VLL model s more accurate for mxtures contanng sooctane, n-hexane or toluene, and the Unquac-VLL model for mxtures contanng cyclohexane and n-heptane. In realty the mxture water - ethanol - toluene forms homoazeotrope. The models RTL-VLL and VLL-Unquac predct the correct type of ths azeotrope. However, models wth the coeffcents taken from Chemcad databank predct the occurrence of heteroazeotrope. Ths suggests that dehydraton of ethanol by heterogeneous azeotropc dstllaton wth toluene may be acheved, whch n practce s not possble. Table 6. Mean devatons of VLLE predcton for the followng systems: a) water ethanol cyclohexane n-heptane, b) water ethanol n-hexane toluene and c) water ethanol acetone MEK system a b c RTL- Chemcad d Unquac- Chemcad RTL-VLL Unquac-VLL ΔX ΔY ΔT ΔX ΔY ΔT ΔX ΔY ΔT d for system (c) parameters descrbe the VLE for all bnary mxtures Table 7. Mean devatons of VLLE predcton for water ethanol acetone n-butyl acetate system P, bar RTL- Chemcad a Unquac- Chemcad RTL-VLL Unquac-VLL ΔX ΔY ΔT ΔX ΔY ΔT ΔX ΔY ΔT a parameters descrbe the VLE for all bnary mxtures For homoazeotrope water - ethanol - MEK models wth coeffcents taken from Chemcad predcted correctly the type of azeotrope, but the temperature and concentratons were obtaned wth poor precson. The models RTL-VLL and Unquac-VLL do not predct the formaton of ths homoazeotrope at all. However, the coeffcents of the last two models were ftted to the expermental VLLE data, but concentratons at these equlbra are sgnfcantly dfferent from the composton of the homoazeotrope of ths partcular system. The values of the correlaton equatons coeffcents ftted to the expermental VLLE data are the result of a compromse between the accuracy of the VLE and LLE descrpton and they are not able to predct concentratons sgnfcantly dfferent from the VLLE compostons wth hgh accuracy. Authentcated Download Date /8/2 7:09 PM 47

10 A. Wyczesany, Chem. Process Eng., 202, 33 (3), Table 8. Comparson of expermental and calculated temperatures and compostons of ternary azeotropes exper. RTL- Unquac- RTL- Unquac- VLL VLL Chemcad Chemcad water ethanol cyclohexane T, K water ethanol sooctane T, K water ethanol n-hexane T, K water ethanol n-heptane T, K water ethanol toluene T, K water ethanol MEK T, K Ref. Goms et al., 2005 Font et al., 2003 Goms et al., 2007 Goms et al., 2006 Goms et al., 2008 Szany et al., 2004 Fg.. Expermental and calculated pseudoternary VLLE for water ethanol cyclohexane - sooctane (M = 0.4) and water ethanol cyclohexane - toluene (M = 0.4) systems 472 Authentcated Download Date /8/2 7:09 PM

11 Calculaton of vapour - lqud - lqud equlbra n quaternary systems Fg. 2. Expermental and calculated pseudoternary VLLE for water ethanol cyclohexane n-heptane (M = 0.2) and water ethanol n-hexane - toluene (M = 0.6) systems Fg. 3. Expermental and calculated pseudoternary VLLE for water ethanol acetone - MEK (M = 0.4) and water ethanol acetone n-butyl acetate (M = 0.4) systems Authentcated Download Date /8/2 7:09 PM 473

12 A. Wyczesany, Chem. Process Eng., 202, 33 (3), Fg. 4. Expermental and calculated pseudoternary VLLE for water ethanol acetone n-butyl acetate system. For P = 0.8 bar M = 0.2, and for P = 0.48 bar M = COCLUSIOS For each expermental pont the mnmsed objectve functon FC calculates the full VLLE and t can compute the VLE or the LLE when such types of data are used. The functon s flexble because t has two weght parameters W and W2. They allow to ft the calculated equlbrum temperatures and compostons of the VLE and the LLE to the expermental data wth a varyng degree of accuracy. The parameters W and W2 are chosen by a tral and error method to get the best ft. In the case of the RTL equaton a quaternary system s descrbed by 8 parameters and n the case of the Unquac model by 2 coeffcents. In the frst stage of parameter fttng the number of these coeffcents was halved by treatng the prevously calculated parameters for the ternary mxtures (beng the part of the consdered quaternary system) as known values. The coeffcents obtaned n ths way were used n the second stage as a carefully selected startng pont for the calculaton of all the 8 or 2 parameters. The calculated coeffcents more precsely descrbed the VLLE than n the frst stage, but the accuracy ncreased only slghtly. A comparson of the calculated results wth the expermental data for all the four nvestgated models shows that n almost every case the devatons Δx, Δy, ΔX, ΔY and ΔT are the lowest for the models RTL-VLL and Unquac-VLL, wth a sgnfcant predomnance of the former. For the frst four systems (water - ethanol - two hydrocarbons) the predcton accuracy s really hgh. In three cases ΔT does not exceed 0.25 K and for the fourth system t equals 0.33 K. Also, the devatons ΔX and ΔY, wth one excepton do not exceed mole %. The Model RTL-VLL s also the most precse one for mxtures of water, ethanol and acetone wth MEK or n-butyl acetate, although the accuracy s no longer as hgh as n the case of mxtures contanng water, ethanol and two hydrocarbons. The devaton ΔT equals 0.5 for the system contanng MEK, and for the mxtures wth n-butyl acetate ths value s slghtly less than K. In most cases the values ΔX are less than mole %, whereas the devatons ΔY do not exceed 2 %. The models wth the coeffcents taken from Chemcad have a much worse accuracy. But also n ths case hgher accuracy of the RTL equaton can be observed. Fgures showng the pseudoternary VLLE confrm hgh accuracy of the RTL-VLL model. They also ndcate that a slghtly worse fttng of the coeffcents for the systems contanng MEK or n- butyl acetate may be explaned by the qualty of the expermental data. Fgure 4 shows that the expermental ponts representng the composton of the lqud organc phase are not lyng on smooth but hghly corrugated curves. In the case of temperature and composton predctng for ternary 474 Authentcated Download Date /8/2 7:09 PM

