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The Gerry O. Wood Mathematical Model


equation8 		 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 Advisor Genius will do this calculation for you.
How do the results of Wood's Equation compare with Experimental Tests?   See the Comparison.
Supporting Data:

    The parameter We can be estimated using the following equation:

equation3

      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:
equation4

      Mw = molecular weight
      nD = refractive index

    The parameter kv has been estimated by Wood from experimental data to be equivalent to the following equation:
equation5

      I = calculated to be 0.000825
      S = 0.036 for 1% breakthrough
      VL = linear airflow velocity (cm/sec)

    Wood uses an example of hexane with the following information:

      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.

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