18-Env-A1 Principles of Environmental Engineering · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2017 — 04-Env-A1 / Principles of Environmental Engineering. 3 hours duration; closed book with a candidate-prepared 8.5×11 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.); Sawyer, McCarty & Parkin, Chemistry for Environmental Engineering and Science; Mihelcic & Zimmerman, Environmental Engineering: Fundamentals, Sustainability, Design; Guidelines for Canadian Drinking Water Quality (Health Canada); Canadian Council of Ministers of the Environment (CCME) water-quality and municipal solid-waste guidelines; Canadian Environmental Protection Act, 1999 (CEPA) and Canadian Environmental Assessment Act (CEAA 2012); ISO 14040/14044 (Life Cycle Assessment); Bies & Hansen, Engineering Noise Control; 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. A CSTR at steady state with first-order decay $dC/dt=-kC$, $k=0.25\ \text{d}^{-1}$, reactor volume $V=1000\ \text{m}^3$, inflow $Q=100\ \text{m}^3/\text{d}$, inlet concentration $C_{in}=200\ \text{mg/L}$.
Find. The steady-state outlet concentration $C_{out}$.
Approach. Write the completely-mixed steady-state mass balance on the reactor (accumulation = in − out − reaction loss) and solve directly for $C_{out}$.
For context, the hydraulic retention time is $\theta = V/Q = 1000/100 = 10\ \text{d}$ and the Damköhler number $k\theta = 2.5$, giving an overall contaminant removal efficiency of $(1-C_{out}/C_{in})\times100\% = 71.4\%$ — a useful cross-check, since a Damköhler number of order 1–3 is consistent with a completely-mixed reactor removing roughly two-thirds to three-quarters of the incoming load. A CSTR always under-performs an equal-volume plug-flow reactor for the same first-order kinetics, because the reaction proceeds throughout the tank at the already-diluted outlet concentration rather than declining progressively along the flow path.
| Quantity | Value |
|---|---|
| Hydraulic retention time $\theta$ | 10 d |
| Steady-state outlet concentration $C_{out}$ | 57.1 mg/L |
| Overall removal efficiency | 71.4% |
A contaminant with $K_{OW} \ge 4$ (log-scale, so a true octanol-water ratio of at least $10^4$) is strongly lipophilic: it has a very low affinity for the aqueous phase relative to organic or lipid-rich phases. Once emitted to the atmosphere, semi-volatile organics of this kind typically undergo wet and dry deposition onto a lake surface, or partition directly from the gas phase into the surface water via Henry’s Law equilibrium — this is the air-to-water transfer step, driven primarily by the compound’s volatility and its air–water partition behaviour rather than by $K_{OW}$ itself.
Within the water compartment, $K_{OW}$ becomes the controlling parameter. The distribution (partition) coefficient $K_d$ generalizes the octanol-water idea to real environmental sorbing phases: $K_d = C_{sorbed}/C_{water}$, and for neutral organic contaminants it correlates strongly with $K_{OW}$ through the organic-carbon partition coefficient, $K_{oc} \approx 0.41\,K_{OW}$ (a commonly used correlation), with $K_d = f_{oc}K_{oc}$ where $f_{oc}$ is the fraction organic carbon of the sorbing phase — fish lipid content plays the same role for a fish as sediment organic carbon plays for bed sediment. Because $K_{OW}\ge4$ means the contaminant favours a lipid-mimicking phase over water by a factor of $10^4$ or more, it preferentially partitions out of the dissolved phase and into fish lipid tissue rather than remaining in solution. The bioconcentration factor (BCF), which for many nonpolar organics correlates empirically with $K_{OW}$ (commonly $\log BCF \approx \log K_{OW} - 1$ across a wide range of compounds), rises sharply once $\log K_{OW}$ exceeds about 4–5.
The overall fate across the three compartments is therefore sequential and asymmetric: atmospheric transport and deposition move the contaminant from air to water relatively quickly (a physically driven step governed by volatility and precipitation scavenging); but once in the water, the high $K_{OW}$ drives a slow, thermodynamically favoured net transfer out of the dissolved phase and into fish lipid tissue, where uptake outpaces metabolism and elimination. Fish become the ultimate environmental sink of the three compartments, and because predators consume contaminated prey, the body burden can further biomagnify up the food chain — the hallmark behaviour of persistent, high-$K_{OW}$ organic pollutants such as PCBs, DDT and other legacy organochlorines.
Bacterial indicator organisms (classically total/fecal coliforms, and today more specifically E. coli or enterococci) are used because it is impractical to test drinking water directly for every pathogen of concern: culturing and identifying actual disease-causing bacteria, viruses and protozoa individually is slow, expensive and technically demanding for a routine monitoring program, whereas an indicator organism is inexpensive and rapid to detect, and its presence signals that fecal contamination has occurred and/or that disinfection has failed to achieve an adequate log-reduction of enteric organisms generally.
Two advantages of indicator testing: (1) the tests are inexpensive, fast (often 18–24 h) and use standardized, widely available culture methods, making frequent routine monitoring across an entire distribution system practically and economically feasible in a way that pathogen-specific testing is not; (2) a well-established statistical and epidemiological correlation exists between indicator presence and elevated risk of gastrointestinal illness, so a positive result is a defensible, regulator-recognized trigger for a boil-water advisory or corrective action without requiring pathogen-specific confirmation first.
Two limitations of relying on indicators alone: (1) many indicator bacteria are considerably less resistant to chlorine disinfection than protozoan cysts/oocysts (Giardia, Cryptosporidium) and some enteric viruses, so the absence of the indicator does not guarantee the absence or inactivation of these more resistant pathogens — a false sense of security for public health; (2) indicator organisms can regrow or be reintroduced within the distribution system itself (biofilms, cross-connections, main breaks) independent of how well the treatment plant is performing, so a positive indicator result downstream does not always mean the source water or treatment process is compromised, which can complicate identifying the true root cause.
