Dilution Ventilation for a Fugitive Solvent Leak and Risk Management: 24-MMP-B4 Mine Ventilation and Occupational Hygiene, May 2014, Q6

Question 6: Dilution Ventilation for a Fugitive Solvent Leak and Risk Management (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.

Note: the source booklet labels both sub-parts of this question "a)"; the second is answered here as (b), and reads "Solvent A" after first naming the solvent "RXP" (the same substance) — treated as one solvent throughout, per the source's own inline note.

(a) Dilution ventilation rate for fugitive RXP/Solvent-A emission

Part (a) — This sub-part uses the “average” mixing condition, expressed here as the reciprocal $k=1/5$ of the ACGIH mixing factor $K=5$, an equivalent mixing-efficiency convention.

Given. Evaporation rate 3.0 gal per 8-hour shift; TLV-TWA = 50 ppm; $T=77\ ^\circ\text{F}$, $P=1$ atm; $SG=0.85$; $MW=145$; mixing condition "average", $k=1/5$.

Find. The dilution air flow rate required to keep the area below the TLV.

Approach. Convert the liquid evaporation rate to a molar vapour generation rate, use the ideal gas law at the stated conditions to get the pure-vapour volumetric generation rate, then divide by the TLV (as a volume fraction) and scale up by the imperfect-mixing factor. The exam states this as an efficiency $k=1/5$ ("average" mixing is less than ideal), so the actual required airflow is the ideal (perfect-mixing) airflow divided by $k$ — equivalently, multiplied by $K=1/k=5$, ACGIH's usual "average" mixing-factor value expressed the more common way round.

Liquid evaporation rate. $$ER=\frac{3.0\ \text{gal}}{8\times60\ \text{min}}=0.00625\ \text{gal/min}$$
Mass and molar generation rate. Liquid density $\rho_L=SG\times8.34=0.85\times8.34=7.09\ \text{lb/gal}$: $$\dot m=ER\times\rho_L=0.00625\times7.09=0.0443\ \text{lb/min}$$ $$\dot n=\frac{\dot m}{MW}=\frac{0.0443}{145}=0.000306\ \text{lbmol/min}$$
Vapour volumetric generation rate (ideal gas, 77°F, 1 atm). $$\dot V_{vap}=\frac{\dot nRT}{P}=\frac{(0.000306)(10.731)(537)}{14.696}=\boxed{0.12\ \text{ft}^3/\text{min pure vapour}}$$
Required dilution air flow. Dividing by $k=1/5$ is the same as multiplying by $K=5$: $$Q=\frac{\dot V_{vap}}{TLV\times k}=\frac{0.12}{(50\times10^{-6})(1/5)}=\boxed{11{,}982\ \text{ft}^3/\text{min}}$$

Quantity	Value
Vapour generation rate (pure solvent)	0.12 ft³/min
Required dilution ventilation rate, $Q$ ($k=1/5$)	≈ 11,982 ft³/min (≈ 339 m³/h)

Roughly 12,000 cfm of dilution air is needed to hold this fugitive emission below its TLV even though the raw vapour generation rate is only about 0.12 ft³/min of pure solvent — the TLV of 50 ppm is a 20,000:1 dilution ratio on its own, and the imperfect-mixing factor multiplies that by another 5× because real room air never mixes perfectly with a point-source leak.

Check: "average" ventilation condition ($k=1/5$, i.e. $K=5$) is taken as the ACGIH mid-point mixing factor for fair/average mixing effectiveness; a poorer-mixing facility would require proportionally more airflow for the identical leak.

(b) Risk Management steps

Part (b) — Risk management in a hazardous operation follows a cyclical, proactive sequence rather than a one-time calculation, and is best contrasted with the purely reactive (post-accident) response it is designed to replace:

Fig. 6b — The five-step proactive risk-management cycle, contrasted with a purely reactive (post-accident) response.

Hazard identification. Systematically identify every hazard present in the operation (e.g. process hazard reviews, HAZOP, job safety analyses).
Risk assessment. For each identified hazard, estimate the likelihood and severity of harm and rank hazards by the resulting risk level.
Control design. Select controls for the highest-ranked risks, following the hierarchy of controls (elimination/substitution preferred over engineering, administrative, and PPE measures).
Training and SOPs. Implement the chosen controls through written procedures and worker training so they are actually followed in practice.
Audit and review. Periodically verify that controls remain effective and that no new hazards have been introduced, feeding findings back into a fresh round of hazard identification — closing the loop.

Example. Applied to this paper's own Question 6(a) scenario: a Ni refinery first identifies the fugitive RXP/Solvent-A emission as a hazard (hazard ID), assesses that 3.0 gal/shift evaporating into an averagely-mixed process area drives the airborne concentration well above what a 50 ppm TLV allows without active control (risk assessment — this is exactly the calculation in part (a)), designs the 12,000 cfm dilution system plus, ideally, source controls such as better solvent-transfer containment (control design, preferring elimination of the fugitive path over ventilation alone), trains operators on leak detection and confirms the ventilation system's rated airflow against the design requirement before start-up (implementation), and then periodically re-measures airborne solvent concentration and ventilation performance to confirm the control remains effective as equipment ages or process rates change (audit and review) — demonstrating why risk management is a continuing operational discipline, not a single calculation performed once at design time.

Topic: Dilution ventilation design and the risk-management cycle.

Key relations: $$Q=\frac{\dot V_{vap}}{TLV\times K^{-1}}=\frac{\dot V_{vap}}{TLV}\times K$$ five-step risk-management cycle (hazard ID → risk assessment → control design → training/SOPs → audit/review, looping back to hazard ID).

Why this works: the dilution-ventilation formula is simply a molar (or volumetric) mass balance on the contaminant — generation rate in, dilution airflow out, at steady state — scaled up by an empirical mixing-effectiveness factor because real ventilation air never achieves the perfect, instantaneous mixing the basic balance assumes; the risk-management cycle is deliberately closed-loop because hazards, controls, and operating conditions all change over the life of a facility, so a single point-in-time assessment goes stale.

Common pitfall: inverting the mixing-factor convention (dividing by $K$ instead of multiplying, or multiplying by $k$ instead of dividing) — always check that a poorer-mixing condition increases, never decreases, the required dilution airflow; and, for risk management, treating it as a one-time sign-off rather than the continuous audit/review loop shown above.

Source: ACGIH, Industrial Ventilation: A Manual of Recommended Practice (dilution ventilation, mixing factor $K$); Crowl & Louvar, Chemical Process Safety, Ch. 1 (risk management).

Question 6 of 6: Dilution Ventilation for a Fugitive Solvent Leak and Risk Management

Question 6: Dilution Ventilation for a Fugitive Solvent Leak and Risk Management (20 marks)

(a) Dilution ventilation rate for fugitive RXP/Solvent-A emission

(b) Risk Management steps