Water and Wastewater · Study · FE Environmental · FE → PE Prep
Water and Wastewater
12% of exam
Water and wastewater characteristics, mass balance and removal-efficiency loading rates, physical, chemical, and biological treatment processes, sludge treatment and handling, and water conservation and reuse.
7 concepts
A. Water and wastewater characteristics
Water and Wastewater Characteristics and Loading
Read water quality the way a treatment plant does: organic, solids, and nutrient measures, then convert concentrations into mass loads and removal efficiencies.
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C. Physical processes
Coagulation, Sedimentation, and Filtration
The clarification train as loading-rate arithmetic: overflow rate versus settling velocity, detention and weir loading, and rapid-filter rates and backwash.
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Chemical Treatment: Coagulation and Lime–Soda Softening
Coagulant chemistry and alkalinity demand, the velocity gradient G that sizes mixing, hardness as CaCO3, the lime–soda dose, and the meq/L bar chart.
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E. Biological processes
Activated Sludge: F/M, SRT, and Clarifiers
The workhorse of biological wastewater treatment, sized by F/M and solids retention time, balanced across the aeration basin and coupled secondary clarifier.
Activated sludge is the central process of modern wastewater treatment: a suspension of microorganisms in an aerated basin consumes the organic load (BOD), and a downstream secondary clarifier settles that biomass so it can be returned to the basin and kept working. The whole design lives or dies on two control parameters — the food-to-microorganism ratio (F/M) and the solids retention time (SRT, or mean cell residence time θc) — and on recognizing that the basin and clarifier are one coupled system. The governing relations appear in the NCEES FE Reference Handbook — Environmental Engineering under Activated Sludge and the accompanying design-parameter table.
The F/M ratio
The food-to-microorganism ratio is the organic load applied per unit of biomass per day — the 'how much are we feeding each microbe' parameter. Food is the influent BOD load Q0S0; microorganisms are the mass of mixed-liquor suspended solids in the basin, VXA
MLSS and the aeration basin mass balance
The biomass concentration in the basin, the mixed-liquor suspended solids XA, results from a balance between growth on substrate and loss by decay and wasting. Combining the steady-state biomass and substrate balances gives the design relation linking basin concentration to the kinetic constants, the retention times, and the substrate removed. This is what couples the biological kinetics to the physical sizing.
XA=θ(1+kdθc)θcY(S0−Se)
Hydraulic retention time versus solids retention time
Two residence times govern the process, and confusing them is the classic error. Hydraulic retention time θ=V/Q is how long the water stays in the basin — hours. Solids retention time θc (SRT, sludge age) is how long the biomass stays in the system — days — because settled solids are recycled rather than flushed out with the flow. The recycle is precisely what decouples θc
SRT, wasting, and process control
Solids retention time is the master control variable: it sets the sludge age, the effluent quality, and whether slow-growing organisms (like nitrifiers) survive. You control θc by wasting — deliberately removing biomass at Qw, Xw
Sludge recycle (RAS) and the coupled clarifier
The secondary clarifier thickens settled biomass to a concentration Xr, and most of it is returned as return activated sludge (RAS) at flow QR to maintain the basin MLSS. A solids mass balance around the clarifier ties everything together: what flows in from the basin must leave in the effluent, the recycle, and the waste streams. Neglecting the small effluent and waste solids, the recycle ratio needed to hold a target MLSS follows directly from the basin and underflow concentrations.
(Q0+QR)XA=QeXe+QRXr+QwXw
Settleability and clarifier loading
The clarifier can only return solids it can settle, so its loading must match the sludge's settling character. The sludge volume index (SVI) — the volume one gram of settled solids occupies after 30 minutes — gauges settleability; below about 100mL/g settles well, above 150mL/g signals bulking. A secondary clarifier is checked on two loadings: the surface overflow rate (a settling criterion) and the solids loading rate (a thickening criterion), the latter being what usually controls because the unit must thicken a heavy recycled solids flux.
Identify the loading type before computing: F/M and volumetric loading use the BOD mass load over basin mass or volume; θ uses volume over flow; θc uses basin solids inventory over the daily solids leaving. Keep θ (hours, water) and θc
Key equations
Food-to-microorganism ratioF/M=VXAQ0S0
Worked examples
F/M, HRT, and volumetric loading
Problem. An aeration basin of V=2,500m3 treats Q0=10,000m3/d
Common pitfalls
•Confusing hydraulic retention time θ (hours, follows the water) with solids retention time θc (days, follows the recycled biomass). They differ by the recycle — that is the whole point of activated sludge.
•Computing F/M with effluent BOD or with the wrong solids. Food is the influent BOD load Q₀S₀; microorganisms are the basin inventory V·XA (MLSS, sometimes MLVSS) — not the recycle solids.
•Dividing influent flow by effluent flow inconsistently in the clarifier balance. Use one steady-state solids balance: (Q₀+QR)XA = QeXe + QRXr + QwXw.
•Sizing the secondary clarifier on overflow rate alone. For activated sludge the solids loading (thickening) rate usually controls, because the unit must handle the heavy recycled solids flux.
