The influence of non-ideal vapor-liquid-equilibrium on vaporization of multicomponent hydrocarbon fuels

Transcription

1 ICLASS 202, 2 th Trennal Internatonal Conference on Lqud Atomzaton and Spray Systems, Hedelberg, Germany, September 2-6, 202 The nfluence of non-deal vapor-lqud-equlbrum on vaporzaton of multcomponent hydrocarbon fuels A. Bader, P. Keller, C. Hasse, B. Meyer Department of Energy Process Engneerng and Chemcal Engneerng, Techncal Unversty of Freberg, Germany Andre.Bader@ec.tu-freberg.de, Peter.Keller@ec.tu-freberg.de, Chrstan.Hasse@ec.tu-freberg.de, Bernd.Meyer@ec.tu-freberg.de Abstract In ths work the dfferences between deal and non-deal vapor-lqud-equlbrum (VLE) and the effect on vaporzaton for multcomponent hydrocarbon fuels, whch are representatve for engnes or gasfers, are nvestgated. Based on these devatons, a parametrc study of non-deal VLE-behavor for a pressure range of bar and a temperature range tll 600 C, whch are typcal vaporzaton condtons n techncal systems, s performed. The VLE results are then appled for a 0D sngle droplet vaporzaton model, whch can be consdered as a base model for most CFD applcatons. The droplet lfe tme and the vaporzaton rates of the sngle components are compared between deal and non-deal behavor varyng the pressure, the temperature and the partcle Reynolds number. The observed dfferences suggest that non-deal VLE have a sgnfcant mpact on the droplet vaporzaton characterstcs for complex hydrocarbon mxtures. Introducton The vaporzaton of fuels s a relevant process n many practcal devces lke engnes, furnaces and gasfers whch effects mxture formaton and further steps lke burnng, gasfcaton or pollutant formaton. The accuracy of the droplet vaporzaton affects all the further steps sgnfcantly. Snce real fuels consst of a large number of speces, t s mportant to model the fuels wth a multcomponent approach. Fuels are usually depcted wth contnuous thermodynamcs, where all the sngle components are lumped together. The descrpton of the real vapor pressure for mxtures has the man mpact on the vaporzaton. Hence, the vapor-lqud-equlbrum (VLE) wll be determned wth sutable real approaches n contrast to the deal approach of Raoult. The non-deal VLE for mxtures s a classcal topc of the multcomponent thermodynamcs whch s essental n all flud separaton technologes lke n petrol chemstry or n gas treatment processes. In praxs there are sgnfcant dfferences n non-deal behavor compared to the deal assumptons. A very popular example s the mxture of ethanol and water whch form an azeotrope. Several studes n the lterature looked at non-deal mxtures and ther VLE. As an example Neroorkar et al. [] analyzed already non-deal vapor-lqud equlbrum propertes of gasolne-ethanol fuel blends wth an emprcal Gasolne-Ethanol Flash model and Aspen Plus up to hgh temperatures but below ts vapor pressure. Zhang et al. studed n [2] the vaporzaton of 00 µm ol droplets n pure ntrogen wth contnuous thermodynamcs and especally for bo-ol droplets n [3]. Wthn the scope of ths work the fuel vaporzaton s nvestgated wth a sngle droplet of dscrete components whereby deal and non-deal VLE approaches are compared. The hydrocarbon fuel vaporzaton s consdered for sngle component fluds and bnary mxtures. The fuel s assumed to be a mxture of so-octane (2,2,4 trmethylpentane) and ethanol, whch results n a ternary vapor-lqud equlbrum (VLE) wth the surroundng ntrogen atmosphere. Iso-octane was chosen n order to model gasolne and was mxed wth ethanol n all mxture ratos, for nstance to model E0 (0 vol.