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Modeling and transport parameters during nanofiltration of degreasing effluent from a tannery.

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2011; 6: 101–109
Published online 28 June 2010 in Wiley Online Library
(wileyonlinelibrary.com) DOI:10.1002/apj.478
Special Theme Research Article
Modeling and transport parameters during nanofiltration
of degreasing effluent from a tannery
C. Prabhavathy and S. De*
Department of Chemical Engineering, Indian Institute of Technology, Kharagpur 721 302, India
Received 14 August 2009; Revised 24 May 2010; Accepted 24 May 2010
ABSTRACT: Degreasing effluent from a tannery is treated using a single-step membrane separation (nanofiltration)
process in continuous cross-flow mode. The flow regimes encompass the laminar and turbulent zones, including laminar
flows with turbulent promoters. Experimental results are reported in the range of transmembrane pressure drop from
828 to 1242 kPa for all three flow regimes. More than 50% flux enhancement is observed by using turbulent promoters
compared to purely laminar flow. The performance criteria of the filtration are evaluated in terms of chemical oxygen
demand (COD), total dissolved solids (TDS), total solids (TS), pH and conductivity of the permeate. The proposed
scheme successfully reduces COD to well below the permissible limits (250 mg/l). A combination of osmotic pressure
and solution-diffusion model is used for nanofiltration. Three relevant transport coefficients, namely, the effective
osmotic coefficient, solute diffusivity and solute permeability through the membrane are estimated by minimising the
sum of errors between the experimental and calculated permeate flux and permeate concentrations.  2010 Curtin
University of Technology and John Wiley & Sons, Ltd.
KEYWORDS: degreasing effluent; cross-flow nanofiltration; solution-diffusion model; steady-state; permeate flux
INTRODUCTION
Standard methods are not available for handling and
safe disposal of tannery effluents in view of the fact that
they depend on the process employed for leather making and on the type of leather produced. To partially
balance the effluent treatment costs, reuse of water and
recovery of chemicals would be advisable.[1] Among
the industrial wastes, tannery effluent pollutes receiving water the most. When unprocessed effluents are
discharged to nearby environment without prior treatment they create severe ecological imbalance.[2] Various
unit operations involved in a typical tannery include
soaking, liming, deliming, bating, pickling, degreasing,
tanning, neutralization, dyeing, fatliquoring, etc. Each
of these operations consumes large amount of chemicals
and produces huge volumes of wastewater containing
appreciable amount of organic and inorganic materials causing high chemical oxygen demand (COD), total
dissolved solids (TDS), total solids (TS), conductivity,
etc.[3]
Due to increased awareness of environmental conservation, government policy is now becoming stricter and
*Correspondence to: S. De, Department of Chemical Engineering,
Indian Institute of Technology, Kharagpur 721 302, India.
E-mail: sde@che.iitkgp.ernet.in
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Curtin University is a trademark of Curtin University of Technology
appropriate treatment protocol for industrial wastewater
has become an important social issue.[4] In this regard,
membrane-based separation processes offer a promising alternative to the conventional chemical intensive
processes. Membrane-based separation process is found
to be an industrially feasible ‘cleaner technology’[5 – 13]
The advantages of these processes are low energy
requirement, selective separation capabilities, treatment
of heat sensitive materials, ease of scaling-up, etc. Usually the top skin layer of the membrane governs the
separation performance of a membrane. Search of literature indicates two directions of research efforts in
this field. The first one is the treatment of combined
effluent except chrome tanning, because of high toxicity of tanning effluent.[14] Here, the common effluent
is subjected to a series of hybrid treatment processes
including pretreatment by coagulation, coarse filtration,
nanofiltration and reverse osmosis. The second trend
suggests treatment of effluent emerging from individual unit operations.[15] This scheme not only recovers
water but also recovers useful chemicals that can be
recycled back to the upstream unit directly and reduces
the operating costs of the plant. Thus, for better recovery of chemicals, individual treatment of effluent is
desirable. Alves and Pinho suggested ultrafiltration as a
suitable process to decolorize the wastewater emerging from dyeing unit of the tannery.[16] Das et al .
