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.

The parameter W_e can be estimated using the following equation:

Wo = carbon micropore volume (cm³/g)
dL = liquid density of adsorbate (g/cm³)
T = absolute temperature (°K = °C + 273)
r = partial pressure corresponding to concentration Cx
rsat = 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.

The parameter Pe can be estimated using the following equation:

Mw = molecular weight
nD = refractive index

The parameter kv has been estimated by Wood from experimental data to be equivalent to the following equation:

T = 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.