Mass Transfer Operations

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1 College of Engineering Tutorial # 1 Chemical Engineering Dept. 14/9/ Methane and helium gas mixture is contained in a tube at k Pa pressure and 298 K. At one point the partial pressure methane is p A1 = 61 k Pa and at a point 0.02 m distance away, p A2 = 21 k Pa. If the total pressure is constant through the tube, calculate the flux of methane at steady-state for equimolar counter diffusion. 2. Helium and nitrogen gas are contained in a conduit 6 mm in diameter and 0.1 m long at 298 K and a uniform constant pressure of 1.0 atm abs. The partial pressure of He at point one of the tube is 0.06 atm. and 0.02 atm at the other end (point two). Calculate the following for steady-state equimolar counter diffusion. a. Flux of He in kg mol/s. m 2. b. Flux of N 2. c. Rate of He in kg mol/s. d. Partial pressure of He at a point 0.03 m from point one.

2 College of Engineering Tutorial # 2 Chemical Engineering Dept. 21/9/ Ammonia gas is diffusing through N 2 under steady-state conditions with N 2 nondiffusing. The total pressure is x 10 5 Pa and the temperature is 298 K. The partial pressure of NH 3 at one point is x 10 4 Pa and at the other point 25 mm away it is x 10 3 Pa. The D AB for the mixture at x 10 5 Pa and 298 K is 2.3 x 10-5 m 2 /s. a. Calculate the flux of NH 3 in kg mol/s.m 2. b. Do the same as (a) but assume that N 2 also diffuses; i.e. the flux is eqimolar counter diffusion. In which case the flux greater? 2. Methane gas is diffusing in a straight tube 0.15 m long containing helium at 298 K and a total pressure of x 10 5 Pa. The concentration of CH 4 at one end is mole % and mole % at the other end. Helium is insoluble in one boundary, and hence is nondiffusing or stagnant. Calculate the flux of methane in kg mole/s. m 2 at steady-state. 3. Oxygen (A) is diffusing through carbon monoxide (B) under steady-state conditions, with CO nondiffusing. The total pressure is 1 x 10 5 N/m 2, and the temperature 0 ºC. The partial pressure of oxygen at two planes 2.0 mm apart is, respectively and 6500 N/m 2. The diffusivity for the mixture is 1.87 x 10-5 m 2 /s. Calculate the rate of diffusion of oxygen in kgmol/s through each square meter of the two planes.

3 College of Engineering Tutorial # 3 Chemical Engineering Dept. 12/10/ The gas CO 2 is diffusing at steady-state through a tube 0.2 m long having a diameter of 0.01 m and containing N 2 at 298 K. The total pressure is constant at kpa. The partial pressure of CO 2 at one end is 456 mm Hg and 76 mm Hg at the other end. The diffusivity D AB is 1.67 x 10-5 m 2 /s at 298 K. Calculate the flux of CO 2 for equimolar counterdiffusion. 2. For a mixture of ethanol vapor and methane, predict the diffusivity using the method of Fuller et al. a. At x 10 5 Pa and 298 and 373 K. b. At x 10 5 Pa and 298 K. 3. Determine the mass transfer for the conical section shown in Fig. (1) below. The concentration of CO 2 in air is 30 mole % at the 10 cm opening, and 3 mole % at the 5 cm opening. For this mixture, the diffusion coefficient is cm 2 /s. The gas is at 1 atm and 25 ºC ( K) everywhere. The section is 30 cm thick. 10 cm 5 cm x 30 % CO2 3 % CO2 Fig. (1): A conical section for mass transfer

4 College of Engineering Tutorial # 4 Chemical Engineering Dept. 19/10/ For a mixture of ethanol vapor and methane, predict the diffusivity using the method of Fuller et al. a. At x 10 5 Pa and 298 and 373 K. b. At x 10 5 Pa and 298 K. 2. The diffusivity of dilute methanol in water has been determined experimentally to be 1.26 x 10-9 m 2 /s at 288 K. a. Estimate the diffusivity at 293 K using the Wilke-Chang equation. b. Estimate the diffusivity at 293 K by correcting the experimental value at 288 K to 293 K. (Hint: Do this by using the relationship D AB T/µ. 3. Equimolarcounter diffusion is occurring at steady-state in a tube 0.11 m long containing N 2 and CO gases at a total pressure of 1 atm abs. The partial pressure of N 2 is 80 mm Hg at one end and 10 mm at the other end. Predict the D AB by the method of Fuller et al. a. Calculate the flux in kg mol/s m 2 at 298 K for N 2. b. Repeat at 473 K. does the flux increase? c. Repeat at 298 K but for a total pressure of 3.0 atm abs. The partial pressure of N 2 remains at 80 and 10 mm Hg, as in part (a). Does the flux change? 4. It is desired to predict the diffusion coefficient of dilute acetic acid (CH3COOH) in water at K and at 298 K using the Wilke-Change method. Compare the predicted values with the experimental values in Table