102
C. PRABHAVATHY AND S. DE
attempted a hybrid separation process involving gravity settling, coagulation by alum followed by nanofiltration and reverse osmosis for treatment of soaking
effluent discharged from a tannery.[17] Bes-Piá et al .
reported reclamation of pickling wastewater from a
tannery by means of nanofiltration.[18] The viability
of using nanofiltration membranes for elimination of
chromium content present in tannery effluents is also
investigated.[19] Pilot-scale studies have also been carried out for removal of toxic chemicals from spent
tanning effluent.[20]
Incorporation of recycling technology reduces capital investment on water treatment and reduces overall water consumption. The present study emphasizes
treatment of degreasing effluent discharged from a tannery. Residual grease present in hides and skin after
liming operation leads to uneven dyeing and finishing, waxy patches on alum tanned leathers and pink
stains on chrome blue.[21] In order to remove the grease,
degreasing method is employed to the pelt by treating
them with suitable organic solvent extraction technique.
After removing grease from the pelt, large quantity of
water is essential for complete removal of the solvent
adhering to the pelt by repeated washing. The wastewater exhausted from the degreasing drain contains huge
amount of COD that cannot be discharged directly to
the surface water.
Membrane-based processes show significant promise
to treat the degreasing effluent. There are few studies available on the treatment of degreasing effluent
by using membrane separation process. Cassano et al .
had explained the major applications of membrane processes in various operations of a tannery.[22] Recovery
and reuse of chemicals in unhairing, degreasing and tanning processes had been investigated, and the effects
of membrane type and operating parameters are also
discussed. Ultrafiltration is proposed to reduce fatty substances present in the skin by avoiding use of organic
solvents. Calculations for overall mass balance, and
influence on mass transfer of chemicals and reactants
between fats and skins are reported. It is stated that
around 95% of COD is removed by use of ultrafiltration for degreasing operation but still it seems to
be much higher when compared to Indian discharge
standards.[23,24]
To overcome this problem, in the present study, a
denser nanofiltration membrane preceded by a suitable
pretreatment protocol is selected so that COD of the
processed water meets the Indian standard of 250 mg/l.
An attempt is also made to model the performance of
nanofiltration. Systematic laboratory-scale experiments
are conducted to quantify the transport parameters.
Calculated results are compared successfully with the
experimental data under a wide range of operating
conditions. The proposed schematic for treatment of
degreasing effluent is presented in Fig. 1.
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pacific Journal of Chemical Engineering
Degreasing
Effluent
Gravity settling
chamber
Coagulation
with alum
Cloth filtration
NF
Permeate
Sludge chamber
Fertilizer
Figure 1. Proposed schematic for treatment of degreasing effluent.
THEORY
An available model comprising of film theory, solutiondiffusion model for solute flux and osmotic pressure
model for solvent flux is used to calculate the permeate
flux and concentration at the steady state.[14] Osmotic
pressure model quantifies solvent flow through the
membrane,[25]
J = Lp (P − π )
(1)
where Lp is the membrane permeability. The osmotic
pressure difference across the membrane is given as
π = πm − πp
(2)
where πm is the osmotic pressure at the membrane
surface and πp is that in the permeate stream. Since the
effluent is a complex mixture of organic and inorganic
with unknown properties, the osmotic pressure of the
solution is assumed to obey van’t Hoff relation in terms
of TS concentration:
π = ac
(3)
where ‘a’ is the effective osmotic coefficient. Using
Eqns 1–3, the permeate flux is described as
J = Lp [P − a(cm − cp )]
(4)
According to stagnant film theory, the permeate flux
is expressed in terms of mass transfer coefficient (k =
D/δ) as
cm − cp
(5)
J = k ln
c0 − cp
Asia-Pac. J. Chem. Eng. 2011; 6: 101–109
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
MODELING AND TRANSPORT PARAMETERS DURING NANOFILTRATION
Combining Eqns 4 and 5, the following expression is
obtained:
cm − cp
0
(6)
Jw [1 − α(cm − cp )] = k ln
c0 − cp
a and J 0 = L P .
where α = P
p
w
According to solution-diffusion model, the solute flux
through the membrane is proportional to concentration
difference across the membrane surface. Therefore, the
following equation is obtained:
Jcp = B (cm − cp )
(7)
Combining Eqns 1 and 7, and after algebraic simplification, the term cm in terms of cp can be expressed as
cm = cp +
cp
αcp + β
(8)
On substituting Eqn 8 in Eqn 6, the following nonlinear
algebraic equation of cp is obtained:
cp
β Jw0
− k ln
=0
α cp + β
(α cp + β)(c0 − cp )
(9)
where β = B /Jw0 .
