3.MASS-TRANSFER THEORIES (1)Mass Transfer Coefficient .For steady-state mass transfer through a stagnant layer of fluid mass transfer rate can be predicted by following equations: (1)Equimolal diffusion NA=JA DPM(yA-yA） (17.19) or NA=J= D.(CA) (17.20)
1 3.MASS-TRANSFER THEORIES (1)Mass Transfer Coefficient •For steady-state mass transfer through a stagnant layer of fluid , mass transfer rate can be predicted by following equations: (1)Equimolal diffusion ( ) (17.20) ( ) (17.19) 0 A i A T v A A A i A T v M A A y y v M A B A A A A v M c c B D N J y y B D N J N db D dy db dy J N D A Ai T = = − = = − = − = = − ( ) (17.20) ( ) (17.19) 0 A i A T v A A A i A T v M A A y y v M A B A A A A v M c c B D N J y y B D N J N db D dy db dy J N D A Ai T = = − = = − = − = = − or
(2)One-component mass transfer (one-way diffusion) N.=D. 1-y4 (17.24) B 1-yai D.PM yAi-yA (17.26) Br (1-yA)L .More common used type of equations: Analogous to heat transfer, Heat transfer rate=(Heat transfer coefficient)x (Heat transfer driving force) Mass transfer rate=(Mass transfer coefficient)x (Mass transfer driving force)
2 (2)One-component mass transfer (one-way diffusion) (17.24) 1 1 ln 1 1 ln (1 ) (1 ) (1 ) (17.21) 0 A i A T v M A A i A y y A A v M A T B v M A A A v M A A A A v M A A A A v M y y B D N y y y dy D N B D N db y dy D N db db dy N y D db dy N y N D A Ai T − − = − − = − = = − − = − − = − = − (17.26) (1 ) 1 1 ln (1 ) (1 ) (1 ) (17.21) 0 A L A i A T v M A A i A y y A A v M A T B v M A A A v M A A A A v M A A A A v M y y y B D N y y y dy D N B D N db y dy D N db db dy N y D db dy N y N D A Ai T − − = − − = − = = − − = − − = − = − •More common used type of equations: Analogous to heat transfer, Heat transfer rate=(Heat transfer coefficient) (Heat transfer driving force) Mass transfer rate=(Mass transfer coefficient) (Mass transfer driving force)
.Definition of mass transfer coefficient:The rate of mass transfer per unit area per unit concentration difference,usually based on equal molal flows. JA DDu0ya-y)=k,0a-y4） =D(cu-c)=k.cu-ca） B Other forms of mass transfer equations: JA=kx(xAi-xA) JA=kg(PAi-PA)
3 ( ) (17.20) ( ) ( ) 0 A i A T v A A A i A y A i A T v M A y y v M A B A A A A v M c c B D N J y y k y y B D J N db D dy db dy J N D A Ai T = = − = − = − = − = = − ( ) ( ) ( ) (17.19) 0 A i A c A i A T v A A i A T v M A A y y v M A B A A A A v M c c k c c B D J y y B D N J N db c D dy db dy J N D A Ai T = − = − = = − = − = = − •Definition of mass transfer coefficient: The rate of mass transfer per unit area per unit concentration difference, usually based on equal molal flows. Other forms of mass transfer equations: ( ) (17.20) ( ) 0 A i A T v A A A g A i A y y v M A B A A A A v M c c B D N J J k P P N db D dy db dy J N D A Ai T = = − = − = − = = − ( ) (17.20) ( ) 0 A i A T v A A A x A i A y y v M A B A A A A v M c c B D N J J k x x N db D dy db dy J N D A Ai T = = − = − = − = = −
Therefore, ke= (17.36) (CAi-CA) =mass transfer coefficient based on molal concentration driving force kgmol [k]=[ s.m2.kgmol/ 3]=[m/s] JA (17.40) PA -PA =gas phase mass transfer coefficient based on the partial pressure driving force [k]= kgmol s.m2.kPa
4 (17.36) ( ) ( ) (17.19) 0 Ai A A c Ai A T v M A A y y v M A B A A A A v M c c J k y y B D N J N db c D dy db dy J N D A Ai T − = = = − = − = = − Therefore, (17.36) ( ) ( ) (17.19) 0 A i A A c A i A T v M A A y y v M A B A A A A v M c c J k y y B D N J N db c D dy db dy J N D A Ai T − = = = − = − = = − =mass transfer coefficient based on molal concentration driving force ] [ / ] / [ ] [ ( ) (17.19) 2 3 0 m s s m kgmol m kgmol k y y B D N J N db c D dy db dy J N D c A i A T v M A A y y v M A B A A A A v M A Ai T = = = = − = − = = − ( ) (17.20) (17.40) 0 A i A T v A A A i A A g y y v M A B A A A A v M c c B D N J P P J k N db D dy db dy J N D A Ai T = = − − = = − = = − =gas phase mass transfer coefficient based on the partial pressure driving force ( ) (17.20) (17.40) 0 Ai A T v A A Ai A A g y y v M A B A A A A v M c c B D N J P P J k N db D dy db dy J N D A Ai T = = − − = = − = = − [ ] [ ] ( ) (17.19) 2 0 s m kPa kgmol k y y B D N J N db c D dy db dy J N D g A i A T v M A A y y v M A B A A A A v M A Ai T = = = − = − = = −
JA (17.37) yai-ya -gas phase mass transfer coefficient based on the mole fraction differences XAi一XA =liquid phase mass transfer coefficient based on the mole fraction differences kgmol [k]=[k]=[ ]=[W4] ·m.unit mole fraction
