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18-Env-B5 Industrial & Hazardous Waste Management · December 2019

Question 5 of 10: Volatilization Rate from an Open Vat of Spent MIBK

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.; Davis & Cornwell, Introduction to Environmental Engineering, 6th ed.; Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery, 5th ed.; Cooper & Alley, Air Pollution Control: A Design Approach; ACGIH, Industrial Ventilation: A Manual of Recommended Practice; Ontario Environmental Protection Act, R.S.O. 1990, c. E.19 and O. Reg. 347 (Waste Management – General); U.S. EPA SW-846 Method 1311 (Toxicity Characteristic Leaching Procedure).

Question 5: Volatilization Rate from an Open Vat of Spent MIBK (10 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. Vat plan dimensions $1.25\ \text{m}\times0.75\ \text{m}$ (depth $0.3\ \text{m}$ sets the vat's freeboard/capacity only — it does not enter a still-air surface-evaporation estimate). $T = 20^{\circ}\text{C}$. MIBK: $M = 100\ \text{g/mol}$, vapour pressure $VP = 15\ \text{mmHg}$. No forced ventilation/wind speed is stated, so the vat surface is treated as quiescent (still-air) — distillation feedstock storage vats are typically unagitated between batches.

Find. The estimated rate of volatilization (evaporation) of MIBK across the open vat surface.

Approach. Compute the exposed liquid surface area, then apply the ACGIH still-air solvent evaporation-rate correlation, which estimates the mass evaporation rate directly from the exposed area, the pure-component vapour pressure, and the molecular weight — the standard screening tool for exactly this "no forced air movement" scenario, since it needs no separately-measured diffusion coefficient or wind speed.

  1. Exposed surface area. Only the plan area of the vat is exposed to the headspace: $$A = 1.25\ \text{m}\times0.75\ \text{m} = 0.9375\ \text{m}^2 = 10.09\ \text{ft}^2$$
  2. Apply the still-air evaporation correlation. The ACGIH Industrial Ventilation Manual gives the evaporation rate of a solvent from a quiescent open surface as $$E\ (\text{lb/hr}) = 1.39\times10^{-5}\times A(\text{ft}^2)\times VP(\text{mmHg})\times M$$ Substituting $A = 10.09\ \text{ft}^2$, $VP = 15\ \text{mmHg}$, $M = 100$: $$E = 1.39\times10^{-5}\times10.09\times15\times100 = \boxed{0.210\ \text{lb/hr}}$$
  3. Convert to SI. $$E = 0.210\ \text{lb/hr}\times453.6\ \tfrac{\text{g}}{\text{lb}} = \boxed{95.4\ \text{g/hr}} \approx 0.0954\ \text{kg/hr} \approx 2.29\ \text{kg/day}$$
Final results
QuantityValue
Exposed surface area0.9375 m² (10.09 ft²)
Volatilization rate0.210 lb/hr $\approx$ 95.4 g/hr $\approx$ 2.29 kg/day
Check: the ACGIH correlation is a still-air (no mechanical ventilation, no significant cross-draft) screening estimate calibrated across common organic solvents; it bundles an average gas-phase diffusivity into its $1.39\times10^{-5}$ constant rather than computing one from first principles. Any real draft across the vat (open shop doors, an exhaust hood) would raise the true rate above this quiescent estimate — this is consistent with 15 mmHg being close to MIBK's actual vapour pressure at 20°C, i.e. the exam is using realistic solvent data for this correlation.