The mass transfer coefficient under laminar flow
conditions is given by Leveque’s equation[25] :
Sh =
kde
de
= 1.86 Re Sc
D
L
1/3
(10)
and that for turbulent flow is given by[25]
Sh =
kde
= 0.023(Re)0.8 (Sc)0.33
D
(11)
where de is the equivalent diameter of the flow channel.
For a thin channel, the value of de is 4h, where, h is
the half-height of the channel. With a knowledge of the
parameter values, i.e. D, a and B , Eqn 8 can be solved
iteratively to obtain the value of cp , cm and permeate
flux.
Numerical solution
Since the pretreated degreasing effluent contains various
salts at different concentration levels as well as some
smaller sized organic materials, the three parameters,
namely, diffusivity (D), osmotic coefficient (a) and
solute permeability through membrane (B ) are difficult
to obtain. Hence, an optimization method is employed
with an initial guess of these three parameters and
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
minimizing the following error function to obtain the
values of these parameters:
2
exp
2
N
N
cp − cpcalc
J exp − J calc
+
S =
exp
J
cpexp
i =1
i =1
(12)
BCPOL subroutine of IMSL library using unconstrained
direct search algorithm is used for optimization and
Newton–Raphson algorithm is employed for solution
of Eqn 8. The algorithm for calculation is presented in
Fig. 2.
EXPERIMENTAL
Membranes
Organic thin film composite (TFC) membrane consisting of a thin film polyamide skin over a polysulfone support is used for nanofiltration. The molecular
weight cut-off (MWCO) of the membrane is 400. The
membranes are procured from M/s Genesis Membrane
Sepratech Pvt. Ltd., Mumbai, India. The permeability of
the membrane is determined using distilled water and
is found to be 2.84 × 10−11 m/Pa s for nanofiltration.
Chemicals used
Commercial grade alum is used for coagulation. It is
procured from the local market. The chemicals required
for determination of COD are procured from M/s Loba
Chemie, India. The chemicals are used without further
treatment.
Effluent
The wastewater (effluent) used in this study was collected from the degreasing unit of M/s Olympic Tannery, Banthala Leather complex, Kolkata, India. The
characterization of the effluent has been carried out and
is presented in Table 1.
Table 1. Characterization of degreasing effluent from
tannery and effects of alum dosing.
Properties
pH
Conductivity
(S/m)
TS
(g/l)
TDS
(g/l)
COD
(mg/l)
Feed
After alum
dose
0.7%
(w/v)
8.6
7.1
2.6
2.9
31.3
27.4
17.5
19.1
3737.3
734.4
Asia-Pac. J. Chem. Eng. 2011; 6: 101–109
DOI: 10.1002/apj
103
104
C. PRABHAVATHY AND S. DE
Asia-Pacific Journal of Chemical Engineering
Known Parameters
Operating conditions: ∆P, c0, u0
Flow Dimensions: L, h
Membrane Characteristics: Lp
Guess set of Parameters
a, D, B
For experiment number I = 1, 36
Optimization
subroutine BCPOL is
employed to update the
parameter values
Calculate mass transfer coefficient
either from Eq. (10) or Eq. (11)
Calculate cp from Eq. (9) by using
Newton Raphson method
Calculate cm from Eq. (8)
Obtain the value of J from Eq. (5)
Check
36
i=1
Jexp − Jcal
Jexp
2
+
cp,exp − cp,cal
2
cp,exp
≤ 0.01
NO
YES
Compute converged parameters a, D, B
Figure 2. Algorithm for estimation of parameters.
