




Using a Math Model 

to determine a cartridge's service life 

Mathematical
equations have been used to predict the service lives of organic vapor respirator
cartridges when used for protection against single contaminants. Using an equation developed by G. Wood, OSHA
has precalculated and presented some service lives in a table. You can calculate others using The Advisor Genius. It is suggested that you reduce the service life estimate by some safety factor to give a change schedule that you should document in your written respiratory
program.





Using a Math Model Table 





Steps

Example

1. Determine the concentration level of airborne
contaminants in the work area

Grant owns a midsize furniture company that
paints with lacquers. They use a volatile solvent, toluene to quickly dry the
lacquer. His several measurements of the toluene vapor reveal a worst case exposure
of 200 ppm over an eighthour day.

2. Obtain access to a predictive table that is
based on research

Grant surfs to the web page on this Advisor site
called Wood Model Table, which lists cartridge service lives for 120 chemicals at
varying concentrations.

3. Use the table to come up with a cartridge
service life estimate

Grant looks across the top of the table and finds
the column for 200 ppm — the concentration equal to or above the level of toluene at
his work place. Then he scrolls down the table and finds toluene in the aromatic
group. He discovers that the service life estimate is 307 minutes. He writes
down the number.

4. Account for differences in the real work
environment and those assumptions used by the math model
 humidity and temperature
 breathing rate




Grant looks at the standard conditions given at
the top of the table. He sees that the assumed relative humidity is 50% — much
lower than the 75% humidity found in his work area. Grant is aware that such a high
humidity will seriously affect organic vapor cartridge performance, so he applies a safety
factor of two by cutting the estimate in half, giving him 154 minutes. The other
standard conditions assumed by the table match his work environment.

5. Create a written change schedule for the
cartridges

Grant
applies a further safety factor to the estimate and creates a change schedule requiring
his employees to turn in their used cartridges for new ones every 2 hours. He also
prints a copy of the Wood Model Table and
circles the 307 minute value and notes the factor applied for humidity and the safety
factor reduction to 2 hours, and includes them in his written respiratory program.





Using a Math Model Equation
Steps 
Example 
1.
Determine the following:
 Number of cartridges used by the respirator
 Weight of sorbent in each cartridge in grams
 Carbon micropore volume in cubic centimeters per gram
 Density of the packed bed in units of grams per cubic centimeter
 The maximum temperature expected in the workplace
 The maximum humidity expected in the workplace
 The maximum concentration of contaminants in the workplace in units of parts per million
 The workrate (volumetric flow rate) in units of liters per minute (LPM).


The lacquerdrying technique has been modified at
Grant's shop, which has lowered the amount of airborne toluene to 125 ppm. While this
is below the OSHA PEL, Grant still wants his painters to wear respirators. When
Grant looks to the Wood table for this concentration to figure a service life estimate, he
finds there is no column for 125. It gives data for 100 ppm and then jumps right up
to 200 ppm. Grant understands that he must go with the 200 ppm estimate of 154
minutes to be safe, yet he thinks the cartridges should last longer than that. He
determines to use the Wood calculation for his exact concentration of 125 ppm. So,
Grant does a little research to come up with the required data. He calls the
manufacturer to get data on its respirator cartridges.

2.
Put the information from Step 1 into a
mathematical equation and calculate for the unknown service life

Grant
hears that the OSHA Advisor will perform the calculation for
him. All he has to do is provide his information to the Advisor
Genius, which asks for the data one step at a time. Grant
is delighted with how easy it is, and at the end, the Genius gives
him the service life estimate of 224 — 70 minutes longer than if
he had used the table.

3. Use the table to come up with a cartridge
service life estimate

Grant looks across the top of the table and finds
the column for 200 ppm — the concentration equal to or above the level of toluene at
his work place. Then he scrolls down the table and finds toluene in the aromatic
group. He discovers that the sevice life estimate is 307 minutes. He writes
down the number.



Keep In Mind
 The math models are usually only directly applicable for single contaminant exposures.
If you have a multiple contaminant situation, you may need to use other methods to
derive a schedule or increase the safety factors.
 The Wood Math Model is just one
equation you can use. Also, because it is a predictive type of model (as opposed to
a descriptive type), you should not rely on it without some experimental confirmation of
the calculation or use of appropriate safety factors.



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Change Scedules 