-% ethanol n gasolne). The droplet vaporzaton s dscussed n a pressure range from 0.5 bar tll 20.0 bar and n a ntrogen atmosphere wth temperatures between 0 C and 600 C. The paper starts wth a descrpton of the chosen non-deal VLE model and follows wth an explanaton of the 0D sngle droplet model for multcomponents. After that, the dependency of the ambent gas temperature, relatve droplet velocty and the pressure mpact on the droplet vaporzaton are dscussed n the followng secton. Thereby, the dfferences between deal and non-deal VLE droplet vaporzaton are compared wth each other. Numercal Model The numercal modelng can be dvded nto two parts. The frst part deals wth the descrpton of the nondeal VLE where the correcton factors to account for the non-deal thermo-chemcal equlbrum of lqud and Correspondng author: Andre.Bader@ec.tu-freberg.de

2 2 th ICLASS 202 The nfluence of non-deal vapor-lqud-equlbrum on vaporzaton of multcomponent hydrocarbon fuels gas mxtures are determned. In addton, the teraton process wll be ntroduced to determne the new bolng temperature of the mxture. The second part concerns the zero-dmensonal descrpton of the vaporzaton of a sngle droplet combned wth the frst part. Here, a multcomponent vaporzaton model s presented as gven by Law n [4] and extended by mprovements due to convecton and non-deal behavor. Vapor-lqud equlbrum The Gbbs phase rule says that vapor and lqud are at the equlbrum-state f the pressures of both phases are equal. In order to descrbe the non-deal behavor the pressure of speces or mxtures s replaced n the Gbbs- Duhem equaton by a corrected pressure, the so-called fugacty f. The non-deal VLE s acheved f the fugacty of the vapor f v s equal to the one of the lqud phase f l for all sngle components, see eq. (). f l = f v () In general, the two ways besde the deal approach of Raoult to determne the fugacty are the equatons-ofstates (EoS) models and excess Gbbs energy (G E ) models. A typcal EoS model s the Redlch-Kwong-Soave- Wong-Sandler (RKSWS) model. Commonly used G E models are the non-random-two-lquds-model (NRTL) and the Unversal Quaschemcal Functonal Group Actvty Coeffcents model (UNIFAC). The VLE of the ternary mxture consstng of so-octane, ethanol and ntrogen and t s bnary mxture combnatons s llustrated n Fg.. The VLE determnaton was done usng mass fractons and transformed wth a lnear mxng rule nto volume Fgure. VLE of the ternary mxture consstng of so-octane, ethanol and ntrogen and t s bnary mxture combnatons at.0 bar. 2

3 2 th ICLASS 202 The nfluence of non-deal vapor-lqud-equlbrum on vaporzaton of multcomponent hydrocarbon fuels fractons. The volume fracton s used to descrbe common lqud mxng ratos n the droplet on volume base, lke 0 vol.-% ethanol n gasolne, called E0. The VLE models are determned wth Aspen Plus for Raoult s law and for the non-deal methods NRTL, RKSWS and UNIFAC. Furthermore the results of an own mplemented NRTLmodel and the expermental data from Wen [5] for the bnary mxture of so-octane and ethanol are gven n Fg.. The bnary mxture of so-octane and ethanol shows an azeotrope pont at around 0.40 kg/kg ethanol and lower bolng and condensaton temperatures for the non-deal approaches as n Raoult s law, whch s typcally used n CFD calculatons. The bnary mxture of so-octane wth ntrogen and the mxture of ethanol wth ntrogen are almost equal for the condensaton temperatures of all of the four methods for both mxtures. In contrast to that the bolng temperature devates. As