Page 251 - Materials Chemistry, Second Edition

234 Practical Design Calculations for Groundwater and Soil Remediation

where q is the adsorbed COC concentration (in mass of COC/mass of acti-
vated carbon), C is the aqueous COC concentration (in mass of COC/volume
of the solution), and a, b, k, and n are constants. The adsorbed COC con-
centration (q) obtained from Equations (6.6) or (6.7) is an equilibrium value
(the one in equilibrium with the aqueous COC concentration). It should be
considered as the theoretical adsorption capacity for a specified aqueous
COC concentration. The actual adsorption capacity in the field applications
should be lower because the adsorption isotherms are usually developed in
a laboratory setting, where other compounds that would compete for the
adsorption sites are absent. Normally, design engineers take 25% to 50% of
this theoretical value as the design adsorption capacity as a factor of safety.
Therefore,

q ) (6.8)
q design = (50%)( theoretical
The maximum amount of COCs that can be removed from water and held
by a given amount of activated carbon (M removal ) can be determined as:

)( )
M removal = q( design M activated carbon
)[( ρ )] (6.9)
= q ( design V activatedcarbon )( b

where M activated carbon is the mass, V activated carbon is the volume, and ρ is the bulk
b
density of the activated carbon, respectively.
The following procedure can be used to determine the adsorption capacity
of an activated-carbon adsorption unit (often called an adsorber):

Step 1: Determine the theoretical adsorption capacity of the activated
carbon by using Equations (6.6) or (6.7).
Step 2: Determine the design adsorption capacity of the activated car-
bon by using Equation (6.8).
Step 3: Determine the amount of activated carbon in the adsorber.
Step 4: Determine the maximum amount of COCs that can be held by
the activated carbon in the adsorber using Equation (6.9).

Information needed for this calculation:

• The adsorption isotherm
• COC concentration of the influent liquid, C in
• Volume of the activated carbon, V activated carbon
• Bulk density of the activated carbon, ρ b