Question 8 of 10: Packed-Tower Air Stripper Design for Benzene-Contaminated Groundwater

Question 8: Packed-Tower Air Stripper Design for Benzene-Contaminated Groundwater (15 points)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Find. The dimensionless Henry's constant at 25 °C, the stripping factor $R$, the number and height of transfer units, and the resulting packing height.

Approach. Use the supplied temperature-dependent correlation to get Henry's constant at 25 °C, convert to dimensionless form and combine with the air-to-water ratio to get the stripping factor $R$; use the Kavanaugh & Trussell equation for NTU from the required removal ratio; get HTU from the water loading and $K_La$ over the column's cross-sectional area; multiply to get the packing height.

1. Henry's constant from the supplied correlation. With $\ln H = A/T + B$, $T=298.15\ \text{K}$: $$\ln H = \frac{-3.19\times10^3}{298.15} + 5.53 = -10.70 + 5.53 = -5.169 \quad\Rightarrow\quad H = e^{-5.169} = 5.69\times10^{-3}\ \text{atm}\cdot\text{m}^3/\text{mol}$$ This matches the literature value used in Question 6 ($5.55\times10^{-3}$) closely, confirming the correlation.
2. Dimensionless Henry's constant. $$H_c = \frac{H}{RT} = \frac{5.69\times10^{-3}}{(8.206\times10^{-5})(298.15)} = \boxed{0.2325}$$ (again consistent with Question 6's independently looked-up $H' = 0.227$.)
3. Stripping factor. $$R = H_c\left(\frac{Q_a}{Q_w}\right) = (0.2325)(50) = \boxed{11.63}$$
4. Number of transfer units (Kavanaugh & Trussell). With $C_{in}/C_{out} = 150/0.130 = 1154$, $$\text{NTU} = \frac{R}{R-1}\ln\!\left[\frac{(C_{in}/C_{out})(R-1)+1}{R}\right] = \frac{11.63}{10.63}\ln\!\left[\frac{(1154)(10.63)+1}{11.63}\right] = (1.094)\ln(1055) = \boxed{7.62}$$
5. Height of a transfer unit. Column cross-sectional area $A_c = \dfrac{\pi}{4}D^2 = \dfrac{\pi}{4}(0.765\ \text{m})^2 = 0.4596\ \text{m}^2$, and $$\text{HTU} = \frac{Q_w}{K_La \cdot A_c} = \frac{2.19\times10^{-3}\ \text{m}^3/\text{s}}{(0.015\ \text{s}^{-1})(0.4596\ \text{m}^2)} = \boxed{0.318\ \text{m}}$$
6. Packing height. $$Z = \text{HTU}\times\text{NTU} = (0.318\ \text{m})(7.62) = \boxed{2.42\ \text{m}}$$

The design also fixes the blower air flow, $Q_a = (Q_a/Q_w)\,Q_w = (50)(2.19\ \text{L/s}) = 109.5\ \text{L/s}$. A packed height of about 2.4 m in a 0.765 m-diameter column is a physically reasonable, buildable air stripper for this duty; the large stripping factor ($R\approx11.6\gg1$) reflects benzene's high volatility (Question 6) and is why only a modest tower height is needed to achieve the required >1000× concentration reduction.