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Using a Math Model
The Advisor Genius
The Wood Math Model Table

 

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Respiratory Protection Advisor
Calculator
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.

Example using Math Model Table

Example using Math Model Equation
Using a Math Model Table
Steps Example
1. Determine the concentration level of airborne contaminants in the work area Grant owns a mid-size 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 eight-hour 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 sevice 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 work-rate (volumetric flow rate) in units of liters per minute (LPM).
The lacquer-drying 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. Apply a safety reduction to the service life estimate, create a written change schedule for the cartridges and include in written respiratory protection program. Grant applies a safety reduction to the service life estimate and sets his change schedule at 3 hours. The Advisor Genius also offers to print out a report for Grant that can serve as the basis for written change schedule as part of the respirator program.  Grant prints out the form, notes the adjustment factors and is done! 
Keep in MindKeep 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.
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  • 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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