
The Gerry O. Wood Mathematical Model 

t_{b}= breakthrough time (min)
W_{e} = equilibrium adsorption capacity (g/g carbon)
W = weight of carbon adsorbent
r_{b} = bulk density of the packed bed (g/cm³)
Q = volumetric flow rate (cm³/min)
C_{o} = inlet concentration (g/cm³)
C_{x} = exit concentration (g/cm³) 
Wood, Gerry O., Estimating Service Lives of Organic Vapor Cartridges,
American Industrial Hygiene Association Journal, (1994, January), pages 1115. 
How do the results of Wood's Equation compare with Experimental Tests?
See the Comparison.
Supporting Data:
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 105.
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 min1
The result of this calculation is: 94 minutes.