Pretreatment
Pretreatment of the effluent is carried out with different
doses of alum. The optimum coagulant dose is determined by adding various amounts of coagulant and
then measuring COD, TS, conductivity and TDS. After
coagulation, the sludge settles at the bottom and the
supernatant is siphoned out. A fine nylon filter cloth
is used for further clarification of the collected supernatant. The sludge produced is sun-dried and pulverized
to powder form and analyzed for its fertilizer value.
It may be noted that ferric chloride can be another
possible coagulant. But, the cost of alum is one tenth
that of ferric chloride. Cost of ferric chloride is Rs.
300/ kg (US$6.67/ kg), and, on the other hand, the
cost of commercial alum is Rs. 30/ kg (US$0.67/ kg)
only. Secondly, alum is easily available in local market.
Based on these two reasons, alum was selected as the
desired coagulant. It may also be mentioned here that
microfiltration may be another alternative pretreatment.
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
But coagulation with commercial alum will be definitely
cost effective than any membrane filtration module with
pump.
Membrane filtration cell
A rectangular cross-flow cell, made of stainless steel, is
designed and fabricated. Two neoprene rubber gaskets
are placed over the membrane forming the flow channel.
The effective length of the membrane is 14.6 × 10−2 m
and width is 5.5 × 10−2 m. The channel height after
tightening the two flanges is found to be 3.4 × 10−3 m.
The cell consists of two rectangular matching flanges.
The inner surface of the top flange is mirror polished.
The bottom flange is grooved, forming the channels
for the permeate flow. A porous stainless-steel plate
is placed on the lower flange that provides mechanical support to the membrane. For experiments with
turbulent promoters, nine equispaced wires of diameter 1.66 mm are placed laterally (along the width of
Asia-Pac. J. Chem. Eng. 2011; 6: 101–109
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
MODELING AND TRANSPORT PARAMETERS DURING NANOFILTRATION
the channel) in between the two gaskets. The spacing
between the turbulent promoters is 15.0 mm. Localized
turbulence is created in the flow path due to the presence
of these turbulent promoters. Two flanges are tightened
to create a leak-proof channel for conducting experiments in cross-flow mode.
The clarified effluent is pumped by a high-pressure
reciprocating pump from the stainless-steel feed tank to
the cross-flow cell. The retentate stream is recycled to
the feed tank routed through a rotameter. The pressure
and the cross-flow rate inside the membrane channel
are independently set by operating the valves in the
bypass line and that at the outlet of the membrane cell.
Permeate samples are collected from the bottom of the
cell and are analyzed for COD, TS, TDS, conductivity
and pH. Detailed description of the membrane module
assembly is available elsewhere.[26]
Operating conditions
The filtration experiments of the degreasing effluent are
performed by modifying the most important operating
variables like transmembrane pressure and cross-flow
velocity. The selected operating pressures for treatment
of degreasing effluent are 828, 966, 1104 and 1242 kPa
by using nanofiltration membranes. The cross-flow rates
are 60 (Re = 606), 90 (Re = 909) and 120 l/h (Re =
1212). Corresponding cross-flow velocities are 0.1, 0.15
and 0.2 m/s, respectively, in laminar regime both with
and without promoters, and 0.7 (Re = 4242), 0.8 (Re =
4848) and 0.9 m/s (Re = 5454) are used in the turbulent
regime.
Experimental procedure
A fresh membrane is compacted at a pressure higher
than the maximum operating pressure for 3 h using distilled water and then its permeability is measured. The
effluent is placed in a stainless-steel feed tank of 2 l
capacity. A high-pressure reciprocating pump is used
to feed the effluent into the cross-flow membrane cell.
Cumulative volumes of permeate are collected during
the experiment. The permeate stream is recycled to
maintain a constant concentration in the feed tank. Permeate samples are collected at different time intervals
for analysis. A bypass line is provided from the pump
delivery to the feed tank. Retentate and bypass control valves are used to vary the pressure and flow rate
accordingly. Values of permeate flux are determined
from the slopes of cumulative volume vs time plot. The
precision of flux measurement is ±5%. Duration of the
cross-flow experiment is 1 h.
