pH Control, Ion Exchange, Reverse Osmosis and Activated Sludge Design: 23-Chem-B2 Environmental Engineering, December 2019, Q4

Problem 4: pH Control, Ion Exchange, Reverse Osmosis and Activated Sludge Design (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) pH control, ion exchange and reverse osmosis — example and design parameter

Technology	Example application	Key process design parameter
(a) pH control	Neutralizing low-pH industrial (e.g. metal-finishing) wastewater with lime or caustic soda before biological treatment.	Reagent dose set from the wastewater's titration (buffering) curve, not just its raw pH, because alkalinity/acidity determines how much reagent is actually needed to shift the pH into the target range.
(b) Ion exchange	Softening a hard groundwater supply by exchanging Ca₂⁺/Mg₂⁺ for Na⁺ on a strong-acid cation resin.	Resin exchange capacity (equivalents of hardness removable per unit resin volume before breakthrough), which sets the bed volume and regeneration (brine) frequency for a given raw-water hardness and flow.
(c) Reverse osmosis	Desalinating brackish groundwater or polishing tertiary wastewater effluent for potable reuse.	Operating pressure relative to the feedwater's osmotic pressure — the applied pressure must exceed the osmotic pressure of the (increasingly concentrated) reject stream by enough net driving pressure to sustain the target permeate flux across the membrane.

(ii) Activated sludge preliminary process design

Given.

Quantity	Value
Flow, Q₀	200,000 m³/d
Influent BOD₅, S₀	250 mg/L
Effluent BOD₅, S	10 mg/L
Yield coefficient, Y	0.4
Decay rate, k_d	0.05 d⁻¹
MLSS, X	5,000 mg/L
Waste MLSS, X_w	12,000 mg/L
Mean cell residence time, θ_c	8 d

Find. (a) Aeration tank volume V (m³) and HRT θ (h). (b) Sludge wasted daily Q_w (kg/d). (c) Recycle ratio Q_r/Q₀.

Approach. Classic Lawrence–McCarty design-SRT formulation: a biomass steady-state mass balance over the aeration tank + clarifier at the fixed target SRT gives the tank volume directly, the net biomass production sets the daily wasted-sludge mass, and a solids balance at the aeration-tank inlet gives the recycle ratio.

Aeration tank volume from the design-SRT relation. $V = \frac{Y\,\theta_c\,Q_0\,(S_0-S)}{X\,(1+k_d\,\theta_c)} = \frac{0.4\times8\times200{,}000\times(250-10)}{5{,}000\times(1+0.05\times8)}$ $V = \frac{153{,}600{,}000}{7{,}000} = \boxed{21{,}943\ \text{m}^3}$
Hydraulic retention time. $\theta = \frac{V}{Q_0} = \frac{21{,}943}{200{,}000} = 0.1097\ \text{d} = \boxed{2.63\ \text{h}}$
Sludge wasted daily from the net biomass yield. $P_x = \frac{Y\,Q_0\,(S_0-S)}{1+k_d\,\theta_c} = \frac{0.4\times200{,}000\times(250-10)}{1.4\times1000} = \boxed{13{,}714\ \text{kg/d}}$
Recycle ratio from the aeration-tank solids balance. A steady-state solids balance around the aeration-tank inlet (Q₀X₀≈0, return-line concentration X_r=X_w) gives (Q₀+Q_r)X = Q_rX_w, which rearranges to: $\alpha = \frac{Q_r}{Q_0} = \frac{X}{X_w-X} = \frac{5{,}000}{12{,}000-5{,}000} = \boxed{0.71}$

Quantity	Value
Aeration tank volume, V	21,943 m³
Hydraulic retention time, θ	2.63 h
Sludge wasted daily, P_x	13,714 kg/d
Recycle ratio, Q_r/Q₀	0.71

Topic: pH control, ion exchange, reverse osmosis design basis; Lawrence–McCarty activated-sludge preliminary process design.

Key relations: V=Yθ_cQ₀(S₀−S)/[X(1+k_dθ_c)]; P_x=YQ₀(S₀−S)/(1+k_dθ_c); recycle ratio α=X/(X_w−X); RO net driving pressure > osmotic pressure.

Why this works: Fixing θ_c (mean cell residence time) rather than θ (hydraulic retention time) is what decouples biomass concentration from flow-through time via recycle; here a higher waste-MLSS concentration (X_w=12,000 mg/L) relative to X (5,000 mg/L) than a typical plant gives a comparatively low recycle ratio (0.71) — less return flow is needed to maintain the target MLSS when the return-line solids are already highly concentrated.

Common pitfall: Swapping X and X_w in the recycle-ratio formula (inverts the answer); forgetting that RO operating pressure must overcome the osmotic pressure of the concentrated reject stream, not just the feed.

Source: Metcalf & Eddy, Wastewater Engineering, 4th ed., Ch. 8 (activated sludge design); Davis & Cornwell, Introduction to Environmental Engineering, 5th ed., Ch. 6 (pH control, ion exchange, reverse osmosis).

Question 4 of 7: pH Control, Ion Exchange, Reverse Osmosis and Activated Sludge Design

Problem 4: pH Control, Ion Exchange, Reverse Osmosis and Activated Sludge Design (20 marks)

(i) pH control, ion exchange and reverse osmosis — example and design parameter

(ii) Activated sludge preliminary process design