Two-Stage Biogas Plant Example¶

The examples/two_stage_plant.py example demonstrates a complete two-stage biogas plant with mechanical components, energy integration, and comprehensive process monitoring.

Plant Schematic¶

System Architecture¶

graph TB
    %% Substrate feed
    Feed[Substrate Feed<br/>Corn silage: 15 m³/d<br/>Cattle manure: 10 m³/d]

    %% Feed pump
    Feed -->|25 m³/d| FeedPump[Feed Pump<br/>Progressive Cavity<br/>30 m³/h capacity]

    %% First stage - Hydrolysis
    FeedPump --> Dig1[Digester 1 - Hydrolysis<br/>V_liq: 1977 m³, V_gas: 304 m³<br/>T: 45°C thermophilic<br/>Enhanced hydrolysis]

    %% Mixer 1
    Mixer1[Mixer 1<br/>Propeller, 15 kW<br/>High intensity<br/>25% duty cycle] -.->|Mixing| Dig1

    %% Gas storage 1
    Dig1 -->|Biogas ~850 m³/d| Storage1[Gas Storage 1<br/>Membrane<br/>304 m³ capacity]

    %% Heating 1
    Heating1[Heating System 1<br/>Target: 45°C<br/>Heat loss: 0.5 kW/K] -.->|Heat| Dig1

    %% Transfer pump
    Dig1 -->|Effluent 25 m³/d| TransPump[Transfer Pump<br/>Progressive Cavity<br/>25 m³/h capacity]

    %% Second stage - Methanogenesis
    TransPump --> Dig2[Digester 2 - Methanogenesis<br/>V_liq: 1000 m³, V_gas: 150 m³<br/>T: 35°C mesophilic<br/>Stable CH₄ production]

    %% Mixer 2
    Mixer2[Mixer 2<br/>Propeller, 10 kW<br/>Medium intensity<br/>25% duty cycle] -.->|Mixing| Dig2

    %% Gas storage 2
    Dig2 -->|Biogas ~400 m³/d| Storage2[Gas Storage 2<br/>Membrane<br/>150 m³ capacity]

    %% Heating 2
    Heating2[Heating System 2<br/>Target: 35°C<br/>Heat loss: 0.3 kW/K] -.->|Heat| Dig2

    %% Combined gas flow to CHP
    Storage1 -->|Gas supply| CHP[CHP Unit<br/>500 kWe nominal<br/>ηe: 40%, ηth: 45%<br/>Total: ~1250 m³/d]
    Storage2 -->|Gas supply| CHP

    %% CHP outputs
    CHP -->|Electrical| Power[Power Output<br/>~480 kWe]
    CHP -->|Thermal ~540 kW| HeatDist[Heat Distribution]
    CHP -->|Excess gas| Flare[Flare<br/>Safety combustion<br/>98% destruction]

    %% Heat distribution
    HeatDist -->|Heat supply| Heating1
    HeatDist -->|Heat supply| Heating2

    %% Final outputs
    Dig2 -->|Digestate<br/>25 m³/d| Effluent[Digestate Output]

    %% Styling
    classDef processBox fill:#e1f5fe,stroke:#01579b,stroke-width:3px
    classDef storageBox fill:#fff3e0,stroke:#e65100,stroke-width:2px
    classDef mechanicalBox fill:#f3e5f5,stroke:#4a148c,stroke-width:2px
    classDef energyBox fill:#e8f5e9,stroke:#1b5e20,stroke-width:3px
    classDef inputBox fill:#f1f8e9,stroke:#33691e,stroke-width:2px
    classDef outputBox fill:#fce4ec,stroke:#880e4f,stroke-width:2px

    class Dig1,Dig2 processBox
    class Storage1,Storage2 storageBox
    class FeedPump,TransPump,Mixer1,Mixer2 mechanicalBox
    class CHP,Heating1,Heating2,HeatDist,Flare energyBox
    class Feed inputBox
    class Power,Effluent outputBox

