A real-time activated-sludge calculator built on Monod kinetics and a completely-mixed (CSTR) steady-state mass balance. Move sliders for influent BOD, reactor volume, flow and SRT to see how effluent BOD, MLSS, excess sludge and F/M ratio respond — and how to size an aeration basin.
Parameters
Influent BOD S₀
mg/L
Biochemical oxygen demand at the plant inlet
Reactor volume V
m³
Effective volume of the aeration tank
Flow rate Q
m³/day
Volumetric influent to the plant
SRT (sludge retention time)
day
Mean residence time of biomass (θ_c)
Biomass yield Y
kg/kg
Biomass produced per unit substrate consumed
Max specific growth rate μ_max
1/day
Growth rate under excess-substrate conditions
Half-saturation constant K_s
mg/L
Substrate concentration giving μ = μ_max/2
Decay coefficient k_d
1/day
Endogenous respiration rate of biomass
Results
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HRT (day)
—
Effluent BOD (mg/L)
—
BOD removal (%)
—
MLSS biomass (mg/L)
—
Excess sludge (kg/day)
—
F/M ratio (kg-BOD/kg-MLSS/day)
—
Aeration tank cross-section — inflow, treatment and sludge return
Brown organic matter enters from the left and is degraded by air bubbles and green microbial particles, leaving as blue treated water. The bottom recycle line keeps MLSS up.
Excess sludge production P_x (kg/day) and F/M ratio (kg-BOD/kg-MLSS/day). Conventional plants operate in F/M = 0.2–0.5.
What is the Activated Sludge (CSTR / Monod) Simulator?
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On a wastewater-plant tour I kept hearing "activated sludge". What is actually happening in those frothy tanks?
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Picture the aeration tank as a microbial farm. The organic matter in sewage (BOD) is food, and a community of bacteria and protozoa — the "activated sludge" — grows on it while oxidising the organics. Air is blown in to supply oxygen so the aerobic microbes work flat-out, and over about a day they remove 95-99% of the influent BOD. Then a clarifier settles the sludge, the supernatant is discharged, and part of the settled sludge is returned to the aeration tank so the biomass stays high.
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Got it, a microbial farm! Then what is "SRT" on the slider on the left? Is that different from flow?
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Good question. Flow defines HRT (hydraulic retention time) — the average time a water molecule stays in the tank. SRT (sludge retention time) is the average time a microbe stays in the system, and it is set independently by the ratio of return to wastage. Even with HRT = 0.5 day (12 h), if you waste less sludge you can hold SRT at 10 or 20 days. A longer SRT lets the biomass mature and chew through low-concentration BOD, so effluent quality improves. SRT is the single most important design parameter in activated-sludge processes.
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If longer SRT is better, why not crank it up forever?
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Because the curve bends. With very long SRT, endogenous decay (k_d) eats away at the biomass — the sludge "ages". Aged sludge settles poorly, escapes the clarifier and degrades effluent quality. And if F/M falls too far, filamentous bacteria take over and cause bulking — a billowing sludge that will not settle at all. The sweet spot for conventional activated sludge is F/M = 0.2-0.5. Try sliding SRT to 20 or 25 days in the tool and watch how F/M drops.
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I also keep seeing K_s in the Monod equation — what does that one mean?
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K_s is the half-saturation constant — the substrate (BOD) concentration that gives exactly half of μ_max. The smaller it is, the better the microbes can grow on dilute BOD. For sewage heterotrophs K_s ≈ 30-100 mg/L, methanogens are in the hundreds, and autotrophic nitrifiers are below 1 mg/L. Look at the formula S_eff = K_s(1/SRT + k_d)/(μ_max - 1/SRT - k_d) and you will see effluent BOD scales with K_s. It is basically the microbe's "affinity for food". K_s rises in cold water, which is one reason plants struggle to meet limits in winter.
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Last question — is this the same as the famous "ASM1" model?
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Well spotted. The full IWA ASM1 splits organic matter into soluble / particulate × biodegradable / inert, adds heterotrophs and autotrophs plus inerts and nitrogen species — 13 state variables in all. This tool is the simplest educational subset: carbon-only, single substrate, single biomass. Real-plant design and dynamic predictions are done in commercial simulators like GPS-X or WEST built around ASM1-3. But for feeling the Monod × CSTR interaction, nothing beats moving the sliders here — try doubling influent BOD and SRT and see what changes.
Frequently Asked Questions
In a completely mixed activated-sludge reactor, the effluent substrate concentration S is fixed by SRT and the Monod equation. The specific growth rate μ = μ_max·S/(K_s+S) minus the endogenous decay k_d balances 1/SRT, so S = K_s·(1/SRT + k_d) / (μ_max − 1/SRT − k_d). A striking feature of the CSTR model is that effluent BOD does not depend on influent BOD — only on SRT and the kinetic parameters. The longer the SRT, the lower S and the higher the removal efficiency.
Steady-state MLSS (mg/L) is X = Y·SRT/(HRT·(1+k_d·SRT))·(S₀−S), where Y is the biomass yield and HRT is the hydraulic retention time. X grows with SRT but is capped by endogenous decay k_d. The excess sludge production (kg/day) is Y·Q·(S₀−S)/(1+k_d·SRT)/1000; longer SRT enlarges the denominator and reduces excess sludge. Extending SRT therefore cuts disposal cost, but be careful not to push the F/M ratio too low.
