Chapter 1 Environmental Engineering: Indoor Air quality modeling

Chapter 1 Environmental Engineering: Indoor Air quality modeling#

  1. Introduction: BOD equation

  2. Simulation: BOD

  3. Self-Assessment

1. Introduction#

🏠 Indoor Air Quality (IAQ) – Definition, Risks, and Management#

Indoor Air Quality (IAQ) refers to the condition of air inside buildings and structures — including homes, offices, schools, and hospitals — as it affects the health, comfort, and productivity of occupants.

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With people spending 90%+ of their time indoors, IAQ often poses a greater health risk than outdoor air pollution.

☣️ Key Toxic Parameters in Indoor Air#

Pollutant

Source Examples

Health Risks

Particulate Matter (PM2.5, PM10)

Cooking, smoking, dust, outdoor infiltration

Respiratory and cardiovascular issues

Volatile Organic Compounds (VOCs)

Paints, cleaning agents, furniture

Headaches, nausea, long-term toxicity

Formaldehyde

Building materials, adhesives

Eye irritation, cancer risk

Carbon Monoxide (CO)

Gas stoves, heaters, tobacco smoke

Lethal at high levels, dizziness

Radon

Soil gas infiltration

Lung cancer (radioactive gas)

Nitrogen Dioxide (NO₂)

Combustion appliances

Asthma, respiratory inflammation

Mold & Biological Agents

Humidity, poor ventilation

Allergies, infections

🔍 Factors Influencing IAQ#

Category

Examples

Building Design

Ventilation rate, airtightness, HVAC systems

Occupant Behavior

Smoking, cooking, cleaning habits

Outdoor Air Quality

Pollutant infiltration from traffic or industry

Materials & Furnishings

Off-gassing from carpets, paints, furniture

Moisture & Humidity

Promotes mold and microbial growth

Maintenance

Filter changes, duct cleaning, leak repairs

🧮 How IAQ Is Modeled#

Approach

Description

Use Case

Box Models

Simplified mass balance of pollutants

Quick IAQ screening

CFD Models

Computational Fluid Dynamics for airflow

Detailed design and ventilation analysis

Exposure Models

Estimate occupant exposure over time

Health risk assessment

Sensor Networks

Real-time monitoring and feedback

Smart building management

Modeling helps predict pollutant concentrations, optimize ventilation, and assess health risks under different scenarios.

Governing Equation: Mass Balance Model (CSTR)#

The Indoor Air Quality model is a simple model that treats the indoor space as a well-mixed box with sources and sinks for pollution [Masters and Ela, 2008]. The model assumes a well-mixed indoor space and applies the following differential equation:

\[ \frac{dC}{dt} = \frac{E}{V} - \left( \frac{Q}{V} + k \right) C \]

Where:

  • \(( C(t) \)): pollutant concentration at time ( t ) (mg/m³)

  • \(( E \)): emission rate (mg/hr)

  • \(( V \)): room volume (m³)

  • \(( Q \)): ventilation rate (m³/hr)

  • \(( k \)): decay rate (1/hr), representing filtration or chemical decay

  • \(( \frac{Q}{V} \)): air exchange rate (1/hr)

This equation balances pollutant input from emissions and removal via ventilation and decay.

🛠️ How to Control and Manage IAQ#

Strategy

Examples

Source Control

Low-VOC materials, no smoking, sealed radon entry

Ventilation

Natural or mechanical systems, air exchange

Filtration

HEPA filters, activated carbon, air purifiers

Humidity Control

Dehumidifiers, leak repair, moisture barriers

Monitoring

CO₂ sensors, VOC meters, PM detectors

Design Integration

IAQ planning during building design phase

📌 Insight#

Indoor air quality is a critical public health issue — especially in energy-efficient buildings with limited ventilation.
Proactive design, monitoring, and management can reduce exposure to toxic pollutants and improve well-being for millions.

🔗 Resources#

Foundational Literature#

[Masters and Ela, 2008] presents indoor air quality modeling using simplified mass balance equations, assuming well-mixed zones and focusing on ventilation rates, pollutant sources (e.g., VOCs, radon), and regulatory thresholds—ideal for introductory environmental engineering education. In contrast, [Venkatram and Thé, 2003] apply more advanced transport models based on eddy diffusivity and gradient formulations, capturing spatial and temporal variations in pollutant concentrations, especially for aerosols, and linking them to exposure and mitigation strategies—suited for research and regulatory applications.

2. Simulation#

Indoor Air Quality Simulation: Methodology & Model Description#

This simulation estimates the concentration of indoor air pollutants over time using a simplified mass balance model for a single enclosed space. It accounts for:

  • Room volume

  • Ventilation rate

  • Pollutant emission rate

  • Natural decay or removal processes

  • Initial pollutant concentration

Governing Equation: Mass Balance Model#

The model assumes a well-mixed indoor space and applies the following differential equation:

\[ \frac{dC}{dt} = \frac{E}{V} - \left( \frac{Q}{V} + k \right) C \]

Where:

  • \(( C(t) \)): pollutant concentration at time ( t ) (mg/m³)

  • \(( E \)): emission rate (mg/hr)

  • \(( V \)): room volume (m³)

  • \(( Q \)): ventilation rate (m³/hr)

  • \(( k \)): decay rate (1/hr), representing filtration or chemical decay

  • \(( \frac{Q}{V} \)): air exchange rate (1/hr)

This equation balances pollutant input from emissions and removal via ventilation and decay.

