Tutorial

1. Tutorial/HW Week #11WWWR Chapter 29 & 30 Tutorial #11 WWWR # 29.4, 29.19, 29.24 To be discussed the week of Apr 2 � 6 2012. By either volunteer or class list. Homework #11 (self practice) WWWR # 29.18 and 29.25

2. Convective Mass Transfer Mass transfer between two moving contacting phases Gas-liquid, or liquid-liquid (if immiscible) Overall mass-transfer convective coefficient

3. Equilibrium Deviations from equilibrium is the concentration driving force within a phase For 2 phases, we consider interphase equilibrium Use equilibrium plots

5. Equations relating equilibrium: Ideal liquid, use Raoult�s law Ideal gas, use Dalton�s law Dilute solutions, use Henry�s law Immiscible liquids, use �distribution-law� Basic concepts for interphase mass transfer: Gibbs� phase rule at fixed T, P No net mass transfer at equilibrium Mass transfer occurs at non-equilibrium

6. Example 1

8. Example 2

10. Two-Resistance Theory Transfer between 2 contacting phases 3 steps of interphase transfer The theory: Rate of transfer is controlled by diffusion through the phases on each side of interface No resistance across the interface

13. Individual mass-transfer coefficient Convective mass-transfer coefficient in gas/liquid phase Combining both and rearrange to

15. Overall mass-transfer coefficient Similar to overall heat-transfer coefficient Using equilibrium partial pressure or concentration Ratio of resistances in individual phase to total resistance

16. At low concentrations, we have linear equilibrium relations From which, we get And thus

17. And similarly, The phase where major resistance occurs is controlling, ie. Gas-phase controlled. Coefficient is dependent on concentration, unless linear equilibrium line

18. Example 3

23. Example 4

29. Mass transfer to plates Correlate experimental data with predictions from laminar/turbulent boundary layers: ReL < 2 x 105, ReL > 2 x 105,

30. At distance x from leading edge, In terms of j-factor, Laminar Turbulent 0.6 < Sc < 2 500 and 0.6 < Pr < 100

31. If hydrodynamic and concentration boundary layers have different starting position along x, Boundary conditions change: 0 ? x < X , cA = cA? X ? x < ? , cA = cAs Analogous to heat transfer situation,

33. Example 1

40. Single Sphere Mass-transfer correlation If no forced convection, Sh = 2,

41. Transfer into liquid stream, the Brian-Hales equation for PeAB < 10 000, For PeAB > 10 000, Transfer into gas stream, the Fr�essling eq, 2 < Re < 800 and 0.6 < Sc < 2.7

42. When no free or natural convection, With natural convection, the Steinberger and Treybal correlation, Where ScGr < 108 ScGr > 108 2 ? Re ? 30 000 and 0.6 ? Sc ? 3 200

43. Spherical Bubble Swarm Eg. Bubbling of gas into liquid 2-part correlation from Calderbank and Moo-Young, db < 2.5 mm, db ? 2.5 mm,

44. To calculate flux, must know gass holdup ratio, ?g, Propotional to ratio of superficial gas velocity and terminal velocity.

45. Example 2

52. Single Cylinder Bedingfield and Drew correlation, 400 < ReD < 25 000 and 0.6 < Sc < 2.6

53. Example 3

57. Flow Through Pipes From inner wall of tube to moving fluid, the Gilliland and Sherwood correlation, 2 000 < Re < 35 000 and 0.6 < Sc < 2.5

58. Combined with Linton and Sherwood correlation: 2 000 < Re < 35 000 and 1 000 < Sc < 2 260 For laminar flow, analogous to Sieder-Tate eq, 10 < Re < 2 000

59. Wetted- Wall Columns Gas flows up while liquid flows down the perimeter Falling liquid film is thin and high velocity, evenly wets column surface

60. Convective mass-transfer coefficient for gas film similar to flow through pipes Liquid film mass-transfer coefficient from Vivian and Peaceman correlation, where

61. Example 4

68. Packed and Fluidized Beds For packed beds with single phase fluid and gas flow, Sherwood, Pigford and Wilke estimated 10 < Re < 2 500 where

69. Accounting for bed void fraction, ?, Wilson and Geankoplis correlation 0.0016 < Re��� < 55 and 165 < Sc < 70 600 and 0.35 < ? < 0.75 55 < Re��� < 1 500 and 165 < Sc < 10 690 Gupta and Thodos correlation 90 < Re��� < 4 000