CSTR - Continuously Stirred Tank Reactor

Completely mixed biological reactor providing uniform conditions throughout the tank volume for COD oxidation, nitrification, and denitrification.

Overview

The Continuously Stirred Tank Reactor (CSTR) is the fundamental building block of activated sludge systems. Its completely mixed regime ensures uniform substrate, biomass, and oxygen concentrations throughout the reactor volume.

When to Use

• Complete-mix activated sludge systems
• High-rate biological treatment
• Systems requiring shock load attenuation
• Industrial wastewater with variable loads
• Nitrification/denitrification applications

Key Characteristics

• Uniform concentration throughout
• Rapid dispersion of influent
• Excellent shock load dampening
• Lower average driving force than PFR
• Simpler modeling (single compartment)

Biokinetic Models

ASM1 Integration

ErgoPlanner implements full ASM1 kinetics:

Heterotrophic Growth: $$\mu_H = \mu_{H,max} \times \frac{S_s}{K_s + S_s} \times \frac{S_O}{K_O + S_O}$$

$$r_{X_B} = \mu_H \times X_{B,H}$$

$$r_{S_s} = -\frac{\mu_H \times X_{B,H}}{Y_H}$$

Autotrophic Growth (Nitrification): $$\mu_A = \mu_{A,max} \times \frac{S_{NH}}{K_{NH} + S_{NH}} \times \frac{S_O}{K_{O,A} + S_O}$$

$$r_{S_{NO}} = \frac{\mu_A \times X_{B,A}}{Y_A}$$

Denitrification: $$\mu_{H,denit} = \mu_{H,max} \times \eta_g \times \frac{S_s}{K_s + S_s} \times \frac{S_{NO}}{K_{NO} + S_{NO}} \times \frac{K_O}{K_O + S_O}$$

$$r_{S_{NO},denit} = -\frac{(1 - Y_H) \times \mu_{H,denit} \times X_{B,H}}{2.86 \times Y_H}$$

Decay: $$r_{decay} = -b_H \times X_{B,H}$$

Temperature Correction

All kinetic rates are temperature-corrected using Arrhenius:

$$k(T) = k(20°C) \times \theta^{(T-20)}$$

Parameter	θ Value
μ_max	1.07
b	1.04
K values	1.0

Extended Models

• ASM2d: Includes biological phosphorus removal (PAO kinetics)
• ASM3: Storage-based model with improved yield prediction

Mass Balance

Steady-State CSTR Equation

For any component C:

$$V \times \frac{dC}{dt} = Q \times (C_{in} - C) + r_C \times V$$

At steady state (dC/dt = 0):

$$C = \frac{C_{in}}{1 + \tau \times (-r_C / C)}$$

Where τ = V/Q = HRT

Oxygen Mass Balance

$$\frac{dS_O}{dt} = \frac{Q}{V}(S_{O,in} - S_O) + KLa \times (S_{O,sat} - S_O) - OUR$$

Where:

• OUR = Oxygen Uptake Rate (heterotrophs + autotrophs)
• KLa = Volumetric oxygen transfer coefficient

Solids Balance

$$\frac{dX}{dt} = \frac{Q_{in}}{V} \times X_{in} + \mu \times X - b \times X - \frac{Q_{out}}{V} \times X$$

Design Equations

Hydraulic Retention Time (HRT)

$$HRT = \frac{V}{Q}$$

Typical values:

• High-rate: 2-4 hours
• Conventional: 4-8 hours
• Extended aeration: 18-36 hours

Solids Retention Time (SRT)

$$SRT = \frac{V \times X}{Q_w \times X_w + Q_e \times X_e}$$

Design guidelines:

• Carbon oxidation only: 3-5 days
• Nitrification: 8-15 days
• Nutrient removal: 10-25 days

Food-to-Microorganism Ratio (F:M)

$$F:M = \frac{Q \times S_0}{V \times X}$$

Typical ranges:

• High-rate: 0.4-1.0 kg BOD/kg MLSS/d
• Conventional: 0.2-0.4 kg BOD/kg MLSS/d
• Extended aeration: 0.05-0.15 kg BOD/kg MLSS/d

Sludge Production

$$P_x = Y_{obs} \times Q \times (S_0 - S) + X_{i,in} \times Q$$

Where observed yield:

$$Y_{obs} = \frac{Y}{1 + b \times SRT}$$

Oxygen Transfer

Standard Oxygen Transfer Rate (SOTR)

$$SOTR = KLa \times C^*_{s,20} \times V$$

Actual Oxygen Transfer Rate (AOTR)

$$AOTR = SOTR \times \frac{\alpha \times \beta \times C^_{s,T} - C_L}{C^_{s,20}} \times \theta^{(T-20)}$$

Alpha Factor

Application	α Range
Clean water	1.0
Municipal WW	0.5-0.8
Industrial WW	0.3-0.6
High MLSS (>6 g/L)	0.4-0.5

Oxygen Demand

$$OD = \frac{Q \times (S_0 - S)}{f} + 4.57 \times Q \times (N_0 - N) - 2.86 \times Q \times NO_3$$

Where f = COD/BOD ratio (typically 1.5-2.0)

Parameters

Kinetic Parameters (ASM1)

Parameter	Symbol	Unit	Default	Range	Description
Max. heterotrophic growth	μ_H,max	1/d	6.0	3-10	Heterotrophs
Max. autotrophic growth	μ_A,max	1/d	0.8	0.3-1.5	Nitrifiers
Heterotrophic yield	Y_H	g COD/g COD	0.67	0.5-0.7	Cell yield
Autotrophic yield	Y_A	g COD/g N	0.24	0.15-0.3	Nitrifier yield
Heterotrophic decay	b_H	1/d	0.4	0.2-0.6	Endogenous
Autotrophic decay	b_A	1/d	0.15	0.05-0.25	Nitrifier decay
Substrate half-sat	K_s	mg COD/L	20	5-40	Monod constant
Ammonia half-sat	K_NH	mg N/L	1.0	0.5-2.0	Nitrification
Oxygen half-sat	K_O	mg O2/L	0.2	0.1-0.5	Aerobic growth
Anoxic factor	η_g	-	0.8	0.6-0.9	Denitrification

Design Parameters

Parameter	Unit	Default	Range	Description
Volume	m³	calculated	-	Reactor volume
HRT	hours	6	2-36	Hydraulic retention
SRT	days	12	3-25	Solids retention
MLSS	mg/L	3500	2000-6000	Mixed liquor SS
DO setpoint	mg/L	2.0	1.0-4.0	Dissolved oxygen
Temperature	°C	15	10-25	Operating temp

Aeration Parameters

Parameter	Unit	Default	Range	Description
KLa	1/h	10	5-30	Transfer coefficient
α factor	-	0.6	0.4-0.9	Alpha correction
β factor	-	0.95	0.90-0.99	Salinity correction
SOTE	%	25	15-35	Fine bubble
Floor coverage	%	10	5-15	Diffuser area

Operating Modes

Aerobic (Carbon Oxidation + Nitrification)

• DO: 1.5-3.0 mg/L
• Removes BOD and ammonia
• Produces nitrate

Anoxic (Denitrification)

• DO: <0.5 mg/L
• Requires carbon source
• Reduces nitrate to N₂

Anaerobic (Bio-P Release)