a consequence the solublty for ntrogen n so-octane and ethanol s set to zero n the sngle drop model, whch wll be dscussed n the next secton. The reason to use the NRTL-model n ths work for the so-octane/ethanol/ntrogen mxture s that the results from the NRTL-model match the measurement data from Wen [5] n good agreement. Furthermore, t s much easer mplementable than the other models, RKSWS and UNIFAC. The fugacty of the vapor phase s defned by eq. (2), where ỹ s the molar fracton of the vapor of component, ϕ v are the fugacty coeffcents of the vapor speces and p the system pressure. f v = ϕ v p = ỹ ϕ v p (2) The fugacty of the lqud phase s formed by the actvaton a and a standard fugacty f + whch has a freely selectable reference state, eq. (3). The actvaton of the lqud phase s determned by the molar fractons x of the lqud components and the actvaton coeffcents γ. Usually, the fugacty of the pure component at saturaton state s selected. Therefore, the vapor pressures p 0 can be used together wth the Poyntng correctons κ whch descrbes the pressure dependency of the fugacty. f l = a f + = γ x f + = γ x f 0 = γ x ϕ 0 p 0 exp p p 0 V 0 RT dp } {{ } κ 0 (3) In order to determne the vapor fracton n the vapor lqud equlbrum, equatons (2) and (3) are nserted n eq. () and result n (4). ỹ = γ x f 0 ϕ v p = ( p γ x p 0 ϕ0 exp p 0 ϕ v p V 0 RT dp ) = γ x p 0 p ϕ 0 exp ( p p 0 ϕ v V 0 RT dp ) = γ x p 0 p ϕ0 ϕ v κ 0 (T, p) (4) The Poyntng correcton can be determned by eq. (5), where ṽ l 0, are the molar volumes of the lqud components, T the temperature and R the unversal gas constant. {ṽl κ 0 0, (T ) ( (T, p) = exp p p 0 RT (T ) )} (5) The fugacty coeffcents of the vapor at system pressure and saturaton state are calculated usng eq. (6) and (7), respectvely. { } B ϕ v (T ) = exp RT p ϕ 0 = exp { } B (T ) RT p 0,(T ) (6) (7) 3

4 2 th ICLASS 202 The nfluence of non-deal vapor-lqud-equlbrum on vaporzaton of multcomponent hydrocarbon fuels The second Vral coeffcents B are determned by the method of Tsonopoulos [6], and are n the form of eq. (8) whch use the crtcal pressure p c, the crtcal temperature T c, the current drop temperature T and the reduced temperature T r = T/T c. Ths method s based on the correspondence prncple of Ptzer and Curl [7]. B p c RT c = f (0) (T r ) + ωf () (T r ) + f (2) (T r ) (8) The actvaton coeffcents γ are determned applyng the NRTL (non random two lquds) model, whch was developed by Renon et. al [8], and can be calculated usng equaton (9). The NRTL model base on mass fracton x and on the temperature dependent NRTL parameters τ j and G j, whch can be determned wth eq. (0) tll (2). The coeffcents A j, B j, C j, D j come from the Aspen database. K x j G j τ j j= K ln γ = + K x k G j= k k= k= K x j G x l G l τ l j K τ l= j K x k G kj x k G kj k= (9) τ j = A j + B j T (0) G j = exp { α j τ j } () α j = C j + D j (2) In contrast to the non-deal VLE, n deal approaches the actvaton and fugacty coeffcents are equal to one n eq. (4) whch s well known as Raoult s law. The results from the NRTL-model correspond wth the measurement data from Wen [5] and are equal to the results obtaned from the software ASPEN Plus. The VLE of the ternary mxture consstng of so-octane, ethanol and ntrogen and ts bnary mxture combnatons s calculated wth eq. (4). The non-deal vapor-lqud-equlbrum s calculated teratvely wth eq. (4) by adjustng the temperature at a gven system pressure, as γ = f(x, T ), s temperature dependent. Hgher pressures lead to hgher bolng and condensaton