Liquid vapour equilibrium calculations for MTBE/MEOH binary system by using Patel & Teja equation of state

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1 34 Peet trool lleeuum & Cooaal ll IISSN Avalable onlne at Petroleum & Coal 46 (), 34-40, 004 Lqud vapour equlbrum calculatons for MTBE/MEOH bnary system by usng Patel & Teja equaton of state M. Bazm, K. Ghanbar and J. Alae Research Insttute of petroleum Industry Tehran Iran P.O.Box ,Phone: 98(1) Ext Fax: 98 (1) ,Emal: Receved 16 August 004;receved n revsed form 18 October 004; accepted 8 October 004 Abstract Ths work presents vapour-lqud equlbrum calculatons for a bnary system, whch s based on a computer program. For ths purpose Patel & Teja equaton of state has been used for the measurement of equlbrum data, whch has hgh effcency for polar systems. By usng ths program, varous equlbrum datum such as bubble and dew pont temperature/ pressure, flash calculatons, and equlbrum coeffcent (k value) could been calculated. The flowchart of ths program and many appled example for MTBE/MEOH system are presented n ths artcle and conclusons are reflected as graphs and tables. Key words: modellng; equlbrum, Patel & Teja equaton of state, k j, flash, bubble and dew pont Introducton Thermodynamcs and equlbrum datum are needed for desgn operatng unts such as dstllaton column, extracton and so on. The fallowng two methods are exst: 1) Expermental and laboratory methods ) Calculatng methods (Actvty coeffcent and equaton of state) Datum that wll obtaned wth expermental methods are the most relable, but calculatng methods have preference to laboratory methods because of expensveness and long tme. In actvty coeffcent Method two separate thermodynamc models would be used for lqud phase actvty coeffcent and vapour phase fugacty coeffcent and because of that to result n thermodynamc ncompatblty. Ths model s used for polar systems, but because of above motoned reason s not recommended. Equaton of state method has preference to actvty coeffcent Method, because only one equaton s used for components fugacty coeffcent n lqud and vapour phases but the best equaton of state wth hgh effcency must be selected for system. Here PT equaton of state has been used that s one of the best equatons and has applcaton for polar systems. 34

2 35 P&T equaton of state Ths equaton s a 3rd order equaton of state that has presented n 198, and t has 3 parameters that are related to crtcal propertes by fallowng equatons: RT α P = (1) v b v ( v b ) c ( v b ) a =Ω. R T / P. α () a C C b =Ω. RT / P (3) b C C c =Ω C. RTC / PC (4) Ω C = 1 3ξ C (5) Ω = 3ξ 3 1 ξ. Ω Ω 1 3ξ (6) a C C b b C 3 3 b 3 ξc. b 3 ξc. b ξc 0 Ω Ω Ω = (7) Ω That b s the smallest postve root of above equaton, and α s presented by soave and peng-robnson equaton: α 1 (1 ) = m T R (8) ξ m and C parameters are obtaned by numercal methods and quanttes of these parameters for MTBE/MEOH system are shown n table 1. For mult-component systems, mxng rules should be used. For P&T equaton of state, these equatons are as fallow: a b C = x. x. a (11) m j j j = x. b (1) m = x. c (13) m 1. a = k a a (14) j j jj k j parameters namely bnary nteracton coeffcent are expermental parameter and are calculated by usng equlbrum data n bnary systems. k j quantty for MTBE/MEOH system s Computer Program Flowchart For bubble pont temperature /pressure calculatons, the fallowng equatons are confrmed: y = k. x = 1, N (15) y = 1 = 1, (16) y N s number of components and, x are mole fracton n vapour and lqud phases. Smlarly, for dew pont calculatons, the followng equatons are confrmed: k x = y / = 1, N (17) x = 1 = 1, (18) For calculatng of k value, Flash calculatons as followng equaton are used. Fz. = Vy. Lx. (19) 35

3 36 F s feed mole rate; z feed mole fracton; V, L n order are component mole rate n equlbrum vapour and lqud phases. Ths equaton wll obtan wth overall mass balance and fallowng equatons should be confrmed: y = k. x (0) y = 1 (1) x = 1 () z x = L/ F V. k / F (3) The flowchart of bubble pont and flash calculatons are shown n Fg 1 &. In order to know more about that, refer to reference (4). Equatons of Fugacty calculaton are n Appendx A. In flash calculatons, note that to guess frst k, deal quanttes are used (Wlson equaton): Pv P C 5.4(1 ω ) k = = Exp W. eq. P P 1 TC / T (4) Dscusson and results: For show prepared computer program effcency, MTBE/MEOH bnary system s selected and results are compared wth expermental datum, that conclusons are n related tables and fgures. Results for bubble pont pressure/temperature calculatons are shown n tables &3. As t s seeng, absolute devaton average n pressure/ temperature and mole fracton are less than 5 percent. Conclusons for dew pont temperature/pressure calculatons are shown n tables 3&4. Devaton n pressure and temperature for bubble and dew ponts are shown n Fg. 3,4,5,6 as graphs. Just as tables and graphs are saw, PT equaton of state wll be able to cover expermental ponts as well. Thus t s good for desgn calculatons n MTBE system. Component T c ( o R) P c (psa) ω M.W. ζ c m Methanol MTBE Table 1:Thermodynamc and physcal propertes P exp. (Psa) X,exp. MTBE Y,exp. MTBE P cal. Y,cal. Abs. Dev. P Abs. Dev.Y Total% %4.56 %