5 [ ] [ ] [ ] [ ] ( ) (17.19) 2 0 y x A A i A T v M A A y y v M A B A A A A v M J s m unit mole fraction kgmol k k y y B D N J N db c D dy db dy J N D A Ai T = = = = = − = − = = − ( ) (17.20) (17.37) 0 A i A T v A A A i A A y y y v M A B A A A A v M c c B D N J y y J k N db D dy db dy J N D A Ai T = = − − = = − = = − =gas phase mass transfer coefficient based on the mole fraction differences ( ) (17.20) (17.37) 0 Ai A T v A A Ai A A y y y v M A B A A A A v M c c B D N J y y J k N db D dy db dy J N D A Ai T = = − − = = − = = − ( ) (17.20) 0 A i A T v A A A i A A x y y v M A B A A A A v M c c B D N J x x J k N db D dy db dy J N D A Ai T = = − − = = − = = − =liquid phase mass transfer coefficient based on the mole fraction differences ( ) (17.20) 0 Ai A T v A A Ai A A x y y v M A B A A A A v M c c B D N J x x J k N db D dy db dy J N D A Ai T = = − − = = − = = −
.Relations between mass transfer coefficients: .C=yAPM .k,= JA一= yai-ya CAil =PM CAi-CA k P .k,=PM·k。= (17.38) RT Similarly,in liquid phase, .CA=XAPM ..ky= XAi-XA CAi/ CA PM CA-CA PM /PM (17.39) M
6 •Relations between mass transfer coefficients: (17.38) RT k P k k c c J c c J y y J k c y c y M c A i A A M M A M A i A A i A A y A A M = = − = − = − = = Similarly, in liquid phase, (17.39) M k k k c c J c c J x x J k c x c x x M c A i A A M M A M A i A A i A A x A A M = = − = − = − = =
Here, -density of liquid,kg/m3 M =average molecular weight of liquid :kg= JA JA JA 二 PAi -PA Pyai-Pya P(yai-ya) k2= ..kg ke (17.41) RT Significance of kc:from D.(Cn-e)-k.(Cn-cA) B D (17.42)
7 Here, (17.39) M k k k c c J c c J x x J k c x c x x M c Ai A A M M A M Ai A Ai A A x A A M = = − = − = − = = (17.39) M k k k c c J c c J x x J k c x c x x M c Ai A A M M A M Ai A Ai A A x A A M = = − = − = − = = =density of liquid, kg/m3 =average molecular weight of liquid ( ) (17.20) ( ) 0 A i A T v A A A i A A A i A A A i A A g y y v M A B A A A A v M c c B D N J P y y J Py Py J P P J k N db D dy db dy J N D A Ai T = = − − = − = − = = − = = − ( ) (17.20) (17.41) 0 A i A T v A A y c g y y v M A B A A A A v M c c B D N J RT k P k k N db D dy db dy J N D A Ai T = = − = = = − = = − Significance of kc: from (17.42) T v c B D k = ( ) ( ) ( ) (17.19) 0 A i A c A i A T v A A i A T v M A A y y v M A B A A A A v M c c k c c B D J y y B D N J N db c D dy db dy J N D A Ai T = − = − = = − = − = = −
Ke D (17.42) Br .For steady-state equimolal diffusion in a stagnant film,mass transfer coefficient kc is the molecular diffusivity divided by the thickness of the stagnant layer (Br). .When we are dealing with unsteady-state diffusion or diffusion in1 owing streams(对宽)，Eq-(17.42)can still be used to give an effective film thickness Br from known values of kc and Dv.对于对流传质， (17.42)式有效，B7为有效膜厚度
8 •For steady-state equimolal diffusion in a stagnant film, mass transfer coefficient kc is the molecular diffusivity divided by the thickness of the stagnant layer（BT）. •When we are dealing with unsteady-state diffusion or diffusion in flowing streams（对流）, Eq.(17.42) can still be used to give an effective film thickness BT from known values of kc and Dv.对于对流传质， （17.42）式有效, BT为有效膜厚度 (17.42) T v c B D k =
(2)Film Theory .Analogous to convective heat transfer, Heat transfer rate q: Effective heat boundary layer g=冬(T-T)=T-T) q T Fluid Laminar Metal wall layer
9 (2)Film Theory •Analogous to convective heat transfer, Laminar layer Fluid Effective heat boundary layer Metal wall ( ) w t w t T T k q T T q = − ( ) w t w t T T k q T T q = − ( ) w t w t T T k q T T q = − ( ) w t w t T T k q T T q = − ( ) ( ) w w t w t T T h T T k q T T q = − = − Heat transfer rate q:
.The basic concept of the 膜理论基本概念是传质阻力相等于 停滞膜厚度 film theory is that the resistance to diffusion Effective film can be considered thickness equivalent to that in B a stagnant film of a certain thickness Liquid C D.(CA-CA NA=JA Gas A NA ke= D (17.42) B Laminar layer Illustrational diagram Interface thickness of wetted wall tower 10
10 Laminar layer thickness Liquid Effective film thickness Interface Gas A A Ai T N c c B A A Ai T N c c B A A Ai T N c c B A A Ai T N c c B Illustrational diagram of wetted wall tower (17.42) T v c B D k = •The basic concept of the film theory is that the resistance to diffusion can be considered equivalent to（相等于） that in a stagnant film of a certain thickness •Then, ( ) ( ) (17.19) 0 A Ai T v A A Ai A T v M A A y y v M A B A A A A v M c c B D N J y y B D N J N db c D dy db dy J N D A Ai T = = − = = − = − = = − BT 膜理论基本概念是传质阻力相等于 停滞膜厚度