eTools Home: Respiratory Protection Regulations & Documents | Definitions | Bibliography | Site Map | Credits
Respiratory Protection

Respiratory Protection eTool


<< Back to Using a Math Model

The Yoon-Nelson Mathematical Model

The Yoon-Nelson model is a descriptive model that uses experimental data to calculate parameters that are then entered into the model.
  1. Yoon, Y.H., J.H. Nelson, Breakthrough Time and Adsorption Capacity of Respirator Cartridges, American Industrial Hygiene Association Journal, 53:303-316 (1992).

  • The basic equation for the model is:
For problems with accessibility in using figures and illustrations in this document, please contact the Directorate of Technical Support and Emergency Management at (202) 693-2300.

t = breakthrough time (min)
Τ = 50% contaminant breakthrough time (min)
k' = rate constant (min-1)
P = probability of contaminant breakthrough.
  • The value of Τ is determined from experimental data.

  • The value of k' has been shown to be related to Τ by the following formula:
For problems with accessibility in using figures and illustrations in this document, please contact the Directorate of Technical Support and Emergency Management at (202) 693-2300.

k = proportionality constant that is constant independent of concentration and varies only slightly with humidity.
  • The value of Τ is related to the contaminant concentration by the equation:

For problems with accessibility in using figures and illustrations in this document, please contact the Directorate of Technical Support and Emergency Management at (202) 693-2300.

K", a = constants that can be derived from experimental data. They vary with humidity, but for humidities 50% they are essentially constant.
CI = contaminant assault concentration. (ppm)

  • It is possible to determine the constants k, K", and a from a minimum of 3 experimental data points. However, the inclusion of additional data points increases the accuracy of the model.

How does it compare with experimental results? See the comparison.




eTools Home: Respiratory Protection Regulations & Documents | Definitions | Bibliography | Site Map | Credits