13 Calculaton of vapour - lqud - lqud equlbra n quaternary systems azeotropes (whch can be formed n the consdered quaternary mxtures) the models RTL-VLL and Unquac-VLL are also much more accurate than those usng the coeffcents from the Chemcad database. Models wth parameters ftted to the VLLE data correctly predct that the mxture of water - ethanol - toluene forms homoazeotrope. Models usng the coeffcents from the Chemcad database predct that ths ternary mxture can form heteroazeotrope, suggestng that ethanol could be dehydrated by heterogenc azeotropc dstllaton wth toluene, whch s not possble n practce. These models correctly predct that the system water - ethanol MEK can form homoazeotrope, but the temperature and compostons are calculated wth poor precson. On the contrary, the models RTL-VLL and Unquac-VLL do not predct the formaton of ths homoazeotrope. Ths phenomenon may be explaned by the fact that the coeffcents of these last two models were ftted to the expermental VLLE data, but concentratons at these equlbra are sgnfcantly dfferent from the composton of the homoazeotrope of ths partcular system. SYMBOLS A j, A j parameters of the RTL and the Unquac equatons, K FC objectve functon number of expermental ponts P total pressure, bar s P saturated vapour pressure of pure component at T, bar q van der Waals molecular surface area parameter R gas constant, J/(mol. K) r van der Waals molecular volume parameter T temperature, K ΔT absolute mean devaton between expermental and calculated equlbrum temperature, K W, W2 weght factors x, y mole fractons n the lqud and the vapour phase, respectvely ΔX, ΔY mean devaton defned n Equaton (2) Δx, Δy absolute mean devaton between expermental and calculated equlbrum composton n the lqud and the vapour phase, respectvely z mole fracton of component n the entre mxture or n the entre lqud phase Greek symbols α j parameter of the RTL equaton β aqueous phase fracton n total lqud actvty coeffcent of speces γ Subscrpts exp cal aq org expermental calculated aqueous phase organc phase REFERECES Abrams D.S., Prausntz J.M., 975. Statstcal thermodynamcs of lqud mxtures: A new expresson for the excess Gbbs energy of partly or completely mscble systems. AIChE J., 2, DOI: 0.002/ac Authentcated Download Date /8/2 7:09 PM 475

