3.14b. Material balances: adsorption of benzene vapor on activated carbon.
Activated carbon is used to recover benzene from a nitrogen-benzene vapor mixture. A nitrogen-benzene mixture at 306 K and 1 atm containing 1% benzene by volume is to be passed countercurrently at the rate of 1.0 m3/s to a moving stream of activated carbon so as to remove 85% of the benzene from the gas in a continuous process. The entering activated carbon contains 15 cm3 benzene vapor (at STP) adsorbed per gram of the carbon. The temperature and total pressure are maintained at 306 K and 1 atm. Nitrogen is not adsorbed. The equilibrium adsorption of benzene on this activated carbon at 306 K is reported as follows:

Benzene vapor adsorbed Partial pressure benzene, mm Hg
cm3 (STP)/g carbon
15 0.55
25 0.95
40 1.63
50 2.18
65 3.26
80 4.88
90 6.22
100 7.83
a) Plot the equilibrium data as X' = kg benzene/kg dry carbon, Y' = kg benzene/kg nitrogen for a total pressure of 1 atm.

Solution
b) Calculate the minimum flow rate required of the entering activated carbon (remember that the entering carbon contains some adsorbed benzene).

Solution
On the XY diagram, locate the point (X2,Y2). Since the operating line is above the equilibrium curve and the equilibrium curve is concave upwards, the minimum operating line is obtained by locating, at the intersection of Y = Y1 with the equilibrium curve, X1max.
c) If the carbon flow rate is 20% above the minimum, what will be the concentration of benzene adsorbed on the carbon leaving?

Solution
d) For the conditions of part (c), calculate the number of ideal stages required.

Solution
See stepwise construction on the XY graph
3.15b. Material balances: desorption of benzene vapor from activated carbon.
The activated carbon leaving the adsorber of Problem 3.14 is regenerated by countercurrent contact with steam at 380 K and 1 atm. The regenerated carbon is returned to the adsorber, while the mixture of steam and desorbed benzene vapors is condensed. The condensate separates into an organic and an aqueous phase and the two phases are separated by decantation. Due to the low solubility of benzene in water, most of the benzene will be concentrated in the organic phase, while the aqueous phase will contain only traces of benzene. The equilibrium adsorption data at 380 K are as follows:



Benzene vapor adsorbed Partial pressure benzene, kPa
kg benzene/100 kg carbon
2.9 1.0
5.5 2.0
12.0 5.0
17.1 8.0
20.0 10.0
25.7 15.0
30.0 20.0

a) Calculate the minimum steam flow rate required.
Solution
Equilibrium curve
From Problem 3.14
From the XY diagram:

b) For a steam flow rate of twice the minimum, calculate the benzene concentration in the gas mixture leaving the desorber, and the number of ideal stages required.
Solution
3.16b. Material balances: adsorption of benzene vapor on activated carbon; cocurrent operation.
If the adsorption process described in Problem 3.14 took place cocurrently, calculate the minimum flow rate of activated carbon required.

Solution

Fom Problem 3.14:
From the XY diagram: