**Transport Phenomena 2**

Mass Transport

Mass Transport

Basic laws and definitions

Ex 1: The pressure in a pipeline that transports helium gas at a rate of 2 kg/s is maintained at 1 atm by venting helium to the atmosphere through a 5mm diameter tube that extends 15 m into the air. Assuming both the helium and the air to be at 25°C, determine the mass flow rate of helium lost to the atmosphere and the mass flow rate of air that infiltrates into the pipeline ( D = 7.2 * 10-5 m2/s )

Ex 2: Pyrex glass is almost impermeable to all gases but helium. For example, the diffusivity of He through pyrex is about 25 times the diffusivity of Hz through pyrex, hydrogen being the closest "competitor" in the diffusion process. This fact suggests that a method for separating helium from natural gas could be based on the relative diffusion rates through pyrex. Suppose a natural gas mixture is contained in a pyrex tube with dimensions shown in the figure. Obtain an expression for the rate at which helium will "leak" out of the tube, in terms the diffusivity of helium through pyrex, the interfacial concentrations of the helium in the pyrex, and the dimensions of the tube.

Ex 3: One way of measuring gas diffusivities is by means of a two-bulb experiment. The left bulb and

the tube from z = - L to z = 0 are filled with gas A. The right bulb and the tube from z = 0 to

z = +L are filled with gas B. At time t = 0 the stopcock is opened, and diffusion begins; then the

concentrations of A in the two well-stirred bulbs change. One measures xA+ as a function of time,

and from this deduces D. We wish to derive the equations describing the diffusion.

Since the bulbs are large compared with the tube, x i and x i change very slowly with time.

Hence the diffusion in the tube can be treated as a quasi-steady-state problem, with the

boundary conditions that xA = xA- and z = -L, and that xA = xA+ at z = +L.

Ex 4: An open cylindrical tank is filled with pure methanol within 2 ft from the top. The tank is plotted shown in the figure below. The air within the tank is stationary but circulation of air immediately above the tank is adequate to assume a negligible concentration of methanol at 77°F and 1 atm. Derive a relation for the methanol flux and calculate the rate of loss of methanol from the tank at steady state. Diffusivity of methanol in air at 77°F and 1 atm is 0.62 ft2/hr (Methanol vapor pressure@77F = 126 mm Hg)

Diffusion flux

Combined flux

Equimolar counter diffusion

Unidirectional Diffusion

N1 = -N2

N2 = 0

N = C*D*(X11-X12)

(Z2-Z1)