Waste water treatment: Sorption

The Fruendlich model nonlinear sorption 3... Five bottles containing 1 liter of the waste were dosed with powdered activated carbon.. Determine the best sorption isotherm model to be use

Sorption and Ion Exchange

Sorption is a process which involves the accumulation of substances at a surface or interface

C S

Sorption equilibrium is established when the concentration

of the contaminant remaining in solution (C) is in dynamic balance with that at the surface (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

S = K C 1

The Linear model

2 The Fruendlich model (nonlinear sorption

3

The Langmuir behavior

C

1 ab

1 b

1 S

1

+

=

Note that K, k, n, a, and b are constants usually determined

in the laboratory for each sorbate-sorbent combination.

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

Example

Bottle Carbon, g Equilibrium concentration of

the aqueous phase (C), mg/l

Bottle M, g C, mg/l S, mg/g

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)

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

P N

P P

P N

SSR N

AIC c

−

+ +

+ + +













= ln 2 ( 1 ) 2( 1)( 2)

N= Number of data points

SSR= Sum of squares residuals

P= Number of model parameters

Corrected Akaike Information Criteria (AIC c )

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

Linear model Freundlich model

Bottle Estimated S Predicted S Residual residualsSquares Predicted S Residual Squares residual

SSR

The linear model is better than the

Freundlich model for this case

Design of Carbon beds

Co Q

Cout Q

Carbon

bed

Breakthrough

Scale-up Approach

L r

Vcolumn = π 2

Moisture content of column

column

water

V

V

=

θ

field

treated laboratory

treated

M

V M

V equation











=













:

Packed carbon density

column

V

M

=

ρ

Design criteria: The hydraulic retention time in the lab and field are the same

field

column laboratory

column

Q

V Q

V









=









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

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

Breakthrough time = Vtreated-field/Qfield= 1006/150= 6.7 days

Mfield= (400)(3.74)= 1500 kg

field col field

col lab

col

V

M









Vcol-field= [7.37 (liter)/12.39 (liter/hr)] [150 (m3/d)/24 (hr/d)]= 3.74 m3

field lab

col field

Q

V

V − =     ×

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

field lab

treated field

M

V











=

−

Thus, the breakthrough volume (Vtreated) in the field= 1006 m3

liter L

r

Vcolumn−lab = π 2 = π ( 4 75 )2( 104 ) / 1000 = 7 37

Ion Exchange

Ca2+ + Na2R CaR +2Na+

Resin

Ca hardness

Ca

Hard

water

Soft water

Na Na Ca

Ca Ca

Na

Na

Na Na

NO3 or SO4 + RCl (resin) RNO3 or RSO4 +Cl

exchange reaction.

• 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