temperatures. The azeotrope ponts change from 0.37 kg/kg at atm at hgher pressures to hgher ethanol concentratons (0.57 kg/kg at 0 bar and 0.63 kg/kg at 20 bar). The dfferences between the non-deal NRTL model compared wth Raoult s law ncrease wth pressure, especally at so-octane contents lower than the azeotrope. Fnally, t s demonstrated that the NRTL-model gves the same results as the ASPEN-NRTL-model even at hgh pressures and hence can be used n the sngle droplet model up to 20 bar. Sngle Droplet Vaporzaton The vaporzaton rate and change of composton, radus and temperature are calculated usng the method of Law [4]. Assumng a unbounded atmosphere, the quas-steady, sobarc and sphercally symmetrc vaporzaton of a sngle multcomponent droplet s descrbed. The equatons to calculate the mole fractons of the lqud components, the radus and the surface temperature of the droplet are wrtten for a zero-dmensonal droplet (dscretzed n tme) and read x (n ) x (n) (r (n ) ) 3 3 Ω ṁ F δt 4πM = (r (n ) ) 3 ex (n ) M ρ (n ),l ex (n ) M Ω 3 ṁ ρ (n ) F δt,l 4πM (3) ( r (n) = 3 (r (n ) ) 3 3 4π δt Ω ṁ F ρ (n ),l ) ex (n) M ρ (n),l ex (n) M ρ (n ),l 4 (4)

5 2 th ICLASS 202 The nfluence of non-deal vapor-lqud-equlbrum on vaporzaton of multcomponent hydrocarbon fuels T (n) s = T (n ) s + ṁ F δth 4 c p,g 3 π(r(n ) ) 3 ρ (n ) m,l (5) wth total vaporzaton rate ṁ F, fractonal vaporzaton rates Ω, heat nput functon H, molar masses M, denstes of lqud components ρ,l and lqud mxture ρ m,l, tme step sze δt, heat capacty of gas mxture c p,g, radus r and surface temperature T s. The superscrpts (n ) and (n) denote the old and new state, respectvely. All of the spece propertes are calculated temperature dependent wth the equatons and coeffcents from Yaws [9]. The orgnal equaton was formulated by Law [4] for stagnant envronments only. As the drop has a moton relatve to the ambent atmosphere, the heat and mass transfer across the drop surface are ncreased. Hence, the Nusselt number requres a convecton correcton as proposed by Turns [0]. The total vaporzaton rate then reads wth ṁ F = 2Nu πλ gr c p,g ln ( + y ) F,s y F,s Nu = Re/2 P r /3 ( ReP r 4/3 ) /2, (7) thermal conductvty of the gas mxture λ g and total surface mass fracton of vapor y F,s. Ths surface mass fracton s determned usng the VLE-model mentoned prevously and hence ncludes non-deal behavor of lquds and gases, too. The Reynolds number Re represents the relatve moton between droplet and the ambent medum. The sngle droplet model s solved by ntegratng the eq. (3) tll (5) wth fxed tme steps of order δt 0 5 s. Results and Dscusson In ths secton the temperature, relatve droplet velocty and the pressure dependency applyng the sngle droplet model s dscussed. The mpacts are descrbed for dfferent ntal compostons, frst for the sngle components so-octane and ethanol and second for the mxtures. For nstance, E90 represents a mxture of 90 vol.-% ethanol and 0 vol.-% so-octane. For all cases, the sngle droplet model s ntalzed wth a dameter of D d = 00 µm and at lqud temperature of T lqud = 25 C. The soluton of sngle droplet model s obtaned by ntegratng the equatons of the prevous secton and ended because of numercal reasons at a fnal droplet sze wth r = 5 µm. Temperature dependency The temperature dependency s dscussed at a system pressure of 0 bar. The results are llustrated n Fg. 2 whereas an ambent gas temperature of 25 C s represented n the left column and 600 C at the rght column. Varous ntal compostons are used for both ambent gas temperatures. All