pH control, ion exchange and reverse osmosis design principles, and activated-sludge process design: 23-Chem-B2 Environmental Engineering, May 2015, Q4

Question 4: pH control, ion exchange and reverse osmosis design principles, and activated-sludge process 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) Design principle and O&M parameter per technology

Technology	Key design principle	Important O&M parameter
(a) pH control	The reagent dose (lime, caustic, or acid) must be sized against the influent's actual titration/buffering curve, not a naive stoichiometric target, since a poorly buffered stream can swing far past a pH set-point on a small overdose.	Continuous in-line pH monitoring feeding a closed-loop dosing-pump control (not a static, un-monitored dose), since influent pH/flow can vary faster than a manual adjustment can track.
(b) Ion exchange	Resin exchange capacity and selectivity must be matched to the target ion against the competing-ion background (e.g. strong-acid cation resin affinity Ca²⁺>Mg²⁺>Na⁺), since a high concentration of a competing higher-affinity ion prematurely exhausts capacity for the target.	Defined breakthrough monitoring (effluent hardness/target-ion trigger) governing the regeneration cycle (brine dose, frequency), since exchange efficiency falls sharply once breakthrough begins.
(c) Reverse osmosis	Applied pressure must exceed the feed osmotic pressure by a sufficient net driving pressure for the target flux/recovery; higher-TDS feed requires correspondingly higher operating pressure and membrane/vessel rating.	Pretreatment performance monitoring (fine filtration, antiscalant dose) and periodic membrane cleaning-in-place, since fouling/scaling of the concentrating reject stream is the dominant driver of RO operating cost and membrane life.

Given.

Quantity	Symbol	Value
Influent flow	$Q_0$	$500{,}000\ \text{m}^3/\text{d}$
Influent BOD₅/TSS	$S_0$	$200\ \text{mg/L}$
Effluent BOD₅/TSS	$S$	$2\ \text{mg/L}$
Yield coefficient	$Y$	$0.7$
Decay rate	$k_d$	$0.04\ \text{d}^{-1}$
Mean cell residence time	$\theta_c$	$20\ \text{d}$
Mixed-liquor suspended solids	$X$	$4{,}000\ \text{mg/L}$
Waste (recycle) MLSS	$X_w$	$12{,}000\ \text{mg/L}$

Find. (a) Aeration tank volume $V$ and HRT $\tau$. (b) Daily sludge mass wasted $Q_w$ (kg/d). (c) Recycle ratio $Q_r/Q_0$.

Approach. The Lawrence–McCarty SRT-based design equation sizes the aeration tank directly from $\theta_c$, $Y$, $k_d$ and the substrate removed; sludge production follows from the same substrate balance, and the recycle ratio comes from a pure solids balance around the clarifier, independent of the biological kinetics.

Aeration tank volume. $$V=\frac{\theta_c\,Y\,Q_0(S_0-S)}{X(1+k_d\theta_c)}=\frac{20\times0.7\times500{,}000\times(200-2)}{4{,}000\times(1+0.04\times20)}=192{,}500\ \text{m}^3$$ ==**V = 192,500 m³**==
Hydraulic retention time. $$\tau=\frac{V}{Q_0}\times24=\frac{192{,}500}{500{,}000}\times24=9.24\ \text{h}$$ ==**τ = 9.24 h**==
Daily sludge mass wasted. $$Q_w=P_x=\frac{Y\,Q_0(S_0-S)}{1+k_d\theta_c}=\frac{0.7\times500{,}000\times198}{1.8}=38{,}500\ \text{kg/d}$$ ==**Qw = 38,500 kg/d**==
Cross-check via the SRT identity. Independently, $Q_w=VX/\theta_c=(192{,}500\times4{,}000\times10^{-3})/20=38{,}500\ \text{kg/d}$ — the two routes agree exactly, confirming $V$ and $Q_w$ are internally consistent.
Sludge recycle ratio. A solids balance around the clarifier alone (no biology, no $\theta_c$) gives $$\frac{Q_r}{Q_0}=\frac{X}{X_w-X}=\frac{4{,}000}{12{,}000-4{,}000}=0.5$$ ==**Qr/Q0 = 0.5**==

Quantity	Result
Aeration tank volume	192,500 m³
Hydraulic retention time	9.24 h
Sludge wasted daily	38,500 kg/d
Recycle ratio $Q_r/Q_0$	0.5

Fig. 3: Conventional activated-sludge process flow — aeration tank → secondary clarifier, with return activated sludge (RAS) recycled to the aeration tank inlet and waste activated sludge (WAS) removed from the RAS line to solids handling.

Check — recycle-ratio independence from θ𝑐

The recycle ratio $Q_r/Q_0=X/(X_w-X)$ follows purely from a steady-state solids mass balance across the clarifier/recycle split and does not depend on $\theta_c$, $Y$ or $k_d$ — a useful self-check, since an answer that appears to need the biokinetic parameters for part (c) signals an error.

Concept & Theory

Topic. pH neutralization, ion exchange and reverse osmosis design fundamentals, and SRT-based activated-sludge process design.

Key relations. $V=\theta_c Y Q_0(S_0-S)/[X(1+k_d\theta_c)]$; $P_x=Y Q_0(S_0-S)/(1+k_d\theta_c)=VX/\theta_c$; $Q_r/Q_0=X/(X_w-X)$.

Why this works. Sizing the reactor directly from the target mean cell residence time (rather than from an assumed F/M ratio) is the modern, mechanistically grounded design approach because $\theta_c$ is what actually controls whether the biomass (particularly slow-growing populations, e.g. nitrifiers) can be sustained; the recycle ratio is a pure mass balance because, at steady state, the solids entering the clarifier must exactly equal the solids leaving via RAS+effluent, independent of the biological reaction rates upstream.

Common pitfall. Forgetting the $(1+k_d\theta_c)$ endogenous-decay correction in either $V$ or $P_x$ (they must use the same denominator, the basis of the identity cross-check); trying to compute the recycle ratio from a biokinetic equation instead of the simple clarifier solids balance.

Source. Davis & Cornwell Ch. 8 (pH control), Ch. 9 (ion exchange, reverse osmosis); Metcalf & Eddy Ch. 8 (activated-sludge design, SRT).

Question 4 of 7: pH control, ion exchange and reverse osmosis design principles, and activated-sludge process design

Question 4: pH control, ion exchange and reverse osmosis design principles, and activated-sludge process design (20 marks)

(i) Design principle and O&M parameter per technology