Numerical Solution#

The model uses a forward Euler method to simulate concentration over

import numpy as np
import matplotlib.pyplot as plt
from ipywidgets import interact, FloatSlider, Dropdown
from IPython.display import display

# 📐 IAQ model: mass balance for a single zone
def simulate_iaq(t, V, Q, E, k, C0):
    # V: room volume (m³)
    # Q: ventilation rate (m³/hr)
    # E: emission rate (mg/hr)
    # k: decay rate (1/hr)
    # C0: initial concentration (mg/m³)

    C = np.zeros_like(t)
    C[0] = C0
    for i in range(1, len(t)):
        dt = t[i] - t[i-1]
        dC = (E/V - (Q/V + k) * C[i-1]) * dt
        C[i] = C[i-1] + dC
    return C

# 📊 Plotting function
def plot_iaq(V, Q, E, k, C0, duration_hr):
    t = np.linspace(0, duration_hr, 500)
    C = simulate_iaq(t, V, Q, E, k, C0)

    plt.figure(figsize=(10, 5))
    plt.plot(t, C, color='darkgreen', label='Pollutant Concentration (mg/m³)')
    plt.axhline(1000, color='red', linestyle='--', label='Threshold (e.g. CO₂ ppm)')
    plt.title("🏠 Indoor Air Quality Simulation")
    plt.xlabel("Time (hours)")
    plt.ylabel("Concentration (mg/m³)")
    plt.grid(True, linestyle='--', alpha=0.5)
    plt.legend()
    plt.tight_layout()
    plt.show()

    peak = np.max(C)
    print(f"📈 Peak concentration: {peak:.2f} mg/m³")
    if peak > 1000:
        print("⚠️ Air quality exceeds recommended threshold. Consider increasing ventilation or reducing emissions.")
    else:
        print("✅ Air quality remains within acceptable limits.")

# 🎛️ Interactive controls
interact(
    plot_iaq,
    V=FloatSlider(value=50, min=10, max=200, step=5, description="Room Volume (m³)"),
    Q=FloatSlider(value=25, min=5, max=100, step=5, description="Ventilation Rate (m³/hr)"),
    E=FloatSlider(value=100, min=0, max=500, step=10, description="Emission Rate (mg/hr)"),
    k=FloatSlider(value=0.1, min=0.0, max=1.0, step=0.05, description="Decay Rate (1/hr)"),
    C0=FloatSlider(value=0, min=0, max=500, step=10, description="Initial Conc. (mg/m³)"),
    duration_hr=FloatSlider(value=8, min=1, max=24, step=1, description="Duration (hr)")
)

<function __main__.plot_iaq(V, Q, E, k, C0, duration_hr)>

Indoor Air Quality Simulation: Quiz, Conceptual & Reflective Questions#

This module reinforces understanding of indoor air quality dynamics using a mass balance model. It supports learning through multiple-choice questions, conceptual prompts, and reflective challenges.

Conceptual Questions#

  1. What does the term ( \frac{Q}{V} ) represent in the IAQ model?

    • A. Pollutant emission rate

    • B. Air exchange rate (1/hr)

    • C. Room volume

    • D. Decay coefficient

  2. Which factor most directly reduces indoor pollutant concentration over time?

    • A. Increasing room volume

    • B. Increasing emission rate

    • C. Increasing ventilation rate

    • D. Increasing initial concentration

  3. Why is the decay rate ( k ) included in the model?

    • A. To simulate pollutant accumulation

    • B. To represent natural removal or filtration

    • C. To adjust for temperature effects

    • D. To model CO₂ generation

  4. If the emission rate is zero and ventilation is active, what happens to pollutant concentration over time?

    • A. It increases

    • B. It remains constant

    • C. It decreases

    • D. It oscillates

  5. Which of the following would most likely cause the model to predict unsafe air quality?

    • A. High decay rate

    • B. Low emission rate

    • C. Low ventilation rate

    • D. Large room volume

Interpretation#

  1. Why is the pollutant concentration initialized with ( C_0 ) and updated using a time-stepping loop?

  2. How does the model ensure that concentration changes are proportional to both emission and removal processes?

  3. Why is the threshold set at 1000 mg/m³, and how could it be adapted for different pollutants (e.g., PM2.5, VOCs)?

  4. What assumptions are made by treating the room as a well-mixed zone?

  5. How would you modify the model to include multiple rooms or pollutant types?

Reflective Questions#

  1. How do ventilation and source control interact to influence indoor air quality?

  2. Why is it important to simulate pollutant dynamics over time rather than using static values?

  3. What are the limitations of this model when applied to real buildings with complex airflow patterns?

  4. How could this simulation support decisions in building design, HVAC upgrades, or public health policy?

  5. What insights can be gained by comparing different scenarios (e.g., high occupancy vs. low ventilation)?

Design Insight#

“Indoor air quality is shaped by a dynamic balance between pollutant sources and removal mechanisms. Modeling helps visualize this balance and supports smarter design and healthier environments.”

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