5 College of Engineering Tutorial # 5 Chemical Engineering Dept. 26/10/ Mass transfer is occurring from a sphere of naphthalene having a radius of 10 mm. The sphere is in a large volume of still of air at 52.6 ºC and 1 atm. Abs. The vapor pressure of the naphthalene at 52.6 ºC is 1.0 mm Hg. The diffusivity of the naphthalene in air at 0º is 5.16 x 10-6 m 2 /s. Calculate the rate of evaporation of naphthalene from the surface in kg mol/s. m 2. [D is proportional to T 1.75 ] 2. The solute HCl (A) is diffusing through a film of water (B) 1.5 mm thick at 283 K. The concentration of HCl at point 1 at one boundary of the film is 14.0 wt % HCl (desity, ρ 1 = kg/m 3 ), and at the other boundary at point 2 it is 7.0 wt % HCl (ρ 2 = kg/m 3 ). The diffusion coefficient of HCl in water is 2.5 x 10 9 m 2 /s. Assuming steady-state at one boundary impermeable to water, calculate the flux of HCl in kg mol/s.m A flat plug 30 mm thick having an area of 4 x 10-4 m 2 and made of vulcanized rubber is used for closing an opening in a container. The gas CO 2 at 25 ºC and 2 atm pressure is inside the container. Calculate the total leakage or diffusion of CO 2 through the plug to the outside in kg mol CO 2 /s at steady-state. Assume that the partial pressure of CO 2 outside is zero. The solubility of the CO 2 gas is 0.9 m 3 gas (at STP of 0 ºC and 1 atm.) per m 3 rubber per atm pressure of CO 2. The diffusivity is 0.11 x 10-9 m/s.

6 College of Engineering Tutorial # 6 Chemical Engineering Dept. 4/11/ The gas hydrogen is diffusing through a sheet of vulcanized rubber 20 mm thick at 25 ºC. The partial pressure of H 2 inside is 1.5 atm and 0 outside. Using the data from table 6.5-1, calculate the following. a. the diffusivity D AB from the permeability P M and solubility S and compare with the value in Table b. The flux N A of H at steady-state. 2. Nitrogen gas at 2 atm and 30 ºC is diffusing through a membrane of nylon 2.0 mm thick and polyethylene 7.0 mm thick in series. The partial pressure at the other side of the two films is 0 atm. Assuming no other resistances, calculate the flux N A at steadystate. 3. It is desired to calculate the rate of diffusion of CO 2 gas in air at steady-state through a loosely packed-bed of sand at 276 K and a total pressure of 1.013x10 5 Pa. The bed depth is 1.3 m and the void fraction ε is the partial pressure of CO 2 at the top of the bed is x 10 3 Pa and 0 Pa at the bottom. Use τ of A mixture of He (A) and Ar (B) is diffusing at x 10 5 Pa total pressure and 298 K through a capillary having a radius of 100Ǻ. a. Calculate the Knudsen diffusivity of He (A). b. Calculate the Knudsen diffusivity of Ar (B). 5. A mixture of He (A) and Ar (B) at 298 K is diffusing through an open capillary 15 mm with a radius 1000 Å. The total pressure is x 10 5 Pa. The molecular diffusivity D AB at x 10 5 Pa is 7.29 x 10-5 m 2 /s. c. Calculate the Knudsen diffusivity of He (A). d. Predict the flux N A using equation (7.6-18) and Equation (7.6-12) if x A1 =0.8 and x A2 = 0.2. Assume steady state. e. Predict the flux N A using the approximate equations (7.6-14) and (7.6-16).

