CEE 6560
Prob. Set No. 6
Due: Oct. 23, 2009
1. An isotherm study was conducted for the adsorption of an azo-dye on activated carbon.
Varying amounts of carbon were added to 500 ml of a 95 mg/L azo-dye solution. The
results of this isotherm study are given in the following table.
Carbon added Final soluble TCE
(g)
conc. (mg/L)
0.593
6
0.382
11
0.296
18
0.220
31
0.147
45
0.030
84
a) Determine a Langmuir and a Freundlich isotherm equation for the data. For the
Langmuir isotherm determine determine K and Q0a using plots of 1/qe vs. 1/Ce and Ce/qe
vs C. Plot the resulting isotherms on a single graph for comparison.
b) Based on the R2 for each regression determine which regression gives the best data fit.
2. A refractory organic compound is to be removed from a waste stream by carbon
adsorption. The concentration of this organic in the waste stream is 1000 mg/L. The
carbon contactor to be used is an upflow fluidized bed. Fresh carbon is to be added as
exhausted carbon is removed on a continuous, counterflow basis. The contactor is to be
15 ft. in length. A superficial approach velocity of 7 gpm/ft2 is required to fluidize the
bed. At this fluidization velocity the apparent bulk density of the bed is 0.7 g/cm3. True
density of the activated carbon is 2.1 g/cm3. Kinetic experiments yielded the following
relationship between the overall mass transfer coefficient and the superficial velocity for
this waste:
k’ = 3.44U0.5
U = approach velocity in cm/min and k’ has units of (1/min).
Isotherm studies with the same carbon and waste yielded Q* = 0.0461 (g/g) and a
Langmuir constant K = 0.428 liters/g. Note Q* = saturation value for activated carbon at
Co = 0.001 g/cm3.
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a) Design of the contactor requires that the adsorption zone be allowed to penetrate the
bed before counterflow carbon exchange begins. How long must the contactor run so that
the adsorption zone has penetrated the bed to the extent that C = 500 mg/L at z = 7.5 ft?
b) Assume that once the adsorption zone has developed as in (a) the counterflow of
carbon may begin. Select the counterflow rate of carbon such that the adsorption pattern
remains stationary.
c) Calculate the mass flow rate (g/min/cm2 ) of fresh carbon needed to sustain the
operation of the system.
d) Calculate the effluent concentration (C @ z = 15 ft.) of the refractory compound under
steady-state, continuous counterflow operation.
3. Activated carbon is used to remove a pesticide residual from a waste stream. Pesticide
concentration in the waste stream is 100 mg/liter. The process is done in a batch mode
in a series of three stirred tanks. The waste is processed in series by allowing the waste
to contact carbon in the first tank until the system is at equilibrium. The waste stream is
then separated from the exhausted carbon and sent to the second tank where it again is
equilibrated. The waste stream is again separated from the exhausted carbon and sent to
a third tank where it it allowed to equilibrate with the activated carbon in this tank. If
each tank initially contains fresh carbon, determine the final concentration of the
pesticide in the third tank. The adsorption isotherm for this pesticide can be
approximated by:
qe  K  Ce
K = 0.08 liters/mg
Volume of each tank is 5 m3 (assume this is the waste volume applied to each tank).
Tanks 1, 2 and 3 contain 1 kg, 0.75 kg and 0.25 kg of activated carbon, respectively.
4. A packed-bed (downflow) contactor contains activated carbon at a depth equal to 8
meters. The cross-sectional area of the contactor is 2 m2. Bulk density of the carbon is
0.8 g/cm3. True density of the carbon is 2.1 g/cm3. The contactor is used to treat a waste
stream that has a volumetric flow rate equal to 45 m3/hr. The waste stream contains
Atrazine which is to be removed by adsorption on the activated carbon. The influent
concentration of Atrazine is 30 mg/liter. Atrazine exhibits the following isotherm.
qe 
K  Q 0  Ce
a
1  K  Ce
Qa0  0.1
gm
gm
K = 0.3
liter
mg
After the column is exhausted the AC is regenerated but because of a furnace malfunction
the activated carbon still contains 0.075 gm Atrazine per gram of carbon. If the
contaminated AC is used again in the packed-bed contactor determine how long it will
take for the effluent of the contactor to contain 30 mg/L of Atrazine? Assume that the
contactor behaves as a system at equilibrium (square-wave response).
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