Once an experimental run is over, the membrane
is thoroughly washed, in situ, with distilled water for
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
15 min at a pressure of 200 kPa. The cross-flow channel is then dismantled and the membrane is dipped in
dilute acid solution for 3 h. Then, it is washed carefully
with distilled water to remove traces of acid. The crossflow cell is reassembled and the membrane permeability
is again measured. It is observed that the membrane permeability remains almost constant between successive
runs. All the experiments are conducted at a temperature
of 32 ± 2 ◦ C.
Analysis
The conductivity, TDS and pH of all samples (feed,
permeate and retentate streams) are measured at room
temperature using a water and soil analysis kit, model
no.191E, manufactured by M/s Toshniwal Instruments
Ltd, India. TS of all the samples are measured by taking
a known volume of the sample in a petridish and placing
in an oven maintained at 105 ± 2 ◦ C till complete
drying of the sample. COD values are determined using
standard techniques.[27]
RESULTS AND DISCUSSION
Pretreatment
The characterization of the degreasing effluent is presented in Table 1. Degreasing of skins and hides are
done by leaching these with organic solvents or surfactants. For shipskin containing about 30–40% fatty
substances, this operation is essential. The effluent generated from this step has a very high COD due to the
presence of these fatty substances which give troubles in
biological treatment plant.[21] Alum is used as a coagulant for pretreatment of degreasing effluent which is
basic in nature.[28] Optimum dosage of alum is added
to the effluent and the supernatant is tested for different
properties like pH, COD, conductivity, TDS, etc. The
optimum alum dose is found to be 0.7% (w/v). The values of pH, COD, TS and TDS obtained after optimum
alum dose and sludge separation are 7.1, 734.4 mg/l,
27.4 g/l and 19.1 g/l, respectively.
The properties of degreasing effluent (feed) from
tannery and effects of alum dosing are presented in
Table 1. After pretreatment, the produced sludge is
dried, pulverized and analyzed for its fertilizer value.
The sludge generated can be used as an organic
fertilizer after drying. The results of chemical analysis
of degreasing effluent sludge are given in Table 2. From
this table, it can be observed that the fertilizer quality
of the sludge is comparable with vermin compost. The
supernatant liquor after a coarse filtration by a fine cloth
is subjected to nanofiltration in the cross-flow mode.
Asia-Pac. J. Chem. Eng. 2011; 6: 101–109
DOI: 10.1002/apj
105
C. PRABHAVATHY AND S. DE
Asia-Pacific Journal of Chemical Engineering
Table 2. Results of chemical analysis for degreasing
effluent sludge.
6.0
Re = 5454
5.5
Sample
pH
O.C.
(wt%)
Degreasing
(sludge)
Vermi
compost
6.8
12.16
7.1–7.8 9.97–10.62
N
P
K
(wt %) (wt %) (wt %)
5.49
0.35
0.13
1.8
0.4
0.9
Nanofiltration of the effluent
The experiments are conducted in three different flow
regimes: laminar, laminar with promoter and purely
turbulent. The flux decline behaviors of the effluent at
1242 kPa and different Reynolds numbers reveals that
the time required to reach steady state decreases with
an increase in Reynolds number. Flux decline is lower
at high cross-flow velocities. Changes in hydrodynamic
conditions in the flow channel by use of turbulent
promoters enhance the permeate flux. Steady state is
achieved faster for turbulent promoter compared to
laminar flow. For example, the steady state is attained
in about 133 s for Re = 1212 and 1242 kPa pressure,
whereas at the same pressure and Reynolds number,
the steady state is attained within 129 s in turbulentpromoter-assisted cases. Turbulent promoters create
local turbulence and hence reduce the concentration
polarization at the membrane surface. Similarly, in
turbulent region steady state is attained in about 115 s
for Re = 5454 and 1242 kPa pressure.
Figure 3 shows that steady-state permeate flux
increases linearly with operating pressure. Higher flux
is achieved at higher pressure due to enhanced driving
force. It can be observed that the use of promoters leads
to a significant flux enhancement compared to the purely
laminar flow regime. The permeate flux increases with
increase in operating pressure and Reynolds number.