14 A. Wyczesany, Chem. Process Eng., 202, 33 (3), Asens J.C., Molto J., del Mar Olaya M., Ruz F., Goms V., Isobarc vapour lqud equlbra data for the bnary system -propanol + -pentanol and sobarc vapour lqud lqud equlbra data for the ternary system water + -propanol + -pentanol at 0.3 kpa. Flud Phase Equl., 200, DOI: 0.06/S (02) Chemcad VI. Process Flowsheet Smulator, v , Chemctatons Inc., Huston 200. Font A., Asens J.C., Ruz F., Goms V., Applcaton of sooctane to the dehydraton of ethanol. Desgn of a column sequence to obtan absolute ethanol by heterogeneous azeotropc dstllaton. Ind. Eng. Chem. Res., 42, DOI: 0.02/e Goms V., Front A., Pedraza R., Saquete M.D., Isobarc vapor lqud and vapor lqud lqud equlbrum data for the water + ethanol + cyclohexane system. Flud Phase Equl., 235, 7-0. DOI: 0.06/j.flud Goms V., Front A., Saquete M.D., Vapour lqud lqud and vapour lqud equlbrum of the system water + ethanol + heptane at 0.3 kpa. Flud Phase Equl., 248, DOI: 0.06/j.flud Goms V., Front A., Pedraza R., Saquete M.D., Isobarc vapor lqud and vapor lqud lqud equlbrum data for the water ethanol hexane system. Flud Phase Equl., 259, DOI: 0.06/j.flud Goms V., Front A., Saquete M.D., Homogenty of the water + ethanol + toluene azeotrope at 0.3 kpa. Flud Phase Equl., 266, 8-3. DOI: 0.06/j.flud Grgante M., Strngar P., Scalabrn G., Ihmels E.C., Fscher K., Gmehlng J., (Vapour + lqud + lqud) equlbra and excess molar enthalpes of bnary and ternary mxtures of sopropanol, water, and propylene. J. Chem. Therm., 40, DOI: 0.06/j.jct Hseh C.T., Lee M.J., Ln H.M., Multphase equlbra for mxtures contanng acetc acd, water, propylene glycol monomethyl ether, and propylene glycol methyl ether acetate. Ind. Eng. Chem. Res., 45, DOI: 0.02/e05245t. Hseh C.T., J W.Y., Ln H.M., Lee M.J., Multphase equlbra for mxtures contanng water, acetc acd, proponc acd, methyl acetate and methyl proponate. Flud Phase Equl., 27, DOI: 0.06/j.flud James F., 967. FOWL, CER Program Lbrary, program D506. Avalable at Kosuge H., Iwakabe K., Estmaton of sobarc vapor lqud lqud equlbra for partally mscble mxture of ternary system. Flud Phase Equl., 233, DOI: 0.06/j.flud Kundu D., Banerjee T., 20. Multcomponent vapor lqud lqud equlbrum predcton usng an a pror segment based model. Ind. Eng. Chem. Res., 50, DOI: 0.02/e20864y. Lee L.S., Chen W.C., Huang J.F., 996. Experments and correlatons of phase equlbra of ethanol ethyl acetate water ternary mxture. J. Chem. Eng. Jap., 29, Lu F.Z., Mor H., Hraoka S., Yamada I., 993. Phase equlbra and smulaton method for beterogeneous azeotropc dstllaton. J. Chem. Eng. Jap., 26, Pequenn A., Asens J.C., Goms V., 200. Isobarc vapor-lqud-lqud equlbrum for the quaternary system water-ethanol-cyclohexane-sooctane at 0.3 kpa. J. Chem. Eng. Data, 55, DOI: 0.02/je900604a. Pequenn A., Asens J.C., Goms V., 20a. Vapor-lqud-lqud equlbrum and vapor-lqud equlbrum for the quaternary system water-ethanol-cyclohexane-toluene and the ternary system water-cyclohexane-toluene. Isobarc expermental determnaton at 0.3 kpa. Flud Phase Equl., 309, DOI: 0.06/j.flud Pequenn A., Asens J.C., Goms V., 20b. Quaternary sobarc (vapor-lqud-lqud) equlbrum and (vaporlqud) equlbrum for the system water-ethanol-cyclohexane-heptane at 0.3 kpa. J. Chem. Therm., 43, DOI: 0.06/j.jct Pequenn A., Asens J.C., Goms V., 20c. Expermental determnaton of quaternary and ternary sobarc vaporlqud-lqud equlbrum and vapor-lqud equlbrum for the systems water-ethanol-hexane-toluene and waterhexane-toluene at 0.3 kpa. J. Chem. Eng. Data, 56, DOI: 0.02/je Renon H., Prausntz J.M., 968. Local composton n thermodynamc excess functons for lqud mxtures. AIChE J., 4, DOI: 0.002/ac Ruz F., Goms V., Botella R.F., 987. Extracton of ethanol from aqueous soluton.. Solvent less volatle than ethanol: 2-ethylhexanol. Ind. Eng. Chem. Res., 26, Authentcated Download Date /8/2 7:09 PM

15 Calculaton of vapour - lqud - lqud equlbra n quaternary systems Szany A., Mzsey P., Fonyo Z., ovel hybrd separaton processes for solvent recovery based on postonng the extractve heterogeneous-azeotropc dstllaton. Chem. Eng. Process., 43, DOI: 0.06/S (03) Wyczesany A., 200. Calculaton of vapour-lqud-lqud equlbra. Chem. Proc. Eng., 3, Ye K., Freund H., Sundmacher K., 20. Modellng (vapour + lqud) and (vapour + lqud + lqud) equlbra of {water (H 2 O) + methanol (MeOH) + dmethyl ether (DME) + carbon doxde (CO 2 )} quaternary system usng the Peng Robnson Eos wth Wong Sandler mxng rule. J. Chem. Therm., 43, DOI: 0.06/j.jct Youns O.A.D., Prtchard D.W., Anwar M.M., Expermental sobarc vapour-lqud-lqud equlbrum data for the quaternary systems water ()-ethanol (2)-acetone (3)-n-butyl acetate (4) and water ()-ethanol (2)- acetone (3)-methyl ethyl ketone (4) and ther partally mscble-consttuent ternares. Flud Phase Equl., 25, DOI:0.06/j.flud Receved 26 June 202 Receved n revsed form 05 September 202 Accepted 07 September 202 Authentcated Download Date /8/2 7:09 PM 477