We are trying to remove acetone from nitrogen gas using an adsorption column wit

Question

We are trying to remove acetone from nitrogen gas using an adsorption column with diameter 5cm and length 20cm. The column is packed with 100g of activated carbon. The inlet gas stream enters the column with the mass flow rate of 5g/min. The molar fraction of acetone in the feed mixture is 0.01. The experimental breakthrough curve could be fitted to the following Klinkenberg equation. Co The unit of time t is hour in this equation. (a) What is the break-point time to (at which c/co 0.01)? (b) Calculate t, and t (c) Calculate Huns (d) Calculate the total amount (g) of acetone that adsorbed at the break-point time (e) Calculate the total length of the column that is needed to get 3kg of pure nitrogen gas (f) Plot c/coas a function of time for the following approximate solutions. Based on the shape of the curves, discuss the general strategies to decrease HuNB for a given adsorption process

Explanation / Answer

A) Transform original equation from c/co = 0.5 [ 1 + 2.645(7t) + 0.047 / (7t) + 8(50) - (50) ] to

c/co = 0.5 [ 1 + 2.645(7t) + 0.047 / (7t) - 7.053 ]

that is to decimal form with accuracy upto 3 digits to get rid of quare-roots (one can follow original equation also).

Putting c/co = 0.01 in above

0.01 = 0.5 [ 1 + 2.645(7t) + 0.047 / (7t) - 7.053 ]

then we multiply the equation with (t) , to get a quadratic equation,

t2 - 5.403t+ 0.047 = 0

Which upon solving gives us root as

t0.008 and t=5.394 hr , these two are two breakthrough time.

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