Presentation on theme: "高等輸送二 — 質傳 Lecture 7 Fundamentals of Mass Transfer"— Presentation transcript:
1 高等輸送二 — 質傳 Lecture 7 Fundamentals of Mass Transfer 郭修伯 助理教授
2 Understand diffusion? What is Diffusion? How to study diffusion? process by which molecules, ions, or other small particles spontaneously mix, moving from regions of relatively high concentration into regions of lower concentrationHow to study diffusion?Scientific description: By Fick’s law and a diffusion coefficientEngineering description: By a mass transfer coefficient
3 Based on empirical arguments, the amount transferred at the interface: Concentration differenceInterfacial areaRate of mass transferred= kconcentration in the bulkFlux at the interface(include both diffusion and convection)concentration at the interfacemass transfer coefficient
4 c1 (t) k = 3.4 x 10-2 cm/sec t = 8.3 x 103 sec The vessel is isothermal at 25 C, so the water’s vapor pressure is 23.8 mmHg. The vessel has 0.8 liter of water with 150 cm2 of surface area in a total volume of 19.2 liters. After 3 min, the air is 5% saturated. What is the mass transfer coefficient? How long will it take to reach 90% saturation?c1 (t)k = 3.4 x 10-2 cm/sect = 0, c1 = 0t = 8.3 x 103 sec
5 2 cm-diameter spheres of benzoic acid are packed into a bed 0.2 cm-diameter spheres of benzoic acid are packed into a bed. The spheres have 23 cm2 surface area per 1 cm3 of bed. Pure water flowing at a superficial velocity of 5 cm/sec into the bed is 62% saturated with benzoic acid after it has passed through 100 cm of beds. What is the mass transfer coefficient?From mass balance:z = 0, c1 = 0k is defined at the interface between the sphere’s face and liquid
6 Bromine is rapidly dissolved in water Bromine is rapidly dissolved in water. Its concentration is about half saturated in 3 min. What is the mass transfer coefficient?From mass balance:t = 0, c1 = 0
7 A bubble of oxygen originally 0 A bubble of oxygen originally 0.1 cm in diameter is injected into excess stirred water. After 7 min, the bubble is cm in diameter. What is the mass transfer coefficient?Mass balance on the bubble itselfc1 : the oxygen concentration in the bubble ~ constant (P/RT)c1sat : the oxygen concentration at saturation ~ constantt = 0, r = 0.05 cmk = 1.6 x 10-3 cm/sec
8 Mass transfer coefficient Concentration differenceInterfacial areaRate of mass transferred= kMass per unit volume, or?Local or average?Real contact area is?Partial pressure? Molar concentration? Mass concentration? Mole fraction?
9 A blood oxygenatorA blood oxygenator is used to replace the human lungs during open-heart surgery. From published correlations of mass transfer coefficients, the mass transfer coefficient based on the oxygen concentration difference in the water is 3.3 x 10-3 cm/sec. The equation given by the oxygenator manufacturer is:Hypothetical oxygen partial pressure in equilibrium with water under the experimental conditions.Actual oxygen partial pressure in the gasThe Henry’s law constant of oxygen in water at the experimental condition is:Mole fraction of the total oxygen in the waterFind kp
11 Mass transfer coefficient The values of the coefficients are usually reported as correlations of dimensionless numbersSherwood and Stanton numbers involve the mass transfer coefficientSchmidt, Lewis and Prandtl numbers involve different kind of diffusionReynolds, Grashof and Peclet numbers describe flow(forced convection)(free convection)
12 Sherwood numberThe variation of Sherwood number with flow is complex because the flow has two physical origins:Forced convectionthe flow is caused by external stirring or pumpingFree convectionthe fluid velocity is a result of the mass transfer itself.The mass transfer causes density gradients in the surrounding solution and then in turn cause flow.
13 Correlations Correlations for fluid-fluid interfaces Accuracy ~ 30%k ~ v0.7k ~ DCorrelations for fluid-solid interfacesmuch like the heat transfer equivalentsaccuracy ~ 10% or lessk ~ v0.5k ~ D2/3
14 A disc of benzoic acid 2.5 cm in diameter is spinning at 20 rpm and 25C. How fast will it dissolve in a large volume of water? How fast will it dissolve in a large volume of air? The diffusion coefficients are 1.0 x 10-5 cm2/sec in water and cm2/sec in air. The solubility of benzoic acid in water is g/cm3. Its equilibrium vapor pressure is 0.3 mmHg.The dissolution rate is:For waterFor airThe flux in air is about 1/3 of that in water.
15 Air containing a water-soluble vapor is flowing up and water is flowing down in the experimental column. The water flow in the 0.07 cm-thick film is 3 cm/sec, the column diameter is 10 cm and the air is essentially well mixed right up to the interface. The diffusion coefficient in water of the absorbed vapor is 1.8 x 10-5 cm2/sec. How long a column is needed to reach a gas concentration in water that is 10% of saturation?From mass balance:absorptionz = 0, c1 = 0z = 4.8 cm
16 Mass transfer across interfaces From one well-mixed bulk phase into another different onesolute flux relative to the interfaceoverall mass transfer coefficient
17 Overall mass transfer coefficient GasLiquidp10p1ic1ic10overall liquid-side mass transfer coefficientoverall gas-side mass transfer coefficient
18 Estimate the overall liquid-side mass transfer coefficient at 25C for oxygen from water into air. For oxygen in air, the diffusion coefficient is 0.23 cm2/sec; for oxygen in water, the diffusion coefficient is 2.1 x 10-5 cm2/sec. The Henry’s law constant is 4.4 x 104 atm.
19 We are studying gas absorption into water at 2 We are studying gas absorption into water at 2.2 atm total pressure in a packed tower containing Berl saddles. For both ammonia and methane the mass transfer coefficient times the packing area per tower volume is 18 lb-mol/hr-ft3 for the gas side and 530 lb-mol/hr-ft3 for the liquid size. Their Henry’s law constants are different: 9.6 atm for ammonia and atm for methane. What is the overall gas-side mass transfer coefficient for each gas?For ammonia:For methane: