Andrew F. Oberta, MPH, CIH
The Environmental Consultancy
September 10, 2015

The exponential decay of the concentration of airborne contaminants in a ventilated space with a well-mixed atmosphere has been established for industrial ventilation purposes as well as for determining air exchange rates in buildings. For industrial hygiene applications, the following equation has been published: 1


t = time, minutes or hours
Vr = room volume, ft³
Qdil = air dilution rate, ft³/minute or hour
C1 = initial concentration, ppm or mg/m³
C2 = final concentration, ppm or mg/m³

This equation assumes that the space is continously ventilated with clean air and that no additional contaminants are introduced into the space. It does not depend on the physical state of the contaminant, which can be a gas or solid particles. If the air exchange rate, Qdil / Vr , is known, the time needed to reduce concentration C1 to C2 can be calculated.

For building ventilation studies, the concentration is measured at intervals to determine the air exchange rate according to the following equation in Section 8 of ASTM E741: 2


A = average air change rate
C(t1) = concentration at time t1
C(t2) = concentration at time t2

This equation is derived in a paper by Grot and Lagus 3

Studies conducted with tracer gases and smoke particles have shown that the concentration follows an exponential decay. These studies have the advantage of instantaneous measurements of tracer gas and smoke particle concentrations, whereas measurements of fiber concentration require sampling over a period of time and yield an average concentration during that time.

A paper by Pavelchak et al. 4 presents the results of a study using tracer gas and smoke particles in the 0.5 µm to 5 µm range that showed exponential decay of both contaminants. The results of one test with 0.5 µm smoke particles are plotted in the following chart from this paper and show the particle concentration decay closely following the solid line for theoretical exponential decay.

Figure 1. Smoke particle concentration decay at 20 ac/hr air exchange rate (from Pavelchak et al.)

It is reasonable to conclude that airborne fibers in the size range present at an abatement project would behave similar to the smoke particles in this test and follow an exponential decay during clearance testing.

Return to Air Volumes for PCM Clearance

1Useful Equations – Practical Applications of Math Related to Ventilation, Excerpt for AIHA Web Course, page 15 - September 2, 2010, D. Jeff Burton, PE, CIH (accessed on-line)

2ASTM E741-11 Standard Test Method for Determining Air Change in a Single Zone by Means of a Tracer Gas Dilution, ASTM International, www.astm.org

3 The Evaluation of Ventilation Systems Using Tracer Gas Methods, Richard A. Grot and Peter L. Lagus, Lagus Applied Technology. July, 1991 Industrial Hygiene News.

4 A Simple and Inexpensive Method for Determining the Effective Ventilation Rate in a Negatively Pressurized Room Using Airborne Particles as a Tracer, Nicholas Pavelchak,William Palmer, Ronald P. DePersis,and Matthew A. Londo, Applied Occupational and Environmental Hygiene, Volume 17(10): 704–710, 2002