#### Respirator Change Schedules » Using a Math Model Table to Determine a Cartridge's Service Life

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.
• is an example of a descriptive math model.

Mathematical equations have been used to predict the service lives of organic vapor respirator cartridges when used for protection against single contaminants. Using an developed by G. Wood, OSHA has precalculated and presented some service lives in a . You can calculate others using NIOSH's MultiVapor™ Version 2.2.3 Application. 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.

##### Factors That Can Reduce Cartridge Service Life
###### Worker Exertion Level: a worker breathing twice as fast as another will draw twice the amount of contaminant through the respirator cartridge

The service life of a cartridge or canister respirator depends upon the total amount of contaminant captured by the absorbent. The total amount of captured contaminant is directly related to the work rate or breathing rate; i.e., a worker breathing twice as fast as another will draw twice the amount of contaminant through the respirator cartridge. Most cartridge studies have used a breathing rate, 50-60 liters per minute, that approximates a high end of moderate work rate. For work rates that exceed this level (e.g., heavy shoveling, running) you may need to apply or take into account a correction factor when determining a service life.

###### Respirator Cartridge Variability: some cartridges contain more activated charcoal than others

The service life of a respirator cartridge is directly related to the amount of active material in the cartridge. For instance, most dual cartridge organic vapor respirators contain between 35-50 grams of activated charcoal in each cartridge. If the specific cartridge being evaluated can be reproducibly determined to have a certain amount of active material, then modifications to the service life may be justified. You can obtain information on cartridge specifications from manufacturers.

###### Temperature: the hotter it is, the shorter the service life

High temperatures can adversely affect the adsorptive capacity of respirator cartridges and canisters. The high temperature may act by thermally loosening the attractive forces that make adsorption happen or may act in concert with humidity by increasing the moisture carrying capacity of air. This latter mechanism may represent the greatest likely effect on service lives of cartridges. Temperature effects alone have been reported to reduce the service life 1-10% for every 10 degrees Celsius rise depending on the specific solvent (Nelson, et. al., 1976). Corrections to cartridge estimated service life for this effect alone are probably not necessary under normal working temperatures.

###### Relative Humidity: water vapor will compete with the organic vapors for active sites on the adsorbent

Relative Humidity is a measure of the amount of water vapor the air will hold at a specified temperature and is expressed in percentage values. Since warmer air will hold more water than colder air, the same relative humidity at a higher temperature represents a significantly greater amount of moisture. High relative humidity is a significant negative factor in the capacity of organic vapor cartridges since the large quantity of water vapor will compete with the organic vapors for active sites on the adsorbent. Most of the laboratory work determining adsorbent capacity has been performed at a low relative humidity of 50% at approximately 70 degrees F.

If the actual use of the organic vapor respirators will take place in a significantly more humid environment, then you may need to apply or take into account a safety factor when determining a service life. The exact magnitude of the humidity effect is complex, dependent in part upon chemical characteristics and concentrations of both the contaminant and the water vapor. Based upon relatively few studies, a reduction by a factor of 2 in the cartridge service life originally estimated based upon 50 % relative humidity, may be made when the relative humidity reaches 65% (Nelson, et. al., 1976; Werner, 1985). If the relative humidity exceeds 85%, you should consider experimental testing or another method to more specifically determine the service life. Mathematical modeling may be an appropriate, albeit complex, approach to predict the effect of humidity at various chemical concentrations (Wood, 1987; Underhill, 1987).

###### Multiple Contaminants: predictions should be derived from the least well adsorbed compound

Multiple contaminants introduce a great deal of variability into the prediction of service life for respirator cartridges. Much of the laboratory testing and the mathematical models have utilized a single contaminant to determine service lives. Only a limited number of multiple contaminant situations have been studied and reported in the literature (e.g. Yoon, 1996; Jonas et. al., 1986). Cartridge service life for mixtures of compounds with significantly different chemical characteristics is probably best determined by experimental methods. Predictions based upon models without experimental data should probably be very conservative and ascribe the service life derived from the least well adsorbed compound to the total mixture concentration in terms of parts per million. The displacement of a less well adsorbed compound by a more highly adsorbed one may alter the actual service life from the estimated one in some cases.

