Pollution Concentration Rooms

Overview

Engineering reference data for Pollution Concentration Rooms in environment.

Key Formulas

CO₂ Emissions

$E = E_F \cdot EF$

Emission factor × activity.

Carbon Footprint

$CF = \sum (Activity_i \times EF_i)$

Sum of all emission sources.

Variables

Pollution Concentration Formula

The concentration of a homogeneous pollutant (like carbon dioxide) in a room over time can be calculated using the following general formula:

$c = \left( \frac{q}{n V} \right) \left( 1 - \frac{1}{e^{n t}} \right) + (c_0 - c_i) \left( \frac{1}{e^{n t}} \right) + c_i$

Where:

• $c$ = concentration of the pollutant in the room ($m^3/m^3$ or ppm)
• $q$ = rate of pollutant supplied to the room ($m^3/h$)
• $V$ = volume of the room ($m^3$)
• $n$ = number of air shifts per hour ($1/h$)
• $t$ = time ($h$)
• $e$ = the mathematical constant approximately equal to 2.718
• $c_i$ = concentration of the pollutant in the inlet (make-up) ventilation air ($m^3/m^3$)
• $c_0$ = concentration of the pollutant in the room at the start ($t=0$) ($m^3/m^3$)

Application Example: Cinema CO₂ Concentration

Scenario: A 500 m³ cinema with 100 people. The average CO₂ emission per person is 0.05 m³/h. The ventilation system provides 1 air shift per hour. The initial CO₂ concentration in the room and in the inlet air is assumed to be 0 and 0.0004 m³/m³ (400 ppm), respectively.

Calculation:

1. Total CO₂ supply rate (q): $100 \text{ persons} \times 0.05 \, m^3/h \text{ per person} = 5 \, m^3/h$
2. Apply the formula for $t = 1$ hour: $c = \left( \frac{5}{1 \cdot 500} \right) \left( 1 - \frac{1}{e^{1 \cdot 1}} \right) + (0 - 0.0004) \left( \frac{1}{e^{1 \cdot 1}} \right) + 0.0004$ $c = (0.01)(1 - 0.368) + (-0.0004)(0.368) + 0.0004$ $c \approx 0.0063 + (-0.00015) + 0.0004 = 0.0066 \, m^3/m^3$ This is approximately 6600 ppm.

Important Notes & Context

• General Applicability: The formula above is valid for calculating the concentration of any homogeneous pollutant mixed with air.
• Global CO₂ Baseline: The normal concentration of carbon dioxide in outdoor ambient air is approximately 400-428 ppm (or 0.0004 m³/m³).
• Health & Comfort Threshold: As indicated in the example, a concentration of 6700 ppm (0.0067 m³/m³) can lead to adverse health effects and indicates inadequate ventilation. Acceptable indoor levels for comfort are typically well below 1000-1500 ppm.

References

• Original Source