•Forgetting the effluent solids in the SRT denominator. Neglecting QeXe overstates the required wasting rate Qw — include it when effluent SS is given.
•Reading SVI backwards: a HIGH SVI (>150 mL/g) means poor, bulking sludge that settles badly; a low SVI settles and thickens well.
•Mixing concentration units mid-problem. Keep MLSS, RAS, and BOD all in mg/L or all in kg/m³ before substituting; 2,500 mg/L = 2.5 kg/m³.
References
NCEES FE Reference Handbook — Environmental Engineering
Davis & Cornwell, Introduction to Environmental Engineering — F/M, sludge age, secondary clarifier loading
Fixed-Film Processes and Nutrient Removal
Trickling filters and RBCs, Monod growth kinetics, and biological/chemical nitrogen and phosphorus removal — the attached-growth half of secondary treatment.
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F. Sludge treatment and handling
Disinfection and Sludge Treatment
The CT concept and Chick-Watson inactivation, chlorine chemistry and breakpoint, UV dose, and the thickening-digestion-dewatering train that turns sludge into biosolids.
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G. Water conservation and reuse
Water Conservation and Reuse
Demand management and graywater, reclaimed-water classes, membrane treatment (MF/UF/NF/RO recovery and rejection) and advanced oxidation, and indirect potable reuse.
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. A high
F/M
means a heavily loaded, fast-growing, young sludge; a low
F/M
means a lightly loaded, well-stabilized sludge. Conventional plants run
F/M≈0.2
–
0.4kg BOD/(kg MLSS⋅d)
.
F/M=VXAQ0S0
from
θ
, letting a basin with a
6
-hour hydraulic time hold a
10
-day-old sludge.
θ=QV,θc=QwXw+QeXeVXA
from the system each day. Because the wasted and effluent solids equal the daily biomass production at steady state, increasing the wasting rate lowers the sludge age and
F/M
moves inversely to
θc
.
θc1=VXAQwXw+QeXe
(days, solids) rigorously separate. For wasting, solve the SRT definition for
Qw
; for recycle, write the clarifier solids balance and, if effluent/waste solids are negligible, use
R=XA/(Xr−XA)
. Convert all concentrations to consistent mass units (kg/m³ or mg/L) before substituting, and sanity-check answers against the handbook's design-parameter ranges.
Applied BOD load per unit biomass per day (kg BOD/(kg MLSS·d)). Q0=influent flow, S0=influent BOD, V=basin volume, XA=MLSS. Conventional 0.2–0.4.
Solids retention time (SRT)θc=QwXw+QeXeVXA
Mean cell residence time / sludge age (d). Basin solids inventory divided by solids leaving in waste + effluent.
Hydraulic retention timeθ=QV
Liquid residence time in the basin (h). Typically 4–8 h for conventional activated sludge; distinct from SRT.
Volume (mL) of 1 g settled solids after 30 min. <100 good settling, >150 bulking. Underflow Xr ≈ 10⁶/SVI.
Solids loading rateSLR=A(Q0+QR)XA
Thickening criterion for the secondary clarifier (kg/(m²·d) or lb/(ft²·d)); often controls over overflow rate.
Volumetric organic loadingLv=VQ0S0
BOD load per basin volume (kg BOD/(m³·d)). Conventional ~0.3–0.6.
of primary effluent with
S0=150mg/L
BOD, holding
XA=2,500mg/L
MLSS. Find the F/M ratio, hydraulic retention time, and volumetric loading, and compare to conventional ranges.
Solution. F/M ratio (mg/L cancels in the ratio):
F/M=VXAQ0S0=2,500×2,50010,000×150=6.25×1061.5×106=0.24d−1.
Hydraulic retention time:
θ=Q0V=10,0002,500=0.25d=6.0h.
Volumetric loading (with S0=0.150kg/m3):
Lv=VQ0S0=2,50010,000×0.150=0.60kg BOD/(m3⋅d).
Sanity check: F/M=0.24 (range 0.2–0.4), θ=6h (range 4–8h), Lv=0.60 (range 0.3–0.6) — all consistent with a conventional plant. Final: F/M=0.24d−1, θ=6.0h, Lv=0.60kg/(m3⋅d).
Solids retention time and wasting rate
Problem. For the same basin (V=2,500m3, XA=2,500mg/L), the plant targets θc=10d. Waste sludge is at Xw=10,000mg/L; the effluent carries Xe=15mg/L at Qe≈10,000m3/d. Find the required waste flow Qw.
Solution. From the SRT definition, the daily solids leaving must equal the inventory over θc:
QwXw+QeXe=θcVXA=102,500×2,500=625,000(mg/L⋅m3/d).
Settleability, recycle ratio, and solids loading
Problem. The mixed liquor (XA=2,500mg/L) gives a 30-minute settled volume of 250mL/L. The secondary clarifier has surface area A=400m2. Find the SVI, estimate the RAS (underflow) concentration, the recycle ratio needed to hold the MLSS (neglecting effluent/waste solids), and the solids loading rate for Q0=10,000m3/d.