7 College of Engineering Tutorial # 7 Chemical Engineering Dept. 11/11/ A value of k G was experimentally determined to be 1.08 lbmol/h.ft 2.atm for A diffusing through stagnant B. For the same flow and concentrations it is desired to predict k`g and the flux of A for equimolar counter diffusion. The partial pressures are p A1 = 0.2 atm, p A2 = 0.05 atm, and P = 1.0 atm abs total. Use English and SI units. 2. In a wetted-wall tower an air- H 2 S mixture is flowing by a film of water which is flowing as a thin film down a vertical tube. The H 2 S is being absorbed from the air to the water at a total pressure of 1.5 atm abs and 30 ºC. The value of k`c of x 10-4 m/s has been predicted for the-gas phase-mass transfer coefficient. At a given point the mole fraction of H 2 S in the liquid at the liquid gas interface is 2 x 10-5 and p A (atm) = 609 x A (mole fraction liquid). Calculate the rate of absorption of H 2 S. [Hint: Call point 1 the interface and point 2 the gas phase. Then calculate p A1 from Henry s law and the given x A. The value of p A2 is 0.05 atm]. 3. It is desired to estimate the mass transfer coefficient k G in kg mol/s. m 2.Pa for water vapor in air at K and kpa flowing in a large duct past different geometry solids. The velocity in the duct is 3.66 m/s. The water vapor concentration in the air is small, so the physical properties of air can be used. Water vapor is being transferred to the solids. Do this for the following geometries: a. A single 25.4 mm diameter sphere. b. A packed bed of 25.4 mm spheres with ε = 0.35

8 College of Engineering Tutorial # 8 Chemical Engineering Dept. 18/11/ Pure water at 26.1 ºC is flowing at a velocity of m/s in a tube having an inside diameter of 6.35 mm. The tube is m long with the last 1.22 m having walls coated with benzoic acid. Assuming that the velocity profile is fully developed, calculate the average concentration of benzoic acid at the solute. [Hint: first calculate the Reynolds number. Then calculate N Re N Sc (D/L)(π/4), which is the same as W/D AB.ρL] Useful data: C Ai = kgmole/m 3 (Solubility) 3. A tube is coated on the inside with naphthalene and has an inside diameter of 20 mm and a length of 1.1 m. Air at 318 K and an average pressure of kpa flows through this pipe at a velocity of 13 m/s. Assuming that the absolute pressure remains constant, calculate the mass transfer coefficient of the naphthalene (K C ). Calculate the exit concentration C A2 of naphthalene in leaving air. Data: a. D AB = 6.92 X 10-6 m/s b. Vapor pressure of 318 K = 70 Pa c. Hint: Flux = K C ( C M ). C M = log mean concentration difference. 4. Mercury at 26.5 ºC is flowing through a packed bed of lead spheres having a diameter of mm with a void fraction of The superficial velocity is m/s. The solubility of lead in mercury is wt %, the Schmidt number is 124.1, the viscosity of the solution is x 10-3 Pa.s, and the density is kg/m 3. a. Predict the value of J D. Use Eq. (7.3-38) if applicable. Compare with the experimental of J D = b. Predict the value of k c for the case A diffusing through non diffusing B.

9 College of Engineering Tutorial # 9 Chemical Engineering Dept. 30/11/ A thin plate of solid salt, NaCl, measuring 6 in. by 6 in., is to be dragged through seawater (edgewise) at a velocity of 2 ft/s. The 64 ºF seawater has a salt concentration of g/cm 3 ; if saturated, the seawater would have a concentration of 35 g/cm 3. The kinematic viscosity of seawater is approximately 1.1 x10-5 ft 2 /s. Estimate the rate at which the salt goes into solution if the edge effects can be ignored. 2. Air at 100 ºF and 1 atm flows over a naphthalene ball. Since naphthalene exerts a vapor pressure of 5 mm Hg at 100 ºF, it will sublime into the passing air stream, which has a negligibily small concentration of naphthalene in the bulk airstream. If a ¾ -in. naphthalene ball is suspended into a 5 ft/s airstrem, where the physical properties at the film temperature are: mass diffusivity = 0.37 ft 2 /hr kinematic viscosity of air = ft 2 /hr Determine: a. The mass transfer coefficient. b. The molar flux of naphthalene into the airstream. 3. Air passes through a naphthalene tube that has an inside diameter of 2.5 cm, flowing at a bulk velocity of 15 m/s. The air is at 283 K and an average pressure of x 10 5 Pa. Assuming that the change in pressure along the tube is negligible and that the naphthalene surface is at 283 K, determine the length of tube that is necessary to produce a naphthalene concentrationin the exiting gas stream of 4.75 x 10 4 mol/m 3. At 283 K, naphthalene has a vapor pressure of 3 Pa and a diffusivity in air of 5.4x 10-6 m 2 /s.

