Find. Liquid loading rate, stripping factor, packing height, and a sketch of the countercurrent packed-tower unit.
Countercurrent packed-tower air stripper for toluene removal — D = 0.61 m, air:water = 15, packing height Z ≈ 5.5 m.
Approach. Design follows the standard Kavanaugh & Trussell packed-tower method: (1) liquid loading rate from the given flow and column area, (2) stripping factor from Henry's constant and the air:water ratio, (3) number of transfer units (NTU) from the required removal and the stripping factor, (4) height of a transfer unit (HTU) from $K_La$ and the column area, and (5) packing height $Z=\text{HTU}\times\text{NTU}$.
Liquid loading rate. Convert the water flow to SI and divide by the column cross-sectional area:
$$Q_w=110\ \text{gal/min}=6.940\times10^{-3}\ \text{m}^3/\text{s}, \qquad A=\frac{\pi D^2}{4}=\frac{\pi(0.61)^2}{4}=0.2922\ \text{m}^2$$
$$q_L=\frac{Q_w}{A}=\frac{6.940\times10^{-3}}{0.2922}=\boxed{0.0237\ \text{m/s}\ (85.5\ \text{m}^3/\text{m}^2\cdot\text{hr},\ 35.0\ \text{gpm/ft}^2)}$$
This falls within the typical packed-tower design range (roughly 15–40 gpm/ft² for random packing), confirming the given 0.61 m diameter is a reasonable choice for this flow.
Stripping factor. The problem does not supply toluene's Henry's constant directly (this is an OPEN BOOK exam — looking it up is expected); the standard literature value for toluene's dimensionless Henry's constant at 20°C is $H\approx0.26$ (Munz & Roberts data, as tabulated in Davis & Cornwell). The stripping factor is then:
$$R=H\left(\frac{Q_a}{Q_w}\right)=0.26\times15=\boxed{3.90}$$
$R>1$ confirms stripping is thermodynamically favourable at this air:water ratio — a necessary check before proceeding, since $R\le1$ would mean no packing height could achieve the target removal.
Number of transfer units (NTU). Apply the Kavanaugh & Trussell NTU equation with the required removal ratio $C_{in}/C_{out}=2.1/0.05=42$:
$$\text{NTU}=\frac{R}{R-1}\ln\!\left[\frac{(C_{in}/C_{out})(R-1)+1}{R}\right]=\frac{3.90}{2.90}\ln\!\left[\frac{42(2.90)+1}{3.90}\right]=\boxed{4.64}$$
Height of a transfer unit (HTU) and packing height. HTU follows directly from the given overall transfer coefficient and the liquid flow/area already computed:
$$\text{HTU}=\frac{Q_w}{K_La\cdot A}=\frac{6.940\times10^{-3}}{0.020\times0.2922}=1.187\ \text{m}$$
$$Z=\text{HTU}\times\text{NTU}=1.187\times4.64=\boxed{5.51\ \text{m}}$$
Final results
Quantity
Value
Liquid loading rate
0.0237 m/s (35.0 gpm/ft²)
Stripping factor, R
3.90
Number of transfer units, NTU
4.64
Height of a transfer unit, HTU
1.19 m
Packing height, Z
5.51 m
Check: assumes toluene's dimensionless Henry's constant $H\approx0.26$ at 20°C (standard literature/textbook value; not supplied in the exam data and legitimately looked up under the open-book condition). A real design would also add freeboard above the packing (typically 1–1.5 m for the liquid distributor/mist eliminator zone already shown in the sketch) beyond the calculated packing height, and would round the diameter/height to the nearest available commercial packing-column size.