The values of flux obtained in the turbulent regime are
compared to laminar and turbulent–promoter-assisted
cases due to the result of turbulence created at high
Reynolds numbers. The use of turbulent promoters in
laminar region results in substantial increase in flux of
around 10–20% for nanofiltration (NF). For example,
at 828 kPa pressure the flux enhancement is 20% and
11% at Re = 606 and 966, respectively. For purely turbulent flow, flux enhancement is still higher compared
to laminar flow. At Re = 4242 and 828 kPa pressure,
the percentage flux enhancement for purely turbulent
case is about 56%.
A detailed study is conducted to observe the effects
of the operating conditions on the permeate flux and
permeate quality. The results of the permeate analysis
after nanofiltration under various operating conditions
are presented in Table 3. It may be observed from
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Permeate flux x 106 (m3/m2 s)
106
5.0
Re = 1212
4.5
Re = 1212
4.0
3.5
Laminar
Laminar+promoter
Turbulent
3.0
2.5
2.0
800
900
1000
1100
1200
1300
Pressure drop (kPa)
Figure 3. Variation of permeate flux with operating
pressure in NF.
Table 3 that COD values are well within the permissible level, i.e. 250 mg/l for all the operating conditions. It is also observed that with an increase in the
transmembrane pressure and Reynolds number, the permeate quality improves. For example, at Re = 1212,
COD value decreases from 147 to 73 mg/l for operating
pressure 828–1242 kPa in the laminar region. Higher
pressures lead to more solvent flux through the membrane, leading to a reduction in COD value. This is
more common to denser membranes like nanofiltration
and reverse osmosis.[29] It can also be observed from
Table 3 that the TS values in the permeate decrease with
Reynolds number and operating pressure. As Reynolds
number increases, the membrane surface concentration
becomes less due to forced convection, resulting in
lower permeation of solutes (less TS) through the membrane.
Osmotic pressure and solution-diffusion models are
used in conjunction with film theory to calculate
steady-state permeate flux and permeate concentration values. The effective osmotic pressure coefficient (a), solute diffusivity (D) and solute permeability (B ) are estimated by comparing the calculated and
experimental data, as described earlier in theory section. The estimated values are: a = (4.9 ± 0.033) ×
104 Pa m3 / kg, D = (1.45 ± 0.012) × 10−9 m2 /s and
B = (2.49 ± 0.45) × 10−6 m/s. The feed to NF after
pretreatment contains large amount of organic as well
as inorganic solutes. Thus, the effective osmotic coefficient ‘a’ is less than that of pure salt, i.e. sodium
chloride (about 8.5 × 104 Pa m3 / kg). This fact is supported by the diffusivity value as well. For sodium
chloride, the diffusivity is 1.5 × 10−9 m2 /s, whereas the
effective diffusivity obtained is slightly lower than that
of sodium chloride. Since the parameters a, D and B
obtained by this method are independent of the flow
Asia-Pac. J. Chem. Eng. 2011; 6: 101–109
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
MODELING AND TRANSPORT PARAMETERS DURING NANOFILTRATION
Table 3. Permeate analysis after nanofiltration in different flow regimes.
S. No.
Pressure (kPa)
Turbulent regime
1
828
2
966
3
1 104
4
1 242
Laminar regime
1
828
2
966
3
1 104
4
1242
With turbulent promoter
1
828
2
966
3
1 104
4
1 242
Reynolds no.
