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18-Env-B5 Industrial & Hazardous Waste Management · May 2018

Question 12 of 14: Packed-Tower Air Stripping Height for Chloroform

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Reference texts: LaGrega, Buckingham & Evans, Hazardous Waste Management, 2nd ed.; Nemerow & Dasgupta, Industrial and Hazardous Waste Treatment, 2nd ed.; Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery, 5th ed.; Davis & Cornwell, Introduction to Environmental Engineering, 6th ed.; Cooper & Alley, Air Pollution Control: A Design Approach; CCME, Guidelines for the Management of Biomedical Waste in Canada (1992); Ontario Environmental Protection Act, R.S.O. 1990, c. E.19 and O. Reg. 347 (Waste Management – General); Transportation of Dangerous Goods Act, 1992 (Canada) and Regulations; Canadian Environmental Protection Act (CEPA), 1999.

Question 12: Packed-Tower Air Stripping Height for Chloroform (20 marks)

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.

QuantitySymbolValue
Influent chloroform concentration$C_{in}$150 µg/L
Effluent (target) concentration$C_{out}$10 µg/L
Water (hydraulic) loading$q_L$100 m/hr
Air (gas) loading$q_G$3000 m/hr
Henry's constant (mass basis)$H_D$$2.558\times10^{-5}$ atm·L/mg
Overall mass transfer coefficient$K_La$30 h-1
Temperature$T$$20^{\circ}\text{C}$ (293.15 K)

Find. The packed height of the stripping tower, $Z$.

Approach. Convert Henry's constant to its dimensionless form; compute the stripping factor $R=H'(Q_a/Q_w)$; use the Kavanaugh-Trussell equation to find the number of transfer units (NTU) from the required removal ratio; compute the height of a transfer unit ($\text{HTU}=q_L/K_La$); and multiply, $Z=\text{HTU}\times\text{NTU}$.

  1. Dimensionless Henry's constant. Converting the mass-basis $H_D$ (atm·L/mg) to the dimensionless gas/liquid concentration ratio $H'$ via the ideal-gas relation $p=H_D\,C_L$ and $C_g = p\,MW/(RT)$, with chloroform $MW=119.4$ g/mol, $R=0.08206$ L·atm/(mol·K), $T=293.15$ K: $$H' = \frac{H_D\times MW\times1000}{R\,T} = \frac{2.558\times10^{-5}\times119.4\times1000}{0.08206\times293.15} = \boxed{0.1270}$$
  2. Stripping factor. $R = H'\times(Q_a/Q_w)$ — the air-to-water ratio is dimensionless, so it is the same whether $Q_a,Q_w$ are read as total flows or as loadings: $$R = 0.1270\times\frac{3000}{100} = 0.1270\times30 = \boxed{3.81}$$
  3. Number of transfer units (NTU). Kavanaugh-Trussell equation, with $C_{in}/C_{out}=150/10=15$: $$\text{NTU} = \frac{R}{R-1}\ln\!\left[\frac{C_{in}}{C_{out}}\cdot\frac{R-1}{R}+\frac{1}{R}\right] = \frac{3.81}{2.81}\ln\!\left[15\times\frac{2.81}{3.81}+\frac{1}{3.81}\right]$$ $$= 1.356\times\ln(11.06+0.263) = 1.356\times\ln(11.33) = 1.356\times2.428 = \boxed{3.29}$$
  4. Height of a transfer unit (HTU). Using the water loading rate $q_L$ directly (no separate tower cross-sectional area is given, so $q_L$ is taken as the superficial hydraulic loading rate, m/hr — see check note): $$\text{HTU} = \frac{q_L}{K_La} = \frac{100\ \text{m/hr}}{30\ \text{hr}^{-1}} = \boxed{3.33\ \text{m}}$$
  5. Tower height. $$Z = \text{HTU}\times\text{NTU} = 3.33\times3.29 = \boxed{10.97\ \text{m} \approx 11.0\ \text{m}}$$
Final results
QuantityValue
Dimensionless Henry's constant, $H'$0.1270
Stripping factor, $R$3.81
Number of transfer units, NTU3.29
Height of a transfer unit, HTU3.33 m
Packed tower height, $Z$≈ 11.0 m
Check: no tower cross-sectional area or diameter is given anywhere in the source, so a height cannot be computed from total volumetric flows alone (Q/A is dimensionally required to reach a length). The water and air flow rates (100 and 3000 m3/hr) are therefore read as already being superficial hydraulic and gas LOADING rates (m/hr, i.e. per unit plan area) — both values fall within typical packed-tower design ranges (liquid loading 20–100+ m/hr; gas loading up to a few thousand m/hr) — consistent with the exam's own "state any assumptions made" instruction. This reading does not affect the stripping factor $R$ (a pure ratio, unaffected by the area basis), only the HTU/height step.