F/M ratio (food-to-microorganism, kg BOD/kg MLSS/day) is the headline operational indicator for activated sludge. Conventional plants run between 0.2 and 0.5. Low-F/M (0.05-0.15) plants — extended aeration, oxidation ditches — tend to age the sludge and worsen settling. High-F/M above 0.5 is overloading, which triggers filamentous bulking. This tool reports F/M automatically so you can see how it shifts when SRT or reactor volume change.
Once SRT drops below the minimum growth time (washout SRT), the activated sludge is washed out faster than it can grow, biomass falls to zero, and BOD removal collapses. The critical value is SRT_min = 1/(μ_max·S₀/(K_s+S₀) − k_d) — higher influent BOD reduces it. In practice keep SRT at 2-3 × SRT_min for safety. This tool flags a warning when SRT approaches the critical value and shows the sharp deterioration of effluent BOD. In winter μ_max drops, so a longer SRT must be maintained in cold weather.
Real-World Applications
Municipal wastewater plants (conventional activated sludge): Most of the 2,200+ wastewater plants in Japan, and tens of thousands worldwide, are built around activated sludge. Typical design values are influent BOD 150-300 mg/L, HRT 6-8 hours and SRT 5-10 days, so the Monod × CSTR equations used here translate directly into early-stage plant sizing. Doubling the flow rate Q in this tool halves HRT and quickly degrades effluent BOD — an instant demonstration of why combined sewer overflow (CSO) controls matter.
Food, chemical and paper-mill effluent: For high-strength industrial wastewater of BOD 1,000-5,000 mg/L, anaerobic pretreatment (UASB and similar) is typical, with activated sludge polishing the effluent. Pushing S₀ to 2,000 mg/L in this tool dramatically increases MLSS, but in a real plant MLSS above 4,000 mg/L breaks settler hydraulics, forcing a switch to membrane bioreactors (MBR) or dilution.
Operating cost and energy optimisation: Roughly 60% of activated-sludge operating cost is aeration power, 20% is sludge disposal. Extending SRT reduces excess sludge but increases oxygen demand and ageing risk — a tug-of-war operators face daily. Compare SRT = 5 and 20 in the simulator to see excess sludge halve while MLSS rises and loads the clarifier more heavily.
University and college environmental-engineering teaching: Monod kinetics with a CSTR mass balance is foundational in textbooks worldwide (e.g. Metcalf & Eddy "Wastewater Engineering"). By visualising the classical closed-form solution, this tool lets students perform an 8-parameter sensitivity study in seconds — a useful stepping stone toward mastering full ASM1 in graduate research.
Common Misconceptions and Pitfalls
The first misconception is, "if I change influent BOD the effluent BOD does not move, so the calculator must be broken." In the CSTR steady-state model, effluent S_eff is determined entirely by SRT, μ_max, K_s and k_d, independent of S₀. This is a mathematical property: when influent rises, MLSS scales up proportionally and absorbs the extra load. In a real plant there are ceilings (clarifier capacity, oxygen supply) that the model deliberately leaves out, so very high influent does break treatment in practice — but flat S₀ sensitivity in this tool is correct.
The second pitfall is, "Monod parameters μ_max, K_s, k_d and Y from a textbook can be plugged straight into a real plant". They change strongly with temperature (μ_max roughly halves between 20 °C and 10 °C), pH (drops sharply outside neutral), organic composition (biodegradable vs refractory), and toxic species. Serious plant designs measure them in batch tests (OUR, SOUR) on the actual wastewater. The defaults here are representative of municipal sewage and are not safe for industrial effluents.
The third caveat is, this model treats carbon removal only — nitrogen and phosphorus removal are out of scope. Real nutrient-removal plants combine nitrification (NH₄⁺ → NO₃⁻, aerobic) and denitrification (NO₃⁻ → N₂, anoxic) with PAO-driven phosphorus uptake under anaerobic conditions; ASM2 / ASM2d / ASM3 carry 13-19 state variables. Nitrifiers have small μ_max and need SRT ≥ 8 days, dropping further in cold weather. Designing modern nutrient-removal facilities requires the ASM2d-class simulators, not this single-substrate tool.
How to Use
Enter influent BOD concentration (typically 200–400 mg/L for municipal wastewater)
Set reactor volume in cubic meters and hydraulic flow rate in m³/day
Specify solids retention time (SRT) in days—standard design range 5–15 days for carbonaceous removal
Run simulation to calculate HRT, effluent BOD, removal percentage, MLSS concentration, excess sludge production, and F/M ratio
Worked Example
Municipal treatment plant receives 500 m³/day of wastewater at 300 mg/L BOD. Reactor volume set to 800 m³, SRT 10 days. Simulation yields: HRT = 1.6 days, effluent BOD = 18 mg/L (94% removal), MLSS = 3200 mg/L, excess sludge = 85 kg/day, F/M = 0.35 kg-BOD/kg-MLSS/day. This mid-range F/M indicates stable heterotrophic growth without filament dominance.
Practical Notes
Target F/M below 0.5 to minimize bulking; above 1.0 risks washout and poor settling. Adjust SRT to control biomass inventory.
Effluent BOD depends on Monod half-saturation constant (Ks ≈ 60 mg/L typical)—lower Ks substrates converge faster at low residual concentrations.
MLSS of 3000–4500 mg/L suits conventional clarifier design; higher values increase solids handling and aeration costs.
For nitrification (NH₄⁺ removal), increase SRT to 15–25 days and ensure DO > 2 mg/L.