these cases are calculated wth Raoult s law as well as the NRTL-model. Fgure 2 shows the transent normalzed squared dameter n the frst row. The tme scale s normalzed wth the droplet lfe tme (DLT). Ths tme scale s appled for all the pctures n Fg. 2. For pure so-octane (E00) at 25 C gas temperature the DLT s.0444 s n the deal case and s n the NRTL-model case, whch results n an error of 5.7%. The error decreases wth a hgher ethanol content. For nstance to 34.7% at 0.60 mol/mol ethanol, whereas the DLT ncrease to.6448 s n the deal case and.224 s n the NRTL-model case. The mnmal error s at 0.92 mol/mol ethanol wth 9.5% and ncreases at.00 mol/mol ethanol to 20.4%. At 600 C gas temperature the droplet vaporze 40 tll 60 tmes faster than at 25 C gas temperature both wth the NRTL as well wth the Raoult approach. In the case of 600 C gas temperature the DLT s longer n the NRTL-model case compared to the deal DLTs at 25 C gas temperature. The error s always lower then 2.0%. The transent surface temperatures of the droplet are llustrated n the second row of Fg. 2. Fgure 3 gves the transent equlbrum molar fractons n the gas phase of so-octane and ethanol for the ntal compostons E0 and E90. The reman to 00 % s ntrogen. In Fgure 2 at 25 C gas temperature, both pure ethanol and pure so-octane show a lnear D 2 -law behavor for the Raoult approach as well as for the NRTL-model. Even for mxtures wth less ethanol lke E0, the droplet dameter decreases wth an almost lnear D 2 -law behavor, as the vapor pressures are close to each other. Only for hgher ethanol contents wth a non-deal NRTL approach, the droplet shrnkng velocty shows a characterstc turnng pont after ethanol left the droplet completely. At the same tme the droplet surface temperature ncreases because the enthalpy of vaporzaton of so-octane s lower than the one of ethanol. For the deal approach the droplet 5 (6)

6 2 th ICLASS 202 The nfluence of non-deal vapor-lqud-equlbrum on vaporzaton of multcomponent hydrocarbon fuels D 2 /D p = 0.0 bar; T Gas = 25 C; T lqud = 25 C Raoult; E00 NRTL; E00 Raoult; E0 NRTL; E0 Raoult; E60 NRTL; E60 Raoult; E90 NRTL; E90 Raoult; E00 NRTL; E00 D 2 /D p = 0.0 bar; T Gas = 600 C; T lqud = 25 C tme/tme end [s/s] 0 tme/tme end [s/s] Temperature [ C] Temperature [ C] tme/tme end [s/s] 20 tme/tme end [s/s] Fgure 2. Normalzed droplet square dameter and surface temperature at T gas = 25 C (left) and T gas = 600 C (rght) at 0 bar, T lqud = 25 C, Re = 0 Vapor mole fracton at droplet surface [mol/mol] Iso Octane Raoult; E0 Iso Octane NRTL; E0 Ethanol Raoult; E0 Ethanol NRTL; E0 Iso Octane Raoult; E90 Iso Octane NRTL; E90 Ethanol Raoult; E90 Ethanol NRTL; E expands at the begnnng of the vaporzaton because of thermal expanson and has a hgher vaporzaton rate the densty reduces 0.00at hgher temperatures by the equatons of 0.00 Yaws [9], whereby no correcton for the property Vapor mole fracton at droplet surface [mol/mol] Iso Octane Raoult; E0 Iso Octane NRTL; E0 Ethanol Raoult; E0 Ethanol NRTL; E0 Iso Octane Raoult; E90 Iso Octane NRTL; E90 Ethanol Raoult; E90 Ethanol NRTL; E90 vaporzaton rate and the temperature are constant for the most of the tme as the dfferences between condensaton and the bolng curve are almost equal, see Fg.. The conclusons derved from the 25 C gas temperature case can be adapted to the 600 C case. But the droplet n the case of gas temperature 600 C compared to 25 C n the ambent atmosphere. The droplet expands, as mxng s mplemented as the error s assumed to be small. The