TDS (g/l)
TS (g/l)
pH
Conductivity (S/m)
COD (mg/l)
4 242
4 848
5 454
4 242
4 848
5 454
4 242
4 848
5 454
4 242
4 848
5 454
11.5
11.2
10.6
10.2
9.8
9.7
9.2
8.7
8.4
8.3
8.3
8.0
14.8
13.6
12.5
12.1
11.8
11.6
11.2
10.6
10.3
10.1
9.9
9.7
6.7
7.1
7.7
6.8
7.4
7.6
6.9
7.3
7.6
7.2
7.5
7.6
17.4
16.9
16.1
15.4
14.8
14.7
13.9
13.2
12.7
12.7
12.5
12.1
151
145
140
136
131
125
120
107
99
87
75
63
606
909
1 212
606
909
1 212
606
909
1 212
606
909
1 212
12.9
12.7
12.4
11.1
10.7
10.0
9.9
9.8
9.3
9.1
9.0
8.7
15.3
15.1
14.8
14.3
13.9
13.2
12.7
12.7
11.9
11.7
11.5
10.6
6.4
6.8
7.2
6.4
6.9
7.3
6.8
6.9
7.5
7.0
7.3
7.5
19.6
19.2
18.8
16.8
16.4
15.2
14.9
14.8
14.0
13.8
13.6
13.5
163
156
147
141
135
129
125
118
109
97
94
73
606
909
1 212
606
909
1 212
606
909
1 212
606
909
1 212
12.8
12.5
11.6
10.9
10.7
10
9.6
9.3
9.2
9.0
8.9
8.5
15.1
14.7
13.9
13.2
12.6
12.0
11.8
11.4
11.1
10.9
10.7
10.4
7.1
7.4
7.6
7.3
7.3
7.6
6.9
7.0
7.4
7.0
7.4
7.5
19.4
18.9
17.6
16.6
16.2
15.2
14.9
14.2
14.0
13.6
13.5
12.9
158
149
143
138
133
126
123
113
101
95
82
69
regime, calculations are done using these values in the
case of laminar flow with promoters. But the expression of Sherwood number is not known in this case.
Hence, the following expression of Sherwood number
is considered:
Sh = α0 (Re)n (Sc)1/3
(13)
For all the seven experimental runs with turbulent promoters, calculations are carried out to evaluate the values of α0 and n, which are found to be
(0.407 ± 0.02) and (0.516 ± 0.006), respectively. From
Eqns 9 and 10, α0 value should be in the range of
0.023–1.86, and value of n should be in the range of
0.33–0.8. At these optimized parameter combinations,
the comparison between experimental and calculated
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
permeate flux and permeate concentrations are presented in Figs 4 and 5 for all the flow regimes. It is
observed from Fig. 4 that the calculated permeate flux
values are within ±15% of the experimental data. The
comparison between calculated and experimental permeate concentration (as TS) is shown in Fig. 5. Here
calculated permeate concentrations are within ±10% of
the experimental data.
The separation of a solute by the membrane gives
rise to an increased concentration of the solute at
the membrane surface called concentration polarization.
On increasing turbulence using promoters or increased
cross-flow velocity, membrane surface concentration
as well as permeate concentration decrease. Membrane surface concentration is observed to be higher
in the case of laminar flow regime with low cross-flow
Asia-Pac. J. Chem. Eng. 2011; 6: 101–109
DOI: 10.1002/apj
107
C. PRABHAVATHY AND S. DE
Asia-Pacific Journal of Chemical Engineering
6
Laminar
Laminar+Promoter
Turbulent
1.50
+15%
Polarization Modulus
SS
Jexp x 106 (m3/m2 s)
5
4
-15%
1.35
Laminar
Re=606
Re=909
Re=1212
Turbulent
Re=4242
Re=4848
Re=5454
Laminar+Promoter
Re=606
Re=909
Re=1212
1.20
3
1.05
2
800
2
3
4
5
6
JCal x 106 (m3/m2 s)
900
1000
1100
1200
Transmembrane pressure drop (kPa)
1300
Figure 6.
Variation of polarization modulus with
transmembrane pressure during NF.
SS
Figure 4. Comparison between the experimental and
calculated flux for different operating conditions in NF.
220
18
200
Laminar
Laminar+Promoter
Turbulent
+10%
Laminar
Laminar+Promoter
Turbulent
180
Sh
16
exp
cp SS
x 106 (m3/m2 s)
108
14
100
80
-10%
12
60
10
8
40
500
8
10
12
14
16
18
cal x 106 (m3/m2 s)
cp SS
Figure 5. Comparison between the experimental and
calculated permeate (TS) concentrations for different
operating conditions in NF.