10 College of Engineering Tutorial # 10 Chemical Engineering Dept. 29/4/ The solute A is being absorbed from a gas mixture of A and B in a wetted-wall tower with the liquid flowing as a film downward along the wall. At a certain point in the tower the bulk gas concentration y AG = 0.38 mol fraction and the bulk liquid concentration is x AL = The tower is operating at 298 K and x 10 5 Pa and the equilibrium data are as follows: x A y A The solute A diffuses through a stagnant B in the gas phase and then through a nondiffusing liquid. Using correlations for dilute solutions in wetted-wall towers, the film mass transfer coefficient for A in the gas phase is predicted as k y = x 10-3 kg mol A/s.m 2.mol frac. (1.08 lb mol/h. ft 2. mol frac) and for the liquid phase as k x = x 10-3 kg mol A/s. mol frac (1.45 lb mol/h. ft 2. mol frac.). Calculate the interface concentrations y Ai and x Ai and the flux N A. 2. Using the same data as in (1), calculate the overall mass-transfer coefficient K`x and K x, the flux, and the percent resistance in the gas film. 3. Use the same equilibrium data and film coefficients k`y and k`x as in (1). However use bulk concentration of y AG = 0.25 and x AL = Calculate the following: a. Interface concentrations y Ai and x Ai and flux N A. b. Overall mass-transfer coefficients K`y and K y and flux N A. c. Overall mass-transfer coefficients K`x and flux N A.

11 College of Engineering Tutorial 11 Chemical Engineering Dept. 30/12/ In an experimental study of the absorption of NH 3 by water in a wetted-wall column, the value of K G was found to be lb mole NH 3 /h ft 2 atm. At one point in the column, the gas contained 8 mole % NH 3 and the liquid phase concentration was mole of NH 3 per ft 3 of solution. The temperature was 68 ºF, and the total pressure was one atmosphere. 85% of the total resistance to the mass transfer was found to be in the gas phase. If Henry`s constant at 68 ºF is atm/(lb mole NH 3 /ft 3 of solution), calculate the individual film coefficients and the interfacial compositions. 2. In the absorption of component A from an air stream into an aqueous stream, the bulk composition of the two adjacient streams were analyzed to be p A,G = 0.1 atm and c A,L = 0.25 lb mole/ft 3. The Henry`s constant for this system is atm/(lb mole A/ft 3 of solution). The overall gas coefficient, K G = lb mole A/(h ft 2 atm). If 57 % of the total resistance of mass transfer is encountered in the gas film, determine a. The mass flux of A. b. The concentration on the liquid side of the interface c A,i. c. The gas-film coefficient k G. d. The liquid-film coefficient, k L.

12 College of Engineering Tutorial 12 Chemical Engineering Dept. 7/1/ Calculate the diameter of an absorption column that packed with ceramic Rashing rings 25 mm in size to treat 1000 m 3 /h of a gas mixture by absorbing liquid. For special circumstances in this absorption operation the ratio of liquid to gas flow is not to exceed the double and the column operates at 75% of the flooding rate. Liquid density ρ L = 1000kg/m 3 and has a viscosity of Pa.s. The average gas density ρ G = 1.0 kg/m 3 and the packing coefficient F P for the ceramic Rashing rings 25mm in size is 525/m. 2. Water is used to absorb SO 2 from air flowing in a packed column. The following data were recorded during the actual operation of the column. Water enters the column at the top free of SO 2 at a rate of 4 kmoles/s. The gas mixture enters at the bottoms with a concentration of 2% mol SO 2 and a rate of 0.08 kmoles/s and leaves the column at the top containing 0.5 %mol SO 2. The column cross-sectional area is 1.0 m 2 and the height of the packing material in the column is 5 m. The operation is at 1 atm and 25 ºC. Equilibrium relationship between the liquid phase and the gas phase at the column operating conditions is given by: yi = 40 xi From the above data, calculate the overall mass transfer capacity coefficient for the gas phase, K y a

ERT 216 HEAT & MASS TRANSFER SEM2, 2013/2014

ERT 216 HEAT & MASS TRANSFER SEM2, 2013/2014 ERT 16 HET & MSS TRNSFER SEM, 01/014 Tutorial: Principles of Mass Transfer (Part 1) gas of CH 4 and He is contained in a tube at 10 kpa pressure and 98 K. t one point the partial pressure of methane is