PFR - Plug Flow Reactor

Longitudinal flow biological reactor providing concentration gradient for optimal substrate utilization and selector conditions.

Overview

The Plug Flow Reactor (PFR) creates a concentration gradient along its length, with high substrate at the inlet tapering to low levels at the outlet. This gradient provides natural selector conditions and higher average reaction rates than CSTRs.

When to Use

• Conventional activated sludge systems
• Selector zones for bulking control
• Systems requiring high treatment efficiency
• Step-feed configurations
• Long narrow tank geometries

Key Characteristics

• Concentration gradient along length
• Higher average driving force than CSTR
• Natural selector at inlet
• Sensitive to shock loads at inlet
• Multiple compartment modeling

Theory

Ideal Plug Flow

For first-order kinetics in an ideal PFR:

$$\frac{dS}{dV} = -\frac{r_s}{Q}$$

Integrated: $$S_{out} = S_{in} \times e^{-k \times \tau}$$

Where τ = V/Q = HRT

Comparison with CSTR

For the same HRT and kinetics:

$$\frac{S_{out,PFR}}{S_{out,CSTR}} = \frac{e^{-k\tau}}{1/(1+k\tau)} < 1$$

PFR achieves better removal than CSTR at equal HRT.

Tanks-in-Series Model

Real PFRs are modeled as N CSTRs in series:

$$S_n = S_0 \times \left(\frac{1}{1 + k\tau/N}\right)^N$$

As N→∞, approaches ideal PFR.

Typical N values:

• Long narrow tanks: 8-15
• Wide tanks: 3-5
• With baffles: 10-20

Biokinetics

Monod Kinetics Along Length

At position x: $$\mu(x) = \mu_{max} \times \frac{S(x)}{K_s + S(x)} \times \frac{DO(x)}{K_O + DO(x)}$$

Selector Effect

At inlet (high S):

• Fast-growing floc formers dominate
• Filament suppression
• Improved settleability

Oxygen Demand Profile

$$OD(x) = \frac{r_s(x)}{Y} + 4.57 \times r_{NH}(x)$$

Higher at inlet → tapered aeration beneficial.

Design Equations

Length-to-Width Ratio

$$\frac{L}{W} > 5:1$$ for plug flow behavior

Typical: 10:1 to 20:1

Dispersion Number

$$d = \frac{D}{u \times L}$$

Where:

• D = dispersion coefficient (m²/s)
• u = velocity (m/s)
• L = length (m)

d Value	Flow Regime
d → 0	Ideal plug flow
d → ∞	Complete mix
d < 0.01	Approximate plug flow
d = 0.01-0.1	Moderate dispersion

Number of Stages

To achieve N tanks-in-series:

$$N = \frac{1}{2 \times d}$$

Parameters

Geometric Parameters

Parameter	Unit	Default	Range	Description
Length	m	100	50-200	Tank length
Width	m	10	5-20	Tank width
Depth	m	4	3-6	Liquid depth
L:W ratio	-	10	5-20	Plug flow indicator
Segments	-	10	5-20	Model compartments

Operating Parameters

Parameter	Unit	Default	Range	Description
HRT	hours	6	4-12	Total retention
SRT	days	10	5-20	Solids retention
MLSS	mg/L	3500	2000-5000	Mixed liquor
DO profile	mg/L	variable	0.5-4.0	Along length
Tapered aeration	bool	true	-	Inlet-biased

Biokinetic Parameters

Same as CSTR - see CSTR for full ASM parameter tables.

Step-Feed Configuration

Concept

Influent distributed along reactor length to:

• Balance oxygen demand
• Reduce inlet shock
• Improve denitrification
• Increase effective SRT

Step-Feed Locations

[Feed 1] ──→ [Zone 1] ──→ [Zone 2] ──→ [Zone 3] ──→ Effluent
   50%          ↑            ↑
            [Feed 2]     [Feed 3]
               30%          20%

Benefits

• Uniform oxygen demand profile
• Better utilization of entire volume
• Improved storm handling
• Enhanced denitrification potential

Tapered Aeration

Concept

More air at inlet where OD is highest:

Zone	% of Length	% of Air
Inlet	0-25%	40-50%
Middle	25-75%	30-40%
Outlet	75-100%	15-25%

Calculation

$$Air(x) = OD(x) / SOTE(x)$$

Where SOTE may vary with depth and α factor.

Configuration

Example Configuration

{
  "type": "pfr",
  "id": "aeration-basin",
  "parameters": {
    "length": 100,
    "width": 10,
    "depth": 4,
    "segments": 10,
    "mlss": 3500,
    "operatingMode": "aerobic",
    "stepFeed": {
      "enabled": true,
      "locations": [0, 0.3, 0.6],
      "fractions": [0.5, 0.3, 0.2]
    },
    "aeration": {
      "profile": "tapered",
      "totalKLa": 12,
      "distribution": [0.4, 0.35, 0.25]
    },
    "doSetpoints": [2.5, 2.0, 1.5]
  }
}

Worked Example

Given

• Flow: 20,000 m³/d
• BOD: 200 mg/L
• Design for 90% BOD removal
• k = 0.3 h⁻¹ at 15°C

CSTR vs PFR Comparison

CSTR Design: $$S/S_0 = \frac{1}{1 + k\tau} = 0.1$$ $$\tau = 9/k = 30 \text{ hours}$$

PFR Design: $$S/S_0 = e^{-k\tau} = 0.1$$ $$\tau = 2.3/k = 7.7 \text{ hours}$$

PFR requires only 26% of CSTR volume for same removal!

Practical PFR (N=8)

$$S/S_0 = (1 + k\tau/N)^{-N} = 0.1$$ $$\tau = 8.5 \text{ hours}$$

Still 28% of CSTR requirement.

Troubleshooting

Issue	Cause	Solution
Poor outlet quality	Low N (mixing)	Add baffles
Inlet overload	No selector	Add anoxic selector
Uneven DO	Poor distribution	Adjust diffusers
Filamentous bulking	Missing selector	Enable step-feed
High inlet OD	Concentrated feed	Distribute feed

Related Topics

• CSTR - Continuously Stirred Tank Reactor
• Oxidation-Ditch - Oxidation Ditch
• Step-Feed-Activated-Sludge
• Selector-Design

References

1. Levenspiel, O. (1999). Chemical Reaction Engineering, 3rd Ed.
2. Henze, M. et al. (2008). Biological Wastewater Treatment. IWA Publishing.
3. WEF (2018). Design of Municipal Wastewater Treatment Plants, MOP 8.