error occurs as well n the deal and n the nondeal case. Consequently, the assumpton has no mpact on0.000 the dfference between deal and non-deal droplet vaporzaton, whch s the focus n tme/tme ths end work. [s/s] The transent droplet surface temperature tme/tme end [s/s] converges to so-octane bolng temperature (T bol = C at 0 bar) when ethanol left the droplet completely. Fgure 3 shows the ethanol and the so-octane content n the vapor phase at the droplet surface. If the vapor phase content of a spece s zero, the spece does not exst n the droplet anymore, too. Ethanol leaves the droplet completely n the deal and the NRTL approach f only less ethanol, lke E0, s n the ntal composton of the droplet. At hgher ntal ethanol content, lke E90, ethanol leaves the droplet completely only for the deal approach. For the NRTL approach the droplet surface temperature s close to the mxture bolng pont temperature at 0 bar, and the droplet conssts of both ethanol and so-octane tll the end of the droplet lfe tme, see Fg. 3. Fnally, t can be concluded that the vaporzaton takes longer the hgher the ntal content of ethanol s and that at hgher temperatures, the dfference n the DLT between the deal and the non-deal behavor s reduced. But for ntal compostons wth a hgh ethanol content the error ncreases agan after a decrease, see Fg. 4. At 25 C gas temperature, the maxmum error s at +82% related to an ntal composton of 40 vol.-% ethanol. Whereas at 600 C gas temperature the maxmum error s at 2% related to an ntal composton of 70 vol.-% ethanol. The regons of error maxma can be better derved from Fg. 4 whch wll be dscussed n a later secton. 6

7 Tempe 6 Tempe tme/tme end [s/s] 2 th tme/tme ICLASS 202 The nfluence end [s/s] of non-deal vapor-lqud-equlbrum on vaporzaton of multcomponent hydrocarbon fuels Iso Octane Raoult; E0 Iso Octane NRTL; E0 Ethanol Raoult; E0 Ethanol NRTL; E0 Iso Octane Raoult; E90 Iso Octane NRTL; E90 Ethanol Raoult; E90 Ethanol NRTL; E90 Iso Octane Raoult; E0 Iso Octane NRTL; E0 Ethanol Raoult; E0 Ethanol NRTL; E0 Iso Octane Raoult; E90 Iso Octane NRTL; E90 Ethanol Raoult; E90 Ethanol NRTL; E90 Vapor mole fracton at droplet surface [mol/mol] p = 0.0 bar; T Gas = 25 C; T lqud = 25 C tme/tme end [s/s] Vapor mole fracton at droplet surface [mol/mol] p = 0.0 bar; T Gas = 600 C; T lqud = 25 C tme/tme end [s/s] Fgure 3. Equlbrum vapor mole fracton for E0 and E90 at T gas = 25 C (left) and T gas = 600 C (rght) at 0 bar, T lqud = 25 C, Re = 0 Relatve droplet velocty dependency The vaporzaton rate of the droplet s affected by the gas flow around the droplet. Increasng relatve veloctes between gas and droplet are represented by an ncreasng Reynolds number Re. The Reynolds number can only be ncreased to a maxmum value of Re = 00 n order to avod droplet break-up. Because of ntegraton nto the vaporzaton rate, the DLT of course decreases wth ncreasng Re. The relatve error of the vaporzaton rate between the deal and the non-deal approach can be calculated wth the help of eq. (6) n eq. (8). As eq. (8) can be reduced by the Nu(Re, P r), the relatve moton has no mpact on the error. The error has the maxmum at ntal composton around the azeotrope concentraton. ṁ F,deal ṁ F,non-deal ṁ F,non-deal = 2Nu(Re, P r) πλ g c p,gr +yf,s,deal ln y F,s,deal 2Nu(Re, P r) πλg +yf,s,non-deal c p,gr ln y F,s,non-deal (8) 2Nu(Re, P r) πλg +yf,s,non-deal c p,gr ln y F,s,non-deal Pressure dependency The vaporzaton of the fuel droplet s analyzed wth the sngle droplet model wth pressures at 0.5 bar, 5 bar, 0 bar and 20 bar. Furthermore, the ambent gas temperature s varated n a range from T = 0 C to T = 600 C and the ntal mxture s changed from 0 vol.