Overview¶

The two-stage plant demonstrates: - Temperature-Phased Anaerobic Digestion (TPAD): Thermophilic hydrolysis (45°C) followed by mesophilic methanogenesis (35°C) - Mechanical Components: Pumps for material transport and mixers for process enhancement - Energy Integration: CHP for power generation and waste heat recovery - Process Control: Multiple heating systems for precise temperature management - Gas Management: Dedicated storage for each digester with automatic overflow protection and centralized flare

Plant Configuration¶

Biological Components¶

Total Organic Loading Rate (OLR): 25 m³/d ÷ 2977 m³ ≈ 0.0084 d⁻¹ or 8.4 kg COD/(m³·d)

Mechanical Components¶

Total Parasitic Load: ~20 kW (mixers run 25% duty cycle)

Energy Components¶

Gas Management System¶

Gas Flow Architecture: 1. Each digester produces gas → Dedicated storage 2. Both storages supply gas → Single CHP unit 3. CHP excess/overflow → Automatic flare combustion

Code Walkthrough¶

1. Enhanced Imports¶

from pyadm1.components.mechanical.mixer import Mixer
from pyadm1.components.mechanical.pump import Pump

These import the mechanical components that weren't used in the basic example.

2. Two-Stage Digester Configuration¶

# Digester 1: Thermophilic hydrolysis
configurator.add_digester(
    digester_id="digester_1",
    V_liq=1977.0,
    V_gas=304.0,
    T_ad=318.15,  # 45°C for enhanced hydrolysis
    Q_substrates=[15, 10, 0, 0, 0, 0, 0, 0, 0, 0],
)

# Digester 2: Mesophilic methanogenesis
configurator.add_digester(
    digester_id="digester_2",
    V_liq=1000.0,
    V_gas=150.0,
    T_ad=308.15,  # 35°C optimal for methanogens
    Q_substrates=[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],  # Only receives effluent
)

Design Rationale: - Stage 1 (Thermophilic): Higher temperature enhances hydrolysis of complex substrates (cellulose, hemicellulose, proteins) - Stage 2 (Mesophilic): Lower temperature is more stable and efficient for methanogenesis - Effluent-only feed to Stage 2: Prevents overloading, receives pre-hydrolyzed material

Automatic Gas Storage Creation: - add_digester() automatically creates: - digester_1_storage (304 m³ membrane storage) - digester_2_storage (150 m³ membrane storage) - Storages are automatically connected to their digesters

3. Adding Mechanical Components¶

Feed Pump¶

feed_pump = Pump(
    component_id="feed_pump",
    pump_type="progressive_cavity",  # Handles thick slurries
    Q_nom=30.0,  # m³/h nominal
    pressure_head=5.0,  # Low pressure (gravity assist)
)

Progressive Cavity Pumps are ideal for biogas substrates because: - Handle high solids content (>12% TS) - Low shear (preserves fiber structure) - Self-priming capability - Wide viscosity range

Transfer Pump¶

transfer_pump = Pump(
    component_id="transfer_pump",
    pump_type="progressive_cavity",
    Q_nom=25.0,  # m³/h
    pressure_head=8.0,  # Higher head for inter-digester transfer
)

Higher pressure head needed for: - Overcoming pipe friction losses - Elevation differences - Injection into pressurized digester

Mixers¶

mixer_1 = Mixer(
    component_id="mixer_1",
    mixer_type="propeller",
    tank_volume=1977.0,
    mixing_intensity="high",  # Aggressive for hydrolysis
    power_installed=15.0,
    intermittent=True,
    on_time_fraction=0.25,  # 6 hours on, 18 hours off
)

Mixing Strategy: - Intermittent operation: Reduces energy consumption by 75% - High intensity in hydrolysis: Breaks up floating layers, enhances substrate contact - Medium intensity in methanogenesis: Gentle mixing prevents inhibition of sensitive methanogens

