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18-Env-A1 Principles of Environmental Engineering · December 2013

Question 6 of 7: Disinfection Kinetics, Ecology and Treatment Principles

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National Exams — December 2013 — 04-Env-A1 / Principles of Environmental Engineering. 3 hours duration; closed book with an 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.); Guidelines for Canadian Drinking Water Quality (Health Canada); Canadian Council of Ministers of the Environment (CCME) water-quality guidelines; Canadian Environmental Protection Act, 1999 (CEPA).

Question 6: Disinfection Kinetics, Ecology and Treatment Principles (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.

(i) Chick–Watson Disinfection Kinetics

Given. 99% inactivation ($N(t_c)/N(0)=0.01$) achieved at $C\cdot t_c=\alpha=30\ \text{min}\cdot\text{mg/L}$.

Find. (a) the rate constant $k$ at $C=3\ \text{mg/L}$; (b) percentage inactivated at $C=0.5\ \text{mg/L}$, $t_c=50\ \text{min}$.

Check: part (b) uses a different $C\cdot t_c$ product (25 min·mg/L) than part (a)'s calibration point (30 min·mg/L), so the combined Chick–Watson model $N(t_c)/N(0)=\exp(-k'\,C\,t_c)$ with $n=1$ (consistent with Watson's Law as given) is used to extrapolate, rather than assuming 99% inactivation applies at every $C\cdot t_c$.

Approach. (a) Use Watson's Law to convert the given $C\cdot t_c$ target into a contact time at $C=3$ mg/L, then solve Chick's Law for $k$. (b) Recognize that $k$ at a fixed $C$ is the product of an underlying Chick–Watson coefficient $k'=k/C$ and the disinfectant concentration; use $k'$ with the new $C$ and $t_c$ to find the new inactivation ratio.

  1. (a) Contact time at C = 3 mg/L. From Watson's Law, $t_c = \alpha/C = 30/3 = 10\ \text{min}$.
  2. (a) Rate constant from Chick's Law. $0.01 = e^{-k(10)}$, so $$k = \frac{-\ln(0.01)}{10} = \boxed{0.4605\ \text{min}^{-1}}\ \text{at } C=3\ \text{mg/L}.$$
  3. (b) Chick–Watson coefficient. Since $k$ scales with $C$ (Watson's Law with $n=1$), $k' = k/C = 0.4605/3 = 0.1535\ \text{L/(mg}\cdot\text{min)}$.
  4. (b) Inactivation at the new conditions. With $C=0.5\ \text{mg/L}$, $t_c=50\ \text{min}$ (so $C\,t_c=25\ \text{min}\cdot\text{mg/L}$, below the 30 needed for exactly 99%), $$\frac{N(t_c)}{N(0)} = e^{-k' C t_c} = e^{-(0.1535)(25)} = e^{-3.838} = 0.0215.$$ Percentage inactivated $= (1-0.0215)\times100 = \boxed{97.9\%}$.
QuantityValue
Contact time at C = 3 mg/L for 99% kill10 min
Rate constant $k$ (at C = 3 mg/L)0.4605 min⁻¹
Chick–Watson coefficient $k'$0.1535 L/(mg·min)
% inactivated at C = 0.5 mg/L, 50 min≈ 97.9%

(ii) The Phosphorus Cycle

Unlike carbon or nitrogen, phosphorus has no significant atmospheric gas phase, so it cycles almost entirely through the lithosphere, hydrosphere and biosphere — a sedimentary cycle. The main components are: weathering of phosphate-bearing rock, which slowly releases orthophosphate ($\text{PO}_4^{3-}$) into soil and water; plant uptake of dissolved phosphate into biomass; transfer up the food chain as organisms consume plants and each other; and mineralization, in which decomposers return organic phosphorus to the soil/water as inorganic phosphate again, closing the biological loop. Because there is no atmospheric reservoir to buffer supply, phosphorus is very often the growth-limiting nutrient in freshwater systems (Liebig's law of the minimum), which is why phosphorus loading is the primary lever engineers manage to control eutrophication.

Two important sources: (1) phosphate-rock mining and its use in agricultural fertilizer, which mobilizes geological phosphorus into the active cycle far faster than natural weathering; and (2) municipal wastewater discharge (human waste and phosphate-containing detergents), a major point-source input to receiving waters. Two important sinks: (1) deep ocean and lake-bottom sediment deposition, which removes phosphorus from active cycling on a geological timescale; and (2) uptake and storage in terrestrial and aquatic biomass, a shorter-term biological sink that is continuously recycled through the food web.

(iii) Key Functions in Water/Wastewater Treatment

Primary sedimentation. A gravity-settling basin ahead of biological treatment that removes readily settleable solids and grit (typically 50–60% of TSS and 25–40% of BOD) by gravity alone, protecting downstream biological units from solids overload and reducing the sludge burden on subsequent processes.

pH control. Chemical addition (acid, lime, or CO₂ injection) that brings the water into the optimum range for downstream processes — coagulation/flocculation has an optimum pH window, and biological nitrification requires a near-neutral pH to proceed efficiently — and ensures the finished water or effluent meets discharge/drinking-water pH standards without corrosion or scaling problems in the distribution or collection system.

Filtration. A polishing step, typically through granular media (sand/anthracite) or membranes, that removes the fine residual suspended solids and associated turbidity/pathogens that gravity settling cannot capture, producing a clarified stream that meets turbidity targets ahead of final disinfection.