18-Env-B3 Contaminant Transport · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2013 — 04-Env-B3 / Contaminant Transport. 3 hours duration; closed-book exam (any non-communicating calculator permitted). The paper prints five problems, each worth 25 marks; the source notes state that only the first four problems as they appear in the answer book are marked and that any of a problem's sub-parts may be treated independently. All five are solved below for completeness. The source labels a second, unrelated sub-part of Problem 1 as another “(a)” (a printing quirk noted on the extraction) — it is presented here as Problem 1(c) for clarity, with its own three roman-numeral parts kept intact.
Reference texts. Davis & Cornwell, Introduction to Environmental Engineering (6th ed.); Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery (5th ed.); Freeze & Cherry, Groundwater; Cooper & Alley, Air Pollution Control: A Design Approach; Wark, Warner & Davis, Air Pollution: Its Origin and Control.
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.
Normally the atmosphere cools with height, which is what allows the convective mixing described in Problem 2(c). A temperature inversion is a layer in which this reverses — temperature increases with height — and because warm air overlying cooler, denser air is exceptionally stable (an extreme case of the stable condition in Problem 2(c)(ii)), an inversion layer acts as a lid that traps vertical mixing and, with it, any pollutants released beneath it. Four types are commonly distinguished: (1) Radiation (nocturnal) inversions form on clear, calm nights when the ground radiates heat away rapidly, cooling the air immediately above it faster than the air aloft; they typically dissipate within an hour or two after sunrise as solar heating re-establishes normal mixing. (2) Subsidence inversions occur when a large mass of air in a high-pressure system slowly sinks and is compressed, warming adiabatically as it does so, capping the cooler surface air below — these can persist for days and are responsible for the worst multi-day urban smog episodes. (3) Frontal inversions form where a warm air mass overrides a retreating cold air mass along a weather front, with the temperature reversal occurring at the sloped frontal surface rather than at a fixed elevation. (4) Advective inversions occur when warm air moves horizontally over a colder surface (e.g. warm air over a cold lake, or over snow cover), cooling the near-surface layer by conduction from below. All four share the same air-quality consequence: whatever pollutant mass is emitted into the trapped layer accumulates rather than disperses, until the inversion breaks.
Given. A completely-mixed (CSTR) lagoon receiving Q = 430 m³/day of raw sewage at C0 = 180 mg/L; lagoon surface area = 100,000 m², depth = 1 m; first-order decay constant k = 0.70 d−1; steady state, no net water loss/gain.
| Quantity | Symbol | Value |
|---|---|---|
| Inflow rate | Q | 430 m³/d |
| Influent concentration | C₀ | 180 mg/L |
| Lagoon surface area | A | 100,000 m² |
| Lagoon depth | d | 1 m |
| First-order decay constant | k | 0.70 d−1 |
Find. The pollutant concentration C in the lagoon effluent at steady state.
Approach. Write a steady-state mass balance on a completely-mixed reactor (CSTR) with first-order decay of the pollutant.
| Quantity | Value |
|---|---|
| Lagoon volume, V | 100,000 m³ |
| Hydraulic retention time, τ | 232.6 d |
| Effluent pollutant concentration, C | 1.10 mg/L |
| Removal efficiency | 99.4% |
Advection is the transport of a dissolved or suspended chemical by the bulk, directed motion of the carrying fluid itself — the chemical simply rides along with the river current or the prevailing wind, moving at (or very close to) the fluid's own velocity, with no net redistribution of mass relative to the fluid. Diffusion (molecular diffusion, and its much larger environmental analogue, turbulent/eddy diffusion or dispersion) is transport driven by a concentration gradient rather than by bulk fluid motion: random molecular or turbulent-eddy motion tends to spread a chemical from where it is concentrated toward where it is dilute, even in still or uniformly-moving fluid, until the gradient is erased. The key differentiator is therefore the driving force and its dependence on concentration structure: advective flux scales with the fluid velocity and is independent of the concentration gradient's shape, whereas diffusive flux is exactly proportional to (and driven by) the local concentration gradient and vanishes once the chemical is uniformly mixed. In a real river or plume, both act simultaneously — advection carries the pollutant cloud downstream/downwind while diffusion spreads and dilutes it as it travels, which is precisely the combination modelled by the Gaussian plume equation used in Problem 5(a).
The governing one-dimensional flux equations are:
$$J_{advection} = u\,C$$ $$J_{diffusion} = -D\,\frac{\partial C}{\partial x}$$where J is the mass flux per unit cross-sectional area (mass · area−1 · time−1), u is the fluid (or wind) velocity, C is the local concentration, and D is the diffusion (or dispersion) coefficient; the diffusive form is Fick's First Law, and the negative sign reflects that mass flows from high to low concentration — down the gradient.
