## Info

Assume diameter of actual column 4 m; As = n (4 )/4 = i2.57 m Using 2 columns, adsorbate retained in S length of the columns = 2(i2.57)(0.005i)(i4.23) = i.82 kg

Assuming carbon replacement is to be done every week, adsorbate retained in column length of length L - S = 237(7) - i.82 = i657 kg

Carbon required for the i657 kg of adsorbate = i657/0.02 = 82,850 kg = 4i,425 kg/column Therefore,

4i.425

= 4.75, say 4.8 m including freeboard and other allowances. Ans Diameter = 4 m Ans

Interval of carbon replacement = once every week Ans

As soon as the bed is exhausted, as determined by the breakthrough of concenJ trations, the carbon may be replaced. The replaced carbon may be reactivated again for reuse. Up to 30 or more reactivations may be made without appreciable loss of adsorptive power of the reactivated carbon.

### 8.3.6 Relative Velocities in Bed Adsorption

As mentioned before, the unit operation of bed adsorption may be carried out in a moving-bed mode, either co-currently or countercurrently. When the breakthrough experiment is carried out, the superficial velocity should also be recorded. The reason is that adsorption is a function of the time of contact between the liquid phase containing the solute to be adsorbed and solid-phase carbon bed. Thus, for the breakthrough data to be applicable to an actual prototype adsorption column, the relative velocities that transpired during the test must be maintained in the actual column. When the relative velocities between the flowing water and the carbon bed are maintained, it is immaterial whether or not the bed is moving.

Consider first the co-current operation. Let Vs be the superficial velocity of the flowing water relative to the stationary earth and Vb be the velocity of the bed also relative to the stationary earth. Thus, the relative velocity of the flowing water VsJb relative to the bed is

Vs = Vs/b + Vb For the countercurrent operation, the formula is

In a breakthrough experiment, the superficial velocity may be obtained by dividing the volume V of water collected in t time by the superficial area of the experimental column. Breakthrough experiments are invariably conducted in stationary beds. Thus, from the previous equations this superficial velocity is actually the relative velocity of the flowing water with respect to the bed, with Vb equal to zero. This relative velocity must be maintained in the actual column design, if the data collected in the breakthrough experiment are to be applicable.

Example 8.9 Design the column of the previous example if the feed is introduced at the bottom. The carbon is continuously removed at the bottom and continuously added at the top. Due to the countercurrent operation, assume the bed expands by 40%.

Solution: The design will include, in addition to those in the previous example, the determination of the carbon removal and addition rates at the bottom and top of column, respectively. These rates are determined from the length of the packed carbon in the column and the interval of replacement as stated in the previous example.

Removal rate = addition rate = (i2.57)(72i.58) = 246.73 kg/h Ans

The superficial velocity, from the previous example = 0.0088 m/s, velocity relative to the stationary bed. In the countercurrent operation, this relative velocity must be maintained if the breakthrough curve is to be applicable. Because of the expansion, Vb is increased by 40%. Thus, Vs in present design considering the expansion:

Vs = Vs/b - Vb = 0.0088 - 7(24576ox60) = 0.0088 - 0.0000i = 0.0088 m/s Therefore,

A. = ^0.01L = 12.5 m2 ^ diameter = 4 m Ans s 0.0088

L = 1.4 (4.57) = 6.4 m say 6.7 m, including freeboard and other allowances Ans