The table below provides breakthrough times for 120 chemicals at various concentrations. OSHA derived these breakthrough times from the (Wood, G.O., Estimating Service Lives of Organic Vapor Cartridges, American Industrial Hygiene Association Journal, 55:11-15, 1994).

Keep In Mind

If the conditions in your case are significantly different from these, in particular relative humidities greater than 65%, you will need to make the appropriate corrections to the time given by the table. Another section of this advisor provides a discussion of these factors.

##### OSHA used the following standard conditions:
• Number of respirator cartridges: 2
• Temperature: 72 degrees Fahrenheit (22 degrees Celsius)
• Sorbent: Activated charcoal
• Relative humidity: less than or equal to 50%
• Sorbent mass per cartridge: 26 g
• Breakthrough: 10%
• Flow rate: 53.3 liters per minute
##### How to use this Table:

Look down the left column to find the chemical and across the row to the column with the identified concentration, and there you will find the service life time in minutes.

These tables are best viewed on tablets, notebooks, or desktop computer screens.

Breakthrough Times (min)
Name CAS # Contaminant Concentration (ppm)
50 100 200 500 1000
Aromatics
Benzene 71-43-2 Work Shift Limited to a maximum concentration of 50 ppm for negative pressure APR
See the Benzene Standard [29 CFR 1910.1028(g)]
Toluene 108-88-3 1018 562 307 135 72
Ethylbenzene 100-41-4 1133 604 319 135 70
m-Xylene 108-38-3 1143 608 321 136 70
Cumene 98-82-8 1122 586 304 126 64
Mesitylene 108-67-8 1159 603 311 128 65
p-Cymene 99-87-6 1104 566 289 117 59
Alcohols
Methanol 67-56-1 This calculation is not applicable to this compound
Ethanol 64-17-5 123 105 85 60 43
Isopropanol 67-63-0 425 286 186 101 61
Allyl alcohol 107-18-6 789 495 303 152 87
Propanol 71-23-8 551 364 233 123 73
sec-Butanol 78-92-2 773 464 272 130 72
Butanol 71-36-3 1073 615 345 156 84
2-Pentanol 6032-29-7 1091 601 327 143 75
3-Methyl-1-butanol 123-41-3 1242 672 358 152 78
4-Methyl-2-pentanol 108-11-2 1076 578 307 130 67
Pentanol 71-41-0 1281 690 366 155 79
2-Ethyl-1-butanol 97-95-0 1246 657 342 142 72
Monochlorides
Methyl chloride 74-87-3 Not applicable, boiling point below ambient temperatures
Vinyl chloride 75-01-4 Not applicable, boiling point below ambient temperatures
See the Vinyl Chloride Standard [29 CFR 1910.1017(g)]
Ethyl chloride 75-00-3 Not applicable, boiling point below ambient temperatures
2-Chloropropane 75-29-6 224 150 99 54 34
Allyl chloride 107-05-1 264 177 116 64 40
1-Chloropropane 540-54-5 492 301 181 90 52
2-Chloro-2-methylpropane 507-20-0 655 374 212 98 54
1-Chlorobutane 109-69-3 733 422 239 111 61
2-Chloro-2-methylbutane 594-36-5 705 398 222 101 55
1-Chloropentane 543-59-9 852 474 260 116 62
Chlorocyclopentane 930-28-9
Chlorobenzene 108-90-7 1327 709 376 160 83
1-Chlorohexane 544-10-5 993 530 281 119 62
o-Chlorotoluene 95-49-8 1297 682 356 148 76
1-Chloroheptane 629-06-1 930 492 258 109 56
3-(Chloromethyl) heptane 123-04-6 771 410 216 92 48
Dichlorides
Dichloromethane 75-09-2 See the Methylene Chloride Standard [29 CFR 1910.1052(g)]
trans-1,2-Dichloroethylene 156-60-5 296 198 129 71 44
1,1-Dichloroethane 75-35-4 234 157 103 57 35
cis-1,2-Dichloroethylene 156-59-2 356 236 152 82 50
1,2-Dichloroethane 107-06-2 482 310 194 101 60
1,2-Dichloropropane 78-87-5 776 452 259 121 67
cis-1,2-Dichloropropene 6923-20-2
trans-1,2-Dichloropropene 7069-38-7
1,4-Dichlorobutane 110-56-5 846 475 263 118 64
o-Dichlorobenzene 95-50-1
Trichlorides
Chloroform 67-66-3 409 263 166 87 52