Specific Power Input: - Digester 1: 15 kW × 0.25 ÷ 1977 m³ = 1.9 W/m³ (high) - Digester 2: 10 kW × 0.25 ÷ 1000 m³ = 2.5 W/m³ (medium)

4. Energy Integration with Automatic Flare¶

# Add CHP (automatically creates flare)
configurator.add_chp(
    chp_id="chp_1",
    P_el_nom=500.0,
    eta_el=0.40,
    eta_th=0.45,
    name="Main CHP Unit",
)

# Automatic connections handle gas routing
configurator.auto_connect_digester_to_chp("digester_1", "chp_1")
configurator.auto_connect_digester_to_chp("digester_2", "chp_1")

# Heat recovery for both digesters
configurator.auto_connect_chp_to_heating("chp_1", "heating_1")
configurator.auto_connect_chp_to_heating("chp_1", "heating_2")

Connection Chain:

Digester 1 → Storage 1 ↘
                        → CHP → Flare (automatic)
Digester 2 → Storage 2 ↗      ↓
                          Heat → Heating 1 & 2

Automatic Flare Creation: - add_chp() automatically creates a flare component - Flare ID: {chp_id}_flare (e.g., "chp_1_flare") - Function: Safety combustion of excess gas (98% CH₄ destruction) - Automatic connection: CHP → Flare

5. Three-Pass Gas Flow Simulation¶

The simulation executes in three passes for realistic gas management:

Pass 1 - Gas Production:

# Digesters produce gas → Storage tanks
Digester 1: Q_gas = 850 m³/d → Storage 1
Digester 2: Q_gas = 400 m³/d → Storage 2

Pass 2 - Storage Update:

# Storages receive gas, update pressure and volume
Storage 1: stored_volume += 850 * dt
Storage 2: stored_volume += 400 * dt
# If full: vent excess to atmosphere

Pass 3 - Gas Consumption:

# CHP requests gas from storages
CHP demand: 1150 m³/d biogas
Storage 1 supplies: ~675 m³/d
Storage 2 supplies: ~475 m³/d
# CHP operates with actual supply
# Excess to flare: (supply - consumption)

This ensures: - Realistic pressure management in storages - CHP operates with available gas, not idealized supply - Automatic venting prevents overpressure - Flare handles all excess gas safely

Expected Output¶

Plant Summary¶

=== Two-Stage Plant with Mechanical Components ===
Simulation time: 0.00 days

Components (12):
  - Hydrolysis Digester (digester)
  - Hydrolysis Digester Gas Storage (storage)
  - Methanogenesis Digester (digester)
  - Methanogenesis Digester Gas Storage (storage)
  - Substrate Feed Pump (pump)
  - Digester Transfer Pump (pump)
  - Hydrolysis Mixer (mixer)
  - Methanogenesis Mixer (mixer)
  - Main CHP Unit (chp)
  - Main CHP Unit Flare (flare)
  - Hydrolysis Heating (heating)
  - Methanogenesis Heating (heating)

Connections (10):
  - Hydrolysis Digester -> Methanogenesis Digester (liquid)
  - Hydrolysis Digester Gas Storage -> Main CHP Unit (gas)
  - Methanogenesis Digester Gas Storage -> Main CHP Unit (gas)
  - Main CHP Unit -> Main CHP Unit Flare (gas)
  - Main CHP Unit -> Hydrolysis Heating (heat)
  - Main CHP Unit -> Methanogenesis Heating (heat)

Final Results (Day 10)¶

RESULTS ANALYSIS
======================================================================

Final State (Day 10.0):
----------------------------------------------------------------------

Hydrolysis Digester:
  Biogas production:        850.3 m³/d
  Methane production:       493.2 m³/d
  pH:                         7.15
  VFA:                        3.82 g/L
  Temperature:               45.0 °C
  Gas Storage:
    - Stored volume:         152.1 m³ (50%)
    - Pressure:               1.00 bar
    - Vented:                  0.0 m³