velocity. For example, at a pressure of 1242 kPa and
u0 = 0.1, 0.15 and 0.2 m/s, membrane surface concentration is in the range of 33.5–34.5 g/l for laminar
and 31.8–33.1 g/l for laminar flow with turbulent promoters. Similarly, at a pressure of 1242 kPa and Re
number in the range of 4242–5454, cm varies from
29.8 to 30.3 g/l for purely turbulent flow regime. Concentration polarization cannot be completely avoided in
any membrane-based separation processes but its effects
can be minimized. Polarization modulus increases with
transmembrane pressure and decreases with Reynolds
number. Polarization modulus is the extent of polarization on the membrane surface, which can be defined
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
750
1000
1250
NRe
4500
5000
5500
Figure 7. Variation of Sherwood number with different
flow regimes in NF.
as (cm − cp )/(c0 − cp ). Variations of polarization modulus with transmembrane pressure are shown in Fig. 6.
On increasing turbulence using promoters or increased
cross-flow velocity, membrane surface concentration as
well as permeate concentration decrease leading to a
decrease in polarization modulus. For example, at a
pressure of 1242 kPa, the polarization modulus is 1.39
for laminar, 1.26 for flow with turbulent promoter and
1.13 for pure turbulent flow regime.
In the case of NF, the variation of Sherwood number
with Reynolds number for purely laminar, laminar with
promoter, and turbulent flow regimes are shown in
Fig.7. The Sherwood number for laminar region lies
between 51.86 and 65.32 for Re between 606 and 1212.
Similarly, the Sherwood number for turbulent region
lies between 175.36 and 214.41 for Re between 4242
and 5454. Sherwood number relations are developed for
Asia-Pac. J. Chem. Eng. 2011; 6: 101–109
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
MODELING AND TRANSPORT PARAMETERS DURING NANOFILTRATION
the case of laminar flow with turbulent promoters. The
Sherwood number for laminar with promoter case lies
between 70.83 and 101.33 for overall Re lying between
606 and 1212.
CONCLUSION
A treatment protocol for the degreasing effluent released
from a tannery is proposed using nanofiltration. The
transport coefficients, namely the effective osmotic
coefficient, solute diffusivity and solute permeability, are estimated during nanofiltration of the pretreated degreasing effluent. The values are: a = (4.9 ±
0.033) × 104 Pa m3 / kg, D = (1.45 ± 0.012) × 10−9
m2 /s and B = (2.49 ± 0.45) × 10−6 m/s. Combination
of film theory, solution-diffusion and osmotic pressure
model is used to estimate the above transport coefficients. The solution methodology provides a basic
calculation route to predict the system performance
of a complex industrial effluent. The calculated flux
and permeate concentration values are within 15% and
10%, respectively, with respect to the experimental
data.
NOMENCLATURE
a
Osmotic pressure coefficient (Pa m3 / kg)
B
Solute permeability through the membrane (m/s)
c
Concentration (kg/m3 )
cm Membrane surface concentration (kg/m3 )
cp Permeate concentration (kg/m3 )
exp
cp experimental permeate concentration (kg/m3 )
cpcalc calculated permeate concentration (kg/m3 )
c0 Feed concentration (kg/m3 )
de Hydraulic diameter (m)
D Effective solute diffusivity (m2 /s)
h
Channel half-height (m)
k
Mass transfer coefficient (m/s)
K Potassium
L
Channel length (m)
Lp Membrane permeability (m/Pa s)
N Nitrogen
n
Concentration in Eqn 13
O.C. Organic Carbon
P
Phosphorous
Re Reynolds number (ρu0 de /µ)
Sh Sherwood number (kde /D)
Sc Schmidt number (µ/ρ D)
uo Average velocity (m/s)
J
Permeate flux (m3 /m2 s)
0
Jw Pure water flux (m3 /m2 .s)
J exp Experimental permeate flux (m3 /m2 s)
J calc Calculated permeate flux (m3 /m2 s)
 2010 Curtin University of Technology and John Wiley & Sons, Ltd.
Greek symbols
α0
P
π
πm
πp
Concentration in Eqn 13
transmembrane pressure drop (Pa)
osmotic pressure difference (Pa)
osmotic pressure at the membrane surface (Pa)
osmotic pressure at the permeate side (Pa)
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DOI: 10.1002/apj
109
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