4 37 Input Data Read P,all X Readjust T Estmate T Ф=1.0 NO f L =f V YES NO Sum=1.0 Calculate Mx. Parameters Lqud Phase Y,new = f L /f v Y Sum =Σy,new YES Calculate f L Calculate f v Results T, Y, K Y = f L /Ф P Sum1 =ΣY Y =Y /Sum1 Calculate Mx. Parameters Vapor phase Fg.1 Flowchart for bubble pont calculatons Input Datas Read T,P Estmate K Calculatons X,Y K=(f L /X )/(f V /Y ) Calculaton Mx. Parameters Lqud phase NO f L =f V YES Results X, Y, K Calculaton f L Calculaton f V Sum1=ΣY Y =Y /Sum1 Calculaton Mx. Parameter Vapor Phase Fg. Flowchart for flash calculatons 37

5 38 Table: Bubble pont pressure calculatons for MTBE/MEOH system (T= o R) X,exp. P exp. Y,exp. T cal Abs. Abs. o Y (Psa) MTBE MTBE,cal. ( R) Dev. P Dev.Y Total% % %5.39 Table 3: Bubble pont temperature calculatons for MTBE/MEOH system (T exp. = o R) P exp. X,exp. Y,exp. P cal. Abs. Abs. X psa MTBE MTBE,cal. Dev. P Dev. X Total% %.87 %8.605 Table4: Dew pont pressure calculatons for MTBE/MEOH system(t exp. = o R) P exp. X,exp. Y,exp. T cal. Abs. Abs. X psa MTBE MTBE,cal. Dev.T Dev.X Total% % %5.659 Table 5: Dew pont temperature calculatons for MTBE/MEOH system (T exp. = o R) 38

6 39 Fg.3 - Devaton n bubble pont pressure (temperature C) Fg.4 - Devaton n bubble pont temperature (Exp. Temperature 49.8 o C) 0.10 Devaton, psa Devaton MTBE mole fracton (X) MTBE mole fracton (X) Fg.5 - Devaton n Dew pont pressure (temperature o C) Fg.6 - Devaton n Dew pont temperature (Exp. Temprature o C) 0.05 Devaton, psa Devaton Appendx A MTBE mole fracton (X) MTBE mole fracton (X) The equatons for fugacty calculaton by P&T equaton of state: a) Component fugacty n pure case: f a Z M In( ) = Z 1 In( Z B) In( ) p RTN Z Q bp B = RT b c P M =. N RT N = Q = ( b c bc b c P N RT ) b) Component fugacty n mxture: f x a b RTIn( ) = RTIn( Z B) RT x P v b d a( b ( Q c ) a d ) 8d 3 { c (3b c) b (3c b) } j Q In( Q Q In( Q d ) d d Qd ) d Q d 39

7 40 b c Q = V bpc B = RT ( b c) d = bc 4 Abbrevatons c a, b, c, m,α,ζ, Ω : PT equaton of state parameters f : fugacty Φ: fugacty coeffcent K j : nteracton coeffcent N: number of components P: pressure T: temperature v : volume R: unversal gas constant F: feed mole rate L: lqud phase mole rate V: gas phase mole rate X: component mole fracton n lqud phase. Y: component mole fracton n vapour phase. Z: component mole fracton n feed. Subscrpt C: Crtcal propertes,j: Component No. m: mxture Superscrpt: L: Lqud phase propertes V: Vapour phase propertes References [1] Alm K., Vapour-pressure, Refractve ndex at 0 0 C and vapour lqud equlbra at kpa n the MTBE /MEOH system, J. Chem. Eng. Data, 5, , [] Edmster, Wayne C. Lee: Appled Hydrocarbon Thermodynamcs, Gulf- Publshng Co.,1988 [3] Holland C.D.: Fundamentals and Modellng of Separaton Processes, Prentce-Hall Inc., 1975 [4] Maddox R.N.: Gas condtonng and processng, Vol. 3, Gulf-Publshng Co., 1990 [5] Mullns R.: Expermental vapour-lqud equlbra for the system MTBE/MEOH, AICHE Symposum Seres, No. 37, Vol 85. [6] Patel N.C., Teja A.S.: A new cubc equaton of state for fluds and flud mxtures, Chem. Eng. Sc, Vol 37, No 3, , 198. [7] Peng D.Y, D.B Robnson: A New Two-Constant Equaton of State, Ind. Chem. Eng., Fundamentals, Vol. 15, No 1, 59-64, 1976 [8] Soave G.: Equlbrum constants from a modfed Redlch-Kwong equaton of state, Chem. Eng. Sc, Vol. 7, No 6, ,197 40

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