Methanogenesis Digester:
  Biogas production:        402.8 m³/d
  Methane production:       258.7 m³/d
  pH:                         7.32
  VFA:                        1.95 g/L
  Temperature:               35.0 °C
  Gas Storage:
    - Stored volume:          75.0 m³ (50%)
    - Pressure:               1.00 bar
    - Vented:                  0.0 m³

Total Plant Production:
  Total biogas:            1253.1 m³/d
  Total methane:            751.9 m³/d
  Methane content:           60.0 %

CHP Performance:
  Electrical output:        480.5 kW
  Thermal output:           540.6 kW
  Gas consumption:         1150.0 m³/d
  Gas from Storage 1:       675.2 m³/d
  Gas from Storage 2:       474.8 m³/d
  Excess to flare:          103.1 m³/d
  Operating hours:          240.0 h

Flare Performance:
  Gas received:             103.1 m³/d
  CH₄ destroyed:             60.6 m³/d (98% efficiency)
  Cumulative vented:       1031.0 m³

Hydrolysis Mixer:
  Power consumption:          3.75 kW
  Mixing quality:             0.92
  Reynolds number:         12500

Methanogenesis Mixer:
  Power consumption:          2.50 kW
  Mixing quality:             0.88
  Reynolds number:          8300

Energy Balance¶

ENERGY BALANCE
======================================================================

Energy Production:
  Electrical (gross):       480.5 kW
  Thermal:                  540.6 kW

Parasitic Load:
  Mixer 1:                    3.75 kW
  Mixer 2:                    2.50 kW
  Pumps (estimated):          2.00 kW
  Total parasitic:            8.25 kW

Net Electrical Output:      472.3 kW

Heat Utilization:
  Heating demand:           125.4 kW
  CHP thermal supply:       540.6 kW
  Heat coverage:            431.0 %

Gas Management:
  Total production:        1253.1 m³/d
  CHP consumption:         1150.0 m³/d
  To flare:                 103.1 m³/d (8.2%)

Analysis: - Net efficiency: (472 kW + 125 kW) ÷ (751.9 m³/d × 10 kWh/m³ ÷ 24 h) = 190% (excellent heat recovery) - Parasitic ratio: 8.25 ÷ 480.5 = 1.7% (very low) - Excess heat: 540.6 - 125.4 = 415 kW available for external use - Flare usage: 8.2% of production vented (typical when CHP at part load)

Process Stability¶

PROCESS STABILITY ASSESSMENT
======================================================================

Digester 1 (Hydrolysis):
  pH stability:         CHECK (7.15 - slightly low)
  VFA level:            HIGH (3.82 g/L)
  FOS/TAC ratio:        0.418 (Monitor)
  Storage status:       NORMAL (50% full)

Digester 2 (Methanogenesis):
  pH stability:         GOOD (7.32)
  VFA level:            GOOD (1.95 g/L)
  FOS/TAC ratio:        0.245 (Stable)
  Storage status:       NORMAL (50% full)

Interpretation: - Digester 1: Higher VFA is expected in thermophilic hydrolysis stage - acids are consumed in stage 2 - Digester 2: Excellent stability indicators - methanogens effectively consume VFAs - pH gradient: 7.15 → 7.32 shows proper two-stage function - Gas storages: Both at healthy 50% fill level with stable pressure

Advantages of Two-Stage Design¶

1. Process Optimization¶

2. Substrate Flexibility¶

The two-stage system handles difficult substrates better: - High-fiber materials: Enhanced hydrolysis in Stage 1 - High-protein substrates: Ammonia buffering across stages - Variable feed composition: Stage 2 provides buffer capacity

3. Operational Benefits¶

• Reduced foaming: Separate hydrolysis phase
• Better pathogen reduction: Thermophilic stage (45°C) kills pathogens
• Easier process control: Monitor and control each stage independently
• Recovery from upsets: Stage 2 can buffer Stage 1 disturbances

Performance Comparison¶

Single-Stage vs Two-Stage¶

Cost-Benefit: - Additional investment: ~15-20% (second digester, pumps) - Energy gain: ~9% more biogas - Stability: Significantly reduced risk of process failure - ROI: Typically 3-5 years for difficult substrates

Mechanical Component Performance¶

Pump Operation¶

Feed Pump: - Operating point: 25 m³/d ÷ 24 = 1.04 m³/h (3.5% of nominal capacity) - Efficiency at low flow: Progressive cavity pumps maintain ~60% efficiency even at 3% capacity - Annual energy: 5 kW × 8760 h = 43,800 kWh

Transfer Pump: - Operating point: 25 m³/d ÷ 24 = 1.04 m³/h - Actual power: 8 kW × (1.04/25) × 1.2 (low efficiency penalty) ≈ 0.4 kW - Annual energy: 0.4 kW × 8760 h = 3,504 kWh

Mixer Performance¶

Hydrolysis Mixer: - Mixing time: ~15 minutes (from Reynolds number and geometry) - Tip speed: ~4.5 m/s (turbulent regime) - Shear rate: ~50 s⁻¹ (high intensity) - Power number: 0.32 (typical for propeller at Re > 10,000)

Methanogenesis Mixer: - Mixing time: ~20 minutes - Tip speed: ~3.8 m/s - Shear rate: ~35 s⁻¹ (medium intensity) - Prevents stratification without damaging sensitive methanogens

Gas Storage and Flare Management¶

Storage Dynamics¶

Storage 1 (Hydrolysis): - Receives ~850 m³/d (higher production due to enhanced hydrolysis) - Supplies ~675 m³/d to CHP (proportional to total demand) - Net accumulation: +175 m³/d - Reaches 50% capacity in ~0.9 days

Storage 2 (Methanogenesis): - Receives ~400 m³/d (lower but more stable) - Supplies ~475 m³/d to CHP - Net draw: -75 m³/d (supplements Storage 1) - Provides buffer for production variations

Flare Operation¶

When does the flare activate?: 1. Storage overflow: When either storage reaches 100% capacity 2. CHP part-load: When CHP operates below full capacity 3. Maintenance: When CHP is offline but digesters continue 4. Start-up/shutdown: During transient operations

Flare performance: - Destruction efficiency: 98% CH₄ conversion to CO₂ - Temperature: ~1000°C combustion temperature - Emissions: 2% uncombusted CH₄ + CO₂ from combustion - Safety: Automatic ignition, flame detection

Process Control Strategies¶

Temperature Control¶

# Heating 1 maintains 45°C for hydrolysis
heating_1.target_temperature = 318.15  # K
heating_1.heat_loss_coefficient = 0.5  # Higher due to ΔT

# Heating 2 maintains 35°C for methanogenesis
heating_2.target_temperature = 308.15  # K
heating_2.heat_loss_coefficient = 0.3  # Lower ΔT

Heat Demand Calculation: - Digester 1: Q = 0.5 kW/K × (45 - 15)°C = 15 kW base loss + 80 kW process heating = 95 kW - Digester 2: Q = 0.3 kW/K × (35 - 15)°C = 6 kW base loss + 24 kW process = 30 kW - Total: 125 kW (well covered by 541 kW CHP thermal output)

Mixing Control¶

Strategy: Intermittent mixing with adaptive timing

# High mixing when feeding (4× daily)
if feeding_event:
    mixer.on_time_fraction = 0.5  # 50% duty cycle
else:
    mixer.on_time_fraction = 0.15  # 15% baseline

Feed Control¶

Model Predictive Control (MPC) approach: 1. Measure current VFA and pH 2. Predict 48h response with different feed rates 3. Select feed rate optimizing CH₄ while maintaining pH > 7.0

Common Issues and Solutions¶

Issue 1: High VFA in Digester 1¶

Symptoms: - VFA > 5 g/L - pH < 7.0 - Reduced gas production

Solutions:

# Reduce organic loading
Q_substrates = [12, 8, 0, 0, 0, 0, 0, 0, 0, 0]  # Reduce from [15, 10, ...]

# Increase Stage 1 temperature (careful - max 55°C)
T_ad_1 = 323.15  # 50°C

# Increase mixing to prevent accumulation
mixer_1.on_time_fraction = 0.35

Issue 2: Low Methane Content¶

Symptoms: - CH₄ < 55% - CO₂ elevated - Low specific gas production

Solutions:

# Increase HRT (reduce feed)
Q_substrates = [12, 8, 0, 0, 0, 0, 0, 0, 0, 0]

# Optimize Stage 2 temperature
T_ad_2 = 311.15  # 38°C (optimal for many methanogens)

# Check for air leaks (O₂ inhibits methanogens)

Issue 3: Foaming in Digester 1¶

Symptoms: - Gas storage shows pressure fluctuations - Effluent contains excessive gas bubbles

Solutions:

# Reduce mixing intensity
mixer_1.mixing_intensity = "medium"

# Add antifoaming agent (substrate index 8)
Q_substrates = [15, 10, 0, 0, 0, 0, 0, 0, 0.05, 0]  # 50 L/d antifoam

# Increase transfer rate to Stage 2
# (implement timer-based periodic drawdown)

Issue 4: Excessive Flare Usage¶

Symptoms: - Flare operates continuously - >20% of production to flare - High storage pressure

Causes: - CHP undersized for gas production - CHP in part-load operation - Excess substrate feed

Solutions:

# Option 1: Reduce substrate feed
Q_substrates = [12, 8, 0, 0, 0, 0, 0, 0, 0, 0]

# Option 2: Increase CHP capacity
configurator.add_chp("chp1", P_el_nom=600, ...)  # Increase from 500

# Option 3: Add second CHP unit
configurator.add_chp("chp2", P_el_nom=200, ...)
configurator.auto_connect_digester_to_chp("digester_1", "chp2")

# Option 4: Increase gas storage capacity
# (modify V_gas when adding digesters)

Advanced Applications¶

1. Parameter Sweep for Optimization¶

from pyadm1.simulation import ParallelSimulator

# Test different Stage 1 temperatures
parallel = ParallelSimulator(adm1, n_workers=4)
scenarios = [
    {"T_ad_1": 313.15, "Q": [15, 10, 0, 0, 0, 0, 0, 0, 0, 0]},  # 40°C
    {"T_ad_1": 318.15, "Q": [15, 10, 0, 0, 0, 0, 0, 0, 0, 0]},  # 45°C
    {"T_ad_1": 323.15, "Q": [15, 10, 0, 0, 0, 0, 0, 0, 0, 0]},  # 50°C
]
results = parallel.run_scenarios(scenarios, duration=30)

2. Online Calibration¶

from pyadm1.calibration import Calibrator

# Calibrate Stage 1 hydrolysis parameters
calibrator = Calibrator(plant.components["digester_1"])
params = calibrator.calibrate_initial(
    measurements=measurement_data,
    parameters=["k_hyd_ch", "k_hyd_pr", "k_hyd_li"],
)

3. Model Predictive Control¶

# Predict optimal feed for next 48 hours
Q_best, Q_ch4_pred = simulator.determine_best_feed_by_n_sims(
    state_zero=current_state,
    Q=current_feed,
    Qch4sp=800,  # Setpoint: 800 m³/d CH4
    feeding_freq=48,
    n=20  # Test 20 scenarios
)

References¶

• TPAD Design: Simeonov, I., Chorukova, E., & Kabaivanova, L. (2025). Two-stage anaerobic digestion for green energy production: A review. Processes, 13(2), 294.
• Process Control: Gaida (2014). Dynamic real-time substrate feed optimization of anaerobic co-digestion plants. PhD thesis, Leiden University.

Related Examples¶

• basic_digester.md: Simple single-stage system
• calibration_workflow.md(calibration_workflow.md): Parameter estimation from measurement data
• substrate_optimization.py: Optimal feed strategy
• parallel_two_stage_simulation.py: Parallel simulations