A gas purification system needs to produce 2 kg/hour of purified product. If the purification membrane is 100 m2 and 0.05mm thick, and the supply gas is at 0.75 kg/m3 and the take-off side maintains a pressure of 0.05 kg/m3 find required membrane Diffusivity in sq m/sec.

The membrane diffusivity would be 3.968 x  /s

Explanation:

According to Fick's law of diffusion, the rate of the purified product is related with to membrane diffusivity with the expression in equation 1.

..............................1

Where

V is the rate of purified product = 2 kg/hr = 2 kg/hr  x 1 hr / 3600 sec  =     1/1800 kg/sec

is the pressure at the supply gas point = 0.75 kg/

is the pressure at the take-off side = 0.05 kg/

A is the area of the membrane = 100

T is the thickness of the membrane = 0.05 mm = 0.05/ 1000 = 5 x m

Substituting the values into equation 1 we have;

5 x  = 126000 x D

D =  5 x / 126000

D = 3.968 x  /s

Therefore the membrane diffusivity would be 3.968 x  /s

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