pH Control / Ion Exchange / RO and Activated Sludge Design: 23-Chem-B2 Environmental Engineering, May 2018, Q5

Problem 5: pH Control / Ion Exchange / RO 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: function and operational issues

Selecting the low-pH ground-aquifer drinking-water example (acidic, corrosive groundwater, e.g. pH 5.5–6.0):

Technology	Main function	Operational issue
(a) pH control	Raises the finished-water pH into the non-corrosive/non-scaling Langelier range (typically pH 7.5–8.5) by feeding a base (lime, soda ash, or caustic) into the raw or finished water, protecting the distribution system from corrosion (lead/copper leaching) and reducing coagulant/disinfectant demand shifts caused by low pH.	Overdosing risks excessive scaling (calcium carbonate deposition) and turbidity from precipitated hydroxides; the dosing system must be flow-paced and continuously monitored since demand tracks raw-water alkalinity, which can vary seasonally.
(b) Ion exchange	Exchanges the aquifer's hardness/metal ions (Ca²⁺, Mg²⁺, Fe/Mn) for Na⁺ on a resin bed, indirectly improving the finished water's aesthetic and corrosivity properties without necessarily changing pH directly.	Resin fouling by iron/manganese precipitates or organic matter progressively reduces exchange capacity, requiring periodic backwash and acid/brine regeneration and generating a saline regenerant waste stream that needs disposal.
(c) Reverse osmosis	Removes dissolved ions (hardness, metals, TDS) across a semi-permeable membrane under applied pressure, producing a high-purity permeate. Dissolved CO₂ (the usual cause of low groundwater pH) passes through the membrane, so the permeate stays acidic and has almost no alkalinity; it must be degassed and re-mineralized/pH-adjusted afterward for distribution stability.	Membrane scaling/fouling from the concentrated reject stream requires antiscalant dosing and periodic chemical cleaning, and the reject (concentrate) brine stream requires its own disposal — RO is energy-intensive relative to pH control or ion exchange alone.

(ii) Conventional activated sludge preliminary design (Lawrence–McCarty)

Given.

Quantity	Value
Influent flow, Q₀	100,000 m³/d
Influent BOD5/TSS, S₀	300 mg/L
Effluent BOD5/TSS, S	40 mg/L
Yield coefficient, Y	0.5 kg VSS/kg BOD5
Decay rate, k_d	0.04 d⁻¹
Aeration-tank MLSS, X	5,000 mg/L
Waste (clarifier underflow) MLSS, X_w	8,000 mg/L
Mean cell residence time, θ_c	8 days

Find. (a) Aeration tank volume V and hydraulic retention time θ; (b) daily sludge wasting rate P_x (kg/d); (c) sludge recycle ratio Q_r/Q₀.

Approach. Apply the standard Lawrence–McCarty design equations for a completely-mixed activated-sludge system relating θ_c (solids retention time) to reactor volume and biomass production, then close a steady-state solids balance around the aeration tank/clarifier for the recycle ratio.

(a) Aeration tank volume, from the θ_c design equation. $$V = \frac{Y\,\theta_c\,Q_0(S_0-S)}{X(1+k_d\theta_c)} = \frac{0.5\times8\times100{,}000\times(300-40)}{5{,}000\times(1+0.04\times8)}$$ $$V = \frac{104{,}000{,}000}{6{,}600} = \boxed{15{,}758\ \text{m}^3}$$
Hydraulic retention time. $$\theta = \frac{V}{Q_0} = \frac{15{,}758}{100{,}000} = 0.1576\ \text{d} = \boxed{3.78\ \text{h}}$$
(b) Daily sludge wasting rate. $$P_x = \frac{Y\,Q_0(S_0-S)}{1+k_d\theta_c} = \frac{0.5\times100{,}000\times260}{1.32} = \boxed{9{,}848\ \text{kg/d}}$$ This is the net solids production that must leave the system each day (P_x = VX/θ_c), the standard preliminary-design answer when effluent solids are neglected. As a refinement, if the stated effluent TSS of 40 mg/L is counted as leaving over the weir (about (Q₀−Q_w) × 0.040 ≈ 4,000 kg/d), the balance Q_wX_w + (Q₀−Q_w)X_e = 9,848 kg/d gives Q_w ≈ 735 m³/d, so the sludge actually wasted from the clarifier underflow is about 5,880 kg/d.
(c) Sludge recycle ratio, from a steady-state solids balance around the aeration tank. Combining the influent (negligible X0) and recycle streams to give the aeration-tank MLSS X: $$Q_r X_w = (Q_0+Q_r)X \ \Rightarrow\ \alpha=\frac{Q_r}{Q_0}=\frac{X}{X_w-X} = \frac{5{,}000}{8{,}000-5{,}000} = \boxed{1.67}$$

Quantity	Value
(a) Aeration tank volume, V	15,758 m³
(a) Hydraulic retention time, θ	3.78 h
(b) Daily sludge wasted, P_x	9,848 kg/d
(c) Recycle ratio, Q_r/Q₀	1.67

Topic: Groundwater pH/hardness treatment technology selection, and Lawrence–McCarty activated-sludge preliminary design.

Key relations: $V=\dfrac{Y\theta_cQ_0(S_0-S)}{X(1+k_d\theta_c)}$, $P_x=\dfrac{YQ_0(S_0-S)}{1+k_d\theta_c}$, recycle ratio $\alpha=\dfrac{Q_r}{Q_0}=\dfrac{X}{X_w-X}$.

Why this works: The θ_c-based design equations come directly from a biomass balance on the reactor: net growth (Y·substrate utilized minus endogenous decay) at steady state must exactly equal the biomass wasted per unit time, which is what fixes θ_c; the recycle ratio is simply a separate steady-state solids balance (concentrated recycle flow must resupply exactly the biomass concentration maintained in the aeration tank).

Common pitfall: Confusing θ (hydraulic retention time, based on reactor volume/flow) with θ_c (mean cell residence time, based on total biomass mass/wasting rate) — they are numerically very different (here 3.78 h vs. 8 days) because the recycle/wasting scheme intentionally retains solids in the system far longer than the water itself.

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

Question 5 of 7: pH Control / Ion Exchange / RO and Activated Sludge Design

Problem 5: pH Control / Ion Exchange / RO and Activated Sludge Design (20 marks)

(i) pH control, ion exchange and reverse osmosis: function and operational issues

(ii) Conventional activated sludge preliminary design (Lawrence–McCarty)