TKP4105 Separation Technology Exercise 1 Mass Transfer Solution to problems

Transcription

1 TKP415 Separation Technology Exercie 1 Ma Tranfer Solution to problem Problem Steady tate diffuion plu convection: Counterdiffuion mean N A + N B =. Fick law i J A = cd AB : The diffuivity D AB i aumed contant while the molar flux N A i contant (teady tate). The total differential of c A i = c A d = (c +x A )d. At contant total concentration c, i.e. ideal ga kept at contant temperature and preure the differential redue to: = c d: N A d = D AB N A = D AB c A Ideal ga law i PV = n i RT P = crt where c = n i /V : N A = D AB P o A P A RT a) N NH3 A = (2 6666) π = mol/ = kmol/ b) N N2 A = N NH3 A = kmol/ N A i contant over the entire diffuion path (teady tate). Therefore, knowing N A at one end of the tube mean we can evalute the concentration profile inide the tube: N A D AB = Solving for 1 and 2 :, 1 1 d =, 2 2 d =... =, n n d

2 c A,2 = c A,= (c A,1 c A,= ) P A,2 = P A,= (P A,1 P A,= ) c)p NH3,=.35m = (6666 2) = 13333P a Problem From Fuller et al: D AB [m 2 1 ] = 1 7 T ( [K] )1.75 [gmol 1 ] M A + [gmol 1 ] M B P [atm] [ 3 υ i,a + 3 υ i,b ] 2 υ C = 16.5 υ H = 1.98 υ O = 5.48 a) D EtOH CH4 = [ m2 = ] 2 b) D EtOH CH4 = ( ) m2 = b) D EtOH CH4 = m =

3 Problem Steady tate diffuion plu convection: Counterdiffuion mean that N A + N B =. Fick law i J A = cd AB : The diffuivity D AB i aumed contant while the molar flux N A i contant (teady tate). The total differential of c A i = d = (c + x A c )d. At contant total concentration c, i.e. ideal ga kept at contant temperature and preure the differential reduce to = c d : N A d = cd AB N A = D AB c A Ideal ga law i PV = n i RT P = crt where c = n i /V : N A = D AB P o A P A RT From Fuller et al: D AB [m 2 1 ] = 1 7 T ( [K] )1.75 [gmol 1 ] M A + [gmol 1 ] M B P [atm] [ 3 υ i,a + 3 υ i,b ] 2 υ N2 = 17.9 υ CO =

4 a) N N2 = [ ( ) 18.9] 2 b) N N2 = ( ) mol = m 2 c) N N2 = ( mol = m 2 4 mol c) N N2 = m = mol m 2 Problem Steady tate diffuion plu convection: Diffuion of A through a tagnant layer of B mean N B JA = cd AB : =. Fick law i + c A c N A N A (1 c A c ) = cd AB The total differential of c A i = d = (c + x A c )d. At contant total concentration c, i.e. ideal ga kept at contant temperature and preure the differential reduce to = c d : N A d = cd AB c c A ( ) c ca c 4

5 N A = cd ( ) AB 1 xa 1 x o A ( xb x o B ) Ideal ga law i P V = n i RT P = crt where c = n i /V :.874 g d N A = P D AB RT a) N H2O A = e 5 π ( ) P PA P PA o ( ) 7 mol = = Problem Wilke-Chang correlation: D AB [m 2 1 = ] ϕ M B [gmol 1 ] T [K] µ B [P a] (1 3 V A [m 3 mol 1 ] ).6 ϕ = 2.6 Le Ba correlation: V A = υ i,a 6 m3 υ c = mol 6 m3 υ H = mol 6 m3 υ O = mol 5

6 Vicoity from the Appendix: V A = υ i,a µ H2O(287.15K) = P a µ H2O(289.15K) = P a µ H2O(293.15K) = P a a) D MeOH H2O = ( ) = m2 1 b) D MeOH H2O µ H2 O(288) 288 µ H m2 O(293) = Problem Steady tate diffuion plu convection: Diffuion of A through a tagnant layer of B mean N B =. (helium ga i moving while the ilica gla i fixed). Fick law i JA = cd AB : + c A c N A N A (1 c A c ) = cd AB 6

7 The total differential of c A i = d = (c + x A c )d. At contant total concentration c, i.e. ideal ga kept at contant temperature and preure the differential reduce to = c d : N A d = cd AB c c A ( ) c ca c ( ) 1 xa 1 x o A In thi cae x o A 1 which mean that a Taylor expanion i OK: N A cd ( ) AB 1 xa 1 x o 1 A N A D AB( c A) Ideal ga law i PV = n i RT P = crt wherec = n i /V : N A = D AB(p o A p A) RT Introducing void fraction ɛ and tortuoity τ: N A = ɛd AB(p o A p A) τrt a) N CO2 = (226 6 mol = m 2 = 6.12 g m 2 d 7

8 Problem Steady tate diffuion plu convection: Diffuion of A through a tagnant layer of B mean N B JA = cd AB : =. Fick law i + c A c N A N A (1 c A c ) = cd AB The total differential of c A i = d = (c + x A c )d. At contant total concentration c, i.e. ideal ga kept at contant temperature and preure the differential reduce to = c d : N A d = cd AB c c A ( ) c ca c ( ) 1 xa 1 x o A In thi cae x o A 1 which mean that a Taylor expanion i OK: N A cd ( ) AB 1 xa 1 x o 1 A N A D AB( c A) 8

9 It can alo be aumed that c A = (there i little helium in the atmophere): N A D AB = D ABSP A υ A,1atm,o C a) N He = mol 15 kmol = = h Problem Knuden diffuivity: D K,A = 97. T [K] M A [gmol 1 ] a) D K,He = m2 = b) D K,Ar = m2 = m2 c) D He Arr = d) Same a in a) e) Same a in b) r f) D He Arr = = m2 (note the change!) The molecular diffuivity varie inverely proportional to P. The Knuden diffuivity i inenetive to preure. Thi i N A f(p ) while N K,A P (for ideal ga of coure). 9