pH Control, Ion Exchange, Reverse Osmosis and Activated Sludge Design: 23-Chem-B2 Environmental Engineering, Undated paper, 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) Operating approach and monitoring method

Technology	Example application	Key operating approach	Monitoring method
(a) pH control	Precipitating Cr and Cu from metal-finishing wastewater as insoluble hydroxides (any Cr(VI) is first reduced to Cr(III) at low pH).	Reagent (lime/caustic) dose is trimmed continuously against the wastewater's own titration/buffering curve, not a fixed setpoint, since alkalinity varies with influent and shifts how much reagent is needed to reach the target pH window where both metals' hydroxides are minimally soluble.	In-line pH probes (calibrated daily against certified buffer standards) with a feedback-controlled reagent-metering pump; periodic grab-sample ICP-MS analysis of the settled effluent confirms Cr/Cu are actually being removed to the target residual, not just that pH is in range.
(b) Ion exchange	Softening a hard surface-water supply by exchanging Ca²⁺/Mg²⁺ for Na⁺ on a strong-acid cation resin.	Bed operation is stopped and the resin regenerated with brine before the exchange capacity is exhausted, using either a fixed throughput volume or an on-line hardness set point as the regeneration trigger, whichever is reached first.	Continuous or frequent effluent hardness titration (EDTA titrimetric method); a rising hardness trend signals approaching breakthrough before the resin is fully exhausted.
(c) Reverse osmosis	Removing total dissolved solids from a brackish groundwater supply.	Feed (applied) pressure is maintained comfortably above the rising osmotic pressure of the increasingly concentrated reject stream, and antiscalant dosing/periodic membrane flushing prevent scaling that would otherwise force pressure up further and damage the membrane.	Continuous permeate conductivity (or TDS) monitoring combined with tracking normalized permeate flux and salt rejection over time, which reveals membrane fouling or scaling (declining flux/rejection at constant pressure) before a hard failure occurs.

(ii) Activated sludge preliminary process design

Given.

Quantity	Value
Flow, Q₀	100,000 m³/d
Influent BOD₅, S₀	200 mg/L
Effluent BOD₅, S	15 mg/L
Yield coefficient, Y	0.6
Decay rate, k_d	0.04 d⁻¹
MLSS, X	4,000 mg/L
Waste MLSS, X_w	10,000 mg/L
Mean cell residence time, θ_c	10 d

Find. (a) Aeration tank volume V (m³) and HRT θ (h). (b) Sludge wasted daily Q_w (kg/d). (c) Recycle ratio R=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, the net biomass production converts (via the waste MLSS concentration) into a volumetric wasting rate, and a solids balance at the aeration-tank inlet gives the recycle ratio.

Aeration tank volume from the design-SRT relation. $V = \frac{Y\,\theta_c\,Q_0\,(S_0-S)}{X\,(1+k_d\,\theta_c)} = \frac{0.6\times10\times100{,}000\times(200-15)}{4{,}000\times(1+0.04\times10)}$ $V = \frac{111{,}000{,}000}{5{,}600} = \boxed{19{,}821\ \text{m}^3}$
Hydraulic retention time. $\theta = \frac{V}{Q_0}\times24 = \frac{19{,}821}{100{,}000}\times24 = \boxed{4.76\ \text{h}}$
Sludge wasted daily (mass basis, as asked). At steady state the sludge wasted each day equals the net biomass production rate P_x (effluent solids neglected): $Q_w = P_x = \frac{Y\,Q_0\,(S_0-S)}{1+k_d\,\theta_c} = \frac{0.6\times100{,}000\times185\ \text{g/d}}{1.4}$ $Q_w = \boxed{7{,}929\ \text{kg/d}}$
For pump sizing, this corresponds to a waste-sludge flow of 7,929 kg/d ÷ 10.0 kg/m³ ≈ 793 m³/d drawn from the clarifier underflow at X_w = 10,000 mg/L.
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: $R = \frac{Q_r}{Q_0} = \frac{X}{X_w-X} = \frac{4{,}000}{10{,}000-4{,}000} = \boxed{0.67}$

Quantity	Value
Aeration tank volume, V	19,821 m³
Hydraulic retention time, θ	4.76 h
Sludge wasted daily, Q_w	7,929 kg/d (≈ 793 m³/d at X_w)
Recycle ratio, R	0.67

Topic: pH control, ion exchange, reverse osmosis operating/monitoring 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); Q_w=P_x/X_w; recycle ratio R=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; the waste-sludge volumetric rate is simply the mass production rate divided by whatever concentration the sludge is actually wasted at (X_w), which is why Q_w and P_x differ from one plant design to another even at the same P_x.

Common pitfall: Giving only the volumetric waste flow (m³/d) when the question asks for Q_w in kg/d (an easy unit-target mismatch); running an RO system with the applied pressure only marginally above the osmotic pressure, leaving little net driving force as the reject stream concentrates along the module.

Source: Davis & Cornwell, Introduction to Environmental Engineering, 5th ed., Ch. 6 (ion exchange, membrane processes); Metcalf & Eddy, Wastewater Engineering, 4th ed., Ch. 8 (activated-sludge process design).

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) Operating approach and monitoring method

(ii) Activated sludge preliminary process design