Waste water treatment: Sorption

Sorption and Ion Exchange


Sorption
Sorption is a process which involves the accumulation of
substances at a surface or interface.
Sorption equilibrium is established when the concentration
of the contaminant remaining in solution (C) is in dynamic
balance with that at the surface (S).
C

S


A common sorbent is activated carbon

Sorbate: the chemical which is sorbed

Sorbent: the solid surface where
the chemical is sorbed


Equilibrium Sorption Models

The Linear model. 1

S=KC

)The Fruendlich model (nonlinear sorption. 2
The Langmuir behavior. 3

S= kCn

1 1 1 1
= +
S b ab C

Note that K, k, n, a, and b are constants usually determined
in the laboratory for each sorbate-sorbent combination.


Example
Laboratory tests were conducted on a waste containing 50 mg/l
phenol. Five bottles containing 1 liter of the waste were dosed with
powdered activated carbon. When equilibrium was reached, the
contents of each bottle were analyzed for phenol. The results are
shown in the following table. Determine the best sorption isotherm
model to be used.

Bottle

Carbon, g

Equilibrium concentration of
the aqueous phase (C), mg/l

1

0.1

13

2

0.2

6.0

3

0.9

1.0

4

1.6

0.25

5

2.7

0.08


Solution
Determine the equilibrium
concentration on the solid phase (on
the carbon) using the mass balance

approach:
CoV=CV+MS
where Co is the initial concentration
(=50 mg/l) and V is the volume of
solution (= 1 liter for each bottle)

Bottle

M, g C, mg/l

S, mg/g

1

0.1

13

370

2

0.2

6.0

220

3

0.9

1.0

54.4

4

1.6

0.25

31.1

5

2.7

0.08

18.5

Now plot
• S versus C (linear model),
• log S versus log C (Freundlich model), and
• 1/S versus 1/C (Langmuir model)


Based on r2 values, the Freundlich model would
be the best as its r2 is 0.98 (closer to 1.0), then

the linear (r2 =0.96) and then the Langmuir
(r2=0.91).
But the linear model has one parameter and the
Freundlich model has two. To account for
differences in the number of model parameters,
we use the corrected Akaike Information Criteria
(AICc) to judge between the Linear and
Freundlich models.


Corrected Akaike Information Criteria (AICc)
2( P + 1)( P + 2)
 SSR 
AICc = N ln
 + 2( P + 1) +
N −P
 N 

N= Number of data points
SSR= Sum of squares residuals
P= Number of model parameters

Criterion: The smaller the AICc value, the better the model is.


Linear model
Bottle

Estimated
S

Predicted
S

1

370

2

Freundlich model

Residual

Squares
residuals

Predicted S

Residual

Squares
residual

390.7

20.7

429.6

333.4

36.6-

1338.9

220

180.3

39.6-

1573.2

210.2

9.8-

96.6

3

54.4

30.1

24.4-

594.8

72.1

17.7

313.1

4

31.1

7.5

23.6-

556.0

31.5

0.4

0.2

5

18.5

2.4

16.1-

258.7

15.9

2.5-

6.3

=SSR

3412.4

=SSR

1755.1

Model

N

P

P+1

SSR

AICc

Linear

5

1

2

3412.4

39.6

Freundlich

5

2

3

1755.1

43.3

The linear
model is
better than
the
Freundlich
model for
this case

Design of Carbon beds
Co
Q
Carbon
bed

Cout
Q

Breakthrough


Scale-up Approach
Design criteria: The hydraulic retention time in the lab and field are the same

 Vcolumn 
V



=  column 
 Q  laboratory  Q  field

Vcolumn = πr 2 L
Packed carbon density

ρ=

Moisture content of column

M
Vcolumn

Vwater
θ=
Vcolumn

Note that the moisture
content and the bulk
density are usually the
same in the lab and the
field

 Vtreated 
 Vtreated 
Design equation : 
=


 M laboratory  M  field


Example
A phenolic wastewater having a TOC of 200 mg/l is to be treated by a fixed
bed granular activated carbon with a wastewater flow of 150 m3/d, and the
allowable effluent concentration is 10 mg/l as TOC. A breakthrough curve
shown in the figure below has been obtained from an experimental pilot
column. The laboratory column has the following characteristics:
Column diameter= 9.5 cm

Length= 1.04 m
Mass of carbon= 2.98 kg
Flow rate= 12.39 liter/hr
Bulk density= 400 kg/m3

Using the scale-up approach determine
The design column volume
The design mass of carbon
The breakthrough time
The breakthrough volume


Solution
Vcolumn −lab = πr 2 L = π (4.75) 2 (104) / 1000 = 7.37 liter
V 
Vcol − field =  col  × Q field
 Q lab
Vcol-field= [7.37 (liter)/12.39 (liter/hr)] [150 (m3/d)/24 (hr/d)]= 3.74 m3

M field

M
= 
 Vcol


 × Vcol − field = ρ × Vcol − field
lab

Mfield= (400)(3.74)= 1500 kg

From graph, Vtreated-lab= 2000 liters with carbon mass of 2.98 kg. Using

V

Vtreated − field =  treated  × M field
 M lab
.Thus, the breakthrough volume (Vtreated) in the field= 1006 m3
Breakthrough time = Vtreated-field/Qfield= 1006/150= 6.7 days


Ion Exchange
Objective: To remove specific cations or anions by a chemical
exchange reaction.
Resin

Ca hardness

Ca2+ + Na2R

CaR +2Na+

Hard
water
Resin
Soft
water

NO3 or SO4 + RCl (resin)

Ca

Ca

Ca
Ca
Ca
Na Na
Na Ca
Ca Na
Na
Na
Ca
Na

Na
Na

RNO3 or RSO4 +Cl-


• Resin: A naturally or chemically manufactured material. A common
resin is a polystyrene resin of small spheres (0.5 mm-dia).
• The meq/l bar graph of water after ion exchange has the same
number of meqs as the raw water. Since ions are just exchanged.
• Maximum Na for softened water with ion exchange should have
less than 100 mg/l Na, or less than 20 mg/l for people on restricted
diet.
• The quantity of waste brine for regeneration is approximately 5% of
water processed.

When the resin is exhausted it is regenerated using a concentrated
solution of NaCl.
CaR + NaCl

Excess
NaCl

Ca2+ + Na2R