Methyl chloroform 71-55-6 618 366 214 102 57
Trichloroethylene 79-01-6 749 441 256 122 68
1,1,2-Trichloroethane 79-00-5 976 558 314 143 77
1,2,3-Trichloropropane 96-18-4
Tetrachlorides
Carbon tetrachloride 56-23-5 677 398 231 109 61
Perchloroethylene 127-18-4 1106 609 331 145 77
1,1,2,2-Tetrachloroethane 79-34-5
Pentachlorides
Pentachloroethane 76-01-7
Acetates
Methyl acetate 79-20-9 182 131 92 55 36
Vinyl acetate 108-05-4 389 251 158 82 49
Ethyl acetate 141-78-6 483 299 182 91 53
Isopropyl acetate 108-21-4 668 386 219 102 56
Isopropenyl acetate 108-22-5
Propyl acetate 109-60-4 768 438 246 112 61
Allyl acetate 591-87-7
sec-Butyl acetate 105-46-4
Butyl acetate 123-86-4 935 508 273 118 62
Isopentyl acetate 123-92-2 1007 530 277 116 59
1,3-Dimethylbutyl acetate 540-88-5
Pentyl acetate 628-63-7 1023 537 280 117 59
Hexyl acetate 142-92-7
Ketones
Acetone 67-64-1 118 92 69 44 30
2-Butanone 78-93-3 423 271 170 88 52
2-Pentanone 107-87-9 729 424 243 113 62
3-Pentanone 96-22-0 744 433 248 115 63
4-Methyl-2-pentanone 108-10-1 884 488 266 117 62
Mesityl oxide 141-79-7 1063 581 314 136 71
Cyclopentanone 120-92-3 1020 589 333 153 83
2,4-Pentanedione 123-54-6 1103 612 335 147 78
3-Heptanone 106-35-4 1061 561 294 123 63
2-Heptanone 110-43-0 791 432 234 102 54
Cyclohexanone 108-94-1 1257 683 366 157 81
5-Methyl-3-heptanone
3-Methylcyclohexanone 625-96-7
Diisobutyl ketone 108-83-8 963 496 254 103 52
4-Methylcyclohexanone 589-92-4
Alkanes
Pentane 109-66-0 332 205 124 63 37
2,3-Dimethylbutane 79-29-8 533 307 175 82 45
Hexane 110-54-3 585 334 189 87 48
Methylcyclopentane 96-37-7 613 357 205 96 53
Cyclohexane 110-82-7
2,2,4-Trimethylpentane 540-84-1 747 401 214 92 48
Heptane 142-82-5 769 420 227 99 52
Methylcyclohexane 108-87-2 842 463 252 111 59
1,3,5-Cycloheptatriene 544-25-2
2,2,5-Trimethylhexane 3522-94-9 817 429 224 93 48
5-Ethylidene-2-orbornene
Cyclooctane 292-64-8 747 410 224 99 53
Nonane 111-84-2 907 470 242 100 51
Decane 124-18-5 902 461 234 95 48
Amines
Methylamine 74-89-5 Not applicable, boiling point below ambient temperatures
Dimethylamine 124-40-3 Not applicable, boiling point below ambient temperatures
Ethylamine 75-04-7 Not applicable, boiling point below ambient temperatures
Isopropylamine 75-31-0 167 117 80 46 30
Propylamine 107-10-8 226 155 104 59 37
Diethylamine 109-89-7 498 299 177 86 49
Butylamine 109-73-9 580 349 207 100 57
Triethylamine 121-44-8 747 412 225 100 53
Dipropylamine 142-84-7 871 474 255 111 58
Diisopropylamine 108-18-9 716 395 216 96 51
Cyclohexylamine 108-91-8 1065 575 308 132 69
Dibutylamine 111-92-2 980 507 261 107 54
Miscellaneous
Methyl iodide 74-88-4 This calculation is not applicable to this compound
Acrylonitrile 107-13-1 Work Shift 465 Limited to a maximum concentration of 100 ppm
See the Acrylonitrile Standard [29 CFR 1910.1045(h)]
Dibromomethane 74-95-3 947 565 331 158 89
Pyridine 110-86-1 1031 599 342 158 87
Epichlorohydrin 106-89-8 866 525 310 150 84
2-Methoxyethanol 109-86-4
1,2-Dibromoethane 106-93-4 1252 699 384 170 90
1-Nitropropane 108-03-2 933 548 315 147 80
2-Ethoxyethanol 110-80-5 1105 624 345 154 81
Acetic anhydride 108-24-7 1095 623 348 156 83
2-Methoxyethyl acetate 32718-56-2 1092 594 319 137 71
Bromobenzene 108-86-1 1448 761 397 165 84
2-Ethoxyethyl acetate 111-15-9 1143 600 312 129 65
"Work Shift" Indicates that the service life for this contaminant is limited to a single workshift by the OSHA Standard.
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 , 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 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.