-% to 00 vol.-% ethanol for a parameter study. The dfference n the DLT between the deal and the non-deal approach f rel s calculated wt eq. (9) and s represented n Fg. 4. f rel = DLT deal DLT real DLT real (9) The DLT wth the Raoult approach s longer than wth the NRTL approach at low temperatures. Ths s because the vapor pressure s ncreased usng the NRTL approach for the ethanol/so-octane mxture. Thereby, the dfferences ncrease wth hgher pressures. Whereas hgh temperatures reduce the dfferences between the vapor pressure. Hence, the DLT error between deal and non-deal decreases. Except for hgh ethanol contents n the ntal composton at hgh temperatures the DLT s longer wth the NRTL approach than wth deal approach as the vaporzaton of so-octane s preferred at the begnnng n the non-deal approach n contrast to the deal approach. Ths behavor can be derved from Fg.. In general, the DLT ncreases wth the pressure ncrease. The postve maxmum of the DLT error s always at 0 C. Only the ntal ethanol content vares whch results n a maxmum shft from 37 vol.-% to 23 vol.-% at a pressure change from 0.5 bar to 20 bar. The maxmum of the negatve error s at the lmt of the dscussed regon at 600 C and at 74 vol.-% ethanol for 5, 0 and 20 bar. Only at 0.5 bar, the maxmum of the negatve error s at a gas temperature of 270 C and at 68 vol.-%. 7

8 2 th ICLASS 202 The nfluence of non-deal vapor-lqud-equlbrum on vaporzaton of multcomponent hydrocarbon fuels Fgure 4. Error of droplet-lfe-tme between Raoult and NRTL approach at 0.5,.0, 0 and 20 bar for ntal mxtures of ethanol an so-octane between 0% - 00% ( + / red non-deal s faster than deal) and ( - / blue deal s faster than non-deal) by T lqud = 25 C and ndependent of Re. Colorbar s scaled to +20% and -20%. Summary and Conclusons The use of Raoult s law nstead of a non-deal approach lke NRTL can lead to an error n the droplet lfe tme up to more than 400%. Crtcal regons are at ambent gas temperatures lower than around 00 C especally at ntal compostons wth lower ethanol content than at the azeotrope pont. The error ncreases wth hgher pressures and lower temperatures. For the current formulaton, the Reynolds number has no mpact n a 0D sngle droplet model on the error between deal and non-deal approaches. Fnally, t can be concluded that non-deal descrptons of vapor-lqud-equlbrums should be ncluded n CFD solvers, as sgnfcant dfferences between deal and non-deal approaches can be notced even n smple sngle droplet models. Acknowledgements The authors acknowledge the funded research by the Federal Mnstry of Educaton and Research of Germany n the framework of Vrtuhcon (project number 03Z2FN), the Bavaran Scence Foundaton n the project WDKO(project number AZ-932-0) and by Ar Lqude S.A. References [] Neroorkar, K. and Schmdt, D., Fuel Vol. 90, p (200). [2] Zhang, L. and Kong, Song-Charng, Combuston and Flame Vol. 58, p (20). [3] Zhang, L. and Kong, Song-Charng, Fuel Vol. 95, p (202). [4] Law, C.K., Combuston and Flame Vol. 26, p (976). [5] Wen, C.C. and Tu. C. H., Flud Phase Equlbrum Vol. 258, p (2007). [6] Tsonopoulos, C., AIChEJ Vol. 2 p (975). [7] Ptzer, K. S. and Curl, R. F., J. Am. Chem. Soc. Vol. 79 p (957). [8] Renon, H. and Prausntz, J.M., AIChEJ Vol. 4 p (968). [9] Yaws, C. L., Chemcal propertes handbook ISBN (999). [0] Turns, S.R., McGraw-Hll, 3 rd Internatonal Edton ISBN (2000). 8