PETE 310 Lectures # 24 & 25 Chapter 12 Gas Liquid Equilibrium

Transcription

1 ETE 30 Lectures # 24 & 25 Chapter 2 Gas Lqud Equlbrum

2 Thermal Equlbrum Object A hgh T, Object B low T Intal contact tme Intermedate tme. Later tme

3 Mechancal Equlbrum ressure essels Vale Closed Vale Open

4 Chemcal Equlbrum Mass transfer Coffee Mlk Sugar

5 Vapor Lqud Equlbrum (VLE) Two phases gas (or apor) coexst n equlbrum when There s no pressure dfference across the phases There s no temperature dfference across the phases There s no NET mass transfer across the phases

6 Vapor Lqud Equlbrum (VLE) No NET mass transfer across the phases does not mply the composton of these two phases s the same t means the composton of each phase remans the same

7 Mathematcal Defnton The equlbrum crtera between 2 phases α and β s that α = β T α = T β α ˆ = ˆ μ, = μ β,2,... N c

8 Equlbrum Condtons The last crtera mples tendency of a component to be n phase α or β s balanced net mass transfer across phases s zero μ α μ ˆ = ˆ, =,2,... β N c

9 hase Equlbrum Models Low pressures (.e. separator pressures) Hgh pressures (.e. reseror pressures) Types and proportons of components Black Ol Models Volatle Ol Models Complex Mxtures

10 Ideal Behaor Model Low ressure Applcatons Assumes that Gas phase behaes as an deal gas (IG Lqud phase behaes as an deal soluton (IS). These assumptons mply that IG: molecular nteractons are zero, molecules hae no olume. IS: forces of attracton/repulson between molecules are the same regardless of molecular speces. Volumes are addte (Amagat s Law).

11 Forces between molecular speces A A B B A B F = F = AA BB F AB

12 Statement of Equlbrum y = x IG/IS Raoult s law 2 3 T

13 Types of VLE Calculatons C T a Lqud ressure C 2 Flash 2 2 Vapor Temperature x, y T a 0

14 hase Equlbra Computatons

15 hase Equlbra Computatons

16 Recall Molar Compostons By conenton lqud compostons (mole fractons) are ndcated wth an x and gas compostons wth ay. lqud n n n x + = 2 gas n n n y + = 2

17 wth In general Mathematcal Relatonshps l f y f x z + = f y f x z + = ) ( ( ) ( ) l n n n n n n f = ) ( x y x z f = x y x z f =

18 Depleton ath Isothermal Reseror Depleton rocess for a Reseror Ol wth 2 Components B z = fxed C M T = T a A B ressure C D T a Temperature 0 x z y z =oerall mole fracton of [], y =apor mole fracton of [], x =lqud mole fracton of []

19 Quanttate hase Equlbrum Exercse

20 Bubble ont Ealuaton (Ideal Behaor Model) The bubble pont pressure at a gen T s y bp = z bp = z

21 Bubble ont from Raoult's law T 2 z =x x,y

22 Bubble ont Ealuaton Under Raoult s law, the bubble pont has a lnear dependence wth the apor pressures of the pure components. Once the bubble pont pressure s found, the equlbrum apor compostons are found from Raoult s law.

23 Dew ont Calculaton At the dew pont the oerall flud composton concdes wth the gas composton. That s. z = y

24 Dew ont Calculaton (Ideal Behaor Model) Fnd D pressure and equlbrum lqud compostons = = x z x y = x z = = c N dp z

25 Dew ont from Raoult's law T 2 z =y x,y

26 Flash Calculatons In ths type of calculatons the objecte s to: fnd fracton of apor aporzed (f) and equlbrum gas and lqud compostons gen the oerall mxture composton, and T.

27 Flash Calculatons (Ideal Behaor Calculatons) Start wth the equlbrum equaton y = x Materal balance l ( f ) y f z = x f + y f = x +

28 Flash Calculatons Now replace ether lqud or gas compostons usng equlbrum equaton z = y + y x = ( f ) y f Here replaced x

29 Flash Calculatons Rearrange and sum oer all y ( ) f f z y + = ( ) + = f f z y

30 Separaton process y (T, 2 ) z (T, ) T, 2 > 2 x (T, 2 )

31 Flash Calculatons Objecte functon (flash functon) s ( ) 0 ) ( = + = f f z f F Ths s /k deal equlbrum rato

32 Flash Calculatons Seeral equalent expressons for the flash functon (a) (b) y x = 0 = 0 (c) y x = 0

33 Flash Calculatons Once f s found the equlbrum gas and lqud compostons are ealuated from y = z ( f ) + f y and = x

34 Constants depend upon the component Dfferent Unts ln = a T b + c

35 Vapor ressure Models Antone Equaton (Constants depend upon the component Dfferent Unts) ln = a T b + c

36 ( ) + = N c k f z ( ) + = N c k f k z ( ) = + N c k f k z ) ( Exercses n our web ste excel fle VLE_30