18-Env-A1 Principles of Environmental Engineering · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2016 — 04-Env-A1 / Principles of Environmental Engineering. 3 hours duration; closed book with an 8×11 in double-sided aid sheet; Casio or Sharp approved calculator only. Any five questions constitute a complete paper (first five answers marked); all seven are solved below for completeness. Each question is worth 20 marks.
Reference texts. Davis & Cornwell, Introduction to Environmental Engineering (6th ed.); Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery (5th ed.); MWH’s Water Treatment: Principles and Design (3rd ed.); Guidelines for Canadian Drinking Water Quality (Health Canada); Canadian Council of Ministers of the Environment (CCME) water-quality and landfill guidelines; Canadian Environmental Protection Act, 1999 (CEPA); Impact Assessment Act, 2019 (Canada); Andrews, Canadian Professional Engineering and Geoscience (professional ethics).
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. Lake mass-balance data for total phosphorus (TP), as printed on the exam:
| Quantity | Symbol | Value |
|---|---|---|
| Lake volume | $V$ | $1\times10^{4}$ m³ |
| River inflow | $Q_u$ | $1\times10^{3}$ m³/yr |
| Evaporation loss | $Q_e$ | $4\times10^{4}$ m³/yr |
| Lake outflow | $Q_o$ | $2\times10^{4}$ m³/yr |
| Inflow TP concentration | $C_u$ | 25 mg/L |
| TP decay rate in lake | $k$ | 0.05 /yr |
Find. The steady-state TP concentration $C$ in the (well-mixed) lake and in its outflow stream.
Approach. Model the lake as a single well-mixed (CSTR) reactor and write a steady-state mass balance on TP, with first-order decay removing mass within the lake volume; the outflow leaves at the lake's own (uniform) concentration.
| Quantity | Value |
|---|---|
| Effective removal capacity, $Q_o+kV$ | $2.05\times10^{4}$ m³/yr |
| Steady-state lake TP concentration, $C$ | 1.22 mg/L |
| Steady-state outflow TP concentration | 1.22 mg/L (same as the lake, well-mixed) |
The Freundlich isotherm $q = KC^{1/n}$ is an empirical relation describing equilibrium partitioning of a dilute solute (here, a PAH) between the dissolved phase and a solid sorbent (soil/aquifer particles) once sorption equilibrium has been reached. Each term carries a distinct physical meaning:
$q$ is the equilibrium sorbed-phase concentration — the mass of PAH sorbed per unit mass of solid (e.g., mg PAH per kg soil). It is the quantity of contaminant effectively immobilized on the solid matrix at equilibrium.
$C$ is the equilibrium dissolved-phase (aqueous) concentration of the PAH remaining in the groundwater once sorption equilibrium is reached (e.g., mg/L). $q$ and $C$ are the two coordinates measured (or predicted) at equilibrium.
$K$ is the Freundlich capacity coefficient: it sets the overall magnitude of sorption — a larger $K$ means the soil sorbs more PAH mass at a given aqueous concentration, reflecting properties such as organic-carbon content, mineral surface area and the PAH's own hydrophobicity (higher-molecular-weight, more hydrophobic PAHs generally have larger $K$).
$1/n$ is the intensity (or heterogeneity) exponent: it describes how sorption capacity changes with concentration and reflects the energetic heterogeneity of sorption sites on the solid surface. When $1/n = 1$ the isotherm is linear (constant partition coefficient $K_d$); when $1/n < 1$ the isotherm is favourable/concave — sorption capacity increases less than proportionally as $C$ rises, typical of dilute organic-contaminant sorption onto natural soil organic matter, which is the regime this question specifically flags ("dilute concentrations").
Source waters carry pathogens with markedly different resistance to disinfection, so a treatment train must be designed around the most resistant organism actually present, not just the easiest to kill.
Bacteria (e.g., E. coli, Salmonella) are vegetative, metabolically active cells with a relatively permeable cell wall; disinfectants readily penetrate and damage their enzymes and membranes, so bacteria are comparatively easy to inactivate at modest disinfectant exposure. Protozoan cysts/oocysts (e.g., Giardia lamblia cysts, Cryptosporidium parvum oocysts) are dormant, thick-walled resting stages specifically evolved to survive harsh environmental conditions; they are dramatically more resistant to chemical disinfection — Cryptosporidium in particular is highly resistant to chlorine at the doses/times normally used in drinking-water practice — so they typically govern the design disinfection requirement (or are instead targeted by physical removal, such as filtration, or by UV, to which they are comparatively susceptible).
The two parameters routinely varied by the engineer to achieve adequate inactivation of whichever organism governs the design are the disinfectant dose (concentration $C$, for chemical disinfectants, or delivered UV fluence for UV systems) and the contact/exposure time ($T$, or $t$ for UV). For chemical disinfection these combine into the CT (or C·T) product, and regulators publish minimum CT tables by organism, since bacteria require a far smaller CT than Giardia cysts, which in turn require far less CT than would be needed for Cryptosporidium by chlorine alone (hence UV or ozone is often selected specifically for Cryptosporidium control). Temperature and pH are secondary parameters that also shift the required CT, but dose and time are the two primary design levers.