• DO: 0, NO₃: 0
• VFA uptake by PAOs
• Phosphorus release

Configuration

Step-by-Step Setup

1. Define Volume

   • Calculate from HRT and flow
   • Or specify target SRT

2. Set Operating Parameters

   • MLSS concentration
   • DO setpoint
   • Temperature

3. Select Biokinetic Model

   • ASM1 for COD/N
   • ASM2d for COD/N/P
   • ASM3 for storage

4. Configure Aeration

   • Diffuser type
   • Alpha/beta factors
   • Control mode

Example Configuration

{
  "type": "cstr",
  "id": "aeration-1",
  "parameters": {
    "volume": 5000,
    "mlss": 3500,
    "doSetpoint": 2.0,
    "temperature": 15,
    "mode": "aerobic",
    "biokinetics": {
      "model": "ASM1",
      "muHMax": 6.0,
      "muAMax": 0.8,
      "yH": 0.67,
      "yA": 0.24,
      "bH": 0.4,
      "bA": 0.15,
      "ks": 20,
      "kNH": 1.0,
      "kO": 0.2
    },
    "aeration": {
      "kla": 10,
      "alpha": 0.6,
      "beta": 0.95,
      "diffuserType": "fineBubble"
    }
  }
}

Worked Example

Given

• Flow: 10,000 m³/d
• Influent BOD: 250 mg/L
• Influent NH₄-N: 40 mg/L
• Target effluent: BOD <20, NH₄-N <1 mg/L
• Temperature: 12°C

Design

Step 1: Select SRT for Nitrification

At 12°C, μ_A,max = 0.8 × 1.07^(12-20) = 0.47 d⁻¹

Minimum SRT: SRT_min = 1/(μ_A,max - b_A) = 1/(0.47-0.09) = 2.6 d

Design SRT = 3 × SRT_min = 8 days (safety factor)

Step 2: Calculate Volume

For SRT = 8d, F:M ≈ 0.25:

$$V = \frac{Q \times S_0}{F:M \times X} = \frac{10,000 \times 0.25}{0.25 \times 3.5} = 2,857 \text{ m}^3$$

Round to V = 3,000 m³

HRT = 3,000/10,000 × 24 = 7.2 hours ✓

Step 3: Oxygen Demand

Carbonaceous: OD_C = 10,000 × (250-20) × 0.001 / 1.6 = 1,438 kg O₂/d

Nitrogenous: OD_N = 4.57 × 10,000 × (40-1) × 0.001 = 1,782 kg O₂/d

Total OD = 1,438 + 1,782 = 3,220 kg O₂/d

Step 4: Aeration Requirements

At α=0.6, β=0.95, T=12°C, SOTE=25%:

SOTR = 3,220 / (0.6 × 0.95 × 0.86) = 6,568 kg O₂/d

Air flow = 6,568 / (0.25 × 0.28 × 1.2 × 24) = 3,270 m³/h

Integration

Connected Units

• Upstream: Primary clarifier, equalization
• Downstream: Secondary clarifier, membrane
• Sidestreams: RAS, WAS, dewatering return

Control Integration

• DO control via aeration
• SRT control via WAS
• MLSS control via RAS ratio

Troubleshooting

Issue	Cause	Solution
High effluent ammonia	Insufficient SRT	Increase SRT, reduce WAS
	Low DO	Increase aeration
	Low temperature	Account in design
Poor settling	Filamentous bulking	Selector, adjust F:M
	Low DO	Maintain >1.5 mg/L
High sludge production	High F:M	Reduce loading
Foaming	Nocardia	Reduce SRT, add chlorine

Best Practices

1. DO Control: Maintain 1.5-2.5 mg/L for nitrification
2. SRT Management: Regular WAS to maintain target
3. MLSS Monitoring: Daily measurement
4. Temperature Compensation: Adjust SRT seasonally
5. Nutrient Balance: C:N:P ratio ~100:5:1

Related Topics

• PFR - Plug Flow Reactor
• SBR - Sequencing Batch Reactor
• Oxidation-Ditch - Oxidation Ditch
• Anoxic-Zone - Anoxic Zone
• Secondary-Clarifier

References

1. Henze, M. et al. (2000). Activated Sludge Models ASM1, ASM2, ASM2d and ASM3. IWA Publishing.
2. Metcalf & Eddy (2014). Wastewater Engineering, 5th Ed.
3. WEF (2018). Design of Municipal Wastewater Treatment Plants, MOP 8.
4. Grady, C.P.L. et al. (2011). Biological Wastewater Treatment, 3rd Ed.