Civil Engineering Reference
In-Depth Information
The adsorption isotherm describes the relationship, under given environmental con-
ditions, between the amount of a specific compound adsorbed (concentration in grams
compound per gram carbon) and the liquid-phase concentration at equilibrium. For
example, Figure 17-2 shows a typical equilibrium relationship found for total organic
carbon (TOC) removal in Colorado River water.
16
For design purposes it can be very useful to mathematically describe the adsorbate/
adsorbent interaction. In single-solute systems the Freundlich isotherm equation is
commonly used and has been shown to accurately describe most adsorption data. The
Freundlich equation is empirically derived and assumes a straight logarithmic isotherm.
The mathematical formula for the Freundlich isotherm is as follows:
x
kC
(17-1)
1/
n
m
where:
x
mass of compound adsorbed, g
m
mass of carbon, g
x
m
amount of compound adsorbed per unit weight of carbon
C
residual concentration of compound left in solution, mg / L or
g/L
The terms
k
and
n
are isotherm constants determined experimentally for a specific
compound of interest and the specific GAC product under specific test conditions.
X
M
=40 C
1.05
X = Mass Adsorbed, mg
M = Carbon Mass, g
C = Concentration, mg/L
0.01
0.1
1.0
Liquid-Phase Concentration (mg/L)
Fig. 17-2.
Example isotherm for total organic carbon (TOC) adsorption in Colorado River water
(
Source:
Reference 15. Adapted from
Optimization and Economic Evaluation of Granular Acti-
vated Carbon for Organic Removal.
Copyright
1989, American Water Works Association and
the American Water Works Research Foundation.)