The NIOSH MultiVapor™ Version 2.2.3 Application will do this calculation for you.

These equations are best viewed on tablets, notebooks, or desktop computer screens.

tb = (WeWCoQ) - (WeρβkvCo) ln[(Co - Cx)Cx]

• tb= breakthrough time (min)
• We = equilibrium adsorption capacity (g/g carbon)
• W = weight of carbon adsorbent
• rb = bulk density of the packed bed (g/cm3)
• Q = volumetric flow rate (cm3/min)
• Co = inlet concentration (g/cm3)
• Cx = exit concentration (g/cm3)
• Wood, Gerry O., Estimating Service Lives of Organic Vapor Cartridges, American Industrial Hygiene Association Journal, (1994, January), pages 11-15.

See the comparison of how the results of Wood's Equation compares with Experimental Tests.

##### Supporting Data:

These equations are best viewed on tablets, notebooks, or desktop computer screens.

We = WodL exp [-b′WoPe-1.8R2Τ2(ln{ρρsat})2]

• Wo = carbon micropore volume (cm3/g)
• dL = liquid density of adsorbate (g/cm3)
• Τ = absolute temperature (°K = °C + 273)
• ρ = partial pressure corresponding to concentration Cx
• ρsat = saturation vapor pressure at temperature T
• Pe = molar polarization
• R = ideal gas constant (1.987)
• b′ = an empirical coefficient with value 3.56 x 10-5.

These equations are best viewed on tablets, notebooks, or desktop computer screens.

Pe = ((nD2 - 1)(nD2 + 2) )MwdL

• Mw = molecular weight
• nD = refractive index

These equations are best viewed on tablets, notebooks, or desktop computer screens.

1kV = ((1VL) + 0.027)(I+SPe)

• Τ = 22 °C (295 °K).
• Pair of cartridges with a work rate of 53.3 L/min.
• Wo = 0.454 [determined from experimental data]
• dL = 0.6603 [available from scientific handbooks]
• Pe = 29.877 [calculated from available data]
• rsat = 121 torr [available from scientific handbooks]
• r = .38 torr (500 ppm challenge concentration) [calculated from available data]
• VL = 11.22 cm/s [calculated from available data]
• W = 70.6 g [calculated from available data]
• Co = .00178 g/cm3 [calculated from available data]
• kv = 4242 min-1
The result of this calculation is: 94 minutes.

The Yoon-Nelson model is a descriptive model that uses experimental data to calculate parameters that are then entered into the model.

• 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:

These equations are best viewed on tablets, notebooks, or desktop computer screens.

t = Τ + 1κ′ ln Ρ1 - Ρ

• t = breakthrough time (min)
• Τ = 50% contaminant breakthrough time (min)
• κ′ = rate constant (min-1)
• Ρ = probability of contaminant breakthrough.

The value of Τ is determined from experimental data. The value of κ′ has been shown to be related to τ by the following formula:

κ′ = κτ

κ = 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:

log τ = Κ″–a log CΙ

Κ″, a = constants that can be derived from experimental data. They vary with humidity, but for humidities ≤ 50% they are essentially constant.

CΙ = contaminant assault concentration. (ppm)

It is possible to determine the constants κ, Κ″, and a from a minimum of 3 experimental data points. However, the inclusion of additional data points increases the accuracy of the model.

See the comparison of how the results of Wood's Equation compares with Experimental Tests.

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 NIOSH computer tool will perform the calculation for him. All he has to do is provide his information to NIOSH's MultiVapor™ Version 2.2.3 Application, which asks for the data one step at a time. Grant is delighted with how easy it is.

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.